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Solution by Dr. Ananya Rao:Answered in 42 mins

Fringe width is given by β = λD/d. When the apparatus is immersed in liquid of refractive index μ, the wavelength decreases according to λ’ = λ/μ. Therefore, the new fringe width becomes β’ = β/μ. This causes the interference fringes to become narrower and closer together.

Solution by Prof. Kabir Mehta:Answered in 30 mins

At constant pressure, adding an inert gas increases the total volume of the container. This dilution decreases the partial pressure of each gaseous component. According to Le Chatelier’s principle, the system compensates by shifting towards the side with a greater number of moles of gas (Δn = 2 - 1 = +1, which is the forward direction).

Solution by Sara Iqbal, M.Sc.:Answered in 18 mins

During non-cyclic electron transport, water photolysis on the inner surface of the thylakoid membrane releases H+ ions into the lumen. Additionally, the cytochrome b6f complex pumps protons from the stroma into the lumen. Simultaneously, NADP+ reductase in the stroma consumes H+ to form NADPH. This creates a steep proton accumulation in the lumen (pH drops to ~4.5–5.0), making it acidic.

Solution by Er. Rohan Deshmukh:Answered in 25 mins

Use King’s property: ∫[a,b] f(x) dx = ∫[a,b] f(a+b-x) dx. Here a+b-x = π/2 - x. Replacing x gives I = ∫[0,π/2] (cos^n x)/(cos^n x + sin^n x) dx. Adding original I and transformed I yields 2I = ∫[0,π/2] 1 dx = π/2. Therefore, I = π/4 regardless of the power n.