JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 5 April 2026, Shift 1, Maths Q4

Question 4 of 75 in this shift, Maths question 4 of 25, Section A.

Consider the system of linear equations in

x, y, z

x + 2y + tz = 0

6x + y + 5tz = 0

3x + t^2y + f(t)\,z = 0

, where

f: \mathbb{R} \to \mathbb{R}

is a differentiable function. If this system has infinitely many solutions for all

t \in \mathbb{R}

, then

f

(1)is a constant function
(2)is strictly increasing on $\mathbb{R}$ Official answer
(3)is strictly decreasing on $\mathbb{R}$
(4)has two critical points

Official answer

Option 2

NTA final key.

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Parameter Evaluation in Homogeneous Systems

Same idea in other shifts

Asked 5× in all

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18 Mar 2021, Shift 1 · Q64Let $\alpha,\beta,\gamma$ be the real roots of the equation, $x^3+ax^2+bx+c=0$ , ( $a,b,c\in\mathbf{R}$ and $a,b\ne0$ ). If the system of…HardSingle correct
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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.