**Question 1: Find the moment of inertia for a badminton racket about an axis passing through ‘A’ and perpendicular to the plane as shown in the figure. Mass of the circular portion is M and that of the straight is;**

a.

b.

c.

d.

Answer: (a)

**Question 2: An amplitude modulated wave is represented by, C _{m }= 10(1 + 0.2sin12560t)sin(1.11 × 10^{4}t) V the modulating frequency in kHz will be;**

Answer: 2 kHz

As we know that,

⇒ 2πf_{m }= 12560

f

**Question 3: Two travelling waves produce a standing wave represented by equation y = 1.0mm cos(1.57cm ^{−1} x) sin(78.5s^{−1}) t, the node closest to the origin in the region x > 0 will be at x = _____cm.**

Answer: 1 cm

At node y = 0

⇒ 1 cos(1.57 x) sin (178.5)t = 0

⇒ cos (1.57 x) = 0

⇒ 1.57 x = π/2

⇒ x = 1 cm

**Question 4: Two wires of equal length with diameter 2 mm each having resistivity ρ _{1} = 12 μΩ. cm and ρ_{2} = 51 μΩ. cm respectively. They are connected in parallel so that their equivalent resistance is 3 Ω. Find the length of the wire.**

a. 50 m

b. 97 m

c. 197 m

d. 291 m

Answer: b

**Question 5: Assume an ideal gas is taken from the state from A to state B. The process is isothermal. Then the corresponding P-T graph will be;**

Answer: (c)

As T = constant, so

P ∝ 1/V

**Question 6:****Find the difference in heights in limbs as shown in the given data. Surface tension T =7.3 × 10 ^{−2} N/m, the density of water ρ = 1000 Kg/m^{3} and the angle of contact θ = 0°.**

a. 1.19 m

b. 2.19 m

c. 3.19 m

d. 4.19 m

Answer: (b)

**Question 7: There is a soap bubble of radius 6 cm and it has another soap bubble of radius 3 cm inside it. Find the equivalent radius of the soap bubble which has the same excess pressure, as the pressure inside the bubble of radius 3 cm.**

a. 2 cm

b. 1 cm

c. 9 cm

d. 3 cm

Answer: (a)

We have from the given condition

⇒

⇒R = 2 cm

**Question 8: **In YDSE, d is the distance between slits and D is the distance between screen and slit plane. If y_{1} is the distance of 1^{st }maxima from the central maxima for red light and y_{2} is the distance for violet light then what is the difference between the wavelength of red and violet?

a.

b.

c.

d.

Answer: (b)

From the condition of maximum we have

⇒

**Question 9: Find the capacitance in a series LCR circuit in order to get maximum power. (XL = 250 Ω and f = 50 Hz).**

a. 10.7 μF

b. 12.7 μF

c. 14.7 μF

d. 14.9 μF

Answer: (b)

As we know that, for maximum power, X_{C} = X_{L} (Condition of resonance)

⇒ 1/Cω = ωL

⇒ 1/Cω = 250

As, ω = 2πf = 2π x 50 = 100 π

⇒ C = 1/(100π x 250) = 12.7 μF

**Question 10:****For a hydrogen-like atom, the frequency of transition from n = 3 to n = 1 is 192 × 10 ^{15} Hz, then find the frequency of transition from n = 2 to n = 1**

a. 162 x 10^{15} Hz

b. 226 x 10^{15} Hz

c. 162 x 10^{18} Hz

d. None

Answer: (a)

**Question 11: Chain of length 1 m is hanging as shown in the figure. The mass of the chain is 3 kg. It is released and allowed to move, find kinetic energy (approximate) of the chain when it is completely in the air.**

a. 56 J

b. 90 J

c. 100 J

d. 121 J

Answer: (a)

**Question 12: A sound source and a detector are moving away from each other with an equal speed of 20 m/s. The detector heard a sound of frequency 1800 Hz from the source. What is the original frequency released by the source? Assume speed of sound = 340 m/s.**

a. 2200 HZ

b. 1800 HZ

c. 2025 HZ

d. 1500 HZ

Answer: (c)

f_{app} = 1800 Hz = f_{0} ((330−20)/(300+20))

f_{o} = (350/310)× 1800 = 2032.25 Hz ≈ 2025 Hz

**Question 13: Given statements are based on Bohr’s atomic model for hydrogen-like atoms:**

**Statement-1. As the principal quantum number increases, the speed of the electron also**

**increases.**

**Statement-2. Speed of electron increases as energy increases.**

a. Both Statement-1 and Statement-2 are true

b. Only Statement-1 is true

c. Only Statement-2 is true

d. Both Statement-1 and Statement-2 are false

Answer: (d)

V = V_{0}z/n

as n increases, velocity increases

The energy of electrons,

As n increases, energy increases

**Question 14**:** Find the dimensions of A × (B + C)D where A is mass, dimensions of B is unknown, C is energy and D is dimensionless constant:**

a. M^{2}L^{2}T^{−1}

b. M^{2}L^{2}T^{−2}

c. M^{2}L^{1}T^{−2}

d. M^{1}L^{2}T^{−2}

Answer: (b)

Dimension of A × (B + C)D equal to dimension of A × C × D

M × ML^{2}T^{−2 }= M^{2}L^{2}T^{−2}

**Question 15: In the given circuit, find the power consumed by the circuit.**

a. 1.07 W

b. 2.07 W

c. 3.07 W

d. 4.07 W

Answer: (b)

As we know that,

P = V^{2}/R

⇒ P = (2.2)^{2}/(7/3)

⇒ P = 2.07 W

**Question 16:****Two balls are projected vertically upward with the same speed 35 m/s in a 3-second interval, find height in m at which both balls collide.**

a. 50

b. 30

c. 80

d. 100

Answer: (a)

**Question 17: **A heater is supplying heat at the rate of 6000 J/min. If power produced by gas is 90 W. Find the time taken to increase internal energy by 2.5 × 10^{3} J?

a. 250 s

b. 150 s

c. 500 s

d. 100 s

Answer: (a)

**?**U = Q – w

2500 = 100t – 90t

t = 250 s

**Question 18: Compare the RMS speed of hydrogen, oxygen, and carbon dioxide at the same temperature.**

a. V_{H2} < V_{O2} < V_{CO2}

b. V_{H2} > V_{O2 }> V_{CO2}

c. V_{H2} > V_{O2} < V_{CO2}

d. V_{H2} < V_{O2 }> V_{CO2}

Answer: (b)

As we know that

M_{H2} < M_{O2} < M_{CO2}

V_{H2} > V_{O2} > V_{CO2}

**Question 19: Charge Q is given to a spherical conductor of radius R. It is surrounded by a concentric conducting shell of inner radius a and outer radius b. Corresponding electric field diagram will be:**

Answer: (a)

**Question 20: If a wavelength of incident light changes from 300 nm to 400nm, then find the change in sloping potential. If the work function of metal = 2.5 eV?**

a. 1.03 eV

b. 2.10 eV

c. 1.85 eV

d. 2.03 eV

Answer: (a)

We know that,

**Question 21: Initial fuel in a rocket is 1000 kg. If it was given an acceleration of 20 m/s ^{2} the velocity of fuel with respect to the rocket is 500 m/s. Find the rate of consumption of fuel.**

a. 30 kg/s

b. 60 kg/s

c. 900 kg/s

d. 80 kg/s

Answer: (b)

As we know that for varying mass system

f_{T} − mg = ma

(dm/dt) v_{r} = mg + ma

(dm/dt) 500 = 1000(10 + 20)

(dm/dt) = 60 kg/s

**Question 22: A spherical shell of mass′m′ and radius ′R′ is given, then which of the following is incorrect for inside the shell?**

a. Gravitational field is zero

b. Gravitation potential is zero

c. The gravitational field is the same everywhere

d. Gravitational potential is the same everywhere

Answer: (b)

Gravitational potential due to a uniform spherical shell

Gravitational field due to a uniform spherical shell

**Question 23: Find the equivalent gate**

a. AND gate

b. NOR gate

c. NAND gate

d. OR gate

Answer: (d)

**Question 24: A cube made up of wire each of resistance R. Then find equivalent resistance across its diagonal.**

a. 5R/6

b. 3R/4

c. 7R/12

d. R

Answer: (a)

Due to symmetry C, E, F, same potential and G, D, H, same potential

**Question 25: Two cars A and B moving on a straight road. Car B passes car A by a relative speed of 45 m/s. At what speed does the driver of car B observe car A in the side mirror of focal length 10 cm when car A is at a distance of 1.9 m from car B?**

a. 9/80

b. −9/80

c. −7/80

d. 7/80

Answer: (b)

Given,

u = −1.9 m

f = 10 cm

m = f/(f − u)

=10/(10 − (−190))

=1/20

⇒P_{2}/P_{1} = 2

v_{i} = −m^{2}vo

v_{i} = − (1/20)^{2}× 45

v_{i} = −9/80 m/s

**Question 26:****Find the graph between electric field intensity and distance r from the centre, for the given arrangement of concentric spheres. Charge in the inner solid sphere is uniformly distributed in volume.**

Answer: (b)

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