\(c_P\) and \(c_V\) are specific heats at constant pressure and constant volume respectively. It is observed that \(c_P - c_V = a\) for hydrogen gas \(c_P - c_V = b\) for nitrogen gas The correct relation between \(a\) and \(b\) is

Match List-I with List-II.

List-I	List-II
A. Meter (L)	I. \(\sqrt{\dfrac{hc}{G}}\)
B. Second (S)	II. \(\sqrt{\dfrac{Gh}{c^5}}\)
C. Kilogram (M)	III. \(\sqrt{\dfrac{K^2L^2c^3}{Gh}}\)
D. Kelvin (K)	IV. \(\sqrt{\dfrac{Gh}{c^3}}\)

where \(h\) (Planck's constant), \(G\) (gravitational constant) and \(c\) (speed of light in vacuum) as fundamental units.
Choose the correct answer from the options given below :

The electric field at the point associated with a light wave is given by \(E=200\left[\sin \left(6 \times 10^{15}\right) t+\sin \left(9 \times 10^{15}\right) t\right] \,Vm ^{-1}\) Given : \(h=4.14 \times 10^{-15} \,eVs\) If this light falls on a metal surface having a work function of \(2.50 \,eV\), the maximum kinetic energy of the photoelectrons will be ........... \(eV\)

The width of one of the two slits in Young's double slit experiment is d while that of the other slit is \(x \mathrm{~d}\). If the ratio of the maximum to the minimum intensity in the interference pattern on the screen is \(9: 4\) then what is the value of \(x\) ?
(Assume that the field strength varies according to the slit width.)

The angular momentum of a planet of mass \(M\) moving around the sun in an elliptical orbit is \(\overrightarrow{ L }\). The magnitude of the areal velocity of the planet is:

A paralle plate capacitor is made up of stair like structure with a palte area \(A\) of each stair and that is connected with a wire of length \(b\), as shown in the figure. The capacitance of the arrangement is \(\frac{ x }{15} \frac{\varepsilon_{0} A }{ b }\). The value of \(x\) is ............

The number of molecules in one litre of an ideal gas at \(300 \,{K}\) and \(2\) atmospheric pressure with mean kinetic energy \(2 \times 10^{-9}\, {J}\) per molecules is \(....\, \times 10^{11}\)

A Carnot engine take \(5000 \,k\,cal\) of heat from a reservoir at \(727\,^{\circ}C\) and gives heat to a \(\operatorname{sink}\) at \(127\,^{\circ}C\). The work done by the engine is \(.......... \times 10^{6}\,J\)

Two light beams fall on a transparent material block at point 1 and 2 with angle \(\theta_1\) and \(\theta_{2^{\prime}}\) respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of the block. Given : the distance between 1 and 2, \(\mathrm{d}=4 \sqrt{3} \mathrm{~cm}\) and \(\theta_1=\theta_2=\cos ^{-1}\left(\frac{\mathrm{n}_2}{2 \mathrm{n}_1}\right)\), where refractive index of the block \(\mathrm{n}_2\gt\) refractive index of the outside medium \(\mathrm{n}_1\), then the thickness of the block is ________ cm.

In the given circuit ' \(a\) ' is an arbitrary constant. The value of \(m\) for which the equivalent circuit resistance is minimum, will be \(\sqrt{\frac{ x }{2}}\). The value of \(x\) is ...........

A charged particle going around in a circle can be considered to be a current loop. A particle of mass \(m\) carrying charge \(q\) is moving in a plane with speed \(v\) under the influence of magnetic field \(\overrightarrow{ B }\). The magnetic moment of this moving particle

A \(12.5\,eV\) electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be: