A car accelerates from rest to \(u\,m / s\). The energy spent in this process is \(E\,J\). The energy required to accelerate the car from \(u\,m / s\) to \(2u\,m / s\) is \(nE\,J\). The value of \(n\) is ..............

The stopping potential \(V_0\) (in \(volt\)) as a function of frequency \((v)\) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be : ................. \(eV\) (Given : Planck's constant \((h) = 6.63 \times 10^{-34}\, Js\), electron charge \(e = 1.6 \times 10^{-19}\, C\))

In an adiabatic process, which of the following statements is true?

A radioactive sample decays \(\frac{7}{8}\) times its original quantity in \(15\) minutes. The half-life of the sample is \(......min\)

At the interface between two materials having refractive indices \(n_1\) and \(n_2\), the critical angle for reflection of an em wave is \(\theta_{1 C}\). The \(n_2\) material is replaced by another material having refractive index \(n_3\) such that the critical angle at the interface between \(n_1\) and \(n_3\) materials is \(\theta_{2 \mathrm{C}}\). If \(\mathrm{n}_3\gt\mathrm{n}_2\gt\mathrm{n}_1 ; \frac{\mathrm{n}_2}{\mathrm{n}_3}=\frac{2}{5}\) and \(\sin \theta_{2 \mathrm{C}}-\sin \theta_{1 \mathrm{C}}=\frac{1}{2}\), then \(\theta_{1 \mathrm{C}}\) is :

The temperature of an open room of volume \(30\ m^3\) increases from \(17^o C\) to \(27vC\) due to sunshine. The atmospheric pressure in the room remains \(1 \times 10^5\ Pa\). Ifni and nr are the number of molecules in the room before and after heating, then \(n_f-n_i\) will be :

An electric field \(\overrightarrow{\mathrm{E}}=4 \mathrm{x} \hat{\mathrm{i}}-\left(\mathrm{y}^{2}+1\right) \hat{\mathrm{j}}\; \mathrm{N} / \mathrm{C}\) passes through the box shown in figure. The flux of the electric field through surfaces \(A B C D\) and \(BCGF\) are marked as \(\phi_{I}\) and \(\phi_{\mathrm{II}}\) respectively. The difference between \(\left(\phi_{\mathrm{I}}-\phi_{\mathrm{II}}\right)\) is (in \(\left.\mathrm{Nm}^{2} / \mathrm{C}\right)\)

Given is a thin convex lens of glass (refractive index \(\mu\) ) and each side having radius of curvature \(R\). One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself ?

Match List \(I\) with List \(II\)

LIST \(I\)	LIST \(II\)
\(A\) Planck's constant \(( h )\)	\(I\) \(\left[ M ^1 L ^2 T ^{-2}\right]\)
\(B\) Stopping potential \(( Vs )\)	\(II\) \(\left[ M ^1 L ^1 T ^{-1}\right]\)
\(C\) Work function \((\phi)\)	\(III\) \(\left[ M ^1 L ^2 T ^{-1}\right]\)
\(D\) Momentum \(( p )\)	\(IV\) \(\left[ M ^1 L ^2 T ^{-3} A ^{-1}\right]\)

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved ?