In a cyclic process,the work done by the system is

In Young's double slit experiment,one of the slits is wider than the other,so that the amplitude of the light from one slit is double that from the other slit. If $I_m$ be the maximum intensity,the resultant intensity when they interfere at phase difference $\phi$ is given by:

Consider the two following statements $A$ and $B$,and identify the correct choice given in the answers :
$(A)$ In photovoltaic cells the photoelectric current produced is not proportional to the intensity of incident light.
$(B)$ In gas-filled photoemissive cells,the velocity of photoelectrons depends on the wavelength of the incident radiation.

$A$ cannon shell fired breaks into two equal parts at its highest point. One part retraces its path to the cannon with kinetic energy $E_1$,and the kinetic energy of the second part is $E_2$. The relation between $E_1$ and $E_2$ is:

The solution of the differential equation $\frac{dy}{dx} = \frac{y}{x} + \frac{\phi(y/x)}{\phi'(y/x)}$ is

If $\vec{a} = \hat{i} - \hat{j} - \hat{k}$ and $\vec{b} = \lambda\hat{i} - 3\hat{j} + \hat{k}$ and the orthogonal projection of $\vec{b}$ on $\vec{a}$ is $\frac{4}{3}(\hat{i} - \hat{j} - \hat{k})$,then $\lambda$ is equal to: