A wide slab consisting of two media of refractive indices n₁ and n₂ is placed in air as shown in the figure. A ray of light is incident from medium n₁ to n₂ at an angle $$\theta$$, where sin$$\theta$$ is slightly larger than 1/n₁. Take refractive index of air as 1. Which of the following statement(s) is(are) correct?

A particle of mass M = 0.2 kg is initially at rest in the xy-plane at a point (x = $$-$$l, y = $$-$$h), where l = 10 m and h = 1 m. The particle is accelerated at time t = 0 with a constant acceleration a = 10 m/s² along the positive x-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by $$\overrightarrow L $$ and $$\overrightarrow \tau $$ respectively. $$\widehat i$$, $$\widehat j$$ and $$\widehat k$$ are unit vectors along the positive x, y and z-directions, respectively. If $$\widehat k$$ = $$\widehat i$$ $$\times$$ $$\widehat j$$ then which of the following statement(s) is(are) correct?

Which of the following statement(s) is(are) correct about the spectrum of the hydrogen atom?

A long straight wire carries a current, I = 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at the distances 1 cm and 4 cm from the wire. At time t = 0, the rod starts moving on the rails with a speed v = 3.0 m/s (see the figure).

A resistor R = 1.4 $$\Omega$$ and a capacitor C₀ = 5.0$$\mu$$F are connected in series between the rails. At time t = 0, C₀ is uncharged. Which of the following statement(s) is(are) correct? [$$\mu$$₀ = 4$$\pi$$ $$\times$$ 10^$$-$$7 SI units. Take ln 2 = 0.7]