The standard entropies of $X_2$,$Y_2$,and $XY_3$ are $60$,$40$,and $50 \ J \ K^{-1} \ mol^{-1}$ respectively. For the reaction $\frac{1}{2}X_2 + \frac{3}{2}Y_2 \to XY_3$,$\Delta H = -30 \ kJ$. What will be the temperature in $K$ at equilibrium?

Two bodies of masses $0.1 \,kg$ and $0.4 \,kg$ move towards each other with the velocities $1 \,m/s$ and $0.1 \,m/s$ respectively. After collision,they stick together. In $10 \,s$,the combined mass travels .......... $m$.

The potential difference across the terminals of the battery shown in the figure is ............ $V$. ($r$ = internal resistance of the battery)

The average kinetic energy of a gas molecule at $27\,^{\circ}C$ is $6.21 \times 10^{-21}\,J$. Its average kinetic energy at $227\,^{\circ}C$ will be

Sodium metal crystallizes in a body-centred cubic $(bcc)$ lattice with a unit cell edge of $4.29 \ \mathring{A}$. The radius of the sodium atom is approximately: .............. $\mathring{A}$

Two metal plates each of area $A$ form a parallel plate capacitor with air in between the plates. The distance between the plates is $d$. $A$ metal plate of thickness $d/2$ and of same area $A$ is inserted between the plates to form two capacitors of capacitances $C_1$ and $C_2$ as shown in the figure. If the effective capacitance of the two capacitors is $C^{\prime}$ and the capacitance of the capacitor initially is $C$,then $C^{\prime}/C$ is