The temperature in $K$ at which $\Delta G = 0$ for a given reaction with $\Delta H = -20.5 \ kJ \ mol^{-1}$ and $\Delta S = -50.0 \ J \ K^{-1} \ mol^{-1}$ is:

$A$ bomb moving with velocity $(40 \hat{i} + 50 \hat{j} - 25 \hat{k}) \text{ m/s}$ explodes into two pieces of mass ratio $1:4$. After the explosion,the smaller piece moves away with velocity $(200 \hat{i} + 70 \hat{j} + 15 \hat{k}) \text{ m/s}$. The velocity of the larger piece after the explosion is:

If the power dissipated in the $3\,\Omega$ resistor is $27\,W$,what is the power dissipated in the $2\,\Omega$ resistor (in $,W$)?

The density of gas $A$ is twice that of gas $B$. At the same temperature,the molecular weight of gas $B$ is twice that of gas $A$. The ratio of the pressure of gas $A$ to gas $B$ is:

The integrating factor of the differential equation $x \log x \frac{dy}{dx} + y = 2 \log x$ is given by

$A$ primary coil and a secondary coil are placed close to each other. $A$ current, which changes at the rate of $25 \, A$ in a millisecond, is present in the primary coil. If the mutual inductance is $92 \times 10^{-6} \, H$, then the value of the induced emf in the secondary coil is: