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Friday, 9 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 topic in other shifts

All Cramer's Rule questions
  1. 2 Apr 2026, Shift 1 · Q3Let α,β∈R\alpha, \beta \in \mathbf{R} be such that the system of linear equations x+2y+z=5x+2y+z=5 2x+y+αz=52x+y+\alpha z=5 8x+4y+βz=188x+4y+\beta z=18 has no…MediumSingle correct
  2. 2 Apr 2026, Shift 2 · Q3If the system of equations x+5y+6z=4,x + 5y + 6z = 4, 2x+3y+4z=7,2x + 3y + 4z = 7, x+6y+az=bx + 6y + az = b has infinitely many solutions, then the point (a,b)(a, b)…MediumSingle correct
  3. 4 Apr 2026, Shift 2 · Q3If the system of equations: x+y+z=5x+y+z=5 x+2y+3z=9x+2y+3z=9 x+3y+λz=μx+3y+\lambda z=\mu has infinitely many solutions, then the value of λ+μ\lambda+\mu is:EasySingle correct
  4. 5 Apr 2026, Shift 1 · Q4Consider the system of linear equations in x,y,zx, y, z: x+2y+tz=0x + 2y + tz = 0, 6x+y+5tz=06x + y + 5tz = 0, 3x+t2y+f(t) z=03x + t^2y + f(t)\,z = 0, where…MediumSingle correct
  5. 6 Apr 2026, Shift 2 · Q4The sum of all possible values of θ∈[0,2π]\theta\in[0,2\pi], for which the system of equations : xcos⁡3θ−8y−12z=0x\cos 3\theta-8y-12z=0…MediumSingle correct
  6. 8 Apr 2026, Shift 2 · Q3If the system of linear equations : x+y+z=6x + y + z = 6, x+2y+5z=10x + 2y + 5z = 10, 2x+3y+λz=μ2x + 3y + \lambda z = \mu has infinitely many solutions, then…EasySingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.