A rectangular parallelopiped is measured as \(1\,cm \times 1\,cm \times 100\,cm\). If its specific resistance is \(3 \times 10^{-7}\,\Omega\,m\), then the resistance between its two opposite rectangular faces will be \(..........x^{-7} \Omega\).

A particle of mass \('{m}'\) is moving in time \('t'\) on a trajectory given by \(\overrightarrow{{r}}=10 \alpha {t}^{2}\, \hat{{i}}+5 \beta({t}-5)\, \hat{{j}}\) Where \(\alpha\) and \(\beta\) are dimensional constants. The angular momentum of the particle becomes the same as it was for \({t}=0\) at time \({t}=\) .....\(seconds.\)

From the photoelectric effect experiment, following observations are made. Identify which of these are correct \(A.\) The stopping potential depends only on the work function of the metal. \(B.\) The saturation current increases as the intensity of incident light increases. \(C.\) The maximum kinetic energy of a photo electron depends on the intensity of the incident light. \(D.\) Photoelectric effect can be explained using wave theory of light. Choose the correct answer from the options given below:

Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is

The pressure wave, \(P = 0.01\,sin\,[1000t -3x]\,Nm^{-2},\) corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is \(0\,^oC.\) On some other day when temperature is \(T,\) the speed of sound produced by the same blade and at the same frequency is found to be \(336 \,ms^{-1}\). Approximate value of \(T\) is .... \(^oC\)

Statement \(I :\) When a Si sample is doped with Boron, it becomes \(P\) type and when doped by Arsenic it becomes \(N-\)type semi conductor such that \(P-\)type has excess holes and N-type has excess electrons. Statement \(II\) : When such \(P-\)type and \(N-\)type semi-conductors, are fused to make a junction, a current will automatically flow which can be detected with an externally connected ammeter. In the light of above statements, choose the most appropriate answer from the options given below.

A potential \(V_0\) is applied across a uniform wire of resistance \(R\). The power dissipation is \(P_1\). The wire is then cut into two equal halves and a potential of \(V _0\) is applied across the length of each half. The total power dissipation across two wires is \(P_2\). The ratio \(P_2: P_1\) is \(\sqrt{x}: 1\). The value of \(x\) is \(.............\).

A Carnot engine has efficiency of \(50 \%\). If the temperature of sink is reduced by \(40^{\circ} C\), its efficiency increases by \(30 \%\). The temperature of the source will be\(....K\)

The root mean square speed of molecules of a given mass of a gas at \(27^{\circ} C\) and \(1\) atmosphere pressure is \(200\, ms ^{-1}\). The root mean square speed of molecules of the gas at \(127^{\circ} C\) and \(2\) atmosphere pressure is \(\frac{ x }{\sqrt{3}}\, ms ^{-1} .\) The value of \(x\) will be ......\(ms ^{-1} .\)