When magnetic flux changes from $6.5 \times 10^{-2} \mathrm{~Wb}$ to $11 \times 10^{-2} \mathrm{~Wb}$ and the change in current is 0.03 A , the coefficient of mutual inductance will be

At a place, the length of the oscillating simple pendulum is made $\frac{1}{4}$ times keeping amplitude same then the total energy will be

125 small water drops of same size fall through air with constant velocity $4 \mathrm{~cm} / \mathrm{s}$. They coalesce to form a big drop. The terminal velocity of the big drop is

$$ \begin{aligned} & \text { If }|\vec{a}|=\sqrt{26},|\vec{b}|=7 \\ & |\vec{a} \times \vec{b}|=35 \text {, find } \vec{a} \cdot \vec{b} \end{aligned} $$