JEE Main 2023MathematicsStraight LinesMediumMCQ

JEE Main 2023 — Straight Lines Question with Solution

JEE Main 2023 (29 Jan Shift 1)

Question

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

Choose an option

Show full solutionCorrect option: B
Correct answer
B23+3

Step-by-step explanation

On plotting the diagram of given data we get,

Let Q(h,0)

∵OP reflected by x+y=1

So, the image of Q lies on y=x3

∴ x-h1=y1=-2(h-1)2

⇒x=1, y=1-h

Since it lies on y=x3

∴ 1-h=13

⇒h=1-13=3-13

On rationalising the numerator we get,

⇒h=3-13×3+13+1

⇒h=23+3

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About this question

This is a previous-year question from JEE Main 2023, 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.