$A$ constant torque acting on a uniform circular wheel changes its angular momentum from $A_0$ to $4A_0$ in $4 \ s$. The magnitude of this torque is

$A$ homogeneous equation of second degree in $x$ and $y$ represents which of the following?

$ f: R \rightarrow R $ and $ g:[0, \infty) \rightarrow R $ are defined by $ f(x)=x^{2} $ and $ g(x)=\sqrt{x} $. Which one of the following is not true?

If $\frac{x^3}{(2x-1)(x+2)(x-3)} = A + \frac{B}{2x-1} + \frac{C}{x+2} + \frac{D}{x-3}$,then $A$ is equal to

$A$ $4 \mu F$ capacitor is charged by a $200 \ V$ battery. It is then disconnected from the supply and connected to another uncharged $2 \mu F$ capacitor. During the process,the loss of energy (in $J$) is:

$138 \ g$ of ethyl alcohol is mixed with $72 \ g$ of water. The ratio of mole fraction of alcohol to water is