TS EAMCET · Maths · Binomial Theorem
The coefficient of \(x^{24}\) in the expansion of \(\left(1+x^2\right)^{12}\left(1+x^{12}\right)\left(1+x^{24}\right)\) is
- A \({ }^{12} C_6\)
- B \({ }^{12} C_6+2\)
- C \({ }^{12} C_6+4\)
- D \({ }^{12} C_6+6\)
Answer & Solution
Correct Answer
(B) \({ }^{12} C_6+2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Now, }\left(1+x^2\right)^{12}\left(1+x^{12}+x^{24}+x^{36}\right) \\ & \begin{array}{r}=\left[1+{ }^{12} C_1\left(x^2\right)+{ }^{12} C_2\left(x^2\right)^2+{ }^{12} C_3\left(x^2\right)^3\right. \\ \quad+{ }^{12} C_4\left(x^2\right)^4+{ }^{12}…
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