If \(r_1\) and \(r_2\) are the radii of the atomic nuclei of mass numbers \(64\) and \(125\) respectively, then the ratio \(\frac{r_1}{r_2}\) is:
1. \(\frac{64}{125}\)
2. \(\sqrt{\frac{64}{125}}\)
3. \(\frac54\)
4. \(\frac45\)

The ionization energy of \(\mathrm{Li^{2+}}\) is equal to:
1. \(9hcR \)
2. \(6hcR\)
3. \(2hcR\)
4. \(hcR\)

A current of \(5\) A is passing through a metallic wire of cross-sectional area \(4\times10^{-6}\) m². If the density of charge carriers of the wire is \(5\times10^{26}\) m^-3, then the drift velocity of the electrons will be:
1. \(1\times 10^2\) m/s
2. \(1.56 \times10^{-2}\) m/s
3. \(1.56 \times10^{-3}\) m/s
4. \(1\times 10^{-2}\) m/s

The numerical ratio of displacement to the distance covered is always:

The principle of LASER action involves:

A train is moving towards the east and a car is along the north, both at the same speed. The observed direction of the car to the passenger and the train is:
1. east-north direction
2. west-north direction
3. south-east direction
4. none of the above

Which of the following is a unipolar transistor?
1. p-n-p transistor
2. n-p-n transistor
3. field effect transistor
4. point contact transistor

A solid sphere and a hollow sphere of the same material and of the same size can be distinguished without weighing:

Point masses \(1,\) \(2,\) \(3\) and \(4\) kg are lying at the points \((0,0,0),\) \((2,0,0),\) \((0,3,0)\) and \((-2,-2,0)\) respectively. The moment of inertia of this system about the X-axis will be:
1. \(43~\mathrm{kg-m^2}\) 
2. \(34~\mathrm{kg-m^2}\) 
3. \(27~\mathrm{kg-m^2}\) 
4. \(72~\mathrm{kg-m^2}\) 

The radius of gyration of a body about an axis at a distance \(6~\mathrm{cm}\) from its centre of mass is \(10~\mathrm{cm}\). Then, its radius of gyration about a parallel axis through its centre of mass will be:
1. \(80~\mathrm{cm}\) 
2. \(8~\mathrm{cm}\) 
3. \(0.8~\mathrm{cm}\) 
4. \(80~\mathrm{m}\)