If the coefficient of $x$ in the expansion of $(x^2 + \frac{k}{x})^5$ is $270$,then $k =$

If $\alpha$ is a non-real root of the equation $x^6-1=0$,then $\frac{\alpha^2+\alpha^3+\alpha^4+\alpha^5}{\alpha+1}$ is equal to

Two capacitors $C_1$ and $C_2$ in a circuit are joined as shown in the figure. The potential of point $A$ is $V_1$ and that of $B$ is $V_2$. The potential of point $D$ will be

The velocities of three particles of masses $20 \ g$,$30 \ g$,and $50 \ g$ are $10 \hat{i}$,$10 \hat{j}$,and $10 \hat{k}$ respectively. The velocity of the centre of mass of the three particles is:

Leaf abscission,fruit fall,and bud dormancy occur due to which phytohormone?

If $A$ and $B$ are mutually exclusive events with $P(B) \neq 1$,then $P(A \mid \bar{B})$ is equal to (Here $\bar{B}$ is the complement of the event $B$)