PHYSICS, CHEMISTRY & MATHEMATICS JEE - MAINS 2015 paper class 11.pdf · PHYSICS, CHEMISTRY & MATHEMATICS JEE - MAINS 2015 ... The time of flight of a projectile is proportional to

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PHYSICS, CHEMISTRY & MATHEMATICS

JEE - MAINS 2015 PHASE – I

SET - A

Time Allotted: 3 Hours

Maximum Marks: 360

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Sheet and fill in the particulars carefully.

3. The test is of 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum marks are 360.

5. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having 30

questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response.

6. Candidates will be awarded marks as stated above in instruction No.5 for correct response of each question. ¼ (one

fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will

be made if no response is indicated for an item in the answer sheet.

7. There is only one correct response for each question. Filling up more than one response in any question will be treated as

wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above.

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FIITJEE - JEE (Mains)


Useful Data Chemistry:

Gas Constant R = 8.314 J K1

mol1

= 0.0821 Lit atm K1

mol1

= 1.987 2 Cal K1

mol1

Avogadro's Number Na = 6.023 1023

Planck‘s Constant h = 6.626 10–34

Js

= 6.25 x 10-27

erg.s

1 Faraday = 96500 Coulomb

1 calorie = 4.2 Joule

1 amu = 1.66 x 10-27

kg

1 eV = 1.6 x 10-19

J

Atomic No : H=1, D=1, Li=3, Na=11, K=19, Rb=37, Cs=55, F=9, Ca=20, He=2, O=8,

Au=79.

Atomic Masses: He=4, Mg=24, C=12, O=16, N=14, P=31, Br=80, Cu=63.5, Fe=56, Mn=55,

Pb=207,

Au=197, Ag=108, F=19, H=2, Cl=35.5, Sn=118.6

Useful Data Physics:

Acceleration due to gravity g = 10 2m/ s


Section – I (Physics)

1. Three vectors ,P Q

and R

are such that Q

= 2A and the angles between P

and Q

, Q

and R

, R

and

P

are 900, 150

0 and 120

0 respectively. Find the value of P

.

(A) 2

A (B)

2

3

A (C)

2

3

A (D)

2

A

2. The velocity and acceleration of a particle at time t = 0 are ˆ ˆ2 2 /u a i a j m s

and 0

ˆ â ai aj

respectively. Find the angle made by the velocity of the particle at t = 2sec with initial velocity.

(A) 1tan 2 (B) 1tan 2

(C) 1tan 1 (D)

1 1tan

2

3. When a man walks at the rate of 3 km/hr, rain appears to fall vertically. The speed of rain is 3 2 km/hr. At what

speed man should walk so that the rain appears to fall at an angle of 450 with vertical.

(A) 3 km/hr (B) 4 km/hr (C) 3 2 km/hr (D) 6 km/hr

4. The trajectory of a projectile in a vertical plane is 2 ,y ax bx where a and b are positive constants and x and

y are respectively the horizontal and vertical distances of the projectile from the point of projection. The

maximum height attained by the projectile is

(A)

22a

b (B)

2a

b (C)

2

2

a

b (D)

2

4

a

b

5. A car accelerates from rest at a constant rate for some time after which it decelerates at a constant rate to

come to rest. If the total time elapsed is t, the distance travelled by the car is given by

(A) 21

2t

(B)

21

2t

(C) 2 2

21

2t

(D)

2 221

2t

6. The upper half of an inclined plane of inclination is perfectly smooth while the lower half is rough. A block

starting from rest from the top of the plane will again come to rest at the bottom if the coefficient of friction

between the block and the lower half of the plane is given by

(A) 2tan (B) tan (C) 2

tan

(D)

1

tan

space for rough work


7. A ball of mass m is moving towards a batsman at a speed v. The batsman strikes the ball and deflects it by an

angle without changing its speed. The impulse imparted to the ball is given by

(A) cosmv (B) sinmv (C) 2 cos2

mv

(D) 2 sin2

mv

8. An insect starts crawling up a hemispherical bowl of radius R from its lowest point. If the coefficient of friction is

1

3, the insect will be able to go up to height h equal to (take

30.95

10 )

(A) 5

R (B)

10

R (C)

20

R (D)

30

R

9. A simple pendulum of length 1 m and bob of mass 100 gm is swinging with an angular amplitude of 600. What is

the tension in the string when the bob passes through the equilibrium position? Take g = 10 ms-2

.

(A) 1 N (B) 2 N (C) 3 N (D) 4 N

10. Which one of the following statements is NOT true about the motion of a projectile?

(A) The time of flight of a projectile is proportional to the speed with which it is projected

(B) The horizontal range of a projectile is maximum when angle of projection is 450 for a given speed

(C) The average acceleration for any time interval is varying.

(D) At maximum height the acceleration due to gravity is perpendicular to the velocity of the projectile.

11. A point P moves in counter- clockwise direction in a circular path

as shown in the figure. The movement of P is such that it sweeps

out a length 3 5S t , where S is in metres and t is in sec. The

radius of the path is 20 m. The acceleration of ‗P‘ when t = 2s is

nearly.

(A) 14 m/s2 (B) 13 m/s

2

(C) 12 m/s2 (D) 7.2 m/s

2

A

B

O

20 m

P(x, y)

12. A person standing in a stationary lift drops a coin from a certain height h. It takes time ‗t‘ to reach the floor of the

lift. If the lift is rising up with a uniform acceleration a, the time taken by the coin, dropped from the same height

h, to reach the floor will be

(A) t (B) a

tg

(C)

1

t

a

g

(D)

1

t

a

g



13. A block is placed on the top of an inclined plane of inclination kept on the floor of a lift which is moving down

with an acceleration a a g . The coefficient of friction between the block and the incline so that the block

just remains stationary with respect to incline plane.

(A) tan (B) tana

g (C) 1 tan

a

g

(D) 1 tana

g

14. Force F acting on a body moving in a straight line varies with the velocity v of the body as k

Fv

where k is a

constant. The work done by the force in time t is proportional to

(A) t (B) 3/2t (C)

1/2t (D) 3/2t

15. A bob of mass m is suspended with a string from a fixed point, when it is projected with a velocity which is just

required to loop the circle completely. At what angle with the horizontal, tension in the string will be equal to 2

mg.

(A) 1 1

sin3

(B) 1 2

sin3

(C) 1 1

cos3

(D) 1 1

tan3

16. With what force must a man pull on the rope to hold the plank in the

position as shown in the figure. If the man weighs 60 kg and plank

weighs 40 kg. The rope and pulley are massless

(A) 100 N (B) 150 N

(C) 125 N (D) 250 N

17. The work done by the force

2 2ˆ ˆF x i y j

around the path

shown in the figure is

(A) 32

3a (B) zero

(C) 3a (D)

34

3a

y

xO A

BC(0, a)

(0, 0) (a, 0)

(a, a)



18. A particle is moving with velocity ˆ ˆv k yi xj

where k is a constant. The trajectory equation of the particle

is

(A) 2y x constant (B)

2y x constant

(C) xy constant (D) 2 2y x constant

19. Two fixed frictionless inclined planes making an angle 300

and 600 with the horizontal are shown in the figure. Two

blocks A and B are placed on the two planes. What is the

relative horizontal acceleration of A with respect to B?

(A) 4.9 ms-2

in horizontal direction

(B) 9.8 ms-2

in horizontal direction

(C) zero

(D) 4.9 ms-2

in vertical direction

A

B

060 030

20. A system of wedge and block is as shown in figure. If wedge is fixed

and block is released from rest with spring in its natural length, find

maximum elongation in the spring. All surfaces are frictionless

(A) 2 sinmg

k

(B)

sinmg

k

(C) 4 sinmg

k

(D)

sin

2

mg

k

k

m

21. A particle of mass m is located in a one dimensional potential field where potential energy of the particle has the

form 2

a bU x

x x where a and b are positive constants. The position of equilibrium is

(A) 2

b

a (B)

2b

a (C)

a

b (D)

2a

b

22. In the shown figure mass of A is m and that of B is 2m. All the

surface are smooth. System is released from rest with spring

unstretched. Then, the maximum extension (xm) in the spring will

be

(A) mg

k (B)

2mg

k

(C) 3mg

k (D)

4mg

k

k

A

B



23. In the figure shown all the surfaces are frictionless, and mass of the

block, m = 1kg. The block and wedge are held initially at rest. Now

wedge is given a horizontal acceleration of 10 m/s2 by applying a

force on the wedge, so that the block does not slip on the wedge.

Then work done by the normal force in ground frame on the block in

3s is

(A) 30 J (B) 60 J

(C) 150 J (D) 100 3 J

m10 m/s2

M

24. Three stones A, B and C are simultaneously projected from same point with same speed. A is thrown upwards, B

is thrown horizontally and C is thrown downwards from a building. When the distance between stone A and C

becomes 10 m, then distance between A and B will be

(A) 10 m (B) 5 m (C) 5 2 (D) 10 2m

25. The coefficient of friction between 4 kg and 5 kg blocks is 0.2 and

between 5 kg block and ground is 0.1 respectively. Choose the correct

statements.

(A) minimum force needed to cause system to move on ground is 17 N

(B) When force F = 4N, static friction at all surfaces I 4 N to keep

system at rest.

(C) Maximum acceleration of 4 kg block is 2 m/s2

(D) Slipping between 4 kg and 5 kg block starts when F is 17 N.

F

4 kg

5 Kg

26. A spring of natural length l is compressed vertically downward against the floor so that its compressed length

becomes 2

l. On releasing, the spring attains its natural length. If k is the stiffness constant of spring then work

done by the spring on the floor is

(A) zero (B) 2

2kl

(C)

21

8kl (D)

21

4kl

27. A particle is given an initial speed u inside a smooth spherical

shell of radius R so that it is just able to complete the circle.

Acceleration of the particle, when its velocity is vertical, is

(A) 3g (B) 2g

(C) g (D) 10g u



28. A block is sliding along a smooth incline as shown in figure. If the acceleration

of chamber is ‗a‘ as shown. The time required to cover a distance L along

incline is

(A) 2

sin cos

L

g a (B)

2

sin sin

L

g a

(C) 2

sin cos

L

g a (D)

2

sin

L

g

am

29. Average velocity of a particle in projectile motion between its starting point and the highest point of its trajectory

is (u = projection speed, = angle of projection from horizontal).

(A) cosu (B) 21 3cos

2

u (C)

22 cos2

u (D)

21 cos2

u

30. A particle moves along the curve

2

2

xy . Here x varies with time as

2

2

tx . Where x and y are measured in

metre and t in second. At 2sec.t the velocity of the particle (in ms-1

) is

(A) ˆ ˆ2 4i j (B) ˆ ˆ2 4i j (C) ˆ ˆ4 2i j (D) ˆ ˆ4 2i j



Section – II (Chemistry)

1. The dehydration yield of cyclohexanol 6 11C H OH (m.wt = 100) to cyclohexene

6 10C H (m.wt = 82) is 75%.

What would be the yield if 100 gm of cyclohexanol is dehydrated?

(A) 61.5 gm (B) 16.5 gm (C) 6.15 gm (D) 615 gm

2. Four particles have speed 2, 3, 4 and 5 cm/sec respectively. Their RMS speed is

(A) 3.5 cm/sec (B) (27/2) cm/sec (C) ( 45 / 2 ) cm/sec (D) ( 54 / 2 ) cm/sec

3. Identify the paramagnetic species

(A) K2O (B) KO2 (C) CaO (D) BaO

4. The orbital angular momentum for 11th

electron of Na atom is

(A) 2

h

(B) 2

2

h

(C)

4

h

(D) zero

5. Under identical conditions, helium will diffuse through a pin hole(At. wt. of argon = 40 and helium = 4)

(A) 3.16 times as fast as argon (B) 7.32 times as fast as argon

(C) 1.58 times as fast as argon (D) 10 times as fast as argon

6. Velocity of photoelectron is

(A)

1

20

0

2hc

m

(B)

2

0

0

2hc

m

(C) 2hc

m (D)

2

2

m

hc

Where, m = mass of photoelectron, h = planck‘s constant, 0 Threshold wavelength,

wavelength incident, c velocity of light

7. The normality of 0.3 M boric acid 3 3H BO solution is

(A) 0.3 (B) 0.15 (C) 0.6 (D) 0.9

8. Degree of hardness of a sample of water containing 6 mg of 4MgSO per kg of water is

(m. wt of MgSO4 = 120)

(A) 5 ppm (B) 7 ppm (C) 3 ppm (D) 7.8 ppm

9. Consider a titration of potassium dichromate solution with acidified Mohr‘s salt

4 4 4 22. .6FeSO NH SO H O solution using diphenylamine as indicator. The number of moles of Mohr‘s salt

required per mole of dichromate is

(A) 3 (B) 4 (C) 5 (D) 6



10. Choose the correct formula

(A) Critical pressure = 8

27

a

b (B) Inversion temperature =

2a

Rb

(C) Critical temperature = 227

a

b (D) All the above

11. The first ionization potential of Na is 5.1 eV. The value of electron gain enthalpy of Na will be

(A) - 10.2 eV (B) - 2. 55 eV (C) - 5. 1 eV (D) + 2.55 eV

12. Choose the correct statement

(A) In 7IF molecules, total number of bonds with angle 720 is 5

(B) Number of F – Se – F arrangement with 1800 in

6SeF is 6

(C) F should be placed at equatorial position in 3 2PCl F

(D) Chlorine is 3sp d hybridized in 4HClO molecule

13. Correct order of paramagnetic property is

(A) 2 2 2 2O N N N (B)

2 2 2 2N N N O

(C) 2 2 2N N O N (D)

2 2 2 2O N N N

14. Choose the correct order of periodic property

(A) P > N (electron affinity) (B) S > O (electronegativity)

(C) F < Cl (Ionisation energy) (D) N > C (electron affinity)


(A) Both Li and Mg are solid (B) Both Li and Mg forms nitride

(C) Both Li2O and MgO are basic (D) All the above

16. Bond length of x – y bond is 100 pm and its observed dipole moment is 2 D. It is % covalent character is

approximately

(A) 41.67 % (B) 58.33 % (C) 47.1 % (D) 61.3 %

17. Boiling point of glycol 2 2HO CH CH OH is much higher than that of propyl alcohol

3 2 2CH CH CH OH due to

(A) Presence of dipole moment (B) Presence of two bonds

(C) Presence of back bonding (D) Presence of hydrogen bonding

18. Momentum of particle ‗A‘ is thrice to the momentum of particle ‗B‘. The ratio of wavelength associated with B to

A is

(A) 3 : 1 (B) 1 : 3 (C) 1 : 2 (D) 3 : 2



19. Distance of electron of hydrogen atom from nucleus is .o

Ax The distance of shell in which 3rd

electron of Li

atom is present is

(A) 3

4

o

Ax

(B) 9

2

o

Ax

(C) 4

3

o

Ax

(D) 2

9

o

Ax

20. Oleum sample is identified as 102.25 %. The % free SO3 present in this sample is

(A) 20 % (B) 10% (C) 40 % (D) 80 %

21. Number of peroxylinkage (O – O) present in 2 8K CrO is(Given: Oxidation state of Cr = 6)

(A) 2 (B) 8 (C) 4 (D) 2

22. During preparation of H2, by electrolysis of acidic water, correct statement is

(A) O2 is liberated at anode (B) O2 is liberated at cathode

(C) H2 is liberated at anode (D) Both H2 and O2 are liberated at anode

23. The correct order of basic nature is

(A) LiOH NaOH KOH RbOH CsOH

(B) NaOH KOH RbOH CsOH LiOH

(C) LiOH KOH NaOH RbOH CsOH

(D) CsOH RbOH LiOH KOH NaOH


(A) BeO is amphoteric (B) Be forms polymeric halide

(C) Be forms polymeric hydride (D) All the above

25. Which of the following element shows hydride gap?

(A) Sc (B) Mg (C) Fe (D) Zn

26. Inert pair effect is shown by

(A) Pb (B) Mg (C) Si (D) I

27. Element which gives negative flame test is

(A) Na (B) Rb (C) Ca (D) Mg

28. Two vessels having equal volumes contains H2 and He at 1 and 2 atm respectively at the same temperature. Select

the correct statement.

(A) 2rms H rms HeU U (B) 2

2rms H rms He

U U

(C) 23

rms H rms HeU U (D)

22

rms H rms HeU U

29. The maximum number of electrons that can have principal quantum number, n = 3 and spin quantum number,

1

2s is

(A) 3 (B) 6 (C) 9 (D) 18

30. The equivalent weight of an element is 4. It‘s chloride has a vapour density 59.25. The valency of element is

(A) 2 (B) 3 (C) 4 (D) 5

pace for rough work


Section – III (Mathematics)

1.

2

0

cos 2

cos sin

xI dx

x x

is equals to

(A) 2 (B) 1 (C) 0 (D) None of these

2. 2lim 2x

x x x

is equals to

(A) 1 (B) -1 (C) -2 (D) 1

2

3. The number of solution of equation 16 4log log 2x x is equals to

(A) 0 (B) 1 (C) 2 (D) 3

4. The value of 3 5 9 11 13

sin sin sin sin sin sin14 14 14 14 14 14

is equal to

(A) 1

32 (B)

1

64 (C)

1

16 (D)

1

128

5. Total number of lines of the form 1ax by , 0a b which intersect the circle 2 2 50x y at two

integral points is/are equals to

(A) 66 (B) 60 (C) 56 (D) 78

6. If , lie on the circle 2 2 4x y then maximum value of 3 4 is equal to

(A) 4 (B) 6 (C) 8 (D) 10

7. Let points A, B, C form a acute angled triangle and P is a point inside the ABC such that

2 2 2

PA PB PC is maximum then for ,ABC P is …………

(A) ortho centre (B) circum centre (C) centroid (D) Incentre

8. Let p and q be two statements, then ~p q p is

(A) tautology (B) contradiction

(C) Both tautology & contradiction (D) neither tautology nor contradiction



9. The solution set of

3

42

1 20

5

x x

x x

is

(A) 1,2 0x (B) , 5 5, 1 2,x

(C) 1,2x (D) , 1 2,x

10. The complete set of values of x satisfying the inequality

10

3

x

x

is

(A) 1,3x (B) 3, 1 1,3x

(C) 1,3x (D) 3, 1 1,3x

11. Tangents 1PT and 2PT are drawn from a point P lying on the line 0ax by c to the circle

2 2 2 ,x y r then the locus of circumcentre of 1 2PTT is

(A) 02

cbx ay (B) 0

2

cbx ay

(C) 2 2 0ax by c (D) 2 2 0ax by c

12. Let 0 0 0tan18 cot18 tan18

0 0 0

1 2 3tan18 , tan18 , cot18t t t and 0cot18

0

4 cot18 ,t then

(A) 1 2 3 4t t t t (B) 4 3 1 2t t t t (C) 3 1 2 4t t t t (D) 4 3 2 1t t t t

13. Let the coordinate axes is shifted as well as rotated in such a way that new x-axes is along the line

3 4 10 0x y and new y –axes is along the line 4 3 20 0x y . If the old coordinates of point P is (5,

5), then new coordinate of P can be

(A) (11, 1) (B) (1, 11) (C) (11, -1) (-1, 11)

14. The number of points equidistant from the lines 0, 0x y x y and 2 0y is/are

(A) 1 (B) 2 (C) 3 (D) 4

15. Total number of lines touching two circles of the family of circles defined as 2 2 4 4 0x y x y is

(A) 8 (B) 10 (C) 12 (D) 14

16. The acute angle between the medians drawn from the acute angle of a right angles isosceles triangle is

(A) 1 2

cos3

(B)

1 3cos

4

(C)

1 4cos

5

(D)

1 5cos

6



17. If A = 2 4sin cos , then

(A) 1 2A (B) 3

14

A (C) 13

116

A (D) 3 13

4 16A

18. Given the family of lines 3 4 6 2 0a x y b x y . The line of the family, situated at the greatest

distance from the point 2,3P has equation

(A) 4 3 8 0x y (B) 5 3 10 0x y (C) 15 8 30 0x y (D) None

19. The contrapositive of ―if two triangles are identical, then these are similar‖ is

(A) if two triangle are not similar, then these are not identical

(B) if two triangles are not identical then these are not similar

(C) if two triangles are not identical then these are similar

(D) none of these

20. Let .....y x x x then dy

dx at x = 2 is equal to

(A) 1 (B) 3 (C) 1

2 (D)

1

3

21. Let in ABC coordinates of A is (0, 0). Internal angle bisector of ABC is 1 0x y and mid point of

BC is (1, 3). Then ordinate of ‗C‘ is

(A) 2 (B) 4 (C) 5 (D) 6

22. If sin 2 0.44x then, sin cosx x is equal to

(A) 4

3 (B)

5

4 (C)

6

5 (D)

7

6

23. If 0 0 0

2 2 2log 1 tan1 log 1 tan 2 ......... log 1 tan 45 is a two digit number, whose sum of

digits equals to

(A) 3 (B) 5 (C) 7 (D) 9

24. If 20, 15n A n B , max 5n A B , 30n C , then min n A B C equals to

(A) 40 (B) 35 (C) 45 (D) 30



25. If circle 2 2 0x y ax c is completely inside the circle

2 2 0x y bx c , then

(A) 0c (B) 0c (C) 0ab (D) None of these

26. The value of ‗k‘ for which circles 2 2 81 0x y and

2 2 4 6 0x y x y k are orthogonal is

(A) 81 (B) -81 (C) 68 (D) None of these

27. The portion of the line 1ax by intercepted between the lines 1 0ax y and 0x by subtends a

right angle at origin then

(A) 22 2 0a b b (B)

22 0a b b (C) 2 2 0a a b (D)

2 0a b ab

28. Let line 2 7 0x y cuts the circle 2 2 16 0x y at points A and B. If P is (6, 5) then PA PB is

equals to


29. The number of values of ‗a‘ for which lines 1 0, 2 1 0x y ax y and 4 2 7 0x ay are

concurrent is equal to


30. Lines L1 and L2 are rotating in anticlockwise direction about points (-2, 0) and (2, 0) respectively in such a way

that angle of rotation of line L2 is double that of L1. If initially equation of lines are y = 0 and angle of rotation of

line L2 varies between 0 to 2

, then locus of point of intersection of L1 and L2 is part of circle with radius equals

to

(A) 2 (B) 4 (C) 6 (D) 8




JEE - MAINS 2015

PHASE – I

SET - A

ANSWERS PHYSICS

1. B 2. B 3. D 4. D

5. A 6. A 7. C 8. C

9. B 10. C 11. A 12. C

13. A 14. A 15. A 16. D

17. B 18. D 19. C 20. A

21. D 22. D 23. C 24. C

25. C 26. A 27. D 28. C

29. B 30. B

CHEMISTRY

1. A 2. D 3. B 4. D

5. A 6. A 7. A 8. A

9. D 10. B 11. C 12. A

13. D 14. A 15. D 16. B

17. D 18. A 19. C 20. B

21. C 22. A 23. A 24. D

25. C 26. A 27. D 28. D

29. C 30. B

MATHEMATICS

1. C 2. D 3. B 4. B

5. B 6. D 7. C 8. A

9. A 10. D 11. C 12. B

13. C 14. D 15. D 16. C

17. B 18. A 19. A 20. D

21. D 22. C 23. B 24. D

25. B 26. D 27. B 28. A

29. B 30. B



HINTS & SOLUTIONS

PHYSICS 1. B

Sol. 0tan 30

P

Q

2

3

AP

P

Q

R

090

0150

0120

030

2. B

Sol. u

and at

are perpendicular vectors

Also v u at

At 2sect , 2 , 2 2 2 2u a at a a

1/22 2

12v u at a

tanat

u

1tan 2

at

u

v

3. D

Sol. Let ˆ ˆRV ai bj

Case I ˆ3MV i

ˆ ˆ3RM R MV V V a i bj

Now 3 0a as RMV

is vertical

Also 2

2 2

RV a b

2

2 23 2 3 b

b = 3

Case II ˆMV ki

ˆ ˆ ˆ ˆ3 3 3RMV a k i j k i j

For angle to be 450, ˆ ˆ3 3RMV i j

6k

4. D

Sol. When x = R, y = 0

0 = aR – bR2

a

Rb

When max,

2

Rx y H

2y ax bx

2 2

max2 2 4

a a aH a b

b b b

5. A


Sol. max 1 2V t t

2 1t t

1 2t t t

1t t

Distance = Area under Vt graph

= 1

1

2t t

21

2D t

V

Vmax

t1 t

1 + t

20

6. A

Sol. For the block to come to rest at the bottom of the inclined plane, the acceleration in the first half must be equal to

the retardation in the second half

sin cos sing g

2tan

7. C

Sol. 1 2P P mv

2 1P P P

1/2

2 2

2 1 2 12 cos 180P P P P P

1/22 2 22 cosP P P P

2 cos2

P

2 cos2

mv

P

2P

1P

0180

8. C

Sol. sinf mg

cos sinmg mg

1tan

3

3

cos 1 1 0.9510

h R R R R

0.05R

20

R

cosmg mgsinmg

N

hf

9. B

Sol. Speed at equilibrium position

2 2 1 cosv gR gR

2

2 2mv

T mg mg NR

m

v

060

10. C

Sol. avga g

always

11. A


Sol. 3 5S t

23

dsv t

dt

6t

dva t

dt , At t = 2sec, v = 12 ms

-1

212ta ms

2 2212 144

7.220 20

n

va ms

R

2 2

t na a a

214a ms

12. C

Sol. 21

2h gt when lift is stationary

When lift is accelerating upwards.

21

'2

h g a t

22 'gt g a t

1

1

g tt t

g a a

g

13. A

Sol. FBD of block wrt to inclined plane

/maxsin s sm g a f N

cosN m g a

sin cossm g a m g a

tans

N

ma

mg a

14. A

Sol. k

P Fv v kv

0

t

w Pdt Kt

15. A

Sol. 2

sin PmvT mg

r

2

sin 2PmvT mg mg

r

2 2 sinPv gr gr …..(1)

From w – E theorem

cosmg

sinmg

mg

O

P

B

2 21 11 sin

2 2P Bmv mv mgr

Also 5Bv gr to loop circle.


2 5 2 1 sinPv gr gr

2 3 2 sinPv gr gr …….(2)

From (1) and (2)

2 sin 3 2 singr gr gr gr

1

sin3

1 1

sin3

16. D

Sol. For the (Man + Plank) system to be at rest

4 100T g

250T N

17. B

Sol. .W F dr

x yW F dx F dy

0

0

A B C

x y x y y x y x y

A B C

W F dx F dy F dx F d F dx F dy F dx F dy

0W

18. D

Sol. ˆ ˆv k yi xj Hence

,x yv ky v kx

dx dy

ky kxdt dt

/

/

dy dy dt kx x

dx dx dt ky y

ydy xdx

Integrating

2 2

2 2

y xc

2 2y x constant

19. C

Sol. Acceleration along the plane is sina g

Horizontal component of a is cos sin cos sin 22

ga g

For Block A, horizontal acceleration is 0 3 3sin 2 60

2 2 2 4

g g g

cosa

sina g

For Block B, horizontal acceleration is 0 3 3sin 2 30

2 2 2 4

g g g

Relation horizontal acceleration of A wrt B = 0

20. A

Sol. W – E theorem

2T T

T

(60 g + 40 g)


g sk w w

21

0 sin2

mgx kx

2 sinmg

xk

21. D

Sol. dU

Fdx

3 2

2a bF

x x

For equilibrium F= 0

3 2

2a b

x x

2a

xb

22. D

Sol. From conservation of energy

21

2 02

mgx kx

4mg

xk

23. C

Sol. Work done by the normal force on the block relative to ground

frame = K

21

2mv

21 300

1 10 3 1502 2

J

m

M

90

N

a

mg

24. C

Sol. Initial velocity of C wrt A

CA C Au u u

ˆ ˆ ˆ2uj uj u j

0CA C Aa a a g g

CA CAS u t

CA CAS u t

10 2ut

5t

u

Initial velocity of B wrt A

ˆ ˆBA B Au u u ui uj

0BA B Aa a a g g

ˆ ˆ5 5BA BAs u t i j

5 2BAs m

25. C


Sol. /maxsf between 4 kg and 5 kg = 1 8f N

/maxsf between 5 kg and ground =

2 9f N

Minimum force needed to move the system

is 9 N

When F = 4N friction between the blocks is

zero

When /maxsf acts on 4 kg it will have

maximum acceleration

21max

82 /

4

fa m s

m

When slipping between 4 kg and 5 kg starts

max. friction acts between them and their

accelerations are just same.

8 9 5 2F

27F N

4 N

4 kg

5 Kg

0f

4f N

F

4 kg

5 Kg

8f N

2 9f N

1 8f N

22 /a m s

22 /a m s

26. A

Sol. Point of application of force is at rest.

27. D

Sol. At lowest point A, 5u gR

When the velocity is vertical, at point B

3v gR

2

3 ,n t

va g a g

R

2 2 10n ta a a g

u

naO

v

ta

B

A

28. C

Sol. acceleration of block wrt chamber

2

( cos sin )

1

2

2

sin cos

BC

BC BC

a a g

s a t

Lt

g a

from the chamber frame

N

ma

cos sinma mg cosmg

sinma BCa

29. B

Sol. 2

2

2

Rs H

2 2 2

2

sin sin cos sin, ,

2 2

1 3cos2

Time of ascent,T

av

u R u uH

g g g

s uv

T

2

R

s

A

H

O

30. B

Sol.

2 2 4

2 2 8

t x tx y

3

2x y

dx tv t v

dt

3

ˆ ˆ2

tv ti j

at t = 2 sec


ˆ ˆ2 4v i j

(m/s)

Chemistry

1. A

Sol. 2

6 11 6 10

H OC H OH C H

m.wt. = 100 m.wt. = 82

100 gm cyclohexanol = 82 gm C6H10

100gm cyclohexanol = 6 10

82 100

100gm C H

Also % yield is 75% wt. of 6 10

82 7561.5

100C H

2. D

Sol.

2 2 2 22 3 4 5 54 54

4 4 2RMS

cm/sec

3. B

Sol. Presence of 1

2O ion which has one unpaired electron.

4. D

Sol. orbital angular momentum = 12

hl l

for 11th

electron, 0l

5. A

Sol. 40

10 3.164

He

Ar

r

r

6. A

Sol.

0

1 1KE hc

2

0

1 1 1

2mv hc

2

0

2 1 1hcv

m

or

1

2

0

2 1 1hcv

m

7. A

Sol. n.f. of boric acid = 1

8. A

Sol. 120 gm 4 3100MgSO gm CaCO

3 3

4 36 10 5 10gm MgSO gm CaCO

36

3

5 1010

1000ppm of CaCO

5 ppm

9. D

Sol. 3 3

2 7 26 14 6 2 7Fe Cr O H Fe Cr H O

21 6Fe

n

10. B

Sol. 8

27C

aT

Rb ,

227C

aP

b ,

2aTi

Rb


11. C

Sol. Electron gain enthalpy of ion = - I.E. of atom = - 5.1 eV

12. A

Sol. In 0

7 , 72 5IF ; 090 10 ;

0180 1

13. D

Sol. 2 22 2

8, 3 , 0O NN N

14. A

15. D

Sol. Diagonal relationship

16. B

Sol. 10 10

100% 4.8 10 100 10

20480 10

184.8 10 esu cm

18

100% 18

4.8 104.8

10D

% ionic = 2

100 41.674.8

% Covalent = 100 41.67 58.33%

17. D

Sol. Glycol has more number of hydrogen bonding as compare to propyl alcohol hence Boiling point of glycol is much

higher than that of propyl alcohol.

18. A

Sol. h

P

1

3 3

A B

B A

P x

P x

3:1B

A

19. C

Sol.

2

0.529o

An

rZ

distance of 1st electron =

20.529 1 x

distance of 3rd

electron = 0.529 4 4

3 3

o

Ax

20. B

Sol. 18 gm H2O reacts with 80 gm SO3

2.25 gm water reacts with = 3

802.25

18gm SO

% 3

80 2.25100 10%

18 100SO

21. C

Sol.

O

O

Cr

O O

O

O

O

O

22. A


Sol. H is reduced at cathode and OH

is oxidized at anode.

23. A

Sol. Basic nature increases down the group

24. D

Sol. Abnormal behavior of Be

25. C

Sol. Hydride gap = No hydride formation

26. A

Sol. 4, 2Pb (common)

27. D

Sol. Due to very high I.E.

28. D

Sol. 3RT

UM

29. C

Sol. Number of orbitals = n2 = 9

Number of electrons with 1

92

s

30. B

Sol. Mole. wt. of 2 . . 2 59.25 118.5nMCl V D

Now 35.5 118.5a n

35.5 118.5 4 35.5 118.5E n n n n

3n

MATHEMATICS 1. C

Sol. /2

/2 /2

0 0

0

cos sin sin cos 0I x x dx x x

2. D

Sol. 2

2

2

21

2 1lim 2 lim lim

21 221 1

x x x

x xx x xx x x

x x

3. B

Sol. 2

16 4log log 2 2 1,4x x x x x

But 1 is rejected

4. B

Sol. 3 5 9 11 13

sin sin sin sin sin sin14 14 14 14 14 14

=

2

2 2 23 5 2 4sin sin sin cos cos cos

14 14 14 7 7 7

2 23

3

8sin 2 sin17 7

82 sin sin

7 7

1

64

5. B

Sol. Total integral points on 2 2 50x y equals to 12

Total lines passing through these points are 11 10 .... 2 1 66 in which 6 lines are diameter

Answer is 60

6. D

Sol. Let 3 4x y k is tangent to 2 2 4x y then k equals to 10 Maximum value of 3 4 is 10


7. C

Sol. Let A be 1 1, ,x y B be 2 2,x y C be 3 3,x y and P be ,x y then 2 2 2

PA PB PC is

2 2 2 2 2 2

1 1 2 2 3 3x x y y x x y y x x y y

2 2

1 2 32 2 1 2 3 1 12

3 23 3 3 3

x x x y y y x yx x y y

2 2

2 2 2 21 133 3

x yx x y y x y

The value is maximum when &x x y y

8. A

Sol.

p q p q ~ p ~p q p

T T T F T

T F T F T

F T T T T

F F F T T

9. A

Sol.

1,2 0x

10. D

Sol. 1,3 3, 1 1,3x x

11. C

Sol. Because 1 2, , , 0,0 &P T O T are

concyclic points, so circumcentre of 1 2PTT is

mid – point of OP which is Q(h, k)

2 , 2h k

Because , lies on line 0ax by c so

2 2 0a h b k c

locus of Q is 2 2 0ax by c

O (0, 0)

,P

2T

1T

,Q h k

12. B

Sol. 4 3t t because 0 0 0cot18 1 & cot18 tan18

3 1t t because 3 11 & 1t t

1 2t t because 0 0 0tan18 0,1 & cot18 tan18

13. C

Sol. Distance of (5, 5) from 3 4 10 0x y is 1 which must be magnitude of new y coordinate similarly distance

of (5, 5) from 4 3 20 0x y is 11 which will be magnitude of new x coordinate.

Now point P be either in 2nd

or IVth quadrant according to new coordinate system.

14. D

Sol. One incentre and 3 excentres

15. D

Sol. Let 1c be circle where equation is 2 2 4 4 0x y x y

2c be circle where equation is 2 2 4 4 0x y x y

Not defined 0 Not defined

3

42

1 2

5

x x

x x

x -5 - 1 0 2

0 + + +


3c be circle where equation is

2 2 4 4 0x y x y

4c be circle where equation is 2 2 4 4 0x y x y

Now new common tangent between 1c & 2c is 2, 1 3&c c is 2,

1 4&c c is 3, 2 3&c c is 3,

2 4&c c is 2 ,

3 4&c c is 2.

16. C

Sol. Let vertices of triangle are (0, 0), (a, 0) and (0, a), then slope of medians through (a, 0) and (0, a) are 1

2 and -2

respectively

12

3 42tan cos1 1 4 5

17. B

Sol. 2

22 2 2 1 3

sin 1 sin sin2 4

A

3

14

A

18. A

Sol. Family of lines concurrent at (-2, 0)

Now the required line is the line passing through (-2, 0) and perpendicular to line segment joining (2, 3) and (-2,

0)

Line is 0 2 2

4 3 8 02 3 0

yx y

x

19. A

Sol. Contrapositive of p q is ~ ~q p

20. D

Sol. 2 2 1

dxy x y x y y y

dy

Now at x = 2, y is also equal to 2

Hence dy

dx at (2, 2) is

1 1

2 2 1 3

21. D

Sol. Reflection of A about 1 0x y is (1,1) which lies on side BC equation of BC is 1x

B is (1, 0) and C is (1, 6)

22. C

Sol. sin cos 1 sin 2x x x

If sin 2 0.44x then sin cos 1.2x x

23. B

Sol. Because 1 tan 1 tan 45 2 , so the two digit number is 23.

24. D

Sol. min 20 15 5 30n A B

If min n A B n C then minimum n A B C equals to 30

25. B

Sol. radical axis of circles is x = 0

y axis goes outside both the circle 0ab

Now on solving x = 0 and 2 2 0x y ax c simultaneously we does not get any point c is positive

26. D

Sol. If we apply the condition of orthogonally 1 2 1 2 1 22 2g g f f c c then we get k = 81


but at k = 81 circle 2 2 4 6 81 0x y x y becomes imaginary

27. B

Sol. Combined equation of 1 0ax y and 0x by is 2 2 1 0ax by ab xy x by

After making it homogeneous equation of degree two with the help of 1ax by we get

2 2 1ax by ab xy x ax by by ax by = 0

Now coefficient of 2x coefficient of

2y must be equal to zero

22 0a b b

28. A

Sol. Let PT is tangent on 2 2 16 0x y from point (6, 5)

Now PA PB = PT2 2 2

1 6 5 16 45for 6,5PA PB S

29. B

Sol.

1 1 1

2 1 0

4 2 7

a

a

13

,22

rejecteda

a = 2 is rejected because at a = 2 lines are parallel

30. B

Sol.

2 2,0A

2,0C

B

6,0D

1L 2L

2BCD BAD Locus of B is circle with centre (2, 0) and radius 4 units.




Maximum Marks: 210

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

You are not allowed to leave the Examination Hall before the end of the test.

INSTRUCTIONS

Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet before attempting the paper. Wrong CODE or no CODE will give wrong results.

A. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.

2. This question paper contains Three Parts.

3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.

4. Each part is further divided into two sections: Section-A & Section-C

5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work.

6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed.

B. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR

sheet. 2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No.

and write in ink your Name, Test Centre and other details at the designated places. 3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Three Parts. (i) Section-A (01 – 10) contains 10 multiple choice questions which have only one correct answer. Each

question carries +3 marks for correct answer and – 1 mark for wrong answer. Section-A (11 – 15) contains 5 multiple choice questions which have one or more than one correct

answer. Each question carries +4 marks for correct answer. There is no negative marking. (ii) Section-C (01 – 05) contains 5 Numerical based questions with single digit integer as answer, ranging from

0 to 9 and each question carries +4 marks for correct answer. There is no negative marking.

Name of the Candidate :__________________________________________

Batch :___________________ Date of Examination :___________________

Enrolment Number :______________________________________________

BA

TC

HE

S –

Tw

o Y

ea

r C

RP

(1

31

5)-

Ad

va

nc

e (

B L

ot)

FIITJEE

CPT1 - 1

CODE: SET-A

PAPER - 1




Gas Constant R = 8.314 J K1 mol1

= 0.0821 Lit atm K1 mol1

= 1.987 2 Cal K1 mol1


Planck‘s Constant h = 6.626 10–34 Js

= 6.25 x 10-27 erg.s



1 amu = 1.66 x 10-27 kg

1 eV = 1.6 x 10-19 J


Au=79.

Atomic Masses: He=4, Mg=24, C=12, O=16, N=14, P=31, Br=80, Cu=63.5, Fe=56,

Mn=55, Pb=207, Au=197, Ag=108, F=19, H=2, Cl=35.5, Sn=118.6




PPPAAARRRTTT ––– III ::: PPPHHHYYYSSSIIICCCSSS SECTION – A

(Single Correct Choice Type)

This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

1. Which of the following is a unit vector

(A) ji (B) cos i - sin j (C) sin jcos2i (D) ji3

1

2. A force ˆ ˆ ˆF 5i 3j 2k N

is applied over a particle which displaces it from its origin to the

point ˆ ˆr 2i j m.

The work done (in J) on the particle is :

(A) + 13 (B) + 10 (C) + 7 (D) – 7

3. A uniform chain of length 2m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table ?

(A) 3.6 J (B) 7.2 J (C) 1200 J (D) 120 J

4. A projectile is thrown with velocity u at an angle above the horizontal. Find the average velocity during the time of ascent

(A) u cos (B) usin

2 (C) 2u

1 3cos2

(D) None of these

5. A block of mass m is attached with a spring in its natural length, of spring constant k. The other end A of spring is moved with a constant acceleration ‗a‘ away from the block as

mAa

shown in the figure. Find the maximum extension in the spring. Assume that initially block and spring is at rest w.r.t ground frame

(A) ma

k (B)

1 ma

2 k (C)

2ma

k (D)

4ma

k.

6. A balloon B is moving vertically upward and viewed by a

telescope T. At a particular angular position = 53° measured

parameters are r = 1 km, dr

3m / sdt

and d

0.02 rad / s.dt

The

magnitude of the linear velocity of the balloon at this instant is

(A) 1.2 m/s (B) 2.4 m/s

(C) 3.6 m/s (D) 4.8 m/s

= 53°

B

r

T

Space For Rough Work


7. Width of a river is 60 m. A swimmer wants to

cross the river such that he reaches from A to B directly. Point B is 45 m ahead of line AC (perpendicular to river) Assume speed of river and speed of swimmer as equal. Swimmer must

try to swim at angle with line AC. Value of is A

BC

River Flow

(A) 37º (B) 53º (C) 30º (D) 16º

8. Find minimum value of the angle so that block of mass m does not move on rough surface, whatever may be the value of applied force F.

The coefficient of state friction between the block and surface is .

F m

() Rough Surface

(A) tan1() (B) 11tan ( )

2

(C) cot1() (D) 11cot ( )

2

9. At time t = 0, a bullet is fired vertically upwards with a speed of 98 ms1. At time t = 5 s (i.e., 5 seconds later) a second bullet is fired vertically upwards with the same speed. If the air resistance is neglected, which of the following statements will be true ?

(A) The two bullets will be at the same height above the ground at t = 12.5 s (B) The two bullets will reach back their starting points at the same time (C) The two bullets will have the same speed at t = 20 s (D) The two bullets will attain the different maximum height 10. Figure shows the changes in speed of a marble as it rolls down

an inclined plane P1, travels on a flat horizontal surface and then up another inclined plane P2. What can you say about the steepness of P1 and P2 from the information given in the figure ?

(A) P1 is steeper than P2 (B) P2 is steeper than P1 (C) P1 and P2 are equally steep (D) Nothing can be said about the relative steepness of P1 and P2

as the information given is insufficient

C

P2

BA20

0

10

ED

P1

20 50 100

Time (s)

Sp

eed

(m

s)

-1

(Multi Correct Choice Type)

This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.

11. A spring and block is placed on a fixed smooth wedge as shown. Following conclusion can be drawn about block.

(i) magnitude of its momentum will be max when Fnet on block is zero

(ii) its kinetic energy will be max when Fnet on block is zero (iii) KE of block is max when block just touches the spring. (iv) net force on block is maximum when KE = 0

m

Block

Spring

Fix Wedge

(A) (i) (B) (ii) (C) (iii) (D) (iv)



12. In the figure, if F = 4 N, m = 2kg, M = 4 kg then

(A) The acceleration of m w.r.t. ground is 22m / s

3

(B) The acceleration of m w.r.t. ground is 1.2 m/s2 (C) Acceleration of M is 0.4 m/s2

F

s=0.1=0m

M

k = 0.08

Ground

z

(D) Acceleration of m w.r.t. ground is 22m / s

3

13. A particle moves along positive branch of the curve x

y2

where 3t

x ,3

x and y are

measured in metres and t in seconds, then :

(A) The velocity of particle at t = 1 s is 1ˆ î j2

(B) The velocity of particle at t = 1 s is 1 ˆ î j2

(C) The acceleration of particle at t = 1 s is ˆ ˆ2i j

(D) The acceleration of particle at t = 2 s is ˆ î 2 j

14. Two blocks of masses m1 and m2 are connected through a massless inextensible string. Block of mass m1 is placed at the fixed rigid inclined surface while the block of mass m2 hanging at the other end of the string, which is passing through a fixed massless frictionless pulley shown in figure. The coefficient of static friction between the block and the inclined plane is 0.8. The system of masses m1 and m2 is released from rest.

m=4kg1m=2kg2

30º Fixed

g=10m/s2

=0.8

(A) The tension in the string is 20 N after releasing the system (B) The contact force by the inclined surface on the block is along normal to the inclined

surface

(C) The magnitude of contact force by the inclined surface on the block m1 is 20 3N

(D) None of these

15. A particle ‗P‘ of mass ‗m‘ is rotating in horizontal circle about vertical axis AB with the help of two strings each of length ‗L‘ as shown in

figure. The separation AB = L, and ‗P‘ rotates with angular velocity ‗‘ about axis AB. Tension in the upper and lower strings are T1 and T2

respectively, then :

(A) T2 will be zero for 2g

L

(B) T1 will always be greater than T2 for any ‗‘

(C) T1 = 3T2, for 4g

L

(D) 2

1T mL for

2g

L

L

L

P

L

T1

A

B

T2



SECTION–C (Integer Type)

This section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.

1. A particle of mass 10 kg is in equilibrium with the help of two ideal

and identical strings. Now one string is cut then, find the ratio of tension in the other string just before cutting and just after cutting.

30°30°

10 kg 2. In a car race, car A takes 4 seconds less than car B to reach the finish line and passes the

finishing line with velocity v more than car B. Assume cars start from rest and travel with constant acceleration aA = 4 m/s2 and aB = 1 m/s2. Find the value of v in m/s.

3. In the figure, find the velocity of m1 in ms–1 when m2 falls by 9m. Given m1 = m m2 = 2m (take g = 10 ms–2)

m1=0.1

m2 4. A ball is projected from some height with initial horizontal speed

20 m/s. There is a wall at a horizontal separation of 100 m from

the building. If collision is perfectly elastic find the time in sec

after which it will hit the wall. (t = 0 is taken when ball is thrown).

All surfaces one smooth.

100 m

20 m/s

5. Figure shows a smooth cylindrical pulley of radius R with centre at origin

of co-ordinates. An ideal thread is thrown over it on the two parts of ideal

thread two identical masses are tied initially at rest with co-ordinates (R, 0)

and (-R, -R) respectively. If mass at x-axis is given a slight upward jerk, it

leaves contact with pulley at (R cos, Rsin). Then find /sin.

x

y

m

m



PPAARRTTIIII :: CCHHEEMMIISSTTRRYY

SSEECCTTIIOONNAA Single Correct Choice Type

This section contains 10 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is

1. The distance between 3rd and 2nd orbit of hydrogen atom is

(A) 2.646108 cm (B) 2.116108 cm (C) 2.646 cm (D) 0.529 cm

2. H–B–H bond angle in 4BH is:

(A) 180° (B) 120° (C) 109° (D) 90° 3. Which of the following has maximum lattice energy? (A) CaO (B) Na2O (C) MgO (D) BaO 4. The atomic radii of F and Ne in angstrom unit are respectively given by (A) 0.72, 1.60 (B) 1.60, 1.60 (C) 0.72, 0.72 (D) 1.60, 0.72 5. The K.E. of N molecule of O2 is x Joules at –123°C. Another sample of O2 at 27°C has a KE of

2x Joules. The latter sample contains. (A) N molecules of O2 (B) 2N molecules of O2

(C) N/2 molecules of O2 (D) N/4 molecule of O2

6. Out of the following, which does not have zero dipole moment is (A) CO2 (B) CCl4 (C) BCl3 (D) NH3 7. The wave function for 1s orbital of hydrogen atom is given by

r /a01s e

2

a0 = radius of Bohr orbit r = distance from nucleus What will be ratio of probability density of finding the electron at the nucleus to the first Bohr‘s

orbit (a0)? (A) e (B) e2 (C) 1/e (D) 0 8. The IP1, IP2, IP3, IP4 and IP5 of an element are 7.1, 14.3, 34.5, 46.8, 162.2 eV respectively.

The element is likely to be (IP ionization potential) (A) Na (B) Si (C) K (D) Ca

Space for rough work


9. 12.25 g KClO3 on heating gives enough O2 to react completely with H2 produced by the action of the Zn on dilute H2SO4.

3 2

2KClO 2KCl 3O , 2 4 4 2

H SO Zn ZnSO H , 2 2 2

2H O 2H O

The weight of Zn required for this is: [At.wt of Zn = 65.5] (A) 9.825 g (B) 19.65 g (C) 39.3 g (D) 8.5 g

10. 2 moles of 4

FeSO in acid medium are oxidised by x moles of 4

KMnO , whereas 2 moles of

2 4FeC O in acid medium are oxidised by y moles of

4KMnO . The ratio of x and y is:

(A) 1

3 (B)

1

2 (C)

1

4 (D)

1

5

Multiple Correct Answer(s) Type

This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONE or MORE are correct.

11. Which of the following statement is correct regarding H2O2?

(A) it has open booklike structure (B) it is both an oxidizing as well as reducing agent (C) it is a bleaching agent (D) it acts as only oxidizing agent 12. Which of the following will represent Boyle‘s law correctly?

(A) PV

P

(B) V

PV

(C) PV

1/P

(D) P

V 13. Which of the following pairs will not diffuse at the same rate through porous plug at same

conditions of temperature and pressure? (A) CO & NO2 (B) NO2 & CO2 (C) NH3 & PH3 (D) CO2 & N2O 14. A gas obeys the equation P(V-b) = RT. Which of the following is/are correct about the graphs

of gas?

(A) The isochoric curves have slope = R

V b

(B) The isobaric curves have slope = R

P and intercept b.

(C) For the gas compressibility factor = 1+Pb

RT

(D) For the gas compressibility factor = 1Pb

RT



15. Highly pure dilute solution of sodium in liquid ammonia: (A) Shows blue colour (B) Exhibits electrical conductivity (C) Shows reducing properties (D) Shows oxidizing properties

SECTIONC Integer Answer Type

This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).

1. 1 g of an acid (Molar mass = 150 g/mol) is completely neutralized by 1.5 g KOH. Calculate the number of neutralizable protons in acid.

2. Find out the number of angular nodes in the orbital to which the last electron of Cr enter. 3. According to molecular orbital theory, the number of electrons present in the antibonding

molecular orbitals of N2 is (are)

4. A 17 gm sample of H2O2 contains a% H2O2 by weight and requires a mL of KMnO4 in acidic

medium for comlete oxidation. Thus what is the molarity of KMnO4? 5. The value of x+y+z in following redox reaction

xFeCl3 + yH2S zFeCl2 + S + HCl, is



PART – III : MATHEMATICS SECTION – A

(Single Correct Choice Type) This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

1. In a triangle ABC, A(2, 4) and internal angular bisector of B & C are y = x & 2x + y = 3, then find the equation of BC

(A) x = 2 (B) y = 2 (C) x + y = 2 (D) none of these 2. Find the equation of minimum radius of that circle which contain all free circles S1, S2 & S3

where S1 x2 + y2 = 1, S2 (x – 2)2 + y2 = 9, S3 (x – 2)2 + (y – 2)2 = 4

(A) x2 + y2 – 2x – 2y = 2 (B) x2 + y2 + 2x + 2y = 9

(C) x2 + y2 – 2x – 2y = 9 2 (D) none of these

3. The value of

20log 0.1 0.01 0.001 .............

0.05

is

(A) 81 (B) 1

81 (C) 20 (D)

1

20

4. The equation of the bisector of the acute angle between the lines 2x – y + 4 = 0 and x – 2y = 1

is : (A) x + y + 5 = 0 (B) x – y + 1 = 0 (C) x – y = 5 (D) x – y + 5 = 0

5. The maximum value of cos2x sin2x27 81 is

(A) 23 (B) 53 (C) 73 (D) 3



6. The pair of straight lines joining the origin to the common points of x2 + y2 = 4 and y = 3x + c

are perpendicular, if c2 = (A) – 1 (B) 6 (C) 13 (D) 20 7. The centre of circle inscribed in square formed by the lines x2 – 8x + 12 = 0 and

y2 – 14y + 45 = 0 is (A) (4, 7) (B) (7, 4) (C) (9, 4) (D) (4, 9) 8. |x + 1| + |x − 2| > 3

(A) (−, −1) (2, ) (B) (2, ) (C) (−1, 2) (D) none of these

9. In the equilateral ABC the side length is 8 unit, inscribe this another triangle is form through the

midpoints of vertices A,B and C is DEF. Inside

DEF another triangle is also form through the

midpoints of vertices D,E & F is PQR Find the

area of PQR.

(A) 2 3 (B) 3

(C) 3

2 (D) none of these

A B

C

D E

F

P

Q R

10. Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the statement ―Suman is brilliant and dishonest if and only if Suman is rich‖

can be expressed as

(A) ~ (Q (P ~ R) (B) ~ Q ~P R

(C) ~ (P ~ R) Q (D) ~ P (Q ~ R)



SECTION – A

(Multiple Correct Answers Type)

This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONE or MORE may be correct.

11. In a ABC

(A) sinA.sinB.sinC 3 3 / 8 (B) 2 2 2sin A sin B sin C 9/ 4

(C) sinAsinBsinC is always positive (D) 2 2sin A sin B 1 cosC

12.

n n

cos A cosB sinA sinB

sinA sinB cos A cosB

(n, even or odd) is equal to

(A) n A B2tan

2

(B) n A B2cot

2

(C) 0 (D) none of these

13. Common tangents to the circles x2 + y2 – 2x – 6y + 9 = 0 & x2 + y2 + 6x – 2y + 1 = 0 are. (A) 3x + 4y – 10 = 0 (B) 4x – 3y = 0 (C) y = 4 (D) x = 0

14. Two circles x2 + y2 + x = 0 & x2 + y2 = c2 touch each other if

(A) + c = 0 (B) c = 0 (C) 2 = c (D) none of these

15. If x satisfies x 1 x 1

2 2log (9 7) 2 log (3 1) then

(A) x Q (B) x {x Q: x 0}

(C) x N (D) x Ne (set of even natural numbers)



SECTION – C

(Integer Answer Type)

This Section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be darkened in the ORS.

1. A(0, 0), B(2, 1) and C(3, 0) are the vertices of a triangle ABC, and BD is its altitude. The line

through D parallel to the side AB intersects the side BC at a point K. If the product of the areas of the triangle ABC and BDK is k, then the value of 2k is

2. If 2sinx sin x 1 then the value of 2 4 4 2cos x cos x cot x cot x is equal to

3. If 1 2 3cos 2cos 3cos 6 then 1 2 3tan tan tan equals to

4. If 2 2 2log x log y log z

4 6 3k and x3y2z = 1

Then |k| is 5. Let the co-ordinates of the circumcentre of the triangle whose vertices are A(5, – 1), B(–1, 5)

and C(6, 6) is (a, b) then [a + b] is (where [.] denotes the greatest integer function)



FIITJEE COMMON TEST

BATCHES: TWO YEAR CRP (1315)-Advance-(B LOT)

PHASE TEST-I (PAPER-1) ANSWER KEY

PART – I (PHYSICS) PART – II (CHEMISTRY) PART – III (MATHS)

SECTION-A

1. B

2. C 3. A 4. C 5. C 6. C 7. D 8. C 9. A 10. A 11. A, B, D 12. B, C 13. A, C 14. A, B, C 15. A, B, C

SECTION-C

1. 2 2. 8 3. 4 4. 5 5. 2

SECTION – A 1. A 2. C 3. C 4. A 5. A 6. D 7. B 8. B 9. B 10. A 11. A,B,C 12. A,B,D 13. A,B,C 14. ABC 15. A,B,C

SECTION–C 1. 4 2. 2 3. 5 4. 2 5. 5

SECTION-A

1. B 2. C 3. A 4. A 5. B 6. D 7. A 8. A 9. B 10. A 11. A,B,C,D 12. B,C 13. A,B,C,D 14. A,B,C 15. A,C

SECTION-C

1. 1 2. 2 3. 0 4. 8 5. 5

Paper Code

SET-A


HINT & SOLUTIONS



1. B

2. C

F.r

= 10 – 3 = 7 3. A (1.2) (10) (0.3) 4. C

av

R ˆ î Hj2

| v |T

2

5. C From work energy in the frame which is attached to point A

2 2 2xm m

1 1 1max k x m(0) m(0)

2 2 2

max

2max .

k

6. C

y = r sin

dy dr d

sin cos .r 3.6m / sdt dt dt

7. D

45

tan60

= 37°

since, VS = VR,

53° = + 37°

= 16°.

vR

vS

53º

37º

8. C Fcos N …..(A)

N Fsin mg …..(B)

By (A) and (B)

Fcos Fsin mg

Fcos Fsin mg


F(cos sin ) mg

if F is . Hence cos sin 0

cos sin 0 cot =

= cot1()


9. A

y1 = 9.8t 4.9t2

y2 = 9.8 (t5) 4.9 (t5)2 y1 = y2 gives t = 12.5 10. A

Acceleration = slope of v/t graph = g sin is greater for P1 where is angle of inclined plane.


11. A, B, D 12. B, C

Here s

mF mg 1

M

For m

kF mg m.a

For M

kmg MA

2A 0.4m / s

13. A, C

2dxt

dt …(i)

31 t

y2 3

2dy t

dt 2 …(ii)

t = 1, vx = 1, vy = 1

2

1ˆ ˆv i j2

2

2

d x2t

dt …(iii)

2

2

d yt

dt …(iv)

at t = 1 s ax = 2 and ay = 1

ˆ â 2i j

.

14. A, B, C If the tendency of relative motion along the common tangent does not exist, then component

of contact force along common tangent will be zero. 15. A, B, C For particle ‗P‘

2

1 2(T T )cos 30 mL cos 30

1 2T sin 30 T sin 30 mg.

SECTION–C

(Integer Type) 1. 2


2. 8

B A

2S 2S4

a a

A B2a S 2a S v

v 8m / s.

3. 4 Applying work energy theorem Kf – Ki = w

2 22 1

1 1m v m (4v)

2 2

2 1m g y m g(4y)

v = 4 m/s.

m1

m2

mg

v

T

4. 5 Horizontal velocity of ball will not change 100 = 20 t t = 5 sec.

5. 2

mgR – mg R sin = ½ (2m)v2 …. (i)

mv2/R = mg sin … (ii)


PPPAAARRRTTT ––– III ::: CCCHHHEEEMMMIIISSSTTTRRRYYY

SECTION – A (Single Correct Choice Type)

1. A

r = r3r2 = r09 r04

r = 5r0 = 50.0529108 = 2.646108 cm 2. C

Hybridization in BH4 is sp3, hence bond angle in 109

3. C Latlic energy in inversely propotional to size 4. A Noble gases have more radii than halogen in respective periods 5. A

KE =3

RT2

; T = – 123 + 273 = + 150 K

3

R 1502

38.314 75

2 = xJ = 225 8.314 = xJ

At 27°C = 27+ 223 = 300K

KE for = 2x Joule = 3

8.314 3002

N molecules

x Joule = 3 8.314 75 In both the cases x Joules correspond to N molecules. 6. D NH3 does not have zero dipole moment 7. B

Probability density 2

02

(r 0) 2

22(r 1)

e2 e

e2

8. B There is large difference between 4th and 5th IP, hence element should contain four valence

electrons. 9. B

Moles of O2 produced = 3/2 moles of KClO3 = 3 12.25

0.152 122.5 mole

According to given equation One moles of O2 required 2 mole of H2 = 2 moles of Zn

Moles of Zn = 2moles of O2=0.152=0.3 mole

Mass of Zn require = 0.365.5 = 19.65 g 10. A

nfactor of 4FeSO 1

nfactor of 2 4FeC O 3

Hence geq. of 4 4FeSO g e.q of KMnO

12 = 5x (1)

geq. of FeC2O4 = geq of KMnO4

32 = 5y Hence x/y = 1/3



11. A,B,C H2O2 is both oxidising and reducing agent 12. A,B,D

According to Boyle‘s law 1

P or PV constantV

13. A,B,C

Rate of diffusion 1

M

CO2 and N2O have same molar mass = 44 g/mol 14. ABC

P(V b) RT

PV Pb RT

PV PbZ 1

RT RT

15. A,B,C Solution of alkali metal in liquid ammonia shows blue colour, exhibit electrical conductivity and

show reducing property SECTION–C

(Integer Type)

1. 4

geq. of acid = geq. of base

1 1.5

n150 56

n=4 2. 2

Last electron of Cr enters in dsubshell, hence l=2 3. 5

Electronic configuration of N2 is

1s2 1s2 2s2 2s22px

22py

22pz

2 2px1

4. 2

geq. of H2O2 = geq. of KMnO4

17 2 a

a 5 M100 34 1000

M = 2 molar 5. 5 Balance equation is

2FeCl3 + H2S 2FeCl2 + S + 2HCl x + y + z = 5


SECTION – A


MATHEMATICS 1. B Take the reflection of A about internal angular bisector of B & C lie on the line BC. 2. C For centre - find the circumcentre of the centres S1, S2 & S3, For radius - find the circum radius from the centres S1, S2 & S3 and add the maximum radius

of the circles S1, S2 & S3 in the circum radius. 3. A Use the log properties 4. A

2x – y + 4 = ( x – 2y 1) For acute angle bisector use + sign 5. B 33cos2x+4sin2x Then maximum value is 35 6. D Use the homogenization 7. A Lines are x = 2 and x = 6, y = 5, and y = 9 Then centre is (4, 7) 8. A 9. B

Area = 232

4

10. A (Multi Correct Choice Type)

11. A,B,C,D

2 2 2 2 2 21 1sin A sin B sin C (1 cos A) (1 cos B) sin C

2 2

22 cos C cosC.cos(A B)

22 (cos C cosC)

2

9 1cosC

4 2

sin2A + sin2A+sin2C 9/4

Now 2 2 2

2 2 2 1/ 3sin A sin B sin C(sin A.sin B.sin C)

3

2 / 39 / 4(sinA.sinB.sinC)

3 or

3 3sinA.sinB.sinC

8

also 2 2 2 2sin A sin B sin C 2 cos C cosC

sin2A + sin2B 1+ cos C. 12. B,C

n n



n nA B B A

2cot cot2 2

If n even, n A B2cot

2

, if n odd, 0.

13. A,B,C,D


Points can be calculated by the internal and external section formula using centres of both the circles and slope can be calculated by using the condition of tangency.

14. A,B,C Use the internal and external touching condition of two circles. 15. A,C

x 1

2 x 1

9 7log 2

3 1

32x2 + 7 = 4(3x1 + 1)

x 1 x 1(3 1)(3 3) 0

x 1 = 0 or x 1 = 1 x = 1, 2.


1. 1 Calculate the area of ABC and BDK then multiply these two 2. 2 Given sin x + cos x + tan x + cot x + sec x + cosec x = 7

1 sinx cosx

sinx cosx 7sinx cosx sinx cosx

1 1

sinx cosx 1 7sinx cosx sinxcosx

2 2

2 21 sin2x 1 7

sin2x sinx

2 2

1 t t 2 7t 2 , where t = sin 2x

3 2t 44t 36t 0

2t 44t 36 0 [sin 2x 0]

244 44 4 36

t 22 8 72

sin2x 22 8 7

3. 0

Given 1 2 3cos 2cos 3cos 6

1 2 3cos cos cos 1

1 2 3 0

1 2 3tan tan tan 0

4. 8 Use the log property. 5. 5 Circum centre can be calculated by using the perpendicular bisectors of vertices of the

triangle.




Maximum Marks: 198

Please read the instructions carefully. You are allotted 5 minutes specifically for

this purpose.


INSTRUCTIONS

Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet before

attempting the paper. Wrong CODE or no CODE will give wrong results.

C. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.



4. Each part is further divided into one section: Section-A

5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for

rough work.

6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any

form, are not allowed.

D. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet.

2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No. and

write in ink your Name, Test Centre and other details at the designated places.

3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Three Parts.

(i) Section-A (01 – 08) contains 8 multiple choice questions which have only one correct answer. Each question

carries +3 marks for correct answer and – 1 marks for wrong answer.

Section-A (09 – 14) contains 3 paragraphs. Based upon paragraph, 2 multiple choice questions have to be

answered. Each question has only one correct answer and carries +3 marks for correct answer and – 1 mark for

wrong answer.

Section-A (15 – 20) contains 6 multiple choice questions which have one or more than one correct

answer. Each question carries +4 marks for correct answer. There is no negative marking.

Name of the Candidate :____________________________________________

Batch :____________________ Date of Examination :___________________

Enrolment Number :_______________________________________________

BA

TC

HE

S –

Tw

o Y

ea

r C

RP

(1

31

5)-

Ad

van

ce

(B

Lo

t)

FIITJEE

CPT1 - 2

CODE:SET-A

PAPER - 2




Gas Constant R = 8.314 J K1

mol1

= 0.0821 Lit atm K1

mol1

= 1.987 2 Cal K1

mol1


Planck‟s Constant h = 6.626 10–34

Js

= 6.25 x 10-27

erg.s



1 amu = 1.66 x 10-27

kg

1 eV = 1.6 x 10-19

J


Au=79.


Mn=55, Pb=207, Au=197, Ag=108, F=19, H=2, Cl=35.5, Sn=118.6




PPPAAARRRTTT ––– III ::: PPPHHHYYYSSSIIICCCSSS

SECTION – A


This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and

(D) out of which ONLY ONE is correct.

1. A body of mass „m‟ is placed on a plank which is tilted till the mass just slips. What is the

maximum horizontal force that can be applied on „m‟ at this position without causing

slipping? 1

.3

(A) mg (B) 2mg (C) 3 mg (D) 3

mg2

2. A stone is projected vertically upwards so as to reach a height h passes points P and Q

with velocities v

2 and

v,

3 where v is initial velocity with which the body is thrown. The

distance between P and Q in terms of h is :

(A) 7

h36

(B) 5

h36

(C) 9

h36

(D) 8

h36

3. A particle moves in a straight line with a velocity tv t 2 m / s, where t is time in

second. What is the distance covered by the particle in 4 s ?

(A) 2m (B) 4m (C) 1m (D) 8m

4. A body of mass 500 g is accelerated from a velocity 1ˆ ˆ3i 4j ms to 1ˆ ˆ6j 2k ms . Find

the work done :

(A) 3.75 J (B) 0 (C) 4.75 J (D) 16 J

5. The minimum work done in moving a particle from a point (1, 1) to (2, 3) in a plane

having force field with potential U = (x + y) is :

(A) 0 (B) (C) 3 (D) – 3

6. A particle of mass m is fixed to one end of a light spring of force

constant K and unstretched length . The particle is rotated about

the other end of the spring with an angular velocity , in gravity free

space. The increase in length of the spring will be :

(A) 2m

K

(B)

2

2

m

K m

(C) 2

2

m

K m

(D) None of these

m K



7. The velocity of a particle moving in the positive direction of x-axis varies as v A x. The

graph of displacement versus time is :

(A)

x

t

(B)

x

t

(C)

x

t

(D)

x

t

8. The bob of a simple pendulum at rest, is given a sharp hit to impart a horizontal velocity

8g where is length of pendulum. The tension in the string :

(A) T = 6 mg when the string is horizontal

(B) T = 4 mg when the bob is at highest point

(C) T = 8 mg when the string is horizontal

(D) T = 6 mg when the bob is at highest point.

(Paragraph Type)

This section contains 3 paragraphs based upon paragraph 2 multiple choice questions have to be

answered. Each of these questions has four choices (A), (B), (C) and (D) out of WHICH ONLY

ONE is correct.

Paragraph for Question Nos. 9 to 10

From the top of a tower of height H, a stone of mass 2 kg is thrown vertically upwards

with a speed U and it hits the ground below in 28 sec. When same stone was thrown with

same speed vertically down from same position, the time taken to hit the ground is 7 sec.

P1 is the average power of gravity in first case and P2 in second case (g = 10 m/s2)

9. The kinetic energy with which the stone was thrown initially is :

(A) 9025 J (B) 11025 J (C) 13225 J (D) 11449 J

10. Taking potential energy at ground level as zero, the maximum potential energy attained

by the stone thrown vertically upwards is :

(A) 30625 J (B) 32825 J (C) 28625 J (D) 31049 J




In figure shown on the right, the spring constant is K. The mass of block is m.

The block is imparted a downward velocity = v0 at t = 0, at its equilibrium

position.

11. The value of v0 for which the block has zero velocity when spring is in its natural position

is

(A) m

gK

(B) m

2gK

(C) m

g2K

(D) m

4gK

12. The value of v0 for which the minimum pull force on ceiling is mg

,2

will be

(A) m

g2K

(B) m

gK

(C) m

2gK

(D) g m

2 K


In the system shown in the figure, the mass 30 kg is

pulled by a force of 210 N. Answer the following

questions at the instant when the 15 kg mass has

acceleration 6 m/s2. Assume the spring to be mass

less and spring constant is 100 N/m. The surface of

ground is smooth.

210 N

30 kg 15 kg

13. Find the acceleration of 30 kg mass

(A) 2 m/s2

(B) 3 m/s2 (C) 3.4 m/s

2 (D) 4 m/s

2

14. Find the elongation in the string at this instant

(A) 0.3 m (B) 0.6 m (C) 0.9 m (D) None of these

(Multiple Correct answers Type)


(D) out of which ONE OR MORE may be correct.

15. Acceleration vs time graph is shown in the figure for a

particle moving along a straight line. The particle is

initially at rest. Find the time instant(s) when the

particle is at rest?

(A) t = 0

(B) t = 1

(C) t = 2

(D) t = 4

+2

O

2

1 2 3 4t(sec)

a(m/s)2



16. A 10 kg block is resting on a rough horizontal

surface. A horizontal force F is applied to it for 4s.

The variation of force with time is shown in the

figure. (µs = µk = 0.5, g = 10 m/s2). Then

(A) At t = 1 sec, velocity of block is 5 m/s

(B) At t = 1 sec, velocity of block is zero

(C) At t = 4 sec, velocity of block is 20 m/s

(D) At t = 4 sec, velocity of block is 5 m/s

10 kg F 100 N

F (N)

4 s

17. A boy in the elevator with open roof shoots a bullet in vertical upward direction from a

height of 1.5 above the floor of the elevator. The initial speed of the bullet with respect to

elevator is 15 m/s. The bullet strikes the floor after 2 seconds. Then (Assuming g = 10

m/s2, acceleration of elevator to be constant).

(A) Lift is moving with constant speed

(B) Lift is moving with upward acceleration of 5.75 m/s2

(C) Lift is moving with downward acceleration of 5.75 m/s2

(D) Lift is moving with acceleration 4.25 m/s2

18. If ˆ â 2i 3j

and ˆ ˆb 2i k

, then

(A) a.b 4

(B) ˆ ˆ â b 3i 2j 6k

(C) a.b 1

(D) â b 4k

19. In the figure small block is kept on m then

(A) The acceleration of m w.r.t. ground is F

m

(B) The acceleration of m w.r.t. ground is zero A B

F

=0=0m

M

(C) The time taken by m to separate from M is 2 m

F

(D) The time taken by m to separate from M is 2 M

F

20. A particle is projected at an angle = 30º with the horizontal, with a velocity of 10 m/s

then

(A) After 2 s the velocity of particle makes an angle of 60º with initial velocity vector

(B) At 1 s the velocity of particle makes an angle of 60º with initial velocity vector

(C) The magnitude of velocity of particle after 1 s is 10 m/s

(D) The magnitude of velocity of particle after 1 s is 5 m/s



PPPAAARRRTTT ––– IIIIII ::: CCCHHHEEEMMMIIISSSTTTRRRYYY

((SECTIONA)

Single Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and

(D), out of which ONLY ONE is correct.

1. A solution containing 32.68 10 mol of nA ions require 31.61 10 mol of 4MnO for the

complete oxidation of nA to 3AO in acidic medium. The value of „n‟ is

(A) 3 (B) 4 (C) 1 (d) 2

2 How many maximum number of electrons of an atom will have the following set of

quantum numbers?

n + l = 6

m = – 1

1s

2

(A) 8 (B) 4 (C) 6 (D) 10

3. Equal weights of a mixture of CO2 and O2 are enclosed in a vessel at 27oC and 1 atm

pressure then which of the following is true (Assuming ideal behaviour of gases)

(A) O2 molecule will hit the wall with greater momentum than CO2

(B) CO2 molecule will hit the wall with greater kinetic energy than O2

(C) Both O2 and CO2 hit the wall with same momentum

(D) CO2 molecule will hit the wall with greater momentum than O2

4. The incorrect statement among the following is:

(A) The first ionisation potential of Al is less than the first ionisation potential of Mg.

(B) The second ionisation potential of Mg is greater than the IE2 of Na.

(C) The first ionisation potential of Na is less than the first ionisation potential of Mg.

(D) The third ionisation potential of Mg is greater than the third ionisation potential of

Al.

5. Which of the following order of lattice energy values (kJ mol-1

) is correct?

(A) CaO > SrO > BaO > MgO (B) MgO > CaO > SrO > BaO

(C) SrO > CaO > MgO > BaO (D) MgO > CaO > BaO > SrO

6. This curve is for np orbital, then the principle

quantum no is

(A) 3

(B) 4

(C) 5

(D) 6 r

2r

radial

probability



7. 5.3g of carbonate of a monovalent metal is dissolved in 150ml of 1N HCl. Unused acid

required 100ml of 0.5N NaOH for complete neutralization. The atomic weight of the

metal is

(A) 13 (B) 24 (C) 46 (D) 23

8. 1 gm of fuming H2SO4 (Oleum is a mixture of conc. H2SO4 saturated with SO3 and having

the formula H2S2O7) is diluted with H2O. This solution is completely neutralized by 27.7

mL of 0.8 N NaOH . Find the percentage of free SO3 in the oleum.

(A) 78.73% (B) 61.85% (C) 69.73 % (D) 38.15 %

(Paragraph Type)



ONE is correct.

Paragraph for Question 9 to 10

Read the paragraph carefully and answer the following questions:

HClA NaOH B white fumes

2 4CaCl KMnO (acid)

white ppt.C colourless

colourless salt

9. The compound A is

(A) (NH4)2C2O4 (B) (NH4)2SO4 (C) NaHSO4 (D) Na2SO4

10. The compound B is

(A) CO2 (B) NH3 (C) O2 (D) HCl





Covalent molecules formed by heteroatoms bound to have some ionic character. The

ionic character is due to shifting of electron pair towards A or B in the molecule AB.

Hence molecule will have dipolemoment which is equal to product of charge(q) and bond

length (d). The unit of dipole moment is Debye(D). 1 D = 1018

esu cm.

The percentage of ionic character of bond can be calculated by formula:

% ionic character=experimental value of dipole moment

100Theoretical value of dipole moment

11. The dipole moment of NF3 is very much less that of NH3 because:

(A) No. of lone pairs in NF3 is much greater than in NH3

(B) Unshaired electron pair is not present in NF3 as in NH3

(C) Both have different shapes

(D) Of different direction of moments of NH and NF bonds

12. A covalent molecule xy, is found to have a dipole moment of 1.51029

Cm and a bond

length is 150 pm. The percentage of ionic character of the bond will be

(A) 50% (B) 62.5% (C) 75% (D) 90%



When electron jumps from higher orbit (n2) to lower orbital (n1), then energy is radiated

in the form of electromagnetic radiation and these radiations are used to record the

emission spectrum.

E = En2 En1 = 13.6 z2

2 2

1 2

1 1

n n

eV/atom

This equation was also used by Rydberg to calculate the wave number of a particular line

in the spectrum.

2 1

2 2

1 2

1 1 1Rz m

n n

Where R = 1.1107 m

1 (Rydberg constant)

13. The ratio of wavelength of first line to that of second line of paschen series of Hatom is

(A) 256: 175 (B) 175 : 256 (C) 15:16 (D) 16:15

14. Calculate the energy emitted when electrons of 1 g atom of hydrogen undergo transition

giving the spectral line of lowest energy in visible region of its atomic spectra

(A) 18.3104 J (B) 9010

3 J (C) 6010

4 J (D) 37.310

4 J



Multiple Correct Answers Type

This section contains 6 multiple correct answer(s) type questions. Each question has 4

choices (A), (B), (C) and (D),

15. Which of the following properties of compounds is correctly matched?

(A) Hydration energy: Li+ > Na

+ > K

+ > Rb

+ > Cs

+

(B) Solubility in water: LiOH < NaOH < KOH < RbOH < CsOH

(C) Lattice energy: RbF < KF < NaF < LiF

(D) Stability: RbH < KH < NaH < LiH

16. Two vessel connected by a valve of negligible volume. One vessel (I) has 2.8 g of N2 at

temperature T1(K). The other vessel (II) is completely evacuated. The container (I) is

heated to T2(K) while vessel (II) is maintained at (T2/3) K. Volume of vessel (I) is half that

of vessel (II). If the valve is opened then what is the weight ratio of N2 in both vessel

(WI/WII)

(A) 1:2 (B) 1:3 (C) 1:6 (D) 3:1

17. The outermost electronic configuration of atom(X) is 4s24p

2. Choose correct statements

regarding the atom.

(A) It is paramagnetic in nature

(B) It contains 10 electrons having azimuthal quantum no. (l) = 2

(C) It forms four covalent bonds in first excited state.

(D) Number of electrons present in the s-orbitals of the atom is higher than that present

in its p-orbitals.

18. In which of the following molecules / ions, the central atom is sp2 hybridized?

(A) NH2 (B) BF3 (C) NO2

(D) H2O

19. For the above graph, drawn for two different

samples of gases at two different

temperatures, 1 2T andT . Which of the

following statement is necessarily true?

(A) If 2 1T >T , BM is necessarily greater than AM

(B) If 1 2T >T , AM is necessarily greater than

BM

(C) 2 1

B A

T T>

M M

(D) Nothing can be predicted

1Gas A T 2TBGas

v

Fra

ctio

n o

f m

ole

cu

les

20. Pick out the isoelectronic structures from the following;

I. CH3, II. H3O

+, III. NH3, IV CH3

+

(A) I and II (B) III and IV (C) I,II and III (D) II and IV



PPPAAARRRTTT ––– IIIIIIIII ::: MMMAAATTTHHHEEEMMMAAATTTIIICCCSSS

SECTION – A




1. The line (p + 2q)x + (p 3q)y = pq for different values of p and q passes through the

point

(A) 3 5

,2 2

(B) 2 2

,5 5

(C) 3 3

,5 5

(D) 2 3

,5 5

2. The number of real solutions of the equation 22 | x | 5 | x | 2 0 is

(A) 0 (B) 2 (C) 4 (D) infinite

3. The number of positive integral solutions of 2 3 4

5 6

x (3x 4) (x 2)0

(x 5) (2x 7)

is

(A) 4 (B) 3 (C) 2 (D) 1

4. 4 4log 3 log X2x 3 27 , then x is equal to

(A) 2 (B) 4 (C) 8 (D) 16

5.

14 4

5

(x x)dx

x

is equal to

(A)

5

4

3

4 11 C

15 x

(B)

5

4

3

4 11 C

5 x

(C)

5

4

3

4 11 C

15 x

(D) none of these

6. The negation of the proposition “if 2 is prime then 3 is odd” is

(A) if 2 is not prime, then 3 is not odd (B) 2 is prime and 3 is not odd

(C) 2 is not prime and 3 is odd (D) if 2 is not prime, then 3 is odd



7. 2 2n

(1 2 3 4 5 6 .... 2n)lim

n 1 4n 1

(A) 1 (B) 1 (C) 1

3

(D)

1

3

8. If y xx .y 16 , then dy

dx at (2, 2) is

(A) 1 (B) 0 (C) 1 (D) none of these

(Paragraph Type)



ONE is correct.

P a r a g r a p h f o r Q u e s t i o n N o s . 9 t o 1 0

The equation of the straight line passing through (x1, y1) and making an angle with the positive

direction of x-axis is 1 1x x y y

r,cos sin

where r is the directed distance between the points (x, y)

and (x1, y1).

9. The angle made with x-axis of a straight line drawn through (2, 3) so that it intersects the

line x+y7=0 at a distance 2 from (2, 3) is

(A) 4

(B)

3

4

(C)

6

(D)

3

10. Which of the following points lie at a distance of 4 units from the point P(2,3) on the line

through P whose inclination with negative direction of x-axis is 30°?

(A) 2 2 3,1 (B) 2 2 3,0 (C) 2 2 3,0 (D) 2 3,1



P a r a g r a p h f o r Q u e s t i o n N o s . 1 1 t o 1 2

A(3,7) and B(6,5) are two points, C:x2+y

24x6y3=0 is a circle

11. The chords in which the circle C cuts the members of the family S of circles through A

and B are concurrent at

(A) (2, 3) (B) 23

2,3

(C) 23

3 2,2

(D) (3,2)

12. Equation of the member of the family S which bisects the circumference of C is

(A) 2 2x y 5x 1 0 (B) 2 2x y 5x 6y 1 0

(C) 2 2x y 5x 6y 1 0 (D) 2 2x y 5x 6y 1 0

P a r a g r a p h f o r Q u e s t i o n N o s . 1 3 t o 1 4

2 2

2 2

1x cosec ,y sec ,z

1 sin cos

13. 2 2

1 1

x y is equal to

(A) 2 z

z

(B)

2 z

z

(C)

z

2 z (D)

z

2 z

14. xyz is equal to

(A) x+y+z (B) xyz (C) x+yz (D) x y

z




This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C)

and (D) out of which ONE or MORE may be correct.

15. The value of „c‟ for which the lines joining the origin to the points of intersection of the

line y 3x c and the curve x2+y

2=2 are perpendicular to each other

(A) 1 (B) 0 (C) 2 (D) 2

16. If the area of the quadrilateral formed by the tangents from the origin to the circle

x2+y

2+6x10y+c=0 and the radii corresponding to the points of contact is 15, then value

of c is

(A) 9 (B) 4 (C) 5 (D) 25

17. p p p p

p p

n times

log log ..... p ,p 0

and p 1, is equal to

(A) n (B) n (C) 1

n (D) n

1

p

log (p )

18. Let y = x8 + e

x then

(A) y10 = y12 (B) y10 = y11 (C) y11 = y14 (D) none of these

19. If a 5cos 3cos 5 b3

, then

(A) a=2 (B) a=2 (C) b=12 (D) b=7

20. xlna xe .e dx is equal to

(A) x

ae (B)

x

ae

ln(ae) (C)

x

ae

1 lna (D) none of these



FIITJEE COMMON TEST


PHASE TEST-I (PAPER2)

ANSWER KEY


SECTION-A

1. C

2. B

3. B

4. A

5. C

6. A

7. B

8. A

9. B

10. A

11. A

12. D

13. D

14. C 15. A, C, D

16. B, D

17. B

18. A, C

19. B, D 20. B, C

SECTION-A 1. D

2. B

3. C

4. B

5. B

6. C

7. D

8. D

9. A

10. B

11. D

12. B

13. A

14. A 15. A,B,C,D 16. C

17. A,B,C

18. B,C

19. B,C

20. C

SECTION-A

1. D

2. C

3. B

4. D

5. A

6. B

7. C

8. A

9. A

10. A

11. B

12. C

13. B

14. A

15. C, D

16. A,D

17. B,D

18. A,B,C

19. A,C

20. B,C

Paper Code

SET-A


HINT & SOLUTIONS



1. C

Mass will slip when 1 1tan 30

3

For equilibrium of mass as shown N mgcos Fsin &

F cos = f + mg sin

sin cos

F mgcos sin

3mg.

mg f

F

N

2. B

2V

h2g

2

2

p

VV 2gh

2

and

2

2

Q

VV 2gh

3

Q P

5hh h .

36

3. B

S = Area under vt curve

= 2 + 2

= 4

2 4

v (m/s)

t (sec)

2

4. A

W K.

5. C

extW U

5 2 3 .

6. A

m

2(+x) kx

2m x kx

2

2

mx

K m

7. B

v A x

dx

a xdt

dx

adtx


2x t

8. A

Velocity at horizontal position 6 g

So, Tension 2mv

6mg

(Paragraph Type)

9. B

21

H U.28 .10. 282

21

H U.7 .10. 72

Solving H = 980 m, U = 105 m/s.

21k mv 11025J.

2

10. A

2

max

UU mg H 30625J.

2g

11. A

From energy conservation 2 2

0

1 1mv mgx kx 0

2 2

and 0

mg mx , v g .

k k

Pull force on the ceiling is kx

min

mgKx

2

12. D

2

0

1 m m 1k mg mv

2 k k 2

21 m mg

k mg.2 2k 2k

2 2 2

2

0

1 (mg) (mg) (mg)mv

2 2k 8k 2k

0

g mV .

2 k

x=0

kx=mg

v0

u=0 2k mg/

mg

K

13. D

For 30 kg block

210 – kx = 30a

2210 90a 4 m / s

30

14. C

For 15 kg block

Kx = ma = 15 × 6

90

x 0.9m100



15. A, C, D

16. B, D

4

2

25t 50V dt

10

17. B

2

r r r

1S U t a t

2

18. A, B

19. B, D

Acceleration of M, F

aM

21 F.t

2 M

2M

tF

.

20. B, C

12 10

2usin 2T 1sg 10

.

30º 30º

30º

30º


PPPAAARRRTTT ––– IIIIII ::: CCCHHHEEEMMMIIISSSTTTRRRYYY

SECTIONA

1. D

MnO4

H 2Mn (‗n‘ factor =5)

Eq. of An+

= eq. of MnO4

2. B

For n+l = 6, orbital will be 5p, 4d, 6s

m= 1 will exist in 5p & 4d only

3. C

In ideal conditions gases will have same momentum

4. B

I.E2 of Na is greater than I.E2 of Mg because Na+ has stable configuration

5. B

Lattice energy 1

size of cation

6. C

From curve, no. of radial nodes = 3

Therefore nl1=3

n = 5

7. D

Eq. of unused HCl = Eq. of NaOH

Eq. of HCl react with carbonate = eq. of total HCl eq. of unused HCl

Eq. of HCl react with carbonate = eq. of metal carbonate

8. D

(eq) of H2SO4 = (eq) of NaOH

w 27.7 0.8

2 1.085 g98 1000

1 g oleum gives 1.085 g H2SO4

100 g oleum gives 108.5 g H2SO4

Therefore % labelling of oleum is 108.5

SO3 + H2O H2SO4

3 2SO H On n

x 8.5

80 18

X=38.15

% of SO3 is 38.15 %

9. A

A = (NH4)2C2O4; B=NH3; C=CaC2O4

10. B

A = (NH4)2C2O4; B=NH3; C=CaC2O4

11. D

Electronegativity difference between N and F is less than N and H

12. B

% ionic character = experimental value of dipole moment

100theoretical value of dipole moment


13. A

For first line put n1=3, n2=4 and for second line n1=3, n2=5

14. A

Put n1= 2, n2= 3 in equation of E

15. A,B,C,D

A = Li+ being smallest in size shows maximum hydration

B = Solubility increases from LiOH to CsOH due to increased ionic character (Fajan‟s

rule)

C = Lattice energy 1

size of cation

D = Li+ will attract H

more strongly because size of Li

+ is smaller

16. C Let ‗x‘ no. of moles transferred from 1

st to 2

nd container

2

st

2

xRTP(2v) II container

3

P(v) (0.1 x)RT I container

On solving I

II

W 1

W 6

17. A,B,C

X has 2 unpaired electron in 4p and in first excited state, 4s(e) will jump to 4p then there

will be four unpaired electron which can form four covalent bond

18. B,C

Using VSEPR theory and hybridization concepts

19. B,C

Most probable velocities of A & B are

1A

A

2B

B

2RTV

M

2RTV

M

20. C

Isoelectronic species are species which have same no. of electrons.


SECTION A

1. D

2. C

3. B

4. D

5. A

6. B

7. C

8. A

9. A

10. A

11. B


12. C

13. B

14. A

15. C, D

16. A,D

17. B,D

18. A,B,C

19. A,C

20. B,C


FIITJEE - JEE (MAINS)

PHASE- 2



Maximum Marks: 360

Do not open this Test Booklet until you are asked to do so.



1. Immediately fill in the particulars on this page of the Test Booklet with Blue / Black Ball Point Pen. Use of pencil is

strictly prohibited.

2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer

Sheet and fill in the particulars carefully.



5. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having 30

questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response.

6. Candidates will be awarded marks as stated above in instruction No.5 for correct response of each question. ¼ (one

fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will

be made if no response is indicated for an item in the answer sheet.



8. Use Blue / Black Ball Point Pen only for writing particulars / marking responses on Side-1 and Side-2 of the Answer

Sheet. Use of pencil is strictly prohibited.

9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any

electronic device, etc. except the Admit Card inside the examination hall / room.




Name of the Candidate (in Capital Letters) :_____________________________________


Batch :________________________ Date of Examination : ________________________


Section – I (Physics)

PART – A

1. From a uniform circular plate of radius R, a small circular plate of radius R/4 is cut off as shown. If O is the center of the complete plate, then the x-coordinate of the new center of mass of the remaining plate will be:

(A) – R/20 (B) – R/16 (C) – R/15 (D) – 4

3 R

Y

O

X

2. The ratio of excess pressure in two soap bubbles is 3 : 1. The ratio of their volumes will be:

(A) 3

1 (B)

9

1 (C)

1

27 (D)

27

1

3. A mass M is supported by a massless string wound round a uniform cylinder of mass M and radius R. On releasing the mass from rest, it will fall with acceleration :

(A) g (B) g2

1 (C) g

3

1 (D) g

3

2

R M

M

4. A 3 kg ball strikes a heavy rigid wall with a speed of 10 m/s at an angle of 60° with the wall. It gets reflected with the same speed at 60° with the wall. If the ball is in contact with the wall for 0.2 s, the average force exerted on the ball by the wall is:

(A) 300 N (B) zero

(C) 150 3 N (D) 150 N

60°

60°

Wall

N

5. A wide vessel is filled with water of density 1 and kerosene of

density 2. The thickness of water layer is h1 and that of kerosene layer is h2. The gauge pressure at the bottom of the vessel will be:

(A) h11g (B) h22g

(C) h11g + h22g (D) h12g + h21g

h2

h1 Water

Kerosene

6. A ball hits a floor and rebounds after an inelastic collision. In this case:

(A) the momentum of the ball just after the collision is the same as that just before the collision

(B) the mechanical energy of the ball remains the same in the collision


(C) the total momentum of the ball and the earth is conserved

(D) the total energy of the ball and the earth is conserved

7. Two balls of masses m1 = 3 kg and m2 = 2 kg are moving towards each other with speeds u1 and u2. The ball m1 stops after collision and m2 starts moving with speed u1. The co-efficient of restitution for the balls is:

(A) zero (B) 1 (C) 3

2 (D)

2

1

8. A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity . Two objects, each of mass m, are attached gently to the opposite ends of a diameter

of the ring. The ring rotates now with an angular velocity:

(A) mM

M

(B)

mM

mM

2

)2(

(C)

mM

M

2

(D)

M

mM )(

9. An isolated particle of mass m is moving in horizontal plane (x-y), along the x-axis, at a certain height above ground. It suddenly explodes into two fragments of masses m/4 and 3m/4. An instant later, the smaller fragment is at y = +15cm. The larger fragment at this instant is at:

(A) y = –5 cm (B) y = -15 cm (C) y = +5 cm (D) y = +15 cm

10. A cylindrical vessel contains a liquid of density upto a height h. The liquid is closed by a piston of mass m and area of cross-section A. There is a small hole at the bottom of the vessel. The speed v with which the liquid comes out of the hole is: (neglect presence of atmosphere)

v

m, A

h

(A) gh2 (B)

A

mggh2 (C)

A

mggh2 (D)

A

mggh 2

11. The magnitude of the force (in N) acting on a body varies with

time t (in s) as shown. AB, BC and CD are straight line segments. The magnitude of the total impulse of the force on

the body from t = 4 s to t = 16 s is:

(A) 5 × 10–3 Ns (B) 5.8 × 10–3 Ns

(C) 5.8 × 103 Ns (D) 5 × 103 Ns

2 4 6 8 10 12 14 16

200

400

600

800

B

A

D

C

F

Fo

rce (

N)

Time (s)

12. Two equal drops of water each of radius r are falling through air with a steady velocity 8 cm/s. The two drops combine to form a big drop. The terminal velocity of big drop will be:

(A) 3

2

)2(8 cm/s (B) 3

2

)2(16 cm (C) 3

2

)2(4 cm/s (D) 32 cm/s


13. The height of water in a vessel is h. The vessel wall of width b is at

an angle to the vertical. The net force exerted by the water on the wall is:

(A) 21cos

3 bh g (B) gbh 2

(C) 21sec

2 bh g (D) zero

h

B

A

14. The acceleration of centre of mass of the system shown in figure will be:

(A) 10 m/s2 (B) 3

10 m/s2

(C) 3

5m/s2 (D) –5 m/s2

5kg

40kg

15. A block Q of mass M is placed on a horizontal frictionless surface AB and a body P of mass m is released on its frictionless slope.

As P slides by a length L on this slope of inclination , the block Q would slide by a distance:

C

A B

Q

M P

(A) cosLM

m (B) L

mM

m

(C)

cosmL

mM (D)

Mm

mL

cos

16. A disc is rolling without slipping with angular velocity . P and Q are two points equidistant from the centre C as shown. The order of magnitude of velocity is:

C

P

Q

(A) VQ > VC > VP (B) VP > VC > VQ

(C) VP > VC, VQ = VC / 2 (D) VP < VC > VQ

17. Moment of inertia of a ring about a diameters is I0. The moment of inertia of the ring about a

tangent perpendicular to the plane of the ring will be: (A) I0 (B) 2I0 (C) 3I0 (D) 4I0


18. An equilateral triangle ABC has its centre at O as shown in figure. Three forces 10 N, 5N and F are acting along the sides AB, BC and AC. Magnitude of force F so that the net torque about ‗O‘ is zero, will be:

(A) 15 N (B) 5 N (C) 50 N (D) 2 N

O

A

B C 5N

F 10N

19. A disc is rotating with an angular velocity 0. A constant retarding torque is applied on it to

stop the disc. Its angular velocity becomes 0/2 after n rotations. How many more rotations will it make before coming to rest?

(A) n (B) 2n (C) 2

n (D)

3

n

20. When a sphere rolls without slipping, the ratio of its kinetic energy of translation to its total

kinetic energy is: (A) 1 : 7 (B) 1 : 2 (C) 1 : 1 (D) 5 : 7

21. One end of a glass U-tube contains oil and the other end contains water as shown. The INCORRECT statement is:

(A) the oil is less dense than water

(B) the pressure at D and E is same

(C) the pressure at B and C is same

(D) the pressure due to column AB of the oil is the same as

that due to column EC of water

E

C B

D

A

Water

Oil

22. An inclined plane makes an angle of 30° with the horizontal. A solid cylinder rolling down this

inclined plane from rest without slipping has a linear acceleration equal to:

(A) 3

g (B)

7

5g (C)

3

2g (D)

14

5g

23. Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line one after another. The velocity of flow of water in the pipe of 2 cm diameter is:

(A) 4 times that in the other pipe (B) 4

1 times that in the other pipe

(C) 2 times that in the other pipe (D) 2

1 times that in the other pipe

24. A concentric hole of radius R/2 is cut from a thin circular plate of mass M and radius R. The

moment of inertia of the remaining plate about its axis will be:

(A) 2

24

13MR (B)

2

24

11MR (C)

2

32

13MR (D)

2

32

15MR


25. A liquid film is formed over a frame ABCD as shown in figure. Wire CD (massless) can slide without friction. The mass to be hung from CD to keep it in equilibrium is: (Surface tension of liquid is T)

(A) Tl

g (B)

g

Tl2

(C) 2

3

Tl

g (D)

2

Tl

g

A B

D C Liquid

Film X Y

l

26. A raft of wood (density 600 kg/m3) of mass 120 kg floats in water. How much weight can be put on the raft to make it just sink?

(A) 120 kg (B) 200 kg (C) 40 kg (D) 80 kg

27. The angular velocity of a wheel increases from 1200 rpm to 4500 rpm in 10 s. The number of revolutions made during this time is

(A) 950 (B) 475 (C) 237.5 (D) 118.75

28. A T shaped object, having uniform linear mass density, with

dimensions shown in the figure is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only translational motion without rotation. The distance of P with respect to C is:

(A) 3

4l (B) l (C)

3

2l (D)

2

3l

l

P

C

F

B A

2l

29. Four particles each of mass m are placed at the corners of a square of side length l. The

radius of gyration of the system about an axis perpendicular to the square and passing through centre is

(A) 2

l (B)

2

l (C) l (D) l)2(

30. A particle of mass m moving eastward with a speed v collides with another particle of same mass moving northward with same speed v. The two particles coalesce on collision. The new particle of mass 2m will move in the north-east direction with a velocity of

(A) v 2 (B) v

2 (C)

v

2 (D) v


CHEMISTRY Part-B

1. For the following equilibrium

NH4HS(s) NH3(g) + H2S(g) ; partial pressure of NH3 will increase

(A) If NH3 is added after equilibrium is established

(B) if H2S is added after equilibrium is established

(C) NH4HS is added into the container

(D) volume of the flask is decreased

2. To 100 mL of 0.1 M AgNO3 solution solid K2SO4 is added. The concentration of K2SO4 that

shows the precipitation is? [KSP for Ag2SO4 = 6.4 10-5

M]

(A) 0.1 M (B) 6.4 10-3

M

(C) 5.4 10-7

M (D) 6.4 10-5

M

3. If heat of neutralization is – 13.7 K.cal and H0

f OH2= – 68.0 Kcal, then enthalpy of formation of

OH- would be

(A) 54.3 kcal (B) – 54.3 kcal

(C) 71.3 kcal (D) – 71.3 kcal

4. The half time of first order decomposition of nitramide is 2.1 hour at 15°C.

NH2NO2(aq.) N2O(g) + H2O(l)

If 6.2 g of NH2NO2 is allowed to decompose, calculate the time in hrs taken for

NH2NO2 to decompose 99%.

(A)10 (B) 21 (C) 4.2 (D)14

For Q 5 - Q6 consider the following data from the reaction between A and B.

Initial rate mol litre–1

sec–1

[A]

mol litre–1

[B]

mol litre–1

300 K 320 K

2.5 × 10–4

5.0 × 10–4

1.0 × 10–3

3.0 × 10–5

6.0 × 10–5

6.0 × 10–5

5.0 × 10–4

4.0 × 10–3

1.6 × 10–2

2.0 × 10–3

-

-

5. The order of reaction with respect to A and with respect to B, respectively -

(A) 2,1 (B) 3,0 (C)2,0 (D) 2,3

6. Select the correct statement

(A) The rate constant at 300 K is 2.6 x 10-6

(B) from the data, it can be concluded that the reaction is endothermic.


(C) The rate of reaction decreases with increase in temperature

(D) The value of pre – exponential factor for the reaction is independent of

temperature

7. Boron nitride on reacting with caustic alkali gives :

(A) NH3 (B) N

2O (C) Na

2BO

2 (D) NO

2

8. Degree of ionisation of 1 M HCOOH is decreased to a maximum extent in presence of :

(A) 1 M HCHO (B) 1 M NaOH (C) 1 M HCOONa (D) equally in all

9. We have acidic buffer of CH3COONa and CH3COOH. One or more of the following

operations will not change pH :

I : diluting the mixture ten times II : adding some HCl

III : adding some NaOH

IV : adding equal moles of CH3COONa and CH3COOH into the buffer

Select correct alternate(s) :

(A) I, III, IV (B) II, III (C) I, II,III (D) I,II,III, IV

10. The rate of a reaction is expressed in different ways as follows :

dt

]B[d

dt

]A[d

4

1

dt

]D[d

3

1

dt

]C[d

2

1

The reaction is:

(A) 4 A + B 2C + 3D (B) B + 3 D 4 A + 2 C

(C) A + B C + D (D) B + D A + C

11. ∆Hvap = 30 kJ/mole and ∆Svap = 75 J mol–1 K–1. Find temperature of vapour, at

one atmosphere.

(A) 400 K (B) 350 K (C) 298 K (D) 250 K

12. For the simultaneous equilibria,

2 12C s O g 2CO g ,Kc

2 2 22CO g O 2CO g ,Kc

Initially 2 and 4 moles of carbon and oxygen respectively are taken in a one litre vessel at

40°C. Calculate the value of 2Kc if the equilibrium moles of oxygen and 2CO are 2.9 and 0.6

respectively.

(A) 0.07 (B) 0.39

(C) 0.12 (D) 0.09

13. Which one of the oxides is neutral?


A) CO B) 2SnO C) ZnO D) 2SiO

14. KSP of CuS, Ag2S and HgS are 10-31

, 10-44

and 10-54

respectively. Select the correct order for

their solubility in water

(A) Ag2S > HgS > CuS (B) HgS > CuS > Ag2S

(C) HgS > Ag2S > CuS (D) Ag2S > CuS > HgS

15. In thermodynamics, a process is called reversible when :

(A) surroundings and system change into each other

(B) there is no boundary between system and surroundings

(C) the surroundings are always in equilibrium with the system

(D) the system changes into the surroundings spontaneously

16. A following mechanism has been proposed for reaction

2A + B D + E

A + B C + D ( slow)

A + C E ( fast)

The rate law expression for the reaction is

(A) r = K[A]2[B] (B) r = K[A][B]

(C) r = K [A]2 (D) r = [A][C]

17. At 298 K, the standard enthalpies of formation of C6H

5COOH(s), CO

2 (g) &

H2O (l) are ; - 400 , - 390 & -280 KJ mol -1 respectively . Calculate the heat of

combustion of benzoic acid at constant pressure in KJ/mole [ R = 8.3 Jmol–1K–1

]

(A)-2130 (B)-5437 (C)-2780 (D)- 3170

18. 50 g of iron is dissolved in HCl at 298 K in a beaker under atmospheric pressure forming FeCl3

, the work done is (at wt Fe = 56)

(A) – 2212.39 J (B) -3318.17 J

(C) – 560.40 J (D) zero

19. 5 moles of 2SO and 5 moles of 2O are allowed to react to form 3SO in a closed vessel. At the

equilibrium stage 60% of 2SO is used up. The total number of moles of 2 2SO ,O and 3SO in

the vessel at equilibrium is

(A) 10.0 (B) 8.5

(C) 10.5 (D) 3.9

20. The correct lewis acid order for boron halides is :

(A) BF3

> BCl3 > BBr

3 > BI

3 (B) BCl

3 > BF

3 > BBr

3 > BI

3


(C) BI

3 > BBr

3 > BCl

3 > BF

3 (D) BBr

3 > BCl

3 > BI

3 > BF

3

21. Which buffer solution has maximum pH ?

(A) mixture which is 0.1 M in CH3COOH and 0.1 M in CH3COONa [pKa (CH3COOH) =

4.74]

(B) mixture which is 0.2 M CH3COOH and 0.2 M in CH3COONa

(C) mixture which is 0.1 M in NH4Cl and 0.1 M in NH4OH [pKa (NH4+) = 9.26]

(D) all the solution have equal pH which is 4.74

22. If enthalpies of formation for C2H4 (g), CO2 (g) and H2O (l) at 25

0C and 1 atm pressure be 52,

– 394 and – 286 kJ mol-1

respectively, enthalpy of combusion of C2H4 (g) will be

(A) + 141.2 kJ mol-1

(B) + 1412 kJ mol-1

(C) – 141.2 kJ mol-1

(D) – 1412 kJ mol-1

23. For the reversible reaction N2(g) + 3H2(g) 2NH3(g) at 500º , the value of Kp is

1.44 × 10–5 when partial pressure is measured in atmospheres. The corresponding value of

KC, with concentration in mole litre–1, is

(A) 2

5

)500082.0(

1044.1

(B) 2

5

)773314.8(

1044.1

(C) 2

5

)773082.0(

1044.1

(D) 2

5

)773082.0(

1044.1

24. The CaCO3 is heated in a closed vessel of volume 1 litre at 600 K to form CaO and CO2. The

minimum weight of required to establish the equilibrium 3(s) (s) 2(g)CaCO CaO CO is

Kp = 4.9atm)

At wt of Ca = 40

(A) 2g (B) 4.57 g (C) 10g (D) 100 g.

25. One litre of water contains 10-7

mole of H+ ions. Degree of ionization of water is

(A) 1.8 10-7

% (B) 0.8 10-9

%

(C) 3.6 10-9

% (D) 3.6 10-7

%


26. Lead shows oxidation state

A) +3, +4 B) +1, +2 C) +2, +4 D) +4

27. 2 mol of an ideal gas expanded isothermally & reversible from 1 litre to 10 litres

at 300 K. What is the enthalpy change

(A) 4.98 kJ (B) 11.47 kJ (C) –11.47 kJ (D) 0 kJ

For Q 28 – Q29

Suppose 50 bacteria are placed in a flask containing nutrients for the bacteria so that they can multiply.

A study at 35°C gives the following results

Time (minutes) 0 15 30 45 60

Number of bacteria 100 200 400 800 1600

Answer Questions 28 - 29 following the above data

28. This multiplication of bacteria follows a

(A) zero order reaction (B) first order reaction

(C) second order reaction (D) third order reaction

29. The rate constant of the reaction is

(A) 0.0462 min1

(B) 0.462 min1

(C) 4.62 min1

(D) 46.2 min1

30. The equilibrium constant for the reaction

HONO(aq) + CN– (aq) HCN(aq) + ONO– (aq) is 1.1 × 10+6. From the magnitude of

this Keq one can conclude that

(A) CN– is stronger base than ONO– (B) HCN is a stronger acid than HONO

(C) The conjugate base of HONO is ONO– (D) The conjugate acid of CN– is HCN


MATHEMATICS PART-C

1. If n n 1 2 1x x ......... x x 1 , then the value of .....x1

n 1

1 2 3 n

xx x x x nlog log log .........log x

(A) 1 (B) 0 (C) 2 (D) none of these 2. If cosxlog sinx 2 , then sin x lies in the interval

(A) 5 1

,12

(B) 5 1

0,2

(C) 1

0,2

(D) none of these

3. If |z + 1| = z + 1, where z is a complex number, then the locus of z is

(A) a straight line (B) a ray (B) a circle (D) an arc of a circle

4. If the roots of the equation 24 2 0 are of the form k

k 1 and

k 1

k 2

then the value of

is

(A) 2k (B) 7 (C) 2 (D) k+1 5. The length of the chord of the parabola x2 = 4y passing through the vertex and having slope

cot is

(A) 4 cos . cosec2 (B) 4 tan sec

(C) 4 sin. sec2 (D) none of these

6. If the normals at the end points of a variable chord PQ of the parabola y2 – 4y – 2x = 0 are

perpendicular, then the tangents at P and Q will intersect at (A) x + y = 3 (B) 3x – 7 = 0 (C) y + 3 = 0 (D) 2x + 5 = 0

7. The point P on the parabola y2 = 4ax for which |PR – PQ| is maximum, where R (– a, 0),

Q (0, a), is (A) (a, 2a) (B) ( a, -2a) (C) (4a, 4a) (D) (4a, -4a) 8. If tangents at A and B on the parabola y2 = 4ax intersect at the point C, then ordinates of

A, C and B are (A) always in A.P. (B) always in G.P. (C) always in H.P. (D) none of these

9. If z 25i 15 , then find the least positive value of arg z is

(A) 1 4tan

3

(B) 1 3tan

4

(C) 1 5tan

12

(D) 1 12tan

5

10. if |z – i| 2 and z0 = 5 + 3i then the maximum value of |iz + z0| is

(A) 2 + 31 (B) 7


(C) 31 - 2 (D) None

11. sin-11

(z 1)i

, where z is a non real, can be the angle of a triangle if

(A) Re(Z) =1 , Im(Z) = 2 (B) Re(Z) =1 , -1 Im(Z) 1 (C) Re(Z) + Im (Z) = 0 (D) None of these

12. If z1 and z2 are two complex numbers satisfying the equation 1zz

zz

21

21

, then

2

1

z

z is a

number which is (A) Positive real (B) Negative real

(C) Zero or purely imaginary (D) None of these 13. If w is a complex cube root of unity and (a + bw + cw2)3 + (a + bw2 + cw)3 = 0, then b, a, c are

in (A)A.P. (B)G.P. (C)H.P. (D) None of these

14. Number of distinct solution for equation 2 2 2

x x 2 x 3 0 , if is a real no. is


15. If the numbers a, b, c, d, e form an A.P. then the value of a 4b + 6c 4d + e is (A) 1 (B) 2 (C) 0 (D) none of these 16. If a, b, c are positive real numbers then the number of real roots of the equation

2ax b | x | c 0 is (|x| is always positive)


17. If a b2 3 43 and a 3 a 12 3 47, then the respectively value of ‗a‘ and ‗b‘ are

(A) 3, 4 (B) 4, 3 (C) 16, 27 (D) 8, 9

18. The number of solutions of the equation 02xlogx2xlog2

1 2 is

(A) 2 (B) 0 (C) 1 (D) 3

19. If both the roots of 2 0x ax a are greater then 2, then

(A) , 4a (B) 0,2a

(C) 4,a (D) none of these

20. Let a,b,c are positive real numbers forming an A.P. If 2 0ax bx c has real roots then

(A) 2 3a c

c a (B) 2 3

a c

c a

(C) 2 3a c

c a (D) 2 3

a c

c a

21. If 1 2 3tan , tan , tan are the real roots of 3 21 0x a x b a x b , where

1 2 3 1 2 30, then is equal to

(A)2

(B)

4


(C) 3

4

(D)

22. Total number of real values of x such that

1/ 7 1/ 7

1/ 712 12 64

12 3

x xx

x

, is equal to

(A)one (B)two (C) zero (D) none of these

23. If a,b,c are odd integers and 2 0ax bx c has real roots then

(A)both roots are rational (B) both roots are irrational (C) both roots are positive (D)roots are of opposite signs

24. Total number of integral values of a such that 2 1 0x ax a has integral roots, is

equal to (A) one (B) two (C) three (D) four

25. If both roots of 2 2 0x ax belong to the interval (0,3) then exhaustive range of ‗a‘ is

(A)(-6,0) (B)11

, 2 23

(C) 11

,03

(D) none of these

26. If two roots of 3 2 0x ax bx c are equal in magnitude but opposite in signs then

(A)a+bc=0 (B)a2=bc (C) ab=c (D)a-b+c=0

27.

x b x cf x

x a

, where a,b,c are distinct real numbers will assume all real values

provided (A)c lies between a and b (B) a lies between b and c (C) b lies between a and c (D) none of these

28. The complete set of values of x satisfying 2log 1 0x x is

(A) 1, (B) 1, 2

(C) 2,

(D) none of these

29. If 2 0ax bx c and

2 0bx cx a have a common root and a,b,c are non zero real

numbers then

3 3 3a b c

abc

is equal to

(A)1 (B)2 (C)3 (D) none of these

30. If tan and sec are the roots of the equation 2 0ax bx c , then

(A) 4 2 22a b ac b (B) 4 2 22b a ac a


(C) 4 2 24a b ac b (D) 4 2 24b a ac a

PHYSICS MAINS ANS

PHYSICS ANSWER KEY

1 A 2 D 3 D

4 C 5 C 6 C

7 C 8 C 9 A

10 B 11 A 12 A

13 C 14 B 15 D

16 B 17 D 18 A

19 D 20 D 21 B

22 A 23 A 24 D

25 B 26 D 27 B

28 A 29 A 30 B

ANSWER CHEMISTRY

1 A 2 B 3 B

4 D 5 A 6 D

7 A 8 C 9 C

10 B 11 A 12 C

13 A 14 D 15 C

16 B 17 D 18 B

19 B 20 C 21 D

22 D 23 D 24 C

25 A 26 C 27 C

28 B 29 A 30 A

ANSWER MATH JEE MAINS 1 A 2 B 3 B

4 B 5 A 6 D

7 A 8 A 9 A

10 B 11 B 12 C

13 A 14 B 15 C

16 C 17 B 18 A

19 D 20 A 21 B

22 A 23 B 24 B

25 B 26 C 27 B


28 B 29 C 30 C

PHYSICS SOLUTION

1. Xcm =

22

22

R 3RR (0)

16 4

RR

16

= –20

R

(A)

2. (D)

3. 21 1TR MR T Ma ......... 1

2 2

Mg T Ma .............. 2

From (1) and (2); 2

a g3

(D)

4. avg

2mv sin 2 3 10sin60F 150 3 N

t 0.2

(C)

5. (C) 6. In an inelastic collision only momentum of the system remains conserved. Some energy may be

lost in the form of deformation, heat, sound etc.

(C)

7. By conservation of linear momentum 22112211 vmvmumum

121 2023 uuu , 2

12

uu ,

2

0

11

1

21

12

uu

u

uu

vve

=

3

2

(C)

8. ')2( 222 MRmRMR , mM

M

2'

(C)

9. Before explosion, particle was moving along x-axis, i.e., it has no y-component of velocity.

Therefore, the centre of mass will not move in y-direction or we can say .0com y

Now, 21

2211com

mm

ymymy

)4/34/(

))(4/3()15)(4/(0

mm

ymm

or cm5y

(A) 10. Applying Bernoulli‘s theorem at 1 and 2

2

2

1v

A

mggh

A

mgghv 2

(B)

v

m, A

h 1 2

11.

interval specified under the

graph time-force of Area Impulse

66 1010800

2

1102)200800(

2

1 = 5 × 10–3 N-s


(A)

12. 33

3

4

3

4rnR ; rnR 3/1 ;

3/2

2

1

2 nr

R

V

V

(A)

13. Average pressure on the wall 2

gh ,

cos

hAB

Therefore area of the wall = bh

cos

Net force exerted by the water on the wall

sec

2

1

cos2

2 gbhbhgh

PA

(C)

h

B

A

PA

14. By constraint relation, if aa 40 , then aa 25

aTg 40240 …(i) and )2(55 agT …(ii)

From (i) and (ii) a 5 m/s2 and 3

10

540

)10(5)5(40cm

a m/s2

(B)

15. Here, the x co-ordinate of centre of mass of the system remains unchanged when the mass m

moved a distance cosL , let the mass )( Mm moves a distance x in the backward

direction.

0cos)( mLxmM Mm

mLx

cos

(D)

16. OP > OC > OQ ; VP > VC > VQ

(B)

C

P

Q O

17. 2 2cm0 dia tangent cm 0

I1I I MR , I I MR 4I

2 2

(D)

18. Fd – 10d – 5d = 0; F = 15 N

(A)

19. Since 22

0

2 where = 2n

n

2

22

2

02

0

and )2)(2(2

0

22

0

n

3

nn

(D)

20.

2

22

2

1

1

2

1

2

12

1

MR

IImv

mv

K

KT

7

5

5

21

1

K

KT

(D)

21. CB pp )()( ECgABg woil


AB > EC ; woil

(B)

22.

2

gsin gsin30a

I 11 1

2MR

= 1

g3

(A)

23. AV = Constant 2

1

2

2

1

2

2

1

d

d

A

A

V

V 4

2

42

2

2

1 V

V

(A)

24. Mass of hole 44

)(2

2

MR

R

MM

Moment of inertial of remaining plate

2

2

2

32

15

22

1

2

1MR

RMMR

(D)

R/2

R

25. TlMg 2 g

TlM

2

(B)

26. Volume of raft = density

massV

3m5

1

600

120

Mass of 3

5

1m water = 1000

5

1200 kg

Extra weight which can be put on the raft = 200 – 120 = 80 kg

(D)

27. radian9501060

2

2

45001200

Number of Revolutions = 4752

950

(B)

28. For pure translational motion, the force F should act at centre of mass

3

4

3

)(2)2( l

m

lmlmYcm

(A)


29. 2mrI

24

2lm )2( 2lm

Radius of gyration 22

4 2

ml lk

m

(A)

m m

m m l

l C.M.

2/l

2/l

2/l

2/l

30. By momentum conservation, mv = 2mv cos (45°) v = v

2

(B)

Answer chemistry SOLUTION

1: A

2: (B)

Ag2SO4(s) 2Ag+

(aq) + SO42-

(aq)

[SO42-

] = = 6.4 x 10-3

3: (B) H+ (aq) + OH

-(aq) → H2O(l)

∆H = -13.7 = [-68] – [0 + ∆Hf OH- ]

∆Hf OH-+

= -54.3

4 : (D)

K = ; t = 14hrs

5 A

6: D ; from the data H cannot be predicted .

7: A

8: C , common ion effect

9: C

pH = pKa + log = pKa + log

pH‘ = pKa + log

so pH ≠pH‘ for most values of a .

10: B

11: A ; T =

12: (C) 2 12C s O g 2CO g ,Kc

Initial conc: 2 4 -

Eqm conc: - 4-x-y 2x-2y

2 2 22CO g O 2CO g ,Kc

Eqm conc: 2x-2y 4-x-y 2y


[CO2] = 0.6 = 2y

[O2] = 4-x-y = 2.9

Solving : y = 0.3 ; x = 0.8 ; Kc2 = =0.12

13 A

14: D

15: C

16: B

17: D

C6H

5COOH(s) + 15/2 O2 →7CO2(g) + 3 H2O(l)

∆H = [-7 x 390 + - 3 x 280 ] – (-400) = -3170

18: B

Fe + 3HCl → FeCl3 + 3/2H2

∆n H2 = 3/2 for each mole Fe ;

W = -P ∆V = - nRT = - x 3/2 x 8.314 x 298 = -3318.17 J

19: (B) 2SO2 + O2 2SO3

Initial conc 5/V 5/V 0

Eqm conc 5/V – x 5/v – x/2 x

X = 0.6 x 5/V = 3/V

[SO2] moles = 2

[O2] moles = 3.5

[SO3] moles = 3

Total moles = 8.5

20: C

21: D

22: (D) C2H4 (g) + 3O2(g) → 2CO2(g) +2 H2O(l)

∆H = [2x-394 + 2 x -286] – [52] = -1412

23: D

24: C

V x pCO2 = nRT ; n = 0.1 mole ; CaCO3 wt = 10 gm

25: A For H2O as weak acid , Cα = [H+] ; α = [H

+]/C = ) 1.8 10

-9

26: C

27: C; W = -nRT ln = - 11486J

∆H = ∆E + P∆V = - 11.48KJ

Sol: Q28. B

Q29. A

if we look at the data ,it seems every 15 min population doubles so order should be 1 .

Alternate way :

Assume order = 0

K =

K1 = (200 – 100)/15 = 6.66

K2 = (400-200)/15 = 13.33 ; hence not zero order


Assume first order ;

K =

K1 = = 0.046 min-1

K2 = = 0.046 min-1

K3 = = = 0.046 min-1

; hence order = 1

Rate constant = = 0.046 min-1

30: A

Conclusion should be drawn by value of Keq

Answer Solution MATH

1.A using log log log 1n

am n m and a

2.B sinx >0: cosx>0; 1cosx

2sin cosx x

2 5 1

sin sin 1 0 sin 0,2

x x x

3.B Let z=x+iy; y=0 and x-1

4.B 1 2

2 2 3

kk

k

1

2 74 4

5. (A) Let A Vertex, AP chord of x2 = 4y such that slope of AP is cot.

Let P ( 2t, t2)

Slope of AP = 2

t cot =

2

t t = 2cot

Now, AP = 42 tt4 = t 2t4 = 4cot cosec = 4cos . cosec2α

6. (D) Since normals at P and Q are perpendicular, the tangents at P and Q will also be

perpendicular but any two perpendicular tangents of a parabola always intersect on its directrix. The parabola is (y – 2)2 = 2( x +2). So its directrix is 2x + 5 = 0

7. (A) We know any side of the triangle is more than the difference of the remaining two sides so

that |PR – PQ| RQ

The required point P will be the point of intersection of the line RQ with parabola which is (a, 2a) as PQ is a tangent to the parabola.

8. (A) A (at12, 2at1)

B (at22, 2at2)

Tangents at A and B will intersect at the point C, whose coordinate is given by ( at1t2, a(t1+t2)) clearly ordinate of A , C and B are always in A.P.


9.A

O

20

C

A

25

Real axis

Im. axis

15

1 4

arg tan3

z

10.B

11.B Let =1 1

sinz

i

be the angle of a triangle. If z-1=iλ z=1+iλ

= 1sin Re 1; 1 Im 1then z z

12.C

2 2

1 11 2 1 2

2 2

1 1z z

z z z zz z

1 1

2 2

0z z

z z

13.A 2 2 0 2a b c a b c a b c

14.B

15.C 3 3 0a b b c c d e d

16.C 2

0a x b x c no real value of x

17. B

18. A

19 D (i) f(2)>0 a<4 (ii) a2-4a0 ,0 4,a

20.A 20 4 0D b ac

2

16 0a c ac

2 12 2 3a c a c

c a c a

21.B

1 1 2 1 2 3tan 1 ; tan tan ; tan .tan .tana b a b

1 2 3 1 2 3tan 14

22 A 23 B 24 B


25 B 11

0 3 0 13

f f a

0 , 2 2 2 2, 24

Da

a

and 6,0 3a

From (1),(2) and (3)

26 Let 2 2, , 1 2 3c

a ba

27 B

28 B 20; 1 0; 1 1 ........... 1x x x x

Now 2 21 1 2 0 2, 2 ........... 2x x x

From (1) and (2) 29 C

22 2 2

3 3 3 3

bc a ab c ac b

a b c abc

30 C Eliminating tan & sec




Maximum Marks: 210


You are not allowed to leave the Examination Hall before the end of t he test.

INSTRUCTIONS


E. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.






F. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR

sheet. 2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No.

and write in ink your Name, Test Centre and other details at the designated places. 3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Three Parts. (i) Section-A (01 – 10) contains 10 multiple choice questions which have only one correct answer. Each

question carries +3 marks for correct answer and – 1 mark for wrong answer. Section-A (11 – 15) contains 5 multiple choice questions which have one or more than one correct

answer. Each question carries +4 marks for correct answer. There is no negative marking. (ii) Section-C (01 – 05) contains 5 Numerical based questions with single digit integer as answer, ranging from

0 to 9 and each question carries +4 marks for correct answer. There is no negative marking.




BA

TC

HE

S –

Tw

o Y

ea

r C

RP

(1

31

5)-

Ad

va

nc

e (

B L

ot)

CPT1 - 1

CODE: SET-A

PAPER - 1





= 1.987 2 Cal K1 mol1



= 6.25 x 10-27 erg.s



1 amu = 1.66 x 10-27 kg

1 eV = 1.6 x 10-19 J


Au=79.


Mn=55, Pb=207, Au=197, Ag=108, F=19, H=2, Cl=35.5, Sn=118.6






This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

1. Which of the following is a unit vector

(A) ji (B) cos i - sin j (C) sin jcos2i (D) ji3

1

2. A force ˆ ˆ ˆF 5i 3j 2k N

is applied over a particle which displaces it from its origin to the

point ˆ ˆr 2i j m.

The work done (in J) on the particle is :

(A) + 13 (B) + 10 (C) + 7 (D) – 7

3. A uniform chain of length 2m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table ?

(A) 3.6 J (B) 7.2 J (C) 1200 J (D) 120 J

4. A projectile is thrown with velocity u at an angle above the horizontal. Find the average velocity during the time of ascent

(A) u cos (B) usin

2 (C) 2u

1 3cos2

(D) None of these

5. A block of mass m is attached with a spring in its natural length, of spring constant k. The other end A of spring is moved with a constant acceleration ‗a‘ away from the block as

mAa

shown in the figure. Find the maximum extension in the spring. Assume that initially block and spring is at rest w.r.t ground frame

(A) ma

k (B)

1 ma

2 k (C)

2ma

k (D)

4ma

k.

6. A balloon B is moving vertically upward and viewed by a

telescope T. At a particular angular position = 53° measured

parameters are r = 1 km, dr

3m / sdt

and d

0.02 rad / s.dt

The

magnitude of the linear velocity of the balloon at this instant is

(A) 1.2 m/s (B) 2.4 m/s

(C) 3.6 m/s (D) 4.8 m/s

= 53°

B

r

T



7. Width of a river is 60 m. A swimmer wants to

cross the river such that he reaches from A to B directly. Point B is 45 m ahead of line AC (perpendicular to river) Assume speed of river and speed of swimmer as equal. Swimmer must

try to swim at angle with line AC. Value of is A

BC

River Flow

(A) 37º (B) 53º (C) 30º (D) 16º

8. Find minimum value of the angle so that block of mass m does not move on rough surface, whatever may be the value of applied force F.

The coefficient of state friction between the block and surface is .

F m

() Rough Surface

(A) tan1() (B) 11tan ( )

2

(C) cot1() (D) 11cot ( )

2

9. At time t = 0, a bullet is fired vertically upwards with a speed of 98 ms1. At time t = 5 s (i.e., 5 seconds later) a second bullet is fired vertically upwards with the same speed. If the air resistance is neglected, which of the following statements will be true ?

(A) The two bullets will be at the same height above the ground at t = 12.5 s (B) The two bullets will reach back their starting points at the same time (C) The two bullets will have the same speed at t = 20 s (D) The two bullets will attain the different maximum height 10. Figure shows the changes in speed of a marble as it rolls down

an inclined plane P1, travels on a flat horizontal surface and then up another inclined plane P2. What can you say about the steepness of P1 and P2 from the information given in the figure ?

(A) P1 is steeper than P2 (B) P2 is steeper than P1 (C) P1 and P2 are equally steep (D) Nothing can be said about the relative steepness of P1 and P2

as the information given is insufficient

C

P2

BA20

0

10

ED

P1

20 50 100

Time (s)

Sp

eed

(m

s)

-1


This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.

11. A spring and block is placed on a fixed smooth wedge as shown. Following conclusion can be drawn about block.

(i) magnitude of its momentum will be max when Fnet on block is zero

(ii) its kinetic energy will be max when Fnet on block is zero (iii) KE of block is max when block just touches the spring. (iv) net force on block is maximum when KE = 0

m

Block

Spring

Fix Wedge

(A) (i) (B) (ii) (C) (iii) (D) (iv)



12. In the figure, if F = 4 N, m = 2kg, M = 4 kg then

(A) The acceleration of m w.r.t. ground is 22m / s

3

(B) The acceleration of m w.r.t. ground is 1.2 m/s2 (C) Acceleration of M is 0.4 m/s2

F

s=0.1=0m

M

k = 0.08

Ground

z

(D) Acceleration of m w.r.t. ground is 22m / s

3

13. A particle moves along positive branch of the curve x

y2

where 3t

x ,3

x and y are

measured in metres and t in seconds, then :

(A) The velocity of particle at t = 1 s is 1ˆ î j2

(B) The velocity of particle at t = 1 s is 1 ˆ î j2

(C) The acceleration of particle at t = 1 s is ˆ ˆ2i j

(D) The acceleration of particle at t = 2 s is ˆ î 2 j

14. Two blocks of masses m1 and m2 are connected through a massless inextensible string. Block of mass m1 is placed at the fixed rigid inclined surface while the block of mass m2 hanging at the other end of the string, which is passing through a fixed massless frictionless pulley shown in figure. The coefficient of static friction between the block and the inclined plane is 0.8. The system of masses m1 and m2 is released from rest.

m=4kg1m=2kg2

30º Fixed

g=10m/s2

=0.8

(A) The tension in the string is 20 N after releasing the system (B) The contact force by the inclined surface on the block is along normal to the inclined

surface

(C) The magnitude of contact force by the inclined surface on the block m1 is 20 3N

(D) None of these

15. A particle ‗P‘ of mass ‗m‘ is rotating in horizontal circle about vertical axis AB with the help of two strings each of length ‗L‘ as shown in

figure. The separation AB = L, and ‗P‘ rotates with angular velocity ‗‘ about axis AB. Tension in the upper and lower strings are T1 and T2

respectively, then :

(A) T2 will be zero for 2g

L

(B) T1 will always be greater than T2 for any ‗‘

(C) T1 = 3T2, for 4g

L

(D) 2

1T mL for

2g

L

L

L

P

L

T1

A

B

T2




This section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.

1. A particle of mass 10 kg is in equilibrium with the help of two ideal

and identical strings. Now one string is cut then, find the ratio of tension in the other string just before cutting and just after cutting.

30°30°

10 kg 2. In a car race, car A takes 4 seconds less than car B to reach the finish line and passes the

finishing line with velocity v more than car B. Assume cars start from rest and travel with constant acceleration aA = 4 m/s2 and aB = 1 m/s2. Find the value of v in m/s.

3. In the figure, find the velocity of m1 in ms–1 when m2 falls by 9m. Given m1 = m m2 = 2m (take g = 10 ms–2)

m1=0.1

m2 4. A ball is projected from some height with initial horizontal speed

20 m/s. There is a wall at a horizontal separation of 100 m from

the building. If collision is perfectly elastic find the time in sec

after which it will hit the wall. (t = 0 is taken when ball is thrown).

All surfaces one smooth.

100 m

20 m/s

5. Figure shows a smooth cylindrical pulley of radius R with centre at origin

of co-ordinates. An ideal thread is thrown over it on the two parts of ideal

thread two identical masses are tied initially at rest with co-ordinates (R, 0)

and (-R, -R) respectively. If mass at x-axis is given a slight upward jerk, it

leaves contact with pulley at (R cos, Rsin). Then find /sin.

x

y

m

m



PPAARRTTIIII :: CCHHEEMMIISSTTRRYY

SSEECCTTIIOONNAA Single Correct Choice Type

This section contains 10 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is

1. The distance between 3rd and 2nd orbit of hydrogen atom is

(A) 2.646108 cm (B) 2.116108 cm (C) 2.646 cm (D) 0.529 cm

2. H–B–H bond angle in 4BH is:

(A) 180° (B) 120° (C) 109° (D) 90° 3. Which of the following has maximum lattice energy? (A) CaO (B) Na2O (C) MgO (D) BaO 4. The atomic radii of F and Ne in angstrom unit are respectively given by (A) 0.72, 1.60 (B) 1.60, 1.60 (C) 0.72, 0.72 (D) 1.60, 0.72 5. The K.E. of N molecule of O2 is x Joules at –123°C. Another sample of O2 at 27°C has a KE of

2x Joules. The latter sample contains. (A) N molecules of O2 (B) 2N molecules of O2

(C) N/2 molecules of O2 (D) N/4 molecule of O2

6. Out of the following, which does not have zero dipole moment is (A) CO2 (B) CCl4 (C) BCl3 (D) NH3 7. The wave function for 1s orbital of hydrogen atom is given by

r /a01s e

2

a0 = radius of Bohr orbit r = distance from nucleus What will be ratio of probability density of finding the electron at the nucleus to the first Bohr‘s

orbit (a0)? (A) e (B) e2 (C) 1/e (D) 0 8. The IP1, IP2, IP3, IP4 and IP5 of an element are 7.1, 14.3, 34.5, 46.8, 162.2 eV respectively.

The element is likely to be (IP ionization potential) (A) Na (B) Si (C) K (D) Ca



9. 12.25 g KClO3 on heating gives enough O2 to react completely with H2 produced by the action of the Zn on dilute H2SO4.

3 2

2KClO 2KCl 3O , 2 4 4 2

H SO Zn ZnSO H , 2 2 2

2H O 2H O

The weight of Zn required for this is: [At.wt of Zn = 65.5] (A) 9.825 g (B) 19.65 g (C) 39.3 g (D) 8.5 g

10. 2 moles of 4

FeSO in acid medium are oxidised by x moles of 4

KMnO , whereas 2 moles of

2 4FeC O in acid medium are oxidised by y moles of

4KMnO . The ratio of x and y is:

(A) 1

3 (B)

1

2 (C)

1

4 (D)

1

5



11. Which of the following statement is correct regarding H2O2?

(A) it has open booklike structure (B) it is both an oxidizing as well as reducing agent (C) it is a bleaching agent (D) it acts as only oxidizing agent 12. Which of the following will represent Boyle‘s law correctly?

(A) PV

P

(B) V

PV

(C) PV

1/P

(D) P

V 13. Which of the following pairs will not diffuse at the same rate through porous plug at same

conditions of temperature and pressure? (A) CO & NO2 (B) NO2 & CO2 (C) NH3 & PH3 (D) CO2 & N2O 14. A gas obeys the equation P(V-b) = RT. Which of the following is/are correct about the graphs

of gas?

(A) The isochoric curves have slope = R

V b

(B) The isobaric curves have slope = R

P and intercept b.

(C) For the gas compressibility factor = 1+Pb

RT

(D) For the gas compressibility factor = 1Pb

RT



15. Highly pure dilute solution of sodium in liquid ammonia: (A) Shows blue colour (B) Exhibits electrical conductivity (C) Shows reducing properties (D) Shows oxidizing properties

SECTIONC Integer Answer Type

This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).

1. 1 g of an acid (Molar mass = 150 g/mol) is completely neutralized by 1.5 g KOH. Calculate the number of neutralizable protons in acid.

2. Find out the number of angular nodes in the orbital to which the last electron of Cr enter. 3. According to molecular orbital theory, the number of electrons present in the antibonding

molecular orbitals of N2 is (are)

4. A 17 gm sample of H2O2 contains a% H2O2 by weight and requires a mL of KMnO4 in acidic

medium for comlete oxidation. Thus what is the molarity of KMnO4? 5. The value of x+y+z in following redox reaction

xFeCl3 + yH2S zFeCl2 + S + HCl, is



PART – III : MATHEMATICS SECTION – A

(Single Correct Choice Type) This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

1. In a triangle ABC, A(2, 4) and internal angular bisector of B & C are y = x & 2x + y = 3, then find the equation of BC

(A) x = 2 (B) y = 2 (C) x + y = 2 (D) none of these 2. Find the equation of minimum radius of that circle which contain all free circles S1, S2 & S3

where S1 x2 + y2 = 1, S2 (x – 2)2 + y2 = 9, S3 (x – 2)2 + (y – 2)2 = 4

(A) x2 + y2 – 2x – 2y = 2 (B) x2 + y2 + 2x + 2y = 9

(C) x2 + y2 – 2x – 2y = 9 2 (D) none of these

3. The value of

20log 0.1 0.01 0.001 .............

0.05

is

(A) 81 (B) 1

81 (C) 20 (D)

1

20

4. The equation of the bisector of the acute angle between the lines 2x – y + 4 = 0 and x – 2y = 1

is : (A) x + y + 5 = 0 (B) x – y + 1 = 0 (C) x – y = 5 (D) x – y + 5 = 0

5. The maximum value of cos2x sin2x27 81 is

(A) 23 (B) 53 (C) 73 (D) 3



6. The pair of straight lines joining the origin to the common points of x2 + y2 = 4 and y = 3x + c

are perpendicular, if c2 = (A) – 1 (B) 6 (C) 13 (D) 20 7. The centre of circle inscribed in square formed by the lines x2 – 8x + 12 = 0 and

y2 – 14y + 45 = 0 is (A) (4, 7) (B) (7, 4) (C) (9, 4) (D) (4, 9) 8. |x + 1| + |x − 2| > 3

(A) (−, −1) (2, ) (B) (2, ) (C) (−1, 2) (D) none of these

9. In the equilateral ABC the side length is 8 unit, inscribe this another triangle is form through the

midpoints of vertices A,B and C is DEF. Inside

DEF another triangle is also form through the

midpoints of vertices D,E & F is PQR Find the

area of PQR.

(A) 2 3 (B) 3

(C) 3

2 (D) none of these

A B

C

D E

F

P

Q R

10. Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the statement ―Suman is brilliant and dishonest if and only if Suman is rich‖

can be expressed as

(A) ~ (Q (P ~ R) (B) ~ Q ~P R

(C) ~ (P ~ R) Q (D) ~ P (Q ~ R)



SECTION – A

(Multiple Correct Answers Type)

This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONE or MORE may be correct.

11. In a ABC

(A) sinA.sinB.sinC 3 3 / 8 (B) 2 2 2sin A sin B sin C 9/ 4

(C) sinAsinBsinC is always positive (D) 2 2sin A sin B 1 cosC

12.

n n



(n, even or odd) is equal to

(A) n A B2tan

2

(B) n A B2cot

2

(C) 0 (D) none of these

13. Common tangents to the circles x2 + y2 – 2x – 6y + 9 = 0 & x2 + y2 + 6x – 2y + 1 = 0 are. (A) 3x + 4y – 10 = 0 (B) 4x – 3y = 0 (C) y = 4 (D) x = 0

14. Two circles x2 + y2 + x = 0 & x2 + y2 = c2 touch each other if

(A) + c = 0 (B) c = 0 (C) 2 = c (D) none of these

15. If x satisfies x 1 x 1

2 2log (9 7) 2 log (3 1) then

(A) x Q (B) x {x Q: x 0}

(C) x N (D) x Ne (set of even natural numbers)



SECTION – C

(Integer Answer Type)

This Section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be darkened in the ORS.

1. A(0, 0), B(2, 1) and C(3, 0) are the vertices of a triangle ABC, and BD is its altitude. The line

through D parallel to the side AB intersects the side BC at a point K. If the product of the areas of the triangle ABC and BDK is k, then the value of 2k is

2. If 2sinx sin x 1 then the value of 2 4 4 2cos x cos x cot x cot x is equal to

3. If 1 2 3cos 2cos 3cos 6 then 1 2 3tan tan tan equals to

4. If 2 2 2log x log y log z

4 6 3k and x3y2z = 1

Then |k| is 5. Let the co-ordinates of the circumcentre of the triangle whose vertices are A(5, – 1), B(–1, 5)

and C(6, 6) is (a, b) then [a + b] is (where [.] denotes the greatest integer function)



FIITJEE COMMON TEST


PHASE TEST-I (PAPER-1) ANSWER KEY


SECTION-A

1. B

2. C 3. A 4. C 5. C 6. C 7. D 8. C 9. A 10. A 11. A, B, D 12. B, C 13. A, C 14. A, B, C 15. A, B, C

SECTION-C

1. 2 2. 8 3. 4 4. 5 5. 2

SECTION – A 1. A 2. C 3. C 4. A 5. A 6. D 7. B 8. B 9. B 10. A 11. A,B,C 12. A,B,D 13. A,B,C 14. ABC 15. A,B,C

SECTION–C 1. 4 2. 2 3. 5 4. 2 5. 5

SECTION-A

1. B 2. C 3. A 4. A 5. B 6. D 7. A 8. A 9. B 10. A 11. A,B,C,D 12. B,C 13. A,B,C,D 14. A,B,C 15. A,C

SECTION-C

1. 1 2. 2 3. 0 4. 8 5. 5

Paper Code

SET-A


HINT & SOLUTIONS



1. B

2. C

F.r

= 10 – 3 = 7 3. A (1.2) (10) (0.3) 4. C

av

R ˆ î Hj2

| v |T

2

5. C From work energy in the frame which is attached to point A

2 2 2xm m

1 1 1max k x m(0) m(0)

2 2 2

max

2max .

k

6. C

y = r sin

dy dr d

sin cos .r 3.6m / sdt dt dt

7. D

45

tan60

= 37°

since, VS = VR,

53° = + 37°

= 16°.

vR

vS

53º

37º

8. C Fcos N …..(A)

N Fsin mg …..(B)

By (A) and (B)

Fcos Fsin mg

Fcos Fsin mg


F(cos sin ) mg

if F is . Hence cos sin 0

cos sin 0 cot =

= cot1()


9. A

y1 = 9.8t 4.9t2

y2 = 9.8 (t5) 4.9 (t5)2 y1 = y2 gives t = 12.5 10. A

Acceleration = slope of v/t graph = g sin is greater for P1 where is angle of inclined plane.


11. A, B, D 12. B, C

Here s

mF mg 1

M

For m

kF mg m.a

For M

kmg MA

2A 0.4m / s

13. A, C

2dxt

dt …(i)

31 t

y2 3

2dy t

dt 2 …(ii)

t = 1, vx = 1, vy = 1

2

1ˆ ˆv i j2

2

2

d x2t

dt …(iii)

2

2

d yt

dt …(iv)

at t = 1 s ax = 2 and ay = 1

ˆ â 2i j

.

14. A, B, C If the tendency of relative motion along the common tangent does not exist, then component

of contact force along common tangent will be zero. 15. A, B, C For particle ‗P‘

2

1 2(T T )cos 30 mL cos 30

1 2T sin 30 T sin 30 mg.

SECTION–C

(Integer Type) 1. 2


2. 8

B A

2S 2S4

a a

A B2a S 2a S v

v 8m / s.

3. 4 Applying work energy theorem Kf – Ki = w

2 22 1

1 1m v m (4v)

2 2

2 1m g y m g(4y)

v = 4 m/s.

m1

m2

mg

v

T

4. 5 Horizontal velocity of ball will not change 100 = 20 t t = 5 sec.

5. 2

mgR – mg R sin = ½ (2m)v2 …. (i)

mv2/R = mg sin … (ii)


PPPAAARRRTTT ––– III ::: CCCHHHEEEMMMIIISSSTTTRRRYYY

SECTION – A (Single Correct Choice Type)

1. A

r = r3r2 = r09 r04

r = 5r0 = 50.0529108 = 2.646108 cm 2. C

Hybridization in BH4 is sp3, hence bond angle in 109

3. C Latlic energy in inversely propotional to size 4. A Noble gases have more radii than halogen in respective periods 5. A

KE =3

RT2

; T = – 123 + 273 = + 150 K

3

R 1502

38.314 75

2 = xJ = 225 8.314 = xJ

At 27°C = 27+ 223 = 300K

KE for = 2x Joule = 3

8.314 3002

N molecules

x Joule = 3 8.314 75 In both the cases x Joules correspond to N molecules. 6. D NH3 does not have zero dipole moment 7. B

Probability density 2

02

(r 0) 2

22(r 1)

e2 e

e2

8. B There is large difference between 4th and 5th IP, hence element should contain four valence

electrons. 9. B

Moles of O2 produced = 3/2 moles of KClO3 = 3 12.25

0.152 122.5 mole

According to given equation One moles of O2 required 2 mole of H2 = 2 moles of Zn

Moles of Zn = 2moles of O2=0.152=0.3 mole

Mass of Zn require = 0.365.5 = 19.65 g 10. A

nfactor of 4FeSO 1

nfactor of 2 4FeC O 3

Hence geq. of 4 4FeSO g e.q of KMnO

12 = 5x (1)

geq. of FeC2O4 = geq of KMnO4

32 = 5y Hence x/y = 1/3



11. A,B,C H2O2 is both oxidising and reducing agent 12. A,B,D

According to Boyle‘s law 1

P or PV constantV

13. A,B,C

Rate of diffusion 1

M

CO2 and N2O have same molar mass = 44 g/mol 14. ABC

P(V b) RT

PV Pb RT

PV PbZ 1

RT RT

15. A,B,C Solution of alkali metal in liquid ammonia shows blue colour, exhibit electrical conductivity and

show reducing property SECTION–C

(Integer Type)

1. 4

geq. of acid = geq. of base

1 1.5

n150 56

n=4 2. 2

Last electron of Cr enters in dsubshell, hence l=2 3. 5

Electronic configuration of N2 is

1s2 1s2 2s2 2s22px

22py

22pz

2 2px1

4. 2

geq. of H2O2 = geq. of KMnO4

17 2 a

a 5 M100 34 1000

M = 2 molar 5. 5 Balance equation is

2FeCl3 + H2S 2FeCl2 + S + 2HCl x + y + z = 5


SECTION – A


MATHEMATICS 1. B Take the reflection of A about internal angular bisector of B & C lie on the line BC. 2. C For centre - find the circumcentre of the centres S1, S2 & S3, For radius - find the circum radius from the centres S1, S2 & S3 and add the maximum radius

of the circles S1, S2 & S3 in the circum radius. 3. A Use the log properties 4. A

2x – y + 4 = ( x – 2y 1) For acute angle bisector use + sign 5. B 33cos2x+4sin2x Then maximum value is 35 6. D Use the homogenization 7. A Lines are x = 2 and x = 6, y = 5, and y = 9 Then centre is (4, 7) 8. A 9. B

Area = 232

4

10. A (Multi Correct Choice Type)

11. A,B,C,D

2 2 2 2 2 21 1sin A sin B sin C (1 cos A) (1 cos B) sin C

2 2

22 cos C cosC.cos(A B)

22 (cos C cosC)

2

9 1cosC

4 2

sin2A + sin2A+sin2C 9/4

Now 2 2 2

2 2 2 1/ 3sin A sin B sin C(sin A.sin B.sin C)

3

2 / 39 / 4(sinA.sinB.sinC)

3 or

3 3sinA.sinB.sinC

8

also 2 2 2 2sin A sin B sin C 2 cos C cosC

sin2A + sin2B 1+ cos C. 12. B,C

n n



n nA B B A

2cot cot2 2

If n even, n A B2cot

2

, if n odd, 0.

13. A,B,C,D


Points can be calculated by the internal and external section formula using centres of both the circles and slope can be calculated by using the condition of tangency.

14. A,B,C Use the internal and external touching condition of two circles. 15. A,C

x 1

2 x 1

9 7log 2

3 1

32x2 + 7 = 4(3x1 + 1)

x 1 x 1(3 1)(3 3) 0

x 1 = 0 or x 1 = 1 x = 1, 2.


1. 1 Calculate the area of ABC and BDK then multiply these two 2. 2 Given sin x + cos x + tan x + cot x + sec x + cosec x = 7

1 sinx cosx

sinx cosx 7sinx cosx sinx cosx

1 1

sinx cosx 1 7sinx cosx sinxcosx

2 2

2 21 sin2x 1 7

sin2x sinx

2 2

1 t t 2 7t 2 , where t = sin 2x

3 2t 44t 36t 0

2t 44t 36 0 [sin 2x 0]

244 44 4 36

t 22 8 72

sin2x 22 8 7

3. 0

Given 1 2 3cos 2cos 3cos 6

1 2 3cos cos cos 1

1 2 3 0

1 2 3tan tan tan 0

4. 8 Use the log property. 5. 5 Circum centre can be calculated by using the perpendicular bisectors of vertices of the

triangle.




Maximum Marks: 240



INSTRUCTIONS


G. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.






H. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet. 2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No. and write in ink

your Name, Test Centre and other details at the designated places. 3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Three Parts. (i) Section-A (01 – 8) contains 10 multiple choice questions which have only one correct answer. Each question carries +3

marks for correct answer and – 1 mark for wrong answer. Section-A (09 – 12) contains 4 multiple choice questions which have one or more than one correct


(ii) Section-B (01 – 02) contains 2 Matrix Match Type questions containing statements given in 2 columns. Statements in the first column have to be matched with statements in the second column. Each question carries +8 marks for all correct answer. For each correct row +2 marks will be awarded. There may be one or more than one correct choice. No marks will be given for any wrong match in any question. There is no negative marking.

(iii) Section-C (01 – 06) contains 6 Numerical based questions with single digit integer as answer, ranging from 0 to 9 and

each question carries +4 marks for correct answer. There is no negative marking.




BA

TC

HE

S –

Tw

o Y

ea

r C

RP

(1

31

5)-

Ad

va

nc

e (

B L

ot)

FIITJEE

CPT2 - 2

CODE: SET-A

PAPER - 2





= 1.987 2 Cal K1 mol1



= 6.25 x 10-27 erg.s



1 amu = 1.66 x 10-27 kg

1 eV = 1.6 x 10-19 J


Au=79.


Mn=55, Pb=207, Au=197, Ag=108, F=19, H=2, Cl=35.5, Sn=118.6


Acceleration due to gravity g = 10 2m / s




This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. A cubical box of wine has a small spout located in one of the bottom

corners. When the box is full and placed on a level surface, opening

the spout results in a flow of wine with a initial speed of v0 (see

figure). When the box is half empty, someone tilts it at 45° so that the

spout is at the lowest point (see figure). When the spout is opened

the wine will flow out with a speed of

(A) v0 (B) v0/2

(C) 0v 2 (D) 4

0v 2

2. A vertical tank, open at the top, is filled with a liquid and rests on a smooth horizontal surface. A small

hole is opened at the centre of one side of the tank. The area of cross-section of the tank is N times the

area of the hole, where N is a large number. Neglect mass of the tank itself. The initial acceleration of the tank

is

(A) g

2N (B)

g

2N

(C) g

N (D)

g

2 N

3. The figure shows an isosceles triangular plate of mass M and base L.

The angle at the apex is 90°. The apex lies at the origin and the base

is parallel to X–axis. The moment of inertia of the plate about the y-

axis is

(A) 2ML

6 (B)

2ML

8

(C) 2ML

24 (D) none of these

4. A cone of radius r and height h rests on a rough horizontal surface, the coefficient of friction between

the cone and the surface being µ. A gradually increasing horizontal force F is applied to the vertex of

the cone. The largest value of µ for which the cone will slide before it topples is

(A) r

2h (B)

2r

5h

(C) r

h (D)

r

h

Space for Rough Work


5. A sphere of mass M and radius R is attached by a light rod of length l to a

point P. The sphere rolls without slipping on a circular track as shown. It

is released from the horizontal position. the angular momentum of the

system about P when the rod becomes vertical is :

(A) 10

M gl [l R]7

(B) 10 2

M gl l R7 5

(C) 10 7

M gl l R7 5

(D) none of the above

6. Two particles of equal mass have velocities ˆ2i ms–1

and ˆ2 j ms–1

. First particle has an acceleration

ˆ ˆ(i j) ms–2

while the acceleration of the second particle is zero. The centre of mass of the two particles

moves in

(A) circle (B) parabola

(C) ellipse (D) straight line

7. A billiard table whose length and width are as shown in the figure. A ball

is placed at point A. At what angle θ the ball be projected so that after

colliding with two walls, the ball will fall in the pocket B. Assume that all

collisions are perfectly elastic (neglect friction)

(A) 1 2a ccot

2b

(B) 1 2a c

tan2b

(C) 1 c acot

2b

(D) 1 c a

cotb

8. A force exerts an impulse I on a particle changing its speed from u to 2u. The applied force and the

initial velocity are oppositely directed along the same line. The work done by the force is

(A) 3

Iu2

(B) 1

Iu2

(C) I u (D) 2 I u




This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of

which ONE OR MORE may be correct.

9. Figure shows a siphon. Choose the wrong statement:

(A) Siphon works when h3 < 0

(B) Pressure at point 2 is P2 = P0 – ρgh3

(C) Pressure at point 3 is P0

(D) Pressure at point 2 is P0

(P0 = atmospheric pressure)

10. Two identical balls are interconnected with a massless and inextensible thread. The system is in gravity

free space with the thread just taut. Each ball is imparted a velocity v, one towards the other ball and

the other perpendicular to the first, at t = 0. Then,

(A) the thread will become taut at t = (L/v)

(B) the thread will become taut at some time t < (L/v).

(C) the thread will always remain taut for t > (L/v).

(D) the kinetic energy of the system will always remain mv2.

11. In the figure shown, the plank is being pulled to the right with a

constant speed v. If the cylinder does not slip then:

(A) the speed of the centre of mass of the cylinder is 2v.

(B) the speed of the centre of mass of the cylinder is zero.

(C) the angular velocity of the cylinder is v/R.

(D) the angular velocity of the cylinder is zero.

12. Two particles move on a circular path (one just inside and the other just outside) with angular velocities

ω and 5ω starting from the same point. Then

(A) they cross each other at regular intervals of time 2

4

when their angular velocities are oppositely

directed.

(B) they cross each other at points on the path subtending an angle of 60° at the centre if their angular

velocities are oppositely directed.

(C) they cross at intervals of time 3

if their angular velocities are oppositely directed.

(D) they cross each other at points on the path subtending 90° at the centre if their angular velocities

are in the same sense.



Part B

Matrix – Match Type

This section contains 2 questions. Each question contains statements given in

two columns, which have to be matched. The statements in Column I are labelled

A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any

given statement in Column I can have correct matching with ONE OR MORE

statement(s) in Column II. The appropriate bubbles corresponding to the answers

to these questions have to be darkened as illustrated in the following example:

If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s and t;

then the correct darkening of bubbles will look like the following:

p q r s

p q r s

p q r s

p q r s

p q r s

D

C

B

A t

t

t

t

t

1. Two bodies A and B are allowed to roll without slipping on a rough inclined plane. Column I shows

some of the physical quantities associated with their motions while Column II gives you the relation

between a physical quantity for two different bodies. Match the entries of Column I with Column II.

Column I Column II

(A) Time taken by two bodies to travel a

distance ‗s‘ on the incline would be

(p) Same if A and B have the same shape and

size but are of different material.

(B) Friction force experienced by two bodies

during their motion would be

(q) Different if A and B are of same size and

same mass but having different shape.

(C) Velocity acquired by A and B after traveling

through a distance ‗s‘ would be

(r) Same if bodies have same size but different

shapes and mass.

(D) Acceleration of COM of A and B would be (s) Different if bodies have same size but

different shapes and mass.

(t) Same irrespective of their size, shape and

mass.

2. Net force on a system of particles in ground frame is zero. In each situation of Column I a statement is

given regarding this system. Match the statements in Column I with results in Column II.

Column I Column II

(A) Acceleration of COM of system in ground

frame.

(p) Is constant.

(B) Net momentum of system in ground frame. (q) Is zero.

(C) Net momentum of system in the CM frame. (r) May be zero.

(D) Kinetic energy of system in the CM frame. (s) May be constant.

(t) Depends on internal forces.



SECTION–C

(Integer Type)

This section contains 6 questions. The answer to each question is a single-digit integer, ranging from 0 to 9.

The correct digit below the question number in the ORS is to be bubbled.

1. A particle of mass 0.5 kg is rotating in a circular path of radius 2m and centripetal force on it is

9 Newtons. What is its angular momentum (in J-sec) about the centre of circle?

2. A ring of mass m and radius R has three particles attached to the ring as

shown in the figure. The centre of the ring has a speed v0. The kinetic

energy of the system is 2

0Kmv (Slipping is absent). Find K

3. In a one-dimensional collision, a particle of mass 2m collides with a particle of mass m at rest. If the

particles stick together after the collision, then 1/n th fraction of the initial kinetic energy is lost in the

collision. Find n

4. A particle of mass "m" is projected from ground with a speed of 50 m/s at an angle of 53° with the

horizontal. It breaks up into two equal parts at the highest point of the trajectory. One of the particles

came to rest immediately after the explosion. The radii of curvatures of the moving particle just after the

explosion will be how many times of that of the particle just before the explosion.

5. A large tank is filled with water (density = 103 kg/m

3). A small hole is

made at a depth 10 m below water surface. The range of water coming

out of the hole is R on ground. What extra pressure (in atm) must be

applied on the water surface so that the range becomes 2R (take 1 atm

= 105 Pa and g = 10 m/s

2):

6. A container whose bottom has round holes with diameter 0.1 mm is filled with water. The maximum

height (in m) upto which water can be filled without leakage is h/10. Find h.

Surface tension = 75 × 10–3

N/m and g = 10 m/s2:



PPPAAARRRTTT ––– IIIIII ::: CCCHHHEEEMMMIIISSSTTTRRRYYY SECTION – A




1. B2O3 + CaF2 + conc. H2SO4 A + B +C Where ‗A‘ is Boron containing compound, A is (A) B2H6 (B) H3BO3 (C) Ca2B6O11 (D) BF3 2. Inorgnaic Benzene (Borozine) is more reactive than that of Benzene is due to: (A) Electronegativity difference in B and N (B) Non-aromatic character of inorganic benzene (C) due to non planar structure of inorganic benzene (D) all of these 3. At 25°C, a saturated solution of BaSO4 is 3.9 × 10

–5 M. What is its solubility in 0.1 M Na2SO4 solution?

(A) 1.5 × 10–9

M (B) 1.5 × 10–8

M (C) 2.4 × 10

–7 M (D) 2.5 × 10

–9 M

4. Calculate the pH of 0.1 M solution of NaHCO3; K1 = 4 × 10

–7 M, K2 = 5 × 10

–11

[Given log 2 = 0.3, log 5 = 0.7] (A) 8.35 (B) 10.2 (C) 9.25 (D) 7.0



5. Which of the following does not work as a Buffer solution? (A) Na2B4O7 Solution (B) NaHCO3 / NaOH (C) NH4Cl (0.1M, 500 ml) + NaOH (0.01M, 500 ml) (D) All of them

6. What can be concluded about the values of H and S from this graph?

(A) H > 0, S > 0 (B) H > 0, S < 0

(C) H < 0, S > 0 (D) H < 0, S < 0

7. The rate constant for the reaction 2N2O5 4NO2 + O2 is 3 × 10

–5 s

–1.

If the rate is 2.4 × 10–5

mol L–1

s–1

, then the concentration of N2O5 is (in mol L–1

) (A) 1.4 (B) 1.2 (C) 0.8 (D) 0.04

88.. IInn VVaann ddeerr WWaaaall‘‘ss eeqquuaattiioonn ooff ssttaattee ffoorr aa nnoonn--iiddeeaall ggaass,, tthhee tteerrmm tthhaatt aaccccoouunnttss ffoorr iinntteerrmmoolleeccuullaarr

ffoorrcceess iiss

((AA)) ((VV –– bb)) ((BB)) RRTT

((CC)) 2

aP

V

((DD)) ((RRTT))

--11


100 200 300 400 500

+100

+50

0

–50

–100

Temp. K

G

kJ m

ol–

1





9. Which of the following option is true? If o 1

Ioniz(HCN) 45.2kJmol and

o 1

ioniz 3H (CH COOH) 2.1kJ mol

(A) pKa(HCN) =pKa(CH3COOH) (B) pKa(HCN) > pKa(CH3COOH) (C) Ka(HCN) < Ka(CH3COOH) (D) Ka(HCN) > Ka(CH3COOH) 10. For which of the following reactions, the degree of dissociation cannot be calculated from the vapour

density data

(A) 2 22HI(g) H (g) I (g)

(B) 3 2 22NH (g) N (g) 3H (g)

(C) 2 22NO(g) N (g) O (g) (D)

5 3 2PCl (g) PCl (g) Cl (g)

11. Which of the following statement(s) is/are true? (A) Work is a state function (B) Temperature is a state function (C) Change of state is completely defined when initial and final states are specified (D) Work appears at the boundary of the system 12. Which of the following is/are endothermic reaction (s)? (A) Combustion of methane (B) Decomposition of water (C) Dehydrogenation of ethane to ethylene (D) Conservation of graphite to diamond



Part B










p q r s

p q r s

p q r s

p q r s

p q r s

D

C

B

A t

t

t

t

t

1. Column I Column II

(A) AlCl3 (p) Also exist as dimer

(B) BH3 (q) Hydrolyzed in water.

(C) (BN)x (r) Lewis acid.

(D) H3BO3 (s) Graphite like structure.

2.

Column I Column II

(A) Isothermal reversible process (p) univ.S 0

(B) Adiabatic reversible process (q) univ.S 0

(C) Adiabatic irreversible process (r) 2

system

1

vS nRln

v

(D) Isothermal irreversible process (s) 2 2

system v

1 1

T vS nC ln nRln 0

T v



SECTION–C

(Integer Type)



1. No. of B–OH bonds in Borax (Na2B4O7.10H2O) are 2. Amongst the following the total numbers of compounds whose aqueous solution turns red litmus paper

blue is KCN, K2SO4, (NH4)2C2O4, NaCl, Zn(NO3)2, FeCl3, K2CO3, NH4NO3, HCN 3. The pressure necessary to obtain 50% dissociation of PCl5 at 400 K is numerically equal to ‗x‘ times of

Kp, x is 4. Total number of extensive properties among the following is heat capacity, Molar heat capacity, Molar Volume, Resistance, Emf. density, volume, enthalpy, entropy. 5. Ratio of the rate of diffusion of He and CH4 under identical condition of P and T will be. 6. Which of the following elements form amphoteric oxide? Na, Be, Mg, B, Al, Ca, Si.



PPPAAARRRTTT ––– IIIIIIIII ::: MMMAAATTTHHHEEEMMMAAATTTIIICCCSSS SECTION – A




1. If tn denotes the nth term of an AP and p

1t

q and q

1t

p , then which of the following is necessarily a

root of the equation (p + 2q – 3r)x2 + (q + 2r – 3p)x + (r + 2p – 3q) = 0 is

(A) tp (B) tq

(C) tpq (D) tp + q

2. If the roots of the equation x3 + bx

2 + cx + 1 = 0 form an increasing G.P., then which of the following

statements is true?

(A) b = c

(B) b ϵ ( –∞, –2)

(C) one of the root is 1

(D) one of the roots is smaller than 1 and one root is more than 1

3. If │z – iRe(z)│= │z – lm(z)│, (where i 1 , then z lies on

(A) Re(z) = 2 (B) lm(z) = 2

(C) Re(z) + lm(z) = 2 (D) None of these

4. If │z – 1│ + │z + 3│ ≤ 4, then the range of values of │z – 4│, (where i 1 ) is

(A) [0, 7] (B) [1, 8]

(C) [3, 7] (D) [2, 5]



5. If the distance of two points P and Q from the focus of a parabola y2 = 4ax are 4 and 9 respectively,

then the distance of the point of intersection of tangents at P and Q from the focus is:

(A) 8 (B) 6

(C) 5 (D) 13

6. The centroid of the triangle formed by the feet of co-normal points on the curve 25x2 + 25y

2 – 250x –

300y + 1525 = (3x + 4y – 12)2 lies on the line:

(A) 4x – 3y + 1 = 0 (B) 4x – 3y – 2 = 0

(C) 4x – 3y + 3 = 0 (D) None of these

7. In a shop oranges are arranged in the shape of complete pyramid. The base of which is an equilateral

triangle of 10 oranges in each side, the total number of oranges in the complete pyramid will be

(A) 230 (B) 260

(C) 220 (D) 360

8. If 25(9x2 + y

2) + 9z

2 – 15(5xy + yz + 3zx) = 0 and x + y + z = 18, then y can be

(A) 4 (B) 6

(C) 10 (D) 12






9. If a, b are the real roots of x2 + px + 1 = 0 and c, d are the real roots of x

2 + qx + 1 = 0, then

(a – c)(b –c)(a + d)(b + d) is divisible by

(A) a + b + c + d (B) a + b – c – d

(C) a – b + c – d (D) a – b – c – d

10. The reflection of the complex number2 i

3 i

, (where i 1 ) in the straight line z(1 + i) = z(i 1) is

(A) 1 i

2

(B)

1 i

2

(C) i(i 1)

2

(D)

1

1 i

11. If S = {a1, a2, a3, a4} where no element is zero and if 23 3 4

2 2

i i i 1 ii 1 i 1 i 2

a x 2x aa a 0

, then a1,

a2, a3, a4 are in

(A) A.P. (B) G.P.

(C) if a1 = a2, then a3 = a4 (D) all (A), (B), (C)

12. If the equation of the parabola is x2 + y

2 – 2xy + 4x – 2y + 1= 0, then

(A) Axis is 2x – 2y + 5 = 0 (B) Tangent at vertex is 5

2x 2y 04

(C) Vertex is 1 11

,8 8

(D) Focus is 3 15

,8 8



Part B










p q r s

p q r s

p q r s

p q r s

p q r s

D

C

B

A t

t

t

t

t

1. If a < b < c < d, then the equation

Column I Column II

(A) (x – a)(x – c)+ λ(x – b)(x – d) = 0, (λ ≠ 0) (p) Has two root between (a, c)

(B) 1 1 1 10

x a x b x c x d

(q) Has two roots between (b, d)

(C) 2 30

(x a)(x c) (x b)(x d)

(r) Has one root between (a, c)

(D) 2 3 4 50

(x a) (x b) (x c) (x d)

(s) Has one root between (b, d)

2.

Column I Column II

(A) If P(1, 1), Q(4, 2) and R(x, 0) be three points such

that PR + RQ is minimum, then x is equal to

(p) 1

(B) The area bounded by the curves max {│x│, │y│} =

1 is equal to

(q) 2

(C) The number of circles that touch all the three lines

2x – y = 5, x + y = 3 and 4x – 2y = 7 is equal to

(r) 3

(D) If the point (a, a) lies between the lines │x + y│ = 6,

then [│a│] can be equal to, ([.] represents the

integral part)

(s) 4



SECTION–C

(Integer Type)



1. The number of solutions of 2 loge 2x = loge(7x – 2 – 2x2) is

2. TP and TQ are any two tangents to a parabola and the tangent at a third point R cuts them in P‘ and

Q‘, then the value of TP' TQ'

TP TQ must be

3. If i

i

1m ,

m

, mi > 0, i = 1, 2, 3, 4 are four distinct points on a circle, the value of 4

i

i 1

m

must be

4. In a ΔABC, A = (α, β), B = (1, 2), C = (2, 3) and point A lies on the line y = 2x + 3, where α, β ϵ I. If the

area of ΔABC be such that [Δ] = 2, where [.] denotes the greatest integer function, then the number of

all possible coordinates of A must be

5. The area of a quadrilateral formed by a pair of tangents from the point (4, 5) to the circle (x – 2)2 + (y –

1)2 = 16 with a pair of radii where tangents touch the circle is λ square unit, then λ must be

6. z1 and z2 are two complex numbers such that 1 2

1 2

z 2z

2 z z

is unimodular, while z2 is not unimodular, then

│z1│ must be equal to



FIITJEE COMMON TEST


PHASE TEST-II (PAPER-2) ANSWER KEY


SECTION-A

1. D 2. C 3. C 4. C 5. D 6. D 7. A 8. B 9. D 10. A, C 11. B, C 12. B, C, D

SECTION-B 1. A → (p, q, s), B → (q, s), C → (p, q, s), D → (p, q, s) 2. A → (p, q), B → (p, r), C → (p, q), D → (r, s, t)

SECTION-C 1. 6 2. 6 3. 3 4. 4 5. 3 6. 3

SECTION – A 1. D 2. A 3. B

4. A 5. B 6. A

7. C 8.

9. B, C

10. A, C 11. B, C, D

12. B, C, D

SECTION-B 1. A→ (p, q, r), B → (p, q, r), C → s, D → (r, q) 2. A→ (p, r), B → (p), C → (q, s), D → (q, r, s)

SECTION–C

1. 4 2. 3 3. 3 4. 5 5. 2 6. 2

SECTION – A 1. C 2. A 3. D 4. C 5. B 6. B 7. C 8. B 9. A, B 10. C 11. B, C 12. C

SECTION-B 1. A → (r, s), B → (p, q), C → ((r, s), D → (p, q) 2. A → (q), B → (s), C → ((q), D → (p, q)

SECTION–C

1. 2 2. 1 3. 1 4. 4 5. 8 6. 2

Paper Code

SET-A


HINT & SOLUTIONS


(Single Correct Choice Type) 1. D

If a is the side length then 0v 2ga . (Before)

and 0

1 4

4

2ga vav ' 2g

2 22

. (After)

2. C

v 2g g2

So, FT = ρav2 = ρag

So, acceleration of tank = TF ag g

M (Na) N

3. C

For a perfect square

2

2

z

LM

ML2I

6 12

So, 2

x y z y

MLI I I I

24

4. C

For sliding F ≥ μmg.

and for toppling Fh > mgr mgr

Fh

so, if r

h than the block will slide first.

5. D

From C.O.E. 2 2

CM C CM

1 1 10mg mv I v g

2 2 7 and Cv

R

P C,P C C CL L L I mv

P

10 2L M g R

7 5

6. D

CMˆ ˆv i j

and CM

1 ˆ â i j2

Since CMv

and CMa

are parallel. So motion will be along a straight line.

7. A

F

r

h

mg

rf

x

y

L

L

2

Na

a v2


From fig., x b x b

tana c y a y

Solving we get 2(a c)b

x2a c

x 2btan

a c 2a c

8. B

I = p

= 2mu + mu I

m3u

Now 2 21 1 1W K m(2u) mu Iu

2 2 2

9. D 10. A, C

Let after time t, 1 and 2 moves a distance x. Then distance

between a and 2 will be 2 2x (L x) which is always less

than L for x < L and greater than L. For x > L,

so for L

tv

the string will be stack and for L

tv

the

string will be taut.

11. B, C

For no slipping, point Q must have velocity v and from constraint relation point P must have velocity v. So, for cylinder IAOR is at C.

So, Cv 0 and

v

R

12. B, C, D

v1 = ωR and v2 = 5ωR 1,2v 6 R . If ω1 and ω2 is in opposite direction.

So, 1,2

2 R 2 RT

v 6 R 3

So, T 603

If ω1 and ω2 is in same direction then v1,2 = 4ωR

T T 902 2

.

SECTION-B 1. A → (p, q, s), B → (q, s), C → (p, q, s), D → (p, q, s)

mgsinθ – fr = maC fr R = Iα and aC = Rα

Solving C

2

mgsina

Im

R

and mgsin

ImR

R

r

Imgsinf

ImR

R

rf

g

v

v

v

c

P

Q

v

x

x v

L

1

2

c

a c

a yya

b x

b x


2 2

C

2

1 1 mgsinS a t t

I2 2m

R

aC depends on shape and size. fr depends on mass, shape and size. vC depends on shape and size.

2. A → (p, q), B → (p, r), C → (p, q), D → (r, s)

ext CM 1F 0 a 0 a

CM 1 2P constant. P P .... constant

In C.M from

CM 1 2P 0 P P ..... 0

K.E. of system depends upon internal forces also.

SECTION-C 1. 6

2

C

mvF v 6

R m/s, L = mvR = 6

2. 6

P 0 0ˆ ˆv v i v j

and

Q 0ˆv 2v i

R 0 0ˆ ˆv v i v j

22 22 2 2

0 P Q R 0

1 1 1 1 1K.E. mv I m v m v 2m v 6mv

2 2 2 2 2

3. 3

2v

2mv 3mv ' v '3

Now 2 2 21 1 1k (2m)v (3m)v ' mv

2 2 3

Fraction = 1

3.

4. 4

At highest point mu cos 53° = m

v v 2ucos532

Before explosion 2

1

(ucos53 )R

g

After explosion 2

2

(2ucos53 )R

g

R2 = 4R1. 5. 3

From Bernoulli‘s theorem, v 2gh when range is R.

If R becomes 2R then 2v ,

so 2 2

ext ext

1P gh (2v) P 2 v gh 3 gh 3

2 atm.

6. 3

Pressure inside the hole= P0 + ρgh. And outside the hole = P0

And from excess pressure inside a drop = 2T

r

2m

m

0vP

Q

mR

x

y


2T 2T 3

gh h 0.3r gr 10

PPPAAARRRTTT ––– IIIIII ::: CCCHHHEEEMMMIIISSSTTTRRRYYY SECTION – A

1. D 2. A 3. B

[Ba2+

] = 2 5

4[SO ] 3.9 10 M unsaturated aqueous solution.

In 0.1 M Na2SO4 → 2

4[SO ] 0.1 M

Ksp of BaSO4 = (3.9 × 10–5

)2 = 1.5 × 10

–9

2[Ba ] in Na2SO4 is = 9

81.5 101.5 10

0.1

4. A

7 11

1 2pKa pKa ( log4 10 ) ( log5 10 ) 6.4 10.3pH 8.35

2 2 2

5. B 6. A On temperature increase, ΔG becomes negative ΔH = +ve and ΔS = –ve because on increasing the temperature TΔS > ΔH. And ΔG becomes –ve.

7. C ΔH = ΔE + ΔngRT = (–3 × 10

3) + (–1 × 2 × 300)

= –3600 Cal. ΔG = ΔH – TΔS = –3600 – [300(–10)] = –600 cal. 8. C

9. B, C 10. A, C 11. B, C, D

12. B, C, D

SECTION-B 1. A→ (p, q, r), B → (p, q, r), C → s, D → (r, q) 2. A→ (p, r, s), B → (p), C → (q, s), D → (q, r, s)

SECTION–C

1. 4 2. 3 KCN, K2CO3, HCN 3. 3

5 3 2PCl PCl Cl

2

p 2

pK

1

α = 0.5

2

pK (0.5)3

p 0.75

4. 5 Heat capacity, resistance, volume, enthalpy and Entropy. 5. 2

4

4

CHHe

CH He

Mr 162

r M 4 .

6. 2


Be, Al


(Single Correct Choice Type) SECTION – A

1. C

pq

1a d t 1

pq (For A.P).

2. A

a

.a.ar 1 a 1r

is a root.

b c

3. D For z = x + iy, we get x

2 = y

2.

4. C z will lie on AB (line segment), A(–3, 0) and B(1, 0). Then 3 ≤│z – 4│≤ 7. 5. B If tangents at P and Q meet at R, and S is focus then SP . SQ = SR

2.

6. B The centroid always lie on the axis of the parabola, and parabola is,

2

2 2 3x 4y 12(x 5) (y 6)

5

Hence, S ≡ (5, 6) and Axis ≡ 4x – 3y – 2 = 0 7. C Total number of oranges = (1) + (1 + 2) + (1 + 2 + 3) + …… + (1 + 2 + ….. + 10)

=10

n

n(n 1)220

2

8. B (15x – 5y

2)2 + (5y – 3z)

2 + (3z – 15x)

2 = 0

x y z x y z

21 3 5 9

y 6 .

9. A, B (a – c)(b – c)(a + d)(b + d) = q

2 – p

2.

10. C

If the reflection of z1 in the line az az c is z2, then 2 1az az c , and so in our case 2

1z (i 1)

2 .

11. B, C (a1x – a2)

2 + (a2x – a3)

2 + (a3x – a4)

2 ≤ 0

31 2

2 3 4

aa a

a a a .

12. A, C, D


Parabola will be, (x – y + L)

2 = (2L – 4)x + (2 – 2L)y + (L

2 – 1)

(where 2L – 4 = 2 – 2L 3

L2

)

23 5

x y x y2 4

Axis is 3

x y 02

and tangent at vertex is 5

x y 04

vertex 1 11

,8 8

.

SECTION-B 1. A → (r, s), B → (p, q), C → ((r, s), D → (p, q) a < b < c < d, let λ be +ve. Let f(x) = (x – a)(x – c) + λ(x – b)(x – d) = 0 f(a) = +ve and f(b) = –ve, f(c) = –ve and f(d) = +ve. All other parts can also be done in the same manner. 2. A → (q), B → (s), C → ((q), D → (p, q)

SECTION–C

1. 2 2. 1

Let the parabola be y2 = 4ax and coordinates of P and Q on this parabola are 2

1 1P at ,2at and

2

2 2Q at ,2at ; T is the point of intersection of tangents at t1 and t2,

Coordinates of T ≡ {at1, t2, a(t1 + t2)} Similarly P‘ ≡ {at3t1, a(t3 + t1)} Q‘ ≡ {at2t3, a(t2 + t3)} Let TP‘ : TP = λ : 1

3 2

1 2

t t

t t

or 3 2

1 2

t tTP'

TP t t

similarly, 1 3

1 2

t tTQ'

TQ t t

TP' TQ'

1TP TQ

3. 1 Let the equation of the circle be x

2 + y

2 + 2gx + 2fy + c = 0

Since the point i

i

1m

m

lie on this circle

2

i i2

ii

1 2fm 2gm c 0

mm

4 3 2

i i i im 2gm cm 2fm 1 0

Clearly its roots are m1, m2, m3 and m4

1 2 3 4

1m m m m

1

(Product of roots of biquadratic equation) = 1


4. 4 5. 8 PA = length of tangent from

(4, 5) to the circle = 1S

= 2 2{(4 2) (5 1) 16} 2

Required area = 2 × area of Δ APC

= 1

2 PA PC2

= 2 × 4 = 8 6. 2



PHASE – III PHYSICS, CHEMISTRY & MATHEMATICS


Maximum Marks: 360

Do not open this Test Booklet until you are asked to do so .



1. Immediately fill in the particulars on this page of the Test Booklet with Blue / Black Ball Point Pen. Use of pencil is strictly

prohibited.

2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer Sheet

and fill in the particulars carefully.



5. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having 30 questions in

each part of equal weight age. Each question is allotted 4 (four) marks for correct response.

6. Candidates will be awarded marks as stated above in instruction No.5 for correct response of each question. ¼ (one fourth)

marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if

no response is indicated for an item in the answer sheet.



8. Use Blue / Black Ball Point Pen only for writing particulars / marking responses on Side-1 and Side-2 of the Answer Sheet.

Use of pencil is strictly prohibited.

9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic

device, etc. except the Admit Card inside the examination hall / room.




Name of the Candidate (in Capital Letters)

:_____________________________________________


______

Batch :________________________ Date of Examination : __________________________


Section – 1 Physics

1. If the period of revolution of an artificial satellite just above the earth‘s surface is T and the

density of earth is , then T2 :

(A) is a universal constant whose value is 3

G

(B) is a universal constant whose value is 3

2G

(C) is proportional to radius of earth R

(D) is proportional to square of the radius of earth R2. Here G = universal gravitational

constant

2. A sphere of mass M and radius R1 has a concentric cavity of radius R2 as shown in figure. The

force F exerted by the sphere on a particle of mass m located at a distance r from the centre of

sphere varies as (0 r )

(A) (B) (C) (D)

3. Four particles each of mass M moves along circle of radius ‗a‘ under the action of their mutual

gravitational attraction. The speed of each particle is

(A) GM

a (B)

2 2GM

a

(C) GM 2 2 1

a 4

(D) GM

(2 2 1)a

4. Which of the following is not simple harmonic function?

(A) y = Asin 2t + Bcos 2t (B) y = Asin 2t + Bcos t

(C) y = 2 2 1 2(a b ) sin t cost. (D) y = 1- 2sin 2t

5. The gravitational field due to a mass distribution is f = 3

k

xin the x-direction where k is a

constant taking the gravitational potential to be zero at infinity. The value of potential at the

distance X is :

(A) k

x (B)

k

2x (C)

2

k

x (D)

2

k

2x

6. When a satellite in a circular orbit around the earth enters the atmospheric region, it encounters

air resistance to its motion. Then

(A) it gains mechanical energy

(B) its kinetic energy increases.

(C) its kinetic energy decreases

(D) its angular momentum about the centre of the earth remains constant


7. ve and vp denotes the escape velocity from the earth and another planet having twice the radius

and the same mean density as the earth. Then

(A) ve = vp (B) ve = Pv

2 (C) ve = 2vp (D) ve = P

v

4

8. A gas for which = 4/3, is heated at constant pressure. What percentage of the total heat

supplied is used up for external work?

(A) 12.5% (B) 25% (C) 35% (D) 70%

9. The figure shows two paths for the change of state of a gas

from A to B. The ratio of molar heat capacities of

path 1 and path 2 is

(a) > 1 (b) < 1

(c) 1 (d) data insufficient

10. A process is said to be adiabatic if it satisfies ( has usual meaning) :

(A) PV = constant (B) TV

–1 = constant (C) Q = 0 (D) All

11. An adiabatic container contains 4 moles of an ideal diatomic gas at temperature T. Heat Q is

supplied to this gas, due to which 2 moles of the gas are dissociated into atoms but temperature

of the gas remains constant. Then:

(A) Q =2RT (B) Q = RT (C) Q = 3RT (D) Q = 4RT

12. A monoatomic ideal gas undergoes a process given by 2dU + 3dW = 0, then the process is :

(A) isobaric (B) adiabatic (C) isothermal (D) None of these

13. The temperature drop through a two layer furnace wall is 900°C. Each layer is of equal area of

cross section. Which of the following actions will result in lowering the temperature of the

interface?

(A) by increasing the thermal conductivity of outer layer

(B) by increasing thermal conductivity of inner layer

(C) by increasing thickness of outer layer

(D) by decreasing thickness of inner layer

14. Time period of a simple pendulum of length L is T1 and time period of a uniform rod of the

same length L pivoted about one end and oscillating in a vertical plane is T2. Amplitude of

oscillations in both the cases is small. Then T1/T2 is :

(A) 4

3 (B) 1 (C)

3

2 (D)

1

3

15. Two particles are executing SHM in a straight line. Amplitude A and time period T of both the

particles are equal. At time t = 0, one particle is at displacement x1 = + A and the other at

2

Ax

2

and they are approaching towards each other. After what time they cross each other :

(A) T/3 (B) T/4 (C) 5T/6 (D) T/6

P

V

A B 1

2


16. Two masses M and m are suspended together by a massless spring of force constant k. When

the masses are in equilibrium, M is removed without disturbing the system. The amplitude of

oscillation is :

(A) Mg

k (B)

mg

k (C)

M m g

k

(D)

M m g

k

17. The angular frequency of a spring block system is 0. This system is suspended from the

ceiling of an elevator moving downwards with a constant speed v0. The block is at rest relative

to the elevator. Lift is suddenly stopped. Assuming the downward as a positive direction,

choose the wrong statement :

(A) The amplitude of the block is 0

0

v

(B) The initial phase of the block is

(C) The equation of motion for the block is 00

0

vsin t

(D) The maximum speed of the block is v0

18. A particle of mass 5×10–5

kg is placed at the lowest point of a smooth parabola having the

equation x2 = 40y(x, y in cm). If it is displaced slightly and it moves such that it is

constrained to move along the parabola, the angular frequency of oscillation will be,

approximately,

(A) 1s

–1 (B) 7s

–1 (C) 5s

–1 (D) None of these

19. A particle starts SHM at time t = 0. Its amplitude is A and angular frequency is . At time t = 0

its kinetic energy is E

4. Assuming potential energy to be zero at mean position, the

displacement-time equation of the particle can be written as (E = total mechanical energy of

oscillation) :

(A) x = A

2 cos (t + /6) (B) 2x = A sin (t +

3

)

(C) 3x = A sin 2

t3

(D) x = A cos (t - /6)

20. A light string is tied at one end to a fixed support and to a heavy string of equal length L at the

other end as shown in figure. A block of mass m is tied to the free end of heavy string. Mass

per unit length of the string are and 9 and the tension is T. Find the ratio of number of loops

n1 (In string of mass per unit length ) and n2 (In string of mass per unit length 9) such that

junction of two wire point A is a node.

(A) 1 : 2 (B) 1 : 3 (C) 1 : 4 (D) None of these

21. In the interference of waves from two sources of intensities I0 and 4I0, the intensity at a point

where the phase difference is is :

(A) I0 (B) 2I0 (C) 3I0 (D) 4I0


22. A uniform metal wire of density, cross-sectional area A and length L is stretched with a

tension T. The speed of transverse wave in the wire is given by :

(A) TL

A (B)

T

AL

(C)

T

A (D)

T

A

23. The power radiated by a black body is P, and it radiates maximum energy around the wavelength 0. If

the temperature of black body is now changed so that it radiates maximum energy around a

wavelength03

4

, the new power radiated by it will be

(A) 4

3P (B)

16

9P (C)

64

27P (D)

256.

81P

24. A traveling wave in a stretched string is described by the equation Y = A sin (kx - t). The

maximum velocity of any particle will be:

(A) At mean position (B) at extreme position

(C) Somewhere between extreme and mean (D) can‘t say

25. A transverse sinusoidal wave of amplitude a wavelength and frequency f is traveling on a

stretched string. The maximum speed at any point on the string is /10, where is the speed of

propagation of the wave. If a = 10–3

m and = 10 ms–1

, then and f are given by :

(A) = 2×10–2

m, f = 103/2 Hz (B) = 10

–2m, f = 10

3 Hz

(C) = 10–3

m, f = 104 Hz (D) = 10

–2/2 m, f = 2 ×

103 Hz

26. When two simple harmonic motions of same periods, same amplitude, having phase difference

of 3/2, and at right angles to each other are super imposed, the resultant wave form is a :

(A) circle (B) parabola (C) ellipse (D) None of these

27. A wave represented by the equation y = a cos (kx – t) is superposed with another wave to

form a stationary wave such that the point x = 0 is a node. The equation of the other wave is :

(A) y‘ = a sin (kx + t) (B) y‘ = – a cos (kx – t)

(C) y‘ = – a cos (kx + t) (D) y‘ = – a sin (kx – t)

28. Two travelling waves Y1 = A sin [k(x + ct)] and Y2 = A sin [k (x – ct)] are suspended on a

string. The distance between adjacent nodes is :

(A) ct/ (B) ct/2 (C) /2k (D) /k

29. If body A is placed in atmosphere of temperature 3T0, assume it follows Newton‘s law of

cooling & heating, then choose graph for TA – t (sec) Initial temp of A is T0.


30. Three moles of an ideal monatomic gas performs a cycle

1 2 3 4 1 as shown. The gas temperatures in different states are T1 = 400 K, T2 = 800 K, T3 = 2400 K and T4 = 1200 K. The work done by the gas during the cycle is

(a) 1200 R (b) 3600 R (c) 2400 R (d) 2000 R

Section – 1I Chemistry

(1) In the following carbocations, the stability order is:

(I) RCH2CH2 (II) C

CH3

CH3

(III) C (III) CH2

(A) III>II>IV>I (B) IV>I>II>III (C) IV>III>II>I (D) III>IV>II>I

(2) The correct order of nucleophilicity among the following is:

(I) CH3 C

O

O (II)CH3O

(III) CN (IV) CH3 S

O

O

O

(A) I>II>III>IV (B) IV>III>II>I (C) II>III>I>IV (D) III>II>I>IV

(3) Among the following structures

C2H5 CH C3H7

CH3

CH3CO CH C2H5

CH3

(I) (II)

H C

H

H

C2H5 CH C2H5

CH3

(III) (IV)

P

T

1

2 3

4

(A) T0

t

(B

) 2T0

t

3T0

(c)

T0

t

3T0

(D)

T0

t

3T0

T

T

T

T


It is true that (A) Only II and IV are chiral compounds (B) All four are chiral compounds (C) Only I and II are chiral compounds (D) Only III is a chiral compound

(4) An alkene on oxidation ozonolysis gives adipic acid. The alkene is (A) cyclohexene (B) 1-methylcyclopentene (C) 1, 2 – dimethylcyclobutene (D) 3-hexene (C) 1, 2 – dimethylcyclobutene (D) 3-hexene

(5) But-1-ene may be concerted to butane by reaction with (A) Pd/H2 (B) Zn/HCl (C) Sn/HCl (D) Zn-Hg

(6) Acetone will be formed by the ozonolysis of (A) but-1-ene (B) but-2-ene (C) iso butene (D) but-2-yne

(7) How many 1°carbon atom will be present in a simplest hydrocarbon having two 3° and one 2° carbon atom?

(A) 3 (B) 4 (C) 5 (D) 6

(8) IUPAC name of is: (A) 5-methyl hexanol (B) 2-methyl hexanol (C) 2-methyl hex-3-enol (D) 4-methyl pent-2-en-1-ol

(9) Which of the following compounds is optically active? (a) CH3CH2COOH (b) CH3CHOHCOOH (c) HOOC.CH2.COOH (d) CH3.CO.COOH

(10) Which of the following does not possess any element of symmetry? (a) ethane (b) (+) tartaric acid (c) carbon tetrachloride (d) meso tartaric acid

(11) Which of the following new man projection formula for 1, 2 - dichloro ethane represents the stable staggered from ?

(a)

Cl Cl

H

HH

H

(b)

ClCl H

H

H

H

(c)

ClClH

H

H

H

(d)

ClH

H

H

HCl

(12) Which of the following structure are super imposable?

(1)

H

Br

HO

Me

Me

Et

(2)

H

Br

OH

Me

Me

Et

(3)

H

Br

OH

Me

Me

Et

(4)

HBr

HO

Me

Et

Me (a) 3 and 4 (b) 1 and 3 (c) 2 and 4 (d) 2 and 3

(13) Which of the following structures are non superimpossable (Mirror Image)?

(1)

H

Br

HO

Me

Et

Me (2)

H

Br

OH

Me

Et

Me (3)

H

Br

OH

Me

Et Me

(4)

HBr

HO

Me

Et

Me (a) 1 and 2 (b) 2 and 4 (c) 1 and 4 (d) 1 and 3

(14) Among the following compounds, the decreasing order of reactivity towards electrophilic substitution is


CH3 OCH3

CF3

I II III IV (A) III > I > II > IV (B) IV > I > II > III

(C) II > I > IV > III (D) III > I > II > IV

(15) Arrange the following in correct activating order towards EAS

3 2 3 3(II)(I) (III) (IV)

O||

NR , NH , NHCOCH , O C CH

(A) II < I < III < IV (B) III < IV < II < I (C)I < IV < III < II (D) I < II < IV < III

(16) Which of the following species would be expected to exhibit aromatic character?

(I) (II) (III) (IV)

(A) I and IV (B) II and IV (C) I and III (D) II and III

(17) The product of reaction between one mole of acetylene and two mole of HCHO in the presence of Cu2Cl2 –

(A) HOCH2 C ≡ C – CH2OH (B) H2C = CH – C ≡ C – CH2OH

(C) HC ≡ C – CH2OH (D) None of these

(18) The reacting species of alc. KOH is –

(A) OH– (B) OR+ (C) OK+ (D) RO–

(19) B Lindlar

R–CC–R 3NH/Na

A A and B are geometrical isomers (R–CH=CH–R) – (A) A is trans, B is cis (B) A and B both are cis

(C) A and B both are trans (D) A is cis, B is trans

(20) A compound (C5H8) reacts with ammonical AgNO3 to give a white precipitate and reacts with excess

of KMnO4 solution to give (CH3)2CH–COOH. The compound is –

(A) CH2=CH–CH=CH–CH3 (B) (CH3)2CH–CCH

(C) CH3(CH2)2CCH (D) (CH3)2C=C=CH2

(21) CH3–CH2–CCH CH3CC–CH3

A and B are – (A) alcoholic KOH and NaNH2 (B) NaNH2 and alcoholic KOH

(C) NaNH2 and Lindlar (D) Lindlar and NaNH2

(22) B

OH/OH

THF/BH

22

3

OH3

A A and B are :

(A) Both (B) Both

(C) (D)

(23) Mixture of one mole each of ethyne and propyne on reaction with Na will form H2 gas at S.T.P. –


(A) 22.4 L (B) 11.2 L (C) 33.6 L (D) 44.8 L

(24) CHCH 22

4

ClCu

ClNH

product Product is – (A) Cu–CC–Cu (B) CH2=CH–CCH (C) CHC–Cu (D) Cu–CC–NH4

(25) 3

33

33

CH|

CHCCHCCH||CHCH

44 KMnO/NaIOproducts, Products are –

(A) 33CHCCH

||O

, (CH3)3C–COOH (B) 33

CHCCH||O

, (CH3)3C–CHO

(C) OHCCH

||O

3

, (CH3)3C–COOH (D) None is correct

(26) OH/NaOH/NaBH)2(

THF/OH/)OAc(Hg)1(

24

22

A is –

(A) (B) (C) (D)

(27) A mixture of CH4, C2H2 and C2H4 gaseous are passed through a Wolf bottle containing ammonical

cuprous chloride. The gas coming out is (A) Methane (B) Acetylene (C) Mixture of methane and ethylene (D) original mixture

(28) CH2=CH–CH=CH2 + CHCOOH||

CHCOOH

product X by reaction R. X and R are

(A) Diels Alder (B) Friedel-Crafts

(C) Diels Alder (D) Friedel-Crafts

(29) Ozone layer in the atmosphere depleted by (A) LPG (B) CFC (C) CNG (D) Acid rain

(30) The gas required for combustion is (A) Oxygen (B) nitrogen (C) carbon dioxide (D) hydrogen

Section – I1I Mathematics




IITJEE - JEE (Mains)

Physics

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

A B C B D C B B B C B D A C D A B B D B

21 22 23 24 25 26 27 28 29 30

A C D A A A C D C C

Chemistry

1.A 2.C 3.C 4.A 5.A 6.C 7.D

8.D 9.B 10.B 11.D 12.B 13.A 14.A

15.C 16.D 17.A 18.A 19.A 20.B 21.A

22.D 23.C 24.B 25.A 26.C 27.C 28.A

29.B 30.A

Mathematics 1. A 2. B 3. A 4. D 5. A 6. A 7. C 8. A 9. C 10. C 11. C 12. A 13. B 14. A 15. A 16. A 17. D 18. D 19. A 20.A 21. C 22. D 23. C 24. B 25. A 26. B 27. B 28. D 29. C 30. D



Time Allotted: 3 Hours Maximum Marks: 243


this purpose.


INSTRUCTIONS



I. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.



4. Each part is further divided into two sections: Section-A & Section-B

5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough

work.

6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form,

are not allowed.

J. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet.

2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No. and write in

ink your Name, Test Centre and other details at the designated places.



(i) Section-A (01 – 09) contains 9 multiple choice questions which have only one correct answer. Each question carries

+3 marks for correct answer and – 1 mark for wrong answer.

Section-A (10 – 13) contains 4 Assertion-Reasoning (multiple choice questions) which have only one correct answer.

Each question carries +3 marks for correct answer and – 1 mark for wrong answer.

Section-A (14 – 19) contains 2 paragraphs. Based upon paragraph, 3 multiple choice questions have to be answered.

Each question has only one correct answer and carries +4 marks for correct answer and – 1 mark for wrong answer.

(ii) Section-B (01-03) contains 3 Matrix Match Type question containing statements given in 2 columns. Statements in

the first column have to be matched with statements in the second column. Each question carries +6 marks for all

correct answer. For each correct row +1 mark will be awarded. There may be one or more than one correct choice.

No marks will be given for any wrong match in any question. There is no negative marking.






BA

TC

HE

S –

CT

Y-1

31

5 B

LO

T

FIITJEE COMMON TEST

CPT3 - 1

CODE: SET-A

PAPER - 1

PH-III




1. Two springs with negligible masses and force constant of

k1 = 200 Nm–1

and k2 = 160 Nm–1

are attached to the

block of mass m = 10 kg as shown in the figure. Initially

the block is at rest, at the equilibrium position in which

both springs are neither stretched nor compressed. At

time t = 0, sharp impulse of 50 Ns is given to the block

with a hammer along the spring.

m

frictionless

k1 k2

(A) Period of oscillations for the mass m is 6

s

(B) Maximum velocity of the mass m during its oscillation is 10 ms–1

(C) Data are insufficient to determine maximum velocity

(D) Amplitude of oscillation is 0.83 m

2. The string of a simple pendulum is replaced by a uniform rod of length L and mass M while

the bob has a mass m . It is allowed to make small oscillations . Its time period is

(A) 2

23

M L

m g

(B)

2 32

3 2

M m L

M m g

(C) 23

M m L

M m g

(D)

22

3 2

m M L

M m g

3. A sample of an ideal gas is taken through the cyclic process

ABCA shown in the figure. It rejects 50 J of heat during the part

AB, does not absorb or reject the heat during BC, and accepts

70 J of heat during CA. 40 J of work is done on the gas during

the part BC. The internal energies at B and C respectively will

be (UA = 1500 J)

P

V

C

B

A

(A) 1450 J and 1410 J (B) 1550 J and 1590 J

(C) 1450 J and 1490 J (D) 1550 J and 1510 J



4. A rod of mass M and length L is hinged at its centre of mass so that it can

rotate in a vertical plane. Two springs each of stiffness K are connected at its ends, as shown in the figure. The time period of SHM is

(A) M

26K

(B) M

23K

Hinge

L, M

(C) M

22K

(D)

M

2K

5. When an ideal gas is taken from state a to b, along a path acb,

84 kJ of heat flows into the gas and the gas does 32 kJ of work.

The following conclusions are drawn. Mark the one which is

not correct.

(A) if the workdone along the path adb is 10.5 kJ, the heat

that will flow into the gas is 62.5 kJ.

(B) when the gas is returned from b to a along the curved

path, the workdone on the gas is 21 kJ, and the system

absorbs 73 kJ of heat

p

v a d

b c

(pressure of the gas)

(volume of the gas)

(C) if Ua = 0, Ud = 42 kJ, and the workdone along the path adb is 10.5 kJ then the heat

absorbed in the process ad is 52.5 kJ

(D) if Ua = 0, Ud = 42 kJ, heat absorbed in the process db is 10 kJ

6. An artificial satellite is first taken to a height equal to half the radius of Earth. Let E1 be the

energy required. It is then given the appropriate orbital speed such that it goes in a circular

orbit at that height. Let E2 be the further energy required. The ratio 1

2

E

E is

(A) 4 : 1 (B) 3 : 1

(C) 1 : 1 (D) 1 : 2

7. An organ pipe closed at one end has a length 1 m and an open organ pipe has a length 1.6 m. The

speed of sound in air is 320 m/s. The two pipes can resonate for a sound of frequency

(A) 100 Hz (B) 240 Hz

(C) 320 Hz (D) 400 Hz



8. A wave disturbance in a medium is described by(select incorrect option)

y(x, t) = 0.02 cos (50 t + /2) cos (10 x), where ‗x‘ and ‗y‘ are in metre and ‗t‘ in seconds. (A) A node occurs at x = 0.15 m (B) An antinode occurs at x = 0.3 m (C) The speed of the component wave is 5.0 m/s (D) The wavelength is 0.1 m. 9. An organ pipe filled with oxygen gas at 47ºC resonates in its fundamental mode at a frequency of 300

Hz. If it is now filled with nitrogen gas, at which temperature will it resonate at the same frequency, in the fundamental mode ?

(A) 7ºC (B) 41.1°C

(C) 280ºC (D) 92.7°C

Reasoning Type

This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D),

out of which ONLY ONE is correct.

10. STATEMENT-1 : Compression and rarefaction involve changes is density and pressure.

STATEMENT-2 : When particles are compressed, density of medium increases and when they

are rarefied, density of medium decreases.

(A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for

Statement – 1.

(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation

for Statement – 1.

(C) Statement – 1 is True, Statement – 2 is False.

(D) Statement – 1 is False, Statement – 2 is True.

11. STATEMENT-1 : Coefficient of adiabatic elasticity of air is greater than the coefficient of

isothermal elasticity.

STATEMENT-2 : Heat is exchanged freely in an isothermal change, but not in an adiabatic

change.


Statement – 1.







12. STATEMENT-1 : If a man with a wrist watch on his hand falls from the top of a tower, its

watch gives correct time during the free fall.

STATEMENT-2 : The working of the wrist watch depends on spring action and it has nothing

to do with gravity.


Statement – 1.





13. STATEMENT-1 : Specific heat of a gas at constant pressure is greater than its specific heat at

constant volume.

STATEMENT-2 : At constant pressure, some heat is spent in expansion of the gas.


Statement – 1.







Paragraph Type

This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to

be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Questions 14 and 16

Figure shows a radiant energy spectrum graph for a black body at a temperature T0. E

T0

m


(A) the radiant energy is equally distributed among all the possible wavelengths

(B) for a particular wavelength the spectral intensity is minimum

(C) the area under the curve is equal to the total intensity (energy per unit area per second)

radiated by the body at that temperature

(D) none of these 15. If the temperature of the body is raised to a higher temperature T, then choose the correct statement

(A) the intensity of radiation for every wavelength decreases

(B) the maximum intensity occurs at a greater wavelength

(C) the area under the graph decreases

(D) the area under the graph is proportional to the fourth power of temperature

16. Identify the graph which correctly represents the spectral intensity versus wavelength graph at

two temperatures T and T0 (< T)

(A)

E

m

T

T0

(B)

E

T

’m

T0

m

(C)

E

T

’m

T0

mO

(D) none of these



Paragraph for Questions 17 and 19 One end of an ideal spring is fixed to a wall at origin O and axis of spring is parallel to x–axis. A block of mass m = 1 kg is attached to free end of the spring and it is performing SHM. Equation of position of the block in co–ordinate system shown in figure is x = 10 + 3 sin (10 t) where t is in second and x in cm. Another block of mass M = 3 kg, moving towards the origin with velocity 30 cm/s collides with the block performing SHM at t = 0 and gets stuck to it.

Om M

x

17. Angular frequency of oscillation after collision is

(A) 20 rad/s (B) 5 rad/s (C) 100 rad/s (D) 50 rad/s 18. New Amplitude of oscillation is (A) 3 cm (B) 20 cm

(C) 10 cm (D) 100 cm

19. New equation for position of the combined body is

(A) (10 + 3 sin 5 t) cm (B) (10 + 3 sin 5 t + π) cm

(C) (10 + 3 cos 10 t) cm (D) (10 – 3 cos 10 t) cm

SECTION–B

MatrixMatch Type This Section contains 3 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in q and r, then for the particular question, against statement B, darken the bubbles corresponding to q and r in the ORS.

p q r s

p q r s

p q r s

p q r s

A B C

D

p q r s t

t

t

t

t

1.

Column I Column II

(A) Temperature of a gas (P) Internal energy increases

(B) Work done by the gas (Q) Intermolecular force decreases

(C) Thermal expansion (R) Path function

(D) Mechanical compression (S) State function



2.

Column I Column II

(A) Surface tension (P) Decreases with temperature

(B) Elasticity (Q) Property of matter

(C) Force must be directed towards a fixed point (R) Uniform circular motion

(D) Projection of uniform circular motion on the

diameter of the circle (S) Simple harmonic motion

3.

Column I Column II

(A) In gravity free space (P) Stress

(B) Due to un–natural change in intermolecular

space (Q) Buoyant force is zero

(C) Buoyant force (R) Lies in the plane of liquid

surface

(D) Force due to surface tension (S) Always directed vertically up



PPAARRTTIIII:: CCHHEEMMIISSTTRRYY SECTION – A

Single Correct Choice Type This section contains 9 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D),


1. E1 follows

(A) 2nd

order kinetics (B) Concerted mechanism

(C) Regio selectivity (D) None of these

2. Number of hyperconjugating structures for

+

(A) 6 (B) 4 (C) 8 (D) 10

3. Which of the following molecule(s) show geometrical isomerism

(A) 3 3CH N NCH

(B) SF4(CHCH3)

(C) D

D

H

D

(D) Both (A) and (B)

4. Which of the following reaction predominantly follows markovnikov‘s rule

(A) HCl

(B) HCl

(C) Cl2

CCl4

(D) All of the above

5. 4KMnO

OHMajorproduct

(A)

COOH

(B)

(C)

CHO

(D) O


6. Cl

O

AlCl3Major Product


(A)

O

(B)

O

(C)

O

(D)

O

7. Cl

O

+AlCl3

Major Product

(A)

O

(B)

O

(C)

O

O

C

(D)

O



8. OH+/H2O

Major Product

(A)

OH

(B)

OH

(C)

OH

(D)

O

9. Which of the following is (are) aromatic?

(A)

O

(B)

O O

(C) Both (A) & (B) (D)

O



Reasoning Type



10. STATEMENT-1 : Furan can undergo addition reaction.

STATEMENT-2 : Furan is less aromatic.


Statement – 1.





11. STATEMENT-1 : Wurtz reaction is mainly for symmetrical alkane preparation.

STATEMENT-2 : Reaction involves radical mechanism.


Statement – 1.





12. STATEMENT-1 : Carbene can exist in three forms.

STATEMENT-2 : Triplet bent carbene is most stable out of all.


Statement – 1.





13. STATEMENT-1 : IUPAC name of the following is 1, 6-dimethylcyclohexene.

STATEMENT-2 : Double has more priority than triple bond always.


Statement – 1.







Paragraph Type





ArSE :

Step-1 : + E

E E

H+

Step-2 :

E

H+

BaseE

14.

SO3H

+ H2SO4 + H2O

Which of the following statement(s) is (are) true about sulphonation

(A) Shows isotopic effect (B) Electrophile of SO3

(C) Electrophile is [SO3H]+ (D) All

15. Arrange the following in decreasing order of reactivity towards ArSE

Cl CH2Cl NO

2NH

2

1 2 3 4 5

(A) 5 > 3 > 2 > 1 > 4 (B) 5 > 3 > 1 > 2 > 4

(C) 1 > 5 > 3 > 4 > 2 (D) 3 > 1 > 5 > 2 > 4



16. Cl2/Fe

Major Product

(A)

Cl

(B)

Cl

(C) Cl

(D)

Cl



Birch Reduction : This is one of the method to reduce double bonds of benzene. Triple bond can be

reduced to double bond.

Li or Na

Liq NH3

ROH

17. The intermediate formed in the following reaction is OMe

Li, Liq NH3

EtOH

(A)

OMe

(B)

OMe

(C)

OMe

(D)

OMe



18. Stereochemistry of product(s) formed in the below reaction

H

Na, Liq NH3

(A) Racemic mixture (B) Diasteriomeric pair

(C) Mesomer (D) Pure enantiomer

19. In which of the following birch reactions, major product is correctly written

(A) COOEt

COOEt

(B)

CHO

OMe OMe

CHO

(C)

OCOCH3

COCH3

OCOCH3

COCH3

(D) All



SSEECCTTIIOONNBB ((Matrix Match Type)

This section contains 3 questions. Each questions contains statements

given in two columns which have to be matched. Statements in Column-I

are labeled as A,B,C and D whereas statements in Column-II labeled as

p, q, r s, and t. The answers to these questions have to be appropriately

bubbled as illustrated in the following example. If the correct match are

A-p,s,t; B-q,r; C-p,q,t; and D-s, then the correctly bubbled 4×5 matrix

should be as follows.

A B C

D

p q r s t

1. Match the following.

Column-I

(Reactive Intermediate)

Column-II

(Effects operating)

(A)

(P) +I effect

(B)

(Q) Resonance

(C)

(R) Aromaticity

(D)

CH2

NO2

(S) -I effect

(T) Hyperconjugation


C H 3

C H 3 C H 3

C H 3

H C—C==C


2. Match the following

Column-I Column-II

(A)

CH3

CH3

H Br

H Br

Zn, CH3OH

(P) Rearrangement

(B)

CH3

CH3

H Br

Br H

NaI

acetone,

(Q) Antielimination

(C)

OH

CH3

CH3

Ph

Conc. H2SO4

(R) Stereospecific

(D)

Br

H

CH3

H

EtO Na+

EtOH,

(S) Stereoselective

(T) Reactive intermediate




Column-I

(Chemical Reaction)

Column-II

(Process involved)

(A

)

CH3—C CH

CH3—CH2—CHO

(P) Tautomerisation

(B)

CH

O

CH3—C

CH3—C—CH3

(Q) Oxo process

(C)

OH

(R) Oxymercuration –

demercuration reaction

(D

) 2 2 3 2CH CH CH CH CHO (S) Hydroboration oxidation

reaction

(T) Oxidation




SECTION – A




1. In any

1 1, ,

8 12

s a s bABC and

1

24

s c then b =

(A) 16 (B) 20

(C) 24 (D) 28

2. 2sin cosx x y y a has no value of x for any y if a belongs to

(A) (0, 3) (B) ( 3, 0) (C) ( , 3) (D) ( 3, )

3. The smallest + ve x satisfying the equation, cos sinlog sin log cos 2,x xx x is

(A) / 2 (B) / 3 (C) / 4 (D) / 6

4. In a triangle, the lengths of two larger sides are 10 and 9 respectively. If the angles are in A.P.,

then the third side can be

(A) 5 6 (B) 5 6 (C) 3 3 (D) 5

5. The letters of the word COCHIN are permuted of and all the permutations are arranged in an

alphabetical order as in an English dictionary. The number of words that appear before the

word COCHIN is

(A) 360 (B) 192 (C) 96 (D) 48

6. 23 23 23 23

0 2 4 22...C C C C equals

(A) 223

– 2 (B) 222

(C) 211

(D) 10 102 4

2

7. Angle subtended by common tangents of two ellipses 2 24( 4) 25 100x y and

2 24( 1) 4x y at origin is

(A)

3 (B)

4 (C)

6 (D)

2



8. There are exactly two points on the ellipse 2 2

2 21

x y

a b whose distance from its centre is the

same and is equal to 2 22

2

a b. Then the eccentricity of the ellipse is

(A) 1

2 (B)

1

2 (C)

1

3 (D)

1

3 2

9. If the normal to given hyperbola at the point

,c

ctt

meets the curve again at

,c

ctt

, then

(a) 3 1t t (b) 3 1t t (c) 1tt (d) 1tt

Reasoning Type



10. STATEMENT - 1 : Number of solution of equation cos2 | sin x |, ,2 2

is ‗4‘

x[–2 2].

STATEMENT - 2 : It is true only for |sin x| = 1 or sin x = ± 1


Statement – 1.





11. STATEMENT – 1 : If 2 2

2 2

x y1

a b be the equation of hyperbola then 0(0, 0) lies outside the

hyperbola

STATEMENT – 2 : S(x, y) = 0 represents a hyperbola, if S(x1, y1) > 0 then (x1, y1) lies inside

the hyperbola


Statement – 1.







12. STATEMENT – 1 : Three consecutive binomial coefficients are always in A.P

STATEMENT – 2 : Three consecutive binomial coefficients are not in H.P. or G.P.


Statement – 1.





13. STATEMENT – 1 : m m n m n n

r r 1 1 r 2 2 rC C . C C . C ........ C 0

, if m + n < r.

STATEMENT - 2 : nCr = 0 if n < r


Statement – 1.





Paragraph Type




H: x2 – y

2 = 9, P: y

2 = 4(x – 5), L: x = 9.

14. If L is the chord of contact of the hyperbola H, then the equation of the corresponding pair of

tangents is

(A) 9x2 – 8y

2 + 18x – 9 = 0 (B) 9x

2 + 8y

2 – 18x + 9 = 0

(C) 9x2 – 8y

2 – 18x – 9 = 0 (D) 9x

2 – 8y

2 + 18x + 9 = 0

15. If R is the point of intersection of the tangents to H at the extremities of the chord L, then

equation of the chord of contact of R with respective to the parabola P is

(A) x = 7 (B) x = 9 (C) y = 7 (D) y = 9

16. If the chord of contact of R with respect to the parabola P meets the parabola at T and T, S is

the focus of the parabola, then Area of the triangle STT is equal to

(A) 8 sq. units (B) 9 sq. units (C) 12 sq. units (D) 16 sq. units




The integers a, b and c are selected from 3n consecutive integers {1, 2, 3, …, 3n}, then in how many

ways can these integers be selected, such that

17. Their sum is divisible by 3?

(A) 2(3 3 2)2

nn n (B) 23 3 2n n (C)

2

n (D) None of these

18. 2 2( )a b is divisible by 3 ?

(A)

2 ( 1)

2

n nn (B)

2 ( 1)

2

n nn (C)

3 ( 1)2

2

n nn (D) None of these

19. 3 3( )a b is divisible by 3 ?

(A) 23

2

n n (B)

23

2

n n (C)

( 1)

2

n n (D) None of these

SECTION–B

MatrixMatch Type

This Section contains 3 questions. Each question has four statements (A, B, C

and D) given in Column I and five statements (p, q, r, s and t) in Column II.

Any given statement in Column I can have correct matching with ONE or

MORE statement(s) given in Column II. For example, if for a given question,

statement B matches with the statements given in q and r, then for the particular

question, against statement B, darken the bubbles corresponding to q and r in

the ORS.

p q r s

p q r s

p q r s

p q r s

A B C

D

p q r s t

t

t

t

t

1. Match following column.

Column-I Column-II

(A)

cot2

A b c

a (P) Always right angled

(B)

tan tan ( ) tan2

A Ba A b B a b (Q) Always isosceles

(C) cos cosa A b B (R) May be right angled

(D) sin

cos2sin

BA

C (S) May be right angled isosceles




Column I Column II

(A

) Number of distinct terms in the expansion of (x + y z)

16

(P) 212

(B) Number of terms in the expansion of

2 6 2 6(x x 1) (x x 1) (Q) 97

(C) The number of irrational terms in 10068( 5 2) (R) 4

(D

)

The sum of numerical coefficients in the expansion of

12x 2y

13 3

(S) 153

(T) 1


Column-I (Equation) Column-II (Solution)

(A) 2 2cos 2 cos 1x x (P)

4 6x n n n Z

(B) cos 3 sin 3x x (Q)

,3

nx n Z

(C) 21 3 tan 1 3 tanx x (R)

2 1 ,6

x n n Z

(D) tan3 tan2 tan 0x x x (S)

2 2 ,

2 6x n n n Z



FIITJEE COMMON TEST


PHASE TEST-III (PAPER-1)

ANSWER KEY


SECTION–A 1. D 2. B 3. C 4. A 5. B 6. C 7. D 8. D 9. A 10. A 11. B

12. A

13. A

14. C

15. D

16. B

17. B

18. A

19. B

SECTION–B

1. A-S; B-R; C-Q; D-P

2. A-PQ, B-PQ, C-RS, D-S

3. A-Q; B-P; C-S; D-R

SECTION–A 1. C 2. C 3. A 4. B 5. A 6. B 7. B 8. A 9. C 10. A 11. B

12. B

13. C

14. D

15. B

16. D

17. A

18. C

19. D

SECTION–B

1.A-QR; B-PQT; C-QR; D-QRS

2.A-QRS; B-QRS; C-PT, D-

QRS

3.A-PST; B-PRT; C-RT;S-QT

SECTION-A

1. A

2. D

3. C

4. A

5. C

6. B

7. D

8. B

9. B

10. A

11. C

12. D

13. A

14. B

15. B

16. C

17. A

18. C

19. BB

SSEECCTTIIOONNBB 1. A-p,r; B-q,r; C-r,s; D-q,r,s

2. A – s, B – r, C – q, D – p

3. A-r; B-s; C-p; D-q

Paper Code

SET-A




Maximum Marks: 243


this purpose.


INSTRUCTIONS



K. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.



4. Each part is further divided into three sections: Section-A, Section-B & Section-C

5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough

work.

6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form,

are not allowed.

L. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet.

2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No. and write in

ink your Name, Test Centre and other details at the designated places.



(i) Section-A (01 – 08) contains 8 multiple choice questions which have only one correct answer. Each question carries


Section-A (09 – 12) contains 4 multiple choice questions which have one or more than one correct


Section-A (13 – 17) contains 2 paragraphs. Based upon paragraph, 3 and 2 multiple choice

questions have to be answered. Each question has only one correct answer and carries


(ii) Section-B (01) contains 1 Matrix Match Type question containing statements given in 2 columns. Statements in the

first column have to be matched with statements in the second column. Each question carries +6 marks for all correct

answer. For each correct row +1 mark will be awarded. There may be one or more than one correct choice. No marks

will be given for any wrong match in any question. There is no negative marking.

(iii) Section-C (01 – 05) contains 5 Numerical based questions with single digit integer as answer, ranging from 0 to 9 and

each question carries +3 marks for correct answer. There is no negative marking.





BA

TC

HE

S –

CT

Y 1

31

5 B

LO

T

FIITJEE COMMON TEST

CPT3 - 2

CODE:SETA

PAPER - 2

PH-III





1. A large number of liquid drops each of radius r coalesce to form a single drop of radius R. The

energy released in the process is converted into the kinetic energy of the big drop so formed.

Assuming that all the particles of the big drop move with the same speed v, this speed is given

by (given surface tension of liquid is T, density of liquid is )

(A) 6 1 1T

r R

(B)

4 1 1T

r R

(C)

6 1 1T

r R

(D)

4 1 1T

r R

2. Which of the following will have a different time period, if taken to the moon ?

(A) A simple pendulum.

(B) A spring mass system oscillating vertically in the gravitational field.

(C) A torsion pendulum.

(D) None of these 3. A wave is represented by the equation :

1 1y (1mm)sin 50s t (2.0m )x

+ 1 1(1mm)cos 50s t (2.0m )x

(A) The wave–velocity is zero, since it is a standing wave.

(B) A node is formed at 3

8x m

.

(C) The amplitude of the oscillation at the antinode is 3 mm.

(D) Energy transfer occurs along the positive x–axis.

4. A solid sphere of mass m is lying at rest on a rough horizontal

surface. The coefficient of friction between ground and sphere is

. The maximum value of F, so that sphere will not slip, is equal to

(A) 7

mg5 (B)

4mg

7 (C)

5mg

7 (D)

7mg

2

F

5. Two constant forces 21 FandF

acts on a body of mass 8 kg. These forces displaces the body

from point P(1, –2, 3) to Q(2, 3, 7) in 2s starting from rest. Force 1F

is of magnitude 9 N and is

acting along vector )ˆˆ2ˆ2( kji . Work done by the force 2F

is

(A) 80 J (B) –80 J (C) –180 J (D) None of these


6. A particle is dropped from a height equal to the radius of the earth

above the tunnel dug through the earth as shown in the figure. R : Radius of earth. M : Mass of earth. (A) Particle will oscillate through the earth to a height R on both

sides (B) Particle will execute simple harmonic motion (C) Motion of the particle is non periodic

(D) Particle passes the centre of earth with a speed = 2R

GM2

R

C

7. A point moves such that its displacement as a function of time is given by x

3 = t

3 + 1. Its acceleration as

a function of time t will be


(A) 5

2

x (B)

5

2t

x

(C) 4

2t

x (D)

2

5

2t

x

8. The moment of inertia of a rod about an axis through its centre and perpendicular to it is

2

12

ML (where

M is the mass and L, the length of the rod). The rod is bent in the middle so that the each halves make an angle of 30º with that axis. The moment of inertia of the bent rod about the same axis would be (The axis lies in the plane of structure)

(A)

2ML

96 (B)

2ML

48

(C)

2ML

12 (D)

2ML

8 3



9. A sound wave is traveling along positive x-direction.

Displacement (y) of particles from their mean positions at any time t is shown in the figure. (A) Particle located at S has zero velocity. (B) Particle located at T has its velocity in the negative direction. (C) Change in pressure at S is zero

Q R S T xP

Y

(D) Particles located near R are under compression.



10. During an experiment, an ideal gas is found to obey a condition 2P

= constant [ = density of

the gas]. The gas is initially at temperature T, pressure P and density . The gas expands

such that density changes to /2.

(A) The pressure of the gas changes to 2 P .

(B) The temperature of the gas changes to 2 T .

(C) The graph of the above process on the P–T diagram is parabola. (D) The graph of the above process on the P–T diagram is hyperbola.

11. 90 calories of heat are required to raise the temperature of 1 mole of CO2 gas at constant

pressure from 30°C to 35°C. Then (the symbols have usual meanings)

(A)

U

Q =

7

9 (B) U = 70 Cal (C) W = 20 Cal

(D) 2

9

W

Q

12. A body of mass 5 kg is suspended by the strings making

angles 60 and 30 with the horizontal as shown in figure (g = 10 m/s2)

(A) NT 251 (B) NT 252

(C) NT 3251 (D) NT 3252 30

o60o

T2

T1

5kg

(Comprehension Type)

This section contains 2 paragraphs. Based upon one of the paragraphs 2 multiple choice questions

and based on the other paragraph 3 multiple choice questions have to be answered. Each of these

questions has four choices (A), (B), (C) and (D) out of WHICH ONLY ONE is correct.


A narrow tube is bent in the form of a circle of radius R, as shown

in the figure. Two small holes S and D are made in the tube at the

positions right angle to each other. A source placed at S generates

a wave of intensity I0 which is equally divided into two parts: one

part travels along the longer path, while the other travels along the

shorter path. Both the part waves meet at the point D where a

detector is placed.

S

D

R



13. If a maxima is formed at a detector then, the magnitude of wavelength of the wave produced

is given by : (Select wrong option)

(A) R (B) R

2

(C) R

4

(D)

R

3

14. If a minima is formed at the detector then, the magnitude of wavelength of the wave

produced is given by

(A) R2 (B) R2

3

(C) 2 R

3 (D)

2 R

5

15. The maximum intensity produced at D is given by

(A) 4I0 (B) 2I0

(C) I0 (D) 3I0


The figure shows the variation of internal energy (U) of a

2 moles of Argon gas with its density in a cyclic process

ABCA. The gas was initially in the state A whose pressure

and temperature are PA = 2 atm TA = 300 K respectively. It

is also stated that the path AB is a rectangular hyperbola

and the internal energy of the gas at state C is 3000 R.

Based on the above information answer the following

questions.

BC

A

3000 R

U(Joule)

kg/m-3

16. Select the best option (A) The process AB is isobaric, BC is adiabatic and CA is isochoric. (B) The process AB is adiabatic, BC is isothermal and CA is isochoric. (C) The process AB is isochoric, BC is isothermal and CA is isobaric (D) The process AB is isobaric, BC is isothermal and CA is isochoric. 17. The Heat supplied to the gas in the process AB is (A) 700 R (B) 3500 R (C) 4400 R (D) 1600 R



SECTION–B

MatrixMatch Type This Section contains 1 question. Each question has four statements (A, B, C

and D) given in Column I and four statements (p, q, r and s ) in Column II.




question, against statement B, darken the bubbles corresponding to q and r in the

ORS.

p q r s

p q r s

p q r s

p q r s

A B C

D

p q r s


Column A Column B

(A) Latent Heat (P) 1 0 3 4ML T

(B) Thermal Conductivity (Q) 0 2 2M L T (C) Molar Specific Heat (R) 1 1 3 1MLT

(D) Stefan‘s Constant (S) 1 2 2 1ML T

SECTIONC

Integer Answer Type

This section contains 5 questions. The answer to each question is a single digit integer, ranging from

0 to 9 (both inclusive).

1. A ball is dropped from height 5m. Find the time (in seconds) after which ball stops

rebounding if coefficient of restitution between ball and ground is e = ½

2. Force acting on a body of mass 1 kg is related to its position x as F = (x3 – 3x) N. It is at

rest at x = 1. Find its velocity(m/s) at x = 3 .

3. A large tank is filled with water to a height H. A small hole is made at the base of the tank.

It takes T1 time to decrease the height of water to H

, ( > 1) and it takes T2 time to take out the

rest of water. If T1 = T2 , then the value of is ?



4. Two identical smooth balls are projected from points O

and A on the horizontal ground with same speed of

projection. The angle of projection in each case is 30º

(see figure). The distance between O and A is 100 m.

The balls collide in mid air and return to their

respective points of projection. The coefficient of

restitution is 0.7, if the speed of projection of either

ball (in m/s) correct to nearest integer is v then v/19

equals (Take g = 10 ms–2

and 3 = 1.7)

y

O

u

Ax30º 30º

u

5. A particle of mass m is fired from the point A (as shown in the figure) situated at a distance of 2R from the center of the planet with a

velocity 1

2 times the escape velocity from point A. The radius of the

planet is R. The maximum distance of the particle from the centre in the subsequent motion is nR. Find the value of n.

30°

R

R

A



PPAARRTTIIII:: CCHHEEMMIISSTTRRYY

SECTION – A

Single Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D),


1.

O

OH

H+/Major Product

(A)

O

(B)

O

(C)

O

(D) O

A

2.

O

D2O / D+

(A)

CD3

O

(B) CD

3CD

3

OD

(C) CD3

CD3

O

D

(D) CD3

CD3

O

D

D



3. Arrange in decreasing following order of basic strength

(i) N

H

(ii) N

N

H

(iii)

N

(iv) N

H

(v) N—HN

(A) iv > v > ii > iii > i (B) v > iv > ii > iii > i (C) i > ii > iii > iv > v (D) v > iv > iii > ii > i

4. A metal oxide Z2O3 can be reduced by hydrogen to give free metal and water. 0.1596 gm metal

oxide requires 6 mg hydrogen. Then the atomic weight of metal is

(A) 27.9 (B) 159.6 (C) 79.8 (D) 55.8

5. 1 eq. H2

ptA

H+B

1. Hg(OAc)2

2. NaBH4/EtOHProduct(s)

OH

OH

+

A and B are

(A) NOT isomers (B) Diastereomers (C) Mesomers (D) Ring Chain isomers

6. When system undergoes irreversible expansion from 2L to 5L at 270C and the process is

reversible. Then Suniverse is

(A) 15.63 J/2 moles (B) 7.8175J/2 moles (C) 0 (D) 31.27 J/ 2 moles

7. In which of the following pairs, first is not more aromatic than second

(A) ;

(B) ;

(C) N

H

N—H;

(D) All

8. Why iodine is violet in order?

(A) Transition of e– from * and * (B) Transition of e

– from and *

(C) Transition of e– from * and * (D) Transition of e

– from and *





9. Which of the following pair has same net dipole moment

(A) F

F

F

,

(B) ,

(C) F

F

FF

F

,

(D) ,

10. Correct statement(s) is (are) for aqueous solution of borax

(A) Acts as buffer

(B) Needs 2 mole of HCl for 1 mole solution for complete reaction

(C) Can be used as primary standard

(D) Solution is basic in nature

11. Gypsum on heating change to

(A) Orthorhombic form (B) Plaster of paris

(C) Dead plaster (D) CaO

12. Oxidation state of Tl in TlI3

(A) +I (B) +II (C) +III (D) O






questions has four choices (A), (B), (C) and (D) out of WHICH ONLY ONE is correct.


Ionic product of water increases with increase in temperature. pH and pOH of water

depend on the temperature while calculating the pH of very dilute solution of acids and bases the

hydronium ions formed by dissociation of water have also be taken into consideration. Some solution

resists to change in pH of addition of small amount of acids and bases are called buffer solution.

Aqueous solution of salts may be acidic, basic, neutral depends on the salts (composition of salt

forming component). Some salt like AgCl has little solubility in the water, therefore solubility product

(Ksp) of this salt has low value. Solubility product (Ksp) is important data to determine the solubility of

sparingly soluble salt, this depends on the temperature.

Choose the correct answer

13. The average concentration of CO2 in the atmosphere over a city on a certain day was 20 ppm at

300 K. If the solubility of CO2 in water at 300 K was 3.53 mole/litre. The pH of solution

obtained by mixing one litre of rain water with one litre of 3 × 10–5

M NaOH on that day

(given 1aK for H2CO3 = 4.45 × 10

–7)

(A) 5.30 (B) 4.28 (C) 6.22 (D) 3.02

14. How much solid Na2S2O3 in moles should be added to 1 litre of water so that 5 × 10–4

mol

Cd(OH2) would just barely dissolve, Ksp of Cd(OH)2 = 4.5 × 10–15

, assume 2

2 3S O does not

hydrolyse?

Given 2 2 3

2 3 2 3 1Cd S O Cd(S O ), K 8.3 10

2 2 2

2 3 2 3 2 3 2 2Cd(S O ) S O [Cd(S O ) ] , K 2.5 10

(A) 0.543 (B) 0.834 (C) 0.231 (D) 0.153

15. A buffer solution is prepared which is 0.5 M CH3COOH and 0.25 M CH3COONa. Which of

the following ions can be maintained at a concentration of 0.10 M or greater without

precipitating as the hydroxide from this solution?

Given Ksp Mg(OH)2 = 5.5 × 10–6

, Ksp Al(OH)3 = 1.3 × 10–33

, Ksp Fe(OH)3 = 6.3 × 10–31

, Ka for

CH3COOH = 1.8 × 10–5

.

(A) Mg2+

(B) Fe3+

(C) Al3+

(D) All ions will be precipitated





NBSA

LDAB

HBr

(1 eq)

C + D

E

F

O3/S(CH3)2

C2H4

16. F is

(A) O

O

H

(B)

O O

(C)

O

O

(D) H

O

O

H

17. C and D are

(A) Stereoisomers (B) Position isomers (C) Chain isomers (D) Not isomers



SSEECCTTIIOONNBB ((Matrix Match Type)

This Section contains 1 question. Each question has four statements (A, B, C






ORS.

p q r s

p q r s

p q r s

p q r s

A B C

D

p q r s


Column-I

(Reaction)

Column-II

(Intermediate)

(A

) Cl

+ Cl2hv

(P) Cyclic transition state

(B) Br

Br

+ Br2

(Q) Carbocation

(C)

OH

+ H2OH+

(R) Free radicals

(D

)

Br

alc. KOH

(S) Rearrangement



SSEECCTTIIOONNCC

Integer Answer Type



1. How many of the following reagent can be used to distinguish terminal alkynel from alkenes

Br2 water, Bayer‘s reagent, Tollen‘s reagent, Na Metal, CuCl2 + NH4OH, Conc. KMnO4/OH–,

Cl2 water, Lindlar catalyst, ozonolysis

2. How many stereo isomer are produced in the following reaction

H

H

H

HBr

O2/pt2D /pt

3. How many of metals will liberate H2 on reaction with NaOH

Al, Zn, Be, Si, Cu, Mg, Na, Pb, Sn

4. In cyclooctatetraene how many bonds are in conjugation?

5. How many of the following cis forms are stable over trans


F F

C O O H

H H

H O O C

C H 3

H H

C H 3

N==N , C==C

C==C






1. If in the expression of (1 + x)m

(1 – x)n, the coefficient of x and x

2 are 3 and – 6 respectively,

then m is

(A) 6 (B) 9 (C) 12 (D) 24

2. If P(-3, 2) is one end of the focal chord PQ of the parabola y2 + 4x + 4y = 0, then the slope of

the normal at Q is

(A) 1/2 (B) 2 (C) 1/2 (D) –2

3. Tangents are drawn to 3x2 2y

2 = 6 from a point P. If these tangents intersect the coordinate

axes at concyclic points then the locus of P is

(A) x2 + y

2 = 5 (B) x

2 y

2 = 5 (C)

2 2

1 1 1

5x y (D) none of these

4. Given b = 2, c = 3 , A = 300, then the in-radius of ABC is

(A) 3 1

2

(B)

3 1

2

(C)

3 1

4

(D) none of these

5. If z1, z2, z3 be three non-zero complex numbers, such that z2 z1, a = |z1|, b = |z2| and c = |z3|

and

a b c

b c a 0

c a b

, then 3

2

zarg

z

may equal to

(A) 2 1

3 1

z zarg

z z

(B)

2

3 1

2 1

z zarg

z z

(C)

2

2 1

3 1

z zarg

z z

(D) none of these

6. If a sin x + b cos (x + ) + b cos (x ) = d, then the minimum value of |cos | is equal to

(A) 2 21d a

2 | b | (B) 2 21

d a2 | a |

(C) 2 21

d a2 | d |

(D) none of these



7. If tangents PQ and PR are drawn from a point on the circle x2 + y

2 = 25 to the ellipse

22

2

yx1

16 b , (b < 4) so that the fourth vertex S of parallelogram PQSR lies on the circumcircle

of PQR, then eccentricity of the ellipse (Q and R are on the circle) is

(A) 5 /4 (B) 7 /3 (C) 7 /4 (D) 5 /3

8. The maximum value of (sec-1

x)2 + (cosec

-1x)

2 is equal to

(A) 2

2 (B)

254

(C) 2 (D) None of these



9. Which of the following equation in parametric form can represent a hyperbola, where t is a

parameter

(A) a 1 b 1

x t & y t2 t 2 t

(B)

tx y x tyt 0 & 1 0

a b a b

(C) t t t tx e e & y e e (D) 2 2 2x 6 2cost & y 2 4cos t / 2

10. There exists a triangle satisfying

(A) bsinA a,A2

(B) bsinA a,A

2

(C) bsinA a,A2

(D) bsinA a,A ,b a

2

11. For an increasing A.P. 1 2 na ,a ,......,a if 1 3 5a a a 12 and 1 3 5a a a 80, then which of the

following is/are true?

(A) 1a 10 (B) 2a 1 (C) 3a 4 (D) 5a 2

12. If the equation 0349 22 xyx is satisfied for real values of x & y, then

(A) 31 x (B) 32 x (C) 13

1 x (D)

3

1

3

1 y






questions has four choices A), B), C) and (D) out of WHICH ONLY ONE is correct.


Consider an ellipse (E) 2 2

2 2

x y1

a b , centered at point ‗O‘ and having AB and CD as its major and minor

axes respectively, if S1 be one of the foci of the ellipse, radius of incircle of 1

OCS , be 1 unit and OS1

= 6 units then

13. The area of ellipse (E) is

(A) 65

4

sq unit (B)

64

5

sq unit (C) 64 sq unit (D) 65 sq unit

14. Perimeter of 1

OCS is

(A) 20 unit (B) 10 unit (C) 15 unit (D) 25 unit

15. If S be the director circle of ellipse (E), then the equation of director circle of S is

(A) x2 + y

2 = (48.5) (B) 2 2x y 97 (C) x

2 + y

2 = 97 (D) 2 2x y 48.5


If p1, p2, p3 are altitudes of a triangle ABC from the vertices A, B, C respectively and is the

area of the triangle and s is semi perimeter of the triangle.

16. If 1 2 3

1 1 1 1

2p p p then the least value of p1p2p3 is

(A) 8 (B) 27 (C) 125 (D) 216

17. The value of 1 2 3

cos cos cosA B C

p p p is

(A) 1

r (B)

1

R (C)

2 2 2

2

a b c

R

(D)

1



SECTION–B

MatrixMatch Type

This Section contains 1 question. Each question has four statements (A, B, C






ORS.

p q r s

p q r s

p q r s

p q r s

A B C

D

p q r s

1. Consider the word ―HONOLULU‖ for question no 1

Column I Column II

(A

)

Number of words that can be formed using the letters of the

given word in which consonants and vowels are alternate is (P) 26

(B)

Number of words that can be formed without changing the

order of vowels is

(Q

) 144

(C)

Number of ways in which 4 letters can be selected form the

letters of the given word is (R) 840

(D

)

Number of words in which two O‘ s are together but U‘s are

separated (S) 900

SECTIONC

Integer Answer Type



1. If twice the square of the diameter of a circle is equal to the sum of the squares of the sides

of the inscribed triangle ABC, then sin2A + sin

2B + sin

2C is equal to _______ .

2. If the sides of a triangle are determined by throwing a triplet of dice then the number of

different triangles with all distinct sides is ________ .

3. If the curves ax2 + 4xy + 2y

2 + x + y + 5 = 0 and ax

2 + 6xy + 5y

2 + 2x + 3y + 8 = 0 intersect at

four concyclic points, then value of |a| equals to ________ .

4. The number of real solutions of 1 1 2tan x(x 1) sin x x 12

is ______ .

5. Number of triangles formed by the lines represented by x3 x

2 x 2 = 0

and x y2 + 2 x y + 4 x 2 y

2 4 y 8 = 0 is ______ .



FIITJEE COMMON TEST


PHASE TEST-III (PAPER-2)

ANSWER KEY


SECTION–A

1. A

2. A

3. B

4. D

5. D

6. A

7. B

8. B

9. ABCD

10. BD

11. ABCD

12. AD

13. D

14. B

15. B

16. D

17. B

SECTION–B

1. A-Q; B-R; C-s; D-P

SECTION–C

1. 3

2. 4

3. 4

4. 2

5. 3

SSEECCTTIIOONNAA 1. A

2. C

3. B

4. D 5. D 6. C

7. B

8. A

9. AC 10. ABCD 11. ABCD 12. A 13. D

14. B

15. A

16. C

17. B

SSEECCTTIIOONNBB

1. A-R; B-P; C-Q; D-QS

SSEECCTTIIOONNCC

1. 3

2. 4 3. 6 4. 0 5. 3

SECTION-A

1. C

2. A

3. B

4. A

5. B

6. A

7. C

8. B

9. ACD

10. AD

11. AC

12. AD

13. A

14. C

15. C

16. D

17. B

SECTION-B

1. A-Q; B-R; C-P; D-s

SECTION-C

1. 2

2. 7

3. 4

4. 2

5. 0

Paper Code

SET-A

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