JEE Main 2017MathematicsDeterminantsMediumMCQ

JEE Main 2017 — Determinants Question with Solution

JEE Main 2017 (08 Apr Online)

Question

If S=x∈0, 2π :0cos⁡x-sin⁡xsin⁡x0cos⁡xcos⁡xsin⁡x0=0,  then ∑x ∈ Stanπ3+x is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B-4-23

Step-by-step explanation

Given,0cos⁡x-sin⁡xsin⁡x0cos⁡xcos⁡xsin⁡x0=0

Expanding the determinant,

⇒0(0-cos⁡xsin⁡x)-cos⁡x0-cos2⁡x-sin⁡xsin2⁡x-0=0

⇒ cos3⁡x-sin3⁡x=0

⇒ tan3⁡x=1⇒ tan⁡x=1⇒x=π4,5π4  ⇒S=π4, 5π4

∴∑x ∈ Stanπ3+x

=∑x ∈ S3+tanx1−3 tanx

=23+11-3=-4-23

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About this question

This is a previous-year question from JEE Main 2017, covering the Determinants 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.