In any $\triangle ABC$,$a(b \cos C - c \cos B)$ equals

An inductor of inductance $L=400\,mH$ and resistors of resistance $R_1=2\,\Omega$ and $R_2=2\,\Omega$ are connected to a battery of emf $E=12\,V$ as shown in the figure. The internal resistance of the battery is negligible. The switch $S$ is closed at $t=0$. The potential drop across $L$ as a function of time is

$A$ circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

Velocity and acceleration vectors of a charged particle moving perpendicular to the direction of a magnetic field at a given instant of time are $\overrightarrow{v}=2 \hat{i}+c \hat{j}$ and $\overrightarrow{a}=3 \hat{i}+4 \hat{j}$ respectively. Then the value of $c$ is

Assuming the sun to be a spherical body of radius $R$ at a temperature of $T \ K$,evaluate the total radiant power incident on the earth at a distance $r$ from the sun. (Where $r_0$ is the radius of the earth and $\sigma$ is Stefan's constant.)

Two cells $E_1$ and $E_2$ having equal e.m.f '$E$' and internal resistances $r_1$ and $r_2$ $(r_1 > r_2)$ respectively are connected in series. This combination is connected to an external resistance '$R$'. It is observed that the potential difference across the cell $E_1$ becomes zero. The value of $R$ will be