12-MOT-8-JM-24

Test Code: JS-FT-20-24

Instructions:

Subjects: Physics, Chemistry, Mathematics (25 questions per subject)

Question Format:
Multiple Choice Questions (MCQs): Physics (Q1-20), Chemistry (Q26-45), Mathematics
(Q51-70)
Integer-Type Questions: Physics (Q21-25), Chemistry (Q46-50), Mathematics (Q71-75)
Select the correct option for MCQs and enter an integer for integer-type questions.
Marking Scheme: +4 for correct answers, - 1 for incorrect answers, and no penalty for
unattempted questions.

Duration: 180 minutes Total Marks: 300

Physics

Q1: If the intermolecular forces vanish away, the volume occupied by the molecules contained in 4.5 kg water at
standard temperature and pressure will be given by

A. 5.6 m 3
B. 4.5 m 3

C. 11.2 L D. 11.2 m 3

Q2: A physical quantity P is related to four observables a, b, c and d as P is constant) The percentage
√ ab⋅d
= (α
√c

errors in a, b, c and d are 0.5% in each. If the percentage error in P is 2%, then α is....

A. 5

2
B. 2

C. 3

4
D. 3

Q3: The value of alternating emf E in the given circuit will be

A. 220V B. 140V
C. 100V D. 20V

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Q4: In the photoelectric experiment, if we use a monochromatic light, the I − V curve is as shown. If work
function of the metal is 2 eV , estimate the power of light used. (Assume efficiency of photo emission = 10 %,
−3

i.e. number of photoelectrons emitted are 10 % of number of photons incident on metal.)

−3

A. 2W B. 5W
C. 7W D. 10W

Q5: Block A of mass 2 kg is placed over block B of mass 8 kg. The combination is placed over a smooth
horizontal surface. Coefficient of friction between A and B is 0.5. A horizontal force of 20 N is applied on block B
. The force of friction on A is

A. 10 N B. 8 N
C. 6 N D. 4 N

Q6: ABCDE is a channel in the vertical plane, part BCDE being circular with radius r. A block is released from
A and slides without friction and without rolling. The block will complete the loop if h is :-

A. h ≤ 3

2
r B. h ≥ 5

2
r

C. h ≥ 3

2
r D. h ≤ 5

2
r

Q7: The image formed by a convex mirror of focal length 30 cm is a quarter of the size of the object. The distance
of the object from the mirror is:

A. 30 cm B. 90 cm
C. 120 cm D. 60 cm

Q8: A proton and an electron enter into a magnetic field B perpendicular to it with speed v and 10v. Then, the
ratio of the radii of their circular paths is (given that, proton is 1820 times heavier than electron)-

A. 1820 : 1 B. 18200 : 1
C. 1 : 182 D. 182 : 1

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Q9: A planet is revolving around the sun. Which of the following is correct statement?

A. The time taken in travelling DAB is less than that B. The time taken in travelling DAB is greater than
for BCD that for BCD
C. The time taken in travelling CDA is less than that D. The time taken in travelling CDA is lgreater than
for ABC that for ABC

Q10: Assertion: A spherical wavefront is produced by a point source of light.

Reason: It is because, the locus of all points, which are equidistant from the point source, is a sphere.

A. Assertion is true, reason is true; reason is a correct B. Assertion is true, reason is true; reason is not a
explanation for assertion. correct explanation for assertion.
C. Assertion is true, reason is false. D. Assertion is false, reason is true.

Q11: The truth table for the following logic circuit is

A B Y A B Y

0 0 0 0 0 1

A. 0 1 1 B. 0 1 1

1 0 1 1 0 1

1 1 0 1 1 1

A B Y A B Y

0 0 1 0 0 1

C. 0 1 1 D. 0 1 1

1 0 1 1 0 0

1 1 0 1 1 1

Q12: A big water drop is formed by the combination of n small water drops of equal radii. The ratio of the
surface energy of n drops to the surface energy of the big drop is

A. n 2
: 1 B. n : 1
C. √n : 1 D. √n : 1
3

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Q13: A capacitor of capacitance C having initial charge 2Q , is connected to a battery of potential difference
0

V = as shown, then workdone by the battery is

Q0

2 2
Q 3Q
A. 2C
0
B. 2C
0

2 2

C. D.
3Q 2Q
0 0

C 3C

Q14: One end of wire 2m long and diameter 2 mm is fixed in a ceiling. A naughty boy of mass 10 kg jumps to
catch the free end and stays there. The change in length of wire is [Take g = 10 m s , Y = 2 × 10 N m ]
−2 11 −2

A. 31.85 × 10 −5
m B. 2 mm
C. 3 mm D. 4 m

Q15: The equation that represents magnetic field of a plane electromagnetic wave which is propagating along x-
direction with wavelength 10 mm and maximum electric field 60 V m in y-direction is (where, c = speed of
−1

light)

A. (6 × 10 −7 ^
) sin [0.2 π (ct − x)kT ] B. (2 × 10 −7 ^
) sin [200 π (ct − x)kT ]

C. (2 × 10 −7
) sin [200 π (ct − x)^
iT ] D. (6 × 10 −7
) sin [20 π (ct − x)^
iT ]

Q16: Consider the circuit shown in the figure.

Which of the following statements are correct?

A. Current through the battery is 5A B. Current through branch AD is 2A

D. The potential difference between points D and C is
C. Current through branch BC is 3A
4V

→
Q17: The position vector of a particle is given as r = (t − 4t + 6)^i + (t )^j. The time after which the velocity
2 2

vector and acceleration vector becomes perpendicular to each other is equal to

A. 1 sec B. 2 sec
C. 1.5 sec D. not possible

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Q18: Two identical containers A and B having the same volume of an ideal gas at the same temperature have
the mass of the gas as m and m respectively and 2 m = 3 m . The gas in each cylinder expands isothermally to
1 2 1 2

double of its volume. If the change in pressure in A is 300 P a, then the change in pressure in B is

A. 200 P a B. 300 P a
C. 400 P a D. 500 P a

Q19: A sample of hydrogen like atoms produces an emission spectrum consisting of 10 wavelength arising out of
all transitions possible. During this process the maximum angular impulse on an electron going from higher
energy level to a lower energy level is :-

A. h

2π
B. h

C. 2h

π
D. 3h

2π

Q20: The distribution of some charges on two Gaussian surfaces A and B are as shown in the figure. If ϕ and A

ϕB
are electric fluxes linked with the surfaces A and B respectively. then =
ϕA

ϕB

A. − 1

5
B. −3
C. − 3

2
D. − 3

Q21: A metal rod AB of length 50 cm is moving at a velocity 8 ms in a magnetic field of 2T . If the field is at 60
−1 ∘

with the plane of motion as shown in the figure, then the potentials V and V are related by V − V = K , find
A B A B

K.

Q22: A central fringe of the interference produced by light of wavelength 6000Å is shifted to the position of 5 th

bright fringe by introducing a thin glass plate of refractive index 1.5 Calculate the thickness of the plate. If it is
cm. Find n.
−4
n × 10

Q23: When a body of mass 1.0 kg is suspended from a certain light spring hanging vertically, its length increases
by 5 cm. By suspending 2.0 kg block to the spring and if the block is pulled through 10 cm and released, the
maximum velocity in it in m/s is : (Acceleration due to gravity = 10 m/s ) 2

Q24: A particle of mass 15 kg is moving with a uniform speed 8 ms in xy-plane along the line 3y = 4x + 10,
−1

then the magnitude of its angular momentum about the origin in kg ⋅ m s is … (sin 53 = )
2 −1 ∘ 4

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Q25: All the edges of a block with parallel faces are unequal. Its largest edge is twice its shortest edge. The ratio
of the maximum to the minimum resistance between parallel faces is

Chemistry

Q26: An indicator has a pK of 7.5. What is the ratio of the concentration of the base form to the concentration
a

of the acid form ([A ]/[H A]) in a buffer solution in which the pH is 6.5 ?
−

A. 10/1 B. 1/1
C. 1/10 D. 6.5/7.5

Q27: Sucrose (cane sugar) is a disaccharide. One molecule of sucrose on hydrolysis gives

A. 2 molecules of glucose B. 2 molecules of glucose + 1 molecule of fructose

C. 1 molecule of glucose + 1 molecule of fructose D. 2 molecules of fructose

Q28: The correct order of acid strength of the following carboxylic acids is -

A. I > III > II > IV B. III > II > I > IV

C. II > I > IV > III D. I > II > III > IV

Q29: The IUPAC name of the following complex is[Cr(N H 3 ) 3 (H 2 O) 2 Cl]Cl 2 .

A. Triamminediaqua chlorido chromium (III) B. Diaquatriammine chlorido chromium (III)

chloride chloride.
C. Chlorido diaquatriammine chromium (III)
D. Triammine diaqua trichlorido chromium (III).
chloride.

Q30: What is the major product 'R' in the following reaction sequence?

A. o-Nitroaniline B. m-Nitroaniline
C. p-Nitroaniline D. p-Aminobenzene sulphonic acid

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Q31: Molarity of a 50 mL H SO solution is 10.0 M . If the density of the solution is 1.4 g/cc, calculate its
2 4

molality (mark answer to nearest integer) __________.

A. 12 B. 24
C. 72 D. 48

Q32: Which of the following cannot evolve more than one gas (vapour) if heated in dry test tube.

A. P b(N O 3
) 2 (s) B. M gCO 3
(s)

C. F eSO 4
(s) D. (N H 4
) 2 Cr 2 O 7 (s)

Q33: Identify X, Y , Z in the following reaction sequence

B.
A.

C. D.

Q34: Match the following.

Column - I Column - II
A. Acetaldehyde, vinyl alcohol P. Enantiomers
B. Eclipsed and staggered ethane Q. Tautomers
C. (+)2-butanol, (−)2-butanol R. Chain isomers
D. Methyl-n-propylamine and diethylamine S. Conformational isomers
T. Metamers
A, B, C, D match with

A. P, S, R, T B. Q, S, P, T
C. T, P, S, Q D. T, P, R, Q

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Q35: The correct match of the contents in column I with those in column II is

Column - I Column - Ii
A. H e P. Highest electron gain enthalpy
B. Cl Q. Most electropositive element
C. Cs R. Strongest reducing agent
D. Li S. Highest ionisation energy

A. A - R, B - P, C - Q, D - S B. A - S, B - R, C - Q, D - P
C. A - P, B - Q, C - R, D - S D. A - S, B - P, C - Q, D - R

Q36: For a hypothetical H -like atom, which follows Bohr model, some spectral lines are observed as shown. If
it is known that line E belong to visible region., then the line, which possibly belong to U.V. region is/are? (n is 1

not necessarily the ground state)

A. B and D B. D only
C. C only D. A only

Q37: Oxygen is more electronegative than sulphur. Yet H 2

S is acidic while H 2
O is neutral. This is because -

A. Water is a highly associated compound B. Molecular mass of H 2

S is more than that of H 2
O

C. H is gaseous under ordinary conditions while

S
D. H − S bond is weaker than H − O bond
2

H2 O is a liquid

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Q38:

A.
B.

D.
C.

Q39: Which one of the following reactions will not result in the formation of carbon-carbon bond?

A. Reimer-Tieman reaction B. Friedel Craft’s acylation

C. Wurtz reaction D. Cannizzaro reaction

Q40: Which one of the following lanthanide ions does not exhibit paramagnetism?

A. Lu 3+
B. Ce 3+

C. Eu 3+
D. Y b 3+

Q41: Steam distillation process cannot be used for purifying which of the following?

A. Aniline B. p-nitrophenol
C. Toluene D. Nitrobenzene

Q42: Select the set having incorrect statements given here.

i. Manganese exhibits +7 oxidation state.

ii. Zinc forms coloured ions
iii. [CoF ] is diamagnetic
6
3−

iv. Sc forms +4 oxidation state

v. Zn exhibits only +2 oxidation state

A. (i), (ii) and (iii) B. (ii), (iii) and (iv)

C. (i), (iii) and (iv) D. (i), (iii) and (v)

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Q43: The sublimation energy of I 2 (s) is 57.3 kJ mol −1

and the enthalpy of fusion is 15.5 kJ mol −1
. The enthalpy
of vaporization of I is
2

A. 41.8 kJ mol −1
B. −41.8 kJ mol −1

C. 72.8 kJ mol −1
D. −72.8 kJ mol −1

Q44: What are X and Y in the following reaction sequence ?

A. B.

C. D.

Q45: A solution when treated with dimethyl glyoxime gives a rosy red complex. The metal present is
__________

A. N i B. Al
C. Co D. M n

Q46: At 400 K , in a 1.0 L vessel, N O is allowed to attain equilibrium, N O ( g) ⇌ 2N O ( g) At equilibrium,

2 4 2 4 2

the total pressure is 600 mmH g, when 20% of N O is dissociated. The value of K for the reaction is
2 4 p

Q47: The bond order of O +

2
−
, O2 , O2 and O 2−
2
will be A, B, C, D respectively, Find A + 2B + C − D.

Q48: Consider a titration of potassium dichromate solution with acidified Mohr’s salt solution using diphenyl
amine as indicator. The number of moles of Mohr’s salt required per mole of dichromate is

Q49: In the reaction, P + Q → R + S

The time taken for 75% reaction of P is twice the time taken for 50% reaction of P . The concentration of Q varies
with reaction time as shown in the figure. The overall order of the reaction is

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Q50: The molar conductivity of a solution of a weak acid H X(0.01 M ) is 10 times smaller than the molar
conductivity of a solution of a weak acid H Y (0.10 M ). If λ ≈ λ , the difference in their pK values,
0
X
−
0
Y
− a

pK (H X) − pK (H Y ), is (Consider degree of ionization of both acids to ≪ 1)

a a

Maths

Q51: If B, C are square matrices of same order such that C 2

= BC − CB and B 2
= −I , where I is an identity
matrix, then the inverse of matrix (C − B) is

A. C B. C + B
C. C − B D. I

Q52: 3 women and 15 men are to be arranged in a row such that there should be atleast 2 men between all the
two consecutive women. Then number of such arrangements is :

A. 14
C 4 3! B. 3!15!
C. 14
C 12 D. 14
C 3 3!15!

Q53: Let M be the foot of the perpendicular from a point P on the parabola y = 8(x − 3) onto its directrix and 2

let S be the focus of the parabola. If △SP M is an equilateral triangle, then P is equal to

A. (4, √3, 8) B. (8, 4√3)

C. (9, 4√3) D. (4, 3√9)

Q54: The minimum value of the function, f (x) = x 3/2

+ x
−3/2
− 4 (x +
1

x
. for all permissible real values of x, is
)

A. −10 B. −6
C. −7 D. −8

n n

Q55: A data consists of n observations: x 1, x2 , … , xn . If ∑ (x i + 1)

2
= 11n and ∑ (x i − 1)
2
= 7n , then the
i=1 i=1

variance of this data is

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

Q56: If (1!) 2
+ (2!)
2
+ (3!)
2
+ ⋯ + (99!)
2
+ (100!)
2
is divided by 100, then the remainder obtained is

A. 27 B. 28
C. 17 D. 14

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Q57: For some real number λ, if the area of the triangle having a ^ and →
→ = 3^i − ^j + λk b = λ^
i +^ ^ as two of its
j − 3k

sides is , then the number of distinct possible values of λ is

√ 195

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

Q58: The number of points (x, y) satisfying x 2

+ y
2
≤ 4 and tan x + cot
4 4
x + 1 = 3 sin
2
y is equal to

A. 4 B. 2
C. 3 D. 5

Q59: For any three positive real numbers a, b and c, 4 (9c 2

+ b ) + 9 (a
2 2
− 2ac) = 6b(2c + a) . Then:

A. b, c and a are in A.P. B. c, a and b are in A.P.

C. a, b and c are in G.P. D. b, c and a are in G.P.

2 2
x (x sec x+tan x)
Q60: If ∫ , then f (A + B) =
f (x)

2
dx = A log(|x sin x + cos x|) + B + C
(x tan x+1) (x tan x+1)

A. 1 B. 0
C. −1 D. 2

Q61: The number of points P (x, y) with natural numbers as coordinates that lie inside the quadrilateral formed
by the lines 2x + y = 2, x = 0, y = 0 and x + y = 5 is

A. 12 B. 10
C. 6 D. 4

Q62: The solution of the differential equation xy log ( x

y
)dx + {y
2
− x
2
log (
x

y
)}dy = 0 is

A. B.
2 2 2 2
x x x x x x
2
log ( ) − 2
= − log y + log c 2
log ( ) − 2
= log y + log c
2y y 4y 2y 4y 4y

C. log (
2
x

y
) −
x

4y
2
= log y + log c = 0 D. None of these

Q63: There are n sets of observations given as (1), (2, 3), (4, 5, 6), (7, 8, 9, 10), . . . . . The mean of the 13th set of
observations is equal to

A. 70 B. 80
C. 75 D. 85

Q64: Let the tangents drawn from the origin to the circle x 2
+ y
2
− 8x − 4y + 16 = 0 touch it at the point A and
B. The (AB) is equal to
2

A. 32

5
B. 64

C. 52

5
D. 56

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Q65: Let g(x) = 3f ( x

3
) + f (3 − x) and f ′′
(x) > 0 for all x ∈ (0, 3). If g is decreasing in (0, α) and increasing in
(α, 3) then 8α is

A. 24 B. 0
C. 18 D. 20

Q66: If α = sin (cot (tan (cos ))) and β = sin (cosec

−1
(cot (tan
−1
))) are the roots of the quadratic
2

3
−1 −1 1

equation ax + bx + c = 0 where a, b, c are integers and c is prime then the value of (a + b + c) equals
2

A. 20 B. 11
C. 7 D. 2

Q67: Let f (x) = x + bx + c, b is negative odd integer, f (x) = 0 has two distinct prime number as roots, and
2

b + c = 15, then least value of f (x) is

A. −233

4
B. 233

C. − 225

4
D. none of these

Q68: If f : R → R be a differentiable function, such that f (x + 2y) = f (x) + f (2y) + 4xy for all x, y ∈ R then

A. f ′
(1) = f (0) + 1
′
B. f ′ ′
(1) = f (0) − 1

C. f ′
(0) = f (1) + 2
′
D. f ′ ′
(0) = f (1) − 2

Q69: Let R is a relation defined as R = (1, 2), (2, 3), (3, 4). The minimum number of ordered pairs which should
be added to make relation ‘R’ equivalence relation, are

A. 7 B. 9
C. 13 D. 11

Q70: Two numbers 'a' and 'b' are chosen at random from the numbers 1, 2, 3, . . . .30. The chance that a 2
− b
2
is
divisible by '3' is

A. 9

87
B. 12

87

C. 15

87
D. 47

87

π π
sin x+cos x

Q71: If ∫ sin x(sin x+1)e

e
cos x
+1
dx = a + b ∫ e
sin x
dx where a and b are positive rational numbers, then find the value
0 0

of 100 (a 2
+ b )
2
.

Q72: Consider the system of equations ax + y + bz = 0, bx + y + az = 0 and ax + by + abz = 0 where

a, b ∈ {0, 1, 2, 3, 4}. The number of ordered pairs (a, b) for which the system has non-trivial solutions is

Q73: The area (in square units) bounded by the curves y = 2x and y = max{x − [x], x + |x|} in between the 2

lines x = 0 and x = 2 is ( where [⋅] denotes the greatest integer function)

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Q74: Let L :1
x−1

1
=
y−1

2
= and L :
z−1

k
= 2 =
x−3

1
be two intersecting lines and L be a straight line
y−2

−1
z−3

−1
3

which is perpendicular to L and L and passing through their point of intersection. If length of perpendicular
1 2

from (3, 1, 2) to the line L is λ then [λ] equals [Note: [λ] denotes the greatest integer function less than or equal
3

to λ.]

12

∑ |α k+1 −α k |

Q75: For any integer k, let α k

= cos (
kπ

7
) + i sin (
kπ

7
, where i = √−1. The value of the expression
)
k=1

∑ |α 4k−1 −α 4k−2 |
k=1

is

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