1.

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 ratio of the coefficient of second term from the beginning and the end in the expansion of B , is

Answer»

125
625
3125
15625

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 of " T_(2) " in" ((5x)/(2) + (x^(-2))/(2))^(8))/("coefficient of " T_(2) " in" ((x^(-2))/(2) + (5x)/(2))^(8))= (""^(8)C_(1) ((5)/(2))^(7) ((1)/(2)))/(""^(8)C_(1) ((1)/(2))^(7) ((5)/(2))) = 5^(6) = 15625`


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