A) hCG
B) hCG-1
C) \[{{\operatorname{h}}^{-1}}{{K}^{-1}}G\]
D) \[{{\operatorname{h}}^{{}^{1}/{}_{2}}}{{K}^{{}^{1}/{}_{2}}}{{G}^{{}^{-1}/{}_{2}}}\]
Correct Answer: D
Solution :
\[\operatorname{M}\propto {{\left[ C \right]}^{8}}{{\left[ \operatorname{G} \right]}^{b}}{{\left[ h \right]}^{c}}\] \[\propto {{\left[ L{{T}^{-1}} \right]}^{8}}\left[ {{M}^{-1}}{{L}^{3}}{{T}^{-2}} \right]{{\left[ {{\operatorname{ML}}^{2}}{{T}^{-1}} \right]}^{c}}\] \[\propto {{\left[ L \right]}^{\operatorname{a}+3b+2c}}{{\left[ M \right]}^{\operatorname{c}-b}}{{\left[ T \right]}^{-a-2b-c}}\] c - b = 1 (i), a + 3b + 2c = 0 (ii). - a - 2 b - c = 0, a + 2b + c = 0 (iii) from equation (1), (2), and (3) \[\operatorname{a}+3b+2c=0\] \[\operatorname{a}+2b+c=0\] From equation (i), and (iv) \[\operatorname{b}=-\frac{1}{2},\,\,c=\frac{1}{2},\,\,d=\frac{1}{2},\] \[\operatorname{hence}\,\,M\propto {{\left[ C \right]}^{{}^{1}/{}_{2}}}{{\left[ \operatorname{G} \right]}^{{}^{1}/{}_{2}}}{{\left[ \operatorname{h} \right]}^{{}^{1}/{}_{2}}}\]
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