jee-main 2014 Q66

jee-main · India · 19apr Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion

The coefficient of $x ^ { 1012 }$ in the expansion of $\left( 1 + x ^ { n } + x ^ { 253 } \right) ^ { 10 }$, (where $n \leq 22$ is any positive integer), is
(1) ${ } ^ { 253 } C _ { 4 }$
(2) ${ } ^ { 10 } C _ { 4 }$
(3) $4 n$
(4) 1

The coefficient of $x ^ { 1012 }$ in the expansion of $\left( 1 + x ^ { n } + x ^ { 253 } \right) ^ { 10 }$, (where $n \leq 22$ is any positive integer), is\\
(1) ${ } ^ { 253 } C _ { 4 }$\\
(2) ${ } ^ { 10 } C _ { 4 }$\\
(3) $4 n$\\
(4) 1

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