InterviewSolution
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InterviewSolution
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If the coefficients of `x^-2` and `x^-4` the expansion of `(x^(1/3) +1/(2x^(1/3)))^18`, are `m` and `n` respectively, then `m/n` is equal toA. `(5)/(4)`B. `(4)/(5)`C. 27D. 182 |
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Answer» Correct Answer - d Let `T_(r+1)` be the `(r +1)^(th)` term in the expansion of `(x^(1//3) + (1)/(2x^(1//3)))^(18)`. The `T_(r+1) = ""^(18)C_(r) (x^(1//3))^(18-r) ( (1)/(2x^(1//3)))^(r) = ""^(18)C_(r) x ^(6 (2r)/(3))2^(-r)` ltbr. This will contain `x^(-2)` if, ` 6- (2r)/(3) = -2 rArr r = 12` `therefore m = ` Coefficient of `x^(-2) = ""^(18)C_(12) 2^(-12)` For the coefficient of `x^(-4)`, we must have ` 6 - (2r)/(3) = - 4 rArr r = 15` `because n = ` Coefficient of `x^(-4) = ""^(18)C_(15) 2^(-15)` Hence, `(m)/(n) = (""^(18)C_(12) 2^(-12))/(""^(18)C_(15) 2^(-12))= (18!)/(6!12!)xx(3!15!)/(18!)xx2^(3) = (15xx14xx13xx8)/(6xx5xx4)= 182` |
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