20-07-2025

1902CJA101001250057 JA

PART-1 : PHYSICS

SECTION-I (i)

1) Two quantities A and B have different dimensions. Which mathematical operation given below is
physically meaningful :-

(A) A / B
(B) A + B
(C) A – B
(D) None

2) Dimensions of potential energy are :-

(A) MLT–1
(B) ML2T–2
(C) ML–1T–2
(D) ML–1T–1

3)

The maximum force of static friction upto which body does not move is called –

(A) normal reaction

(B) sliding friction
(C) limiting friction
(D) rolling friction

4) Three blocks of masses m1, m2 and m3 kg are placed in contact with each other on a frictionless
table. A force F is applied on the heaviest mass m1; the acceleration of m3 will be :-

(A)

(B)

(C)

(D)
 SECTION-I (ii)

1) Three blocks are connected by strings as shown in figure and pulled by a force F = 60 N. If mA =

10 kg, mB = 20 kg and mC = 30 kg, then :

(A) acceleration of the system is 2 m/s2

(B) T1 = 10 N
(C) T2 = 30 N
(D) T1 = 20 N & T2 = 40 N

2) 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

3) A painter is applying force himself to raise him and the box with an acceleration of 5 m/s2 by a
massless rope and pulley arrangement as shown in figure. Mass of painter is 100 kg and that of box

is 50 kg. If g = 10 m/s2, then:

(A) tension in the rope is 1125 N

(B) tension in the rope is 2250 N
(C) force of contact between the painter and the floor is 375 N
(D) force of contact between the painter and the floor is 750 N

4) Block A and B are connected by light string as shown in figure. All surface are frictionless then

which is the correct F.B.D. of block B and block A.

(A)

(B)

(C)

(D)

5) A metal sphere is hung by a string fixed on a wall. The forces acting on the sphere are shown in
the figure. Which of the following statements are correct?

(A)
(B) T2 = R2 + W2
(C) T = R + W
(D) R = W tan θ

6) Figure shows two blocks A and B connected to an ideal pulley string system. In this system when
bodies are released then :

(neglect friction and take g = 10 m/s2)

(A) Acceleration of block A is 1 m/s2

(B) Acceleration of block A is 2 m/s2
(C) Tension in string connected to block B is 40 N
(D) Tension in string connected to block B is 80 N

SECTION-II

1) Find out acceleration (in m/s2) of 80 kg block (consider all surfaces are frictionless)
2) A block of mass 2 kg is moving horizontally on a smooth plane with an acceleration of 4 m/s2. Now
a vertical force also starts acting on it of 6N. What is the new acceleration of block.

3) If block A is in equilibrium then the value of m0 (in kg) is (Assume there is no friction anywhere)

4) In the arrangement shown all pulleys and strings are ideal. A vertical downward force of 10N is
needed to apply on block A to keep the system in equilibrium. If mass of B is 10kg then find the mass

of A

5) The elevator shown in figure is descending, with an acceleration of 2 ms–2. The mass of the block
A is 0.5 kg. The force exerted by the block A on the block B in newton is :

6) A 5 kg box is kept on a weighing machine in a lift moving with a acceleration. The reading of
machine is 6kg. Find a (take g = 10 m/s2)

7) Express dimensional formula of work done in form Ma Lb T–c. Write the answer of (a × b × c).

8) What is the force of friction acting on the 1 kg block placed on the incline as shown in the figure.

PART-2 : CHEMISTRY

SECTION-I (i)

1) The hybridization of atomic orbitals of nitrogen in and are:

(A) sp, sp3 and sp2 respectively

(B) sp, sp2 and sp3 respectively
(C) sp2, sp and sp3 respectively
(D) sp2, sp3 and sp respectively

2) The state of hybridization in the anionic Part of solid Cl2O6 is

(A) sp3d2
(B) sp3d
(C) sp2
(D) sp3
3) BF3 reacts with (CH3)3N to form an adduct (CH3)3 N→BF3. The bond length B–F bond in the adduct
is

(A) Same as in BF3

(B) less than that in BF3
(C) More than that in BF3
(D) Cannot be predicted

4) Which of the bond length order data is incorrect

(A) P–Cl > P–F in PCl3F2

(B) S–F(axial) > S – F(eq) in SF6
(C) S–F(axial) > S – F(eq) in SF4
– –
(D) NO2 < NO3 (N – O)

SECTION-I (ii)

1) The octet rule is not obeyed in :

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

2) Which of the following compounds possesses zero dipole moment?

(A) Water
(B) Benzene
(C) Carbon tetrachloride
(D) Boron trifluoride

3)

Which of the following species have a bond order of 3 ?

(A) CO
(B) CN⊝
(C) NO⊕
(D)

4) Which of the following molecule is/are planar -

(A) CH2Cl2
(B) XeF4
(C) SO3
(D) NF3

5) In which of the following process(s) hybridisation of underlined atom does not change ?

(A)

(B)

(C)

(D)

6) incorrect order of bond angle is :

(A) OCl2 > SF2

(B) H2O > OF2

(C)

(D) NF3 > NH3

SECTION-II

1) Maximum number of 2c – 2e bonds in B2H6.

2) Total number of angle in SeCl4 which are less than 90°.

3) Find the number of molecules which do not have hybridisation, according to Drago's rule.
PH3, H2S, AsH3, H2Se, SiH4

4) Among the following species

N2, N2+, N2–,N22–, O2, O2+, O2–,O22–
the number of species showing diamagnetism is

5) The number of σ bonds in P4O10 is

[Give your answer as sum of digits and fill OMR sheet]

6) Find the number of species which are planar ?

BrF4 , XeOF2 , BrF3 , H2O, H2S , SF2

7) Calculate the maximum number of atoms lying in a plane in CH4 .

8) Consider y-axis as inter-nuclear axis, how many of following will lead to π bond formation?
(a) py – py
(b) px – px
(c) pz – pz
(d) dxy – dxy
(e) dyz – dyz
(f) px – dxy
(g) dxy – pz
(h) dxz – dxz

PART-3 : MATHEMATICS

SECTION-I (i)

1) The exact value of tan 200o (cot 10o – tan 10o) is

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

2) Let the set of all values of p ∈ R, for which both the roots of the equation x2 – (p + 2)x + (2p + 9)
= 0 are negative real numbers, be the interval (α, β]. Then β – 2α is equal to

(A) 0
(B) 9
(C) 5
(D) 20

3) If θ ∈ [–2π, 2π], then the number of solutions of , is equal

to:

(A) 12
(B) 6
(C) 8
(D) 10

4) Let α and β be the roots of , and γ and δ be the roots of x2 + 3x – 1 = 0. If Pn =

αn + βn and Qn = γn + δn, then is equal to

(A) 3
(B) 4
(C) 5
(D) 7
 SECTION-I (ii)

1) If A + B + C = π, then which of the following is/are correct

(A) tanA + tanB + tanC = tanA tanB tanC

(B)
tan tan + tan tan + tan tan = 1

(C) tan + tan + tan = tan tan tan

(D) tan A tan B + tan B tan C + tan A tan C = 1

2) If sinx + siny = and cosx + cosy = , then which of the following is/are possible.

(A)

(B)

(C)

(D)

3) The real value(s) of a can be for which the quadratic equation 2x2 – (a3 + 8a – 1)x + a2 – 4a = 0
possesses roots of opposite signs is/are

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

4) If α, β, γ be the roots of the equation x(1 +x2) + x2(6 + x) + 2 = 0 then

(A)

(B)

(C)

(D)

5) For the expression

(A) Maximum value is 4

(B) Minimum value is 2
(C) Maximum value is 6
(D) Minimum value is 1

6) Let and
then which of the following relations is(are) correct?

(A) S – C = 0

(B)

(C) S > C

(D)

SECTION-II

1) The number of solutions of the equation

is

2) If the range of the function , x ≠ 1, 2, is , then α2 + β2 is equal to

:

3) Let αθ and βθ be the distinct roots of 2x2 + (cosθ)x –1 = 0, θ ∈ (0, 2π). If m and M are
the minimum and the maximum values of , then 16(M + m) equals :

4) The value of is equal to

5) If the roots of the equation 2x2 – 3x + 5 = 0 are reciprocals of the roots of the equation ax2 + bx +
2 = 0, then the value of a + b is :

6) The value of a for which the sum of the squares of the roots of the equation x2 – (a – 2)x – a – 1 = 0
assume the least value is :-

7) If α, β, γ are roots of equation f(x) = 0 where f(x) = x3 – cx2 + 4x – 2 and then

value of 'c' is

8) Find the value of (1 – cot 35°) · (1 – cot 65°) · (1 – cot 160°) · (1 – cot 190°).
 ANSWER KEYS

PART-1 : PHYSICS

SECTION-I (i)

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

SECTION-I (ii)

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

SECTION-II

Q. 11 12 13 14 15 16 17 18
A. 8.00 4.00 3.00 1.00 4.00 2.00 4.00 6.00

PART-2 : CHEMISTRY

SECTION-I (i)

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

SECTION-I (ii)

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

SECTION-II

Q. 29 30 31 32 33 34 35 36
A. 4.00 4.00 4.00 2.00 7.00 6.00 3.00 5.00

PART-3 : MATHEMATICS

SECTION-I (i)

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

SECTION-I (ii)

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

Q. 47 48 49 50 51 52 53 54
A. 5.00 194.00 25.00 1.00 2.00 1.00 3.00 4.00
 SOLUTIONS

PART-1 : PHYSICS

1)

Correct answer is A

2)

Correct answer is B

3)

Correct answer is C

4)

5)

F = 60N = (m1 + m2 + m3)a ⇒ a = 1 m/s2

T1 = m1a = 10 × 1 = 10N
T2 = (m1 + m2)a = 30 × 1 = 30N

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)

For box we have

T – (50 g + N) = 50 (5) ...(1)
for painter we have
T + N – 100 g = 100 (5) ...(2)
from (1) and (2) we have,
T = 1125 N and N = 375 N

8) Correct answer is (A, C)

9) Net force on the sphere is zero

Hence
Tcos θ = W; Tsin θ = R

10) Applying NLM on 40 kg block

400 – 4T = 40 a
For 10 kg block T = 10.4 a
Solving a = 2m/s2

T = 80 N

11)

Correct answer is 8.00

12)

Correct answer is 4.00

13)
 T – 10N = 1a
30N – T = 3a

14) T = mAg + 10
and 5T = 100
T = 20

15)

Correct answer is B

16)

Correct answer is 2.00

17)

Correct answer is 4.00

18)

Correct answer is 6.00

PART-2 : CHEMISTRY

19) Correct answer is B

20) The anionic part of solid Cl2O6 is ClO4–.

21) Correct answer is (C)

22)
Bond order ∝
∴ Bond length of NO

23) BCl3 is incomplete octet and PCl5 is expanded octet molecule.

24) Non polar molecules are benzene, CCl4, BF3.

25)

(A) CO = 3
(B) CN⊝ = 3
(C) NO⊕ = 3
(D) = 2.5
So, correct option is A,B,C.

26)
27)

28) Incorrect order

(A)OCl2 >SF2 → correct
(B) H2 O > OF2 → correct

(C) > CF4 → incorrect → because equal bond angle

(D) NF3 > NH3 → incorrect, as NH3 > NF3

29)
Terminal B–H bonds are 2c – 2e bonds.

30) due to pair bond pair repulsion.

31)

Correct answer is 4.00

 32) Correct answer is 2.00

33)

Correct answer is (7.00)

34)

Correct answer is 6.00

35)

CH4 is tetrahedral and 3 atoms are lying in a plane.

36)

py – py → σ-bond
px – px → π-bond
pz – pz →π-bond
dxy – dxy →π-bond
dyz – dyz → π-bond
Px – dxy → π-bond
dxy – dxz → δ-bond
dxy – pz → no-bond

PART-3 : MATHEMATICS

37) Correct answer is (C)

38) Using location of roots :

(p + 2)2 – 4 (2p + 9) ≥ 0
(p + 4) (p – 8) ≥ 0
p+2<0
2p + 9 > 0

Intersection
∴ β – 2α = –4 + 9 = 5

39)

Number of solution = 8

40)
Similarly

41) Conditional Identities

Correct option is (A, B)

42)

⇒ .....(1)

Also

....(2)
(1) (2), we get
Now

Square and add (1) & (2)

43) Product of roots =

⇒ a ∈ (0, 4)

44) Correct answer is (B & C)

45)

Corre

46) sin θ sin (60° – θ) sin (60° + θ) =

[Use: sin 20° sin 40° sin 60° sin 80° = ]

So, S = sin 10° sin 20° sin 30° sin 40° ....... sin 90°
= (sin 10° sin 50° sin 70°) (sin 20° sin 40° sin 80°) sin 30° sin 60° sin 90°

sin 30° sin 60° sin 90° =

As, cos (90° – θ) = sin θ So,

Now, verify alternatives.

47)

5 solutions
48)

= 2(48 + 49)
= 194

49)
Correct answer is (25)

50) Correct answer is (1.00)

51) Correct answer is (2.00)

52) Correct answer is (1.00)

53)

α+β+γ=c

54) A + B = 225° ⇒ cot (A + B) = cot 225°

⇒ cot A cot B – 1 = cot B + cot A

⇒ (1 – cot A) (1 – cot B) = 2
∴ (1 – cot 35°) (1 – cot 190°) (1 – cot 65°) (1 – cot 160°) = 2 × 2 = 4.