The product $(A)$ is:

A $6 \, V$ cell with $0.5 \, \Omega$ internal resistance, a $10 \, V$ cell with $1 \, \Omega$ internal resistance and a $12 \, \Omega$ external resistance are connected in parallel. The current (in ampere) through the $10 \, V$ cell is

If $\alpha, \beta, \gamma, \delta$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$,then the value of $4\sin \frac{\alpha}{2} + 3\sin \frac{\beta}{2} + 2\sin \frac{\gamma}{2} + \sin \frac{\delta}{2}$ is equal to

$A$ short magnetic needle is pivoted in a uniform magnetic field of induction $1 ~T$. Now,simultaneously another magnetic field of induction $\sqrt{3} ~T$ is applied at right angles to the first field; the needle deflects through an angle $\theta$ whose value is (in $^{\circ}$)