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JEE Main Mathematics question

MathematicsBinomial TheoremJEE Main

For , in the expansion of , the sum of all binomial coefficients lies between and and the term independent of is . Find the value of .

Answer: 2

Solution

The sum of the binomial coefficients is , and gives . The general term is T_{r+1}=\binom8ra^rx^{-\frac34(8-r)+\frac54r}=\binom8ra^rx^{2r-6}, independent of when , so . Then and

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Question ID VK-021269