**The correct option is C) \(\sqrt{\dfrac{Gh}{c^5}}\)**

Explaination::

\(F = \dfrac{GM^2}{R^2} \Rightarrow G = [M^{-1} L^3 T^{-2}]\)

\(E = hv \Rightarrow h = [ML^2 T^{-1}]\)

\(C = [LT^{-1}]\)

\(t \propto G^x h^y C^z\)

\([M^0 L^0T^1] = [M^{-x + y} L^{3x + 2y + z} T^{-2x - y - z}]\)

on comparing the powers of M, L, T

\(-x + y = 0 \Rightarrow x = y\)

\(3x + 2y + z = 0 \Rightarrow 5x + z = 0\)

\(-2x - y - z = 1 \Rightarrow 3x+ z = -1\)

on solving (i) and (ii) \(x = y = \dfrac{1}{2}, z = -\dfrac{5}{2}\)

\(t \propto \sqrt{\dfrac{Gh}{C^5}}\)