Binomial Theorem And Its Simple Applications Question 108
Question: The coefficient of $ x^{5} $ in the expansion of $ {{(1+x^{2})}^{5}}{{(1+x)}^{4}} $ is
[EAMCET 1996; UPSEAT 2001; Pb. CET 2002]
Options:
A) 30
B) 60
C) 40
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- We have $ {{(1+x^{2})}^{5}}{{(1+x)}^{4}} $ = $ ({}^{5}C_0+{}^{5}C_1x^{2}+,{}^{5}C_2x^{4}+…) $ $ ({}^{4}C_0+{}^{4}C_1x+{}^{4}C_2x^{2}{{+}^{4}}C_3x^{3}+{}^{4}C_4x^{4}) $
So coefficient of $ x^{5} $ in $ [{{(1+x^{2})}^{5}}{{(1+x)}^{4}}] $ = $ {}^{5}C_2.{}^{4}C_1+{}^{4}C_3.{}^{5}C_1=60. $
BETA
