Let (n k) denotes ⁿ C k and [ n k ] = \ (n k), if 0 ≤ k ≤ n 0, otherwise. If A k = Σ i = 0 ⁹ (9 i)[ 12 12 - k + i ] + Σ i = 0 ⁸ (8 i)[ 13 13 - k + i ] and A₄ - A₃ = 190 p, then p is equal to:

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

JEE Main 2021 · 26 Aug, Evening shift · Q26

JEE Main 202126 Aug, Evening shiftMathematicsHardBinomial Theorem and Its Simple Applications131× since 2002

Let

\left( {\matrix{ n \cr k \cr } } \right)

denotes

{}^n{C_k}

and

\left[ {\matrix{ n \cr k \cr } } \right] = \left\{ {\matrix{ {\left( {\matrix{ n \cr k \cr } } \right),} & {if\,0 \le k \le n} \cr {0,} & {otherwise} \cr } } \right.

{A_k} = \sum\limits_{i = 0}^9 {\left( {\matrix{ 9 \cr i \cr } } \right)\left[ {\matrix{ {12} \cr {12 - k + i} \cr } } \right] + } \sum\limits_{i = 0}^8 {\left( {\matrix{ 8 \cr i \cr } } \right)\left[ {\matrix{ {13} \cr {13 - k + i} \cr } } \right]}

and A₄

-

A₃ = 190 p, then p is equal to :

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