A monoatomic ideal gas at pressure $P$ and volume $V$ is first adiabatically compressed to volume $V / 8$ and then is allowed to expand isothermally back to its original volume. What is the final pressure of the gas?

A uniform taut string with two point charges $q$ and $-q$ attached to its ends passes over two massless pullies kept $L$ distance apart as shown in the fgure. If $f$ is the fundamental frequency of the part of the string over pullies, which of the following statements is correct?

Two uniformly charged concentric thin spherical shells of radii $r_1$ and $r_2$ have charges $+Q$ and $-Q$, respectively. How does the electrostatic potential vary with distance from the center of the shells?

Consider a very long cylinder of radius $a$ having a uniform positive charge density $\rho$. A sphere of radius $a$ has been carved out (see figure), leaving no charge in that region. The distance radially outward to the cylinder, as measured from the center of the sphere is $x$. At what value of $x$ will the electric field be maximum?