A source, approaching with speed u towards the open end of a stationary pipe of length L, is emitting a sound of frequency f_s. The farther end of the pipe is closed. The speed of sound in air is v and f₀ is the fundamental frequency of the pipe. For which of the following combination(s) of u and f_s, will the sound reaching the pipe lead to a resonance?

For a prism of prism angle $$\theta$$ = 60$$^\circ$$, the refractive indices of the left half and the right half are, respectively, n₁ and n₂ (n₂ $$\ge$$ n₁) as shown in the figure. The angle of incidence i is chosen such that the incident light rays will have minimum deviation if n₁ = n₂ = n = 1.5. For the case of unequal refractive indices, n₁ = n and n₂ = n + $$\Delta$$n (where $$\Delta$$n << n), the angle of emergence e = i + $$\Delta$$e. Which of the following statement(s) is(are) correct?

A physical quantity $$\overrightarrow S $$ is defined as $$\overrightarrow S = (\overrightarrow E \times \overrightarrow B )/{\mu _0}$$, where $$\overrightarrow E $$ is electric field, $$\overrightarrow B $$ is magnetic field and $$\mu$$₀ is the permeability of free space. The dimensions of $$\overrightarrow S $$ are the same as the dimensions of which of the following quantity(ies)?

A heavy nucleus N, at rest, undergoes fission N $$\to$$ P + Q, where P and Q are two lighter nuclei. Let $$\delta$$ = M_N $$-$$ M_P $$-$$ M_Q, where M_P, M_Q and M_N are the masses of P, Q and N, respectively. E_P and E_Q are the kinetic energies of P and Q, respectively. The speeds of P and Q are v_P and v_Q, respectively. If c is the speed of light, which of the following statement(s) is(are) correct?