JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 April 2023, Shift 1, Maths Q5

Question 5 of 90 in this shift, Maths question 5 of 30, Section A.

Let

P=\begin{bmatrix}\frac{\sqrt{3}}{2}&\frac{1}{2}\\-\frac{1}{2}&\frac{\sqrt{3}}{2}\end{bmatrix}

A=\begin{bmatrix}1&1\\0&1\end{bmatrix}

and

Q=PAP^T

. If

P^TQ^{2007}P=\begin{bmatrix}a&b\\c&d\end{bmatrix}

, then

2a+b-3c-4d

equal to

(1) $2004$
(2) $2005$ Official answer
(3) $2006$
(4) $2007$

Official answer

Option 2

NTA final key.

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
25 Jul 2022, Shift 2 · Q23Let $A=\begin{bmatrix}1&a&a\\0&1&b\\0&0&1\end{bmatrix}$ , $a,b\in\mathbb{R}$ . If for some $n\in\mathbb{N}$ ,…MediumNumerical 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.