A) \[^{12}{{C}_{6}}+2\]
B) \[^{12}{{C}_{5}}\]
C) \[^{12}{{C}_{6}}\]
D) \[^{12}{{C}_{7}}\]
Correct Answer: A
Solution :
\[{{(1+{{t}^{2}})}^{12}}(1+{{t}^{12}})(1+{{t}^{24}})\] = \[(1+{}^{12}{{C}_{1}}{{t}^{2}}+{}^{12}{{C}_{2}}{{t}^{4}}+...{{+}^{12}}{{C}_{4}}{{t}^{8}}+...{{+}^{12}}{{C}_{10}}{{t}^{20}}+....)\]\[(1+{{t}^{12}}+{{t}^{24}}+{{t}^{36}})\] \ Coefficient of \[{{t}^{24}}{{=}^{12}}{{C}_{6}}+2.\]
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