If \( {C}_{r} \) denotes the binomial coefficient \( { _{ ; }^{ n }{ C } }_{ r } \) then \( \left( -1 \right) { C }_{ 0 }^{ 2 }+2{ C }_{ 1 }^{ 2 }+5{ C }_{ 2 }^{ 2 }+......(3n-1){ C }_{ n }^{ 2 }=\quad \)

A \( \left( 3n-2 \right) { _{ }^{ 2n }{ C } }_{ n } \)

B \( \left( \cfrac { 3n-2 }{ 2 } \right) { _{ }^{ 2n }{ C } }_{ n } \)

C \( \left( 5+3n \right) { _{ }^{ 2n }{ C } }_{ n } \)

D \( \left( \cfrac { 3n-5 }{ 2 } \right) { _{ }^{ 2n }{ C } }_{ n+1 } \)

Solution

Correct Answer: Option B

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