InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
The numerically greatest term in the expansion of `(1 + x)^(10)` when ` x = 2//3`, isA. `4^(th)`B. `5^(th)`C. `6^(th) `D. `3^(3d)` |
|
Answer» Correct Answer - b Let `T_(r) and T_( r+1) ` denote the `r^(th) and (r + 1)^(th)` terms in the expansion of `(1 + x)^(10)`. Then ltbr. `T_(r) = ""^(10)C_(r-1) x^(r-1) and T_(r +1) = ""^(10)C_(r) x^(r)` . `therefore (T_(r +1))/(T_(r)) = (""^(10)C_(r) x^(r))/(""^(10)C_(r-1)x^(r-1))` `rArr (T_(r +1))/(T_(r)) = (""^(10)C_(r) )/(""^(10)C_(r-1))x` `rArr (T_(r +1))/(T_(r)) = (10! )/((10-r)!r!)xx((10 - r+1)!(r-1))/(10!)x` `rArr (T_(r +1))/(T_(r)) = (11-r)/(r)x rArr (T_(r +1))/(T_(r))= ((11 -r)/(r))xx(2)/(3) [because x = 2 //3]` Now ` (T_(r +1))/(T_(r))gt1 rArr ( (11-r)/(r))xx(2)/(3) gt 1 rArr22 gt 5r rArr r lt 4 (2)/(5)` `therefore (4 +1) ^(th) `i.e. 5th term is the greatest term. |
|