Class 12th

The current $I_1$ ${}_{}$ (in A) flowing through $$ $1\mathrm{\Omega }$ resistor in the following circuit is

At time $\mathrm{t}=0$ $$ magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next $5\mathrm{s}$ $$ , then induced EMF in the loops is:

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