jee-main 2021 Q64

jee-main · India · session2_16mar_shift1 Binomial Theorem (positive integer n) Evaluate a Summation Involving Binomial Coefficients

Let $[ x ]$ denote greatest integer less than or equal to $x$. If for $n \in N , \left( 1 - x + x ^ { 3 } \right) ^ { n } = \sum _ { j = 0 } ^ { 3 n } a _ { j } x ^ { j }$, then $\sum _ { j = 0 } ^ { \left[ \frac { 3 n } { 2 } \right] } a _ { 2 j } + 4 \sum _ { j = 0 } ^ { \left[ \frac { 3 n - 1 } { 2 } \right] } a _ { 2 j + 1 }$ is equal to :
(1) 2
(2) $2 ^ { n - 1 }$
(3) 1
(4) $n$

Let $[ x ]$ denote greatest integer less than or equal to $x$. If for $n \in N , \left( 1 - x + x ^ { 3 } \right) ^ { n } = \sum _ { j = 0 } ^ { 3 n } a _ { j } x ^ { j }$, then $\sum _ { j = 0 } ^ { \left[ \frac { 3 n } { 2 } \right] } a _ { 2 j } + 4 \sum _ { j = 0 } ^ { \left[ \frac { 3 n - 1 } { 2 } \right] } a _ { 2 j + 1 }$ is equal to :\\
(1) 2\\
(2) $2 ^ { n - 1 }$\\
(3) 1\\
(4) $n$

Paper Questions

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