One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight $$\alpha$$W is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of (2$$\sqrt 2 $$)W. Which of the following statement(s) is(are) correct?

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)?