JEE Main 2025 — Straight Lines Question with Solution
JEE Main 2025 (8 Apr Shift 2)
Question
Let a be the length of a side of a square OABC with being the origin. Its side OA makes an acute angle with the positive -axis and the equations of its diagonals are and . Then is equal to
Choose an option
Show full solutionCorrect option: A
Correct answer
A48
Step-by-step explanation
A Lies on other diagonal
$\begin{aligned}
& \therefore\left(\frac{\sqrt{3}-1}{2}\right) a-\left(\frac{\sqrt{3}+1}{2}\right) \cdot \sqrt{3} a+8 \sqrt{3}=0 \\ & a\left[\frac{\sqrt{3}-1-3-\sqrt{3}}{2}\right]=-8 \sqrt{3} \\ & a=4 \sqrt{3} \\ & \therefore a^2=48
\end{aligned}$
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This is a previous-year question from JEE Main 2025, covering the Straight Lines chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.