During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of \(\frac{C_p}{C_v}\) for the gas is:

The energy required to remove the electron from a singly ionized Helium atom is \(2.2\, times\) the energy required to remove an electron from Helium atom . The total energy required to ionize the Helium atom completely is......\(eV\)

A batsman hits back a ball of mass \(0.4 \; kg\) straight in the direction of the bowler without changing its initial speed of \(15 \; ms ^{-1}\). The impulse imparted to the ball is \(\dots \; Ns\)

Moment of inertia of a dise of mass \(M\) and radius ' \(R\) ' about any of its diameter is \(\frac{ MR ^2}{4}\). The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, \(\frac{ x }{2} MR ^2\). The value of \(x\) is \(..........\).

A thin prism with angle \( 5^{\circ} \) of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is ___________.

A big drop is formed by coalescing \(1000\) small droplets of water. The surface energy will become _______.

Two identical charged spheres are suspended by string of equal lengths. The string make an angle of \(37^{\circ}\) with each other. When suspended in a liquid of density \(0.7 \mathrm{~g} / \mathrm{cm}^3\), the angle remains same. If density of material of the sphere is \(1.4 \mathrm{~g} / \mathrm{cm}^3\), the dielectric constant of the liquid is _______\(\left(\tan 37^{\circ}=\frac{3}{4}\right)\).

The exit surface of a prism with refractive index \(n\) is coated with a material having refractive index \(\frac{ n }{2}\). When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle is _________

Which of the following are true? \(A.\) Speed of light in vacuum is dependent on the direction of propagation. \(B.\) Speed of light in a medium in independent of the wavelength of light. \(C.\) The speed of light is independent of the motion of the source. \(D.\) The speed of light in a medium is independent of intensity. Choose the correct answer from the option given below :

A thin rod of mass \(0.9\, kg\) and length \(1 \,m\) is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move \(0.1\, kg\) moving in a straight line with velocity \(80\,m / s\) hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in \(rad/s\)) of the rod immediately after the collision will be

In the below circuit the current in each resistance is

The relation between root mean square speed \(\left( v _{ rms }\right)\) and most probable speed \(\left( v _{ p }\right)\) for the molar mass \(M\) of oxygen gas molecule at the temperature of \(300\, K\) will be

The parameter that remains the same for molecules of all gases at a given temperature is _______.