Mathematics · 2026
JEE Main · 23 January 2026, Shift 1 · Q24
Let f be a twice differentiable non-negative function such that (f(x))^2=25+∫_0^x((f( t ))^2+(f^′( t ))^2) dt. Then the mean of f( log_e (1)), f(…
Let $\displaystyle f$ be a twice differentiable non-negative function such that $\displaystyle (f(x))^2=25+\int_0^x\left((f(\mathrm{t}))^2+\left(f^{\prime}(\mathrm{t})\right)^2\right) \mathrm{dt}$.
Then the mean of $\displaystyle f\left(\log _{\mathrm{e}}(1)\right), f\left(\log _{\mathrm{e}}(2)\right), \ldots . ., f\left(\log _{\mathrm{e}}(625)\right)$ is equal to $\displaystyle \_\_\_\_$.
Official answer
From NTA’s final answer key for this paper.
1565
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JEE Main 2026 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.