Let [ x ] denote greatest integer less than or equal to x. If for n N, (1 - x + x³)ⁿ = Σ j = 0 ³ⁿ a j x^(j), then Σ j = 0 ^([ 3n/2 ]) a 2j + 4 Σ j = 0 ^([ (3n - 1)/2 ]) a 2j + 1 is equal to:

Binomial Theorem and Its Simple Applications: JEE Main 2021 Mathematics question

JEE Main 2021 · 16 Mar, Morning shift · Q2993

JEE Main 202116 Mar, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

Let [ x ] denote greatest integer less than or equal to x. If for n

\in

{(1 - x + {x^3})^n} = \sum\limits_{j = 0}^{3n} {{a_j}{x^j}}

, then

\sum\limits_{j = 0}^{\left[ {{{3n} \over 2}} \right]} {{a_{2j}} + 4} \sum\limits_{j = 0}^{\left[ {{{3n - 1} \over 2}} \right]} {{a_{2j}} + 1}

is equal to :

JEE Main 2021 · 16 Mar, Morning shift · Q2993

JEE Main 202116 Mar, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

Let [ x ] denote greatest integer less than or equal to x. If for n

\in

{(1 - x + {x^3})^n} = \sum\limits_{j = 0}^{3n} {{a_j}{x^j}}

, then

\sum\limits_{j = 0}^{\left[ {{{3n} \over 2}} \right]} {{a_{2j}} + 4} \sum\limits_{j = 0}^{\left[ {{{3n - 1} \over 2}} \right]} {{a_{2j}} + 1}

is equal to :