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Saturday, 31 October

JEE Main 2024 · MathsMultiple choiceTwo statementsEasyConceptual

JEE Main 27 January 2024, Shift 1, Maths Q4

Question 4 of 90 in this shift, Maths question 4 of 30, Section A.

Consider the matrix f(x)=[cos⁡x−sin⁡x0sin⁡xcos⁡x0001]f(x)=\begin{bmatrix}\cos x & -\sin x & 0\\ \sin x & \cos x & 0\\ 0 & 0 & 1\end{bmatrix}. Given below are two statements : Statement I : f(−x)f(-x) is the inverse of the matrix f(x)f(x). Statement II : f(x) f(y)=f(x+y)f(x)\,f(y)=f(x+y). In the light of the above statements, choose the correct answer from the options given below
  1. (1)Both Statement I and Statement II are trueOfficial answer
  2. (2)Both Statement I and Statement II are false
  3. (3)Statement I is true but Statement II is false
  4. (4)Statement I is false but Statement II is true

Official answer

Option 1

NTA final key.

Chapter
Matrices
Topic
Matrix Inverse
Idea tested
Inverse of Orthogonal Matrices

Same topic in other shifts

All Matrix Inverse questions
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  2. 4 Apr 2026, Shift 1 · Q6Let A=[112−201135]A=\begin{bmatrix}1&1&2\\-2&0&1\\1&3&5\end{bmatrix}. Then the sum of all elements of the matrix…MediumSingle correct
  3. 5 Apr 2026, Shift 1 · Q3Let A be a 3×33 \times 3 matrix such that AT[101]=[522]A^T\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}5\\2\\2\end{bmatrix},…HardSingle correct
  4. 5 Apr 2026, Shift 2 · Q4Let M be a 3×33\times 3 matrix such that M(100)=(123)M\begin{pmatrix}1\\0\\0\end{pmatrix}=\begin{pmatrix}1\\2\\3\end{pmatrix},…MediumSingle correct
  5. 6 Apr 2026, Shift 1 · Q21Let A=[−11−1101001]A=\begin{bmatrix}-1&1&-1\\1&0&1\\0&0&1\end{bmatrix} satisfy…MediumNumerical value
  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.