20-07-2025

1001CJA101023250010 JA

PART-1 : PHYSICS

SECTION-I (i)

1) 10 gm of ice at –20°C is dropped in a container containing 10 gm of water at 10°C. When the

equilibrium is reached the container contains :-

(A) 20 gm H2O
(B) 20 gm ice
(C) 10 gm ice and 10 gm H2O
(D) 5 gm ice and 15 gm H2O

2) Two wires have the same diameter and length. One is made of copper and the other brass. They
are connected together at one end. When free ends are pulled in opposite direction by same force,
then :-

(A) The wires will have same strain.

(B) The wires will have same stress.
(C) Both the wires will break at the same force.
(D) Both wires will have same elongation.

3) At t = 0 switch S is closed then the graph of potential difference across resistor with time will be

(A)
(B)

(C)

(D)

4) The correct circuit for the determination of internal resistance of cell by using potentiometer is :-

(A)

(B)

(C)
(D)

SECTION-I (ii)

1) A parallel plate air-core capacitor is connected across a source of constant potential difference.
When a dielectric plate is introduced between the two plates then :

(A) some charge from the capacitor will flow back into the source.
(B) some extra charge from the source will flow back into the capacitor.
(C) the electric field intensity between the two plate does not change.
(D) the electric field intensity between the two plates will decrease.

2) In the given figure, E = 12V, R1 = 3Ω ,R2 = 2Ω and r = 1Ω. Then choose the correct option/s.

(A) Potential of point M is 6V.

(B) Potential of point N is –4V.
(C) Potential of point M is 12V.
(D) Current in wire AG is zero.

3) An oil drop has a charge –9.6 × 10–19 C and mass 1.6 × 10–15 gm. When allowed to fall, due to air
resistance force it attains a constant velocity. Then if a uniform electric field is to be applied
vertically to make the oil drop ascend up with the same constant speed, which of the following is/are
correct? (g = 10 ms-2) (Assume that the magnitude of resistance force is same in both the cases)

(A) The electric field is directed upward

(B) The electric field is directed downward

(C)
The intensity of electric field is

(D)
The intensity of electric field is

4) An equilateral triangular plate of side length ℓ has two cavities, one square and one rectangular
as shown in figure. The plate is heated :-

(A) a increase, b decrease

(B) a and b both increase
(C) a and b increase, x and ℓ decrease
(D) x and ℓ increase

SECTION-II

1) Two spherical bodies A & B are at temperature TA & TB respectively. The maximum intensity in
the emission spectrum of A and B is at 600 nm and 1800 nm respectively. Considering them to be
black bodies, if the total energy radiated by A & B in same time are same, then find the ratio of
radius of B to that of A.

2) A rod CD of thermal resistance 10.0 KW–1 is joined at the middle of an identical rod AB as shown
in figure, The end A, B and D are maintained at 200°C, 100°C and 125°C respectively. The heat

current in CD is P watt. The value of P is ....... .

3) A very stiff bar (AB) of negligible mass is suspended horizontally by two vertical rods as shown in
figure. Length of the bar is 2.5L. The steel rod has length L and cross sectional radius of r and the
brass rod has length 2L and cross sectional radius of 2r. A vertically downward force F is applied to

the bar at a distance X from the steel rod and the bar remains horizontal. Find the value of if it is

given that ratio of Young's modulus of steel and brass is .

4) In the following circuit C1 = 12 μF, C2 = C3 = 4 μF and C4 = C5 = 2 μF. The energy stored in C1 is

_______ μJ.

5) How much energy in kilowatt hour is consumed in operating ten 50 watt bulbs for 10 hours per
day in a month (30 days)?

6) A uniform rod of length 6m is hanged vertically from one end and given a small angular
displacement from mean position then it starts performing angular SHM. Calculate the time period
(in sec) of that SHM. (Take : g = π2)

7) If the speed of image is formed by given mirror according to figure is cm/sec, then find the

value of n.

8) Figure shows a binary star system revolving about their COM. The masses of star A & B are 15 ×
1030 kg and 45 × 1030 kg respectively. Find the ratio of area swept by star A to area swept by star B
in a common time interval.

PART-2 : CHEMISTRY

SECTION-I (i)

1) During initial treatment, preferential wetting of ore by oil and gangue by water takes place in

(A) Levigation (gravity separation)

(B) Froth floatation
(C) Leaching
(D) Magnetic separation

2) A gas discharge lamp emits 5 W of UV radiation of about 198 nm wavelength. Then number of
photons of this wavelength emitted in one minute are : (Given : h = 6.6 × 10–34 J-S, C = 3 × 108 m/s)

(A) 2 × 1016
(B) 3 × 1020
(C) 5 × 1018
(D) 8.3 × 1016

3) Given :
(i) C(graphite) + O2(g) → CO2(g); ΔrH° = x KJ mol–1

(ii) C(graphite)+ O2(g) → CO(g); ΔrH° = y KJ mol–1

(iii) CO(g) + O2(g) → CO2(g); ΔrH° = z KJ mol–1

Based on the above thermochemical equations, find out which one of the following algebraic
relationships is correct ?

(A) z = x + y
(B) x = y – z
(C) x = y + z
(D) y = 2z – x

4) In the following reaction, the major product is

(A)

(B)

(C)

(D)

SECTION-I (ii)

1) Which of the following is (are) regarded as iron ores?

(A) Haematite
(B) Magnetite
(C) Malachite
(D) Iron pyrite

2) For the reaction given below equilibrium constant is Keq.

log (where temperature is in K) curve is obtained as following.

Which of the following change will increase the concentration of Cl2 in

an equilibrium mixture of Cl2, F2 & ClF3:

(A) Addition of inert gas at constant pressure

(B) Increase in temperature at constant volume
(C) Addition of catalyst at constant volume
(D) Removal of F2(g) at equilibrium

3) For a substance A, undergoing parallel chemical reaction as shown : (ln 2 = 0.693)

Starting with only A at 1 M concentration, identify the statement(s) which is/are correct ?

(A)
Concentration of A will decrease to 0.5 M in
(B) Ratio of concentration of D to C at any instant will be 2 : 1
(C) Ratio of concentration of B to the sum of concentrations of D and E at any instant will be 1 : 2
(D) Percentage of C after very long time in the final mixture is approximately 16.7%

4) Identify reactions correctly matched with their major products ?

(A)

(B)

(C)
Me–C≡CH

(D)

SECTION-II

1) In how many of the following :

Pyro siliciate, Sheet silicate, Pyroxene and Amphiboles
'Si' atoms are sp3 hybrid -

2) Find the total stereoisomers for :

(a) Ma3b3 = x
(b) Ma3b2c = y
(c) Ma3bcd = z
Hence write the value of (x + y + z).
(a, b and c represent monodentate ligands)

3) Total number of the following molecules that do not exist

OF2 , OF4 , SF6 , PH5 , , NCl5 , XeH6 , XeF6 , SH6

4) The enthalpy of combustion of propane(g), graphite(s) and dihydrogen(g) at 298 K are: –2220.0 kJ
mol–1,
–393.5 kJ mol–1 and –285.8 kJ mol–1 respectively. The magnitude of enthalpy of formation of propane
(C3H8)(g) is………kJ mol–1.

5) 0.5 mole of an ideal gas A (CV = R) is taken in a container and expanded reversibly and
adiabatically from V = 1 litre to V = 4 litre starting from initial temperature T = 300 K. |ΔH| for the
process is (in cal).

6)

How many compounds are more reactive than towards SN1 (hydrolysis)?

(i) (ii) CH3–CH2–Cl (iii) (iv)

(v) (vi) CH2=CH–Cl (vii) CH3–Cl (viii)

7) total elimination products (alkenes) by E2 mechanism are?

8)

Number of molecules which gives immediate turbidity on reaction with Lucas reagent :

(i) Me3C–OH (ii) Ph–OH (iii) (iv)

(v) (vi) (vii)

PART-3 : MATHEMATICS

SECTION-I (i)

1) If where C is constant of integration and

and is equal to :

(A)

(B)

(C)

(D)

2) equals
(where C is integration constant)

(A)
+C

(B)
+C

(C)
+C

(D)
+C

3) The equation of the normal to the curve y = (1+x)2y + cos2 (sin–1x) at x = 0 is

(A) y = 4x + 2
(B) x + 4y = 8
(C) y + 4x = 2
(D) 2y + x = 4
4) If ƒ(x) = x3 – 9ax2 + 15a2x + 30, (a > 0) has its maximum value at x = α and its local minimum
value at x = β such that 5α2 = 2β, then possible value of 'a' is divisible by :

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

SECTION-I (ii)

1)

If (where C is constant of integration), then :–

(A) g(2) – g(1) = 3

(B) g(3) – g(2) = 23
(C) g(3) – g(2) = 5
(D) g(2) – g(1) = 7

2) For the function ƒ(x) = (x – 1) |x – 3| – 4x + 12, which of the following holds good ?

(A) Number of critical points on the graph of y = ƒ(x) is 3.

(B) Number of points of local extrema of ƒ(x) are 2.
(C) Number of points of local extrema of ƒ(x) are 3.
(D) Range of ƒ(x) is R.

3) If f(x) = 2x + x3 + 1 and g(x) = f–1(x), then (where dash(') denotes derivative)

(A) g'(2) = 1
(B) g'(2) = log2e
(C) g''(2) = (ℓn2)2
(D) g"(2) = –log2e

4) Let is continuous for all x ∈ R, then which of the following is

true -

(A) Range of ƒ(x) is (0,∞)

(B) ƒ(x) = 1 has one solution
(C) ƒ(x) = |ƒ(x)| for all x ∈ R
(D) ƒ(x) = 1 has two solutions

SECTION-II
1) Let f(x) = 7tan8x + 7tan6x – 4tan5x – 4tan3x and where g(0) = 0,then value of

is -

2) f(x) be a function defined as . The value of

[–f(1)] ______
(where [ . ] denotes the greatest integer function)

3) Let f(x) = sinx – asin2x – sin3x + 2ax, increases throughout the number line then minimum
prime value of 'a' is equal to

4) Let f(x) be a non-constant thrice differentiable function defined as such that

and If P is the minimum number of zero’s of
in the interval [0, 6] then value of P is equal to

5) If f(x) = 10x – 2x2, then is equal to

6) Equation of a tangent to the circle with centre (2, –1) is 3x + y = 0. If the square of the length of

the tangent to the circle from the point (3, –3) is λ, then value of is

7) Let P(x, y) lies on the curve x2 + y2 + 8x – 10y = 40 and . If m & M are

minimum and maximum values of ƒ(x, y), then value of , (where [.] denotes greatest
integer function), is

8) The number of real solutions of equation = sin–1 (sin x), –10 π ≤ x ≤ 10 π, is

 ANSWER KEYS

PART-1 : PHYSICS

SECTION-I (i)

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

SECTION-I (ii)

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

SECTION-II

Q. 9 10 11 12 13 14 15 16
A. 9.00 2.00 1.25 96.00 150.00 4.00 585.00 9.00

PART-2 : CHEMISTRY

SECTION-I (i)

Q. 17 18 19 20
A. B B C B

SECTION-I (ii)

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

SECTION-II

Q. 25 26 27 28 29 30 31 32
A. 4.00 10.00 5.00 103.70 450.00 3.00 4.00 4.00

PART-3 : MATHEMATICS

SECTION-I (i)

Q. 33 34 35 36
A. B B B A

SECTION-I (ii)

Q. 37 38 39 40
A. A,B A,B,D B,D A,B,C
 SECTION-II

Q. 41 42 43 44 45 46 47 48
A. 0.00 2.00 2.00 12.00 4.00 1.50 4.00 20.00
 SOLUTIONS

PART-1 : PHYSICS

1) 10 × 0.5 × {0 – (–20)} = 100 cal Heat to bring ice to 0°C

10 × 80 = 800 cal (heat to melt ice)
Total = 800 + 100 = 900 cal
10 × 1 × (10 – 0) = 100 cal
Heat lost by water at 10°C to become water at 0°C

2)
Force same ⇒ stress same

3)
VR = IR

4)

Conceptual theory based

5)
V = const.

C= C↑, Q = CV↑

E= = const.

6)
 VM
n + 12 = – 2n VN – 1 (2) + 12 = VM
– 3 n = 12 – 4 – 2 + 12 = VM
n = – 4v VM = 6V

i=

7) (initially)
∴ mg = fair

(finally)
∴ QE = mg + fair = 2mg
∴ charge is –ve, so electric field 'E' is directed downwards.
& QE = 2 mg

8)

All dimensions increase on heating

9)

600 TA = 1800 TB ⇒
σeAATA4 = σeABTB4

⇒
10)
Rods are identical so
RAB = RCD = 10 Kw–1
C is mid-point of AB, so
RAC = RCB = 5 Kw–1
at point C

2(200 – T) = T – 125 + 2(T – 100)

400 – 2 T = T – 125 + 2T – 200

T= = 145°C

11)
τF = 0
T2X = T1(2.5L – X)
12)

Potential difference across the terminals of C3 is 2V.

∴ Q3 = CV = (4µ) (2) = 8µC

13)

W = Pt
= 10 × 50 ×10 × 30
= 150000 Watt hour
= 150 Kilowatt hour

14)

15)

16)

Rate of area swept

(r = distance from COM)

⇒
 ⇒

PART-2 : CHEMISTRY

17) Forth floatation : a process that selectively separates materials based upon whether they
are water repelling (hydrophobic) or have an affinity for water (hydrophilic).

18) Total Energy in 1 min = 5 × 60 = 300 J Total Energy = n ×

n= =
20
n = 3 × 10

19) ...(1)

...(2)

...(3)
(1) = (2) + (3)
x = y + z

20) The correct answer is option (B)

21)

Iron ores are Haematite, Magnetite, Iron pyrite

22) Use Lechateleir principle.

23)

(A)

(B)
(C)

(D) %C =

24)

A → syn addn both 50% & 50% product are formed

B→

D → Product is formed with inversion of configuration.

25)

All silicates are sp3 hybridised

26) x = 2, y = 3, z = 5

27)

The correct answer is 5.00

28)
–2220 – [–393.5 + 4(–285.8)]
3 × (–393.5) + 4(–285.8) + 2220.0
= –103.7 kJ mol–1

29) 300(1)2–1 = T2 (4)2–1

⇒ T2 = 75 K
ΔH = nCPΔT
= 0.5 × 2 × 2 [75 – 300]
= –450 cal

30)

(i), (v), (viii)

 31) , , ,

32)

⇒ 3° & allylic alcohol give immediate turbidity.

⇒ (i), (iii), (iv), (vi)

PART-3 : MATHEMATICS

33)

34) Let x = ;

=
=

35) If x = 0, y = 2

Slope = 4

∴ The equation of normal is y – 2 = (x – 0)

x + 4y = 8

36) ƒ(x) = x3 – 9ax2 + 15a2x + 30 ƒ'(x) = 3x2 – 18ax + 15a2 = 0

⇒ x2 – 6ax + 5a2 = 0
⇒ x = a, 5a
ƒ"(x) = 6x – 18a
ƒ"(a) = –12a < 0
ƒ"(5a) = 30a – 18a = 12a > 0
so maxima at x = a = α
minima at x = 5a = β
5α2 = 2β
⇒ 5a2 = 2 (5a)
⇒a=2

37)
g(2) – g(1) = 4 – 1 = 3
g(3) – g(2) = 27 – 4 = 23

38) ƒ(x) = (x – 1) |x – 3| – 4x + 12

ƒ'(3–) = –6
ƒ'(3+) = –2
ƒ'(0) = 0
ƒ'(4) = 0

39) f(x) = 2x + x3 + 1 ⇒ f'(x) = 2xℓn2 + 3x2

g''(2) = –log2e

40)
ƒ(0 + h) = λ
ƒ(x) is a continuous function and λ = 1

Range of ƒ(x) is (0,∞)

ƒ(x) = 1 has one solution
ƒ(x) = |ƒ(x)| is always possible
because ƒ(x) > 0 for all x ∈ R

41)
put tanx = t
sec2x dx = dt

g(0) = 0 ⇒ C = 0

42) Let

43) f ′ (x) = cosx – 2a cos 2x – cos 3x + 2a ≥ 0 ∀ x ∈ R

⇒ 2sin2x(cosx + a) ≥ 0
⇒ a ≥ –cosx
∴a≥1
∴ minimum prime value of a = 2

44) f(x) is symmetrical about x = 3

 and

has 7 roots
has min of 6 roots
will have min of 13 roots

will have minimum of 12 roots

45) f(1) = 8, f(2) = 12, f ′ (1) = 6, f ′ (2) = 2

Now

(using L' hospital rule)

46) Length of ⊥r from centre (2, –1) on the tangent 3x + y = 0 is which

is which is radius of circle.
∴ Equation of circle

⇒ (x – 2)2 + (y + 1)2 =

required length

47) m and M are minimum and maximum distance of P(–2, 3) from circle (x + 4)2 + (y – 5)2 =
81 ⇒ m =
M=

48) Given equation is |cos x| = sin–1 (sin x) –π ≤ x ≤ π

Number of solution = 2