AIITS-1, PT4 PAPER-set-A.pdf

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com

PHYSICS, CHEMISTRY & MATHEMATICS SET A

Time Allotted: 3 Hours

Maximum Marks: 180

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 Sections.

3. Section-1 is Physics, Section-2 is Chemistry and Section-3 is Mathematics.

4. Each section has one part: Part-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.

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

question carries +3 marks for correct answer and 1 mark for wrong answer. Part-A (09 16) contains 4 paragraphs with 2 questions based on each paragraph. Each question

has only one correct answer and each question carries +3 marks for correct answer and 1 mark for wrong answer.

Part-A (17 20) contains 4 multiple choice questions which have one or more than one correct

answer. Each question carries +3 marks for correct answer. There is no negative marking.

Name of the Candidate :____________________________________________

Batch :____________________ Date of Examination :___________________

Enrolment Number :_______________________________________________

FIITJEE - JEE (Advance)

APT - 4

CODE: 080053.1

AIiTS - 1

AIiTS-PT-I-(Paper-1)-SET-A-CMP-IITJEE/13

2

SECTION 1 (Physics) PART A

(Single Correct Choice Type) 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. Three small spheres A, B and C of masses 1kg, 2kg and

3kg are rotating with a circular disc with angular velocity 3 radian/sec and are connected with strings to O as shown in figure. Coefficient of friction between spheres A, B, C and disc is 0.4, 0.3 and 0.2 respectively.

(A) Friction force acting on sphere B is 6 N. (B) Tension in the string connecting sphere A and B is 9 N (C) Tension in the string connecting sphere C and O is 8 N (D) Data insufficient

A

B O

C

50cm

50cm

100cm

=3 rad/sec

2. Two blocks connected with the spring of force constant

100 N/m are given velocities 4i m/s and 3i m/s when the spring is in natural length as shown in figure

2kg 5kg

4 m/s 3 m/s

(A) The velocity of 2kg block is maximum when 5 kg block is at instantaneous rest.

(B) The maximum and minimum velocities of 2kg block is 7i m/s and 3i m/s respectively. (C) The maximum and minimum velocities of 5kg block is 4 m/s and zero respectively. (D) All of the above 3. Two objects were projected simultaneously from the top of hills. One from (0, 0, 0)m, with velocity

15i 4j 3k m/s and the other from (15, 0, 0) m with speed 13 m/s. If the two object collides in

mid air. Then which of the following is incorrect (consider acceleration due to gravity in negative z-direction)

(A) The velocity of other object is 12i 4j 3k m/s.

(B) The time after which collision occur is 5 seconds.

(C) The coordinates of point of collision is (75, 20, 110) m (D) None of the above

Space for Rough work



3

4. A block of mass 2kg starts moving at t = 0

with speed 2m/s on a smooth horizontal surface. A horizontal force F is applied in the direction of velocity which varies with time shown in figure (b) the speed of particle at t = 3 seconds (g = 10 m/s

2)

2kg 2m/s

(a)

F

2N

O t (sec) 1 2 3

(b) (A) 2.5 m/s (B) 3.5 m/s (C) 4.5 m/s (D) none of these 5. A conducting sphere of radius r is carrying a charge Q on its outer

surface. Its inner surface is connected to the ground by means of a wire of resistance R and a switch K as shown in the figure. When the switch k is closed the quantity of charge flowing to the ground equals

(A) Q (B) -Q (C) zero (D) -Q/2

k

r Q

R

6. In the figure, two point charges +q and q are placed on the x-

axis at (+a, 0) and (-a, 0) respectively. A tiny dipole of dipole moment (p) is kept at the origin along the y-axis. The torque on the dipole equals

(A) zero (B) 2

0

qp

2 a

(C) 2

0

qp

4 a (D)

20

qp

a

P

O -q (-a, 0) +q (a, 0) x

y

7. In the figure, a square loop of side a and resistance R is moving in a

uniform and constant magnetic field B with constant velocity V. The induced emf in the loop is equal to

(A) zero (B) Bav

(C) 1

2Bav (D) none of the above.

A B

D C

x x x

x x x

x x x

x x x

x

x

x

x

x

x

x x x

V

B



4

8. In the figure shown current in the long straight wire varies as

I = I0 0

0

t t

t

where Io is the initial current. The charge flown through

resistance R in time t0 is

(A) 0 0bI

2 R

(B) 0 0

I bln

2 R a

(C) 0 0I a b

ln2 R a

(D) 0 0

aI bln

2 R

b

a R

I

(Paragraph Type)

This section contains 4 paragraphs. Based upon each paragraph 2 multiple choice questions have to be answered. Each of these questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Paragraph for Questions 9 and 10

A driver moving on road ABC applies brakes so as to ensure constant retardation throughout its motion. His speed is 27 m/s at the bottom (at A) and 13 m/s at the top (at C). The distance of C from A along ABC is 80 m. The passenger experiences a total acceleration of 4.5 m/s

2 at A

and radius of curvature at C is 130 m. DBE is a straight line

( 8 2.83, 13.94 3.7 )

A D

B

E

C

9. The radius of curvature at A is (A) 257.6 m (B) 247.6 m (C) 208.3 m (D) 200.3 m 10. Magnitude of total acceleration at B is (A) 3.5 m/s

2 (B) 3 m/s

2

(C) 4.5 m/s2 (D) 3.7 m/s

2




5


If the forces are conservative and potential energy is U then we can find force (F) from potential energy U

as dU

Fdr

. If potential energy of a body is minimum at equilibrium then this type of equilibrium is known

as stable equilibrium. When potential energy of the body is constant then equilibrium is called as neutral and when potential energy becomes maximum at equilibrium it is called as unstable equilibrium. Equilibrium happens when force on the body becomes zero.

11. If potential energy for a conservative system is given by 2U ax bx , where a and b are positive

constants. Then at b

xa

(A) equilibrium is stable (B) equilibrium is unstable (C) equilibrium is neutral (D) equilibrium is not possible 12. If force on a body is F = 2x 1, the possible equilibrium is at (A) x = 1 and stable (B) x = and unstable (C) x = and stable (D) x = 1 and unstable


Four metallic plates are placed as shown in the figure. Plate 2 is given a charge Q whereas all other plates are uncharged. Plates 1 and 4 are earthed. The area of each plate is same. 13. The charge appearing on the right side of plate 3 is (A) zero (B) +Q/4

(C) 3Q/4 (D) Q/2 14. The charge appearing on right side of plate 4 is

d

1 2 3 4

Q

2d d

(A) zero (B) Q/4

(C) 3Q/4 (D) Q/2



6


A long cylindrical conductor of radius R having a cylindrical cavity of radius R/2 through out its length is lying with its axis parallel to x-axis. The distance between the axes of the cylinder and the cavity is R/2. A constant current I is passed through the cylinder along its length in the positive x direction. The cross-sectional view of the cylinder is shown in the figure.

x y

z

15. The magnetic induction at point on the cavity is

(A) 0I ( k)

3 R

(B) 0

I (k)3 R

(C) 0I ( j)

6 R

(B) 0

I ( j)6 R

16. A charged particle having specific charge (charge to mass ratio) is 6

0

1810

I

SI unit is projected

from a point on the axis of the cavity along x-axis with the speed of 106 m/s. Radius of curvature

of the path of the particle is equal to (A) R/18 (B) R/9 (C) R/6 (D) R/3

(Multi Correct Choice Type)

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.

17. A conducting wire of length and mass m can slide without friction on two parallel rails and is connected to capacitance C. Whole system lies in a magnetic field B and a constant force F is applied to the rod. Then

(A) the rod moves with constant velocity

C

F

B

(B) the rod moves with an acceleration of 2 2

F

m B c

(C) there is constant charge on the capacitor. (D) charge on the capacitor increases with time




7

18. An electric kettle heater has two coils when one coil is switched on, the water in the kettle begins to boil after 15 minutes, when the other coil is switched on the water boils in 30 minutes.

(A) The waver will boil in 45 minutes if the coils are connected in series. (B) The water will boil in 10 minutes if the coils are connected in parallel. (C) Water boils in 22.5 minutes if coils are connected in series. (D) Water boils in 20 minutes if coils are connected in parallel. 19. Coefficient of friction between the two blocks is 0.3

whereas the surface AB is smooth. (g =10 ms2

) (A) Acceleration of the system of masses is 5.86 ms

2

(B) Tension T1 in the string is 17.7 N (C) Tension T2 in the string is about 41.4 N (D) Acceleration of 10 kg mass is 7.55 ms

2

T2

10kg

3kg

2kg T1

A B

20. Two projectiles are thrown at the same time from two different points. The projectile thrown from

the origin has initial velocity 3i 3j with respect to earth. The projectile has initial velocity ai bj

with respect to earth thrown from the point (10, 5). ( i is a unit vector along horizontal, j along

vertical). If the projectiles collide after two second, then the

(A) value of a is -2 (B) value of a is 1

2

(C) value of b is 1

2 (D) value of b is 2



8

SECTION 2 (Chemistry) PART A


1. Give the correct increasing order of acid strength.

OH OH

OMe

OH

NO2

OH

Cl(I) (II) (III) (IV)

(A) III > IV > I > II (B) IV > III > I > II (C) IV > I > II > III (D) I > II > III > IV 2. Which of the following will easily decarboxylate on heating?

(A)

OH

O

CH3

(B)

O

CH3

OH

O

(C)

CH3

CH3

O

OH

(D) OH

O

OH

OH




9

3. C

O

NH2 4 10 3

23 2

P O CH MgBr Yellow ppt. with

Ca OH , IH OW X Y Z

Final product Z will be

(A) C

O

CH3

(B) COOH

(C) C

O

(D)

4. 3CH OHO

CH3H A(major product)

. The product (A) is

(A) H3C CH CH2OH

OCH3

(B) H3C CH CH2

OH

OCH3

(C) H2C CH2 CH2

OCH3 OH

(D)

H3C CH CH2

OH OH

5. Which of the following is Tshaped?

(A) 2XeOF (B) 3XeO

(C) 4XeOF (D) 6XeF

6. Equal masses of 2 4 2SO , CH and O are mixed in empty container at 298K, when total pressure

is 2.1 atm. The partial pressure of 4CH in the mixture is

(A) 0.5 atm (B) 0.75 atm (C) 1.2 atm (D) 0.6 atm



10

7. If the radius of first Bohr orbit is x, then de Broglie wavelength of electron in 3rd

orbit is nearly.

(A) 2x (B) 6x

(C) 9x (D) x

3

8. If 10 ml of H2O2 solution of volume strength x, required 10 ml of 4N

MnO0.56

solution is acidic

medium then x is (A) 0.56 (B) 5.6 (C) 0.1 (D) 10

(Paragraph Type)



Hybridization in the mixing of atomic orbitals belonging to the same atom but having slightly different

energies so that a redistribution of energy takes place between them resulting in the formation of new

orbitals of equal energies and identical shapes.

Hybridization is used for explaining the geometry molecules. There are several type of hybridization like

sp, sp2, sp

3, sp

3d, sp

3d

2, sp

3d

3 etc.

9. Among the compounds BF3, NCl3, H2S, SF4 & BeCl2 identify the ones in which the central atom

has the same type of hybridization

(A) BF3, NCl3 (B) H2S and BeCl2

(C) SF4 and BeCl2 (D) NCl3 and H2S

10. Pair of species having identical shapes for molecule is

(A) CF4, SF4 (B) BF3, PH3

(C) XeF2, CO2 (D) PF5, IF5




11


The salts of alkali metals are ionic and soluble in water. The solubility of an ionic compound depends on

two factors: (i) Lattice energy and (ii) Hydration energy. These two factors oppose each other. If hydration

energy is high, the ions will have greater tendency to be hydrated and therefore the solubility will be high.

The smaller the cation, the greater is the degree of its hydration. Hydration of ions is an exothermic

process. Higher is the energy released if greater is the degree of hydration. Reducing power of alkali

metals in solutions is also dependent on the hydration energy besides other factors.

11. The radius of which ion (hydrated) is lowest?

(A) [Li(aq.)]+ (B) [Na(aq.)]

+

(C) [K(aq.)]+ (D) [Cs(aq.)]

+

12. Strongest reducing agent amongst alkali metals in aqueous solutions is

(A) Li (B) Na

(C) K (D) Cs



12


Aldehydes undergo disproportionation reaction in presence of aqueous NaOH. Simultaneous oxidation and reduction of a compound is scientifically called as disproportionation.

Aldehydes having no -hydrogen show this reaction called Cannizzaros reaction. Few exception are also there to this generalization. The reaction may be represented as:

NaOH

6 5 6 5 6 5 6 5 2C H CHO C H CHO C H COONa C H CH OH

Answer the following questions: 13. The product formed in the following reaction will be

CHO

CHO

NaOH Product

(A) CH2OH

CH2OH

(B) CH2OH

COONa (C) COONa

COONa

(D) All of these

14. Which of the following compounds gives intramolecular Cannizzaro reaction? (A) H5C6 CH2 C

O

H

(B) H5C6 C

O

CHO (C)

CHO

CHO

(D)

CHO

H2C CHO




13


A reaction characteristic of vicinal diols is their oxidative cleavage on treatment with periodic acid (HIO4). The carbon-carbon bond of the vicinal diol unit is broken and two carbonyl groups result. Periodic acid is reduced to iodic acid (HIO3).

C C

R

OH

R'

OH

R R' + HIO4 C O

R

R

+ C O

R'

R'

+ HIO3 + H2O

Cyclic diols react to give dicarbonyl compounds. The reaction are faster when the hydroxyl groups are cis than when they are trans but both stereoisomers are oxidized by periodic acid. Periodic acid cleavage of vicinal diols is often used for analytic purposes as an aid in structure determination. By identifying the carbonyl compounds produced, the constitution of the diol may be deduced. 15. Which of the following compound(s) is/are obtained when the following compound is oxidized by

HIO4?

CH

OH

C

CH3

OH

CH3

(A) C

O

H

(B) CH3 C

O

H

(C) C

O

CH3

(D) CH3 C

O

H

16. Which of the following products is/are obtained when glycerol is treated with HIO4? (A) HCHO (B) HCOOH (C) HIO3 (D) All of these



14



17. Which of the following molecules is/are tetrahedral?

(A) XeF4 (B) 4NH

(C) CCl4 (D) CH4 18. Which of the following ethers are cleaved by hot conc. HI?

(A) O

CH3

(B) O

(C)

O

(D)

O

19. Which of the following amines can be resolved into two enantiomers?

(A) N

H(A)

(B) N

H(B)

(C)

N

(D) CH

NH2

20. Mixture of C6H5CHO and HCHO is treated with NaOH then Cannizzaro reaction involves (A) oxidation of HCHO (B) reduction of HCHO (C) oxidation of C6H5CHO (D) reduction of C6H5CHO




15

SECTION 3 (Mathematics) PART A


1. An equilateral triangle is inscribed in a circle of radius r. P is any point inside triangle.

Perpendiculars are dropped from P to the sides. The sum of the lengths of the perpendiculars is

(A) 3r (B) 3

2r

(C) 9r (D) none of these 2. The set of solution |x

2 + x| = x

2 + x is given by

(A) (-, -1) (B) [0, )

(C) [-1, 0] (D) (-, -1] [0, ) 3. The chords of contact of the pair of tangents drawn from each point on the line 2x + y = 4 to x

2 +

y2 = 1 pass through the point

(A) (1, 2) (B) 1 1

,2 4

(C) (2, 4) (D) none of these 4. Let y = f(x) be a continuous and differentiable curve. The normals at (1, f(1)), (2, f(2)) and (3, f(3))

make angles , and3 4 6

with positive x-axis respectively. Then value of

2 3

1 2

f x xf x dx f x f x dx is equal to

(A) f(2) + f(1) + 1 (B) 2f(2) f(1) + 1 (C) f(3) f(2) + 1 (D) none of these

5. 2

1x 0

tan sec xlim

xsin x

is equal to

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



16

6. If 1sin / 4

0

4sin

sin 2 ln (1 + tan (sin )) d is k, then 3960k

ln2 is equal to

(A) 11 (B) 10 (C) 12 (D) none of these

7. If A cos x = cos (x + ) + B is an identity in x, then the number of values of ordered triplet (A,

cos, B) is

(A) 0 (B) 1

(C) 2 (D) 3

8. Let f(x) = | x | {x} (where {.} denotes the fractional part of x) and X, Y and its domain and range

respectively, then

(A) f : X Y y = f (x) is one-one function (B) ) x 1

, 0,2

and Y

1,

2

(C) X 1

, 0,2

and Y [0, ) (D) none of these

(Paragraph Type)



A triangle ABC is given where vertex A is (1, 1) and the orthocenter is (2, 4). Also sides AB and BC are members of the family of lines ax + by + c = 0 where a, b, c are in A.P. 9. The vertex B is

(A) (2, 1) (B) (1, 2)

(C) (1, 2) (D) none of these 10. The coordinate of the circumcentre is

(A) (6, 1) (B) 17 1

,2 4

(C)17 1

,2 2

(D) none of these




17


A circle C whose radius is 1 unit, touches the xaxis at point A. The centre Q of C lies in first quadrant.

The tangent from origin O to the circle touches it at T and a point P lies on it such that OAP is a right angled triangle at A and its perimeter is 8 units. 11. The length of QP is

(A) 1

2 (B)

4

3

(C) 5

3 (D) none of these.

12. Equation of circle C is

(A) 2 2{x (2 3)} (y 1) 1 (B) 2 2{x ( 3 2)} (y 1) 1

(C) 2 2(x 3) (y 2) 1 (D) none of these.


Let n be a positive integer such that In =n 2 2x a x dx , then answer the following questions:

13. The value of I1 is

(A) 1/ 2

2 22 a x3

(B) 3 / 2

2 21 a x3

(C) 3 / 2

2 22 a x3

(D) 3 / 2

2 21 a x3

14. If In =

3 / 2n 1 2 2

n 2

x a xkI

n 2

, then the value of k is

(A)n 1

n 2

(B)

n 2

n 1

(C) 2n 1

an 2

(D) 2n 2

an 1



18


If f(x) is a differentiable function wherever it is continuous and f(c1) = f(c2) = 0, f(c1) . f(c2) < 0, f(c1) = 5, f(c2) = 0 and (c1 < c2).

15. If f(x) is continuous in [c1, c2] and f(c1) f(c2) > 0, then minimum number of roots of f(x) = 0 in [c1 1, c2 + 1] is

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

16. If f(x) is continuous in [c1, c2] and f(c1) f(c2) < 0, then minimum number of roots of f(x) = 0 in [c1 1, c2 + 1] is

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




19



17. Two circles C1 and C2 intersect at two distinct points P, Q in a plane. Let a line passing through P

meets the circles C1 and C2 in A and B respectively. Let Y be the mid point of AB and QY meet the circles C1 and C2 in X and Z respectively, then

(A) Y is the mid point of XZ (B) XY 2

YZ 1

(C) YX = YZ (D) XY + YZ = 3YZ 18. If x1 and x2 are positive numbers between 0 and 1, then which of the following is/are true?

(A) 1 2 1 2x x sinx sinx

sin2 2

(B) 1 2 1 2

x x tanx tanxtan

2 2

(C) 1 2 1 2x x logx logx

log2 2

(D)

2 2 21 2 1 2x x x x

2 2

19. If R [0, ] for 1 k 10, then the maximum value of

102 2

R R

R 1

(1 sin )(1 cos )

is

(A)

103

2

(B)

109

4

(C)

203

2

(D)

59

4

20. If y is a function of x given by 2log(y 1) log x log(y 2) = 0, then

(A) domain is [4, ) (B) domain is (0, )

(C) range is (2, ) (D) range is (0, )


Documents

AIITS-1, PT4 PAPER-set-A.pdf