JEE Main 2019MathematicsDeterminantsEasyMCQ

JEE Main 2019 — Determinants Question with Solution

JEE Main 2019 (10 Jan Shift 2)

Question

The number of values of θ∈0, π for which the system of linear equations
x+3y+7z=0
-x+4y+7z=0
sin⁡3θx+cos⁡2θy+2z=0
has a non-trivial solution, is:

Choose an option

Show full solutionCorrect option: A
Correct answer
ATwo

Step-by-step explanation

For non-trivial solutions

137-147sin3θcos2θ2=0

⇒4sin3θ+4sin2θ-3sinθ=0

⇒sinθ=0 or sinθ=12 or sinθ=-32

Since θ∈0, π

⇒θ=π6 and 5π6 will satisfy the equation

because sinθ=-32 is not possible as range of sinθ is -1,1

⇒ Number of θ ' s=2

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About this question

This is a previous-year question from JEE Main 2019, 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.