Three blocks,$A, B$ and $C,$ of masses $4\,kg, 2\,kg$ and $1\,kg$ respectively,are in contact on a frictionless surface,as shown. If a force of $14\,N$ is applied on the $4\,kg$ block,then the contact force between $A$ and $B$ is ....... $N$.

If $\frac{e^x + 2}{(e^x - 1)(2e^x - 3)} = -\frac{3}{e^x - 1} + \frac{B}{2e^x - 3}$,then $B = $

Which of the following statements are true about acceleration due to gravity $(g)$ of the earth (where $r$ is distance from the centre of the earth and $R$ is the radius of the earth)?
$(a)$ $g$ decreases in moving away from the centre,if $r > R$.
$(b)$ $g$ decreases in moving away from the centre,if $r < R$.
$(c)$ $g$ is zero at the centre of the earth.
$(d)$ $g$ at the equator decreases,if the earth stops rotating about its axis.

If $Q$ denotes the set of all rational numbers and $f\left(\frac{p}{q}\right)=\sqrt{p^2-q^2}$ for any $\frac{p}{q} \in Q$,then observe the following statements.
$I$. $f\left(\frac{p}{q}\right)$ is real for each $\frac{p}{q} \in Q$
$II$. $f\left(\frac{p}{q}\right)$ is a complex number for each $\frac{p}{q} \in Q$.
Which of the following is correct?

Molar heat capacity of water in equilibrium with ice at constant pressure is

If $\frac{dy}{dx} = \frac{xy + y}{xy + x}$,then the solution of the differential equation is