The current in an inductor of self-inductance \(4\) H changes from \(4\) A to \(2\) A in \(1\) second. The e.m.f. induced in the coil is:
1. \(-2\) V
2. \(2\)  V
3. \(-4\) V
4. \(8\) V

The correct statement about the variation of viscosity of fluids with an increase in temperature is:

The de-Broglie wavelength of thermal electron at \(27^\circ \text{C}\) is \(\lambda.\) When the temperature is increased to \(927^\circ \text{C},\) its de-Broglie wavelength will become:
1.  \(2\lambda\)
2.  \(4\lambda\)
3.  \(\frac\lambda2\)
4.  \(\frac\lambda4\)

Assuming the earth to be a sphere of uniform density, its acceleration due to gravity acting on a body:

A particle of mass 4M kg at rest splits into two particles of mass M and 3M. The ratio of the kinetic energies of mass M and 3M would be:
1.  3 : 1
2.  1 : 4
3.  1 : 1
4.  1 : 3

During simple harmonic motion of a body, the energy at the extreme position is:

A fluid of density \(\rho~\)is flowing in a pipe of varying cross-sectional area as shown in the figure. Bernoulli's equation for the motion becomes:
             
1.  \(p+\frac12\rho v^2+\rho gh\text{=constant}\)
2. \(p+\frac12\rho v^2\text{=constant}\)
3. \(\frac12\rho v^2+\rho gh\text{=constant}\)
4. \(p+\rho gh\text{=constant}\)

The ratio of the moments of inertia of two spheres about their diameter and having same mass and their radii in the ratio of 1: 2 is:
1.  2 : 1
2.  4 : 1
3.  1 : 2
4.  1 : 4

Assertion (A): A standing bus suddenly accelerates. If there was no friction between the feet of a passenger and the floor of the bus, the passenger would move back.
Reason (R): In the absence of friction, the floor of the bus would slip forward under the feet of the passenger.

1. (A) is true but (R) is false.
2. (A) is false but (R) is true.
3. Both (A) and (R) are true and (R) is the correct explanation of (A).
4. Both (A) and (R) are true but (R) is not the correct explanation of (A).

A linearly polarized monochromatic light of intensity \(10\) lumen is incident on a polarizer. The angle between the direction of polarization of the light and that of the polarizer such that the intensity of output light is \(2.5\) lumen is:
1. \(60^\circ\)
2. \(75^\circ\)
3. \(30^\circ\)
4. \(45^\circ\)