13-07-2025

1001CJA101016250016 JA

PART-1 : PHYSICS

SECTION-I (i)

1) A particle of mass m is at rest in a train moving with constant velocity with respect to ground.
Now the particle is accelerated by a constant force F0 acting along the direction of motion of train
for time t0. A girl in the train and a boy on the ground measure the work done by this force. Which of
the following are incorrect?

(A) Both will measure the same work

(B) Boy will measure higher value than the girl
(C) Girl will measure higher value than the boy
(D) Data are insufficient for the measurement of work done by the force F0

2) A particle is performing circular motion of radius 1m. Its speed is v = (2t2) m/s. Then at t = 1s :

2
(A) Tangential acceleration, aT = 4 m/s
2
(B) Centripetal acceleration, ac = 4m/s
(C) Net acceleration, m/s2
(D) None of these

3) A cart of mass 0.5 kg is placed on a smooth surface and is connected by a string to a block of
mass 0.2 kg. At the initial moment the cart moves to the left along a horizontal plane at a speed of 7

m/s. (Use g = 9.8 m/s2)

(A)
The acceleration of the cart is towards right.
(B) The cart comes to momentary rest after 2.5 s.
(C) The distance travelled by the cart in the first 5s is 17.5 m.
(D) The velocity of the cart after 5s will be same as initial velocity.

4) A smooth sphere A of mass m collides elastically with an identical sphere B at rest. The velocity of
A before collision is 8 m/s in a direction making 60° with the line of centres at the time of impact.
(A) The sphere A comes to rest after collision
(B) The sphere B will move with a speed of 8 m/s after collision
(C) The directions of motion A and B after collision are at right angles
(D) The speed of B after collision is 4 m/s

5) Block A is released on the circular track of bigger block B from rest from the position as shown in
figure. Friction is absent everywhere. Choose INCORRECT statements :-

(A) Acceleration of center of mass of A & B is zero initially

(B) When A reaches Q acceleration of center of mass of A & B is zero
Normal force of the surface below is greater than combined weight of A & B, when A reaches
(C)
at point Q
(D) Acceleration of B is maximum when A reaches Q

6) Let us consider a system of units in which mass and angular momentum are dimensionless. If
length has dimension of L, which of the following statement (s) is/are correct ?

(A) The dimension of force is L–3

(B) The dimension of energy is L–2
(C) The dimension of power is L–5
(D) The dimension of linear momentum is L–1

SECTION-I (ii)

1) In all the four situations in List-I a ball of mass m is connected to a massless string. T is tension in
string & match with List-II.

List–I List–II

(I) (P) T = mgcosθ

conical pendulum
(angle θ is constant)
 (II) (Q) T cosθ=mg

pendulum swings, angular

position θ is extreme position,
T is tension at extreme position

(III) (R) T = mg

Car moving with constant

acceleration Ball is at rest w.r.t. car

Speed of ball
(IV) (S) w.r.t. ground is
constant
The car moving with constant
velocity. The ball is at rest w.r.t. car.

Velocity of ball
(T) w.r.t. ground is
changing
(A) I → Q,S,T;II → P,T;III → Q,T;IV → R,S
(B) I → Q,S,T;II → Q,T;III → P,T;IV → R,S
(C) I → Q,T;II → Q,S,T;III → R,T;IV → R,S
(D) I → R,S,T;II → P,T;III → P,R,T;IV → R,S

2) The centre of mass of given system is at a distance x from geometrical centre of bigger body.

List-I List-II

(I) (P) x = 0 or x > R

(Disk with one circular cavity)

Centre of mass lies outside

(II) (Q)
the bigger body
(Disk with two circular cavity)

(III) (R) 0 < x < R

(Disk with one square cavity)

 Centre of mass lies within
(IV) (S)
bigger body
(Disk with one attached circular
mass)

(T) None of these

(A) I → R,S;II → R,S;III → R,S;IV → R,S
(B) I → R,T;II → R,S;III → P,R;IV → P,Q
(C) I → R,S;II → R,T;III → Q,S;IV → Q,T
(D) I → R,S;II → R,Q;III → P,Q;IV → P,T

3)

List-I shows certain situations and List-II shows information about forces.

List-I List-II

(I) (P) is centripetal

force.

(II) (Q) is static friction.

can be in direction
(III) (R) opposite to that shown in
figure.
 (IV) (S)

(T)

(A) I → P,Q,R;II → P,Q,S;III → P,Q,R;IV → P,Q

(B) I → P,Q;II → P,Q,S;III → P,Q,R;IV → P,Q,R
(C) I → P,Q;II → P,Q,R;III → P,Q,R;IV → P,Q,S
(D) I → P,Q;II → P,R,T;III → P,R,T;IV → P,S

4) A boat is being rowed in a river. Air is also blowing. Direction of velocity vectors of boat, water

and air in ground frame are as shown in diagram.

List-I List-II

Direction in which boat is being

(I) (P)
steered

Direction in which a flag on the boat

(II) (Q)
may flutter

Direction of velocity of water relative

(III) (R)
to boat
 Direction of velocity of air relative to a
(IV) (S)
piece of wood floating on river.

(T)

(A) I → P;II → Q,S;III → S;IV → P,R

(B) I → P;II → Q;III → S;IV → T
(C) I → P;II → R;III → Q;IV → T
(D) I → R;II → P;III → S;IV → P,R

SECTION-II

1) The block of mass m is attached to a frame by spring of force constant k, entire system moves
horizontally without any frictions anywhere. The frame and block are at rest with x = x0, the relaxed
length of spring. If frame is given a constant acceleration a0. Determine the maximum velocity of

block relative to frame. (Given : a = 2 m/s2, m = 4 kg, k = 4 N/m)

2) A particle starts from initial angular velocity ω0 = 2π on a circular track of radius 1m. Such that
its total acceleration is always at angle of 45° from its velocity. Its speed after one revolution will be

(kπ)emπ. So (k + m) will be :

3) A particle P is moving on a circle under the action of only one force, which always acts towards a

fixed point O lying on the circumference. Find ratio of to at the moment

when (C is centre of circle)

4) Force acting on a body of mass 1 kg is related to its position x as F = x3 – 3x N. It is at rest at x =

1. Its velocity at x = 3 can be :

5) The friction coefficient between the board and the floor shown in figure is . Then the maximum

force that the man can exert on the rope so that the board does not slip on the floor is .

Find p + q

6) A body travels 200 cm in the first two seconds and 220 cm in the next 4 seconds with
deceleration. The velocity of the body at the end of the 7th second is (cm/s)

7) Sachin (S) hits a ball along the ground with a speed 30m/s in a direction which makes an angle
30° with the line joining him and the fielder Ponting (P). Ponting runs to intercept the ball with a

speed 20 m/s. At what angle θ should he run to intercept the ball? If , fill the value of ‘n’ in.

8) One has to throw a particle from one side of a fixed sphere, in diametrical plane to another side

such that it just grazes the sphere. Minimum possible speed for this is Find
 PART-2 : CHEMISTRY

SECTION-I (i)

1) A mixture of C3H8(g) & O2 having total volume 100 ml in an eudiometry tube is sparked & it is
observed that a contraction of 45 ml occurred. What can be the composition of reacting mixture ?
Assume only the reaction of complete combustion.

(A) 15 ml C3H8 & 85 ml O2

(B) 25 ml C3H8 & 75 ml O2
(C) 45 ml C3H8 & 55 ml O2
(D) 55 ml C3H8 & 45 ml O2

2) 100 g sample of dolomite (containing 19% H2O, 40% CaCO3.MgCO3, and inert impurities, as rest)
is partially dried so as to contain 10% H2O
Which of the following is/are correct statements (s) ?

2–
(A) The percentage of CO3 ion in partially dried dolomite is 26.09%, by mass.
(B) The mass of Ca in partially dried dolomite is 8.69 g.
(C) The percentage of inert impurity in partially dried dolomite is 45.55%, by mass.
(D) The mass of water evaporated is 10.0 g

3) A compound having molecular formula C4H10O may contain the functional group –

(A) Alcohol (–OH)

(B) Ether (–OR)
(C) Carboxylic acid (–COOH)
(D) Aldehyde (–CHO)

4) Consider the following compound

Which of the following statements is/are correct ?

(A) The compound contains 18 sigma bonds

(B) It is a saturated compound
(C) It is an unsaturated compound
(D) The compound is homocyclic

5) Which of the following statement is/are CORRECT?

(A) In noble gases Helium has lowest boiling point

(B) In NaHCO3(s) hydrogen bonding takes place
(C) Boiling point of SiCl4 is greater than the boiling point of CCl4
(D) Boiling point of H2O is greater than the boiling point of HF

6) Which of the following statement is CORRECT regarding electron gain enthalpy (ΔHeg).

All halogens have higher magnitude of ΔHeg compared to other elements of same period in
(A)
periodic table.
(B) For any neutral atom X
Elements like N, Be or Mg require energy to accept electron in their isolated gaseous atom in
(C)
ground state.
(D) Si, P, S & Cl have highest value in their respective groups.

SECTION-I (ii)

1) Match with the correct concentrations :

List-I List-II

(P) 6.3 gm HNO3 in 100 kg of solution (1)

Xsolvent = (X = mole fraction)

(Q) 4 gm MgO and 360 gm water (2)

%

(R) 2M H2SO4 (dsolution = 1.996 gm/mL) (3) 12 M

(S) 40% NaOH solution (4) 1 m

(dsolution = 1.2 gm/mL)

(5) 63 ppm
Which of the following is only correct combination.
(Assume that MgO dissolves in water without any reaction)
(A) P → 5;Q → 1;R → 2;S → 3
(B) P → 5;Q → 1;R → 2;S → 4
(C) P → 5;Q → 2;R → 4;S → 3
(D) P → 3;Q → 2;R → 1;S → 4

2) Given x = % increase in volume M1 = Theoretical molar mass, M2 = Observed molar mass of gases
mixture.
D1 = Theoretical vapour density, D2 = Observed vapour density of gases mixture

List-I (Extent of reaction = 100%) List-II

(P) (1) x = 25%

NH3(g) —→ N2(g) + H2(g)

(Q) (2) x = 100%

SO3(g) —→ SO2(g) + O2(g)

(R) PCl5(g) —→ PCl3(g) + Cl2(g) (3) x = 50%

(S) (4) M1 > M2

HCl(g) —→ H2(g) + Cl2(g)

(5) D1 = D2
The correct option is :-
(A) P → 2,4;Q → 3,4;R → 2,4;S → 5
(B) P → 1,4;Q → 3,4;R → 3,4;S → 5
(C) P → 2,4;Q → 5;R → 3;S → 2,5
(D) P → 3,4;Q → 3,4;R → 1,4;S → 5

3) Match the oxyacids or their derivatives listed in List-I with properties written in List-II.

List-I List-II

Contain linkage between similar

(P) Hypophosphoric acid (1)
elements

Maximum number of atoms

(Q) Pyrosulphurous acid (2)
present in a ring.

Anhydrous sulphuric acid Contain central atoms (P, S or B) of

(R) (3)
(cyclic allotrope) different oxidation states

Meta boric acid (Trimeric Contain central atoms (P, S or B) in

(S) (4)
form) sp2 hybridisation from List-I

Maximum number of X-O-X

(5)
linkages
The correct option is :
(A) P → 3;Q → 4;R → 2;S → 2
(B) P → 1;Q → 3;R → 2;S → 4
(C) P → 3;Q → 4;R → 5;S → 5
(D) P → 1;Q → 3;R → 3;S → 5

4)

List- I List- II
(elements) (Properties)

(P) P (1) has more size than Na

(Q) Cl (2) has stable half/full filled configuration

 configuration have maximum principle
(R) Ne (3)
quantum number = 4

configuration have maximum azimuthal

(S) K (4)
quantum number = 1

(5) d-Block element

(A) P → 1;Q → 2;R → 4;S → 3
(B) P → 2;Q → 4;R → 3;S → 4
(C) P → 1;Q → 2;R → 4;S → 1
(D) P → 2;Q → 4;R → 4;S → 1

SECTION-II

1) A gaseous mixture of C3H8 and CH4 exerts a pressure of 320 mm Hg at temperature TK in a V liter
flask. On complete combustion of mixture, flask containing only CO2 exerts a pressure of 448 mm Hg
under identical condition. The mole fraction of C3H8 in the given mixture is

2) 40 ml of mixture of C2H2 and CO is mixture with 100 ml of O2 gas and the mixture is exploded. The
residual gases occupied 104 ml and when these are passes through KOH solution, the volume
becomes 48 ml. All the volume are at same temperature and pressure. If ratio of volume of C2H2 &
CO is y : 1, then value of y is

3) Find out the volume (L) of 98% w/w H2SO4 (density = 1.8 gm/ ml), must be diluted to prepare 12.6
litres of 2.0 M sulphuric acid solution.

4) 'X' V H2O2 solution (500 ml) when exposed to atmosphere looses double the amount of oxygen gas,
needed for complete combustion of 2.27 L of propane at STP. Find value of 'X'.

5) Calculate the total number of 2° carbon atoms present in the following hydrocarbon :

6) Calculate the total number of functional groups present in the following compound : -
7) Consider the following species :
S1 :
S2 : XQ2R
S3 :
S4 :
S5 :
In the above species W, X, Y and Z are central atom. P exhibit covalency of two in ground state
whereas Q, P, T exhibit covalency of one in ground state. Hybridisation increases from S1 to
S5 uniformely. Element W has 3rd highest IE in 2nd period.
a = Number of polar species
b = Total lone pair present on S5
c = Total lone pair present on Y in S4

Find the value of

8) How many statements is/are correct ?

(i) Van der waal's forces are responsible for the formation of dry ice (molecular crystal).
(ii) Ion-dipole intractions are responsible for hydration of ions.
(iii) In solidified noble gas, the attraction between molecules arises entirely from weakest dispersion
(London)forces.
(iv) Boiling point of ICl is less than boiling point of Br2.
(v) Ionic bonds are directional in nature.

PART-3 : MATHEMATICS

SECTION-I (i)

1) If 4sinαcosβ + 2cosβ – = sinα, where α,β ∈ [0, 2π] and L = α – β then

(A)
maximum value of L is

(B)
minimum value of L is

(C)
maximum value of L is

(D)
minimum value of L is

2) The solution/s of the equation 9cos12 x + cos2 2x + 1 = 6cos6 x cos2x + 6cos6 x – 2cos2x is/are

(A)
,n∈I

(B)
,n∈I
(C)
,n∈I
(D) x = nπ, n ∈ I

3) then which of the following may be true ?

(where b, d ∈ N)

(A)

(B)

(C)

(D) bd = 32021

4) Which of the following functions have the maximum value unity ?

(A) sin2x – cos2x

(B)

(C)
(D)

5) Given that x + y + z = 15 when a, x, y, z, b are in A.P. and when a, x, y, z, b are in

H.P. then

(A) G.M. of a and b is 3

(B) one possible value of a + 2b is 11
(C) A.M. of a and b is 6
(D) greatest value of a – b is 8

6) Let a > 0, b > 0, c > 0 and a + b + c = 6 then the value of the expression

may be

(A)

(B) 35
(C) 15
(D) 10

SECTION-I (ii)
1) The graph of y = (x – a)2 + b and y = (x – a)2 + c have y-intercepts of 2021 and 1961 respectively.
Each graph has two positive integral x-intercepts. Then match the following List-I with List-II.

List-I List-II

(I) a is equal to (P) –64

(II) b is equal to (Q) –4

(III) c is equal to (R) 0

(IV) number of integral roots of (x – a)2 + b = 5, is (S) 2

(T) 45
(A) I → T;II → R;III → P;IV → S
(B) I → T;II → Q;III → P;IV → S
(C) I → T;II → Q;III → P;IV → R
(D) I → Q;II → P;III → R;IV → T

2) Match the following List-I with List-II.

List-I List-II

Least value of the expression

(I) (P) 2
2log10x – logx0.01 for x > 1 is

The number of solutions of

(II) (Q) 4
log4(x – 1) = log2 (x – 3) is

Least integral value of x which satisfies

(III) (R) 1
log(x + 1)

Number of solutions of the equation [loge x] =

(IV) |x| is (where [.] denotes the greatest integer (S) 0
function)

(T) 5
(A) I → Q;II → R;III → S;IV → P
(B) I → Q;II → P;III → Q;IV → S
(C) I → Q;II → S;III → R;IV → T
(D) I → Q;II → R;III → P;IV → S

3) Match the following List-I with List-II

List-I List-II

If the expression sin2(θ) + sin2(120° + θ) + sin2 (120° – θ)

(I) (P)
remains constant, ∀ θ ∈ R, then value of the constant is

If the sum of the solutions of the equation 2e2x – 5ex + 4 = 0

(II) (Q) 1
is ln k then k equals
 (III) If , find the value of (R)
(wherever defined)

If 3 tan(θ – 30°) = tan(θ + 120°) then the value of cos 2θ

(IV) (S) 2
equals

(T) 0
(A) I → S;II → R;III → Q;IV → P
(B) I → R;II → S;III → P;IV → Q
(C) I → R;II → S;III → Q;IV → T
(D) I → P;II → Q;III → R;IV → S

4) Let & , where an is nth term of an infinite G.P., then match the following
List-I with List-II.

List-I List-II

(I) Common ratio + first term is equal to (P) 45

(II) a5 is equal to (Q)

(III) (R)
is equal to

(IV) (S) 44
is equal to

(T) 0
(A) I → Q;II → T;III → P;IV → R
(B) I → T;II → R;III → Q;IV → S
(C) I → Q;II → R;III → P;IV → S
(D) I → S;II → P;III → T;IV → Q

SECTION-II

1) A real sequence is define as t1 = 20, t2 = 21 and for all n 3. If 5t13 = (where p

and q are coprime), then |p – q| is

2) If positive numbers x, y, z in order are in A.P., then the minimum value of is equal
to

3) The number of distinct solutions in x ∈ [0, π] which satisfy the equation 8 cos x cos 4x cos 5x = 1
is k then is equal to _____

4) The value of cos x·cos 2x·cos 3x ... cos 999x where x = is p then 21000p is equal to

5) Consider the cubic polynomial P(x) = x3 – ax2 + bx + c. If the equation P(x) = 0 has integral roots
such that P(6) = 3 then sum of all possible values of 'a' is _____

6) If the equations x2 – 3x – ai = 0 has integral roots where ai N and ai < 300 then ______

7) If log245 175 = a, log1715 875 = b , then the value of is

8) (where ℓ , m are relatively coprime), then ℓ + m is equal to