In the expansion of {left( frac{a}{x} + bx ri | vedclass

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(C) The general term in the expansion of ${\left( \frac{a}{x} + bx \right)^{12}}$ is given by $T_{r+1} = {^{12}C_r} \left( \frac{a}{x} \right)^{12-r}

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$12a^{11}b$

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(C) The general term in the expansion of ${\left( \frac{a}{x} + bx \right)^{12}}$ is given by $T_{r+1} = {^{12}C_r} \left( \frac{a}{x} \right)^{12-r} (bx)^r$. $T_{r+1} = {^{12}C_r} a^{12-r} x^{-(12-r)} b^r x^r$ $T_{r+1} = {^{12}C_r} a^{12-r} b^r x^{2r-12}$. To find the coefficient of $x^{-10}$,we set the exponent of $x$ equal to $-10$: $2r - 12 = -10$ $2r = 2$ $r = 1$. Substituting $r = 1$ into the general term: $T_{1+1} = {^{12}C_1} a^{12-1} b^1 x^{2(1)-12}$ $T_2 = 12 a^{11} b x^{-10}$. Thus,the coefficient of $x^{-10}$ is $12a^{11}b$.

In the expansion of ${\left( \frac{a}{x} + bx \right)^{12}}$,the coefficient of $x^{-10}$ is:

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