Explanation

(d)
Given, $\sin{\left\lbrack \sin^{- 1}{\left( \frac{1}{5} \right) + \cos^{- 1}x} \right\rbrack = 1}$
$\therefore\ \ \ \sin^{- 1}{\left( \frac{1}{5} \right) + \cos^{- 1}{x = \frac{\pi}{2}}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin^{- 1}{\left( \frac{1}{5} \right) = \sin^{- 1}x}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{1}{5}$