JEE Main 2022MathematicsMatricesHardNumerical

JEE Main 2022 — Matrices Question with Solution

JEE Main 2022 (29 Jun Shift 2)

Question

Let M=0-αα0, where α is a non-zero real number and N=∑k=149M2k. If I-M2N=-2I, then the positive integral value of α is ______.

Enter your answer

Show full solutionCorrect answer: 1
Correct answer
1

Step-by-step explanation

Given, M=0-αα0

Now, M2=-α200-α2=-α2I

Also given, N=∑k=149M2k

⇒N=M2+M4+…….+M98=-α2+α4-α6+…..I

=-α21--α2491+α2.I

⇒N1+α2=-α2α98+1

⇒NI-M2=-α2α98+1

Now comparing with I-M2N=-2I

We get, α=1.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Matrices chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2022, 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.