A diatomic gas \((\gamma=1.4)\) does 100 J of work when it is expanded isobarically. Then the heat given to the gas _________ J.

In an engine the piston undergoes vertical simple harmonic motion with amplitude \(7\, cm\) . A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to ...... \(Hz\)

Given below are two statements Statement \(I\) : When the frequency of an \(a.c.\) source in a series \(LCR\) circuit increases, the current in the circuit first increases, attains a maximum value and then decreases. Statement \(II:\) In a series \(LCR\) circuit, the value of power factor at resonance is one. In the light of given statements, choose the most appropriate answer from the options given below

Diameter of a plano-convex lens is \(6 \,cm\) and thickness at the centre is \(3\, mm\). If the speed of light in the material of the lens is \(2  \times  10^8 m/sec\), the focal length of the lens is.......\(cm\)

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 \(\,\times 10^{15}\))

The distance of the Sun from earth is \(1.5 \times 10^{11} \,m\) and its angular diameter is \((2000) \,s\) when observed from the earth. The diameter of the Sun will be ...........

The mean free path of a molecule of diameter \(5\times10^{-10}\) m at the temperature \(41^{\circ}C\) and pressure \(1.38\times10^{5}Pa\), is given as ___________ m.
(Given \(k_{B}=1.38\times10^{-23}J/K\)).

In a hydrogen like atom, when an electron jumps from the \(M -\) shell to the \(L-\) shell the wavelength of emitted radiation is \(\lambda \). If an electron jumps from \(N-\) shell to the \(L-\) shell the wavelength of emitted radiation will be

The Young's modulus of a steel wire of length \(6\,m\) and cross-sectional area \(3\,mm ^2\), is \(2 \times 11^{11}\,N / m ^2\). The wire is suspended from its support on a given planet. A block of mass \(4\,kg\) is attached to the free end of the wire. The acceleration due to gravity on the planet is \(\frac{1}{4}\) of its value on the earth. The elongation of wire is  (Take \(g\) on the earth \(=10\) \(\left.m / s ^2\right):\)

Two slits are \(1 \mathrm{~mm}\) apart and the screen is located \(1 \mathrm{~m}\) away from the slits. A light wavelength \(500 \mathrm{~nm}\) is used. The width of each slit to obtain \(10\) maxima of the double slit pattern within the central maximum of the single slit pattern is _______ \(\times 10^{-4} \mathrm{~m}\)