WBJEE · Maths · Binomial Theorem
If \(\left(1+x-2 x^2\right)^6=1+a_1 x+a_2 x^2+\ldots+a_{12} x^{12}\), then the value of \(a_2+a_4+a_6+\ldots+a_{12}\) is
- A \(21\)
- B \(31\)
- C \(32\)
- D \(64\)
Answer & Solution
Correct Answer
(B) \(31\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \left(1+x-2 x^2\right)^6=1+a_1 x+a_2 x^2+\ldots+a_{12} x^{12} \\ & x=1 \Rightarrow 0=1+a_1+a_2+\ldots+a_{12} \\ & x=-1 \Rightarrow 64=1-a_1+a_2+\ldots+a_{12} \\ & \text { Adding } 64=2\left(1+a_2+a_4+\ldots+a_{12}\right) \\ &…
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