Explanation

(d) The arrangement of $n$ metal plates separated by dielectric acts as parallel combination of $(n - 1)$ capacitors.
Therefore, $C = \frac{(n - 1)K\varepsilon_{0}A}{d}$
Here, $C = 100\ pF$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 100 \times 10^{- 12}F$
$\ \ \ \ \ \ \ \ \ \ \ \ K = 4,\ \varepsilon_{0} = 8.85 \times 10^{- 12}C^{2}N^{- 1}m^{- 2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ A = \ \pi r^{2} = 3.14 \times \left( 1 \times 10^{- 2} \right)^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ d = 1\ mm = 1 \times 10^{- 3}$
$\therefore\ \ \ 100 \times 10^{- 12} = \ $
$\ \ \frac{\begin{array}{r}
(n - 1) \times 4 \times \left( 8.85 \times 10^{- 12} \right) \times 3.14 \\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \times \left( 1 \times 10^{- 2} \right)^{2}
\end{array}}{1 \times 10^{- 3}}$
or $\ \ \ \ \ n = \frac{1111.156}{111.156} = 9.99 \approx 10$