CT-5 / FTP (J) / PHYSICS / MAIN / 22 SEPTEMBER 2024

PHYSICS
SECTION – A
(FOR ANSWER WITH ONLY ONE OPTION CORRECT TYPE)
Section-A contains 20 Objective questions having 4 options each with only 1 correct option. For
each question 4 Marks will be awarded for every correct answer and 1 Mark will be deducted for
every incorrect answer.
1. A uniform chain AB of length L is located in a smooth horizontal tube so that it’s fraction of
length h hangs freely and touches the surface of the table with it’s end B as shown in fig. At a
certain moment the end A of the chain is set free with what velocity will this end of the chain
slip out of the tube? (Neglect the force on the hanging chain from the table)
A

(A) 2g  L  h (B) 2gh n L  h (C) 2gL (D) g  L  h

Solution (B):

2. A ball ‘A’ is moving with speed v 0 towards another identical stationary ball ‘B’ after collision
both are moving with same speed on the smooth horizontal surface and angle between their
velocity vectors is 600 after collision as shown in figure. Find the coefficient of restitution for
that collision.
A
V0
600
A
B
1 1 2
(A) (B) (C) 2 (D)
2 3 3 5
Solution (B):

3. A ball collides elastically with another ball of same mass. The collision is oblique and initially
one of the ball was at rest. After the collision, the two balls move with same speeds. What will
be the angle between the velocities of the balls after the collision?
(A) 350 (B) 450 (C) 600 (D) 900
Solution (D):

4. A particle is moving in a circular path. The acceleration and momentum of the particle at a

 
  
certain moment are a  4ˆj  3j m/s2 and p  8i  6j kg  m/s The motion of the particle is:
(A) Uniform circular motion
(B) Accelerated motion
(C) Deaccelerated circular motion
 
(D) We cannot say anything with a and p only
Solution (B):

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5. A small body A of mass m and B of mass 3m and same size as A move towards each other
with speeds V and 2V respectively from the positions as shown, along a smooth horizontal
circular track of radius r. After the first elastic collision, they will collide again after the time:
(Neglect the size of the balls when compared to circular track radius r)

.
A V

. 90º
.
2V

2r r r 2r
(A) (B) (C) (D)
V 2V V 3V
Solution (D):

2
6. A is a fixed point at a height above a perfectly inelastic smooth horizontal plane. A light
3
inextensible string of length  has one end attached to A and other to a heavy ball. The ball
is held at the level of A with string just taut and released from rest. The speed of ball just
after striking the plane is (Neglect the size of the heavy ball when compared to length l neglect
the impulse of the string during the collision)
l
A

2l
3

4g 2g 2 g 4 g
(A) (B) (C) (D)
3 3 3 3 3 3
Solution (D):

7. Assertion: Impulse and momentum have equal dimensions

Reason: From Newtons second law of motion, impulse is equal to
change in momentum.
(A) Assertion is True , Reason is True; Reason is correct explanation for Assertion
(B) Assertion is True, Reason is True; Reason is not correct explanation for Assertion.
(C) Assertion is True, Reason is False
(D) Assertion is False, Reason is True.
Solution (C):

8. A ball of mass m is moving towards a batsman at a speed v . The bats man strikes the ball and
deflects it by an angle  without changing its speed. The impulse imparted to the ball is given
by
     
(A) mv cos   (B) mv sin    (C) 2mv cos   (D) 2mv sin  
 2  2  2
Solution (D):

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9. Two billiard balls of the same size and mass are in contact on a billiard table. A third ball of
the same size and mass strikes them symmetrically and remains at rest after the impact. The
coefficient of restitution between the ball is
1 1 2
(A) (B) (C) (D) None
2 4 3
Solution (C):

10. A ball of mass 2 kg strikes a floor as shown in figure. For this situation mark the correct
statement(s)
y

20m/s 15m/s
37 53
x
(A) The impulse experienced by ball during the collision is acting along the + ve y-direction
and is having a magnitude of 25 NS.
(B) Floor may be rough or smooth
(C) The direction of impulse experienced by ball during the collision is along somewhere
between the y axis and + ve x-axis
9
(D) Coefficient of restitution between floor and ball is
16
Solution (D):

11. A particle of mass 1 kg is projected upwards with velocity 60 m/s. At the same instant
another particle of mass 2 kg is dropped from a certain height. After 2 s (g = 10 m/s 2), which
of the following is WRONG?
(A) magnitude of acceleration of COM = 10 m/s2
(B) velocity of COM = zero
(C) displacement of COM = 40 m.
(D) distance travelled by 2 kg is 20 m
Solution (C):

12. The centre of mass of a system of particle is at the origin. It follows that
(A) The number of particles on x-axis should be equal to the number of particles on
y-axis
(B) If there is a particle on the positive x-axis there must be at least one particle on the
negative x-axis
(C) Total mass on the right side of y-axis is same as that on the left side
(D) None
Solution (D):

PARAGRAPH FOR NEXT TWO QUESTIONS:

Two identical smooth discs each of mass m and radius r are moving with the same speed u,
their centres moving along parallel lines separated by a distance r, towards each other on a
friction less horizontal surface. Assume their collision is perfectly elastic.
13. The speed of either of discs after the collision is
u 3 u 5 u
(A) u (B) (C) (D)
2 2 2
Solution (A):

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14. The angle by which each of the mass is scattered (due to collision) with respect to their
original direction of motion is
(A) 60° (B) 90° (C) 120° (D) 150°
Solution (C):

PARAGRAPH FOR NEXT TWO QUESTIONS:

Three identical particles A, B and C (each of mass m) lie on a smooth horizontal table. Light
inextensible strings which are just taut connect AB and BC and ABC is 135° as shown in
diagram. An impulse J is applied to the particle C in the direction BC for a very short time
interval. Then just after applying impulse J,
J

A B

15. Find the speed of the particle ‘A’

2J 3J
(A) Speed of particle A will be (B) Speed of particle A will be
7m 7m
10J J
(C) Speed of particle A will be (D) Speed of particle A will be
7m 3m
Solution (A):

16. Find the speed of the particle ‘C’

J J
(A) Speed of particle C will be (B) Speed of particle C will be
3m m
2J 3J
(C) Speed of particle C will be (D) Speed of particle C will be
7m 7m
Solution (D):

PARAGRAPH FOR NEXT TWO QUESTIONS:

A railroad car of length L and mass m0 when empty is moving freely on a smooth horizontal
dm
track while being loaded with sand from a stationary chute at a rate  q . Knowing that
dt
the car was approaching the chute at a speed v0. (Initially at t=0sec) Total length of the sand
equal to the Railroad car length L. Determine

17. The speed of the car vf at the instant when the car has cleared the chute.
 qL   qL   qL 
     
(A) V0e  m0v0  (B) V0  1  e m0v0  (C) V0e m0v0  (D) None
 
 
Solution (A):

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18. The mass of the car and its load at that instant. when the car has cleared the chute.
 qL  qL    qL 
m0 v0    
(A) m0e (B) m0e  m0 v 0  (C) m0  1  e 0v0 
 m
(D) None
 
 
Solution (A):

PARAGRAPH FOR NEXT TWO QUESTIONS:

Three force 3F, 4F, 5F are acting along the three sides of an equilateral triangle of side length
L taken in order as shown fig.

5F
4F

3F
19. Find the Net Torque about centre of the equilateral triangle
(A) 3FL (B) zero (C) 2 3FL (D) 12FL
Solution (C):

20. Find the magnitude of resultant of these three forces

(A) zero (B) 3F (C) 5  7 F   (D) 7F
Solution (B):

SECTION-B
(FOR ANSWER WITH NUMERIC VALUE)
Section-B contains 10 Numerical questions with numerical value as answer. If the numerical
value has more than two decimal places truncate/round-off the value to TWO decimal places. In
this section students have to attempt any five questions out of 10. For each question 4 Marks
will be awarded for every correct answer and 1 Mark will be deducted for every incorrect answer.
21. A ball collides at B with velocity 10 m/s at 30° with vertical. There is a flag at A and a wall at
C. Collision of ball with ground is perfectly inelastic e = 0 and that with wall is elastic  e 1 .
Given AB  BC 10m . Find the time after which ball will collide with the flag.

Solution (6):

22. A light beam of wavelength 400 nm is incident on a metal plate of work function 2.2 eV. A
particular electron absorbs a photon and makes two collisions before coming out of the metal.
Assuming that 10% of the extra energy is lost to the metal in each collision, find the
maximum number of collisions the electron can suffer before it is unable to come out of the
metal.
Solution (4):

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23. A slender rod of mass M and length L rests on a horizontal frictionless surface. The rod is
pivoted about one of its ends. The impulse of the force exerted on the rod by the pivot when
J
the rod is struck by a blow of impulse J perpendicular to the rod at other end is . Find ' x '
x
Solution (2):

24. A man of mass m stands at one end of a plank of length  which lies at rest on a frictionless
horizontal surface. The man walks to the other end of the plank. If the mass of the plank
m 
is , the distance that the man moves relative to ground is . The value of n is
3 n
Solution (4):

25. A player caught a cricket ball of mass 150 gm moving at the rate of 20ms -1. If catching
process be completed in 0.1 s, the force of the blow exerted by the ball on the hands of the
player is 101 N is:
Solution (3):

26. Two ice skaters A and B approach each other at right angles. Skater A has a mass 30 kg and
velocity 1 m/s skater B has a mass 20 kg and velocity 2 m/s. They meet and cling together.
Their magnitude of final velocity of the couple in m/s is
Solution (1):

27. A force of 6 N acts on a body of mass 1 kg at rest. During this time, the body attains a velocity
of 30 m/s. The time (in sec) for which the force acts on the body is
Solution (5):

28. In the elastic collision of a heavy vehicle moving with a speed of 10m/s and a small stone at
rest, the stone will fly away with a speed (in m/s) equal to
Solution (20):

29. As shown in the figure, a block A moving with a speed of 10 m/s on a smooth horizontal
surface collides with another identical block B at rest initially. The coefficient of restitution is
1/2 . Neglect friction everywhere. The distance (in m) between the blocks at 5 s after the
collision takes place is
10m / s
A B

Solution (25):

30. Mass m1 collides elastically with mass m2 of same size at rest. Ratio of m1 / m2 which
n
ensures the second collision between m1 and m2 is . Collision between m1 and wall is
4
perfectly elastic. Find n
m1 m2
v

Solution (1):

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 CT-05 / FTP-J / CHEMISTRY / 22 SEPTEMBER 2024
CHEMISTRY
SECTION-A
(MULTIPLE CHOICE QUESTIONS)
Section-A contains 20 Objective questions having 4 options each with only 1 correct option. For
each question 4 Marks will be awarded for every correct answer and 1 Mark will be deducted for
every incorrect answer.
31. A mixture of Ca 3N2 & CaH2 on complete hydrolysis gaseous a given mixture of two gases (X) &
(Y). (X) On reaction with sodium metal gives (Y) gas along with salt (A). Bond angle of anionic
portion of compound (A) is:
(A) greater than 120o (B) less than 120o
(C) equal to 120o (D) None of these
Solution (B):

Conc. HNO3
32. Cu  (X)gas
dil. HNO3
(Y)gas (Z)gas
Find the sum of number of unpaired electron present in gas(X), (Y) & (Z).
(A) 4 (B) 3 (C) 2 (D) 1
Solution (A):

CaCO3
33.  Gaseous (X)gas
Ca(NO3 )2 
mixture (Y)gas
CaSO4 (Z)gas
(W)gas
Among these four gases & three gases (X),(Y),(Z) are acidic in nature. Among (X), (Y), (Z) gases (Y)
gas on reaction with of NaOH gives two salt mixture and gas (X) act as oxidizing agent. Now find
(No. of unpaired e in (X) & No. of unpaired e  in(W)
the value of ?
No. of unpaired e in (Y)  No. of unpaired e  (Z)
(A) 2 (B) 1 (C) 1/2 (D) 1/5
Solution (B):


34. NaNO3 (X)gas  (A)

LiNO3 (X)gas  (Y)gas  (B)

Gas (X) + gas (Y) (C)
Oxidation state of central atom of compound (C) is  X. Find the value of (X)?
(A) 3 (B) 5 (C) 4 (D) 2
Solution (B):

H O
35. Alkali metal N2 (A) 
2
(X)gas . Find the total number of antibonding electron present
(M)

in (M2 ) species?
(A) 1 (B) 3 (C) 4 (D) 2
Solution (B):

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
36. KNO3 (X)gas
CaO  C (Y)gas
LiH  H2O (Z)gas
Find the sum of bond order of gas (X), (Y) & (Z).
(A) 2 (B) 2.5 (C) 4 (D) 6
Solution (D):

37. Consider following reaction in equilibrium with equilibrium concentration 0.01 M of every
species

(I) PCl5 (g)  PCl3 (g) + Cl2 (g)

(II) 2HI (g)  H2 (g) + I2 (g)

(III)N2 (g) + 3H2 (g)  2NH3 (g)
Extent of the reactions taking place is :
(A) I > II > III (B) I < II < III (C) II < III < I (D) III < I < II
Solution (B):

38. 1 mole N2 and 3 mol H2 are placed in a closed container at a pressure of 4 atm. The pressure
falls to 3 atm at the same temperature when the following equilibrium is attained N2 (g) + 3H2 (g)

 2NH3 (g). The equilibrium constant KP for dissociation of NH3 is :
1 0.5  (1.5)3 33
(A)  (1.5)3 atm 2 (B) 0.5  (1.5)3 atm2 (C) atm2 (D) atm–2
0.5 33 0.5  (1.5)3
Solution (B):


39. For the reaction PCl5 (g)   PCl3 (g) + Cl2 (g), the forward reaction at constant temperature is
favoured by :
(A) introducing an inert gas at constant volume
(B) introducing chlorine gas at constant volume
(C) introducing an inert gas at constant pressure
(D) None of these
Solution (C):

Dd
40. The equation, a = is correctly matched for :
(n  1)d

(A) A  nB/2 + nC/3 
(B) A  nB/3 + (2n/3)C

(C) A  (n/2)B + (n/4)C 
(D) A  (n/2)B + C
Solution (B):

41. The equilibrium of which of the following reactions will not be disturbed by the addition of an
inert gas at constant volume?

(A) H2 (g) + I2 (g)  2HI (g) 
(B) N2O4 (g)  2NO2 (g)

(C) CO (g) + 2H2 (g)  CH3OH (g) (D) All of these
Solution (D):

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42. The following equilibrium are given


N2 + 3H2  2NH3 -------------- K1

N2 + O2  2NO -------------- K2

H2 + O2   H2O -------------- K3
The equilibrium constant of the reaction
5 
2NH3 + O  2NO + 3 H2O, in terms of K1, K2 and K3 is :
2 2
K1 K 2 K1 K 23 K 2 K 33
(A) (B) (C) (D) K1K2K3
K3 K2 K1
Solution (C):


43. The reaction A + B   C + D is studied in a one litre vessel at 250°C. The initial concentration
of A was 3n and that of B was n. When equilibrium was attained, equilibrium concentration of C
was found to the equal to the equilibrium concentration of B. What is the concentration of D at
equilibrium :
(A) n/2 (B) (3n – 1/2) (C) (n – n/3) (D) n
Solution (A):

k
44. In a reversible reaction A 

k
1
 B , the initial concentration of A and B are a and b in moles per

2
litre and the equilibrium concentration are (a – x) and (b + x) respectively ; express x in terms of
k1, k2, a and b :
k1 a  k 2 b k1 a  k 2 b k1 a  k 2 b k1 a  k 2 b
(A) (B) (C) (D)
k1  k 2 k1  k 2 k1 k 2 k1  k 2
Solution (A):

45. A mixture of SO3 ,SO2 and O2 gases is maintained at equilibrium in 10litre flask at a
temperature at which K c for the reaction, 2SO2 (g)  O2(g)  2SO3 (g) is 100 mol1 litre at
equilibrium.
(a) If number of moles of SO3 and SO2 in flask are same, how many moles of O2 are present
(b) If number of moles of SO3 in flask are twice the number of moles of SO2 , how many moles of
O2 are present
(A) 0.1 and 0.4 (B) 0.5 and 0.7 (C) 0.8 and 0.4 (D) 0.1 and 4
Solution (A):

46. 60 grams CH3COOH and 46 grams C2H5OH react in 5L flask to form 44 grams CH3COOC2H5 at
equilibrium on taking 120 grams CH3COOH and 46 grams C2H5OH , CH3COOC2H5 formed at
equilibrium is
(A) 44 g (B) 20.33 g (C) 22 g (D) 58.66g
Solution (D):

47. If the concentration of OH- ion in the reaction Fe  OH3 s   Fe3  aq   3OH  aq  is decreased
by 1/4 times, then equilirbium concentration of Fe 3+ will be increased by
(A) 4 times (B) 8 times (C) 16 times (D) 64 times
Solution (D):

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48. In a closed container and at constant temperature 0.3 mole of SO2 and 0.2 mole of O2 gas at 750
torr are kept with a catalyst. If at equilibrium 0.2 mole of SO3 is formed the partial pressure of
SO2 is ... torr
(A) 375 (B) 187 (C) 360 (D) 150
Solution (B):

49. A vessel at 1000 K contains CO2 with a pressure of 0.5 atm. Some of the CO2 is converted into
CO on the addition of graphite. If the total pressure at equilibrium is 0.8 atm, the value of KP is
(A) 1.8 atm (B) 3 atm (C) 0.3 atm (D) 0.18 atm
Solution (A):

50. The equilibrium constants KP1 and KP2for the reaction X  2Y and Z  P  Q, respectively are in
the ratio of 1:9. If the degree of dissociation of X and Z be equal, then the ratio of total pressure
at these equilibria is
(A) 1:36 (B) 1:1 (C) 1:3 (D) 1:9
Solution (A):

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 CT-05 / FTP-J / CHEMISTRY / 22 SEPTEMBER 2024
SECTION-B
(FOR ANSWER WITH NUMERIC VALUE)
Section-B contains 10 Numerical questions with numerical value as answer. If the numerical value
has more than two decimal places truncate/round-off the value to TWO decimal places. In this
section students have to attempt any five questions out of 10. For each question 4 Marks will be
awarded for every correct answer and 1 Mark will be deducted for every incorrect answer.

51. For the following gases equilibrium. N2O4 (g)   2NO2 (g) Kp is found to be equal to Kc. This is
attained when temperature in Kelvin is (nearest integer)
Solution (12):

 2 C (g) at a given temperature, Kc = 9.0. What must be the

52. For the reaction 3 A (g) + B (g) 
volume of the flask, if a mixture of 2.0 mol each of A, B and C exist in equilibrium in litre:
Solution (6):

53. One mole of N2O4 (g) at 300 K is left in a closed container under one atm. It is heated to 600 K
when 20% by mass of N2O4 (g) decomposes to NO2 (g). The resultant pressure in atm is :
Solution (2.4):

54. The vapour density of N2O4 at a certain temperature is 30. What is the % dissociation of N 2O4 at
this temperature :
Solution (53.3):

55. Sulphide ion in alkaline solution reacts with solid sulphur to form polysulphide ions having
formulae
S22–, S32–, S4--2– and so on. The equilibrium constant for the formation of S 22– is 12 (K1) & for the
formation of S32– is 132 (K2), both from S and S2–. What is the equilibrium constant for the
formation of S32– from S22– and S ?
Solution (11):


56. In a 7.0 L evacuated chamber, 0.50 mol H2 and 0.50 mol I2 react at 427°C. H2 (g) + I2 (g) 
2HI (g). At the given temperature, KC = 49 for the reaction. What is the value of Kp ?
Solution (49):

57. When alcohol (C2H5OH) and acetic acid are mixed together in equimolar ratio at 27°C, 33% is
converted into ester. And the KC for the equilibrium is found x 102 then value of x (nearest
integer):

C2H5OH () + CH3COOH ()  CH3COOC2H2 () + H2O ()
Solution (25):
H O NaOH
58. PCl3 
2
(A) 
Excess
(B) . Find the number of O-P-O bonds in compound (B).
Solution (3):

59. A mixture of 1 mole SO2Cl2 and 1 mole POCl3 on complete hydrolysis gives a mixture (X). Find
the total number of moles of NaOH required for complete neutralization of mixture (X).
Solution (10):

60. CaO  C (A)  (X)gas .
(Excess)
Find the total number of antibonding electron present in anionic part of (A)?
Solution (4):

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MATHEMATICS
SECTION-A
(MULTIPLE CHOICE QUESTIONS)
Section-A contains 20 Objective questions having 4 options each with only 1 correct option. For
each question 4 Marks will be awarded for every correct answer and 1 Mark will be deducted for
every incorrect answer.

61. If sec   tan   k, then cos  equals to

k2  1 2k k k2  1
(A) (B) (C) (D)
2k k2  1 k2  1 k
Solution (B):

62. If sec 4  sec 2  2 , then the general value of  is

   n 
(A) (2n  1) (B) (2n  1) (C) n  or  (D) None of these
4 10 2 5 10
Solution (C):

2 3
3 1 4 1 5 1
63. The sum of .   .   .    ... to n terms is equal to
1.2  2  2.3  2  3.4  2 
1 1 1 1
(A) 1  (B) 1  (C) 1  (D) 1 
 n  1 2n
n.2n 1
 n  1 2n n.2n 1
Solution (A):

64. The first and last terms of an A.P. are a and l respectively. If s be the sum of all the terms of
the A.P., then common difference is
l2  a 2 l2  a 2 l2  a 2 l2  a 2
(A) (B) (C) (D)
2s   l  a  2s   l  a  2s   l  a  2s   l  a 
Solution (A):

n n
1 1
65. If  tr  12 n  n  1 n  2, the value  t is
r 1 r 1 r
2n n 1 4n 3n
(A) (B) (C) (D)
n 1  n  1 ! n 1 n2
Solution (C):

66. The two roots of an equation x3  9x2  14x  24  0 are in the ratio 3 : 2. The roots will be
(A) 6, 4, – 1 (B) 6, 4, 1
(C) – 6, 4, 1 (D) – 6, – 4, 1
Solution (A):

67. Sum of the series

n  2r 8r 26r 
S   1
r 0
r n
 
Cr  r  2r  3r  ...upto   is
 3 3 3 
2 1 1 2
(A) n
(B) n (C) n
(D) n
3 1 3 1 3 1 3 1
Solution (C):

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 CT-5 / FTP (J) / MATHEMATICS / MAIN / 22 SEPTEMBER 2024
n C12 C22
C2n C23
68. Let Cr  Cr and S  1 2 3  ...  n , then
C0 C1 C2 Cn 1
(A) n|S (B) 2n 1 |S (C) n.2n 1 |S (D) none of these
Solution (B):

 x  b  x  c   b  x  c  x  a   c  x  a  x  b   x
69. If a, b, c are all distinct, then a is equal to
 a  b  a  c   b  c  b  a   c  a  c  b 
x2 x 1
(A) 0 (B) ax2  bx  c 
(C)  a  b  c  x 2  x  1  (D)
a
 
b c
Solution (A):

70. a, b, c are distinct positive real numbers such that a > b > c. If 2 log (a  c), log (a2  c2),
log(a2 + 2b2 + c2) are in A.P., then
(A) a, b, c are in A.P. (B) a , b , c are in A.P.
(C) a, b, c are in G.P. (D) a, b, c are in H.P.
Solution (C):

b
71. Let a, b, c be positive integers such that is an integer. If a, b, c are in geometric progression
a
a 2  a  14
and the arithmetic mean of a, b, c is b  2 , then the value of is _____.
a 1
(A) 3 (B) 4 (C) 5 (D) 6
Solution (D):

72. If  2021
3762
is divided by 17, then the remainder is ____.
(A) 4 (B) 2 (C) 3 (D) 8
Solution (A):

73. The number of ways in which 10 persons can go in two different boats so that there may be 5
on each boat, supposing that two particular persons will not go in the same boat is

(A)
2

1 10
C5  (B) 2 8 C4 
(C)
1 8
2

C5 (D) none of these  
Solution (B):

74. The value of expression


2 sin1  sin2  sin3       sin89  equals-
  
2 cos1  cos 2       cos 44  1 

1 1
(A) 2 (B) (C) (D) 0
2 2
Solution (C):

2n 1
75. The remainder left out when 82n   62 is divided by 9
(A) 2 (B) 7 (C) 8 (D) 0
Solution (A):

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76. Let m and n be the coefficients of seventh and thirteenth terms respectively in the expansion
18
 1  1
1 1   n 3
of  x 3  2  . Then  m  is:
3 
 2x 3 
4 1 1 9
(A) (B) (C) (D)
9 9 4 4
Solution (D):

5

 3 3

1 
77. In the expansion of 1  x  1  x 2 1   2  3  , x  0, the sum of the coefficient of x 3 and
 x x x 
x 13 is equal to ___.
(A) 90 (B) 110 (C) 118 (D) 120
Solution (C):

78. The sum of the coefficients of all even degree terms is x in the expansion of:
6 6
 3   3 
 x  x 1   x  x 1 (x  1) is equal to:
   
(A) 26 (B) 20 (C) 28 (D) 24
Solution (D):

79. If 2x  3y  5z  10 & 81 xyz  100 , where triplet x, y, z  R  , then number of ordered  x, y, z 

is
(A) 4 (B) 1 (C) 3 (D) 2
Solution (B):

1 1 1
80. If      , then the equation    0 has
x  x  x  
(A) imaginary roots (B) real and equal roots
(C) real and unequal roots (D) rational roots
Solution (C):

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SECTION-B
(FOR ANSWER WITH NUMERIC VALUE)
Section-B contains 10 Numerical questions with numerical value as answer. If the numerical
value has more than two decimal places truncate/round-off the value to TWO decimal places. In
this section students have to attempt any five questions out of 10. For each question 4 Marks
will be awarded for every correct answer and 1 Mark will be deducted for every incorrect answer.

81. If one real root of the quadratic equation 81x2  kx  256  0 is cube of the other root, then
value of |k| is:
Solution (300):

 
500
82. The number of terms in the expansion of 4 9  6 8 , which are integers is
Solution (251):

83. The thousand’s digit of 3100 is

Solution (2):

84. The letters of word COCHIN are permuted 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
Solution (96):

85. If one root of the equation x2  x  12  0 is even prime; while x 2  x    0 has equal roots,
then  is
Solution (16):

86. There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons
are selected from each group, then the number of ways of selecting 4 men and 4 women is
______
Solution (5626):

87. The sum of the integers lying between 1 and 100 and divisible by 3 or 5 or 7 is
Solution (2738):

88. The number of ways of painting the six faces of a cube with six different given colours is
Solution (30):

89. Let  and  be two real roots of the equation  k  1 tan2 x  2.  tan x  1  k  , where
 k  1
and  are real numbers. If tan2      50, then a value of  is:
Solution (10):

 
90. If ,,  and  are the solutions of the equation tan      3tan3, no two of which have
 4
equal tangents, then the value of tan   tan   tan   tan  is
Solution (0):

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