A) \[^{12}{{C}_{6}}\]
B) \[^{12}{{C}_{6}}+2\]
C) \[^{12}{{C}_{6}}+4\]
D) \[^{12}{{C}_{6}}+6\]
Correct Answer: B
Solution :
Now,\[{{(1+{{x}^{2}})}^{12}}(1+{{x}^{12}}+{{x}^{24}}+{{x}^{36}})\] \[=[1{{+}^{12}}{{C}_{1}}({{x}^{2}}){{+}^{12}}{{C}_{2}}{{({{x}^{2}})}^{2}}{{+}^{12}}{{C}_{3}}{{({{x}^{2}})}^{3}}\] \[{{+}^{12}}{{C}_{4}}{{({{x}^{2}})}^{4}}{{+}^{12}}{{C}_{5}}{{({{x}^{2}})}^{5}}{{+}^{12}}{{C}_{6}}{{({{x}^{2}})}^{6}}\] \[+...{{+}^{12}}{{C}_{12}}{{({{x}^{2}})}^{12}}]\times (1+{{x}^{12}}+{{x}^{24}}+{{x}^{36}})\] Coefficient of\[{{x}^{24}}{{=}^{12}}{{C}_{6}}{{+}^{12}}{{C}_{12}}+1\] \[{{=}^{12}}{{C}_{6}}+2\]
You need to login to perform this action.
You will be redirected in
3 sec
