A closed vessel contains \(0.1\) mole of a monoatomic ideal gas at \(200\, K\). If \(0.05\) mole of the same gas at \(400\, K\) is added to it, the final  equilibrium temperature (in \(K\) ) of the gas in the vessel will be closed to

An insulated wire is wound so that it forms a flat coil with \(N = 200\) turns. The radius of the innermost turn is \(r_1 = 3\) cm, and of the outermost turn \(r_2 = 6\) cm. If \(20\) mA current flows in it then the magnetic moment will be \(\alpha \times 10^{-2}\) A.m\(^2\). The value of \(\alpha\) is _____.

Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity \(\rho_{ C }, \rho_{ T }, \rho_{ M }\) and \(\rho_{ A }\) espectively Then:

At some instant, a radioactive sample \(S_1\) having an activity \(5\,\mu Ci\)  has twice the number of nuclei as another sample \(S_2\)  which has an activity of  \(10\,\mu Ci.\)  The halflives of \(S_1\)  and  \(S_2\) are

The resistance of a wire is \(5 \Omega\). It's new resistance in ohm if stretched to \(5\) times of it's original length will be :

An unpolarized light of intensity \(I_o\) passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is \(0°\) and intensity of light emerged from analyser is \(\dfrac{3}{8}I_o\), the angle of rotation of the light by the solution with respect to analyser is _______ degrees.

\(2\, moles\) of helium gas is mixed with \(3\, moles\) of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume ....... \(J/mol\, K\) ? \((R = 8.3\, J/mol\, K)\)

Velocity-time graph for a body of mass \(10\, kg\) is shown in figure. Work-done on the body in first two seconds of the motion is  ................ \(\mathrm{J}\)

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is \(....\,{mm} .\) [Refractive index of air \(=1.0003\), wavelength of yellow light in vacuum \(=6000 \,\mathring {{A}}\) ]

Two resistors \({R}_{1}=(4 \pm 0.8) \Omega\) and \({R}_{2}=(4 \pm 0.4)\) \(\Omega\) are connected in parallel. The equivalent resistance of their parallel combination will be

A wire of length \(L\) and radius \(r\) is clamped at one end. If its other end is pulled by a force \(F\), its length increases by \(l\). If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become _______.

Consider the equation \(H = \dfrac{x^p \epsilon^q E^r}{t^s}\), where \(H=\) magnetic field; \(E=\) electric field, \(\epsilon=\) permittivity, \(x=\) distance, \(t=\) time. The values of \(p, q, r\) and \(s\) respectively are:

A \(25\,cm\) long solenoid has radius \(2\,cm\) and \(500\) total number of turns. It carries a current of \(15\,A.\) If it is equivalent to a magnet of the same size and magnetization \(\vec M\) ( magnetic moment/ volume), then \(\left| {\vec M} \right|\)  is