15-06-2025

2401CJA101001250012 JA

PART-1 : PHYSICS

SECTION - I (i)

1) If a particle travels first one third distance with speed V1 and remaining two third distance with
speed V2, then the average speed of particle during journey in :

(A)

(B)

(C)

(D)

2) A particle starts from rest. Its acceleration (a) versus time (t) is as shown in the figure. The

maximum speed of the particle will be :

(A) 110 m/s

(B) 55 m/s
(C) 550 m/s
(D) 660 m/s

3) A river is flowing with a speed of 1 m/s. A swimmer wants to go to point C starting from A. He
swims with a speed of 5 m/s, at an angle θ w.r.t. river flow. If AB = BC = 1000 m. Then the value of θ

is

(A) 30°
(B) 37°
(C) 45°
(D) 53°

4) A swimmer crosses a river with minimum possible time 10 second. And when he reaches the other
end starts swimming in the direction towards the point from where he started swimming. Keeping
the direction fixed the swimmer crosses the river in 15 sec. The ratio of speed of swimmer with
respect to water and the speed of river flow is (Assume constant speed of river & swimmer) :-

(A)

(B)

(C)

(D)

SECTION - I (ii)

1) In a situation, a board is moving with a constant velocity v with respect to earth, while a man A
and man B are running with a velocity 2v with respect to earth and both men are running from the
opposite ends of the board at the same time, as shown. Length of the board is L. If they meet after

time T, then

Value of T is
(A)

Value of T is
(B)

(C) Displacement of man B with respect to board in time T is 3L/4

(D) Displacement of man A with respect to board in time T is L/4

2) Two particles are thrown from same point in same vertical plane as shown in figure

simultaneously. Then indicate the correct statement(s).

(A) Time of flight of B is less than that of A.

(B) Projection speed of B is greater than that of A.
(C) Horizontal component of velocity of B is greater than that of A.
(D) Vertical components of velocities of A and B are always equal through out the flight of A and B.

3) If T is the total time of flight, h is the maximum height and R is the range for horizontal motion,
the x and y co-ordinates of projectile motion and time t are related as

(A)

(B)

(C)

(D)

SECTION - I (iii)

Common Content for Question No. 1 to 2

We have studied projectile motion in great details in previous classes. Apart from many features of
projectile motion, a very interesting fact about projectile motion (which can be shown by a simple
logic) is that whenever distance between point of projection and point of landing is maximum for a
given speed, angle between velocity vectors at these points (at the initial and final instants) is 90°.
For example in figure (i), (ii) and (iii), if AB is maximum for a given speed, then α + β = 90°. (i)

(ii) (iii)

1) A projectile is projected on an inclined plane, up the incline as shown in the figure, if range AB is

maximum then :

(A) β = 35°
(B) β = 40°
(C) β = 45°
(D) β = 50°

2)

For ground to ground projectile motion, if distance between points A and B is maximum in the figure
shown below, then :
(A) β = 30°
(B) β = 45°
(C) β = 60°
(D) β = 90°

Common Content for Question No. 3 to 4

A car is moving on a straight road. The velocity of the car varies with time as shown in the figure.
Initially (at t = 0), the car was at x = 0, where, x is the position of the car at any time 't'.

3) The displacement time graph will be best represented by :

(A)

(B)

(C)
(D)

4) Average speed from t = 0 to t = 70 s will be :

(A)
m/s

(B)
m/s

(C)
m/s
(D) zero

SECTION - II

1) A ball is projected from ground and it crosses point A and B which are on same level after 3 sec

and 5 sec of projection. If ball is at half of maximum height at time t1 & t2, then find

2) If the projected particle strikes the inclined plane perpendicularly. What is the value of cotθ.cotα.

3)

A particle is projected with a velocity v so that its range on a horizontal plane is twice the greatest

height attained. If g is acceleration due to gravity, then its range is Find x

4) Two particles are projected simultaneously on an inclined plane with same speeds at equal angles
with the inclined plane as shown in the figure, if the angle of the inclined plane with the horizontal
is then the ratio of their time of flights is _____.

5) Two inclined planes AB and BC are at inclinations of 60° and 30° as shown in the figure. The two
projectiles of same mass are thrown simultaneously from A and C with speed 2 m/s and v0 m/s

respectively, and they strike at B with same speed. If length of AB is m and BC is 1m, then find

the value of v (in m/s).

6) A body starts from the origin and moves along the X-axis such that the velocity at any instant is
given by (4t3 – 2t), where t is in second and velocity in m/s. What is acceleration (in m/s2) of the
particle, when it is 2 m from the origin.

PART-2 : CHEMISTRY

SECTION - I (i)

1) In which of the following process energy is not absorbed :

(A) Na → Na+
(B) Mg → Mg+2
(C) O → O+
(D) None of these

2) Identify the pair of elements in which first element having greater electron affinity than second.

(A) (F, Cl)

(B) (N, O)
(C) (P, N )
(D) (O, F)

3) A ⇒ [Ar] 3d104s24p1 B ⇒ [Ne] 3s23p3

C ⇒ [Ne] 3s23p1 D ⇒ [He] 2s22p4
Which of the following compound is considered to be as an amphoteric compound
(A) AD
(B) B2D3
(C) C2D3
(D) CB

4)

The successive ionisation energies for an element X are given below

IE1 = 410 kJ / mole
IE2 = 820 kJ / mole
IE3 = 1100 kJ / mole
IE4 = 1500 kJ / mole
IE5 = 7000 kJ / mole
Find out the number of valence electron for the atom X

(A) 4
(B) 3
(C) 5
(D) 2

SECTION - I (ii)

1) How many of the following trend is "INCORRECT" ?

(A) Electron affinity : Se > S > Br > Cℓ

(B) Ionic radii : Ba2+ > Rb+ > K+ > Sr2+
(C) Atomic radii : S > Cℓ > O > F
(D) I.E2 (Be) > I.E2 (Li)

2) Which of the following is/are incorrect?

(A) More electronegative element has more metallic nature

(B) Acidic strength order N2O5 > N2O3
(C) Al2O3 and Li2O are amphoteric oxides
(D) Boron has diagonal relationship with aluminium

3) Which of the following Ist ionisation energy order is/are correct

(A) Be < B
(B) N < O
(C) Mg > Na
(D) P > S

SECTION - I (iii)
Common Content for Question No. 1 to 2
All the elements, on the basis of long form of periodic table, can be divided into four blocks, s, p, d
and f. The Ionization energies, electron affinities, electronegativities, atomic and ionic radii and
other physical properties usually shown a regular pattern of change within a group or along period
with some irregularities.

1) On moving from Li to F in the second period, there would be a decrease in:

(A) non-metallic property

(B) atomic radius
(C) ionization potential
(D) electronegativity

2) Which of the following element has the maximum value of electronegativity?

(A) Nitrogen
(B) Oxygen
(C) fluorine
(D) Chlorine

Common Content for Question No. 3 to 4

Ionisation energies of unknown elements are given below :
Element IE (in kcal / mol)
I II III
M 209 348 919
N 100 735 1101
O 119 1092 1653
P 1500 2017 2320

3) Most metallic element among these is :

(A) N
(B) P
(C) O
(D) M

4)

Which amongst them is expected to be a noble gas ?

(A) M
(B) N
(C) O
(D) P

SECTION - II

1) What is the value of n for given change in an atom A.

2) Out of the following the number of incorrect statements are :
(i) AOH > BOH > COH [Order of basic nature if EN values of A, B and C are 1.5, 2.8 and 3.2
respectively]
(ii) N2O > NO > N2O3 > N2O4 > N2O5 [Order of acidic strength]
(iii) Difference between values of σ (shielding constant ) of Be2+ and B3+ is 0.35
(iv) H2O > H2S > H2Se > H2Te (Order of basic strength)

(v) O2− > F− > Na+ > Mg2+ > Al3+ (Order of , n = number of electrons)
(vi) B > T > Ga > Al (Order of I.P.)

3) Which out of the following options are incorrect ?

According to the mentioned properties.
(i) LICl < NaCl < KCl < RbCl (% covalent character)
(ii) Maximum covalency of halogen including F which can be achieved is 7
(iii) IP1 of ion M+2 > EA1 of M+3. (IP = ionisation potential, EA = electron affinity)
(iv) S > Se > Te > O (order of EA)
(v) Li < Be < B < C(order of electronegativity)
(vi) Mg+2 < Na+ < F− (order of ionic size)
(vii) Li+ > Na+ > K+ (order of hydrated size)
(viii) NaCl > MgCl2 > AlCl3 (order of lattice energy)

4) X - X bond length is 1.00 and C - C bond length is 1.54 . If electronegativities of X and C are
3.0 and 2.0 respectively, then C - X bond length is _______ .

5) How many of the following oxides are amphoteric ?

CO2, SnO2, PbO, PbO2, Pb3O4, Al2O3

6)

Write the number of pairs in which size of first element or ion is higher as compared to IInd out of
following :
(O, S), (He, Ne), (Kr, Ne), (Na, Na+), (Cl, Cl–), (I–, Cl–), (Li, Na), (Li+, Na+)

PART-3 : MATHEMATICS

SECTION - I (i)

1) For what values of k the expression kx2 + (k +1)x + 2 will be a perfect square of a liner
polynomial

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

2) If are roots of x2 + 2x – 4 = 0. The equation whose roots are & is:

(A) x2 – 4x + 3 = 0
(B) x2 – 5x + 6 = 0
(C) x2 – 3x + 2 = 0
(D) x2 – 3x + 4 = 0

3) If the graph of y = 16x2 + 8(a + 5)x – 7a – 5 is strictly above the x-axis, then:

(A) a ∈ (–15,–2)
(B) a ∈ (–2,–1)
(C) a ∈ (–1,1)
(D) a ∈ (5,7)

4) The expression is simplified to.

(A) 16
(B) 4
(C) 2

(D)

SECTION - I (ii)

1)

Let S be the set of all non-zero real numbers α such that the quadratic equation αx2 –x + α = 0 has
two distinct real roots x1 and x2 satisfying the inequality |x1 – x2| < 1. Which of the following intervals
is(are) a subset(s) of S?

(A)

(B)

(C)

(D)

2) Let α, β be roots of x2 – 9x + 2 = 0. Then

(A) (1 – α) (1 – β) = –6
(B) (2 – α) (2 – β) = 10
(C) (1 + α) (1 + β) = 12
(D) (2 + α) (2 + β) = 24

3) For the equation |x2| + |x| – 6 = 0, the correct statement(s) is (are) :

(A) Sum of roots is 0

(B) Product of roots is –4
(C) There are 4 real roots
(D) There are only 2 real roots

SECTION - I (iii)

Common Content for Question No. 1 to 2

The following diagram shows the graph of f(x) = ax2 + bx + c. then

1) Sign of D is

(A) positive
(B) negative
(C) non positive
(D) non negative

2) Sign of c is

(A) positive
(B) negative
(C) non positive
(D) non negative

Common Content for Question No. 3 to 4

Consider quadratic equations x2–ax+b=0 (i)
and x2+px+q=0 (ii)

3) If for the equations(i) and (ii), one root is common and the equation(ii) have equal roots, then b +
q is equal to :

(A) –ap
(B) ap
(C)

(D) 2ap

4) If the above equations have one common root and the other roots are reciprocals of each other,
then (q–b)2 equals

(A) bq(p–a)2
(B) b(p–a)2
(C) q(p–a)2
(D) bq(p + a)2

SECTION - II

1) If is a root of the equation x2 + bx + c = 0 where b, c are rational numbers then |3b + 2c|
is

2) The number of elements in the set is :

3) Number of non-negative integral values of x satisfying the inequality

is

4) The smallest integral value of ‘c’ for which (c – 3) x2 – 2cx + 3c > 6 is satisfied for all real values of
x is :

5) For all real value of x, the maximum value of the expression is

6) If α, β be the roots of 4x2 – 16x + λ = 0, such that 1 < α < 2 and 2 < β < 3 then the number
of integral solutions of λ is/are equal to.....
 ANSWER KEYS

PART-1 : PHYSICS

SECTION - I (i)

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

SECTION - I (ii)

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

SECTION - I (iii)

Q. 8 9 10 11
A. A B B B

SECTION - II

Q. 12 13 14 15 16 17
A. 1.60 2.00 4.00 1.00 2.00 22.00

PART-2 : CHEMISTRY

SECTION - I (i)

Q. 18 19 20 21
A. D C C A

SECTION - I (ii)

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

SECTION - I (iii)

Q. 25 26 27 28
A. B C A D

SECTION - II

Q. 29 30 31 32 33 34
A. 5.00 3.00 4.00 1.18 to 1.2 5.00 3.00

PART-3 : MATHEMATICS
 SECTION - I (i)

Q. 35 36 37 38
A. B C A A

SECTION - I (ii)

Q. 39 40 41
A. A,D A,C,D A,B,D

SECTION - I (iii)

Q. 42 43 44 45
A. A A C D

SECTION - II

Q. 46 47 48 49 50 51
A. 10.00 6.00 3.00 7.00 1.00 3.00
 SOLUTIONS

PART-1 : PHYSICS

1) Ans. (C)

2) The area under the acceleration-time graph gives change in velocity. Since particle starts
with u = 0, therefore change in velocity
= vf – vi
= vmax – 0 area under a – t graph

3)

Ans. (D)
D is the correct answer

4)
V = velocity of man w.r.t . river
u = velocity of river

= ⇒ 10 =
⇒ d = 10 V____(1)

= ⇒ 15 =
⇒ d = 15 v cos θ ___(2)
(1) & (2) ⇒ cos θ = 2/ 3 ⇒ sec θ = 3/ 2

∵ tan θ =

∴
 5)

At the plane VAB = 4V

6)

Component of velocity in vertical direction in same (Hmax is same)

....(1)

(A) Time period

TA = TB

(B)

RB > RA
from eqn – 1

since Hmax is same

7)

so
 8)
for AB max.
α' = 35°
α = 55°
α + β = 90
α = 35°

9)
for AB max
α = 45°
α + b = 90°
β = 90 – a
β = 45°

10)

Ans. (B)
B is the correct answer

11)

Ans. (B)
B is the correct answer

12)

13)

For the perpendicular collision from inclined ⇒ The velocity along inclined would be zero.

∴ ucosα – gsinθT = 0

and also;

cotα.cotθ = 2
 14)

Given,

15)

16)

Ans. (2.00)
(2.00) is the correct answer

17)

Ans. (22.00)
(22.00) is the correct answer

PART-2 : CHEMISTRY

18)

Ans. (D)
D is the correct answer

19)

Ans. (C)
C is the correct answer

20) Explanation :-
Amphoteric compound is asked by given e– configuration.

Concept :-
Amphoteric wrath of compound.

Solution :-
G = [Ne]3S23P1 = Al
D = [He]2S22P4 = 0
∴ Compound equivalent to Al2O3
C2D3

21)

Ans. (A)
A is the correct answer

22)

Ans. (A, B, D)
A, B, D is the correct answer
(B) G-1 and G-2 Ionicradii
G-1 G-2
3 1(smallest)
5 2
8 4
9 6
10(Highest) 7
(D) I.E3 (Li) > I.E2 (He)

23)

Ans. (A, C, D)
A, C, D is the correct answer

24)

Answer - Option (3,4 )

Explanation - Let's analyze each option for the ionization energy order:
The species with the lowest nuclear charge and hence the lowest ionization energy is S2-, since
its electrons are least tightly bound by the nucleus.

25)

Ans. (B)
B is the correct answer

26)
Ans. (C)
C is the correct answer

27)

Ans. (A)
A is the correct answer

28)

Ans. (D)
D is the correct answer

29)

Ans. (5.00)
(5.00) is the correct answer

30)

Ans. (3.00)
(3.00) is the correct answer

31)

Ans. (4.00)
(4.00) is the correct answer

32)

33)

Ans. (5.00)
(5.00) is the correct answer

34)
 size order —→ On moving down in a group size ↑
Na > Na+ (Neutral atom > cation)
Cl < Cl– (Neutral atom < anion)
I– > Cl–
In I last e is present in 5th shell, whereas in Cl– last e– is present in 3rd shell.
– –

Li+ < Na+

In Na+ last e– is present in 3rd shell, whereas in Li+ last e– is present in 2nd shell.

PART-3 : MATHEMATICS

35)

Ans. (B)
B is the correct answer

36) (Reference to B.B-01)

Roots are 1, 2
Equation

37) Question Explanation:

In this question given that graph of y = 16x2 + 8(a + 5)x – 7a – 5 lies entirely above the x-axis
means roots of this quadratic equation y = 0 are imaginary for that we need to find the values
of 'a'.

Concept:
This question is based on Nature of Roots.
Graph lies entirely above the x-axis.
f(x) > 0 ∀ x ∈ R
I&

Solution:
Let y = f(x) = 16x2 + 8(a + 5)x – 7a – 5
a = 16 > 0
Thus we need D < 0 or roots to be imaginary for the entire graph to be above the x-axis.
(8(a + 5))2 –4 (16)(–7a – 5) < 0
⇒ a2 + 10a + 25 + 7a + 5 < 0
⇒ a2 + 17a + 30 < 0
⇒ (a + 15)(a + 2) < 0
⇒ a ∈ (–15, –2)

Final Answer:
The correct option is (1)

38)

39)

αx2 – x + α = 0, a ≠ 0
|x1 – x2| < 1

⇒ <1

⇒ <1
⇒ < |a|
⇒ 1 – 4α2 < α2

⇒ α2 >

⇒
⇒Option A, D are correct.

40) x2 – 9x + 2 = (x – α) (x – β)
x=1 (1 – α) (1 – β) = –6
x=2 (2 – α) (2 – β) = –12
x = –1 (1 + α) (1 + β) = 12
x = –2 (2 + α) (2 + β) = 24

41)

Ans. (A,B,D)
A, B, D, is the correct answer

42)

Ans. (A)
A is the correct answer

43)

Ans. (A)
A is the correct answer
44)

Ans. (C)
C is the correct answer

45)

Ans. (D)
D is the correct answer

46)

Let

Sum of roots α + β = –b

b = –4
αβ = c ⇒ C = =4–3=1
|3b + 2c| = |3(–4) + 2(1)| = 10

47)

Ans. (6.00)
(6.00) is the correct answer

48)

⇒ ⇒

⇒ ⇒

required value of x = {0, 1, 2}.

49)

c>3 …(i)
2
4c – 4(c – 3) (3c – 6) < 0
c2 – (c – 3) (3c – 6) < 0
c2 – [3c2 – 15c + 18] < 0
–2c2 + 15c – 18 < 0
⇒ 2c2 – 15c + 18 > 0
⇒ 2c2 – 12c – 3c + 18 > 0
⇒ (2c – 3) (c – 6) > 0

⇒ …(ii)
(i) ∩ (ii) ⇒ c ∈ (6, ∞)= 7

50)
yx2 – 5xy + 9y = x
x2 y – x[5y + 1] + 9y = 0
x∈R D≥0
(5y + 1)2 – 36y2 ≥ 0
25y2 + 1 + 10y – 36y2 ≥ 0
–11y2 + 10y + 1 ≥ 0
11y2 – 10y – 1 ≤ 0
11y2 – 11y + y – 1 ≤ 0
11y(y – 1) + 1(y – 1) ≤ 0
(y – 1)(11y + 1) ≤ 0

maximum value of y is 1

51)

Ans. (3.00)
(3.00) is the correct answer