JEE Main 2020MathematicsStraight LinesEasyMCQ

JEE Main 2020 — Straight Lines Question with Solution

JEE Main 2020 (02 Sep Shift 2)

Question

The set of all possible values of θ in the interval 0,π for which the points1, 2 and  sinθ, cosθ lie on the same side of the line x+y=1 is?

Choose an option

Show full solutionCorrect option: A
Correct answer
A0,π2

Step-by-step explanation

We know that if Ax1,y1 & Bx2,y2 lies on the same side to line L=0, then LAx1,y1 LBx2,y2>0.

Given, the points A1,2 & Bsinθ,cosθ lies on the same side of the line x+y-1=0.

∴1+2-1sinθ+cosθ-1>0

⇒sinθ+cosθ>1

⇒sinθ×12+cosθ×12>1×12

⇒sinθ.cosπ4+cosθ.sinπ4>12

⇒sinθ+π4>12

⇒π4<θ+π4<3π4

⇒0<θ<π2

⇒θ∈0,π2

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About this question

This is a previous-year question from JEE Main 2020, 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.