jee-main 2013 Q66

jee-main · India · 25apr Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms

If for positive integers $r > 1 , n > 2$, the coefficients of the $( 3r ) ^ { \text {th} }$ and $( r + 2 ) ^ { \text {th} }$ powers of $x$ in the expansion of $( 1 + x ) ^ { 2n }$ are equal, then $n$ is equal to:
(1) $2r + 1$
(2) $2r - 1$
(3) $3r$
(4) $r + 1$

If for positive integers $r > 1 , n > 2$, the coefficients of the $( 3r ) ^ { \text {th} }$ and $( r + 2 ) ^ { \text {th} }$ powers of $x$ in the expansion of $( 1 + x ) ^ { 2n }$ are equal, then $n$ is equal to:\\
(1) $2r + 1$\\
(2) $2r - 1$\\
(3) $3r$\\
(4) $r + 1$

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