InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Find the middle term (terms) in the expansion of (i) `((x)/(a) - (a)/(x))^(10)` (ii) `(3x - (x^(3))/(6))^(9)` |
|
Answer» (i) Given expansion is `((x)/(a) - (a)/(x))^(10)` Here, the power of Binomial i.e., `n = 10` is even Since, it has one middle term `((10)/(2) + 1)` th terms i.e., 6 th term `:. T_(6) = T_(5 + 1) = .^(10)C_(5) ((x)/(a))^(10 - 5) ((-a)/(x))^(5)` `= -.^(10)C_(5) ((x)/(a))^(5) ((a)/(x))^(5)` `= - (10 xx 9 xx 8 xx 7 xx 6 xx 5!)/(5! xx 5 xx 4 xx 3 xx 2 xx 1) ((x)/(a))^(5) ((x)/(a))^(-5)` `= - 9 xx 4 xx 7 = - 252` (ii) given expansion is `(3x - (x^(3))/(6))^(9)` Here, `n = 9` Since, the Binomial expansion has two middle terms i.e., `((9 + 1)/(2)) th` and `((9 + 1)/(2) + 1)th` i.e., 5th term and 6th term. `:. T_(5) = T_((4 + 1)) = .^(9)C_(4) (3x)^(9 - 4) (-(x^(3))/(6))^(4)` `= (9 xx 8 xx 7 xx 6 xx 5!)/(4 xx 3 xx 2 xx 1 xx 5!) 3^(5) x^(5) x^(12) 6^(-4)` `= (7 xx 6 xx 3 xx 3^(1))/(2^(4)) x^(17) = (189)/(8) x^(17)` `:. T_(6) = T_(5) = .^(9)C_(5) (3x)^(9 - 5) (- (x^(3))/(6))^(5)` `= - (9 xx 8 xx 7 xx 6 xx 5!)/(5! xx 4 xx 3 xx 2 xx 1) . 3^(4). x^(4). x^(15). 6^(-5)` `= (-21 xx 6)/(3 xx 2^(5)) x^(19) = (-21)/(16) x^(19)` |
|