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

$A$ wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of $15^{\circ}$ in time $t \ s$. The increase in angle through which it rotates in the next $2t \ s$ is (in $^{\circ}$)

Two solutions of $KNO_3$ and $CH_3COOH$ are prepared separately. The molarity of both is $0.1 \ M$ and their osmotic pressures are $P_1$ and $P_2$ respectively. The correct relationship between the osmotic pressures is:

In which of the following,ortho/para substitution by an electrophile is very facile?

$A$ thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net electric field $\vec{E}$ at the center $O$ is:

Magnetic induction at the centre of a circular loop of area $\pi \ m^2$ is $0.1 \ T$. The magnetic moment of the loop is ( $\mu_0 = \text{permeability of air}$ ).