Explanation

(d)
The position of the points $(1,\ 2)$ and $(2,\ 1)$ with respect to the circle $x^{2} + y^{2} = 9$ is given by $1^{2} + 2^{2} = 5 < 9$ and $2^{2} + 1^{2} = 5 < 9$. Thus, both $P$ and $Q$ lie incide $C$
The position of the points $(1,\ 2)$ and $(2,\ 1)$ with respect to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$ is given by
$\because\frac{1^{2}}{9} + \frac{2^{2}}{4} = \frac{1}{9} + 1 > 1$
And $\frac{2^{2}}{9} + \frac{1}{4} = \frac{16 + 9}{36} = \frac{25}{36} < 1,$
$P$ lies outside $E$ and $Q$ lies inside $E$. Thus, $P$ lies inside $C$ but outside $E$