$A$ Carnot engine whose low temperature reservoir is at $7^{\circ} C$ has an efficiency of $50 \%$. It is desired to increase the efficiency to $70 \%$. By how many degrees should the temperature of the high temperature reservoir be increased in $K$?

In the circuit shown,the energy stored in the $1\,\mu F$ capacitor is ..... $\mu J$.

The adjoining diagram shows the spectral energy density distribution $E_{\lambda}$ of a black body at two different temperatures. If the areas under the curves are in the ratio $16 : 1$,the value of temperature $T$ is ........ $K$. (in $,000$)

The wavelengths of two notes in air are $\frac{36}{195} ~m$ and $\frac{36}{193} ~m$. Each note produces $10$ beats per second separately with a third note of fixed frequency. The velocity of sound in air in $m/s$ is

Many ionic crystals dissolve in water because

Two masses of $10\,kg$ and $20\,kg$ respectively are connected by a massless spring as shown in the figure. $A$ force of $200\,N$ acts on the $20\,kg$ mass. At the instant when the $10\,kg$ mass has an acceleration of $12\,m/s^2$ towards the right,the acceleration of the $20\,kg$ mass is: (in $,m/s^2$)