11-01-2025

6001CJA10102124033 JM

PHYSICS

SECTION-I

1) In a series resonant R-L-C circuit, if L is increased by 25% and C is decreased by 20%, then the
resonant frequency will :–

(A) increase by 10%

(B) decrease by 10%
(C) remain unchanged
(D) increase by 2.5%

2) A thin steel ring of inner radius r and cross-sectional area A is fitted on to a wooden disc of radius
R (R > r). If Young's modulus be Y, then the tension in the steel ring is

(A)

(B)

(C)

(D)

3) In a YDSE, light of two different wavelengths (λ1 & λ2) are incident normal to the plane of slits.
The nth maxima of λ1 coincides with the mth maxima of λ2 exactly in front of one of the slits.

Given D = 1.5 m; d = 3 mm
4500 Å < λ1 , λ2 < 7000 Å
then n, m and λ1 are

(A) 3, 4, 4000 Å
(B) 5, 6, 6000 Å
(C) 2, 3, 5000 Å
(D) 4, 5, 3000 Å
4) A 2μF capacitor is charged as shown in the figure. The percentage of its stored energy dissipated

after the switch S is turned to position 2 is

(A) 0 %
(B) 20 %
(C) 75 %
(D) 80 %

5) The figure shows a conducting loop ABCDA placed in a uniform magnetic field (strength B)
perpendicular to its plane. The part ABC is the (3/4)th portion of the square of side length ℓ. The part
ADC is a circular arc of radius R. The points A and C are connected to a battery which supply a
current I to the circuit. The magnetic force on the loop due to the field B is

(A) zero
(B) BIℓ
(C) 2BIR

(D)

6) Two blocks (from very far apart) are approaching towards each other with velocities as shown in

figure. The coefficient of friction for both the blocks is µ = 0.2

Linear momentum of the system is :

(A) conserved all the time

(B) never conserved
(C) is conserved upto 5 seconds
(D) none of these
7)

Find equivalent resistance between A & B.

(A)

(B)

(C) R
(D) 4R

8) A particular type of nucleus whose decay constant is λ is produced at a steady rate of p nuclei per
second. The number of nuclei N present t second after the production starts is :

(A)

(B)

(C)

(D) None of these

9) A square plate of edge a/2 is cut out from a uniform square plate of edge 'a' as shown in figure.
The mass of the remaining portion is M. The moment of inertia of the shaded portion about an axis
passing through 'O' (centre of the square of side a) and perpendicular to plane of the plate is :
(A)

(B)

(C)

(D)

10) A metal ball of mass 0.1 kg is heated upto 500°C and dropped into a vessel of heat capacity 800
JK–1 and containing 0.5 kg water. The initial temperature of water and vessel is 30°C. What is the
approximate percentage increment in the temperature of the water ? [Specific Heat Capacities of
water and metal are, respectively, 4200 Jkg–1K–1 and 400 JKg–1K–1]

(A) 30%
(B) 20%
(C) 25%
(D) 15%

11) Five parallel infinite wires are placed at the vertices of a regular polygon. Four wires carry
current I0 each. While the fifth wire carries current 3I0 as shown. The resultant magnetic field at the

centre O is :-

(A) 0

(B)

(C)

(D)

12) Two particles A and B having equal charges after being accelerated through the same potential
difference, enter a region of uniform magnetic field and describe circular paths of radii R1 and R2
respectively. The ratio of mass of A to that of B is :

2
(A) (R1/R2)
1/2
(B) (R1/R2)
3/2
(C) (R2/R1)
(D) (R1/R2)

13) The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U = 3PV + 4.
The gas is:

(A) Diatomic only

(B) Polyatomic only
(C) Either monoatomic or diatomic
(D) Monoatomic only

14) A uniformly charged ring of mass m, charge q and radius 3R and a particle of equal mass m and
charge –q are arranged in a gravity free space and both are released from rest as shown.

Maximum speed of ring in subsequent motion is :-

(A)

(B)

(C)

(D)

15) Two particles perform simple harmonic motion of same frequency and about same mean
position. Their amplitude is same and is equal to A and their time period is T. If at t = 0 their

separation is A with one particle at mean position, their separation at t = is :-

(A)

(B) A

(C)

(D) 0

16) In a plane electromagnetic wave, the directions of electric field and magnetic field are
represented by and , respectively. What is the unit vector along direction of propagation of
the wave.

(A)
(B)

(C)

(D)

17) If the velocity V of a particle moving along a straight line decreases linearly with its
displacement S from 20 m/s to a value zero at S = 30 m, then acceleration of the particle at S = 15

m is :-

(A)
m/s2

(B)

(C)

(D)

18) A prism of refractive index √2 and apex angle A is shown. Light is incident from PQ side at angle

of incidence i (0 < i ≤ 90°). Choose the wrong option:

(A) If A = 40° then light incident at all angles will emerge from surface PR.
If A = 80° then light incident at some angles will emerge from surface PR and at some other
(B)
angles light will suffer TIR at surface PR.
(C) If A = 100° then light incident at all angles will be reflected back from surface PR.
(D) whatever is the value of A, light will emerge from the surface PR for some value of i.

19) A particle of mass m moving with velocity u makes an elastic one-dimensional collision with a
stationary particle of mass m. They are in contact for a very brief time T. Their force of interaction

0 0
increases from zero to F linearly in time . The magnitude of F is
(A)

(B)

(C)

(D)

20) The earth is moving around the sun in an elliptical orbit. Point A is the closest and point B is the
farthest point in the orbit, as shown. In comparison to the situation when the earth passes through
point B :

(A) total energy of the earth-sun system is greater when the earth passes through point A.
gravitational potential energy of the earth-sun system is greater when the earth passes through
(B)
point A.
kinetic enrgy of the earth due to the motion around the sun is greater when it passes through
(C)
the point A.
magnitude of angular momentum of the earth about the sun is greater when the earth passes
(D)
through point A.

SECTION-II

1) In the given figure the angle (in degree) between the velocity vector of object and image is α. Find

the value of α/10 is :

2) If potential of A is 5V, then potential of B in volt is

3) A spherical ball of density ρ and radius 0.003m is dropped into a tube containing a viscous fluid.
Viscosity of the fluid = 1.260 SI unit and its density ρL= ρ/2 = 1260 kg.m–3. Find its terminal speed in
cm/s. (g = acceleration due to gravity = 10 ms–2)

4) A particle is thrown horizontally with speed 10 m/s along the rim of a smooth fixed cylinder of
height 20m. Taking g = 10 m/s2, the time taken by the particle to reach the bottom assuming it to be

always in contact with the cylinder is (in sec).

5) A uniform magnetic field of 0.06 T is inside plane of the figure. The resistance of rod is 25Ω, mass
is 36 gm and it can slide freely on smooth parallel rails which are perfectly conducting. The whole
system is in horizontal plane. The rod starts from rest. If terminal velocity of the rod (in m/s) is v

then find .

CHEMISTRY

SECTION-I

1) If for a reversible reaction ΔH = 0, then what will be the effect of increasing temperature on the
equilibrium constant -

(A) It increases
(B) It remains constant
(C) It decreases
(D) Cannot be predicted
2) Correct orders of 1st I.P. are -

(A) (i), (ii)

(B) (ii), (iii)
(C) (i), (iii)
(D) (i), (ii), (iii)

3) The maximum number of electrons that can have principal quantum number n = 3 and spin

quantum number is-

(A) Nine
(B) Eight
(C) Five
(D) Ten

4) (P) & (Q) are two functional isomer of molecular formula 'C3H8O'. If (Q) gives yellow crystal with
NaOI then compound (P) may be :

(A)

(B)

(C)

(D)

5) Which is the most basic among the following :

(A)
(B)
(C)
(D)

6) Pyrimidine bases present in RNA are -

(A) cytosine + adenine

(B) thymine + cytosine
(C) cytosine + uracil
(D) thymine + uracil

7) One among the following compounds will not give effervescence with sodium bicarbonate.

(A)
(B)

(C)

(D)

8)

(A)

(B)

(C)

(D)

9) Identify the compound which rotate the plane polarised light.

(A)

(B)

(C)

(D)

10) 50mL of 0.2M KOH is added to 40mL, 0.5M HCOOH. The pH of the resultant solution (if Ka of
HCOOH is 10-4)

(A) 3
(B) 4
(C) 5
(D) 7

11) For the following cell

When the concentration of Zn+2 is 10 times the concentration of Cu+2, the expression for the ΔG
(J/mol) is:
[F - Faraday constant, R is gas constant, T - Temperature , ]

(A) 2.303RT+1.1F
(B)
(C) 1.1F
(D) -2.2F

12) A first order reaction is 50% completed in 1.26 × 1014 s. How much time would it take for 100%
completion?

(A)
(B)
(C)
(D) Infinite

13) Which of the following ion is responsible for the brown colour in the ring test for nitrate?

(A)

(B)

(C)

(D)

14) Which of the following reagents may be used to distinguish between phenol and benzoic acid?

(A) Aqueous NaOH

(B) Tollen's reagent
(C) Molisch reagent
(D) Neutral FeCl3

15) Among the following the strongest acid is

(A)
(B)
(C)
(D)
16) The IUPAC name of the following compound is

(A) 2-Amino-4-hydroxy-3-chloro pentane

(B) 2-Amino-3-chloro-4-hydroxy pentane
(C) 3-chloro-4-hydroxy-2-pentanamine
(D) 4-amino-3-chloro-2-pentanol

17)
Which of the following reactants gives the above reaction most successfully?

(A)

(B)

(C)

(D)

18) KMnO4 on heating gives

(A) K2MnO4
(B) Mn2O3
(C) Mn2O7
(D) K2O

19)
The values of X, Y and Z in the above redox reaction are respectively

(A) 2, 1, 3
(B) 3, 1, 6
(C) 2, 1, 2
(D) 3, 1, 4

20) The enthalpy of vaporization of a liquid is 30 kJ mol-1 and entropy of vaporisation is 75J mol-1K-1.
The boiling point of the liquid at 1 atm is

(A) 250 K
(B) 400 K
(C) 450 K
(D) 600 K

SECTION-II

1) A sample of 0.50 g of an organic compound was treated according to Kjeldahl’s method. The
ammonia evolved was absorbed in 50 ml of 0.5 M H2SO4. The residual acid required 60 mL of 0.5 M
solution of NaOH for neutralisation. The percentage composition of nitrogen in the compound.

2) If enthalpy of neutralisation of HCl by NaOH is -57 kJ mol-1 and with NH4OH is -50 kJ mol-1.
Calculate enthalpy of ionisation of NH4OH(aq).

3) The number of electron pairs in bonding molecular orbitals of O2 is

4)
Number of monochlorinated products including stereo isomers

5) The number of essential amino acids among the following compound is

Valine, Serine, Lysine, Leucine, Aspartic acid, Threonine, Tyrosine,

Tryptophan, Glutamine and Methionine.

MATHEMATICS

SECTION-I

1) The integral equal to :

(A) 37/6 – 35/6

(B) 35/3 – 31/3
(C) 34/3 – 31/3
(D) 35/6 – 32/3

2) Number of rational terms in the expansion of is

(A) 25
(B) 26
(C) 27
(D) 28

3) A curve y = f (x) is passing through (0, 0). If the slope of the curve at any point (x, y) is equal
to (x + xy), then the number of solution(s) of the equation f (x) = 1, is :

(A) 0
(B) 1
(C) 2
(D) 4

4) If the line is one of the angle bisector of the lines and

, then the ordered pair (α, β) is -

(A) (0, 0)
(B) (2, 3)
(C) (–2, –3)
(D) (1, 4)

5) Let and . If is a vector of magnitude 2, then maximum value of

is

(A)
(B)
(C)
(D)

6) A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then
the length of the semi-major axis is-

(A)

(B)

(C)

(D)

7)

If a2b3c4, a3b4c5, a4b5c6 are in A.P. (a,b,c > 0), then minimum value of (a + b + c) is equal to-

(A) 1
(B) 3
(C) 4
(D) 8

8) Tangents are drawn from (4, 4) to the circle x2 + y2 – 2x – 2y – 7 = 0 to meet the circle at A and B.
The length of the chord AB is -

(A) 2
(B) 3
(C) 2
(D) 6

9) If the image of point P(2, 3) in a line L is Q (4, 5) then, the image of point R (0, 0) in the same line
is :

(A) (4, 5)
(B) (2, 2)
(C) (3, 4)
(D) (7, 7)

10) Given & , then -

(A) S + P < 0
(B) S.P > 0
(C)
(D) logP(1+S) > 0

11) For (where { } denotes fractional part function)

(A) LHL exist but RHL does not exist

(B) RHL exist but LHL does not exist.
(C) neither LHL nor RHL does not exist
(D) both RHL and LHL exist and equals to 1

12) Mr. X walk up 16 steps, going up either 1 or 2 steps at a time. There is an explosive material on
the 8th step so he cannot step there. The number of ways in which Mr. X can go up 16 steps
(Assuming he starts from the ground level) is ?

(A) 441
(B) 420
(C) 462
(D) 400

13) Let and ƒ(0) = 0 then value of ƒ(1) be

(A)

(B)

(C)

(D)

14) Let z ∈ C, the set of complex numbers. Then the equation, 2|z + 3i| = |z – i| represents :

(A)
an ellipse with length of major axis

(B)
a circle with diameter

(C)
a circle with radius

(D)
an ellipse with length of minor axis

15) If then is equal to :

(A)

(B)

(C)

(D)

16) If , then-

(A) tanθ1,tanθ2,tanθ3 are in A.P.

(B) tanθ1,tanθ2,tanθ3 are in G.P.
(C) tanθ1,tanθ2,tanθ3 are in H.P.
(D) tanθ1,tanθ2,tanθ3 are not in A.P./G.P./H.P.

17) Let A and B be two invertible matrices of order 3 × 3. If det(ABAT) = 8 and det(AB–1) = 8,
then det (BA–1 BT) is equal to :

(A) 16

(B)

(C)

(D) 1
18) The mean and variance of 5 observations of an experiment are 4 and 5.2 respectively. If from
these observations three are 1, 2 and 6, then the remaining will be-

(A) 2, 9
(B) 5, 6
(C) 4, 7
(D) 3, 8

19) Let If ƒ(x) is differentiable in [0,2], then value of p is-

(A)

(B)

(C)

(D)

20) For an initial screening of an admission test, a candidate is given fifty problems to solve. If the

probability that the candidate can solve any problem is , then the probability that he is unable to
solve less than two problems is :

(A)

(B)

(C)

(D)

SECTION-II

1) If the area bounded by curve x + |y| = 1 and the y-axis is k, then k is equals to :

2) Let f be a function such that f(3) = 1 and f(3x) = x + f(3x – 3) for all x. Then find the value of
f(300).

3) Let y = mx + c, m > 0 be the focal chord of y2 = –64x, which is tangent to (x + 10)2 + y2 = 4.

Then, the value of (m + c) is equal to_______.
4) The greatest value of , & is k, then the value

of is

5) If α, β, γ are the roots of the equation x3 + 2x2 – x + 1 = 0, then value of is

:
 ANSWER KEYS

PHYSICS

SECTION-I

Q. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A. C B B D B C B A B B C A B A B A B D B C

SECTION-II

Q. 21 22 23 24 25
A. 9 7 2 2 4

CHEMISTRY

SECTION-I

Q. 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
A. B D A D D C C C B B B D A D D D A A B B

SECTION-II

Q. 46 47 48 49 50
A. 56 7 5 6 6

MATHEMATICS

SECTION-I

Q. 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
A. A B C C D A B B D C B A B C D B B C A B

SECTION-II

Q. 71 72 73 74 75
A. 1 5050 34 5 5
 SOLUTIONS

PHYSICS

1)

2)

Strain =

Strain =

, A=F

F = AY

3) ; n = 1, 2, 3, 4.....

; m = 1, 2, 3, 4......

from central fringe.

5) ≡
F = Bi1ℓ + Bi2ℓ
= Bℓ(i1 + i2) = Biℓ

6)
1kg comes to rest in 5 sec after that ext friction on left blocks remain.
So momantum after 5 sec is not conserved.
7) Opening the upper node and removing the two resistors from the middle branches, we get.

Solving we get Req = .

8) The instantaneous rate of growth of the nuclei is

or

On integrating,

at t = 0, N = 0

or

or

or

9)

M1 = mass of square plate of side a

M2 = mass of square plate of side .

...(1)

Now,

10)

0.1 × 400 × (500 – T) = 0.5 × 4200 × (T – 30)+ 800 (T – 30)

⇒ 40(500 – T) = (T – 30) (2100 + 800)
⇒ 20000 – 40T = 2900 T – 30 × 2900
⇒ 20000 + 30 × 2900 = T(2940)
T = 30.4°C
 ×100=

11)

If current in all wire are same, then magnetic field at centre will be zero.

12) = qvB

⇒r=

13)

U = 3PV + 4

= 3PV + 4

= 3PV + 4

f=6+
Since degree of freedom is more than 6 therefore gas is polyatomic

14) By energy and momentum conservation

15)

at t = ϕ=π
x = Asinπ = 0

16)

Direction of wave propagation =

17)

=
at s = 15 m , V = 10 m/s

a= m/s2

18) Light will emerge from prism if A < θC

Light will not emerge from prism if A > 2θC ∴ θC = 45°

19)

21)

23) Ma = Fnet = Mg – B – 6πηrv

at v = vT , a = 0
⇒ Mg – B = 6πηrvT
 ⇒ vT =

24)

25)

ε = Blv = 36

v= = 1200 m/s

CHEMISTRY

26)

If ΔH = 0 then
i.e.: K2=K1

28)

______
9e-
_____

29) gives iodoform test

is the functional isomer

30) Aliphatic amines are more basic than arylamines and 2º aliphatic>1º aliphatic amines

32) H2CO3 is stronger acid than alcohol

33) BH3/THF is a syn addition

34) (2s, 3s)-2,3-dichloro butane is Dys-Symmetric

35) KOH + HCOO HCOOK + H2O

10mmol 20mmol __ __
0 10 10 __

=4

36)
-nFEcell = -2 × Fl.1+ 2.303RT

37) A first order reaction takes infinite time to complete

38) Brown ring complex is

39) violet colour

40)
(-ve) charge on more electro (-ve) element

41) Order of priority -OH> -NH2

42) Halide is most successful

43)

44) The balanced equation is given below.

The value of X, Y and Z are 3, 1 and 6 respectively.

45)

= 400 K

46)
=56
 48)

49)

MATHEMATICS

51)

= 37/6 – 35/6

52)
for rational terms
r = 0, 4, 8, 12, ....., 100

53) = x + xy

– xy = x
I.F. =

y· = =
y= –1
at x = 0, y = 0
∴ C=1
∴ f (x) = –1
∴ f (x) = 1 ⇒ =2

Number of solution is 2

54) Clearly point of intersection of lines is (1, 2, 3).

Angle bisector must pass through this point.

Hence ⇒

55)

56) PS2 = e2Pm2

x2 + y2
4x2 + 4y2 = x2 – 8x + 16
3x2 + 8x + 4y2 = 16

Length of semi major axis

57)

2a3b4c5 = a2b3c4 + a4b5c6

div. by a2b3c4, we get
2abc = 1 + a2b2c2 ⇒ (abc–1)2 = 0 ⇒ abc = 1

58) Equation chord of contact

4x + 4y – 4 – x – y – 4 – 7 = 0
3x + 3y = 15
Radius = 3

AM2 = OA2 – OM2

= 32 –
Hence option (B) is correct.

59) mid-point A(3, 4)

slope of PQ = = 1
slope of AL = –1
Equation L = y – 4 = –1(x – 3)
⇒ x+y–7=0
m1 × m2 = –1

= –1
β=α ... (1)

& ... (2)

equation (1) & (2)
α=β=7

60)

∴
61) as {I + x } = {x} ; as and

as sin{x} → sin(1) and {–x} → 0 ]

62) No. of 1 steps = x, No. of 2 steps = y

x + 2y = 7

; ;

1,2,2,2, =
Total = 21 steps
Again from 9th to 16th steps
(total = 7 steps) we have
x + 2y = 7 (No. of ways = 21)

63)

64) 2|z + 3i| = |z – i|

z = x + iy
4(x2 + (y + 3)2) = (x2 + (y – 1)2)
2 2
= 3x + 3y + 26y + 35 = 0

This is equation of a circle, centre and radius .

65)

66)
using componendo & dividendo,
⇒
⇒

67) |A|2.|B| = 8 and ⇒ |A| = 4 and

∴ det(BA–1.BT)

68)

from (1) & (2) a = 4, b = 7

69) Continuous at x = 1

∴ p + q = –2 +
Differentiable at x = 1

70) P(s) = P(F) =

Probability of at least 49 success is

71)
area = 2 × =1=k

72) f(3) = 1
f(3x) – f(3x–3) = x
x=2 f(6) – f(3) = 2
x=3 f(9) – f(6) = 3
:

73) y2 = –64x
focus : (–16, 0)
y = mx + c is focal chord
⇒ c = 16m .......(1)
y = mx + c is tangent to (x + 10)2 + y2 = 4
⇒
⇒
⇒
⇒ (m > 0)
2 2
⇒ 9m = 1 + m

⇒ &

74)
∴ h(x) = x4 + t2 – 2tx2 + cos2x
h'(x) = 4x3 – 4tx – sin2x
⇒ 4x3 – 5tx – sin2x = 0 ⇒ x = 0
∴ h''(x) = 12x2 – 4t – 2cos2x
at x = 0, h''(0) = –4t – 2 > 0
min value of x4 + t2 – 2tx2 + cos2x is t2 + 1

max ƒ(x) is ⇒

75) P(x) = (x3 + 2x2 – x + 1) = (x – α) (x – β) (x – γ)

P(2) = (15) = (2 – α) (2 – β) (2 – γ)
P(–2) = (–8 + 8 + 2 + 1) = (–2 – α) (–2 – β) (–2 – γ)
–3 = (2 + α) (2 + β) (2 + γ)