Two cylinders \(A\) and \(B\) of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. \(B\) is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is:

Two bodies of mass, \(4~\text{kg}\) and \(6~\text{kg}\), are tied to the ends of a massless string. The string passes over a pulley, which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (\(g\)) is:

For the logic circuit shown, the truth table is:

An iron rod of susceptibility \(599\) is subjected to a magnetizing field of \(1200~\text{A m}^{-1}.\) The permeability of the material of the rod is:
\((\mu_0 = 4 \pi\times 10^{-7}~\text{T mA}^{-1})\)
1. \(8.0\times 10^{-5}~\text{T mA}^{-1}\)
2. \(2.4\pi\times 10^{-5}~\text{T mA}^{-1}\)
3. \(2.4\pi\times 10^{-7}~\text{T mA}^{-1}\)
4. \(2.4\pi\times 10^{-4}~\text{T mA}^{-1}\)

The capacitance of a parallel plate capacitor with air as a medium is \(6~\mu\text{F}.\) With the introduction of a dielectric medium, the capacitance becomes \(30~\mu\text{F}.\)$$ The permittivity of the medium is:
\(\left(\varepsilon_0=8.85 \times 10^{-12} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\right )\)
1. \(1.77 \times 10^{-12}~ \text{C}^2 \text{N}^{-1} \text{m}^{-2}\)
2. \(0.44 \times 10^{-10} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\)
3. \(5.00 ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\)
4. \(0.44 \times 10^{-13} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\)

An AC voltage source is connected to a series \(LCR\) circuit. When \(L\) is removed from the circuit, the phase difference between current and voltage is \(\dfrac{\pi}{3}\). If \(C\) is instead removed from the circuit, the phase difference is again \(\dfrac{\pi}{3}\) between current and voltage. The power factor of the circuit is:
1. \(0.5\)
2. \(1.0\)
3. \(-1.0\)
4. zero

A capillary tube of radius \(r\) is immersed in water and water rises in it to a height \(h.\) The mass of the water in the capillary is \(5\) g. Another capillary tube of radius \(2r\) is immersed in water. The mass of water that will rise in this tube is:

A ray is incident at an angle of incidence \(i\) on one surface of a small angle prism (with the angle of the prism \(A\)) and emerges normally from the opposite surface. If the refractive index of the material of the prism is $\mathrm{}$\(\mu,\) then the angle of incidence is nearly equal to: