Two vessels \(A\) and \(B\) are of the same size and are at same temperature. A contains \(1 \mathrm{~g}\) of hydrogen and \(B\) contains \(1 \mathrm{~g}\) of oxygen. \(\mathrm{P}_{\mathrm{A}}\) and \(\mathrm{P}_{\mathrm{B}}\) are the pressures of the gases in \(A\) and \(\mathrm{B}\) respectively, then \(\frac{\mathrm{P}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{B}}}\) is _______.

Hydrogen \((_1H^1),\) Deuterium \((_1H^2)\),singly ionised Helium \((_2He^4)^+\) and doubly ionised lithium \({\left( {{}_3^6Li} \right)^{ + + }}\), all have one electron around the nucleus. Consider an electron transition from \(n = 2\) to \(n = 1\). If the wavelengths of emitted radiation are \(λ_1,λ_2,λ_3\) and \(λ_4\) respectively then approximately which one of the following is correct?

A system of three polarizers \(P_1, P_2, P_3\) is set up such that the pass axis of \(P_3\) is crossed with respect to that of \(P_1\). The pass axis of \(P_2\) is inclined at \(60^o\) to the pass axis of \(P_3\). When a beam of unpolarized light of intensity \(I_0\) is incident on \(P_1\), the intensity of light transmitted by the three polarizers is \(I\). The ratio \((I_0/I)\) equals (nearly)

There are two identical chambers, completely thermally insulated from surroundings. Both chambers have a partition wall dividing the chambers in two compartments. Compartment \(1\) is filled with an ideal gas and Compartment \(3\) is filled with a real gas. Compartments \(2\) and \(4\) are vacuum . A small hole (orifice) is made in the partition walls and the gases are allowed to expand in vacuum Statement \(-1\) : No change in the temperature of the gas takes place when ideal gas expands in vacuum. However, the temperature of real gas goes down (cooling) when it expands in vacuum Statement \(-2\) : The internal energy of an ideal gas is only kinetic. The internal energy of a real gas is kinetic as well as potential

An inductor of reactance \(100 \Omega\), a capacitor of reactance \(50 \Omega\), and a resistor of resistance \(50 \Omega\) are connected in series with an AC source of 10 V , 50 Hz. Average power dissipated by the circuit is ________ W.

The elongation of a wire on the surface of the earth is \(10^{-4} \; m\). The same wire of same dimensions is elongated by \(6 \times 10^{-5} \; m\) on another planet. The acceleration due to gravity on the planet will be \(\dots \; ms ^{-2}\). (Take acceleration due to gravity on the surface of earth \(=10 \; m / s ^{-2}\) )

At any instant the velocity of a particle of mass \(500\,g\) is \(\left(2 t \hat{ i }+3 t ^2 \hat{ j }\right)\,ms ^{-1}\). If the force acting on the particle at \(t=1 s\) is \((\hat{i}+x \hat{j}) N\). Then the value of \(x\) will be:

In a Wheatstone bridge (see figure) Resistance \(P\) and \(Q\) are approximately equal. When \(R = 400\,\Omega ,\) the bridge is balanced. On interchanging \(P\) and \(Q,\) the value of \(R,\) for balance is \(405\,\Omega .\) The value of \(X\) is close to ................. \(ohm\)

An electric field is given by \((6 \hat{i}+5 \hat{j}+3 \hat{k}) \ N / C\). The electric flux through a surface area \(30 \hat{\mathrm{i}}\; m^2\) lying in \(YZ-\)plane (in SI unit) is _______.