JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 29 June 2022, Shift 2, Maths Q29

Question 29 of 90 in this shift, Maths question 29 of 30, Section B.

Let

M = \begin{bmatrix} 0 & -\alpha \\ \alpha & 0 \end{bmatrix}

, where

\alpha

is a non-zero real number an

N = \sum_{k=1}^{49} M^{2k}

. If

(I - M^2)N = -2I

, then the positive integral value of

\alpha

is ___.

Official answer

NTA final key.

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Square of Skew-Symmetric Matrix

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.