The work done in placing a charge of $8 \times 10^{-18} \ C$ on a capacitor of capacitance $100 \ \mu F$ is:

$A$ curve passes through the point $\left(1, \frac{\pi}{6}\right)$. Let the slope of the curve at each point $(x, y)$ be $\frac{y}{x}+\sec \left(\frac{y}{x}\right)$,where $x>0$. Then,the equation of the curve is:

If $\frac{x^2}{(x^2 + a^2)(x^2 + b^2)} = K \left( \frac{a^2}{x^2 + a^2} - \frac{b^2}{x^2 + b^2} \right)$,then $K =$

If $\left[\begin{array}{rrr}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$ is a singular matrix,then $x$ is equal to

If a polygon of $n$ sides has $275$ diagonals,then $n$ is equal to

What is the nucleus of a bacterium known as?