JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 August 2021, Shift 2, Maths Q63

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

Let

[\lambda]

be the greatest integer less than or equal to

\lambda

. The set of all values of

\lambda

for which the system of linear equations

x + y + z = 4

3x + 2y + 5z = 3

9x + 4y + (28 + [\lambda])z = [\lambda]

has a solution is :

(1) $[-9, -8)$
(2) $(-\infty, -9) \cup [-8, \infty)$
(3)ROfficial answer
(4) $(-\infty, -9) \cup (-9, \infty)$

Official answer

Option 3

NTA final key.

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Evaluating Parameters for Consistency

Same idea in other shifts

Asked 15× in all

2 Apr 2025, Shift 2 · Q4If the system of equations $2x + \lambda y + 3z = 5$ $3x + 2y - z = 7$ $4x + 5y + \mu z = 9$ has infinitely many solutions, then…MediumSingle correct
7 Apr 2025, Shift 1 · Q4Let the system of equations : $2x + 3y + 5z = 9$ , $7x + 3y - 2z = 8$ , $12x + 3y - (4+\lambda)z = 16 - \mu$ , have infinitely many…MediumSingle correct
7 Apr 2025, Shift 2 · Q5Let the system of equations $x+5y-z=1$ $4x+3y-3z=7$ $24x+y+\lambda z=\mu$ $\lambda,\mu\in\mathbf{R}$ , have infinitely many solutions. Then…HardSingle correct
1 Feb 2024, Shift 2 · Q5Let the system of equations $x+2y+3z=5$ , $2x+3y+z=9$ , $4x+3y+\lambda z=\mu$ have infinite number of solutions. Then $\lambda+2\mu$ is…MediumSingle correct
30 Jan 2024, Shift 1 · Q3Consider the system of linear equations $x+y+z=4\mu$ , $x+2y+2\lambda z=10\mu$ , $x+3y+4\lambda^2z=\mu^2+15$ , where…MediumSingle correct
6 Apr 2023, Shift 2 · Q5For the system of equations $x+y+z=6$ $x+2y+\alpha z=10$ $x+3y+5z=\beta$ , which one of the following is NOT true?MediumSingle correct
11 Apr 2023, Shift 2 · Q4If the system of linear equations $7x + 11y + \alpha z = 13$ $5x + 4y + 7z = \beta$ $175x + 194y + 57z = 361$ has infinitely many…MediumSingle correct
13 Apr 2023, Shift 1 · Q4For the system of linear equations $2x+4y+2az=b$ $x+2y+3z=4$ $2x-5y+2z=8$ which of the following is NOT correct?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.