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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 August 2021, Shift 1, Maths Q63

Question 63 of 90 in this shift, Maths question 3 of 30, Section A.

If A=(1525−2515)A = \begin{pmatrix} \frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}} \end{pmatrix}, B=(10i1)B = \begin{pmatrix} 1 & 0 \\ i & 1 \end{pmatrix}, i=−1i = \sqrt{-1}, and Q=ATBAQ = A^T B A, then the inverse of the matrix AQ2021ATA Q^{2021} A^T is equal to :
  1. (1)(10−2021 i1)\begin{pmatrix} 1 & 0 \\ -2021\,i & 1 \end{pmatrix}Official answer
  2. (2)(15−2021202115)\begin{pmatrix} \frac{1}{\sqrt{5}} & -2021 \\ 2021 & \frac{1}{\sqrt{5}} \end{pmatrix}
  3. (3)(1−2021 i01)\begin{pmatrix} 1 & -2021\,i \\ 0 & 1 \end{pmatrix}
  4. (4)(102021 i1)\begin{pmatrix} 1 & 0 \\ 2021\,i & 1 \end{pmatrix}

Official answer

Option 1

NTA final key.

Chapter
Matrices
Topic
Matrix Inverse
Idea tested
Properties of Matrix Inverses

Same topic in other shifts

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  6. 6 Apr 2026, Shift 2 · Q17Let A=[13−121α01−1]A=\begin{bmatrix}1&3&-1\\2&1&\alpha\\0&1&-1\end{bmatrix} be a singular matrix. Let f(x)=∫0x(t2+2t+3)dtf(x)=\int_0^x\left(t^2+2t+3\right)dt,…MediumSingle 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.