A container is divided into two chambers by a partition. The volume of first chamber is \(4.5\) litre and second chamber is \(5.5\) litre. The first chamber contain \(3.0\) moles of gas at pressure \(2.0\, atm\) and second chamber contain \(4.0\) moles of gas at pressure \(3.0\, atm\) .After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is \(x \times 10^{-1} atm\). Value of \(x\) is.........

Mach List-\(I\) with List - \(II\) :

List - \(I\)	List - \(II\)
\((a)\) Ultraviolet rays	\((a)\) Study crystal structure
\((b)\) Microwaves	\((b)\) Greenhouse
\((c)\) Infrared waves	\((c)\) sterilizing surgical instrument
\((d)\) \(x\)-rays	\((d)\) Radar system

Choose the correct answer from the options given below

A fly wheel is accelerated uniformly from rest and rotates through \(5 \,rad\) in the first second. The angle rotated by the fly wheel in the next second, will be.........\(rad\)

Given below are two statements:
Statement I: Pressure of fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.
In the light of the above statements, choose the correct answer from the options given below.

Unpolarised light of intensity \(32\,Wm ^{-2}\) passes through the combination of three polaroids such that the pass axis of the last polaroid is perpendicular to that of the pass axis of first polaroid. If intensity of emerging light is \(3\,Wm ^{-2}\), then the angle between pass axis of first two polaroids is \(............\,^{\circ}\)

Moment of inertia of a body about a given axis is \(1.5\, kg\, m^2\) Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\, J\), the angular acceleration of \(20\, rad/s^2\) must be applied about the axis of rotation for a duration of ......... \(\sec\).

A solid metal cube of edge length \(2\, cm\) is moving in a positive \(y-\) direction at a constant speed of \(6\, m/s\). There is a uniform magnetic field of \(0.1\, T\) in the positive \(z-\) direction. The potential difference between the two faces of the cube perpendicular to the \(x-\) axis, is.....\(mV\)

If two vectors \(\vec{P}=\hat{i}+2 m \hat{j}+m \hat{k}\) and \(\vec{Q}=4 \hat{i}-2 \hat{j}+ mk\) are perpendicular to each other. Then, the value of \(m\) will be :

A circular conducting coil of radius \(1\, {m}\) is being heated by the change of magnetic field \(\vec {B}\) passing perpendicular to the plane in which the coil is laid. The resistance of the coil is \(2\, \mu\, \Omega\). The magnetic field is slowly switched off such that its magnitude changes in time as \(B=\frac{4}{\pi} \times 10^{-3}\, {T}\left(1-\frac{{t}}{100}\right)\) The energy dissipated by the coil before the magnetic field is switched off completely is \(E=.....\,{m} J.\)

Three containers \(\mathrm{C}_{1}, \mathrm{C}_{2}\) and \(\mathrm{C}_{3}\) have water at different temperatures. The table below shows the final temperature \(T\) when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process) \(\begin{array}{|c|c|c|c|}\hline \mathrm{C_{1 }} & {\mathrm{C}_{2}} & {\mathrm{C}_{3}} & {\mathrm{T}} \\ \hline {1 l} & {2 l} & {-} & {60^{\circ} \mathrm{C}} \\ \hline {-} & {1 l} & {2 l} & {30^{\circ} \mathrm{C}} \\ \hline  {2 l} & {-} & {1 l} & {60^{\circ} \mathrm{C}} \\ \hline  {1 l} & {1 l} & {1 l} & {\theta} \\ \hline\end{array}\) The value of \(\theta\) (in \(^{\circ} \mathrm{C}\) to the nearest integer) is

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of _______.

At the centre of a fixed large circular coil of radius \(R\), a much smaller circular coil of radius \(r\) is placed. The two coils are concentric and are in the same plane. The larger coil carries a current \(I\). The smaller coil is set to rotate with a constant angular velocity \(\omega \) about an axis along their common diameter. Calculate the \(emf\) induced in the smaller coil after a time \(t\) of its start of rotation