The frequency for which a $5\,\mu F$ capacitor has a reactance of $\frac{1}{1000}\,\Omega$ is given by

In a longitudinal section of a root,starting from the tip upward,the four zones occur in the following order:

Systematics refers to the

If $\frac{ax - 1}{(1 - x + x^2)(2 + x)} = \frac{x}{1 - x + x^2} - \frac{1}{2 + x}$,then $a = $

The remainder obtained when the polynomial $x^{64} + x^{27} + 1$ is divided by $(x + 1)$ is:

Given that,$a \alpha^2+2 b \alpha+c \neq 0$ and that the system of equations
$\begin{aligned} & (a \alpha+b) x+a y+b z=0 \\ & (b \alpha+c) x+b y+c z=0 \\ & (a \alpha+b) y+(b \alpha+c) z=0\end{aligned}$
has a non-trivial solution,then $a, b$ and $c$ lie in