JEE Main 2020 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 8 January 2020, Shift 1, Maths Q53

Question 53 of 75 in this shift, Maths question 3 of 25, Section A.

For which of the following ordered pairs

(\mu, \delta)

, the system of linear equations

x+2y+3z=1

3x+4y+5z=\mu

4x+4y+4z=\delta

is inconsistent ?

(1) $(1,0)$
(2) $(3,4)$
(3) $(4,3)$ Official answer
(4) $(4,6)$

Official answer

Option 3

NTA final key (Jan 2020).

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Condition for No Solution

Same idea in other shifts

Asked 6× in all

2 Apr 2026, Shift 1 · Q3Let $\alpha, \beta \in \mathbf{R}$ be such that the system of linear equations $x+2y+z=5$ $2x+y+\alpha z=5$ $8x+4y+\beta z=18$ has no…MediumSingle correct
24 Jun 2022, Shift 1 · Q6The number of values of $\alpha$ for which the system of equations : $x+y+z=\alpha$ $\alpha x+2\alpha y+3z=-1$ $x+3\alpha y+5z=4$ is…MediumSingle correct
25 Jul 2021, Shift 1 · Q79The values of a and b, for which the system of equations $2x+3y+6z=8$ $x+2y+az=5$ $3x+5y+9z=b$ has no solution, are :EasySingle correct
2 Sep 2020, Shift 1 · Q55Let $S$ be the set of all $\lambda\in\mathbf{R}$ for which the system of linear equations $2x-y+2z=2$ $x-2y+\lambda z=-4$ …MediumSingle correct
2 Apr 2017 (offline) · Q65If S is the set of distinct values of 'b' for which the following system of linear equations $x+y+z=1$ $x+ay+z=1$ $ax+by+z=0$ has no…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 42 of the 174 JEE Main shifts held from 2017 to 2026.