Ten moles of an ideal monoatomic gas, initially in state $\boldsymbol{a}$ at atmospheric pressure and temperature $T_a=27^{\circ} \mathrm{C}$, is enclosed in a metal cylinder of volume $V_0$ fitted with a frictionless piston. The gas is suddenly compressed to state $\boldsymbol{b}$ with volume $V_0 / 3$. Now, keeping the piston stationary, the cylinder is submerged in a water bath of temperature $11^{\circ} \mathrm{C}$ until the gas reaches the temperature of the water bath, which is denoted as state $\boldsymbol{c}$. Finally, while still in the water bath, the piston is brought slowly to its initial position, which is denoted as state $\boldsymbol{f}$. If $R$ is universal gas constant, then the correct option(s) is/are :

[Given: $9^{1 / 3}=2.08$ ]

Two thin wires, Wire-1 of diameter 0.650 mm and Wire-2 of unknown diameter d are given. To obtain the value of d, the diameters of the two wires are measured with a screw gauge. The screw gauge has a pitch of 0.5 mm and there are 100 divisions on the circular scale (CS). The smallest division on the linear scale (LS) is 0.5 mm. The table shows the readings of LS and CS for the measurements. The value of d (in µm) is :

In a single slit diffraction experiment, a slit of width $(0.016 \pm 0.002)$ mm is used to measure the wavelength of a monochromatic light source. In the diffraction pattern, the angular distance between the central maximum and first minimum is measured to be $(2^{\circ} \pm 40')$. The value of the fractional error in the measurement of wavelength is :

[Given : $\sin(2^{\circ}) = 0.035$]

As shown in the figure, a ray AB of unpolarized light enters from water of refractive index $n_w = \frac{4}{3}$ into a medium of refractive index $n_p = \frac{4}{\sqrt{3}}$ after passing through a glass plate of refractive index $n_g = 1.5$ and a layer of water. At a particular incident angle $i$ the reflected ray CD is polarized in the direction as shown in the figure. The value of $i$ (in degrees) is :