Explanation

(c)
We have, $px^{2} + qx + 1 = 0$, for real roots discriminant $\geq 0$
$\Rightarrow q^{2} - 4p \geq 0\ \Rightarrow q^{2} \geq 4p$
For $p = 1,\ q^{2} \geq 4\ \Rightarrow q = 2,\ 3,\ 4$
$p = 2,\ q^{2} \geq 8\ \Rightarrow q = 3,\ 4$
$p = 3,\ q^{2} \geq 12\ \Rightarrow q = 4$
$p = 4,\ q^{2} \geq 16\ \Rightarrow q = 4$
Total seven solutions are possible.