09-03-2025

3010CJA101002240039 JA

PART-1 : PHYSICS

SECTION-I(i)

1) An artificial satellite moving in a circular orbit around the Earth has a total (kinetic + potential)
energy E0. Its potential energy is

(A) E0
(B) 1.5 E0
(C) 2 E0
(D) 3 E0

2) In a stationary wave

(A) all the medium particles vibrate in the same phase.

(B) all the particles between two consecutive nodes vibrate in the same phase.
(C) any two consecutive nodes vibrate in the same phase.
(D) all the particles between two consecutive antinodes vibrate in the same phase.

3) A disc of mass M and radius R is reshaped in the form of ring of same mass but radius 2R. The
radius of gyration increased by a factor :

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

4) A particle executes SHM on a line 8 cm long. Its K.E. and P.E. will be equal when its distance
from the mean position is :–

(A) 4 cm
(B) 2 cm
(C) 2 cm
(D) cm

SECTION-I(ii)

1) Consider the following statements :

S1 : An object shall weigh more at pole than at equator when weighed by using a physical balance.
S2 : It shall weigh the same at pole and equator when weighed by using a physical balance.
S3 : It shall weigh the same at pole and equator when weighed by using a spring balance.
S4 : It shall weigh more at the pole than at equator when weighed using a spring balance.
Which of the above statements is/are correct?

(A) S1
(B) S2
(C) S3
(D) S4

2) A wave equation which gives the displacement along the Y direction is given by
where x and y are in metres and t is time in seconds. This represents a wave

(A) travelling with a velocity of 30 m/s in the negative x direction.

(B) of wavelength π metre
(C) of frequency 30/π hertz
(D) of amplitude 10–4 metre travelling along the negative x direction

3) A mass of 0.2kg is attached to the lower end of a massless spring of force-constant 200 N/m, the
upper end of which is fixed to a rigid support. Which of the following statements is/are true?

(A) In equilibrium, the spring will be stretched by 1cm.

If the mass is raised till the spring is unstretched state and then released, it will go down by
(B)
2cm before moving upwards.
(C) The frequency of oscillation will be nearly 5 Hz.
(D) If the system is taken to the moon, the frequency of oscillation will be the same as on the earth.

4) The potential energy of a particle of mass 2 kg moving along the x–axis is given by U(x) = 16(x2 –
2x) joule. Its velocity at x = 1 m is 2 m/s. Then :

(A) mean position of particle is x = 2 m

(B) the particle describes oscillatory motion from x1 = 0.5 m to x2 = 1.5m
(C) the particle executes simple harmonic motion
(D) the period of oscillation of the particle is π/2 second

5) In the given figure a ball strikes a rod elastically and rod is smoothly hinged at point A. Then

which of the statement(s) is/are correct for the collision?

(A) linear momentum of system (ball + rod) is conserved.

(B) angular momentum of system about hinged point A is conserved.
(C) KE of the system just before collision is equal to KE of the system just after collision.
(D) linear momentum of ball is conserved.

6) In the figure shown a uniform rod of mass m and length ℓ is hinged. The rod is released when the

rod makes angle θ = 60° with the vertical.

The angular acceleration of the rod just after release is

(A)

The normal reaction due to the hinge just after release is

(B)

The angular velocity of the rod at the instant it becomes vertical is

(C)

(D)
The normal reaction due to the hinge at the instant the rod becomes vertical is mg

SECTION-III

1) Two large spherical object of mass M each (uniformly distributed) are fixed as shown in figure. A
small point mass m is projected from point A heading towards center C2 of second sphere. The

minimum velocity of point mass so that it can reach upto second object at point B is then
calculate n. [Points A & B lie at surfaces of spheres and neglect other gravitational forces]

2) The equation of a plane progressive wave is . Find the value of A for which the
wave speed is equal to the maximum particle speed

3) A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of
air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

4) If the system shown in the figure is compressed slightly and released, then the time period (in
sec) of oscillation will be : [Take : ]

5) A spring -mass system has time period of 20 sec. Now, the spring is cut in to 4 equal parts and
connected in parallel combination to same block. The new time period of the combination is :

6) A wire of linear mass density λ is being rotated about an axis passing through O and

perpendicular to the plane. Its moment of inertia is . Find n :

7) A solid sphere of mass m, radius r undergo pure rolling inside a fixed vertical stationary circular
track of radius R. The sphere just completes vertical circle. The normal at the lowest point of

circular track is . The value of α is

8) A uniform disc of mass M and radius R is projected horizontally with velocity u = 6 ms–1 on a
rough horizontal floor so that it starts off with a purely sliding motion at t = 0. After t0 second, it
acquires a purely roiling motion as shown in Fig. Calculate velocity v of the centre of mass (in ms–1)

of the disc at t .

PART-2 : CHEMISTRY

SECTION-I(i)

1)

1 mole of NH3 gas at 27°C is expanded in reversible adiabatic condition to make volume 8 times (γ =
1.33). Final temperature and work done respectively are :

(A) 150 K, 900 cal

(B) 150 K, 400 cal
(C) 250 K, 1000 cal
(D) 200 K, 800 cal

2) A diatomic ideal gas initially at 273 K is given 100 cal heat due to which system did 209 J work.
Molar heat capacity (Cm) of gas for the process is :
(A)
R

(B)
R

(C)
R
(D) 5 R

3) On the basis of the following thermochemical data :

H2O(ℓ) → H+(aq) + OH–(aq) ; ΔHº = 57.32 kJ mol–1

H2(g) + O2(g) → H2O (ℓ) ; ΔHº = –286.20 kJ mol–1

The value of standard enthalpy of formation of OH– ion at 25°C is :-

(A) +228.88 kJ mol–1

(B) –343.52 kJ mol–1
(C) –22.88 kJ mol–1
(D) –228.88 kJ mol–1

4) IUPAC name of following compound is

(A) N-methyl-N-ethyl cyclobutanamide

(B) N-ethyl-N-methyl cyclobutanamide
(C) N-ethyl-N-methyl cyclobutane carboxamide
(D) N-methyl cyclobutyl propanamide

SECTION-I(ii)

1) For the sublimation of a solid at 1 atm, which of the following may be correct

(A) ΔU > 0 at low temperature

(B) q > 0
(C) ΔU < 0 at high temperature
(D) ΔH > 0

2) The standard enthalpies of formation of CO2(g), and HCOOH(l) are –393.7 kJ/mol and –409.2
kJ/mol respectively :

(A) –393.7 kJ/mol is the enthalpy change for the reaction C(s) + O2(g) → CO2(g)
(B) the enthalpy changes for the reaction CO2(g) + H2(g) → HCOOH(l) would be –15.5 kJ/mol
(C) the enthalpy changes for the reaction H2O + CO → HCOOH is –409.2 kJ/mol
(D) the enthalpy changes for the reaction H2(g) + CO2(g) → H2O(l) + CO(g) is –409.2 kJ/mol

3) Select the correct statement(s).

(A) In a reversible process, ΔG is always zero in a closed system.

(B) In a reversible process, ΔSuniv is always zero in a closed system.
(C) In a reversible process, ΔSsys is always zero in a closed system.
(D) In a reversible process, ΔSsys is always zero in an isolated system.

4) Suppose a system make a transition from state X to state Y.

Given : ΔSXY = 10 J/K

(A) The state Y is more disordered than state X.

(B) ΔSXY for path 1 and 3 is same.
(C) ΔSYX = – 10 J/K
(D) The transition X → Y must be spontaneous.

5) 100 ml of 0.4 M -acidified KMnO4 solution may be decolourised completely by

(A) 200 ml 1N - K2Cr2O7 solution

(B) 300 ml 0.5M - H2O2 solution
(C) 100 ml 0.8N - KI solution
(D) 75 ml 1.4 N - H2C2O4 solution

6) Choose the incorrect statement(s):

(A) 1 mole of ion can oxidize 10 moles of ion in acidic medium

(B) 1 mole of ion can oxidize 12 moles of ion in acidic medium
2 mole of can be oxidize by 2.6 moles of ion in acidic medium
(C)

2 mole of can be oxidize by 8/3 moles of ion in acidic medium

(D)

SECTION-III

1)
A mixture of H2 and O2 in 2:1 mole ratio is used to prepare water vapour by the reaction :

2H2(g) + O2(g) → 2H2O(g) The total pressure of gases in the container is 4.5 atm at 57°C, before the
reaction. The final total pressure of gases (in atm) at 127°C after reaction assuming 80% yield of
water vapour is

2) At 273 K, the density of a gaseous oxide at 10 bar is same as that of nitrogen gas at 5 bar.
Calculate the molecular mass of oxide. (g/mole). write answer as sum of digits until you get single
digit answer.

3) A 10 g mixture of hydrogen and helium is contained in a vessel of capacity 0.0125 m3 at 6 bar and
27oC. The mass of helium in the mixture is.............g.
(nearest integer) Given: R = 8.3 JK–1 mol–1
(Atomic masses of H and He are 1 u and 4 u, respectively).

4) If at 200 K & 500 atm density of CH4 is 0.246 gm/ml then its compressibility factor (Z) is
approx 2.0 × 10x , then x is:

5) For an unknown gas for which Vander waal's constant 'a' is zero at 300 K, a curve is plotted as :

Calculate molar mass (in gm/mole) of gas : (Use : R = 0.08 atom-L/K-

mole)

6) How many isopropyl group are present in the parent chain ?

7) How many total number of substituents are present in the following compound ?
8) A hydrocarbon (R) has six membered ring in which there is no unsaturation. Two alkyl groups are
attached to the ring adjacent to each other. One group has 3 carbon atoms with branching at 1st
carbon atom of chain and another has 4 carbon atoms. The larger alkyl group has main chain of
three carbon atoms of which second carbon is substituted. Number of 2° carbons in R are :

PART-3 : MATHEMATICS

SECTION-I(i)

1) From a point P outside a circle with center at C, tangents PA and PB are drawn such that

, then the length of chord AB is

(A) 6
(B) 8
(C) 4
(D) 12

2) From point P(8, 27) tangents PQ and PR are drawn to the ellipse . Then, angle
subtended by QR at origin is

(A)

(B)

(C)

(D)
3) The length of focal chord AB of ellipse is: (Given A = )

(A)

(B)

(C)

(D)

4) In ΔABC, 2x + 3y + 1 = 0, x + y = 1 and 2x – y + 1 = 0 are median through vertex A, altitude

through vertex B and angle bisector of C respectively.

(A) slope of BC is 7

(B)
area of Δ ABC is
(C) slope of BC is 5
(D) None of these

SECTION-I(ii)

1) For a parabola x2 – 4xy + 4y2 – 32x + 4y + 16 = 0, focus is

(A) (2, 1)
(B) (–2, 1)
(C) (–2, –1)
(D) (2, –1)

2) Let x – 2y – 5 = 0 be the directrix of a parabola and x – y – 7 = 0 be the tangent drawn to the

parabola at the point P(4, –3), then which of the following are INCORRECT?

(A)
length of latus rectum =

(B)
harmonic mean of length of segments of the focal chord =
(C) intersection point of the directrix and the given tangent is (9, 2)
circle drawn on assuming P(4, –3) and Q as diameter, always passes through focus of the
(D)
parabola (where Q is the intersection point of tangent and directrix)

3) If P is any point on the ellipse whose foci are S1 & S2.Let ∠PS1S2 = α & ∠PS2S1 = β
then,

(A) PS1 + PS2 = 2a, if a > b

(B) PS1 + PS2 = 2b, If a < b

(C)
tan . tan =

(D)
tan . tan =

4) If a hyperbola passes through the point P(10, 16) and it has vertices at (+6, 0), then the equation
of the normal to it at P, is

(A) 3x + 4y = 94
(B) 2x + 5y = 100
(C) x + 2y = 42
(D) x + 3y = 58

5) The equation of the common tangent to the parabola y2 = 8x and rectangular hyperbola xy = –1 is

(A) x – y + 2 = 0
(B) 9x – 3y + 2 = 0
(C) 2x – y + 1 = 0
(D) x + 2y – 1 = 0

6) A parabola is drawn through two given points A(2, 0) and B(–2, 0) such that its directrix always
touch the circle x2 + y2 = 16, then locus of focus of the of the parabola is

(A) 3x2 + 4y2 = 48

(B) 3x2 + 4y2 = 60
(C) 4x2 + 3y2 = 48
(D) 4x2 + 3y2 = 60

SECTION-III

1) The value of k > 0 such that the angle between the lines 4x - y + 7 = 0 and kx – 5y – 9 = 0 is 45°
is

2) If x2 + αy2 + 2βy = α2 represents a pair of perpendicular lines, then sum of values of β equals to

3) Let L be a common tangent line to the curves 4x2 + 9y2 = 36 and (2x)2 + (2y)2 = 31 Then the
square of the slope of line L is

4) Two rods of length a and b slide along the axes in a manner that their ends are always concyclic.
If the locus of the centre of the circle passing through these ends is k (x2 – y2) = a2 – b2, then find the
value of k.

5) For how many values of p ∈ N the circle x2 + y2 + 2x + 4y + p = 0 represents a real circle?

6) If the reflection of the ellipse in the line mirror x – y – 2 = 0 is
2 2
k1x + k2y – 160x – 36y + 292 = 0, then |k1 – k2| is equal to

7) Area of the region bounded by |x| + |y| = 2 is

8) Tangent at a point P on meets the x-axis at A and y-axis at B. The locus of the

midpoint of AB is , then find k.

 ANSWER KEYS

PART-1 : PHYSICS

SECTION-I(i)

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

SECTION-I(ii)

Q. 5 6 7 8 9 10
A. B,D A,B,C,D A,B,C,D B,C,D B,C A,B,C,D

SECTION-III

Q. 11 12 13 14 15 16 17 18
A. 8 3 6 1 5 7 7 4

PART-2 : CHEMISTRY

SECTION-I(i)

Q. 19 20 21 22
A. A D D C

SECTION-I(ii)

Q. 23 24 25 26 27 28
A. A,B,C,D A,B B,D A,B,C B A,B,C

SECTION-III

Q. 29 30 31 32 33 34 35 36
A. 4 5 8 0 4 3 4 5

PART-3 : MATHEMATICS

SECTION-I(i)

Q. 37 38 39 40
A. B D B A

SECTION-I(ii)

Q. 41 42 43 44 45 46
A. D A,B A,B,C B A A
 SECTION-III

Q. 47 48 49 50 51 52 53 54
A. 3 0 3 4 5 7 8 4
 SOLUTIONS

PART-1 : PHYSICS

1)

U = 2E0

3)

Moment of inertia of the disc of mass M and radius R

⇒
And for the ring of same mass but radius 2R,
= M(2R)2
⇒ k2 = 2R

Thus,

7)
A = 1 cm (A)
∴ xmax = xeq + A = 2 cm (B)

(C)
f is same as m and k are same (D)

9) External force will act at hinge so linear momentum of system will not remain const. but
torque of external force is zero about hinge so = const., collision is elastic so K.E = const.

10)
(A) mg sin 60° = α

α=

(B) N2 – mg cos60° = 0 ⇒ N2 =

mg sin 60 – N1 = m

mg – . = N1

N1 =

N= = =

(C) mg (1 – cos 60°) = =

ω=

(D) N – mg =

N= mg

14)

We know that time period

μ = reduced mass

17) –2mg(R – r) =

–2mg(R – r) = . mg (R – r) – mvL2

N – mg =
 N=

PART-2 : CHEMISTRY

19)

Given g = 4/3 or 1.33

For reversible adiabatic expansion involving ideal gas

= 1 × 3R × (150 – 300)
= – 450 R
|W| = 900 cal

24) (A) C(s) + O2(g) → CO2(g)

ΔHf(CO2, g) = –393.7 kJ/mol
(B) H2(g) + C(s) + O2(g) → HCOOH(l)
ΔHf(HCOOH, l) = –409.2 kJ/mol
CO2(g) + H2(g) → HCOOH(l);
ΔrH = –409.2 – (–393.7) = –15.5 kJ/mol
(C) It doesn't represent the enthalpy of formation.
(D) It doesn't represent the enthalpy of formation.

25)

(B) In closed system, no matter exchange, only heat exchange occurs.

q = heat lost to surrounding in reversible way

ΔSsys =

ΔSsurr =
ΔSuniv = 0
(D) In isolated system, matter exchange = 0
Heat exchange = 0
ΔSsys = 0

26)

(A) ΔSXY = SY – SX > 0

SY > SX
i.e., Y is more disordered than X
(B) S is a state function, so it does not depend on type of process.
(C) ΔSXY = –ΔSYX
Because S is state function
ΔSYX = –10 J/K
27)

Eq. of KMnO4 used = 100 × 10–3 × 0.4 × 5 = 0.2 eq

We need at least 0.2 equivalents of reducing agent
(A) K2Cr2O7 is not a reducing agent
(B) H2O2 → O2
eq. of H2O2 = 300 × 10–3 × 0.5 × 2 = 0.3 eq.
(C) Eq. of KI = 100 × 10–3 × 0.8 = 0.08 eq.
(D) Eq. of H2C2O4 = 75 × 10–3 × 1.4 = 0.105 eq.

28)

32) ρ =

Z= = =2
= 2 × 10º
x=0

33)

∴ Slope = =6

35)
 36)

PART-3 : MATHEMATICS