Let m, n N and gcd (2, n) = 1. If 30(30 0) + 29(30 1) +...... + 2(30 28) + 1(30 29) = n.2^(m), then n + m is equal to _ _ _ _ _. (Here (n k) = ⁿ C k)

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

JEE Main 2021 · 26 Feb, Morning shift · Q31

JEE Main 202126 Feb, Morning shiftMathematicsHardBinomial Theorem and Its Simple Applications131× since 2002

Let m, n

\in

N and gcd (2, n) = 1. If

30\left( {\matrix{ {30} \cr 0 \cr } } \right) + 29\left( {\matrix{ {30} \cr 1 \cr } } \right) + ...... + 2\left( {\matrix{ {30} \cr {28} \cr } } \right) + 1\left( {\matrix{ {30} \cr {29} \cr } } \right) = n{.2^m}

, then n + m is equal to __________. (Here

\left( {\matrix{ n \cr k \cr } } \right) = {}^n{C_k}

)

Your answerType your answer. Integers and decimals are accepted.