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JEE Main 2021 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 25 February 2021, Shift 2, Maths Q61

Question 61 of 90 in this shift, Maths question 1 of 30, Section A.

If for the matrix,

A = \begin{bmatrix} 1 & -\alpha \\ \alpha & \beta \end{bmatrix}

,

AA^T = I_2

, then the value of

\alpha^4 + \beta^4

is :

(1) $4$
(2) $1$ Official answer
(3) $2$
(4) $3$

Official answer

Option 2

NTA final key.

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Orthogonal Matrix Multiplication Definition

Same idea in other shifts

Asked 2× in all

29 Jan 2024, Shift 1 · Q4Let A be a square matrix such that $AA^T=I$ . Then $\frac{1}{2}A\left[(A+A^T)^2+(A-A^T)^2\right]$ is equal toMediumSingle correct

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.