22-06-2025

1902CJA101001250010 JA

PART-1 : PHYSICS

SECTION-I (i)

1) A lift is moving vertically downwards with speed 10 m/s and acceleration 5 m/s2 downwards. A
coin is released 10 m from floor of lift, find distance travelled by lift when coin strikes the floor of
lift :-

(A) 20 m
(B) 10 m
(C) 25 m
(D) 30 m

2) Velocity of the river with respect to ground is given by v0. Width of the river is d. A swimmer
swims (with respect to water) perpendicular to the current with acceleration a = 2t (where t is time)
starting from rest from the origin O at t = 0. The equation of trajectory of the path followed by the
swimmer is

(A)

(B)

(C)

(D)

3) From a place on the ground that is 20 m away from a wall, a bullet is fired aiming at a 50m high
mark on the wall. The location of the bullet is shown by a circular dot at some point of time. Where
on the wall will the bullet hit ?

(A) 20 m mark
(B) 25 m mark
(C) 30 m mark
(D) 35 m mark

4) Two roads intersect at right angles. Car A is situated at P which is 500m from the intersection
O on one of the roads. Car B is situated at Q which is 400m from the intersection on the other road.
They start out at the same time and travel towards the intersection at 20 m/s and 15 m/s

respectively. What is the minimum distance between them?

(A) 10 m
(B) 20 m
(C) 30 m
(D) 40 m

SECTION-I (ii)

1) A particle is moving in such a way that its velocity versus time graph is a parabola (t = kv2, k is

constant) as shown in the figure. Choose the correct option (s)

(A) Acceleration of the particle is throughout the journey.

(B) Average acceleration of particle is 1 m/s2 for the interval of first 5 sec.
(C) Average acceleration of particle is less than for the interval of 0 sec to 10 sec.
(D) Average acceleration of particle is less than 1 m/s2 for the interval of 5 sec to 10 sec.

2) A particle P is projected at t = 0 from a point on the surface of a smooth inclined plane as shown
in the figure simultaneously another particle Q is released on the smooth inclined plane from the
same position. P and Q collide after t = 4 seconds. Then choose the correct option (s).

(A) Trajectory of particle P in the frame of Q is parabola during the flight of particle P.
(B) Speed of projection of P is 10 m/s.
(C) Relative velocity of particle P in the frame of Q changes linearly with time during the flight of P.
(D) Acceleration of particle P in the frame of Q is zero during the flight of P.

3) A man holding a flag is running in North-East direction with speed 10 m/s. Choose the correct
option(s).

(A) If wind is blowing in east is direction with the speed m/s. then flag will flutter in south
direction

(B) If wind is blowing in east is direction with the speed m/s. then flag will flutter in north
direction

(C) If wind is blowing in north is direction with the speed m/s. then flag will flutter in east
direction

(D) If wind is blowing in north is direction with the speed m/s. then flag will flutter in west
direction

4) A cart is moving along +x direction with a velocity of 4 m/s. A person on the cart throws a stone
with a velocity of 6 m/s with respect to himself. In the frame reference of the cart the stone is
thrown in the y-z plane making an angle of 30° with the vertical z axis. Then with respect to an
observer on the ground :-

(A) the initial velocity of the stone is 10 m/s.

(B) the initial velocity of the stone is m/s.
(C) the velocity at the highest point of its motion is zero.
(D) the velocity at the highest point of its motion is 5 m/s.

5) A boat has a speed of 10 m/s in still water. With this boat a person wants to cross the river from
point A. There is another point B on the other bank as shown. The river velocity is 5 m/s and width is
100 m.

If velocity of boat relative to water is perpendicular to the river bank then it reaches 50 m
(A)
upstream of B.
(B) If velocity of boat relative to water is along AB, it reaches 50 m downstream of B.
(C) Minimum time to cross the river is 10 s.
If the river has to be crossed along the shortest path, boat velocity relative to river should make
(D)
an angle of 120° with river velocity.

6) The motion of a body is given by the equation = 6.0 – 3 v(t) ; where v (t) is the speed in m/s
& t in second, if the body was at rest at t = 0.

(A) the terminal speed is 2.0 m/s

(B) the magnitude of the initial acceleration is 6.0 m/s2
(C) the speed varies with time as v(t) = 2 (1 – e–3t) m/s
(D) the speed is 1.0 m/s when the acceleration is half the initial value

SECTION-II

1) A fighter plane is flying horizontally at a height of 250 m from ground with constant velocity of
m/s. It passes exactly over a cannon which can fire a shell at any time in any direction with a
speed of100 m/s. Find the duration of time (in sec) for which the plane is in danger of being hit by a
cannon shell. Round off to nearest integer if necessary.

2) A train stopping at two stations 4000m apart takes 240s on the journey from one of the station to
the other. Assuming that it first accelerates with a uniform acceleration x and then that of uniform

retardation y. Find the numerical value of if x and y are taken in m/s2

3)

A man can swim in still water with a speed of 3 m/s. x and y axis with respect to ground are drawn
along and normal to the bank of river flowing to right with a speed of 2 m/s. The man starts
swimming from origin O at t = 0 second. Assume size of man to be negligible. Locus of all the

possible points where man can reach at t = 2 sec is (x – a)2 + y2 = c2. Find value of .
4) A man walking downhill with velocity u finds that his umbrella gives him maximum protection
from rain when he holds it such that the stick is perpendicular to the hill surface. When the man
turns back and climbs the hill with velocity u, he find that it is most appropriate to hold the umbrella
stick vertical. Find the speed of raindrops w.r.t. ground. The inclination of the hill is θ = 30°.

5) A boy throws a ball upward with a speed of 12 m/s. The wind imparts a horizontal acceleration of
0.4 m/s2. The angle θ to the vertical, at which the ball must be thrown so that it returns to the point

of release is . What is the value of x?

6) Two particles P and Q are moving on x-axis such that their v-t graphs look like as shown in
diagram. In the graph of P, the initial part upto t = 1 is a parabola of type y = ax2, and there after a
straight line. The graph of Q is a straight line throughout and having slope equal to that of the
straight part of P. If the two particles P and Q start from same point, find the separation between

them (in meter) 2 second after the particle Q starts motion.

7) Two inclined planes are placed as shown in figure. A block is projected from the point A of
inclined plane AB along its surface with a velocity just sufficient to carry it to the top point B at a
height 10 m. After reaching the point B the block slides down on inclined plane BC. Time it takes to

reach to the point C from point A is The value of t is :- (g = 10 m/s2)

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) For an atom or ion having single electron, compare the energies of the following orbitals.
S1 = A spherically symmetrical orbital having two spherical nodes.
S2 = An orbital which is double dumb-bell and has no. radial node.
S3 = An orbital with orbital angular momentum zero and three radial nodes.
S4 = An orbital having one planar and one radial node.

(A) S1 = S2 = S3 = S4
(B) S1 = S2 = S4 < S3
(C) S1 > S2 > S3 > S4
(D) S1 < S4 < S3 < S2

2) Imagine a universe in which the four quantum number can have,the following values.
n = 1 to ∞
ℓ = 0 to n
m = −(ℓ + 1) to + (ℓ + 1) including zero

Total number of elements in the III period of periodic table is

(A) 8
(B) 20
(C) 30
(D) 15
3) The given diagram shows points P1, P2, P3 and P4 in 1s orbital:
The correct order of increasing radial probability at these point is

(A) P1 = P2 = P4 > P3
(B) P1 = P3 < P2 = P4
(C) P1 = P3 > P2 = P4
(D) P1 = P2 = P4 < P3

4) For ion, following successive ΔHIE values are obtained [X may be O, S or Se]

Select the CORRECT statement:

(A) A is endothermic
(B) The value of 'C' is more for 'Sulphur' than 'Oxygen'
(C) The value of 'B' is more for 'Sulphur' than 'Oxygen'
(D) B is exothermic

SECTION-I (ii)

1) For electron, proton, deuterium molecule (D2) & α-particles a curve between λ(De-Broglie

wavelength) v/s u speed is plotted. Select the correct statement(s).

(A) Curve I is for electrons

(B) Curve III is for proton
(C) Curve II is for α-particle
(D) Curve III is for Deuterium (D2)

2) Select the correct statement(s)

(A) Heisenberg's principle is applicable to stationary e−
(B) Pauli's exclusion principle is not applicable to photons
For an e−, the product of velocity and principal quantum number will be independent of
(C)
principal quantum number
(D) Quantum numbers ℓ and m determine the value of angular wave function

3) When photons of energy 4.25 eV strike the surface of a metal A, the ejected photoelectrons have
maximum kinetic energy, TA (expressed in eV) and de-Broglie wavelength λA. The maximum kinetic
energy of photoelectrons liberated from another metal B by photons of energy 4.20 V is TB = TA −
1.50 eV. If the de- Broglie wavelength of these photoelectrons is λB = 2λA, then:

(A) the work function of A is 2.25 eV

(B) the work function of B is 3.70 eV
(C) TA = 2.00 eV
(D) TB = 2.75 eV

4) Select correct statement(s):

(A) Orbital angular momentum depends on two quantum number is ℓ and mℓ

(B) Total energy does not very in 1s orbital of H-atom with distance from nucleus.
Whenever a radiation interacts with matter it displays wave nature while when it propagates it
(C)
exhibit particle nature.
Boundary surface diagram of p atomic orbitals is dumbell but |ψ2| is not same at different points
(D)
on boundary surface.

5) Which of the following statement(s) is/are correct about following plot?

(A) This orbital wave function is associated with one radial node
(B) This orbital wave function is associated with zero radial node
(C) Radial node is at 0.2 nm
(D) This orbital wave function is associated with zero angular node

6) Which of the following statements is/are INCORRECT:

(A) All spectral lines belonging to Balmer series in hydrogen spectrum lie in visible region.
If a light of frequency v falls on a metal surface having work function hv0 photoelectric effect
(B)
will take place only if v ≤ v0
The number of photoelectrons ejected from a metal surface in photoelectric effect depends
(C)
upon the intensity of incident radiations.

(D)
The series limit wavelength of Balmer series for H-atom is , where R is Rydberg's constant.
 SECTION-II

1) For X5+ ion, the successive electron affinities (in eV) are 289.7, 270.9, 30.1, 17.9 and 8.3. The
expected number of electrons in the outermost shell of X-atom is

2) An electron in a He+ ion is in a state with directional dependence and has a total of one node. A

photon of frequency causes this electron to jump into a higher state which can have total five
possible orientations in space. Find magnitude of the change in (n + ℓ) values corresponding to two
states?
(R = Rydbergs constant, C = speed of light)

3) How many oxides are soluble in moderately concentrated aqueous solution of NaOH.

SO3 Cℓ2O7 N2O5 CO

(1) (2) (3) (4)

K2O Cr2O3 BaO GeO2

(5) (6) (7) (8)

4) An electron accelerated from rest by a potential difference of 1.5 V has uncertainty in its de-
broglie wavelength = 0.1%. If uncertainty in position (in Angstron units) is expressed as

then calculate the value of 'y'.

5) In a sample of hydrogen atom in ground state electrons make transition from ground state to a
particular excited state where path length is five times de-broglie wavelength, electrons make back
transition to the ground state producing all possible photons. If photon having 2nd highest energy of
this sample used to excite the electron in a particular excited state of Li2+ ion then find the final
excited state of Li2+ ion.

6) A H-like species emitted a photon corresponding to the first line of Lyman series. The photon
liberated a photo- electron from He+ in ground state. The de-Broglie wavelength of the photo-
electron is 2Å. Calculate the atomic number of H-like specie.

7)

How many of the following are correct

(i) B < Ga < Al < In < Tℓ atomic radius order
(ii) C > Si > Ge > Pb > Sn IE1 order
(iii) C > Pb > Si = Ge = Sn electronegativity order
(iv) Ne > Ar = Kr > Xe > Rn > He electron gain enthalpy [with sign]
(v) Cℓ > F > Br > I electron gain enthalpy (magnitude only)
(vi) HF > HCℓ > HBr > HI acidic nature
8) A chemist has one mole of X-atoms. He finds that on absorption of 410 kJ, half of X− atoms transfer
one electron to the other half. If all the resulting X− ions are subsequently converted to X+ ions, an
addition of 735 kJ is required. Find the electron affinity of X (in kJ/mol ).

PART-3 : MATHEMATICS

SECTION-I (i)

1) If log27 = a and log32 = b, then the value of log14 84 is :-

(A)

(B)

(C)

(D)

2) Three real number x, y, z are such that x2 + 6y = –17, y2 + 4z = 1 and z2 + 2x = 2, then the value
of x3 + y3 + z3 is equal to

(A) 30
(B) -24
(C) -36
(D) -28

3) Consider a sequence < an> such that a1 = (5, 52, 53), a2 = (54, 55, ....., 512), a3 = (513, 514, ....., 539).....

then which term of the sequence contains the number

(A) a6
(B) a7
(C) a8
(D) a9

4) A quadratic equation has roots such that (where kn is any

constant and ). Let be the roots of the equation ,

then find the value of .

(A) 1
(B) –1

(C)
(D) 2

SECTION-I (ii)

1) Find the solution set of

(A)

(B)

(C)

(D)

2) Let Q(x) = 0 be a quadratic equation having roots α and β. If Pn = αn + βn, then choose the correct
option(s).

(A)
If then

(B)
If

(C)
If

(D)
If

3)

Let Sn = –12 – 22 – 32 + 42 + 52 + 62 – 72 – 82 – 92 + ..... + Tn (nth term)

(A) S100 > S99

(B) S98 > S99
(C) T100 + T64 = T36
(D) 2T100 – S100 = 4850

4) If , then which of the following is true:

(A) xyz = 1
(B) xaybzc = 1
(C)
(D) xyz = xaybzc
5) For the roots of the equation can be

(A)
(B)
(C)
(D) none of these

6) Let a0, a1, a2,.....be a sequence of real numbers satisfying

Then, which of the following options is/are correct ?

(A) r8 = 1013

(B)

(C)
(D)

SECTION-II

1) If x < 0, & x2 – x – 1 = 0, then the value of (log10(x4 + 1)(x8 + 1)(x16 + 1) – 14log10(–x)) is log10k. Find
k

2) If a2 + b2 + c2 = 14 ; d2 + e2 + f2 = 77 and ad + be + cf = 32 then value of (ae – bd)2 + (af – dc)2 +

(bf – ce)2

3) If {xn} is a sequence of numbers ∀ n ∈ N such that

&

and .
Then sum of digits of N is equal to

4) If S denotes the sum of first 24 terms of series then is equal to

5) In a book with page numbers 1 to n, four consecutive pages are torn off and the sum of the
numbers on the remaining pages is 1596, then find the sum of possible values of n. (4 consecutive
pages means page numbers m, m+1, m+2 & m+3, m∈ N )

6) Let a(x) = αx + βx ∀ x ∈ R, where α and β are roots of the equation x2 + 3x + 1 = 0. If a(8) + a(6) =

λa(7) then value of is

7) Let a1,a2,a3 ∈ R

, for k = 1,2,3. If , then is

equal to

8) If the range of values of a for which the roots of the equation lie between the

roots of the equation is (p, q) find the value of .

 ANSWER KEYS

PART-1 : PHYSICS

SECTION-I (i)

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

SECTION-I (ii)

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

SECTION-II

Q. 11 12 13 14 15 16 17 18
A. 4.00 7.20 6.00 26.00 1.00 7.00 2.00 3.00

PART-2 : CHEMISTRY

SECTION-I (i)

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

SECTION-I (ii)

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

SECTION-II

Q. 29 30 31 32 33 34 35 36
A. 3.00 2.00 7.00 4.00 12.00 3.00 5.00 325.00

PART-3 : MATHEMATICS

SECTION-I (i)

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

SECTION-I (ii)

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

Q. 47 48 49 50 51 52 53 54
A. 987.00 54.00 7.00 6.00 119.00 0.60 3.00 17
 SOLUTIONS

PART-1 : PHYSICS

1) UL = –10 m/s, aL = –5 m/s2

In lift frame
Ucoin/L = 0
aCL = –10 –(–5) = –5m/s2
∴ SCL = –10 m
–10 = 1/2 ×–5 × t2
t = 2 sec
SL = –10 × 2 + 1/2 × (–5) × 4
= –30 m

2)

Correct Option is A

3)

Correct Option is C

4)

shortest distance = 20m

5) t = kv2
at t = 10 sec, v = 10 sec
v at t = 5

6)

Acceleration of particle P and Q along the incline is same.

Acceleration of particle P perpendicular to the incline plane is 10 cos 60° = 5 m/s2
So, vP – 5(2) = 0
∴ vP=10m/s

7) From given data

Velocity of man
Velocity of wind

The flag will flutter in the direction in which wind is blowing with respect to the man holding
the flag.

This implies direction of wind with respect to man in south.

Flag will flutter in south direction.

8)

Correct Option is B, D

9) For (A)

sx = 10 × 5 = 50 m
For (B)
For (C)

for minimum time : =10s

For (D)

Shortest path :

10)

11) Equation of envelope of trajectory

y = –k(x – α)(x – β)
y = –k(x – Rmax)(x + Rmax)
y = –k(x2 – R2max)

At (0, Hmax)
Hmax = –k(–R2max)

∴
At y = 250m

to traverse half the envelope

∴ 4s are required than plane escacps the of can not ball

12)

Correct Option is 7.20

13)

14) Velocity of rain relative to the man is perpendicular to the incline in this case (i.e. along
the umbrella stick. This keeps umbrella perpendicular to the rainfall and provides maximum
safely)
=
Since has no component
∴ Vx = u
when the man is walking up, is directed vertically downward.

= =

15)

Correct Option is 1.00

16) For P
Parabolic part V = at2
Point (1, 3) lies on it so
a=3
V = 3t2
For Q Vt = 1 = 0 m/s
For motion after 1 sec.
Vrel = 3m/s, arel = 0
Srel = 3 × 2 = 6m
Total separation = 6 + 1 = 7 m

17)

From E.C. =

For A → B
at B, v = 0

a = – g sin 45° =

For B → C

So total time

18)

for u to be minimum
PART-2 : CHEMISTRY

19) correct option is B

20) correct answer is c

21) correct option is C

22) correct option is C

23)

Correct Option is A,D

24)

correct answer is bcd

25) correct option is ABC

26) correct option is AB

27) correct option is AD

28)

correct answer is AB

29) correct answer is 3.00

30) correct answer is 2.00

31)

correct answer is 7.00

32) correct option is 4.00

 33) correct option is 12.00

34) correct option is 3.00

35)

correct option is 5.00

36)

correct answer is 325.00

PART-3 : MATHEMATICS

37) log1484 =

38)

Correct Option is C

39)

40)

Correct Option is A

41)

Case 1: If

ignored
Case 2: if
 ignored

42)

Correct Option is A,C,D

43)

Correct Option is A,C,D

44)
logx = k (b − c), log y = k(c − a) . logz = k(a − b)
logx + logy + logz = k(b − c + c − a + a − b)
log (xyz) = k (0)
xyz = 1

45)

⇒
⇒ Let

⇒
⇒
⇒
⇒
⇒

⇒
⇒ or

46)
47) x2 – x – 1 = 0

log10(x4 + 1)(x8 + 1)(x16 + 1) – 14log10(–x)

= log10 3 × 7 × 47
= log10987

48)

a2 + b2 + c2 = 14
d2 + e2 + f2 = 77
ad + be + cf = 32
⇒ (a2 + b2 + c2) (d2 + e2 + f2) – (ad + be + cf)2 = 14 × 77 – (32)2
⇒ a2d2 + a2e2 + a2f2 + b2d2 + b2e2 + b2f2 + c2d2 + c2e2 + c2f2
–(a2d2 + b2e2 + c2f2 + c2f2 + 2adbe + 2adcf + 2becf) = 54
⇒ (ae – bd)2 + (af – dc)2 + (bf – ce)2 = 54

49)

=
N = 2014

50)

∴ Sum of first 24 terms

⇒

51) Let page numbers k, k + 1, k + 2, k + 3 are torn off.

if n = 59, k = 42
if n = 60, k = 57
Sum = 59 + 60 = 119

52) a(x) = αx + βx
x x
(α + β) a(x) = (α + β) (α + β )
–3a(x) = αx + 1 + βx + 1 + αβ(αx – 1 + βx – 1)
–3a(x) = a(x + 1) + a(x – 1)
for x = 7
–3a(7) = a(8) + a(6)

⇒ λ = –3 Ans.

53) Let
Q(x) = (x2 + 1) (x2 + 2) (x2 + 3)
Let R(x) = P(x) Q(x)

Now P(x) = has root ±1,±2,±3

⇒ P(x) Q(x) = has roots ±1,±2,±3

2
⇒ x R(x) – Q(x) = 0 has roots ±1,±2,±3
x2R(x) – Q(x) = λ(x2 – 1)(x2 – 4)(x2 – 9)
Put x = 0

–6 = λ(–36) ⇒ λ =

⇒
–17.18.19 = 210

54)
Correct Option is 17.00