If the coefficients of ${x}^{7}$ in ${\left(a{x}^{2}+\frac{1}{2bx}\right)}^{11}$ and ${x}^{-7}$ in ${\left(ax-\frac{1}{3b{x}^{2}}\right)}^{11}$ are equal, then [JEE Main 2023, 6 Apr (Shift 2)]

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If the coefficients of \({x}^{7}\) in \({\left(a{x}^{2}+\frac{1}{2bx}\right)}^{11}\) and \({x}^{-7}\) in \({\left(ax-\fr…

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