A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod when placed in thermal contact with the two reservoirs at the same time?

1. Q /4

2. Q/16

3. 2Q

4. Q/2

A ball moving with velocity 2 ms^-1 collides head-on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in ms^-1) after the collision will be:

1. 0, 1

2. 1, 1

3. 1, 0.5

4. 0, 2

A transverse wave is represented by \(y=A\mathrm{sin}(\omega t-kx).\) At what value of the wavelength is the wave velocity equal to the maximum particle velocity?
1. \(\pi A/2\)
2. \(\pi A\)
3. \(2\pi A\)
4. \(A\)

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 ms^-1. The mass per unit length of water in the pipe is $100$ $kg$ $m^{-1}.$What is the power of the engine?

1. 400 W

2. 200 W

3. 100 W

4. 800 W

A thin ring of radius \(R\) metre has a charge \(q\) C uniformly spread on it. The ring rotates about its axis with a constant frequency of \(f\) revolutions/s. The value of magnetic induction in ${}^{}$\(\mathrm{Wb ~m^{-2}}\) at the centre of the ring is:
1. \(\frac{\mu_0 qf}{2\pi R}\)
2. \(\frac{\mu_0 q}{2\pi f R}\)
3. \(\frac{\mu_0 q}{2f R}\)
4. \(\frac{\mu_0 qf}{2R}\)

Which one of the following bonds produces a solid that reflects light in the visible region and whose electrical conductivity decreases with temperature and has a high melting point?

1. Metallic bonding

2. Van der Waals' bonding

3. Ionic bonding

4. Covalent bonding

A particle moves a distance \(x\) in time \(t\) according to equation \(x=(t+5)^{-1}.\) The acceleration of the particle is proportional to:
1. (velocity)^\(3/2\)
2. (distance)^\(2\)
3. (distance)^\(-2\)
4. (velocity)^\(2/3\)

A conducting circular loop is placed in a uniform magnetic field, \(B=0.025~\text{T}\) with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of \(1~\text{mm s}^{-1}\). The induced emf, when the radius is \(2~\text{cm}\), is:
1. \(2\pi ~\mu\text{V}\)
2. \(\pi ~\mu\text{V}\)
3. \(\dfrac{\pi}{2}~\mu\text{V}\)
4. \(2 ~\mu \text{V}\)

The activity of a radioactive sample is measured as N₀ counts per minute at t = 0 and N₀/e counts per minute at t = 5 min. The time (in minutes) at which the activity reduces to half its value is:

1. ${\log }_e\left(\frac{2}{5}\right)$

2. $\frac{5}{{\log }_e\left(2\right)}$

3. 5 ${\log }_{10}2$

4. $5$ ${\log }_{e}2$