A disc of radius \(R\) and mass \(M\) is rolling horizontally without slipping with speed \(v\). It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is _______.

A uniform heating wire of resistance \(36\, \Omega\) is connected across a potential difference of \(240\, {V}\) The wire is then cut into half and potential difference of \(240\, {V}\) is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be \(1: {x}\), where \({x}\) is........... .

\(0.08 \mathrm{~kg}\) air is heated at constant volume through \(5^{\circ} \mathrm{C}\). The specific heat of air at constant volume is \(0.17 \mathrm{kcal} / \mathrm{kg}^{\circ} \mathrm{C}\) and \(\mathrm{J}=4.18\) joule \(/ \mathrm{cal}\). The change in its internal energy is approximately.

The angular frequency of alternating current in a \(L-C-R\) circuit is \(100\, rad / s\). The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

A solid cylinder having radius \(R\) and length \(L\) is slipping on a rough horizontal plane. At time \(t=0\) the cylinder has a translational velocity \(v_0=49\) m/s, perpendicular to its axis and a rotational velocity \(v_0/4R\) about the centre. The time taken by the cylinder to start rolling is ________ seconds. (coefficient of kinetic friction \(\mu_K=0.25\) and \(g=9.8\) m/s\(^2\))

A particle executes simple harmonic motion with an amplitude of \(4 \mathrm{~cm}\). At the mean position, velocity of the particle is \(10 \mathrm{~cm} / \mathrm{s}\). The distance of the particle from the mean position when its speed becomes \(5 \mathrm{~cm} / \mathrm{s}\) is \(\sqrt{\alpha} \mathrm{cm}\), where \(\alpha=\)____________.

A light ray is incident, at an incident angle \(\theta_{1}\), on the system of two plane mirrors \(M_{1}\) and \(M_{2}\) having an inclination angle \(75^{\circ}\) between them (as shown in figure). After reflecting from mirror \(M_{1}\) it gets reflected back by the mirror \(M _{2}\) with an angle of reflection \(30^{\circ}\). The total deviation of the ray will be \(\dots\) degree.

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass \(2 \mathrm{~kg}\) is : _______.

The work functions of Aluminium and Gold are \(4.1\,eV\) and \(5.1\,eV\) respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is \(.......\)

The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is \(2\,s\). The period of oscillation of the same pendulum on the planet would be

A conducting circular loop is placed in a uniform magnetic field of \(0.4\,T\) with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of \(1\,mm / s\). The magnitude of induced emf in the loop at an instant when the radius of the loop is \(2\,cm\) will be \(...........\,\mu V\).

The binding energy for the following nuclear reactions are expressed in MeV .
\({ }_2 He ^3+{ }_0 n ^1 \rightarrow{ }_2 He ^4+20 MeV\)
\({ }_2 He ^4+{ }_0 n ^1 \rightarrow{ }_2 He ^5-0.9 MeV\)
If \(X _3, X _4, X _5\) denote the stability of \({ }_2 He ^3,{ }_2 He ^4\) and \({ }_2 He ^5\), respectively, then the correct order is :

Match the LIST-I with LIST-II

LIST-I		LIST-II
A.	Pressure varies inversely with volume of an ideal gas	I.	Adiabatic process
B.	Heat absorbed goes partly to increase internal energy and partly to do work	II.	Isochoric process
C.	Heat is neither absorbed nor released by a system	III.	Isothermal process
D.	No work is done on or by a gas	IV.	Isobaric process

Choose the correct answer from the options given below: