The dimensions of ${\left({\mu }_0{\epsilon }_0\right)}^{-1/2}$ are:

1.  $[$ $L^{-1}T$ $]$

2.  $[$ $L{T}^{-1}$ $]$

3.  $[$ $L^{1/2}{T}^{1/2}$ $]$

4. $[$ $L^{1/2}{T}^{-1/2}$ $]$

An ideal gas goes from state \(A\) to state \(B\) via three different processes as indicated in the \((P\text-V)\) diagram.

  
If \(Q_1,Q_2,Q_3\)${\mathrm{}}_{}$ indicate the heat absorbed by the gas along the three processes and \(\Delta U_1, \Delta U_2, \Delta U_3\) indicate the change in internal energy along the three processes respectively, then:

To get output \(Y = 1\) in the given circuit which of the following input will be correct?

Two metallic spheres of radii \(1~\text{cm}\) and \(3~\text{cm}\) are given charges of \(-1\times 10^{-2}~\text{C}\) and \(5\times 10^{-2} ~\text{C}\), respectively. If these are connected by a conducting wire, then the final charge on the bigger sphere is:

Two radiations of photons energies \(1\) eV and \(2.5\) eV, successively illuminate a photosensitive metallic surface of work function \(0.5\) eV. The ratio of the maximum speeds of the emitted electrons is:
1. \(1:2\)
2. \(1:1\)
3. \(1:5\) 
4. \(1:4\)

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:

         
1. \(C\)
2. \(D\)
3. \(A\)
4. \(B\)

A train moving at a speed of $220$ $m{s}^{-1}$ towards a stationary object, emits a sound of frequency 1000 Hz. Some of the sound reaching the object gets reflected back to the train as an echo. The frequency of the echo as detected by the driver of the train is:(speed of sound in air is $330$ $m{s}^{-1}$)

1.  4000 Hz 

2.  5000 Hz 

3.  3000 Hz 

4.  3500 Hz

The half-life of a radioactive nucleus is 50 days. The time interval $(t_2-t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and the time $t_1$ when $\frac{1}{3}$ of it had decayed is:

1.  50 days 

2.  60 days 

3.  15 days 

4.  30 days 

A car of mass \(m\) is moving on a level circular track of radius \(R\). If \(\mu_s\) represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by:

A circular platform is mounted on a frictionless vertical axle. Its radius \(R = 2~\text{m}\) and its moment of inertia about the axle is \(200~\text{kg m}^2\). It is initially at rest. A \(50~\text{kg}\) man stands on the edge of the platform and begins to walk along the edge at the speed of \(1~\text{ms}^{-1}\) relative to the ground. The time taken by man to complete one revolution is: