Step 1: Find the dimensions of mass.
We know that the dimensions of \({h}=[{h}]=\left[{ML}^2{T}^{-1}\right]\)
\({[{C}]=\left[{LT}^{-1}\right]\left[{m}_\theta\right]={M}}\)
\({[{G}]=\left[{M}^{-1}{L}^3{T}^{-2}\right]} \)
\({[{e}]=[{AT}]\left[{m}_{{p}}\right]=[{M}]} \)
\(\frac{{hc}}{{G}}=\frac{\left[{ML}^2 {T}^{-1}\right]\left[{LT}^{-1}\right]}{\left[{M}^{-1}{L}^3 {T}^{-2}\right]}=\left[{M}^2\right] \)
\(\Rightarrow {M}=\sqrt{\frac{{hc}}{{G}}} \)$$

Step 2: Find the dimensions of length.
Similarly, \( \frac{{h}}{{c}}=\frac{\left[{ML}^2 {T}^{-1}\right]}{\left[{LT}^{-1}\right]}=[{ML}]\)
\({L}=\frac{{h}}{{cM}}=\frac{{h}}{{c}} \sqrt{\frac{{G}}{{hc}}}=\frac{\sqrt{{G}}}{{c}^{3 / 2}}\)
As, \( {c}={LT}^{-1}\)
\(\Rightarrow [{T}]=\frac{[{L}]}{[{C}]}=\frac{\sqrt{{Gh}}}{{c}^{3 / 2} {C}}=\frac{\sqrt{{Gh}}}{{C}^{5 / 2}} \)
Therefore, (a), (b), or (d) can be used to express \(L, M,\) and \(T\) in terms of three chosen fundamental quantities.
Hence, option (2) is the correct answer.