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Saturday, 31 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 31 January 2024, Shift 2, Maths Q4

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

Let AA be a 3×33\times3 real matrix such that A(101)=2(101)A\begin{pmatrix}1\\0\\1\end{pmatrix}=2\begin{pmatrix}1\\0\\1\end{pmatrix}, A(−101)=4(−101)A\begin{pmatrix}-1\\0\\1\end{pmatrix}=4\begin{pmatrix}-1\\0\\1\end{pmatrix}, A(010)=2(010)A\begin{pmatrix}0\\1\\0\end{pmatrix}=2\begin{pmatrix}0\\1\\0\end{pmatrix}. Then, the system (A−3I)(xyz)=(123)(A-3I)\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}1\\2\\3\end{pmatrix} has
  1. (1)no solution
  2. (2)infinitely many solutions
  3. (3)unique solutionOfficial answer
  4. (4)exactly two solutions

Official answer

Option 3

NTA final key.

Chapter
Determinants
Topic
Cramer's Rule
Idea tested
Condition for Unique Solution

Same idea in other shifts

Asked 4× in all
  1. 24 Jun 2022, Shift 2 · Q3Let the system of linear equations x+y+αz=2x + y + \alpha z = 2 3x+y+z=43x + y + z = 4 x+2z=1x + 2z = 1 have a unique solution (x∗,y∗,z∗)(x^*, y^*, z^*). If…MediumSingle correct
  2. 24 Feb 2021, Shift 2 · Q72For the system of linear equations : x−2y=1x-2y=1, x−y+kz=−2x-y+kz=-2, ky+4z=6ky+4z=6, k∈k\in R, consider the following statements : (A) The system has…MediumOther
  3. 25 Feb 2021, Shift 2 · Q63The following system of linear equations 2x+3y+2z=92x + 3y + 2z = 9 3x+2y+2z=93x + 2y + 2z = 9 x−y+4z=8x - y + 4z = 8EasySingle 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.