Electric Flux & Gauss's Law question from JEE Main 2022 (29 Jul, Shift 1)

Answer: (c)

1. Enclosed charge: $q = \int_0^r \rho_0\left(\frac{3}{4} - \frac{r}{R}\right)4\pi r^2 dr = 4\pi\rho_0\left(\frac{r^3}{4} - \frac{r^4}{4R}\right) = \pi\rho_0 r^3\left(1 - \frac{r}{R}\right)$
2. Gauss's law: $E = \frac{q}{4\pi\varepsilon_0 r^2} = \frac{\rho_0 r}{4\varepsilon_0}\left(1 - \frac{r}{R}\right)$
3. So the answer is (c).