Question

If \( (1 + x - 2x^2)^6 = 1 + a_1 x + a_2 x^2 + \cdots + a_{12x^{12} \), then the value of \( a_2 + a_4 + a_6 + \cdots + a_{12} \) is:}

• A. \( 21 \)
• B. \( 31 \)
• C. \( 32 \)
• D. \( 64 \)

Hint:

To find even coefficient sums: \begin{itemize} \item Use \( \frac{f(1)+f(-1)}{2} \). \item Subtract constant term if needed. \end{itemize}

Answer 1

The Correct Option is D