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Q.If (1+x)3n=∑r=03n(3nr)xr(1 + x)^{3n} = \sum_{r=0}^{3n} \binom{3n}{r} x^r, then ∑r=0n(3n3r)\sum_{r=0}^{n} \binom{3n}{3r} equals

a
43n+2⋅(−2)3n6\dfrac{4^{3n} + 2 \cdot (-2)^{3n}}{6}
b
43n+2⋅(1)3n6\dfrac{4^{3n} + 2 \cdot (1)^{3n}}{6}
c
43n+2⋅(−1)3n6\dfrac{4^{3n} + 2 \cdot (-1)^{3n}}{6}
d
43n3\dfrac{4^{3n}}{3}

Correct Answer: Option A

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

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