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A= (5/2+x/2)^n, B=(1+3x)^m Sum of coefficients of expansion of B is 6561 . The difference of the coefficient of third to the second term in the expansion of A is equal to 117 . The value of m is

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Solution :Since , SUM of coefficient of B is 6561 .
` therefore ((5)/(2) + (1)/(2))^(n) = 6561`
` RARR 3^(n) = 6561rArr 3^(n) = 3^(8) `
` therefore n = 8 `
Coefficient` (T_(3) - T_(2)) = 117`
` ""^(m)C_(2) 3^(2) - ""^(m)C_(1) 3^(1) = 117`
` rArr m = 6`


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