27-07-2025

1001CJA101016250018 JA

PART-1 : PHYSICS

SECTION-I

1) A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the
horizontal frictionless surface of a fixed table. Initially the right edge of the block is at x = 0, in a co-
ordinate system fixed to the table. A point mass m is released from rest at the topmost point of the
path as shown and it slides down. When the mass loses contact with the block, its position is x and
the velocity is v. At that instant, which of the following options is/are correct?

(A)
The x component of displacement of the center of mass of the block M is

(B)
The position of the point mass is

(C)
The velocity of the point mass m is
The velocity of the block M is
(D)

2) A small object moves counter clockwise along the circular path whose centre is at origin as shown
in figure. As it moves along the path, its acceleration vector continuously points towards point S.

Then the object

(A) Speed up as it moves from A to C via B.

(B) Slows down as it moves from A to C via B.
(C) Slows down as it moves from C to A via D.
(D) Speed up as it moves from C to A via D.

3)

A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along

the x-axis. Its kinetic energy K changes with time as where γ is a positive constant of
appropriate dimensions. Which of the following statements is (are) true?

(A) The force applied on the particle is constant

(B) The speed of the particle is proportional to time
(C) The distance of the particle from the origin increases linearly with time
(D) The force is conservative

4) Which of the following statements are correct about a rigid body -

(A) Ideally a rigid body has a perfectly definite and unchangign shape.
(B) Distances between different pairs of particle of rigid body do not change.
(C) Inter molecular forces for a rigid body are weak.
(D) No real body are truly rigid.

5) A projectile is projected at an angle of elevation α. After t seconds, it appears to have an angle of

elevation β as seen from the point of projection. Which of the following are correct?

(A) the y-coordinate of the position of the projectile at time t is , where v is the
velocity of projection
the x-coordinate of the position of projectile at time t is , where v is the velocity of
(B)
projection

(C)
tan β = tan α – , where v is the velocity of projection

(D)
velocity of projection is

6) A trolley of mass 8 kg is standing on a frictionless surface inside which an object of mass 2 kg is

suspended. A constant force F starts acting on the trolley as a result of which the string stood at an

angle of 370 from the vertical. Then :

(A) acceleration of the trolley is 40/3 m/sec2

(B) force applied in 60 N
(C) force applied is 75 N
(D) tension in the string is 25 N
 SECTION-II

1) A 200 g, 20-cm diameter plastic disk is spun on an axle through its center by an electric motor.
What torque (in N-m) must the motor supply to take the disk from 0 to 1800 rpm in 4.0s ? (Take : π =
3.14)

2) A mass m = 2kg connected to inextensible string of length ℓ = 2m lies on a horizontal smooth

ground. Other end of string is fixed. Mass m is imparted a velocity v = 2 m/s such that string
remains taut & motion occurs in horizontal plane. (Take square root of 2 equal to 1.4). The impulse

(in Ns) provided by string during the time string turns through 90° is

3) We have a cube of side 4m as shown in the figure. The cube is massless but has masses at it's
vertices as shown. If the distance of centre of mass from the origin is r (in m) fill r2.

4) A block of mass 2.5 kg is placed over a fix rough incline (µ = 0.8) plane as shown. A time varying
force F = 5t N acting on block upward along the incline. Time (in sec) after which block will starts

upward slipping, is (g = 10 m/s2)

5) Two particles A and B are simultaneously thrown from roof of two buildings as in figure. Their
speed are 2 m/s and 14 m/s and angles 45° and 45° as in figure. Vertical separation between the
buildings is 9m and horizontal separation is 22 m. The minimum gap in meter between the particles
when both are in air is d. Find the value of .

6) Spotlight S rotates in a horizontal plane with constant angular velocity of 0.1 rad/s. The spot of
light P moves along the wall at a distance of 3 m. The velocity of the spot P when θ = 45° (see Fig.)

is m/s.

SECTION-III

1) In the given figure both the blocks are in equilibrium. The acceleration of block 10 kg just after
cut the string is (in m/s2) (Assume both spring identical and massless. String is also massless)

2) In the given figure a force of magnitude 20t is applied on the lower block, where t is time in sec.
Coefficient of static friction between contact surfaces is 0.8. For what value of t upper block begin to
slip relative to lower block.

3) An impulse of I = 30N-sec is given at t = 0 to 3 kg block attached with 2 block with the help of
spring in natural length. Initially the system is at rest and all surfaces are smooth. Find velocity of

centre of mass at t = 5 sec ?

4) v2 Vs t graph of a particle is as shown in figure, find acceleration of particle in m/s2 at t = 1/8 s.

5) The world famous car Audi logo consist of four rings of each mass m and radius R as shown. Then

moment of inertia about axis shown will be the value of 'a' is

6) A boat starts from A with velocity (velocity of boat with respect to river) making an angle α =
30º with line AB and crosses the river. Velocity of river flow is as shown in figure. The line AC

makes an angle β = 60º with line AB. If the boat always remains on line AC then, the value of is
 PART-2 : CHEMISTRY

SECTION-I

1) In which of the following resonance will take place

(A) CH2=C=C=CH2

(B)

(C) CH2=C=CH2
(D) CH2=CH–CH=O

2) Find correct statement for the given organic molecule | X |-

(A) If OH is replaced by COOH, then –CN will get locant 3.

(B) If Br is replaced by COOH then –CN will get locant 2.
(C) If Br is replaced by –NH2 then –CN will get locant 2.
(D) IF Br is replaced by –CN then –OH will get locant 4.

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

(A) In NSF3 both π-bonds are pπ-dπ type.

(B) The ratio of σ-bonds to π-bond in SO3 and SO2 are identical
(C) & are planar
(D) Cl2O6(s) exist as &

4) From the following options which is/are correct for double chain silicates?

(A) Average charge on each tetrahedron = –1.5

(B) Average shared oxygen/corner per tetrahedron = 2.5
(C) All the silicon atoms have +4 oxidation number
(D) All the tetrahedrons have only one unshared oxygen/corner

5) Given
2ZnS + 3O2 2ZnO + 2SO2
SO2 + ½O2 + H2O H2SO4
ZnO + H2SO4 ZnSO4 + H2O
2ZnSO4 + 2H2O 2Zn + 2H2SO4+O2
If 15 mole of ZnS reacts with excess of reactants then which of the following statement(s) is/are
correct?

(A) 15 mole of Zn formed.

(B) 12 mole of SO2 gas released after first reaction.
(C) 4.5 mole of H2SO4 formed after the complete reaction sequence.
(D) 9 mole of ZnSO4 formed after third reaction.

6) 150 ml mixture of CO and CO2 mixed with 50 mL of O2 and sparked in eudiometer tube. The
residual gas after treatment with aq. KOH has a volume of 10 mL which remains unchanged when
treated with alkaline pyrogallol. If all the volumes are under the same conditions, point out correct
option(s) :

(A) The volume of CO that reacts, is 100 mL

(B) The volume of CO that remains unreacted, is 10 mL
(C) The volume of O2 that remains unreacted, is 10 mL
(D) The volume of CO2 that gets absorbed by aq. KOH, is 140 mL

SECTION-II

1) Find multiplication product of x & y in given organic molecule.

Where x = number of groups showing (+I).
y = number of groups showing (–I).

(a) (b) (c)

(d) –OH (e) –OCH3 (f) (g) – (h) –CCl3 (i) –ONa

2) Calculate total sum of x & y in the given organic molecules.

x = Total number of π bonds in Anthracene
y = Total number of π bonds in mesitylene.

3) Total number of molecules in which all the possible bond angles are identical :
BF3, CF4, PF5, IF7, BeF2, SF4 , PF2Cl3 , CF2Cl2

4) Consider the following statements.

(i) Hybridization of central atom in cation of and is same.
(ii) Anionic form of contains only eight bond angles of 90° each.
(iii) XeF4 and are isostructural.
(iv) Hybridization of central atom changes when NH3 combines with H+.
(v) is linear
(vi) The correct order of oxygen-oxygen bond length is .
Out of above statements, x are correct then value of 'x' is

5) The 'roasting' of 100.0 g of a copper ore yielded 72 g pure copper. If the ore is composed of Cu2S
and CuS with 4% inert impurity, calculate mole ratio of Cu2S and CuS in the original ore. The
reactions are : Cu2S + O2 2Cu + SO2 and CuS + O2 Cu + SO2
(Molar mass of Cu is 64 gm/mol)

6) Calculate the contraction in volume (in mL) of reaction mixture obtained by the combustion of 50
ml of a mixture containing 40% C2H4 and 60% CH4 (by volume) with excess of oxygen at room
temperature.

SECTION-III

1) Find total number of functional groups in the following organic compound [X].

2) Total number of correct IUPAC names are-

(i) 1-Chloro-1-ethoxypropane
(ii) 1-Amino-1-ethoxypropane
(iii) 1-Ethoxy-2-propanol
(iv) 1-Ethoxy-1-propanamine
(v) 1, 2-Dimethylcylcohex-2-ene
(vi) 2-Methyl-1-phenylpropan-1-amine

3) Consider given data of lattice energy (in KJ/mol) of Halide of Na & Li.
In which option (1 to 8) lattice energy data most probably belong to NaI

(1) 1036 (2) 704 (3) 747

(4) 853 (5) 807 (6) 786

(7) 923 (8) 757

4) Among the following, total number of species which contain total 4-degeneracy in second excited
state is
Li⊕ , H, He⊕ , Li2+, Be2+, Be3+

5) The reaction aA(g) → bB(g) + cC(g) is such that their is no volume change on conducting reaction.
Find the molar mass of mixture when some moles of A dissociated into B and C. The atomic weight
of A is 20 times molarity of solution when 100 ml, 3% (w/v) NaOH solution is mixed with 100 ml, 9%
(w/v) NaOH solution.
(Fill your answer as sum of digits till you get the single digit answer.)

6) An impure sample of NaHCO3 contains 12% of carbon. The percentage of impurity (by mass)
present in the sample is :
(Fill your answer as sum of digits till you get the single digit answer)

PART-3 : MATHEMATICS

SECTION-I

1) The value(s) of t for which the lines 2x + 3y = 5, t2x + ty – 6 = 0 and 3x – 2y – 1 = 0 concurrent,

can be :

(A) t = 2
(B) t = –3
(C) t = –2
(D) t = 3

2) If x1 & x2 are roots of and y1 & y2 are value of at x = x1 &

x2 respectively, then

(A) x1 + x2 = 12
(B) y1 + y2 = 80
(C) x1 = 8, y1 = 16
(D) x2 = 4, y2 = 64

3) is divisible by :

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

4) The equation 2log2(log2x) + log1/2 has

(A) Product of all its solutions is 8

(B) a rational solution which is not an integer.
(C) has a solution that is a natural number
(D) has no prime solutions

5) Two consecutive sides of a parallelogram are 3x + 5y = 0 and 5x + 3y = 0. If the equation to one

diagonal is 15y + 105x = 32 then the equation of the other diagonal is

(A) 12y + 13x = 0

(B) 11y + 13x = 0
(C) 22y + 15x = 0
(D) None of the above

6) In triangle ABC, vertex A is (1,1) and internal angle bisector x – y = 2 of angle B meets the
perpendicular bisector of side AC at (4,2). If equation of side AC is 2x + y = 3, then the correct
option(s) is/are :

(A)
Coordinate of vertex C is
(B) Image of vertex A in angle bisector x – y = 2 of angle B is (3, –1)

(C)
Slope of side BC is

(D)
Slope of side BC is

SECTION-II

1) The value of k, for which to the following system of equations

x + ky + 3z = 0,
3x + ky – 2z = 0 and
2x + 3y – 4z = 0
possess a non-trivial solution is :

2) If Dp = then

3) A circle of area 20 is centered at the point indicated by a solid dot in the accompanying figure.
Suppose that ΔABC is inscribed in that circle and has area 8. The central angles α, β and γ are as

shown. then the value of is

4) The distance between orthocentre and circumcentre of triangle whose vertices are P(–8, 5),
Q(–15, –19), R(1, –7) is :

5) Consider the pair of lines ax2 + 2hxy + by2 = 0. If slope of one of the line is three times that of

other line, then the value of is

6) Product of solutions of an equation ; is then k =

SECTION-III

1) The bisector of the acute angle between the lines 3x – 4y + 7 = 0 and 12x + 5y – 2 = 0 is ax + by
+ 9 = 0 then a + b is :

2) If α ≠ a, β ≠ b, γ ≠ c and , then equal to

3) Consider a triangle ABC and let a, b and c denote the length of the sides opposite to vertices A,B

and C respectively. Suppose a = 3, b = 5 and the area of the triangle is . If ∠ACB is obtuse and
if r denotes the radius of the incircle of the triangle, then 4r2 is equal to :

4) If line 3ax + 2by = 12 belongs to family of lines x(1 + 2k) – ky – (2 + k) = 0, where k ∈ R, then
value of a + b is-

5) Distance of the origin from the line measured along the line
is

6) If , then value of is
 ANSWER KEYS

PART-1 : PHYSICS

SECTION-I

Q. 1 2 3 4 5 6
A. A,C A,C A,B,D A,B,D A,B,C,D C,D

SECTION-II

Q. 7 8 9 10 11 12
A. 0.04 to 0.05 5.60 12.19 to 12.20 6.20 0.06 0.60

SECTION-III

Q. 13 14 15 16 17 18
A. 5 8 6 2 3 1

PART-2 : CHEMISTRY

SECTION-I

Q. 19 20 21 22 23 24
A. A,B,D A,B,D A,B,C,D A,B,C B,C,D A,B,D

SECTION-II

Q. 25 26 27 28 29 30
A. 14.00 10.00 3.00 3.00 1.00 100.00

SECTION-III

Q. 31 32 33 34 35 36
A. 6 4 2 0 3 7

PART-3 : MATHEMATICS

SECTION-I

Q. 37 38 39 40 41 42
A. A,B A,B,C,D A,B,C A,C,D B A,B,C

SECTION-II

Q. 43 44 45 46 47 48
A. 16.50 24.80 0.80 12.50 75.00 0.25
 SECTION-III

Q. 49 50 51 52 53 54
A. 8 0 3 2 5 9
 SOLUTIONS

PART-1 : PHYSICS

1) Overall centre of mass is displaced vertically only

⇒ X displacement of centre of mass is zero

centre of mass of block shift by (left)

mv = mv'

mgR = mv2 + mv'2

2) When angle between and is less than 90° it speeds up and greater them 90° it retards

3)

v = ct
Speed is proportional to time.

= constant force is constant

force is constant hence conservative.

4)

Correct Answer is (A,B,D)

5) y-coordinate is

y = v sin α t [Therefore A is correct]

x –coordinate is
x = v cos α t [Therefore B is correct]
Equation of trajectory is

⇒
⇒

⇒ [C is correct]

Rearrenging

⇒ [∴ D is correct]

6) atrolly= a0 = ...(1)
from figure we have
T cos 37° = 2g ...(2)
⇒ T = 25 N
T sin 37° = 2a ...(3)
⇒ a0 = 7.5 m/s2
from (i) we have
so, F = 75 N

7)
ωi = 0

ωf = 60π rad/s
τ = Iα

= 10–3 kg-m2
ωf = ωi + ∝

τ = 0.0471 N-m
8)

Impulse =

9)

10)
[5t = mgsinθ + µmgcosθ]

11) Solving from the frame of B.

∴ θ = 37°
from above diagram x + ℓ = 22

ℓ = 10

12) v cos 45° = v⊥

v = 0.6 m/s

13)
kx = 150

just after cut the string

2kx
150 - 100 = 10a

14)

2t – 8 = 8
t=8s

15)

I = ΔP
30 = 3(vf – 0) ⇒ vf = 10 m/s

⇒
Velocity of centre of mass remains constant because there is no external force on the system.

16) at t = s,

a = 2 ms–2

17)

18) For the boat to always remain on the line AB

vbrsin(β – α) = vrcosβ
 vbrsin30° = vrcos60°

PART-2 : CHEMISTRY

19) The correct answer (A), (B) & (D)

20) The correct answer (A), (B) & (D)

21)

22)

Tetrahedrons have one or two unshared oxygen/corner

23)

2ZnS + 3O2 2ZnO + 2SO2

15 mole 15 × 0.8 = 12 mole ZnO
ZnO + H2SO4 ZnSO4 + H2O
12 mole 12 × 0.75 = 9 mole ZnSO4
2ZnSO4 + 2H2O 2Zn + 2H2SO4 + O2
9 mole 9×0.5 9×0.5 4.5×0.5
= 4.5 mole = 4.5 mole = 2.25 mole

24) Let initial volume of CO = x mL

CO + → CO2
Initial volume x 50
Final volume x–100 0 100 x = 110 ml
Total CO2 absorbed finally = 100 + 40 = 140 ml

25) x = a, i (2)
y = b, c, d, e, f, g, h (7)
26)

27) BF3, CF4 and BeF2 have all the possible B.A. identical.

28)

having 12, 90° bond angles.

square planar

⇒X=3

29)

Mass of Cu2S & CuS = 100 – 4 = 96 g

Let mass of Cu2S is x g and mass of CuS = y gm.
Cu2S + O2 2Cu + SO2
CuS + O2 Cu + SO2
x + y = 96 .......(1)

.......(2)
6x + 5y = 540
x = 60 gm
y = 36 gm

30)

CH4 + 2O2 → CO2 + 2H2O

30ml 60 ml – –
0 30ml
C2H4 + 3O2 → 2CO2 + 2H2O
20ml 60 ml – –
0 40ml
Contraction = 100 ml
 31) Amide, amine, ester, ether, aldehyde, alcohol.

32) (i), (iii), (iv), (vi) are correct IUPAC name.

33)

Lattice energy of NaI is lowest

34)

The following degeneracy are given below.

H , He⊕ , Li2+, Be3+ = 9
Li⊕ , Be2+ = 3

35) Total NaOH in 100 ml (Ist solution) = 3 gm

Total NaOH in 100 ml (2nd solution) = 9 gm

∴ Molarity =
Molar mass of A = 1.5 × 20 = 30
If there is no volume change in the given reaction then a = b + c

Mmix =

36) Let the mass of the sample be 100 gm and mass of NaHCO3 be x gm.

wtC =
x = 12 × 7 = 84 gm
Weight of impurity = 16 gm
% Impurity = 16

PART-3 : MATHEMATICS

37) ⇒ t2 + t – 6 = 0

38) log10(98 + |x – 6|) = 2

x = 8, 4
If x1 = 8, y1 = 16
if x2 = 4, y2 = 64

39)

Clearly are factors

40) Put log2 x = a

t = –1, 3

(Rejected)
x = 8 only solution.

41)
On solving 3x + 5y = 0 and 15y + 105x = 32
We will get vertex A
(3x + 5y = 0) × 3
15y + 105x = 32
from equations

96x = 32 ⇒

Similarly

⇒
⇒ Equation of OD

42) Equation of perpendicular bisector of AC is i.e. x – 2y = 0

Let C(α,β)
∵ C is image of A(1,1) in x – 2y = 0

⇒
again image of A in angle bisector x – y–2 = 0
lies on side BC

⇒
⇒ h = 3, k = –1 ⇒ (3,–1)

⇒ slope of side BC is

43)
1(–4k + 6) – k(–12 + 4) + 3(9 – 2k) = 0
–4k + 6 + 12k – 4k + 27 – 6k = 0
2k = 33
44)
C1 → C1 – C2

= –52(150 – 200) + 200(135 – 24)

= 52 × 50 + 200 × 111
= 2600 + 22200
= 24800

45) r2(sin α + sin β + sin γ) = 8 and πr2 = 20

46) r triangle is right angled at R(1, –7).

∴ Circumcentre is , Orthocentre is (1, –7)

∴ Distance between them is 12.50.

47) bm2 + 2hm + a = 0, where m = y/x

roots of this equation are m1 & 3m1

3m1 + m1 = ⇒ m1 =

3m1 . m1 = ⇒ 3
⇒ 3h2 = 4ab

48)

⇒ ⇒ t2 – 10t + 9 = 0
⇒ t = 1, 9 ⇒ tan2x = 0, 1
⇒ tanx = 0, ±1

∴ Product of solutions is =
∴ = 0.25

49) Here equation of bisectors is

⇒ 39x – 52y + 91 = –(60x + 25y – 10)

⇒ 11x – 3y + 9 = 0

50) R1 → R1 – R2, R2 → R2 – R3

(α – a) (γ(β – b) – b (c – γ)) – (b – β) (–a(c – γ)) = 0

γ(α – a) (β – b) – b(α – a) (c – γ) + a(b – β) (c – γ)

51)

–15 = 34 – c2
c2 = 49
c=7

⇒r=

r2 =

52) Family of lines x(1 + 2k) – ky – (2 + k) = 0

or (x – 2) + k(2x – y – 1) = 0, passes through fixed point (2, 3)
⇒ line 3ax + 2by = 12 also passes through (2, 3)
⇒ 6a + 6b = 12 ⇒ a + b = 2
53) where θ = 60°

Now :

r=5

54) Δ = 3 Δcofactor = Δ2