JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 4 August 2021, Shift 2, Maths Q63

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

The system of equations

x+2y+pz=4

x+qy+z=5

2x+4y+z=8

has

(1)a unique solution for $p=1$ and $q=2$
(2)a unique solution for $p=2$ and $q=2$
(3)infinitely many solutions for $p=\frac{1}{2}$ and $q=2$ Official answer
(4)no solution for $p=2$ and $q=1$

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

2 Apr 2026, Shift 2 · Q3If the system of equations $x + 5y + 6z = 4,$ $2x + 3y + 4z = 7,$ $x + 6y + az = b$ has infinitely many solutions, then the point $(a, b)$ …MediumSingle correct
4 Apr 2026, Shift 2 · Q3If the system of equations: $x+y+z=5$ $x+2y+3z=9$ $x+3y+\lambda z=\mu$ has infinitely many solutions, then the value of $\lambda+\mu$ is:EasySingle correct
8 Apr 2026, Shift 2 · Q3If the system of linear equations : $x + y + z = 6$ , $x + 2y + 5z = 10$ , $2x + 3y + \lambda z = \mu$ has infinitely many solutions, then…EasySingle correct
2 Apr 2025, Shift 1 · Q20If the system of linear equations $3x+y+\beta z=3$ $2x+\alpha y-z=-3$ $x+2y+z=4$ has infinitely many solutions, then the value of…MediumSingle correct
5 Apr 2024, Shift 1 · Q4If the system of equations $11x+y+\lambda z=-5$ $2x+3y+5z=3$ $8x-19y-39z=\mu$ has infinitely many solutions, then $\lambda^4-\mu$ is equal…MediumSingle correct
5 Apr 2024, Shift 2 · Q4The values of $m, n$ , for which the system of equations $x+y+z=4$ , $2x+5y+5z=17$ , $x+2y+mz=n$ has infinitely many solutions, satisfy the…MediumSingle correct
6 Apr 2024, Shift 2 · Q22If the system of equations $2x+7y+\lambda z=3$ $3x+2y+5z=4$ $x+\mu y+32z=-1$ has infinitely many solutions, then $(\lambda-\mu)$ is equal…MediumNumerical value
8 Apr 2024, Shift 2 · Q3If the system of equations $x + 4y - z = \lambda$ , $7x + 9y + \mu z = -3$ , $5x + y + 2z = -1$ 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.