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If $p^{2} + q = 2$ then maximum value of the term independent of x in the expansion of ${(p x^{\frac{1}{6}} + q x^{- \frac{1}{3}})}^{9}$ is $(p > 0, q > 0)$

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answer is C.

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Detailed Solution

G.E $= {(p x^{\frac{1}{6}} + \frac{q}{x^{\frac{1}{3}}})}^{9}; r = \frac{9 (\frac{1}{6}) - 0}{\frac{1}{6} + \frac{1}{3}} = 3$
Independent term $T_{4} = {}^{9}C_{3} . P^{6} q^{3} = {}^{9}C_{3} {(p^{2} q)}^{3}$
Maximum of $T_{4}$ is ${}^{9}C_{3}$ =84

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