Verified Solution • 2025–26 Session moderate

QJEEM23Maaf8f: JEE Main 2023 Mathematics - Class 11 JEEM23Maaf8f Solution: A light ray emits from the origin making an angle 30 with the…

A light ray emits from the origin making an angle 30 ∘^\circ with the positive xx -axis. After getting reflected by the line x+y=1x+y=1 , if this ray intersects xx -axis at Q, then the abscissa of Q is :

Multiple Choice Options

  • A 2(3−1){2 \over {\left( {\sqrt 3 - 1} \right)}}
  • B 23−3{2 \over {3 - \sqrt 3 }}
  • C 32(3+1){{\sqrt 3 } \over {2\left( {\sqrt 3 + 1} \right)}}
  • D 23+3{2 \over {3 + \sqrt 3 }}

Step-by-Step Verified Solution

JEE Main 2023 (Online) 29th January Morning Shift Mathematics - Straight Lines and Pair of Straight Lines Question 43 English Explanation

Let Q(h,O)Q(h, O)

∵\because OP reflected by x+y=1x+y=1 .

So, image of QQ lies on y=x3y=\frac{x}{\sqrt{3}}

amp;∴x−h1=y1=−2(h−1)2amp;∴x=1,y=1−h\begin{aligned}& \therefore \quad \frac{x-h}{1}=\frac{y}{1}=\frac{-2(h-1)}{2} \\\\& \therefore \quad x=1, y=1-h\end{aligned}

It lies on y=x3y=\frac{x}{\sqrt{3}}

amp;∴1−h=13amp;∴h=1−13=3−13=23+3\begin{aligned}& \therefore \quad 1-h=\frac{1}{\sqrt{3}} \\\\& \therefore \quad h=1-\frac{1}{\sqrt{3}}=\frac{\sqrt{3}-1}{\sqrt{3}}=\frac{2}{3+\sqrt{3}}\end{aligned}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring