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Q.If (1+2x+3x2)n=∑r=02narxr(1 + 2x + 3x^2)^n = \sum_{r=0}^{2n} a_r x^r, then a0+a2+a4+⋯a_0 + a_2 + a_4 + \cdots equals

a
3n+1n3^n + 1^n
b
3n+(−1)n2\dfrac{3^n + (-1)^n}{2}
c
4n+2n2\dfrac{4^n + 2^n}{2}
d
3n+12\dfrac{3^n + 1}{2}

Correct Answer: Option D

The correct solution involves applying the fundamental concept to derive the final value step by step...

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