Explanation

(c)
Given, $\cos^{- 1}{x + \cos^{- 1}{y + \cos^{- 1}{z + \cos^{- 1}{t = 4\pi}}}}$
Which is possible only when
$\cos^{- 1}{x = \cos^{- 1}{y = \cos^{- 1}{z = \cos^{- 1}{t = \pi}}}}$
[$\because$ Domain of $cos^{- 1}x$ is $\lbrack 0,\ \pi\rbrack$]
$\Rightarrow \ \ x = y = z = t = \cos{\pi = - 1}$
$\therefore x^{2} + y^{2} + z^{2} + t^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ = ( - 1)^{2} + ( - 1)^{2} + ( - 1)^{2} + ( - 1)^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ = 4$