When work is done on a body by an external force,its

When a system is taken from state $i$ to state $f$ along the path $iaf,$ it is found that $Q = 50 \, cal$ and $W = 20 \, cal$. Along the path $ibf$,$Q = 36 \, cal$. Work done along the path $ibf$ will be ........... $cal$.

Two concentric hollow spherical shells have radii $r$ and $R$ $(R \gg r)$. $A$ charge $Q$ is distributed on them such that the surface charge densities are equal. The electric potential at the centre is

If for a real number $y$,$[y]$ is the greatest integer less than or equal to $y$,then the value of the integral $\int_{\frac{\pi}{2}}^{\frac{3\pi}{2}} [2 \sin x] \,dx$ is

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.

If $x$ is real,then the maximum and minimum values of the expression $\frac{x^2-3x+4}{x^2+3x+4}$ are