InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Find the term independent of `x`in the expansion of `(1+x+2x^3)[(3x^2//2)-(1//3)]^9`A. `1//3`B. `17//54`C. `1//4`D. No such term exists in the expansion |
|
Answer» Correct Answer - B Given expansion is `(1+x+2x^(3))((3)/(2)x^(2)-(1)/(3x))^(9)` `=(1+x+2x^(2))[((3)/(2)x^(2))^(9)-""^(9)C_(1)((3)/(2)x^(2))^(8).(1)/(3x).....+""^(9)C_(6)((3)/(2)x^(2))^(3)((1)/(3x))^(6)-""^(9)C_(7)((3)/(2)x^(2))^(2)((1)/(3x))^(7).....]` In the second bracket we have to search out terms of `x^(0) and (1)/(x^(3))` which when multipiled with terms 1 and `2x^(3)` in the first bracket will give a term independent of x. The term containing `(1)/(x)` will not occur in the 2nd bracket. `therefore` Term independent of x `=1-[""^(9)C_(6)(3^(3))/(2^(3)).(1)/(3^(6))]-2x^(3)[""^(9)C_(7)(3^(2))/(2^(2)).(1)/(3^(7)).(1)/(x^(3))]` `=[(9.8.7)/(1.2.3).(1)/(8.27)]-2[(9.8)/(1.2).(1)/(4.243)]` `=(7)/(18)-(2)/(27)=(17)/(54)` |
|