If $a_k$ is the coefficient of $x^k$ in the expansion of $(1+x+x^2)^n$ for $k=0, 1, 2, \ldots, 2n$,then $a_1+2a_2+3a_3+\ldots+2na_{2n}$ is equal to
- A$-a_0$
- B$3^n$
- C$n \cdot 3^{n+1}$
- D$n \cdot 3^n$
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View SolutionIf in the expansion of $(1+x)^p(1-x)^q$,the coefficients of $x$ and $x^2$ are $1$ and $-2$ respectively,then $p^2+q^2$ is equal to :
DifficultJEE MAIN 2025
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