Mathematics · 2024
JEE Main · 4 April 2024, Shift 1 · Q24
If lim_x → 1 ((5 x+1)^1 / 3-(x+5)^1 / 3)/((2 x+3)^1 / 2-(x+4)^1 / 2)=(m √ 5)/(n(2 n)^2 / 3), where gcd (m, n)=1, then 8 m+12 n is equal to ____.
If $\displaystyle \lim _{x \rightarrow 1} \frac{(5 x+1)^{1 / 3}-(x+5)^{1 / 3}}{(2 x+3)^{1 / 2}-(x+4)^{1 / 2}}=\frac{m \sqrt{5}}{n(2 n)^{2 / 3}}$, where $\displaystyle \operatorname{gcd}(m, n)=1$, then $\displaystyle 8 m+12 n$ is equal to
$\displaystyle \_\_\_\_$.
Official answer
From NTA’s final answer key for this paper.
100
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JEE Main 2024 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.