JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 September 2020, Shift 1, Maths Q54

Question 54 of 75 in this shift, Maths question 4 of 25.

If A

= \begin{bmatrix} \cos\theta & i\sin\theta \\ i\sin\theta & \cos\theta \end{bmatrix}

\left(\theta = \frac{\pi}{24}\right)

and A

^5 = \begin{bmatrix} a & b \\ c & d \end{bmatrix}

, where

i = \sqrt{-1}

, then which one of the following is not true ?

(1) $a^2 - d^2 = 0$
(2) $a^2 - b^2 = \frac{1}{2}$ Official answer
(3) $0 \le a^2 + b^2 \le 1$
(4) $a^2 - c^2 = 1$

Official answer

Option 2

NTA final key (Sep 2020).

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Powers of Square Matrices

Same idea in other shifts

Asked 21× in all

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25 Jul 2022, Shift 1 · Q21Let $A=\begin{pmatrix}2&-1&-1\\1&0&-1\\1&-1&0\end{pmatrix}$ and $B=A-I$ . If $\omega=\frac{\sqrt3\,i-1}{2}$ , then the number of elements in…HardNumerical value

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.