Mathematics · 2025
JEE Main · 29 January 2025, Shift 2 · Q24
If lim_t → 0 (∫_0^1(3 x+5)^t d x)^(1/t)=(α)/(5 e)(8/5)^(2/3), then α is equal to ____.
If $\displaystyle \lim _{\mathrm{t} \rightarrow 0}\left(\int_0^1(3 x+5)^{\mathrm{t}} \mathrm{d} x\right)^{\frac{1}{\mathrm{t}}}=\frac{\alpha}{5 \mathrm{e}}\left(\frac{8}{5}\right)^{\frac{2}{3}}$, then $\displaystyle \alpha$ is equal to $\displaystyle \_\_\_\_$.
Official answer
From NTA’s final answer key for this paper.
64
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JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.