A) \[{{\,}^{20}}{{C}_{10}}\]
B) \[{{\,}^{30}}{{C}_{25}}\]
C) 1
D) 0
Correct Answer: B
Solution :
\[\because \] \[{{(1+{{x}^{2}})}^{40}}.{{\left( {{x}^{2}}+2+\frac{1}{{{x}^{2}}} \right)}^{-5}}\] \[={{(1+{{x}^{2}})}^{20}}.{{x}^{10}}\] \[={{(1+{{x}^{2}})}^{30}}.{{x}^{20}}\] \[\therefore \] Coefficient of \[{{x}^{10}}\]in \[{{(1+{{x}^{2}})}^{\,30}}.{{x}^{10}}\] \[\Rightarrow \] Coefficient of \[{{x}^{10}}\]in \[{{(1+{{x}^{2}})}^{30}}\]is \[{{\,}^{30}}{{C}_{5}}\] or \[{{\,}^{30}}{{C}_{25}}.\]
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