InterviewSolution
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InterviewSolution
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What is the coefficient of `x^(17)` in the expansion of `(3x-(x^(3))/(6))^(9)` ?A. `(189)/(8)`B. `(567)/(2)`C. `(21)/(16)`D. None of these |
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Answer» Correct Answer - A Given expansion is `(3x-(x^(3))/(6))^(9)" where "a=3x, b=(-x^(3))/(6), n=9` `"Now, General Term "=T_(r+1)=""^(n)C_(r)(a)^(n-r),b^(r )` `=""^(9)C_(r),(3x)^(9-r)((-x^(3))/(6))^(r )=""^(9)C_(r).3^(9-r)x^(9-r).((-1)^(r )x^(3r))/(6^(r ))` `=""^(9)C_(r)3^(9-r)(-1)^(r)(x^(9+2r))/(6^(r))` We can get coeff of `x^(17)` when `9+2r=17` `rArr" "2r=17-9` `rArr" "r=(8)/(2)=4` Hence, required coefficient `=""^(9)C_(4)(3^(5))/(6^(4))=(126xx3)/(16)=(189)/(8)` |
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