InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If the third term in expansion of `(1+x^(log_2x))^5` is `2560` then `x` is equal to (a) `2sqrt2` (b) `1/8` (c) `1/4` (d) `4sqrt2`A. `4 sqrt(2)`B. `(1)/(4)`C. `(1)/(8)`D. `2 sqrt(2)` |
|
Answer» The `(r + 1)` th term in the expansion of `(a + x)^(n)` is given by `T_(r + 1) = .^(n)C_(r ) a^(n - r) x^(r )` `:. 3^(rd)` term in the expansion of `(1 + x^(log_(2)x))^(5)` is `.^(5)C_(2) (1)^(5 - 2) (x^(log_(2)x))^(2)` `implies .^(5)C_(2) (1)^(5 - 2) (x^(log_(2)x))^(2) = 2560` given `implies 10 (x^(log_(2)x))^(2) = 2560` `implies x^((2log_(2)x)) = 256` `implies log_(2) x^(2log_(2)x) = log_(2) = 256` (taking `log_(2)` on both sides ) `implies 2(log_(2)x)(log_(2)x) = 8` `(log_(2)x) = 4` `implies log_(2) = +- 2` `implies log_(2) x = 2` or `log_(2) x = - 2` `implies x = 4` or `x = 2^(-2) = (1)/(4)` |
|