c
According to questions
$l \propto \,{h^p}{c^q}{G^r}$
$l = k\,\,{h^p}$ ..............($i$)
Writting dimensions of physical quantities on both sides
$\left[ {{M^0}L{T^0}} \right] = {\left[ {M{L^2}{T^{ - 1}}} \right]^p}{\left[ {L{T^{ - 1}}} \right]^q}{\left[ {{M^{ - 1}}{L^3}{T^{ - 2}}} \right]^r}$
Applying the principle of homogeneity of dimensions we get
$P - r = 0$ .........($ii$)
${2_p} + q + 3r = 1$ ............($iii$)
$ - P - q - 2r = 0$ ................($iv$)
Solving eqns. ($ii$), ($iii$), and ($iv$), we get
$P = r = \frac{1}{2},q = - \frac{3}{2}$
From eqn.$\left( i \right)\,l = \frac{{\sqrt {hG} }}{{_c3/2}}$