Let f(x)=Σ k=1 ¹⁰ k x^(k), x R. If 2 f(2)+f^()(2)=119(2)ⁿ+1 then n is equal to _ _ _ _ _ _

Limit, Continuity and Differentiability: JEE Main 2023 Mathematics question

JEE Main 2023 · 13 Apr, Evening shift · Q35

JEE Main 202313 Apr, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f(x)=\sum_\limits{k=1}^{10} k x^{k}, x \in \mathbb{R}

. If

2 f(2)+f^{\prime}(2)=119(2)^{\mathrm{n}}+1

then

\mathrm{n}

is equal to ___________

Your answerType your answer. Integers and decimals are accepted.