InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Find the cofficient of the term independent of x in the expansion of `((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x-x^1/2))^10` |
|
Answer» Correct Answer - 210 `(x+1)/((x^(2//3) - x^(1//3))+1) - (x-1)/(x-x^(1//2))` `= ((x^(1//3) +)(x^(2//3) - x^(1//3)+1))/(x^(2//3) - x^(1//3) + 1) - (x^(1//2) + 1)/(x^(1//2))` `= x^(1//3) + 1 - 1 - x^(-1//2)` ` = x^(1//3) - x^(-1//2)` `:. ((x+1)/(x^(2//3) - x^(1//3) + 1) - (x-1)/(x-x^(1//2)))^(10) = (x^(1//3) - x^(-1//2))^(10)` Let `T_(r+1) = .^(100)C_(r) (x^(1//3))^(10-r) (-1)^(r) (-x^(-1//2))^(r )` For the term independent of x, `(10-r)/(3) - (r )/(2) = 0` `rArr 20 - 2r - 3r = 0` `rArr r = 4` So, required coefficient `= .^(10)C_(4)(-1)^(4) = 210` |
|