A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The rational between temperature and volume for the process is \(TV^x =\) constant, then \(x\) is

In the figure shown, what is the current (in Ampere) drawn from the battery ? You are given \(R_1 = 15\,\Omega \)\(,R _2 = 10\,\Omega ,\)\( R_3 = 20\,\Omega ,\)\( R_4 = 5\,\Omega ,\)\(R_5 = 25\,\Omega ,\)\(R_6 = 30\,\Omega , \)\(E = 15\,V\)

Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for \(V =5 \sin (100 t )\). The values of L and \(R\) are shown in the figure. The capacitance of the capacitor \(( C )\) used is ___________ \(\mu F\).

An ideal gas at pressure \(P\) and temperature \(T\) is expanding such that \(PT^3 = \) constant. The coefficient of volume expansion of the gas is _______.

The de Broglie wavelengths of a proton and an \(\alpha\) particle are \(\lambda\) and \(2 \lambda\) respectively. The ratio of the velocities of proton and \(\alpha\) particle will be _______.

A string is clamed at both the ends and it is vibrating in its \(4^{th}\) harmonic. The equation of the stationary wave is \(Y =0.3\,sin\,(0.157\,x) \,cos\,(200\pi t)\). The length of the string is ..... \(m\) (all quantities are in \(SI\) units)

As per the given figure, two blocks each of mass \(250\,g\) are connected to a spring of spring constant \(2\,Nm ^{-1}\). If both are given velocity \(V\) in opposite directions, then maximum elongation of the spring is:

A positive charge particle of \(100 \,mg\) is thrown in opposite direction to a uniform electric field of strength \(1 \times 10^{5} \,NC ^{-1}\). If the charge on the particle is \(40 \,\mu C\) and the initial velocity is \(200 \,ms ^{-1}\), how much distance (in \(m\)) it will travel before coming to the rest momentarily

In a uniform magnetic field, the magnetic needle has a magnetic moment \(9.85 \times 10^{-2} \,{A} / {m}^{2}\) and moment of inertia \(5 \times 10^{-6} \,{kgm}^{2}\). If it performs \(10\) complete oscillations in \(5\, seconds\) then the magnitude of the magnetic field is \(....\,mT.\) [ Take \(\pi^{2}\) as \(9.85\) ]