JEE Main 2021MathematicsMatricesMediumNumerical

JEE Main 2021 — Matrices Question with Solution

JEE Main 2021 (25 Feb Shift 1)

Question

If A=0-tanθ2tanθ20 and I2+AI2-A-1=a-bba, then 13a2+b2 is equal to _____ .

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Show full solutionCorrect answer: 13
Correct answer
13

Step-by-step explanation

A=0-tanθ2tanθ20

⇒I+A=1-tanθ2tanθ21

⇒I-A=1tanθ2-tanθ21  ∴ |I-A|=sec2θ/2

⇒I-A-1=1sec2θ21-tanθ2tanθ21

⇒I+AI-A-1=1sec2θ21-tanθ2tanθ2 1  1-tanθ2tanθ2  1

=1sec2θ21-tan2θ2-2 tanθ22 tanθ21-tan2θ2

a=1-tan2θ2sec2θ2

b=2 tanθ2sec2θ2

∴ a2+b2=1

∴ 13a2+b2=13

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About this question

This is a previous-year question from JEE Main 2021, covering the Matrices 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.