The temperature of an ideal gas is increased from \(200\,K\) to \(800\,K\). If r.m.s. speed of gas at \(200\,K\) is \(v_0\). Then, r.m.s. speed of the gas at \(800\,K\) will be:

A circular coil has moment of inertia \(0.8 \,kg m ^{2}\) around any diameter and is carrying current to roduce a magnetic moment of \(20\, Am ^{2}\). The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of \(4\, T\) is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by \(60^{\circ}\) will be

A small square loop of wire of side \(l\) is placed inside a large square loop of wire \(L(L \gg l)\). Both loops are coplanar and their centres coincide at point \(O\) as shown in figure. The mutual inductance of the system is.

In a common emitter configuration with suitable bias, it is given than \(R_L\) is the load resistance and \(R_{BE}\)  is small signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given, respectively, by: [ \(\beta \) is current gain, \(I_B\) , \(I_C\) , \(I_E\) are respectively base, collector and emitter currents]

If the magnetic field in a plane electromagnetic wave is given by \(\overrightarrow{\mathrm{B}}=3 \times 10^{-8} \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} \mathrm{t}\right) \hat{\mathrm{j}}\; \mathrm{T}\) then what will be expression for electric field?

A body takes \(4\, {min}\). to cool from \(61^{\circ} {C}\) to \(59^{\circ} {C}\). If the temperature of the surroundings is \(30^{\circ} {C}\), the time taken by the body to cool from \(51^{\circ} {C}\) to \(49^{\circ} {C}\) is \(....\,min\)

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by \(E _{ x }= E _0 \sin ( kz -\omega t )\) \(B _{ y }= B _0 \sin ( kz -\omega t )\) Then the correct relation between \(E_0\) and \(B_0\) is given by

Consider a light ray travelling in air is incident into a medium of refractive index \(\sqrt{2 n}\). The incident angle is twice that of refracting angle. Then, the angle of incidence will be

Two simple pendulums having lengths \(l_1\) and \(l_2\) with negligible string mass undergo angular displacements \(\theta_1\) and \(\theta_2\), from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

Given below are two statements: Statement \(I\) : A uniform wire of resistance \(80\,\Omega\) is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be \(5\,\Omega\). Statement \(II :\) Two resistance \(2\,R\) and \(3\,R\) are connected in parallel in a electric circuit. The value of thermal energy developed in \(3\,R\) and \(2\,R\) will be in the ratio \(3:2.\) In the light of the above statements, choose the most appropriate answer from the options given below