Qua,Trigo,Kinematics,Mole Concpaper 2

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� MARKING SCHEME

� In Section I (Total Marks: 24), for each question you will be awarded 3 marks if you

darken ONLY the bubble corresponding to the correct answer and zero marks if no

bubble is darkened. In all other cases, minus one (-1) mark will be awarded.

� In Section II (Total Marks: 20), for each question you will be awarded 4 marks if

you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY and

zero marks otherwise. There are no negative marks in the section.

� In Section III (Total Marks : 12), for each question you will be awarded 3 marks if

you darken ONLY the bubble corresponding to the correct answer and zero marks if

no bubble is darkened. In all other cases, minus one (-1) mark will be awarded.

� In Section IV (Total Marks: 24), for each question you will be awarded 4 marks if

you darken ONLY the bubble corresponding to the correct answer and zero marks

otherwise, There are no negative marks in this section

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MATHEMATICS

Section - I

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. The equation x 3 – 4 x –1 x 8 – 6 x –1+ + + =1 has

(a) no solution (b) one solution (c) two solutions (d) more than two solutions

2. If the roots of the equation x2 – 2ax + a2 + a – 3 = 0 are real and less than 3, then

(a) a < 2 (b) 2 ≤ a ≤ 3 (c) 3 ≤ a ≤ 4 (d) a > 4 3. The equation sin (cos x) = cos (sin x) has

(a) only one real solution (b) infinitely many solution

(c) no real solution (d) none of the above

4. If 2 2x x− − is factors of 4x xλ µ− − , then( )2 2λ µ− equals

(a) 1 (b) 3 (c) 5 (d) 7

5. The number of solutions of 5

1

cos 5rx =∑ in the interval [ ]0,2π is

(a) 0 (b) 1 (c) 5 (d) 10

6. The number of values of x for which sin 2x + cos 4x = 2 is

(a) 0 (b) 1 (c) 2 (d) infinite

Space for rough work



7. If ( ) ( )tan cos cot sinπ θ π θ= then the value of cos4

πθ −

(a)1

2 (b)

1

2 (c)

1

2 2 (d)N.O.T.

8. Number of values of x satisfying the equation log3(5 + 4log3(x – 1)) = 2 is/are

(a) 0 (b) 1 (c) 2 (d) 4

Section – II

(Multiple Correct Answer (s) 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.

9. For what values of a in the interval 7 5

6, 4

π π

does the quadratic expression

2 cot 2 tan tanx a x a a+ + , assumes only positive values.

(a)

7 5,

6 4a

π π ∈ (b)

3 7,

2 4a

π π ∈

(c)

5 7,

6 6a

π π ∈ (d)

3 7,

2 4a

π π ∈

10. If a + 3b + 9c = 0, ac < 0 and one root of the equation ax2 + bx + c = 0 is square of the other,

then (a) a and b have same sign (b) b and c have opposite sign (c) both roots are rational (d) a, b, c are irrational




11. 21 1 2 2 4 4– – – 0Let x x

p q q r r p + + =

has both the roots equal, then

(a) 1 1 1

( ) , ,ar p q

are in A.P.

2 2–

( ) 41 1

–

r qb

p q

=

(c) pq, rq, rp are in A.P. 1 1 1

( ) , ,dr p q

are in G.P.

12. The inequation 4sin3x + 5 ≥ 4cos2x + 5sinx

(a) is equivalent to sinx ≤ 1 (b) is equivalent to sinx ≥ 1

(c) is true for all x (d) is true only when sinx = 1

13. If roots of ax2 + 2bx + c = 0 (a ≠ 0) are non real and a + c < 2b, then

(a) c > 0 (b) c < 0 (c) 4a + c < 4b (d) 5a + c > 4b




Section – III

( Assertion Reason Type)

Directions : Question number 14 to 17 are Assertion Reason type questions. Each of these

Questions contains two statements : Statement-1(Assertion) and Statement-2 (Reason). You

have four alternative choices, only one of which is correct answer. Select the correct choice.

(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.

14. Statement-1 : The equation 22x + (a – 1)2x + 1 + a = 0 has roots of opposite signs for

10,

3a ∈

.

Statement-2 : If roots of the quadratic equation ax2 + bx + c = 0 are of opposite sign, then D > 0 and af(0) < 0.

15. Statement-1 : If ( )( )

( )

2 2 –1( )

– 3

x x a xf x

x

+ +=+

; f (x) < 0 then x ∈ (–1, 1)∪(3, ∞).

Statement-2 : If f (x) ≥ 0 then x ∈ ( ] [ )– , –1 1,3∞ ∪ .

16. Statement – 1 : The equation sin2x + cos2y = 2sec2z is only solvable sin x = 1, cos y = 1 and sin z = 1, where x, y, z ∈ R. Statement – 2 : Maximum value of sin x and cos y is 1 and minimum value of sec z is 1.

17. Statement-1: 0.2

1log 1

xif

x

+ ≥ then

[ )–1.25, –1x∈

Statement-2: 0 1log log 0a aif a x y y x< < ≥ ⇔ ≥ >




Section – IV

(Integer Answer Type)

This section contains 6 questions. The answer to each of the questions is a single-digit

integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be

darkened in the Answer sheet.

18. Find the number of integral values of k for which x2 – 2(4k – 1)x + 15k2 – 2k – 7 ≥ 0 hold for

all x .

19. Find the no. of solutions of the equation tan sec 2cosx x x+ = lying in the interval [ ]0,2 .π

20. Find the no. of solutions of the equation sec cos 2 2x ecx+ = in [ ]0,2π

21. Find the sum of all the real roots of the equations 2

– 2 – 2 – 2 0.x x+ =

22. Number of roots of the equation cos7x + sin4x = 1 in the interval [0, 2π] is

23. Sum of all roots of the equation

radical signs

2 2 ..... 2 2 3

n

x x x x x x+ + + + + =��

must be equal to ____________




PHYSICS

Section - I



1.A particle has an initial velocity of ̂ ˆ3 4i j+ and an acceleration of ˆ ˆ0.4 0.3i j+ .Its speed after 10s is

a)7 2units b)7units c)8.5units d)10 units

2.When the angle of projection is 75 degrees , a ball falls 10m short of the target .When the angle of

projection is 45 degrees , it falls 10m ahead of the target.Both are projected from the same point with

the same speed in same direction, the distance of the target from the point of projection is

a)15m b)30m c)45m d)10m

3.A body travels a distance of 20m in the 7th second and 24 m in the 9th second . How much distance

shall it travel in the 15th second?

a)10m b)16m c)24m d)36m

4.Two particles A and B are projected with same speed so that the ratio of their maximum height

reached is 3:1 .If the speed of A is doubled without altering other parameters, the ratio of the

horizontal ranges attained by A and B is

a)1:1 b)2:1 c)4:1 d)3:2




5. Two paper screens A and B are separated by a distance of 200m. A bullet pierces A and then B.

The hole in B is 40cm below the hole in A. If the bullet is travelling horizontally at the time of hitting

A , then the velocity of the bullet at A is

a)200m/sec b)400m/sec c)600m/sec d)700m/sec

6. A drunkard is walking along a straight road. He takes 5 steps forward and 3 steps backward

followed again by 5 steps forward and 3 steps backward and so on. Each step is one metre long and

takes one second. There is a pit on the road 11 metre away from the starting point. The drunkard will

fall into the pit after

a)21sec b)29sec c)31 sec d)41sec

7.The components of vector ˆˆ ˆx y zA a i a j a k= + +

�

along the direction of ̂ ˆi j− is

a) x y za a a− + b) x ya a− c)2

x ya a−

d) x y za a a+ +

8. A particle starts from rest and has an acceleration of 2m/sec for 10 sec .After that ,it travels for 30

seconds with constant speed and then undergoes a retardation of 4m/sec and comes back to rest.The

total distance covered by the particle is

a) 650m b)750m c)700m d)800m




Section – II




9. The circular scale of a screw gauge moves by 1 mm when given one full rotation. If there are a total

of 100 divisions on the circular scale.

a) The pitch of the instrument is 100. b) The pitch of the instrument is 0.1cm

c) The least count of the instrument 0.001 cm d) The zero error in the instrument is 0.01 cm.

10. The equation of motion of a particle is given by 3 23 2 7 1r t t t= + − +�

.

a) The particle has might have turned back not more than 3 times

b) The velocity of the particle is zero at 2 points.

c) The particle may turn back 2 times d) The particle has turned back 2 times.

11. Which of the following share the same units as the maximum number of shared units given in the

options .

a) P x V, where P is the pressure and V is the volume.

b) S x A, where S is the surface tension and A is the area.

c) F x v where F is the force and v is the velocity.

d) q x V where q is the charge and V is the potential difference.



12. The equation of trajectory of a particle is given by y= x +2x2.

a) The particle is covering the maximum range for the given velocity.

b) The initial speed of the particle is 5 m/sec. c) The motion is a uniformly accelerated motion.

d) The average speed of the particle is 2

um/sec.

13.Which of the following is possible

a)Acceleration zero with a non zero velocity b)Velocity zero with a non zero acceleration

c)Velocity zero with a non zero relative velocity d)Zero displacement with a non zero velocity.




Section – III






Statement-1.


Statement-1.


14.Statement 1:A physical quantity cannot be called as a vector if its magnitude is zero .

Statement 2:A vector has both, magnitude and direction.

15. Statement 1::For a particle moving in a plane , the displacement in a particular time interval is

independent on the choice of origin.

Statement 2:The displacement is a vector that points from an object’s initial position towards its

final position and its magnitude is equal to the shortest distance between the two positions.

16. Statement 1:The time of flight of a projectile is independent of the acceleration in the x direction.

Statement 2:For the calculation of time of flight ,its only the y direction that is dealt with.

17 . Statement 1:Work ,energy and heat all have same dimension.

Statement 2:Work ,energy and heat all have same units.




Section – IV





18.If 4 3a i j= − +� ��

and b�

=2 5i j+� �

. And C= a�

xb�

, an the vector c makes an angle 180/k with

the z axis ,then the value of k is equal to.

19. The ratio of the time taken for a projectile to cover the entire range to the time taken to reach

the maximum height is equal to .

20. The total number of vector in the following data is Area,velocity, thrust, pressure, electric

field, acceleration, displacement, coefficient of viscosity, resistance, magnetic field, relative

density, relative velocity, refractive index, current.

21. If the 50 reading of the cirucular scale coincides with the main scale line in an unloaded

instrument with least count 1/10 ,then the zero error in the instrument is equal to .

22. If the time of flight of a particle is doubled then by increasing the velocity , Then the ratio of

final maximum height to initial maximum height.

23.

.( )

| |

A AXB

AXB

� � �

� � has z component of p units along x axis , then the value of p is.




CHEMISTRY

Section - I



1.Photo electrons are ejected from metals A and B ,when a light beam of wavelength 1λ is used to

irradiate them. But electrons are ejected only from metal B,when another radiation of wavelength 2λ

is used .Then the false statement among the following is

a)Electron need more energy to escape from metal A. b) 2λ > 1λ

c)Threshold frequency of A is higher than that of metal B

d)When irradiated by light beam of wavelength 1λ ,the electrons ejected out from metal A have more

kinetic energy

2.The ratio of energies of electrons in the ground state of H,He+ and Li2+ is

a)9:4:1 b)1 1

: :19 4

c)1 1

1: :4 9

d)1:4:9

3. The energy of an electron in the first orbit of hydrogen atom is -y Joule. The kinetic energy of

electron in the second orbit in joule will be

a)2

y b)-

2

y c)-

4

y d)

4

y

4.An electron in the ground state of hydrogen atom absorbed 12.75 eV of energy and get excited.The

number of spectral lines formed due to all possible transitions when electrons jumps back from

highest possible energy level,during this excitation, to L-shell of the atom is

a)15 b)3 c)1 d)10


APEX INSTITUTE

APEX INSTITUTE FOR IIT- JEE /

5.One of the functions of the catalytic converter in your car is to oxidize carbon monoxide to carbon

dioxide . If 15.0 g of carbon monoxide reacts with 9.0 g of oxygen, how many grams of which

compound remains unreacted? The balanced chemical equation is

2CO (g) + O2

a)0.4g of oxygen remains unreacted

b)7.1 g of carbon monoxide remains unreacted

6.How many moles of electrons weigh one kilogram

a)6.023 x 1023 b)1

9.108

8.The gaseous elements H2 and O

of oxygen and mixture is ignited in a strong steel vessel. If the gas volumes

same temperature and pressure ,which gas remain unreacted and what is its volume?

a)O2,0.5 L


.

E / PMT ; 9910817866 , 9990495952

ions of the catalytic converter in your car is to oxidize carbon monoxide to carbon


compound remains unreacted? The balanced chemical equation is

→ 2 CO2 (g)

of oxygen remains unreacted b)0.8g of carbon monoxide remain unreacted

of carbon monoxide remains unreacted d)8.1 g of oxygen remains unreacted

eigh one kilogram

31109.108

x c) 546.02210

9.108× (d)

1

9.108 6.022×

and O2 react explosively to form water.3L of hydrogen is mixed with 2 L

of oxygen and mixture is ignited in a strong steel vessel. If the gas volumes are all measured at the

and pressure ,which gas remain unreacted and what is its volume?

b)O2 c)H2,1L d)H2,2L

TEST PAPER-2

Page 14

ions of the catalytic converter in your car is to oxidize carbon monoxide to carbon


b)0.8g of carbon monoxide remain unreacted

d)8.1 g of oxygen remains unreacted

8109.108 6.022

×

react explosively to form water.3L of hydrogen is mixed with 2 L

are all measured at the

and pressure ,which gas remain unreacted and what is its volume?

,2L



Section – II




9. Helium can be singly ionized by losing one electron to become the He+ cation. Which of the

following statements is true concerning this helium cation?

(a) The line spectrum of this helium cation will resemble the line spectrum of a hydrogen atom.

(b) The line spectrum of this helium cation will resemble the line spectrum of a lithium cation.

(c) The line spectrum of this helium cation will remain the same as for unionized helium.

(d) The line spectrum of this helium cation will resemble the line spectrum of a lithium atom.

10. 120 gms urea contains;

(a) 4gms-atoms nitrogen (b) 8mole hydrogen atom

(c) 44NAelectrons (d) 4NA carbon and oxygen atoms

11-which of the following statement is/are correct when360 gms of glucose dissolved in 1800 ml of

water (dH2O=1g/ml)

(a) Molarity of solution is 1.11 (b) strength of solution is 0.2 Kg/ L

(b) Mole fraction of glucose is0.196 (d) Mole fraction of water is 0.98

12. -which of the following statement is/are correct when two radiation one with a wavelength of

6000A0 and other with 2000A0

(a)energy of second is three times than first

(b)frequency of second radiation is less than first radiation

(c) velocity of both radiation is equal

(d) product of frequency and wavelength for both radiation is constant

13.Which of the following depends on temperature?

a)molarity b)molality c)normality d)formality




Section – III






Statement-1.


Statement-1.


14. Statement I: when 5.6 g iron and 6.5 g sulphure react together onstrongly heating 8.8 g iron (2)

sulphide are formed

Statement II: sulphure present in excess remains unreacted

15. Statement I: 2 mol BaCl2 react with 3 mol of Na3PO3 to form 0.66 mol Ba3(PO4)2

Statement II; BaCl2 is the limting reagent and some Na3PO3 remains unreacted

16. Statement I::. On heating a solid for a longer time radiation , radiation becomes white and then

blue as the temperature becomes very high

Statement II; radiation emitted go from a lower frequency to higher frequency as temperature

increases Elevation in b

17. Statement I::electron revolve around the nucleus in a circular track

Statement II: force of attraction by nucleus on electrons are managed by centrifugal force




Section – IV





18- What is de Broglie wavelength associated with an e- accelerated through P.D. = 100 KV

19-Hydrogen atom in its ground state is excited by means of monochromatic radiation of wavelength

975A. How many different lines are possible in the resulting spectrum?

20-The wavelength of a certain line in the Paschen series in 1093.6 nm. What is the value of nhjgh for

this line. given (Rh = 1.0973 xl0-7)

21- If you react 1.00 L of ethane at STP with 3.00 L of oxygen at STP, how many grams of carbon

dioxide will be formed? One mole of any gas occupies 22.4 L at STP. The balanced chemical

equation- 2C2H2(g) + 7O2 → 4CO2(g) + 6H2O

22- A certain dye absorbs 4530 and fluoresces at 5080A0 these being wavelengths of maximum

absorption that under given conditions 47% of the absorbed energy is emitted. Calculate the ratio of

the no. of quanta emitted to the number absorbed.

23- How many moles of nitrogen gas is needed to react with 44.8 litres of hydrogen gas to produce

ammonia gas?




Answers

Section-I(Only one Option is correct)

1. d 2.a 3.c 4.b 5.b 6.a 7.c 8.b

Section – II (Multiple Correct Answer (s) Type)

9. a 10.a,b 11.a,c 12.a,c 13.b,c

Section – III


14. a 15.b 16.b 17.a

Section – IV


18. ( 3) 19. (2) 20. (3) 21. (4) 22. (2) 23. (3)

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Qua,Trigo,Kinematics,Mole Concpaper 2