$\int_2^3 \frac{dx}{x^2-x}$ is equal to

Two circular loops $P$ and $Q$ of radii $r$ and $nr$ respectively are made from a uniform wire. The moment of inertia of $Q$ about its axis is four times that of $P$ about its axis. The value of $n$ 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 $a, b$ and $c$ are three non-coplanar vectors and $p, q$ and $r$ are vectors defined by $p=\frac{b \times c}{[a b c]}, q=\frac{c \times a}{[a b c]}$ and $r=\frac{a \times b}{[a b c]}$,then the value of $(a+b) \cdot p+(b+c) \cdot q+(c+a) \cdot r$ is equal to

$\sin ^{-1}\left(\sin \frac{7 \pi}{6}\right) = $

Diffusion current in a $p$-$n$ junction is greater than the drift current in magnitude when: