Electric Flux & Gauss's Law question from MHT CET 2020 (16 Oct, Shift 1)

Answer: (c)

1. Charge $q = 4\pi R^2 \sigma$; outside, $E = \frac{q}{4\pi\varepsilon_0 r^2} = \frac{\sigma R^2}{\varepsilon_0 r^2}$.
2. $\sigma = \varepsilon_0 E \left(\frac{r}{R}\right)^2$
3. So the answer is (c).