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

Assertion : In the purely resistive element of a series $LCR$ $AC$ circuit,the maximum value of $rms$ current increases with an increase in the angular frequency of the applied $emf$.
Reason : $I_{\max} = \frac{\varepsilon_{\max}}{Z}$,where $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$ and $I_{\max}$ is the peak current in a cycle.

The equation $\frac{1}{r} = \frac{1}{8} + \frac{3}{8} \cos \theta$ represents

The accessory glands of the human male reproductive system are:

Water is being poured at the rate of $36 \ m^3 / min$ into a cylindrical vessel,whose circular base has a radius of $3 \ m$. Then the water level in the cylinder is rising at the rate of:

$A$ particle moves along the curve $y=x^2+2x$. The point on the curve such that the $x$ and $y$ coordinates of the particle change at the same rate is