20-07-2025

5301CJA101021250010 JM

PHYSICS

SECTION-I

1) The current in a metallic conductor is plotted against voltage at two different temperatures T1 and
T2. Which is correct :-

(A) T1 > T2
(B) T1 < T2
(C) T1 = T2
(D) None

2) A cylindrical solid of length 1m and radius 1 m is connected across a source of emf 10V and
negligible internal resistance shown in figure. The resistivity of the rod as a function of x (x
measured from left end) is given by ρ = bx [where b is a positive constant]. Find the electric field (in

SI unit) at point P at a distance 10 cm from left end.

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

3) The equivalent resistance between the terminal points A and B in the network shown in figure is :-

(A)

(B)
(C)

(D)

4)

The resistance of a wire is 5 ohm at 50°C and 6 ohm at 100°C. The resistance of the wire at 0°C will
be :–

(A) 2 ohm
(B) 1 ohm
(C) 4 ohm
(D) 3 ohm

5) Two conductors have the same resistance at 0°C but their temperature coefficients of resistance
are α1 and α2. The respective temperature coefficients of their series and parallel combinations are
nearly :–

(A)
, α1 + α2

(B)
α1 + α2,

(C)
α1 + α2,

(D)
,

6) A battery of internal resistance 4 ohm is connected to the network of resistance as shown. In the
order that the maximum power can be delivered to the network, the value of R in ohm should be :–

(A) 4/9
(B) 2
(C) 8/3
(D) 18

7) In the circuit shown, the cell has emf = 10V and internal resistance = 1Ω :–

(A) The current through the 3Ω resistor is 2A

(B) The current through the 3Ω resistor is 0.5A
(C) The current through the 4Ω resistor is 0.5A
(D) The current through the 4Ω resistor is 0.25A

8) A cylindrical metal tube of length L and resistivity ρ has inner radius a and outer radius b. The
resistance of the tube between the inner and outer surfaces is

(A)

(B)

(C)

(D)

9) A current of 5 A passes through a copper conductor (resistivity = 1.7 × 10–8 Ωm) of radius of
cross-section 5 mm. Find the mobility of the charges if their drift velocity is 1.1 × 10–3 m/s.

(A) 1.3 m2/Vs

(B) 1.5 m2/Vs
(C) 1.8 m2/Vs
(D) 1.0 m2/Vs

10) A uniform wire of ohmic material length of 2m is streched till its length increased by 10%. The
percentage change in resistance to nearest integer is :-

(A) 10
(B) 9
(C) 21
(D) 20

11) A current through a wire depends on time as i = (4t + 6t2)A. Find charge crossed through a
section in 5 second in C :-

(A) 170
(B) 300
(C) 200
(D) 500

12) In the given circuit it is observed that the current I is independent of the value of the resistance
R6. Then the resistance value must satisfy

(A) R1R2R5 = R3R4R6

(B)

(C) R1R4 = R2R3

(D) R1R3 = R2R4 = R5R6

13) In the circuit shown in the figure, the current through :

(A) the 3Ω resistor is 0.50 A

(B) the 3Ω resistor is 0.25 A
(C) 4 Ω resistor is 0.50 A
(D) the 4Ω resistor is 0.25 A

14) A wire has a non-uniform cross-section as shown in figure. A steady current flows through it. The

drift speed of electrons at points P and Q is vP and vQ.

(A) vP = vQ
(B) vP < vQ
(C) vP > vQ
(D) Data insufficient

15) A uniform metal rod of length 4 m is bent at 90°, so as to form two arms of equal length. the
centre of mass of this bent rod is

(A) On the bisector of the angle, 0.707 m from the vertex

(B) On the bisector of the angle, 0.5 m from the vertex
(C) On the bisector of the angle, 0.4 m from the vertex
(D) On the bisector of the angle, √2 m from the vertex

16) Internal forces in a system can change

(A) Linear momentum only
(B) Kinetic energy only
(C) Both kinetic energy and linear momentum
(D) Neither the linear momentum nor the kinetic energy of the system

17) A body of mass M at rest explodes into pieces, in the ratio of masses 2 : 2 : 1. Two bigger pieces
fly off perpendicular to each other with velocities of 30 ms-1 and 40 ms-1 respectively. The velocity of
the third piece will be:

(A) 100 ms-1

(B) 25 ms-1
(C) 35 ms-1
(D) 50 ms-1

18) The centre of mass of a non uniform rod of length L whose mass per unit length p varies as

where K is a constant and x is the distance of any point from one end, is (from the same
end):

(A)

(B)

(C)

(D)

19) A rod of length L has non-uniform linear mass density given by where a and b
are constants and 0 ≤ × ≤ L. The value of x for the centre of mass of the rod is at :

(A)

(B)

(C)

(D)

20) Two particles of equal mass m have respective initial velocities and . They collide
completely inelastically. The energy lost in the process is :

(A)
(B)

(C)

(D)

SECTION-II

1)
Four resistances 40Ω, 60Ω, 90Ω and 110Ω make the arms of a quadrilateral ABCD. Across AC is a
battery of emf 40V and internal resistance negligible. The potential difference across BD is V is
_______.

2) In the circuit shown if point O is earthed, the potential of point X is equal to 5 × N Volt.

Determine the value of N.

3) Three objects A,B and C are kept in a straight line on a frictionless horizontal surface. These have
masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an
elastic collision with it. There after, B makes completely inelastic collision with C. All motions occur

on the same straight line. Find the final speed (in m/s) of the object C.

4) The disc of mass M with uniform surface mass density is shown in the figure. The centre of

mass of the quarter disc (the shaded area) is at the position where x is ______.
5) A body A of mass m = 0.1 kg has an initial velocity of it collides elastically with another
body. B of the same mass which has as initial velocity of .

After collision. A moves with a velocity . . The energy of B after collision is written as

The value of x is

CHEMISTRY

SECTION-I

1) Which order of dipole moment is correct ?

(A) CCl4 < CH3Cl < CH2Cl2 < CHCl3

(B) CH3Cl > CH3F > CH3Br > CH3I
(C) BF3 > NH3 > NF3
o-dichlorobenzene < m-dichlorobenzene
(D)
< p-dichloro benzene

2) For which of the following molecule significant ?

a b c d

(A) Only (c)

(B) (c) and (d)
(C) Only (d)
(D) (a) and (b)
3) A molecule A–B has a bond length of 1.6Å and dipole moment of 0.64 Debye. Find % covalent
character in this molecule.
[Electronic charge = 4.8 × 10–10 esu)

(A) 8.33
(B) 91.67
(C) 17
(D) 83

4) Which of the following set of molecule/ion will has same bond order.

(A) CO, NO

(B) ,

(C) ,

(D) CN– , CO+

5) The molecules having square pyramidal geometry are

(A) BrF5 & XeOF4

(B) SbF5 & XeOF4
(C) SbF5 & PCl5
(D) BrF5 & PCl5

6) Which of the following hydrogen bonds is the strongest ?

(A) O - H ... F
(B) O - H ... H
(C) F - H ... F
(D) O - H ... O

7) Which set of molecules is polar ?

(A) XeF4, IF7, SO3

(B) PCl5, C6H6, SF6
(C) SnCl2, SO2, NO2
(D) CO2, CS2, C2H6

8) Which of the following equation represent a reaction of enthalpy of formation as well as

combustion:-

(A)
Cgraphite + O2 (g) → CO (g)
(B) Cdiamond + O2 (g) → CO2 (g)
(C)
Cdiamond + O2 (g) → CO (g)
(D) Cgraphite + O2 (g) → CO2 (g)

0
9) For which of the following ΔHf is zero at 298 K

(A) Br2(g)
(B) I2(g)
(C) D2(g)
(D) H+(g)

10)

Which of the following compounds will undergo racemisation when solution of KOH hydrolyses?

(A) PhCH2Cl

(B)

(C)

(D) None

11)

Which of the following statement(s) is/are correct regarding type of compound and their donating
nature.

I KCN is ionic & attack takes place through 'N' atom

II KCN is covalent & attack takes place through 'N' atom

III AgCN is covalent & attack takes place through 'N' atom

IV KCN is ionic & attack takes place through 'C' atom

(A) Only III
(B) Only IV
(C) III & IV
(D) None of these

12)

Which of the following product will be obtained when neopentyl alcohol is treated with conc. HCl in
presence of ZnCl2.
(A) t– butyl chloride
(B) isobutylene
(C) t– pentyl chloride
(D) Neo pentyl chloride

13)

Among the given reactions, which is the best example of SN2 reaction ?

(A)

(B)

(C)
Ph-CH2–Cl Ph–CH2–OCH3

(D)

14) The synthesis of alkyl fluoride is best accomplished by :

(A) Finkelstein reaction

(B) Swarts reaction
(C) Free radical fluorination
(D) Sandmeyer's reaction

15) The major product of the following reaction is :

(A)

(B)

(C)
(D)

16) Select schemes A, B, C, respectively, out of

I. Acid catalysed hydration
II. HBO
III. Oxymercuration–demercuration

(A) I in all cases

(B) I, II, III
(C) II, III, I
(D) III, I, II

17)

Correct order of rate of SN2 reaction :

(A)

(B)

(C)

(D)

18) Statement-1:
Statement-2: Major product of above reaction is given by SNi mechanism.

(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for
(B)
statement-1.
(C) Statement-1 is true, statement-2 is false.
(D) Statement-1 is false, statement-2 is true.

19) Arrange the following three chlorides in decreasing order towards reactivity ?
(A)

(B)

(C)

(A) A > B > C`

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

20)

Anisole Product :-

(A)
+ CH3I

(B)
+ CH3OH

(C)
+ CH3I

(D)
+ CH3CH2I

SECTION-II

1) 800The bond dissociation energies of X2, Y2 and XY are in the ratio of 1 : 0.5 : 1. ΔH for the
formation of XY is –200 kJ mol–1. The bond dissociation energy of X2 will be (in kJ mol–1)

2) 2.4 g coal is burnt in a bomb calorimeter in excess of oxygen at 298 K and 1 atm pressure.
The temperature of the calorimeter rises from
298 K to 300 K. The enthalpy change during the combustion of coal is – x kJ mol–1. The value of x is
___________. (Nearest Integer)
(Given : Heat capacity of bomb calorimeter 20.0 kJ K–1 . Assume coal to be pure carbon)

3) Among the number of molecules or molecular ions which have back

bonding is

4) Number of the following alcohols would give imediate turbidity with lucas reagent.
(1)

(2)

(3)
(4) Vinyl alcohol
(4) phenol
(6) CH2 = CH – CH2 – OH
(7) benzyl alcohol

(8)
(9) CH3–O–CH2–OH

5) How many of the following compound which can not be prepared by willionson's ether synthesis
method
(1) CH3 – O – Et

(2)

(3)

(4)

(5)

(6)

(7)

MATHEMATICS

SECTION-I

1) Let x = ƒ(t) and y = g(t) where x and y are twice differentiable functions. If ƒ′(0) = 3, g′(0) = 2,
ƒ′′(0) = 3, g′′(0) = 8 then the value of is equal to

(A) 0

(B)

(C)

(D)

2) Let and = g(y), then the value of y g(y) is :

(A) 2
(B) 1

(C)

(D)

3) If f : R → R is a function such that f(x) = x3 + x2 f ′(1) + xf ′′(2) + f ′′′(3) for x ∈ R then the value of
f(2) is

(A) 5
(B) 10
(C) 6
(D) –2

4) Let f (x) and g(x) be differentiable functions on R. If h(x) = , where f (2) = 1, g(1) = 2

and f '(2) = g'(1) = 4, then is equal to :

(A) 4
(B) 6
(C) 8
(D) 10

5) If f'(x2) = and f(1) = then which of the following is incorrect :

(A) f(e) = 0
f'(e) =
(B)

(C) f"(e) = f(e)

(D) f"(e) = f'(e)
6) The curve y = has a vertical tangent at -

(A) (2, 1)
(B) (0, –1)
(C) (1, 0)
(D) no point

7) Which of the following points lies on the tangent to the curve x4ey + 2 = 3 at the point (1,
0) ?

(A) (2, 2)
(B) (–2, 6)
(C) (–2, 4)
(D) (2, 6)

8) If the tangent to the curve y = x3 at the point P(t, t3) meets the curve again at Q, then the ordinate
of the point which divides PQ internally in the ratio 1 : 2 is :

(A) –2t3
(B) 0
(C) –t3
(D) 2t3

9) If the angle made by the tangent at the point (x0, y0) on the curve x = 12(t + sin t cos t),

, with the positive x-axis is , then y0 is equal to

(A)

(B)

(C) 27
(D) 48

10) If f(x) = 1 – x – x3, then the set of all real values of x satisfying the inequality 1 – f(x) – f3(x) > f(1 –
5x) is

(A) (–2, 0) ∪ (2, ∞)

(B) (–∞, –2)
(C) (1, 2)
(D) (0, 2)

11) Which of the following is not an increasing function in its domain

(A) y = x7 + x5 + x3
(B) y = ℓnx + tanx
(C) y = cotx – x3
(D) y = x11 + 2x5 + 3

12) If Rolle's theorem holds for the function f(x) = 2x3 + ax2 + bx in x ∈ [–1, 1] for the point c = ,
then the value of (4a – b) is equal to

(A) –4
(B) 4
(C) 0
(D) 2

13) If c is a point at which Rolle’s Theorem holds for the function, in [1, 2] ,
then c is

(A)

(B)

(C)

(D)

14) Let where x ∈ [1,3]. Then the value of c for which Langrange's mean value
theorem is applicable is

(A) 2
(B)
(C)
(D) 2.5

15) Let y = g(x) is shown in the figure below

& . The value of

(A) 4
(B) 2
(C) 5
(D) 0

16) is equal to -

(A) 1

(B)

(C)

(D)

17) Let ƒ(x) be a continuous function in [–1, 1] such that , then (p

+ q + r) is equal to

(A) 3
(B) 2
(C) 1/3
(D) 5

18) Let ƒ : A → B be a function such that & . The set of

points where ƒ (x) is differentiable is -

(A) A–{0}
(B) A
(C) A–{1, 0}
(D) A–{–1,1,0}

19) Let f(x) = . The complete set of real values of 'a' for which f(x) has
smallest value at x = 1, is
(A) (0, 8]
(B) [8, ∞)
(C) (0, 16]
(D) [16, ∞)

20) The sum of global maximum and global minimum value of in x ∈

(A) 3/8
(B) 1/2
(C) 4/27
(D) 0

SECTION-II

1) Let and ƒ'(8) = 0, then value of is equal to

2) The slope of the tangent to the curve at the point (1, 3) is

3) The number of solutions to the equation is

4) Let a function ƒ(x) = min{e–x, {x}}, then number of points in x ∈ (–2,4), where ƒ(x) is non
differentiable, is (where {.} denotes fractional part function)

5) The total number of local maxima and local minima of the function f(x) = cos (πx + 3π) +

sin (πx + 3π), where 0 < x < 4 is equal to

 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. B B A C D B D C D C B C D C A B A A D B

SECTION-II

Q. 21 22 23 24 25
A. 2 3 4 4 1

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 B B C A C C D C C C C C B A C D A B C

SECTION-II

Q. 46 47 48 49 50
A. 800 200 3 5 4

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. C B D C D C B A C A C B A B C B B B D A

SECTION-II

Q. 71 72 73 74 75
A. 4 8 1 9 2
 SOLUTIONS

PHYSICS

1)

Ans : (2)

2)

Ans : (2)

3)

Ans : (1)

4)

Let R = R0 at 0ºC, R = R0, 0ºC

5 = R0(1 + α × 50) …(i)
6 = R0(1 + α× 100) …(ii)
Solving (i) and (ii) ⇒ R0 = 4Ω

5)

Let R be their individual resistance at 0ºC.

Their resistance at any other temperature t is R1 = R(1 + α1t) and R2 = R(1 + α2t)
In series
Rseries = R1 + R2 = R[2 + (α1 + α2).t]

αseries =
In parallel

RParallel =

αParallel =

6)
Condition for maximum power is r = R

R=2

7) Equivalent resistance Req = 10 Ω so current passing through battery and 3 Ω resistance is

i=
and current passing through 4 Ω is 0.25 A

8)

Ans : (3)

9) μ = E = ρJ

= =

10)

= 1.21

11)

= 50 + 250 = 300 C

12) This is condition for balance Wheatstone bridge

13)

Ans : (4)

14) ∴ V α
∴ VP > VQ

15)

Ans : (1)

16)

Ans : (2)

17) Conceptual

18) (A) Consider an element of mass dm and length dx at a distance x from end of rod. Here
mass dm is
19)

∴ correct answer (D)

20)

From momentum conservation

Final kinetic energy =

Initial kinetic energy

Loss in K.E. = ki – kf =

21) i1 =

i2 =
vB + i1 (40) – i2 (90) = vD

vB – vD =
vB – vD = 18 – 16 = 2

22) Taking the path having no resistor from O to X-

V0 + 10 – 5 + 10 = Vx ⇒ Vx = 15 V
∴N=3
 23)

Ans : (4)

24)

25)

CHEMISTRY

26) Correct order of dipole moment :

CCl4 < CHCl3 < CH2Cl2 < CH3Cl
BF3 < NF3 < NH3
O-dichlorobenzene > m-dichlorobenzene
> p-dichlorobenzene

27)

Owing to the lone pairs & H present on OH & SH in c & d

28)

% ionic - character

= 8.33%
% covalent character = 100 – 8.33 = 91.67%

29)

Ans : (3)
30)

BrF5 : Square pyramedal

XeOF4 : Square pyramedal

SbF5 : Trigonal bipyramidal

PCl5 : Trigonal bipyramidal

31)

Ans : (3)

32) When μ ≠ 0, then molecule is polar.

33) Cgraphite + O2 (g) → CO2 (g)

It represent enthalpy of combustion of graphite as well as enthalpy of formation of CO2(g)

34)

Ans : (3)

35)

The carbon to which halogen is attached should be chiral

36)

Refer from NCERT

37)

Ans : (3)

38)
In case of (C) option, CH3O– is a strong nucleophile in DMSO and confirms SN2.

39)

Ans : (2)

40)

Ans : (1)

41)

Ans : (3)

42)

Ans : (4)

43)

Ans : (1)

44) Reactivity for SN1 reaction µ stability of carbocation.

45)

46)

Ans : (800)

47) C (s) + O2 (g) → CO2 (g) ; ΔH = –x kJ/mole

Q = CΔT = 20 kJ × 2
40 kJ heat is released for 2.4 g of C

For 1 mole ‘C’ :

= 200 kJ/mole
Q = ΔE = ΔH = 200 kJ (∵ Δng = 0)
x = 200

48)

Ans : (3)
 49)

Ans : (5)

50)

Ans : (4)

MATHEMATICS

51)

52) y =
2y2 + 8y = 4x

53) Putting x = 0 in the given equation,

We have f(0) = f′′′(3) and putting x = 1, we get f(1) = 1 + f′(1) + f′′(2) + f′′′(3).
Thus, f(1) – f(0) = 1 + f′(1) + f′′(2).
Also differentiating the given equation, we have
f′(x) = 3x2 + 2x f′(1) + xf′′(2) .... (i)
f′′(x) = 6x + 2f′(1), f′′′(x) = 6
Thus f′′′(3) = 6 and f′′(2) = 12 + 2f′(1)
Putting x = 1 in (i), we have
f′(1) = 3 + 2f′(1) + f′′(2) = 3 + 2 f′(1) + 12 + 2 f′(1)
= 15 + 4f′(1)
f′(1) = –5 and so f′′(2) = 12 – 10 = 2.
⇒ f(2) = –2

54) We have h(x) =

∴ h'(x) = g'(f (x)) f '(x)
Now, h'(2) = f '(g(f (2))) · g'(f (2) · f '(2) = f '(g(1)) g'(1) f '(2) = g'(1) = (4)2 × 4 = 64

Hence = = 8.
55)

, (B)

⇒ (A)

⇒ ƒ"(e) = 0 (C)

56)

57) x4ey + 2 =3
d.w.r. to x

x4 ey y′ + ey 4x3 + =0
at P(1, 0)
y′P + 4 + y′P = 0
⇒ y′P = –2
Tangent at P(1, 0) is
y – 0 = –2 (x – 1)
2x + y = 2
(–2, 6) lies on it

58) Slope of tangent at P(t, t3) =

= (3x2)x=t = 3t2
So equation tangent at P(t, t3) :
y – t3 = 3t2(x – t)
for point of intersection with y = x3
x3 – t3 = 3t2x – 3t3
⇒ (x – t)(x2 + xt + t2) = 3t2(x – t)
for x ≠ t
x2 + xt + t2 = 3t2
⇒ x2 + xt – 2t2 = 0
⇒ (x – t)(x + 2t) = 0
So for Q : x = –2t, Q(–2t, –8t3)

ordinate of required point :

 59)

60) f(x) = 1 – x – x3
f(f(x)) = 1 – f(x) – f3(x)
f ′ (x) = –1 – 3x2 (decreasing function)
∴ f(x) < 1 – 5x
1 – x – x3 < 1 – 5x
x3 – 4x > 0
x(x2 – 4) > 0

61) (a)

(b)

(c)
(d) y' = 11x10 + 10x4 > 0

62) f(–1) = f(1) ⇒ b = –2

f' =0⇒a=

63) f(x) is continous and differentiable

f(1) = f(2) = 0
so f ′ (c) = 0, c ∈ (1, 2)
(c – 2)2 + (c – 1).2 (c – 2) = 0
c = 4/3

64)

65)

|ƒ(g(0–)) – ƒ(g(0+))| = |ƒ(3+) – ƒ(2–)|

= |6 – 1| = 5

66)
 (using L'Hôpital)

67) r = 1 and = 1 ℓn(ep) = 1 ⇒ p = 1, q = 0

68) ƒ (x) =
One should check the derivability at x = 0 only

ƒ '(0) = = =–
⇒ function is derivable at x = 0 ⇒ A

69) f(x) ≥ f(1) ⇒ a ≥ 16

70)
ƒ(–1) = 0 , ƒ(0) = 0,

71)

ƒ(x) = ax–1/3 + bx1/3

ƒ'(x) =

72)

at point (1, 3)

∴ 2(3 – 1) =4+8
73)
No of solution = 1

74)

75)

f '(x) = (2 – x) sin (πx)

∴ Local maximum at x = 1 and local minimum at x = 3.