If lim x→1 ((5x+1)^(1/3)−(x+5)^.... | JEE Main 2024

JEE MAIN 2024

04-04-2024 S1

Question

If $\lim _{x \rightarrow 1} \frac{(5 x+1)^{1 / 3}-(x+5)^{1 / 3}}{(2 x+3)^{1 / 2}-(x+4)^{1 / 2}}=\frac{m \sqrt{5}}{n(2 n)^{2 / 3}}$, where $\operatorname{gcd}(m, n)=1$, then $8 m+12 n$ is equal to

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JEE Main

Mathematics

Easy

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