JEE Main 2020MathematicsDeterminantsMediumMCQ

JEE Main 2020 — Determinants Question with Solution

JEE Main 2020 (06 Sep Shift 1)

Question

Let m and M be respectively the minimum and maximum value values of cos2x1+sin2xsin2x1+cos2xsin2xsin2xcos2xsin2x1+sin2x Then the ordered pair (m, M) is equal to:
 

Choose an option

Show full solutionCorrect option: B
Correct answer
B-3,-1

Step-by-step explanation

D=cos2x1+sin2xsin2x1+cos2xsin2xsin2xcos2xsin2x1+sin2x

C1→C1+C2

D=21+sin2xsin2x2sin2xsin2x1sin2x1+sin2x

R1→R1-2R3 and R2→R2-2R3

D=0cos2x-(2+sin2x)0-sin2x-(2+sin2x)1sin2x1+sin2x⇒D=-2-sin2x

As range of sin2x∈-1,1, thus

m=-3,M=-1

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About this question

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