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Saturday, 31 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 30 January 2024, Shift 2, Maths Q4

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

Consider the system of linear equations x+y+z=5x + y + z = 5, x+2y+λ2z=9x + 2y + \lambda^2 z = 9, x+3y+λz=μx + 3y + \lambda z = \mu, where λ,μ∈R\lambda, \mu \in \mathbb{R}. Then, which of the following statement is NOT correct?
  1. (1)System is consistent if λ≠1\lambda \neq 1 and μ=13\mu = 13
  2. (2)System is inconsistent if λ=1\lambda = 1 and μ≠13\mu \neq 13
  3. (3)System has unique solution if λ≠1\lambda \neq 1 and μ≠13\mu \neq 13Official answer
  4. (4)System has infinite number of solutions if λ=1\lambda = 1 and μ=13\mu = 13

Official answer

Option 3

NTA final key.

Chapter
Determinants
Topic
Cramer's Rule
Idea tested
Condition for Infinite Solutions

Same idea in other shifts

Asked 25× in all
  1. 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
  2. 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
  3. 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
  4. 2 Apr 2025, Shift 1 · Q20If the system of linear equations 3x+y+βz=33x+y+\beta z=3 2x+αy−z=−32x+\alpha y-z=-3 x+2y+z=4x+2y+z=4 has infinitely many solutions, then the value of…MediumSingle correct
  5. 5 Apr 2024, Shift 1 · Q4If the system of equations 11x+y+λz=−511x+y+\lambda z=-5 2x+3y+5z=32x+3y+5z=3 8x−19y−39z=μ8x-19y-39z=\mu has infinitely many solutions, then λ4−μ\lambda^4-\mu is equal…MediumSingle correct
  6. 5 Apr 2024, Shift 2 · Q4The values of m,nm, n, for which the system of equations x+y+z=4x+y+z=4, 2x+5y+5z=172x+5y+5z=17, x+2y+mz=nx+2y+mz=n has infinitely many solutions, satisfy the…MediumSingle correct
  7. 6 Apr 2024, Shift 2 · Q22If the system of equations 2x+7y+λz=32x+7y+\lambda z=3 3x+2y+5z=43x+2y+5z=4 x+μy+32z=−1x+\mu y+32z=-1 has infinitely many solutions, then (λ−μ)(\lambda-\mu) is equal…MediumNumerical value
  8. 8 Apr 2024, Shift 2 · Q3If the system of equations x+4y−z=λx + 4y - z = \lambda, 7x+9y+μz=−37x + 9y + \mu z = -3, 5x+y+2z=−15x + y + 2z = -1 has infinitely many solutions, then…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.