List of practice Questions

A wire of resistance \( R \) is bent in the form of a circular loop. Two points on the circle separated by a quarter circumference are connected to a battery of emf \( E \) and negligible internal resistance. The heat generated in the wire per second is:

When a wire is connected in the left gap of a metre bridge, the balancing point is at \( 40 \) cm from the left end of the bridge wire. If the wire in the left gap is stretched so that its length is doubled and again connected in the same gap, then the balancing point from the left end of the bridge wire is:

If a charged particle enters a uniform magnetic field normally with certain velocity, then the time period of revolution of the particle:

The internal energy of one mole of a rigid diatomic gas at absolute temperature \( T \) is:

In a closed organ pipe, the number of nodes formed in fifth and ninth harmonics are respectively:

Radius of gyration of a thin uniform rod of length \( L \) about an axis passing through its centre and perpendicular to its length is:

A thin circular ring and a circular disc of equal mass are rolling without sliding. If their linear velocities are equal and the total kinetic energy of the disc is 6 J, then the total kinetic energy of the ring is:

A body of mass \( 4 \) kg attached to a spring of force constant \( 64 \) N/m executes simple harmonic motion on a frictionless horizontal surface. The time period of oscillation is:

A particle is executing simple harmonic motion with amplitude \( A \). At a distance \( x \) from the mean position, when the particle is moving towards the extreme position, it receives a blow in the direction of motion that instantaneously doubles its velocity. The new amplitude of the particle is:

A mass of \( 6 \times 10^{24} \) kg is to be compressed in the form of a solid sphere such that the escape velocity from its surface is \( 3 \times 10^5 \) m/s. The radius of the sphere is:

If the pressure on a body is increased from \( 200 \) kPa to \( 250 \) kPa, the volume of the body decreases by \( 0.25% \). The compressibility of the material of the body (in \( m^2 N^{-1} \)) is:

A mercury drop of radius \( 1 \) cm is divided into \( 10^6 \) droplets of equal size. If the surface tension of mercury is \( 35 \times 10^{-3} \) N/m, then the change in surface energy in the process is:

If the distance travelled by a freely falling body in the last but one second of its motion is 5 m, then the last second is:

The angle of projection of a projectile whose path is shown in the given figure is:

If the equation of motion of a projectile is \( Y = AX - B X^2 \), then the ratio of the maximum height reached and the range of the projectile is:

If a particle is moving along a circle of radius \( r \) with constant speed \( v \), then the magnitude of the change in velocity when the particle moves from \( P \) to \( Q \), where \( PQ \) makes an angle \( \theta \) at the center of the circle is:

If the tension in the horizontal wire shown in the figure is 30 N, then the weight \( W \) and tension in the wire \( OA \) are respectively:

A car of mass \( 2000 \) kg is accelerating from rest. If its engine is supplying constant power of \( 10 \) kW, then the velocity of the car at a time of \( 10 \) s is:

A body of mass \( M \) is moving with a uniform speed \( v \) on a frictionless horizontal surface under the influence of two forces \( F_1 \) and \( F_2 \) as shown in the figure. The net power of the system is:

Find the area (in square units) of the region bounded by the lines \( x=0 \), \( x=\frac{\pi}{2} \), and the curves \( f(x) = \sin x \), \( g(x) = \cos x \):

Evaluate the integral: \[ I = \int_{\pi/6}^{\pi/3} \cos^{-4} x \, dx \]

Evaluate the integral: \[ I = \int_0^{3\pi/2} \frac{\cos^5 x}{\cos^3 x+\sin^3 x}dx \]

The general solution of the differential equation \( \sec(x - y + 1) dy = dx \) is:

The differential equation for which \( y^2 = 4a(x + a) \) (where \( a \) is a parameter) is the general solution is:

The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2xy-4x+y-2}{2xy+x-4y-2} \] is: