Class 12th

A parallel plate capacitor has plates of area A separated by distance ' $d$ $$ ' between them. It is filled with a dielectric which has a dielectric constant that varies as $k\left(n\right)=k(1+$ $\alpha n)$ $$ $$ where ' $$ $x$ ' is he distance measured from one of the plates.

If $\left(\alpha \mathrm{d}\right)<<1$ $$ , the total capacitance of the system is best given by the expression:

The activity of a radioactive sample falls from $700{\mathrm{s}}^{-1}$ to $500{\mathrm{s}}^{-1}$  in 30 minutes. Its half life is close to

Visible light of wavelength $6000*{10}^{-8}\mathrm{c}\mathrm{m}$ ${}^{}$ falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at ${60}^{?}$ ${}^{}$ from the central maximum. If the first minimum is produced at ${\theta }_1$ ${}_{}$ then ${\theta }_1$ ${}_{}$ is close to:

The figure gives experimentally measured $B$ vs $\mathrm{H}$  variation in a ferromagnetic material. The retentivity, co-ercivity and saturation, respectively, of the material are

A long solenoid of radius $R$ $$ carries a time ( $t)$ $$ dependent current ${}_{}$ $I\left(t\right)=I_{0}t(1-t)$ . A ring of radius $2R$ $$ is placed cordially near its middle. During the time internal $0\le t\le 1$ $$ , the induced current $\left(I_R\right)$ $\left({}_{}\right)$ and the induced $\mathrm{E}\mathrm{M}\mathrm{F}?\left(V_R\right)$ $\left({}_{}\right)$ in the ring changes as:

In finding the electric field using Gauss law the formula $\left|\stackrel{?}{E}\right|=\frac{q_{\text{enc}}}{{\epsilon }_0\left|A\right|}$ $\stackrel{}{}\frac{{}_{}}{{}_{}}$ is applicable. In the formula ${\epsilon }_0$ ${}_{}$ is permittivity of free space, $A$ $$ is the area of Gaussain surface and $q_{\text{enc}}$ ${}_{}$ is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation? Only when the Gaussian surface is an

In a Young's double slit experiment, the separation between the slits is $0.15\mathrm{m}\mathrm{m}$ . In the experiment, a source of light of wavelength $589\mathrm{n}\mathrm{m}$ is used and the interference pattern is observed on a screen kept $1.5\mathrm{m}$  away. The separation between the successive bright fringes on the screen is:

When photon of energy $4.0\mathrm{e}\mathrm{V}$ $$ strikes the surface of a metal $A$ $$ , the ejected photoelectrons have maximum kinetic energy $T_A$ ${}_{}$ eV and de-Broglie wavelength ${\lambda }_A$ ${}_{}$ . The maximum kinetic energy of photoelectrons liberated form another metal B by photon of energy 4.50 $\mathrm{e}\mathrm{V}$ $$ is $T_B=\left(T_A-1.5\right)eV$ ${}_{}\left({}_{}\right)$ . If the de-Broglie wavelength of these photoelectrons ${\lambda }_B=2{\lambda }_A$ ${}_{}{}_{}$ , then the work function of metal $$ $B$ is

Two infinite planes each with uniform surface charge density $+\sigma$ $$ are kept in such a way that the angle between them is ${30}^{?}$ ${}^{}$ . The electric field in the region shown between them is given by:

A polarizer-analyser set is adjusted such that the intensity of light coming out of the analyser is just $10\mathrm{\%}$ $$ of the original intensity. Assuming that the polarizer-analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero is