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Three plane mirrors form an equilateral triangle with each side of length 𝐿. There is a small hole at a distance 𝑙 > 0 from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle 𝜃 and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane. Which of the following statement(s) is(are) correct? (A) The ray of light will come out for 𝜃 = 30∘, for 0 < 𝑙 < 𝐿. (B) There is an angle for 𝑙 = � � at which the ray of light will come out after two reflections. (C) The ray of light will NEVER come out for 𝜃 = 60∘ , and 𝑙 = � � . (D) The ray of light will come out for 𝜃 = 60∘ , and 0 < 𝑙 < � � after six reflections.

An ideal gas of density 𝜌 = 0.2 𝑘𝑔 𝑚�� enters a chimney of height ℎ at the rate of 𝛼 = 0.8 𝑘𝑔 𝑠�� from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is 𝐴� = 0.1 𝑚� and the upper end is 𝐴� = 0.4 𝑚�. The pressure and the temperature of the gas at the lower end are 600 𝑃𝑎 and 300 𝐾, respectively, while its temperature at the upper end is 150 𝐾. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take 𝑔 = 10 𝑚 𝑠�� and the ratio of specific heats of the gas 𝛾 = 2. Ignore atmospheric pressure. Which of the following statement(s) is(are) correct? (A) The pressure of the gas at the upper end of the chimney is 300 𝑃𝑎. (B) The velocity of the gas at the lower end of the chimney is 40 𝑚 𝑠�� and at the upper end is 20 𝑚 𝑠��. (C) The height of the chimney is 590 𝑚. (D) The density of the gas at the upper end is 0.05 𝑘𝑔 𝑚��.