$A$ 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 $K$?

Find the binomial probability distribution whose mean is $3$ and variance is $2$.

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+a x^2+b x+c=0$,then $\alpha^{-1}+\beta^{-1}+\gamma^{-1}$ is equal to

If $x_n = \cos \frac{\pi}{2^n} + i \sin \frac{\pi}{2^n}$,then $\prod_{n=1}^{\infty} x_n$ is equal to

$A$ parallel plate capacitor with air between the plates has a capacitance of $9 \, pF$. The separation between its plates is $d$. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1 = 3$ and thickness $d/3$,while the other one has dielectric constant $K_2 = 6$ and thickness $2d/3$. The new capacitance of the capacitor is .... $pF$.

The differential equation of all circles which pass through the origin and whose centre lies on the $y$-axis is