The equation for real gas is given by \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where \(\mathrm{P}, \mathrm{V}, \mathrm{T}\) and R are the pressure, volume, temperature and gas constant, respectively. The dimension of \(\mathrm{ab}^{-2}\) is equivalent to that of :

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of \(100 \mathrm{~cm}^2\) with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density \(1.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3\). What force one needs to apply on the hinged door so that it does not get opened ?
(Acceleration due to gravity \(=10 \mathrm{~m} / \mathrm{s}^2\))

Given below are two statements :
Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs.
Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries.
In the light of the above statements, choose the correct answer from the options given below.

The maximum and minimum distances of a comet from the Sun are \(1.6 \times 10^{12}\, m\) and \(8.0 \times 10^{10}\, m\) respectively. If the speed of the comet at the nearest point is \(6 \times 10^{4}\, ms ^{-1},\) the speed at the farthest point is ......... \(\times 10^{3}\, m / s\)

The figure given below shows an \(LCR\) series circuit with two switches \(S_1\) and \(S_2\). When switch \(S_1\) is closed keeping \(S_2\) open, the phase difference \((\phi)\) between the current and source voltage is \(30°\) and phase difference is \(60°\) when \(S_2\) is closed keeping \(S_1\) open. The value of \((3L_1 - L_2)\) is _______ H.

During the melting of a slab of ice at 273 K at atmospheric pressure :

A point charge \(2 \times 10^{-2}\,C\) is moved from \(P\) to \(S\) in a uniform electric field of \(30\,NC ^{-1}\) directed along positive \(x\)-axis. If coordinates of \(P\) and \(S\) are \((1,2\), \(0) m\) and \((0,0,0) m\) respectively, the work done by electric field will be \(.........\,mJ\)

In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is \(2.4\) \(\mu\)m. If the experiment is carried out in another medium having refractive index \(1.2\), the fringe width will be _____ \(\mu\)m.

A resistor dissipates \(192\, {J}\) of energy in \(1\, {s}\) when a current of \(4\, {A}\) is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in \(5 \,{s}\) in \(.....\,J.\)

A particular hydrogen like ion emits radiation of frequency \(2.92 \times 10^{15}\, {Hz}\) when it makes transition from \({n}=3\) to \({n}=1 .\) The frequency in \({Hz}\) of radiation emitted in transition from \({n}=2\) to \({n}=1\) will be : (in \(\,\times 10^{15}\))