Binomial Theorem And Its Simple Applications Question 122
Question: The coefficient of $ x^{5} $ in the expansion of $ {{(x^{2}-x-2)}^{5}} $ is
Options:
A) -83
B) -82
C) -86
D) -81
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] $ {{(x-2)}^{5}}{{(x+1)}^{5}} $
$ ={{[}^{5}}C_0{x^{5-5}}C_1x^{4}\times 2+…] $
$ {{[}^{5}}C_0{{+}^{5}}C_1x+…] $
$ \Rightarrow $ Coefficient of $ x^{5} $
$ {{=}^{5}}C_0^{5}C_5{{-}^{5}}C_1\times 2{{\times }^{5}}C_4{{+}^{5}}C_2\times 2^{2}{{\times }^{5}}C_3{{-}^{5}}C_3\times 2^{3}{{\times }^{5}}C_2 $
$ {{+}^{5}}C_4\times 2^{4}{{\times }^{5}}C_1{{-}^{5}}C_5\times 2^{5}{{\times }^{5}}C_0 $
$ =1-5\times 5\times 2+10\times 10\times 4-10\times 10\times 8+5\times 5\times 16-32 $
$ =-81 $
BETA
