Polarisation question from JEE Main 2018 (16 Apr, Shift 1)

Answer: (b)

1. Output $I/2$ with two polarizers means A and B are parallel.
2. C at $\theta$ to A is also at $\theta$ to B: $\frac{I}{2}\cos^2\theta\cos^2\theta = \frac{I}{3}$
3. $\cos^4\theta = \frac{2}{3} \Rightarrow \cos\theta = \left(\frac{2}{3}\right)^{1/4}$
4. So the answer is (b).