The polarising angle of transparent medium is ' $\theta$ '. Let the speed of light in the medium be ' v '. Then the relation between ' $\theta$ ' and ' $\mathbf{v}$ ' is [ $\mathrm{c}=$ velocity of light in air]

A black sphere has radius $R$ whose rate of radiation is E at temperature T . If radius is made R / 2 and temperature 3T, the rate of radiation will be

For a transistor, $\alpha_{\mathrm{dc}}$ and $\beta_{\mathrm{dc}}$ are the current ratios, then the value of $\frac{\beta_{\mathrm{dc}}-\alpha_{\mathrm{dc}}}{\alpha_{\mathrm{dc}} \times \beta_{\mathrm{dc}}}$

Two coils P and Q are kept near each other. When no current flows through coil P and current increases in coil Q at the rate $10 \mathrm{~A} / \mathrm{s}$, the emf in coil P is 12 mV . When coil Q carries no current and current of 1.5 A flows through coil P , the magnetic flux linked with the coil Q in mWb is