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\(\lim _{x\to {0}^{+}}\frac{\tan \left(5(x{)}^{\frac{1}{3}}\right){\log }_{e}\left(1+3{x}^{2}\right)}{{\left({\tan }^{-1…

Q1

\(\lim _{x\to {0}^{+}}\frac{\tan \left(5(x{)}^{\frac{1}{3}}\right){\log }_{e}\left(1+3{x}^{2}\right)}{{\left({\tan }^{-1}3\sqrt{x}\right)}^{2}\left({e}^{5(x{)}^{\frac{4}{3}}}-1\right)}\) is equal to

[JEE Main 2025, 7 Apr (Shift 1)]

a

\(\frac{1}{15}\)

b

\(1\)

c

\(\frac{1}{3}\)

d

\(\frac{5}{3}\)

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