Explanation

(c)
Given, $f(x) = 2x^{4} - 13x^{2} + ax + b$ is divisible by
$(x - 2)(x - 1)$
$\therefore\ \ \ \ f(2) = 2(2)^{4} - 13(2)^{2} + a(2) + b = 0$
$\Rightarrow \ \ \ \ \ \ 2a + b = 20\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
And $f(1) = 2(1)^{4} - 13(1)^{2} + a + b = 0$
$\Rightarrow \ \ \ \ \ \ \ \ a + b = 11\ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(ii)$
On solving Eqs. (i) and (ii), we get
$\ a = 9,\ \ \ \ \ \ \ b = 2$