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Friday, 9 October

JEE Main Maths · Relations and Functions

Functions and Domain in JEE Main

Functions and Domain (Maths, Relations and Functions) came 16 times in 15 of the 42 JEE Main shifts Lumi analysed, across 13 distinct ideas. 11 of them came in 2024–26; it was last asked in 2026.

Questions
16
in 15 shifts
Ideas asked
13
3 asked more than once
Numerical answer
4
25% of its questions
Pattern
Asked most years
last asked 2026
Questions each year
0360’170’202’210’223’235’244’252’26

In the shifts Lumi analysed for each year.

Difficulty and format
Easy 3Medium 9Hard 4

Format

  • Single correct11 Q
  • Numerical value4 Q
  • Other1 Q
Ideas inside the topic
13 ideas
Where it sits

Part of Relations and Functions, which had 60 questions in all. Functions and Domain accounts for 27% of them. In Lumi's JEE taxonomy it belongs to Calculus.

Some questions sit in other chapters too: Application of Derivatives, Inverse Trigonometric Functions, Sequences and Series, Trigonometric Functions.

Every question

All 16 Functions and Domain questions

Newest first, each with its options and official answer.

  1. 2 Apr 2026, Shift 1 · Q21If the domain of the function f(x)=log⁡(0.6)(∣2x−5x2−4∣)f(x)=\sqrt{\log_{(0.6)}\left(\left|\frac{2x-5}{x^2-4}\right|\right)} is…HardNumerical value
  2. 4 Apr 2026, Shift 2 · Q1For the function f:[1,∞)→[1,∞)f:[1,\infty)\to[1,\infty) defined by f(x)=(x−1)4+1f(x)=(x-1)^4+1, among the two statements: (I) The set…HardOther
  3. 2 Apr 2025, Shift 2 · Q1If the domain of the function f(x)=110+3x−x2+1x+∣x∣f(x) = \frac{1}{\sqrt{10+3x-x^2}} + \frac{1}{\sqrt{x+|x|}} is (a,b)(a, b), then (1+a)2+b2(1+a)^2 + b^2 is equal to :EasySingle correct
  4. 3 Apr 2025, Shift 1 · Q2If the domain of the function f(x)=log⁡e(2x−35+4x)+sin⁡−1(4+3x2−x)f(x) = \log_e\left(\frac{2x-3}{5+4x}\right) + \sin^{-1}\left(\frac{4+3x}{2-x}\right) is [α,β)[\alpha, \beta),…MediumSingle correct
  5. 3 Apr 2025, Shift 2 · Q2If the domain of the function f(x)=log⁡7(1−log⁡4(x2−9x+18))f(x) = \log_7 (1 - \log_4 (x^2 - 9x + 18)) is (α,β)∪(γ,δ)(\alpha, \beta) \cup (\gamma, \delta), then…MediumSingle correct
  6. 8 Apr 2025, Shift 2 · Q21Let the domain of the function f(x)=cos⁡−1(4x+53x−7)f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right) be [α,β][\alpha, \beta] and the domain of…MediumNumerical value
  7. 6 Apr 2024, Shift 2 · Q1Let f(x)=17−sin⁡5xf(x)=\frac{1}{7-\sin 5x} be a function defined on R\mathbb{R}. Then the range of the function f(x)f(x) is equal to :EasySingle correct
  8. 8 Apr 2024, Shift 1 · Q21If the range of f(θ)=sin⁡4θ+3cos⁡2θsin⁡4θ+cos⁡2θf(\theta)=\frac{\sin^4\theta+3\cos^2\theta}{\sin^4\theta+\cos^2\theta}, θ∈R\theta\in\mathbb{R} is [α,β][\alpha,\beta], then…MediumNumerical value
  9. 29 Jan 2024, Shift 1 · Q1If f(x)={2+2x,−1≤x<01−x3,0≤x≤3f(x)=\begin{cases}2+2x, & -1\leq x<0\\ 1-\frac{x}{3}, & 0\leq x\leq 3\end{cases} ;…MediumSingle correct
  10. 30 Jan 2024, Shift 2 · Q1If the domain of the function f(x)=log⁡e(2x+34x2+x−3)+cos⁡−1(2x−1x+2)f(x) = \log_e\left(\frac{2x+3}{4x^2+x-3}\right) + \cos^{-1}\left(\frac{2x-1}{x+2}\right) is…MediumSingle correct
  11. 31 Jan 2024, Shift 2 · Q1If the function f:(−∞,−1]→(a,b]f:(-\infty,-1]\to(a,b] defined by f(x)=ex3−3x+1f(x)=e^{x^3-3x+1} is one - one and onto, then the distance of the point…MediumSingle correct
  12. 8 Apr 2023, Shift 2 · Q21If domain of the function log⁡e(6x2+5x+12x−1)+cos⁡−1(2x2−3x+43x−5)\log_e\left(\frac{6x^2 + 5x + 1}{2x - 1}\right) + \cos^{-1}\left(\frac{2x^2 - 3x + 4}{3x - 5}\right) is…HardNumerical value
  13. 11 Apr 2023, Shift 1 · Q5The number of integral solutions xx of log⁡(x+72)(x−72x−3)2≥0\log_{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2x-3}\right)^2 \ge 0 isHardSingle correct
  14. 13 Apr 2023, Shift 2 · Q1The range of f(x)=4sin⁡−1(x2x2+1)f(x)=4\sin^{-1}\left(\frac{x^2}{x^2+1}\right) isMediumSingle correct
  15. 18 Mar 2021, Shift 1 · Q61If the functions are defined as f(x)=xf(x)=\sqrt{x} and g(x)=1−xg(x)=\sqrt{1-x}, then what is the common domain of the following functions :…EasySingle correct
  16. 18 Mar 2021, Shift 1 · Q71The real valued function f(x)=cosec−1xx−[x]f(x)=\dfrac{\mathrm{cosec}^{-1}x}{\sqrt{x-[x]}}, where [x][x] denotes the greatest integer less than or equal to…MediumSingle correct