Mathematics · 2023
JEE Main · 31 January 2023, Shift 2 · Q66
lim_x → ∞ ((√(3 x+1)+√(3 x-1))^6+(√(3 x+1)-√(3 x-1))^6)/((x+√(x^2-1))^6+(x-√(x^2-1))^6) x^3
$$\lim _{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3
$$
Official answer
From NTA’s final answer key for this paper.
(4)
is equal to $\displaystyle 27$
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JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.