From a circular ring of mass \({M}\) and radius \(R\), an arc corresponding to a \(90^\circ\)$$sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \(K\) times \(MR^2\). The value of \(K\) will be:
1. \(\frac{1}{4}\)
2. \(\frac{1}{8}\)
3. \(\frac{3}{4}\)
4. \(\frac{7}{8}\)

A uniform conducting wire of length \(12a\) and resistance '\(R\)' is wound up as a current carrying coil in the shape of,
(i) an equilateral triangle of side '\(a\)'
(ii) a square of side '\(a\)'
The magnetic dipole moments of the coil in each case respectively are:
1. \(3Ia^2~\text{and}~4Ia^2\)
2. \(4Ia^2~\text{and}~3Ia^2\)
3. \(\sqrt{3}Ia^2~\text{and}~3Ia^2\)
4. \(3Ia^2~\text{and}~Ia^2\)

Two conducting circular loops of radii \(R_1\)$\mathrm{and}$\(R_2\) are placed in the same plane with their centres coinciding. If \(R_1>>R_2\) the mutual inductance \(M\) between them will be directly proportional to:
1. \(\frac{R^2_1}{R_2}\)
2. \(\frac{R^2_2}{R_1}\)
3. \(\frac{R_1}{R_2}\)
4. \(\frac{R_2}{R_1}\)

A ball of mass \(0.15~\text{kg}\) is dropped from a height \(10~\text{m}\), strikes the ground, and rebounds to the same height. The magnitude of impulse imparted to the ball is \((g=10 ~\text{m}/\text{s}^2)\) nearly:
1. \(2.1~\text{kg-m/s}\)
2. \(1.4~\text{kg-m/s}\)
3. \(0~\text{kg-m/s}\)
4. \(4.2~\text{kg-m/s}\)

Twenty seven drops of same size are charged at \(220~\text{V}\) each. They combine to form a bigger drop. Calculate the potential of the bigger drop.
1. \(1520~\text{V}\)
2. \(1980~\text{V}\)
3. \(660~\text{V}\)
4. \(1320~\text{V}\)

For the given circuit, the input digital signals are applied at the terminals \(A\), \(B\) and \(C\). What would be the output at terminal \(Y\)?
 

1.
2.
3.
4.

A particle of mass \(m\) is projected with a velocity, \(v=kV_{e} ~(k<1)\) from the surface of the earth. The maximum height, above the surface, reached by the particle is: (Where \(V_e=\) escape velocity, \(R=\) radius of the earth)

A car starts from rest and accelerates at $5$ $\mathrm{m}/{\mathrm{s}}^2$. At \(t=4\) s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at \(t=6\) s? (Take \(g=10\) m/s²)
1. $20\sqrt{2}$ $\mathrm{m}/\mathrm{s}, \mathrm{0 }\mathrm{m}/{\mathrm{s}}^2$
2. $20\sqrt{2}$ $\mathrm{m}/\mathrm{s},$ $10$ $\mathrm{m}/{\mathrm{s}}^2$
3. $20$ $\mathrm{m}/\mathrm{s},$ $5$ $\mathrm{m}/{\mathrm{s}}^2$
4. $20$ $\mathrm{m}/\mathrm{s},$ $0$

A series LCR circuit containing \(5.0~\text{H}\) inductor, \(80~\mu \text{F}\) capacitor and \(40~\Omega\)$\mathrm{}$ resistor is connected to \(230~\text{V}\) variable frequency AC source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be: