The sum $\mathop \sum \limits_{i = 0}^m \left( {\begin{array}{*{20}{c}} {10}\\ i \end{array}} \right)\left( {\begin{array}{*{20}{c}} {20}\\ {m - i} \end{array}} \right),\;\;\left( {{\rm{where}},\;\left( {\begin{array}{*{20}{c}} {\rm{p}}\\ q \end{array}} \right) = 0\;{\rm{if}}\;p < q} \right)$ is maximum, when $m$ is

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

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The sum

\sum \limits_{i = 0}^m \left( {\begin{array}{cccccccccccccccccccc} {10}\\ i \end{array}} \right)\left( {\begin{array}{cccccccccccccccccccc} {20}\\ {m - i} \end{array}} \right),\;\;\left( {\mathrm{where},\;\left( {\begin{array}{cccccccccccccccccccc} \mathrm{p}\\ q \end{array}} \right) = 0\;\mathrm{if}\;p < q} \right)

is maximum, when

m

View answer and explanation

Correct option: C

Option C (15) is correct because the sum is the coefficient of

x^m

(1+x)^{30}

, which is maximum when

m = 30/2 = 15