A) 30
B) 60
C) 40
D) None of these
Correct Answer: B
Solution :
We have \[{{(1+{{x}^{2}})}^{5}}{{(1+x)}^{4}}\] =\[({}^{5}{{C}_{0}}+{}^{5}{{C}_{1}}{{x}^{2}}+\,{}^{5}{{C}_{2}}{{x}^{4}}+...)\]\[({}^{4}{{C}_{0}}+{}^{4}{{C}_{1}}x+{}^{4}{{C}_{2}}{{x}^{2}}{{+}^{4}}{{C}_{3}}{{x}^{3}}+{}^{4}{{C}_{4}}{{x}^{4}})\] So coefficient of \[{{x}^{5}}\]in \[[{{(1+{{x}^{2}})}^{5}}{{(1+x)}^{4}}]\] = \[{}^{5}{{C}_{2}}.{}^{4}{{C}_{1}}+{}^{4}{{C}_{3}}.{}^{5}{{C}_{1}}=60.\]
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