Let K be the sum of the coefficients of the odd powers of x in the expansion of (1+x)⁹⁹. Let a be the middle term in the expansion of (2 + 1/(2))²⁰⁰. If (²⁰⁰C₉₉K)/a = (2^(l)m)/n, where m and n are odd numbers, then the ordered pair (l,n) is equal to

Binomial Theorem and Its Simple Applications: JEE Main 2023 Mathematics question

JEE Main 2023 · 29 Jan, Evening shift · Q2956

JEE Main 202329 Jan, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

Let K be the sum of the coefficients of the odd powers of

x

in the expansion of

(1+x)^{99}

. Let

a

be the middle term in the expansion of

{\left( {2 + {1 \over {\sqrt 2 }}} \right)^{200}}

. If

{{{}^{200}{C_{99}}K} \over a} = {{{2^l}m} \over n}

, where m and n are odd numbers, then the ordered pair

(l,\mathrm{n})

is equal to