An electromagnetic wave, whose wave normal makes an angle of $$45^{\circ}$$ with the vertical, travelling in air strikes a horizontal liquid surface. While travelling through the liquid it gets deviated through $$15^{\circ}$$. What is the speed of the electromagnetic wave in the liquid, if the speed of electromagnetic wave in air is $$3 \times 10^8 \mathrm{~m} / \mathrm{s}$$ ? $$\left(\sin 30^{\circ}=0.5, \sin 45^{\circ}=\frac{1}{\sqrt{2}}\right)$$

The difference in length between two rods $$\mathrm{A}$$ and $$\mathrm{B}$$ is $$60 \mathrm{~cm}$$ at all temperatures. If $$\alpha_{\mathrm{A}}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C}$$ and $$\beta_{\mathrm{B}}=27 \times 10^{-6} /{ }^{\circ} \mathrm{C}$$, the lengths of the two rods are

A parallel plate capacitor is charged by a battery and battery remains connected. The dielectric slab of constant '$$\mathrm{K}$$' is inserted between the plates and then taken out. Then electric field between the plates

From a disc of mass '$$M$$' and radius '$$R$$', a circular hole of diameter '$$R$$' is cut whose rim passes through the centre. The moment of inertia of the remaining part of the disc about perpendicular axis passing through the centre is