List of practice Questions

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \( \frac{R}{\sqrt{R^2 + \omega^2 L^2}} \), where \( \omega \) is the frequency of the supply across resistor \( R \) and inductor \( L \). If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In light of the above statements, choose the most appropriate answer from the options given below:
A coil of area \( A \) and \( N \) turns is rotating with angular velocity \( \omega \) in a uniform magnetic field \( B \) about an axis perpendicular to \( B \). Magnetic flux \( \phi \) and induced emf \( \varepsilon \) across it, at an instant when \( B \) is parallel to the plane of the coil, are:
A body of mass \( m \) connected to a massless and unstretchable string goes in a vertical circle of radius \( R \) under gravity \( g \). The other end of the string is fixed at the center of the circle. If velocity at the top of the circular path is \( v = \sqrt{ngR} \), where \( n \geq 1 \), then the ratio of kinetic energy of the body at bottom to that at top of the circle is:

 

 

 

 

 

 

 

For the circuit shown above, the equivalent gate is:

Match List - I with List - II:

List - I: 

(A) Electric field inside (distance \( r > 0 \) from center) of a uniformly charged spherical shell with surface charge density \( \sigma \), and radius \( R \). 
(B) Electric field at distance \( r > 0 \) from a uniformly charged infinite plane sheet with surface charge density \( \sigma \). 
(C) Electric field outside (distance \( r > 0 \) from center) of a uniformly charged spherical shell with surface charge density \( \sigma \), and radius \( R \). 
(D) Electric field between two oppositely charged infinite plane parallel sheets with uniform surface charge density \( \sigma \). 

List - II: 

(I) \( \frac{\sigma}{\epsilon_0} \) 
(II) \( \frac{\sigma}{2\epsilon_0} \) 
(III) 0 
(IV) \( \frac{\sigma}{\epsilon_0 r^2} \) Choose the correct answer from the options given below:

As shown below, bob A of a pendulum having a massless string of length \( R \) is released from 60° to the vertical. It hits another bob B of half the mass that is at rest on a frictionless table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take \( g \) as acceleration due to gravity):

bob A of a pendulum having a massless

A convex lens made of glass (refractive index = 1.5) has a focal length of 24 cm in air. When it is totally immersed in water (refractive index = 1.33), its focal length changes to:
A plane electromagnetic wave propagates along the \( +x \) direction in free space. The components of the electric field \( \vec{E} \) and magnetic field \( \vec{B} \) vectors associated with the wave in Cartesian frame are:
In an experiment with photoelectric effect, the stopping potential:
A point charge causes an electric flux of \( -2 \times 10^4 \, \text{Nm}^2\text{C}^{-1} \) to pass through a spherical Gaussian surface of 8.0 cm radius, centered on the charge. The value of the point charge is:
Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R).
Three identical spheres of the same mass undergo one-dimensional
Three identical spheres of the same mass undergo one-dimensional motion as shown in the figure with initial velocities \( v_A = 5 \, \text{m/s}, v_B = 2 \, \text{m/s}, v_C = 4 \, \text{m/s} \). If we wait sufficiently long for elastic collision to happen, then \( v_A = 4 \, \text{m/s}, v_B = 2 \, \text{m/s}, v_C = 5 \, \text{m/s} \) will be the final velocities. Reason (R): In an elastic collision between identical masses, two objects exchange their velocities. In light of the above statements, choose the correct answer from the options given below:
A physical quantity \( Q \) is related to four observables \( a \), \( b \), \( c \), and \( d \) as follows: \[ Q = \frac{a b^4}{c d^2} \] Where:
- \( a = (60 \pm 3) \, \text{Pa} \),
- \( b = (20 \pm 0.1) \, \text{m} \),
- \( c = (40 \pm 0.2) \, \text{N·s/m}^2 \),
- \( d = (50 \pm 0.1) \, \text{m} \).
Then the percentage error in \( Q \) is:
The magnetic field inside a 200 turns solenoid of radius 10 cm is \( 2.9 \times 10^{-4} \) Tesla. If the solenoid carries a current of 0.29 A, then the length of the solenoid is:
Match List-I with List-II.
Magnetic induction
Choose the correct answer from the options given below:
A sand dropper drops sand of mass \( m(t) \) on a conveyor belt at a rate proportional to the square root of the speed \( v \) of the belt, i.e., \( \frac{dm}{dt} \propto \sqrt{v} \). If \( P \) is the power delivered to run the belt at constant speed, then which of the following relationships is true?
An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density \( \sigma \). Choose the correct option from the following.
The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level is:
Two planets, A and B are orbiting a common star in circular orbits of radii \( R_A \) and \( R_B \), respectively, with \( R_B = 2R_A \). The planet B is \( \sqrt{2} \) times more massive than planet A. The ratio \( \frac{L_B}{L_A} \) of angular momentum (\( L \)) of planet B to that of planet A (\( L_A \)) is closest to integer:
A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A. If the rate of change of potential difference between the plates is \( 7 \times 10^6 \, \text{V/s} \), then the integer value of the distance between the parallel plates is:
A cup of coffee cools from 90°C to 80°C in \( t \) minutes when the room temperature is 20°C. The time taken by the similar cup of coffee to cool from 80°C to 60°C at the same room temperature is:
Match List-I with List-II.
Young’sModulus:
Choose the correct answer from the options given below:
Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time \( t = 0 \), for the first time. The maximum possible number of crossing(s) (including the crossing at \( t = 0 \)) is:
A poly-atomic molecule (C\(_3\)R, \(C_v = 4R\), where \(R\) is gas constant) goes from phase space point A (\(P_A = 10^4 \, \text{Pa}, V_A = 4 \times 10^{-3} \, \text{m}^3\)) to point B (\(P_B = 5 \times 10^4 \, \text{Pa}, V_B = 6 \times 10^{-7} \, \text{m}^3\)) to point C (\(P_C = 10^4 \, \text{Pa}, V_C = 8 \times 10^{-3} \, \text{m}^3\)). A to B is an adiabatic path and B to C is an isothermal path. The net heat absorbed per unit mole by the system is:
A poly-atomic molecule
A capacitor, \( C_1 = 6 \, \mu F \), is charged to a potential difference of \( V_1 = 5 \, \text{V} \) using a 5V battery. The battery is removed and another capacitor, \( C_2 = 12 \, \mu F \), is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges \( q_1 \) and \( q_2 \) on the capacitors \( C_1 \) and \( C_2 \) when equilibrium condition is reached?
battery is removed and another capacitor
Two identical symmetric double convex lenses of focal length \( f \) are cut into two equal parts \( L_1, L_2 \) by the AB plane and \( L_3, L_4 \) by the XY plane as shown in the figure respectively. The ratio of focal lengths of lenses \( L_1 \) and \( L_3 \) is:
Two identical symmetric double convex lenses