An aqueous solution of potash alum gives:

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

An electron is projected along the axis of a circular conductor carrying current $I$. The electron will experience:

If $\int_{-1}^{4} f(x) \, dx = 4$ and $\int_{2}^{4} (3 - f(x)) \, dx = 7$,then the value of $\int_{2}^{-1} f(x) \, dx$ is

If the charge on a body is increased by $2 \ C$,the energy stored in it increases by $21 \%$. The original charge on the body in coulomb is

If $\vec{P} \cdot \vec{Q} = PQ$,then the angle between $\vec{P}$ and $\vec{Q}$ is ............. $^\circ$.