If 1 + (2 + ⁴⁹C₁ + ⁴⁹C₂ +... + ⁴⁹C₄₉)(⁵⁰C₂ + ⁵⁰C₄ +... + ⁵⁰C₅₀) is equal to 2ⁿ · m, where m is odd, then n+m is equal to _ _ _ _ _.

Binomial Theorem and Its Simple Applications: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jul, Evening shift · Q25

JEE Main 202228 Jul, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

1 + (2 + {}^{49}{C_1} + {}^{49}{C_2} + \,\,...\,\, + \,\,{}^{49}{C_{49}})({}^{50}{C_2} + {}^{50}{C_4} + \,\,...\,\, + \,\,{}^{50}{C_{50}})

is equal to

2^{\mathrm{n}} \cdot \mathrm{m}

, where

\mathrm{m}

is odd, then

\mathrm{n}+\mathrm{m}

is equal to __________.

Your answerType your answer. Integers and decimals are accepted.