JEE SHIKHAR TEST # 09

(Main)
This booklet contains 14 printed pages

XII/Dropper-
SUBJECT : PHYSICS, CHEMISTRY & MATHEMATICS
ALL
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11.06.2023
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4. The Test Booklet consists of 90 questions. The maximum marks are 300.
5. There are three parts in the question paper A, B & C consisting of Physics, Chemistry & Mathematics having
30 questions of equal weightage. Each question is allotted 4 (four) marks for correct response.
Section 1 contains 20 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which
ONLY ONE Option is correct. All questions are compulsory.
Section 2 contains 10 integer type questions, out of which 5 questions are compulsory.
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 PHYSICS (The permeability of the vacuum = 4× 10–7 NA–2)
SECTION-A
A 2 B3
1. If Z = , then the relative error in Z will O
C4 I = 3A I = 3A
be : (1) 6T (2) 1T
DA DB DC (3) 4T (4) 3T
(A) + +
A B C

2DA 3DB 4DC

(B) + -
A B C 4. A coil is placed in magnetic field such that plane of
2DA 3DB 4DC coil is perpendicular to the direction of magnetic
(C) + +
A B C field. The magnetic flux through a coil can be

DA DB DC changed:
(D) + - A. By changing the magnitude of the magnetic
A B C
field within the coil.
2. Given below are two statements : One is labelled B. By changing the area of coil within the
as Assertion A and the other is labelled as Reason R. magnetic field.
Assertion A : Two metallic spheres are charged to C. By changing the angle between the direction of
the same potential. One of them is hollow and magnetic field and the plane of the coil.
another is solid, and both have the same radii. D. By reversing the magnetic field direction
Solid sphere will have lower charge than the abruptly without changing its magnitude.
hollow one. Choose the most appropriate answer from the
Reason R : Capacitance of metallic spheres options given below:
depend on the radii of spheres. (1) A and B only (2) A, B and C only
In the light of the above statements, choose the (3) A, B and D only (4) A and C only
correct answer from the options given below.
(1) A is false but R is true
(2) Both A and R are true and R is the correct r
4. If force F = 3î + 4jˆ - 2kˆ acts on a particle having
explanation of A
(3) A is true but R is false position vector 2î + ˆj + 2kˆ then, the torque
(4) Both A and R are true but R is not the correct about the origin will be :-

explanation of A (A) 3î + 4ˆj - 2kˆ

(B) -10î + 10ˆj + 5kˆ

3. As shown in the figure, a long straight conductor (C) 10î + 5ˆj -10kˆ

 (D) 10î + ˆj - 5kˆ

with semicircular arc of radius m is carrying
10
current I = 3A. The magnitude of the magnetic
field. at the center O of the arc is:

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6. For a body projected at an angle with the 10. As shown in the figure a block of mass 10 kg lying
horizontal from the ground, choose the correct on a horizontal surface is pulled by a force F acting
statement. at an angle 30°, with horizontal. For s = 0.25, the
(1) Gravitational potential energy is maximum at block will just start to move for the value of F:
[Given g = 10 ms–2]
the highest point.
F
(2) The horizontal component of velocity is zero at
highest point.
30°
(3) The vertical component of momentum is
maximum at the highest point.
(4) The kinetic energy (K.E.) is zero at the highest (1) 33.3 N (2) 25.2 N
point of projectile motion. (3) 20 N (4) 35.7 N

11. Given below are two statements : One is labelled as

7. Two objects A and B are placed at 15 cm and 25
Assertion A and the other is labelled as Reason R.
cm from the pole in front of a concave mirror Assertion A : For measuring the potential
having radius of curvature 40 cm. The distance difference across a resistance of 600 , the
between images formed by the mirror is: voltmeter with resistance 1000 will be preferred
(1) 40 cm (2) 60 cm over voltmeter with resistance 4000.
(3) 160 cm (4) 100 cm Reason R : Voltmeter with higher resistance will
draw smaller current than voltmeter with lower
resistance.
8. The Young's modulus of a steel wire of length 6 m In the light of the above statements, choose the
and cross-sectional area 3 mm2, is 2 × 1111 N/m2. most appropriate answer from the options given
below.
The wire is suspended from its support on a given
(1) A is not correct but R is correct
planet. A block of mass 4 kg is attached to the free
(2) Both A and R are correct and R is the correct
end of the wire. The acceleration due to gravity on explanation of A
1 (3) Both A and R are correct but R is not the
the planet is of its value on the earth. The
4 correct explanation of A
elongation of wire is (Take g on the earth = 10 (4) A is correct but R is not correct
m/s2):
(1) 1 cm (2) 1 mm
(3) 0.1 mm (4) 0.1 cm 12. Choose the correct statement about Zener diode:
(1) It works as a voltage regulator in reverse bias
and behaves like simple pn junction diode in
forward bias.
9. Equivalent resistance between the adjacent corners
(2) It works as a voltage regulator in both forward
of a regular n-sided polygon of uniform wire of and reverse bias.
resistance R would be: (3) It works a voltage regulator only in forward
 n  1 R  n  1 R bias.
(1) (2)
n 2
 2n  1  (4) It works as a voltage regulator in forward bias
and behaves like simple pn junction diode in
n2R  n  1 R reverse bias.
(3) (4)
n 1 n

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13. Choose the correct length (L) versus square of time Where R = Rydberg constant
period (T2) graph for a simple pendulum executing c = Speed of light in vacuum
simple harmonic motion.
h = Planck's constant
T2 (1) 13.6 eV
(1) (2) 10.5 eV
(3) 3.4 eV
O L
(4) 40.8 eV

T2

(2)
16. Figures (a), (b), (c) and (d) show variation of force
L
O
with time.
F(N)
T2
0.5
(3)

O L

0 Fig(a) 1.0 t(s)

T2
F(N)
(4)
0.5

O L

0 Fig(b) 2.0 t(s)

F(N)
14. The escape velocities of two planets A and B are in 0.75
the ratio 1 : 2. If the ratio of their radii respectively
is 1 : 3, then the ratio of acceleration due to gravity
of planet A to the acceleration of gravity of planet
0
B will be: Fig(c) 1.0 t(s)
F(N)
4 3
(1) (2)
3 2 0.5
2 3
(3) (4)
3 4

0 Fig(d) 2.0 t(s)

The impulse is highest in figure.

15. An electron of a hydrogen like atom, having Z = 4,
(1) Fig (c) (2) Fig (b)
jumps from 4th energy state to 2nd energy state, The
(3) Fig (a) (4) Fig (d)
energy released in this process, will be:
(Given Rch = 13.6 eV)

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17. If the velocity of light c, universal gravitational SECTION-B
constant G and planck's constant h are chosen as 21. For a train engine moving with speed of 20 ms–1.
fundamental quantities. The dimensions of mass in the driver must apply brakes at a distance of 500 m
the new system is: before the station for the train to come to rest at the
 1
 
1
station. If the brakes were applied at half of this
(1) h c G1 
2 2 (2)  h1c1G 1 
  distance, the train engine would cross the station
–1
with speed x ms . The value of x is ______
 1 1 1   1 1 1 
(3) h 2 c 2 G 2  (4) h 2 c 2 G 2  (Assuming same retardation is produced by brakes)
   

22. A force F = (5 + 3y2) acts on a particle in the y-

18. For three low density gases A, B, C pressure
direction, where F is newton and y is in meter. The
versus temperature graphs are plotted while
work done by the force during a displacement from
keeping them at constant volume, as shown in the
y = 2m to y = 5m is ______j.
figure.
P(atm) Gas A
Gas B
23. Moment of inertia of a dise of mass M and radius
Gas C
K 0°C
Temperature (°C) MR 2
'R' about any of its diameter is . The moment
4
The temperature corresponding to the point 'K' is:
of inertia of this disc about an axis normal to the
(1) –273°C (2) –100°C
disc and passing through a point on its edge will
(3) –373°C (4) –40°C
x
be, MR2. The value of x is _____.
2

19. The ratio of average electric energy density and

total average energy density of electromagnetic
24. Nucleus a having Z = 17 and equal number of
wave is:
protons and neutrons has 1.2 MeV binding energy
(1) 2 (2) 1
per nucleon.
1
(3) 3 (4) Another nucleus B of Z = 12 has total 26 nucleons
2
and 1.8 MeV binding energy per nucleons.
The difference of binding energy of B and A will
be ____MeV.
20. The threshold frequency of metal is f0. When the
light of frequency 2f0 is incident on the metal plate,
25. A square shaped coil of area 70 cm2 having 600
the maximum velocity of photoelectron is .
turns rotates in a magnetic field of 0.4 wbm–2,
When the frequency of incident radiation is
about an axis which is parallel to one of the side of
increased to 5f. the maximum velocity of
the coil and perpendicular to the direction of field.
photoelectrons emitted is . The ratio of  to 
If the coil completes 500 revolution in a minute,
is:
the instantaneous emf when the plane of the coil is
1 1 1 1
(1)  (2)  inclined at 60° with the field, will be ____ V.
2 2 2 8
1 1  1 22
(3)  (4) 1  (Take   )
2 16 2 4 7

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26. A block is fastened to a horizontal spring. The 29. A cubical volume is bounded by the surfaces
block is pulled to a distance x = 10 cm from its
x = 0, x = a, y = 0, y = a, z = 0, z = a. The electric
equilibrium position (at x = 0) on a frictionless
ˆ Where
field in the region is given by E  E0 x i.
surface from rest. The energy of the block at x = 5
cm is 0.25 J. The spring constant of the spring is
E0 = 4 × 104 NC–1 m–1. If a = 2 cm, the charge
–1
____Nm .
contained in the cubical volume is Q × 10–14C. The

value of Q is____.

I1  I3 Take 0 = 9 × 10–12 C2/Nm2)

27. In the given circuit the value of is:
I2
10 V 20 V

10 
I1
10 
I2 30. The surface of water in a water tank of cross

section area 750 cm2 on the top of a house is h m.

13 10 
above the tap level. The speed of water coming out

through the tap of cross section area 500 mm2 is

28. As shown in the figure, in Young's double slit
dh
experiment, a thin plate of thickness t = 10 m and 30 cm/s. At that instant, is x × 10–3 m/s. The
dt
refractive index is inserted infront of slit
value of x will be_____.
S1. The experiment is conducted in air (= 1)
and uses a monochromatic light of wavelength
 = 500 nm. Due to the insertion of the plate,
central maxima is shifted by a distance of x0. 0 is
the fringe-width before the insertion of the plate.
The value of the x is_____.

t
S1

P

S2

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 34. The graph which represents the following reaction
CHEMISTRY
is :
SECTION-A
31. In a reaction, OH 
(C6 H 5 )3 C  Cl 
Pyridine (C 6 H 5 )3 C  OH
OH OH OCOCH 3
COOCH 3 COOH COOH
‘Y’ ‘X’ rate rate
(1) (2)
reagents ‘X’ and ‘Y’ respectively are :

(1) (CH3CO)2O/H+ and CH3OH/H+,  [(C6 H5) 3C–Cl] –

[OH ]

(2) (CH3CO)2O/H+ and (CH3CO)2O/H+

rate rate
+ +
(3) CH3OH/H ,  and CH3OH/H ,  (3) (4)

(4) CH3OH/H+  and (CH3CO)2O/H+

[(C6 H5) 3C–Cl] [Pyridine]

32. The correct order of bond enthalpy (kJ mol–1) is : 35. ‘X’ is : +
HF
X
 Major product
(1) Si – Si > C – C > Sn – Sn > Ge – Ge

(2) Si – Si > C – C > Ge – Ge > Sn – Sn

(3) C – C > Si – Si > Sn – Sn > Ge – Ge

(1)
(4) C – C > Si – Si > Ge – Ge > Sn – Sn

33. All structures given below are of vitamin C. Most

stable of them is :
OH (2)
(1) HO O
O
H
OH OH

(2)

(3)

(3)

(4)

(4)

36. The complex cation which has two isomers is :

(1) [Co(H2O)6]3+ (2) [Co(NH3)5Cl]2+
(3) [Co(NH3)5NO2]2+ (4) [Co(NH3)5Cl]+

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 37. Given below are two statements : 40. Given below are two statements : one is labelled
Statement I : Sulphanilic acid gives esterification
as Assertion (A) and the other is labelled as
test for carboxyl group.
Reason (R).
Statement II : Sulphanilic acid gives red colour in
Lassigne’s test for extra element detection. Assertion (A) : -halocarboxylic acid on reaction
In the light of the above statements, choose the
with dil. NH3 gives good yield of -amino
most appropriate answer from the options given
below : carboxylic acid whereas the yield of amines is very
(1) Statement I is correct but Statement II is low when prepared from alkyl halides.
incorrect.
Reason (R) : Amino acids exist in zwitter ion form
(2) Both Statement I and Statement II are incorrect.
(3) Both Statement I and Statement II are correct. in aqueous medium.

(4) Statement I is incorrect but Statement II is In the light of the above statements, choose the
correct.
correct answer from the options given below :

38. A piston filled with 0.04 mol of an ideal gas (1) Both (A) and (R) are correct and (R) is the

expands reversibly from 50.0 mL to 375 mL at a correct explanation of (A).

(2) Both (A) and (R) are correct but (R) is not the
constant temperature of 37.0°C. As it does so, it
correct explanation of (A).
absorbs 208 J of heat. The values of q and w for the
(3) (A) is correct but (R) is not correct.
process will be
(4) (A) is not correct but (R) is correct.
(R = 8.314 J/mol K) (ln 7.5 = 2.01)
41. The osmotic pressure of a dilute solution of an
(1) q = + 208 J, w = – 208 J
ionic compound XY in water is four times that of a
solution of 0.01 M BaCl 2 in water. Assuming
(2) q = – 208 J, w = – 208 J
complete dissociation of the given ionic compounds
in water, the concentration of XY (in mol L–1) in
(3) q = – 208 J, w = + 208 J
solution is
(4) q = + 208 J, w = + 208 J (1) 16 × 10–4

(2) 4 × 10–4

(3) 6 × 10–2
39. Which element is not present in Nessler’s reagent ?
(1) Mercury (2) Potassium (4) 4 × 10–2
(3) Iodine (4) Oxygen

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42. The structures of major products A, B and C in the In the light of the above statements, choose the
following reaction are sequence. correct answer from the options given below :
O (1) Both (A) and (R) are correct and (R) is the
NaHSO3, dil. HCl LiAlH4
H [A] [B] correct explanation of (A).
NaCN, H2O
(2) (A) is correct but (R) is not correct.
HCl/H2O
[C] (3) (1) is not correct but (R) is correct.

OH CN (4) Both (A) and (R) are correct but (R) is not the
(1) A = ,
H correct explanation of (A).
HO CHO 44. Concentrated HNO3 reacts with Iodine to give
B=
H (A) HI, NO2 and H2O (B) HIO2, N2O and H2O
,
HO CO2H (C) HIO3, NO2 and H2O (D) HIO4, N2O and H2O
C=
H
OSO3Na
(2) A = , 45. A graph of vapour pressure and temperature for three
H different liquids X, Y, and Z is shown below

Vapour pressure
OH
800 X Y Z
B=

(mm Hg)
H 500
,
400
Cl 200
C=
H 0 293 313 333 353
Temp
HO SO3H
(3) A = ,
The following inferences are made
H
(A) X has higher intermolecular interactions
B= OH compared to Y.
,
HO SO2Cl (B) X has lower intermolecular interactions
C= compared to Y
H
(C) Z has lower intermolecular interactions
HO CN compared to Y.
(4) A = ,
H The correct inferences is/are

HO NH2 (1) (B) (2) (C)

B=
H
, (3) (A) and (C) (4) (A)
HO CO2H
C= 46.
H The increasing order of basicity of the following
compound is

NH2 NH
43. Given below are two statements : one is labelled (a) (b)
as Assertion (A) and the other is labelled as
NH2
Reason (R).
(c) (d) NHCH3
Assertion (A) : Cu2+ in water is more stable than NH
Cu+.
(1) (a) < (b) < (c) < (d) (2) (b) < (a) < (c) < (d)
Reason (R) : Enthalpy of hydration for Cu2+ is
(3) (b) < (a) < (d) < (c) (4) (d) < (b) < (a) < (c)
much less than that of Cu+.

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47. Which one of the following sets of ions represents
a collection of isoelectronic species? SECTION – B:
(Given : Atomic Number : F :9 , Cl : 17, Na = 11, (One Integer Value Correct Type)
Mg = 12, Al = 13, K = 19, Ca = 20, Sc = 21) This section contains 10 questions, out of which
(1) (Li+ , Na+ , Mg2+ , Ca2+ 5 question are compulsory. Each question, when
(2) (Ba2+ , Sr2+ , K+ , Ca2+ worked out will result in one integer from 0 to 9
(3) (N3– , O2– , F– , S2– (both inclusive).
(4) (K+ , Cl– , Ca2+ , Sc3+
0 1 2 3 4 5 6 7 8 9
48. The effect of addition of helium gas to the A B C D AB AC AD BC BD CD
following reaction in equilibrium state, is :
51. 0.3 g of ethane undergoes combustion at 27°C in a
PCI5 (g) PCl3 (g)  Cl2 (g)
bomb calorimeter. The temperature of calorimeter
(1) the equilibrium will shift in the forward
system (including the water) is found to rise by
direction and more of Cl2 and PCl3 gases will be
0.5°C. The heat evolved during combustion of
produced. ethane at constant pressure is ________kJ mol–1.
(2) the equilibrium will go backward due to (Nearest integer)
suppression of dissociation of PCl5. [Given : The heat capacity of the calorimeter
(3) helium will deactivate PCl5 and reaction will system is 20 kJ K–1, R = 8.3 JK–1 mol–1.
stop. Assume ideal gas behaviour.
(4) addition of helium will not affect the Atomic mass of C and H are 12 and 1 g mol–1
equilibrium. respectively]

49. For electron gain enthalpies of the elements

denoted as egH, the incorrect option is :
(1) egH (Cl) <egH (F) 52.

(2) egH (Se) <egH (S)

(3) egH (I) <egH (At)
(4) egH (Te) <egH (Po)

50. O–O bond length in H2O2 is X than the O–O bond

length in F2O2. The O – H bond length in H2O2 is
53.
Y than that of the O–F bond in F2O2.
Choose the correct option for X and Y from the
given below.
(1) X – shorter, Y – shorter
(2) X – shorter, Y – longer
(3) X – longer, Y – longer
(4) X – longer, Y - shorter

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54. A B 58. Testosterone, which is a steroidal hormone, has the
The above reaction is of zero order. Half life of following structure.
this reaction is 50 min. The time taken for the OH
concentration of A to reduce to one-fourth of its CH3

initial value is________min. CH3

O Testosterone
55. 20% of acetic acid is dissociated when its 5 g is
The total number of asymmetric carbon atom/s in
added to 500 mL of water. The depression in
freezing point of such water is _______ × 10–3 °C. testosterone is ______
Atomic mass of C, H and O are 12, 1 and 16 a.m.u.
respectively.
[Given : Molal depression constant and density of
59. The spin only magnetic moment of [Mn(H2O)6]2+
water are 1.86 K kg mol–1 and 1 g cm–3
respectively. complexes is _______B.M. (Nearest integer)

(Given : Atomic no. of Mn is 25)

56. The molality of a 10% (v/v) solution of di-bromine
solution in CCl4 (carbon tetrachloride) is 'x'. x
________ × 10–2 M. (Nearest integer)
60.
[Given : molar mass of Br2 = 160 g mol–1
atomic mass of C = 12 g mol–1
atomic mass of Cl = 35.5 g mol–1
density of dibromine = 3.2 g cm–3
density of CCl4 = 1.6 g cm–3]

57. 1×10–5 M AgNO3 is added to 1 L of saturated

solution of AgBr. The conductivity of this solution
at 298 K is ______×10–8 S m–1.
[Given : Ksp(AgBr) = 4.9×10–13 at 298K

0Ag  6  103 Sm 2 mol –1

 0Br   8  103 Sm2 mol –1

 0NO  7  103 Sm2 mol –1 ]

3

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 MATHEMATICS
SECTION-A 1é 1 3ù
2
64. If A = ê ú , then :
¥
2n + 3n + 4 2 êë - 3 1 úû
61. The sum å
n= 1 ( 2n ) !
is equal to :
(1) A30 – A25 = 2I
11e 7 13e 5 (2) A30 + A25 + A = I
(1) + (2) + -4
2 2e 4 4e
(3) A30 + A25 – A = I
11e 7 13e 5 (4) A30 = A25
(3) + -4 (4) +
2 2e 4 4e

65. Two dice are thrown independently. Let A be the

62. Let
event that the number appeared on the 1st die is less
ìï æ1 - x ö æ1 - x 2
ö üï
S = íx Î R : 0 < x < 1and 2 tan -1 ç ÷ = cos -1 ç 2 ÷ý . than the number appeared on the 2nd die, B be the
îï è1 + x ø è1 + x ø þï
event that the number appeared on the 1st die is
If n(S) denotes the number of elements in S then :
even and that on the second die is odd, and C be
1
(1) n(S)= 2 and only one element in S is less then . the event that the number appeared on the 1st die is
2
odd and that on the 2nd is even. Then
1
(2) n(S) = 1 and the element in S is more than . (1) the number of favourable cases of the event
2
1 (A È B) Ç C is 6
(3) n(S) = 1 and the element in S is less than .
2 (2) A and B are mutually exchusive
(4) n(S) = 0 (3) The number of favourable cases of the events
A, B and C are 15, 6 and 6 respectively
(4) B and C are independent

66. Let b= lim

(
ax - e 3x -1 ) for some aΡ . Then
63. Let x ®0
(
ax e - 1 3x
)
r r r
a = 2iˆ - 7jˆ + 5kˆ , b = iˆ + kˆ and c = iˆ + 2jˆ - 3kˆ the value of a + b is :
r
be three given vectors. If r is a vector such that 14 3 5 7
r r r r r r r (1) (2) (3) (4)
r ´ a = c ´ a and r g b = 0 , then r is equal to : 5 2 2 2

11 11
(1) 2 (2)
7 7

11 914
(3) 2 (4)
5 7

CatalyseREduventures (India) Pvt. Ltd. 11

67. The number of integral values of k, for which one 71. The sum of the abosolute maximum and minimum
root of the equation 2x – 8x + k = 0 lies in the
2
values of the function f(x) = |x2 – 5x + 6| – 3x + 2
interval (1, 2) and its other root lies in the interval in the interval [–1, 3] is equal to :
(2, 3), is : (1) 10 (2) 12
(1) 2 (2) 0
(3) 13 (4) 24
(3) 1 (4) 3
68. Let f : R – {0, 1} ® R be a function such that
æ 1 ö
f (x) + f ç ÷ = 1 + x . Then f(2) is equal to :
è1 - x ø
72. Let P(S) denote the power set of S={1,2,3,…., 10}.
9 9
(1) (2) Define the relations R1 and R2 on P(S) as AR1B if
2 4
7 7 (A Ç Bc) È (B Ç Ac) = Æ and AR2B if
(3) (4)
4 3 A È Bc = B È Ac, " A, B Î P(S). Then :
æ 1 ö
ç1 - ÷ ( cosx - sin x ) (1) both R1 and R2 are equivalence relations
69. The integral ò è 3ø
dx is equal to
æ 2 ö (2) only R1 is an equivalence relation
ç1 + sin 2x ÷
è 3 ø (3) only R2 is an equivalence relation

æx p ö (4) both R1 and R2 are not equivalence relations

tan ç + ÷
1 è 2 12 ø + C
(A) loge
2 æx pö
ç2 + 6÷
è ø

æx pö 73. The area of the region given by

tan ç + ÷
1 è2 6 ø +C
(B) log e {(x, y) : xy £ 8, 1, £ y £ x2} is :
2 æ x pö
ç2+ 3÷
è ø (1) 8 loge2 –
13
(2) 16 loge2 –
14
3 3
æ x pö
tan ç + ÷ 7 7
(C) log e è 2 6 ø +C (3) 8 loge2 + (4) 16 loge2 +
æx p ö 6 3
tan ç + ÷
è 2 12 ø

æx p ö
tan ç - ÷
1 è 2 12 ø + C
(D) loge
2 æ x pö 74. Let ax = exp(xbyg) be the solution of the
tan ç - ÷
è2 6ø
differential equation 2x2y dy – (1 – xy2) dx = 0,
70. Let a, b be two real numbers such that ab < 0. If
x > 0, y(2) = log e 2 . Then a + b – g equals :
1 + ai
the complex number is of unit modulus and
b+i (1) 1
a + ib lies on the circle |z – 1| = |2z|, then a possible (2) –1
1 + [a] (3) 0
value of , where [t] is greatest integer
4b
(4) 3
function, is :
1
(1) - (2) –1
2
1
(3) 1 (4)
2
CatalyseREduventures (India) Pvt. Ltd. 12
 r r
p p 78. Let a = 5iˆ - ˆj + 3kˆ and b = ˆi + 3jˆ + 5kˆ be two
4 x+
75. The value of the integral ò 4 dx is :
vectors. Then which one of the following
p 2 - cos 2x
-
4 statements is TRUE?
p2 r r 17
(1) (1) Projection of a on b is and the direction
6 35
p2 r
(2) of the projection vector is same as of b
12 3
r r -17
(2) Projection of a on b is and the direction
p 2
35
(3)
3 3 r
of the projection vector is same as of b
p2
(4) r r 17
6 3 (3) Projection of a on b is and the direction
35
of the projection vector is opposite to the
r
direction of b
r r -17
76. Let 9 = x1 < x2 < …< x7 be in an A.P. with common (4) Projection of a on b is and the direction
35
difference d. If the standard deviation of x1, x2 …,
of the projection vector is opposite to the
x7 is 4 and the mean is x , then x + x6 is equal to : r
direction of b
æ 1 ö
(1) 18 ç1 + ÷ (2) 34
è 3ø

æ 8 ö
(3) 2 ç 9 + ÷ (4) 25
è 7ø
79. Let P(x0, y0) be the point on the hyperbola
3x2 – 4y2 = 36, which is nearest to the line
3x + 2y = 1. Then 2 (y0 – x0) is equal to :

77. For the system of linear equations ax + y + z = 1, (1) –3

(2) 9
x + ay + z = 1, x + y + az = b , which one of the
(3) –9
following statements is NOT correct ?
(4) 3
(1) It has infinitely many solutions if a=2 and b = –1
(2) It has no solution if a = – 2 and b = 1
3
(3) x + y + z = if a = 2 and b = 1
4
80. If y(x) = xx , x > 0, then y’’(2) – 2y’(2) is equal
(4) It has infinitely many solutions if a = 1 and b = 1
to :
(1) 8 loge2 – 2
(2) 4 loge2 + 2
(3) 4 (loge2)2 – 2
(4) 4 (loge2)2 + 2

CatalyseREduventures (India) Pvt. Ltd. 13

 SECTION – B:
(One Integer Value Correct Type)
This section contains 10 questions, out of which
p
5cos x (1 + cos x cos 3x + cos 2 x + cos3 x cos 3x ) dx kp
85. If ò =
1+ 5 cos x
16
5 question are compulsory. Each question, when 0

, then k is equal to ______.

worked out will result in one integer from 0 to 9
(both inclusive).

0 1 2 3 4 5 6 7 8 9 86. Let the sixth term in the binomial expansion of

A B C D AB AC AD BC BD CD
( 2log 2 (10 - 3x ) + 2( )
m
x -2 ) log2 3
5
, in the increasing

powers of 2( x-2 ) log 2 3 , be 21. If the binomial

81. The total number of six digit numbers, formed coefficients of the second, third and fourth terms in
using the digits 4, 5, 9 only and divisible by 6, is the expansion are respectively the first, third and
______. fifth terms of an A.P., then the sum of the squares
of all possible values of x is ______.

82. Number of integral solutions to the equation

x + y + z = 21, where x ³ 1, y ³ 3, z ³ 4, is equal 87. If the term without x in the expansion of
22
to ______. æ 23 a ö
çx + 3 ÷ is 7315, then |a| is equal to ______.
è x ø
83. The line x = 8 is the directrix of the ellipse
2
y2

88. The sum of the common terms of the following

three arithmetic progressions.
3, 7, 11, 15, …………, 399,
2, 5, 8, 11,………….., 359 and
2, 7, 12, 17,……., 197, isequal to ______.

89.

84. If the x-intercept of a focal chord of the parabola

2
y = 8x + 4y + 4 is 3, then the length of this chord
is equal to ______.
90. If the sum of solutions of the system of equations
2sin2θ − cos2θ = 0 and 2cos2θ + 3sinθ = 0 in the
interval [0, 2π] is kπ, then k is equal to _______.

CatalyseREduventures (India) Pvt. Ltd. 14

Read the following instructions carefully :
1. The candidates should fill in the required particulars on the Test Booklet and Answer Sheet (Side-1) with Blue/Black
Ball Point Pen.
2. For writing/marking particulars on Side-2 of the Answer Sheet, use Blue/Black Ball Point Pen only.
3. The candidates should not write their Roll Numbers anywhere else (except in the specified space) on the Test
Booklet/Answer Sheet.
4. Out of four options given for each question, only one option is the correct answer.
5. For each incorrect response, one-fourth (1/4) of the total marks allotted to the question would be deducted from the
total score. No deduction from the total score, however, will be made if no response is indicated for an item in the
Answer Sheet.
6. Handle the Test Booklet and Answer Sheet with care, as under no circumstances (except for discrepancy in Test
Booklet Code and Answer Sheet Code), another set will be provided.
7. The candidates are not allowed to do any rough work or writing work on the Answer Sheet. All calculations/writing
work are to be done in the space provided for this purpose in the Test Booklet itself, marked ‘Space for Rough
Work’. This space is given at the bottom of each.

8. On completion of the test, the candidates must hand over the Answer Sheet to the invigilator on duty in the
Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.
9. Each candidate must show on demand his/her Admit Card to the invigilator.
10. No candidate, without special permission of the Superintendent or Invigilator, should leave his/her seat.
11. The candidates should not leave the Examination Hall without handing over their Answer Sheet to the Invigilator on
duty and sign the Attendance Sheet again. Cases where a candidate has not signed the Attendance Sheet a second
time will be deemed not to have handed over the Answer Sheet and dealt with as an unfair means case. The
candidates are also required to put their left hand THUMB impression in the space provided in the
Attendance Sheet.
12. Use of Electronic/Manual Calculator and any Electronic Item like mobile phone, pager etc. is prohibited.
13. The candidates are governed by all Rules and Regulations of the CatalyseR with regard to their conduct in the
Examination Hall. All cases of unfair means will be dealt with as per Rules and Regulations of the CatalyseR.
14. No part of the Test Booklet and Answer Sheet shall be detached under any circumstances.
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phone, electronic device or any other material except the Admit Card inside the examination hall/room.