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$If the coefficient of x^{7} in {({ax}^{2} - \frac{1}{bx})}^{11} equals the coefficient of x^{- 7} in {(ax - \frac{1}{{bx}^{2}})}^{11}, then a and b satisfy the relation$

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Correct option is D

Coefficient of x7 in ax2+1bx11 is 11C5a61b5 , Coefficient of x−7 in ax−1bx211 is 11C6a51b6 11C6a5⋅1b6=11C5⋅a6−1b5⇒ab= 11C6 11C5=66=1

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If the coefficient of x7 in ax2−1bx11 equals the coefficient of x−7 in ax−1bx211 , then a and b satisfy the relation

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$If the coefficient of x^{7} in {({ax}^{2} - \frac{1}{bx})}^{11} equals the coefficient of x^{- 7} in {(ax - \frac{1}{{bx}^{2}})}^{11}, then a and b satisfy the relation$