The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is:
1. \(1:1\)
2. \(1:-1\)
3. \(2:-1\)
4. \(1:-2\)

The moment of the force, \(\overset{\rightarrow}{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}\) at point (\(2,\) \(0,\) \(-3\)) about the point (\(2,\) \(-2,\) \(-2\)) is given by:

A block of mass \(m\) is placed on a smooth inclined wedge \(ABC\) of inclination \(\theta\) as shown in the figure. The wedge is given an acceleration '\(a\)' towards the right. The relation between \(a\) and \(\theta\) for the block to remain stationary on the wedge is:

A toy car with charge \(q\) moves on a frictionless horizontal plane surface under the influence of a uniform electric field \(\vec {E}.\) Due to the force \(q\vec {E},\) its velocity increases from \(0\) to \(6~\text{m/s}\) in a one-second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between \(0\) to \(3\) seconds are respectively:

In Young's double-slit experiment, the separation \(d\) between the slits is \(2~\text{mm}\), the wavelength \(\lambda\) of the light used is \(5896~\mathring{A}\) and distance \(D\) between the screen and slits is \(100~\text{cm}\). It is found that the angular width of the fringes is \(0.20^{\circ}\). To increase the fringe angular width to \(0.21^{\circ}\) (with same \(\lambda\) and \(D\)) the separation between the slits needs to be changed to:
1. \(1.8~\text{mm}\)
2. \(1.9~\text{mm}\)
3. \(2.1~\text{mm}\)
4. \(1.7~\text{mm}\)

An astronomical refracting telescope will have large angular magnification and high angular resolution when it has an objective lens of:

The volume \((V)\) of a monatomic gas varies with its temperature \((T),\) as shown in the graph. The ratio of work done by the gas to the heat absorbed by it when it undergoes a change from state \(A\) to state \(B\) will be: