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Friday, 9 October

JEE Main Maths · Class 11

Relations and Functions: JEE Main previous year questions

Relations and Functions had 60 questions in the 42 JEE Main shifts Lumi analysed, about 1.3 a shift, asked in 40 of 42 shifts. It ranks 6 of 22 Maths chapters by questions; 13% of its questions were hard.

Questions
60
in 40 of 42 shifts
A shift, on average
1.3
of 25 Maths questions
Since 2024
+0.1
1.2 a shift in 2017–23, 1.3 in 2024–26
Numerical answer
21
35% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
07141’175’205’216’228’2313’2412’2510’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20171
  • 20205
  • 20215
  • 20226
  • 20238
  • 202413
  • 202512
  • 202610
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

6 topics and 23 distinct ideas; 8 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

15 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
8 repeat

Study it on Lumi

Relations and Functions: the interactive lesson

Every question

All 60 Relations and Functions questions

Newest first. Each opens with its options and the official answer.

2026 10 questions

  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. 2 Apr 2026, Shift 2 · Q21Let A={2,3,4,5,6}A = \{2, 3, 4, 5, 6\}. Let RR be a relation on the set A×AA \times A given by (x,y)R(z,w)(x, y)R(z, w) if and only if xx divides zz and…MediumNumerical value
  3. 4 Apr 2026, Shift 1 · Q4The number of functions f:{1,2,3,4}→{a,b,c}f:\{1,2,3,4\}\to\{a,b,c\}, which are not onto, is:EasySingle correct
  4. 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
  5. 4 Apr 2026, Shift 2 · Q16Let for some α∈R\alpha\in\mathbb{R}, f:R→Rf:\mathbb{R}\to\mathbb{R} be a function satisfying f(x+y)=f(x)+2y2+y+αxyf(x+y)=f(x)+2y^2+y+\alpha xy for all…MediumSingle correct
  6. 5 Apr 2026, Shift 1 · Q21Let A={1,2,3,4,5,6}A = \{1, 2, 3, 4, 5, 6\}. The number of one-one functions f:A→Af: A \to A such that f(1)≥3f(1) \geq 3, f(3)≤4f(3) \leq 4 and f(2)+f(3)=5f(2) + f(3) = 5,…MediumNumerical value
  7. 5 Apr 2026, Shift 2 · Q21Let A={1,4,7}A=\{1, 4, 7\} and B={2,3,8}B=\{2, 3, 8\}. Then the number of elements, in the relation…MediumNumerical value
  8. 6 Apr 2026, Shift 2 · Q1Let f:R→Rf:\mathbf{R}\to\mathbf{R} be defined as f(x)=2x2−3x+23x2+x+3f(x)=\frac{2x^2-3x+2}{3x^2+x+3}. Then ff is :MediumSingle correct
  9. 6 Apr 2026, Shift 2 · Q21Let R={(x,y)∈N×N:log⁡e(x+y)≤2}R=\{(x,y)\in\mathbf{N}\times\mathbf{N}:\log_e(x+y)\le2\}. Then the minimum number of elements, required to be added in R to make it…HardNumerical value
  10. 8 Apr 2026, Shift 2 · Q1Consider the relation R on the set {−2,−1,0,1,2}\{-2, -1, 0, 1, 2\} defined by (a,b)∈R(a, b) \in R if and only if 1+ab>01 + ab > 0. Then, among the statements…MediumOther

2025 12 questions

  1. 2 Apr 2025, Shift 1 · Q12Let A be the set of all functions f:Z→Zf:\mathbf{Z}\to\mathbf{Z} and R be a relation on A such that…EasySingle correct
  2. 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
  3. 2 Apr 2025, Shift 2 · Q2Let A={1,2,3,…,100}A = \{1, 2, 3, \ldots, 100\} and RR be a relation on AA such that R={(a,b):a=2b+1}R = \{(a, b) : a = 2b + 1\}. Let…MediumSingle correct
  4. 3 Apr 2025, Shift 1 · Q1Let A={−3,−2,−1,0,1,2,3}A = \{-3, -2, -1, 0, 1, 2, 3\}. Let R be a relation on A defined by xRyx\mathrm{R}y if and only if 0≤x2+2y≤40 \le x^2 + 2y \le 4. Let ll be…MediumSingle correct
  5. 3 Apr 2025, Shift 2 · Q1Let A={−2,−1,0,1,2,3}A = \{-2, -1, 0, 1, 2, 3\}. Let R be a relation on AA defined by xRyxRy if and only if y=max⁡{x,1}y = \max\{x, 1\}. Let ll be the number of…MediumSingle correct
  6. 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
  7. 3 Apr 2025, Shift 2 · Q3Let ff be a function such that f(x)+3f(24x)=4x, x≠0f(x) + 3f\left(\frac{24}{x}\right) = 4x,\ x \neq 0. Then f(3)+f(8)f(3) + f(8) is equal toEasySingle correct
  8. 4 Apr 2025, Shift 2 · Q2Let A={−3,−2,−1,0,1,2,3}A=\{-3,-2,-1,0,1,2,3\} and R be a relation on A defined by xRyxRy if and only if 2x−y∈{0,1}2x-y\in\{0,1\}. Let ll be the number of elements…MediumSingle correct
  9. 7 Apr 2025, Shift 1 · Q24The number of relations on the set A={1,2,3}A = \{1, 2, 3\}, containing at most 6 elements including (1,2)(1, 2), which are reflexive and transitive…HardNumerical value
  10. 7 Apr 2025, Shift 2 · Q2If the range of the function f(x)=5−xx2−3x+2f(x)=\frac{5-x}{x^2-3x+2}, x≠1,2x\ne 1,2, is (−∞,α]∪[β,∞)(-\infty,\alpha]\cup[\beta,\infty), then α2+β2\alpha^2+\beta^2 is…MediumSingle correct
  11. 8 Apr 2025, Shift 2 · Q1Let A={0,1,2,3,4,5}A = \{0, 1, 2, 3, 4, 5\}. Let RR be a relation on AA defined by (x,y)∈R(x, y) \in R if and only if max⁡{x,y}∈{3,4}\max\{x, y\} \in \{3, 4\}. Then…MediumOther
  12. 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

2024 13 questions

  1. 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
  2. 6 Apr 2024, Shift 2 · Q2Let A={1,2,3,4,5}A=\{1,2,3,4,5\}. Let RR be a relation on AA defined by xRyxRy if and only if 4x≤5y4x\le 5y. Let mm be the number of elements in RR…MediumSingle correct
  3. 8 Apr 2024, Shift 1 · Q1Let [t][t] be the greatest integer less than or equal to tt. Let AA be the set of all prime factors of 2310 and f:A→Zf: A \to \mathbb{Z} be…MediumSingle correct
  4. 9 Apr 2024, Shift 1 · Q1If the domain of the function f(x)=sin⁡−1(x−12x+3)f(x)=\sin^{-1}\left(\frac{x-1}{2x+3}\right) is R−(α,β)\mathbf{R}-(\alpha,\beta), then 12αβ12\alpha\beta is equal…MediumSingle correct
  5. 9 Apr 2024, Shift 1 · Q21Let A={2,3,6,7}A=\{2,3,6,7\} and B={4,5,6,8}B=\{4,5,6,8\}. Let R be a relation defined on A×BA\times B by (a1,b1) R (a2,b2)(a_1,b_1)\,R\,(a_2,b_2) if and only if…MediumNumerical value
  6. 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
  7. 29 Jan 2024, Shift 1 · Q2Let R be a relation on Z×Z\mathbb{Z}\times\mathbb{Z} defined by (a,b) R (c,d)(a, b)\,R\,(c, d) if and only if ad−bcad-bc is divisible by 5. Then R isMediumSingle correct
  8. 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
  9. 30 Jan 2024, Shift 2 · Q21The number of symmetric relations defined on the set {1,2,3,4}\{1, 2, 3, 4\} which are not reflexive is ________.MediumNumerical value
  10. 30 Jan 2024, Shift 2 · Q22The number of real solutions of the equation x(x2+3∣x∣+5∣x−1∣+6∣x−2∣)=0x\left(x^2 + 3|x| + 5|x-1| + 6|x-2|\right) = 0 is ________.MediumNumerical value
  11. 31 Jan 2024, Shift 1 · Q1If f(x)=4x+36x−4, x≠23f(x)=\frac{4x+3}{6x-4},\ x\neq\frac{2}{3} and (f∘f)(x)=g(x)(f\circ f)(x)=g(x), where…MediumSingle correct
  12. 31 Jan 2024, Shift 1 · Q21Let A={1,2,3,4}A=\{1,2,3,4\} and R={(1,2),(2,3),(1,4)}R=\{(1,2),(2,3),(1,4)\} be a relation on A. Let S be the equivalence relation on A such that R⊂SR\subset S and…MediumNumerical value
  13. 31 Jan 2024, Shift 2 · Q21Let A={1,2,3,…,100}A=\{1,2,3,\ldots,100\}. Let RR be a relation on AA defined by (x,y)∈R(x,y)\in R if and only if 2x=3y2x=3y. Let R1R_1 be a symmetric…MediumNumerical value

2023 8 questions

  1. 6 Apr 2023, Shift 1 · Q1Let A={x∈R:[x+3]+[x+4]≤3}A=\{x\in\mathbb{R}:[x+3]+[x+4]\le 3\},…MediumSingle correct
  2. 6 Apr 2023, Shift 1 · Q21Let A={1,2,3,4,…,10}A=\{1,2,3,4,\ldots,10\} and B={0,1,2,3,4}B=\{0,1,2,3,4\}. The number of elements in the relation…MediumNumerical value
  3. 8 Apr 2023, Shift 2 · Q1Let A={1,2,3,4,5,6,7}A = \{1, 2, 3, 4, 5, 6, 7\}. Then the relation R={(x,y)∈A×A:x+y=7}R = \{(x, y) \in A \times A : x + y = 7\} isEasySingle correct
  4. 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
  5. 8 Apr 2023, Shift 2 · Q23Let R={a,b,c,d,e}R = \{a, b, c, d, e\} and S={1,2,3,4}S = \{1, 2, 3, 4\}. Total number of onto functions f:R→Sf: R \to S such that f(a)≠1f(a) \neq 1, is equal to…HardNumerical value
  6. 11 Apr 2023, Shift 1 · Q1An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five…EasySingle correct
  7. 13 Apr 2023, Shift 2 · Q21Let A={−4,−3,−2,0,1,3,4}A=\{-4,-3,-2,0,1,3,4\} and R={(a,b)∈A×A:b=∣a∣ or b2=a+1}R=\{(a,b)\in A\times A: b=|a| \text{ or } b^2=a+1\} be a relation on A. Then the minimum number of…MediumNumerical value
  8. 13 Apr 2023, Shift 2 · Q24Let [α][\alpha] denote the greatest integer ≤α\le\alpha. Then [1]+[2]+[3]+…+[120][\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+\ldots+[\sqrt{120}] is equal to ______MediumNumerical value

2022 6 questions

  1. 25 Jul 2022, Shift 1 · Q1The total number of functions, f:{1,2,3,4}→{1,2,3,4,5,6}f:\{1,2,3,4\}\rightarrow\{1,2,3,4,5,6\} such that f(1)+f(2)=f(3)f(1)+f(2)=f(3), is equal to :MediumSingle correct
  2. 28 Jul 2022, Shift 1 · Q8For α∈N\alpha\in\mathbf{N}, consider a relation RR on N\mathbf{N} given by R={(x,y):3x+αy is a multiple of 7}R=\{(x,y):3x+\alpha y\text{ is a multiple of }7\}. The…MediumSingle correct
  3. 28 Jul 2022, Shift 1 · Q18Let α,β\alpha,\beta and γ\gamma be three positive real numbers. Let f(x)=αx5+βx3+γx, x∈Rf(x)=\alpha x^5+\beta x^3+\gamma x,\ x\in\mathbf{R} and…MediumSingle correct
  4. 24 Jun 2022, Shift 1 · Q21The number of one-one functions f:{a,b,c,d}→{0,1,2,…,10}f:\{a, b, c, d\}\to\{0, 1, 2, \ldots, 10\} such that 2f(a)−f(b)+3f(c)+f(d)=02f(a)-f(b)+3f(c)+f(d)=0 is ______.HardNumerical value
  5. 29 Jun 2022, Shift 1 · Q11Let a set A=A1∪A2∪…∪AkA = A_1 \cup A_2 \cup \ldots \cup A_k, where Ai∩Aj=ϕA_i \cap A_j = \phi for i≠ji \ne j, 1≤i,j≤k1 \le i, j \le k. Define the relation R…EasySingle correct
  6. 29 Jun 2022, Shift 1 · Q27Let c,k∈Rc, k \in \mathbf{R}. If f(x)=(c+1)x2+(1−c2)x+2kf(x) = (c + 1)x^2 + (1 - c^2)x + 2k and f(x+y)=f(x)+f(y)−xyf(x + y) = f(x) + f(y) - xy, for all x,y∈Rx, y \in \mathbf{R}, then…MediumNumerical value

2021 5 questions

  1. 3 Aug 2021, Shift 2 · Q61Let R\mathbb{R} be the set of real numbers and '*' be a binary operation on R−{0}\mathbb{R} - \{0\} defined by…MediumSingle correct
  2. 3 Aug 2021, Shift 2 · Q81The number of elements in the set {x∈R:(∣x∣−2)⋅∣2x+3∣=1}\{x \in \mathbb{R} : (|x| - 2)\cdot|2x+3| = 1\} is ‾\underline{\hspace{2em}}.MediumNumerical value
  3. 25 Jul 2021, Shift 1 · Q66Let g:N→Ng:\mathbf{N}\to\mathbf{N} be defined as g(3n+1)=3n+2g(3n+1)=3n+2, g(3n+2)=3n+3g(3n+2)=3n+3, g(3n+3)=3n+1g(3n+3)=3n+1, for all n≥0n\ge0. Then which of the following…HardSingle correct
  4. 16 Mar 2021, Shift 2 · Q71Let A={2,3,4,5,…,30}A=\{2,3,4,5,\ldots,30\} and '≃\simeq' be an equivalence relation on A×AA\times A, defined by (a,b)≃(c,d)(a,b)\simeq(c,d), if and only if…MediumSingle correct
  5. 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

2020 5 questions

  1. 8 Jan 2020, Shift 1 · Q51The inverse function of f(x)=82x−8−2x82x+8−2xf(x)=\dfrac{8^{2x}-8^{-2x}}{8^{2x}+8^{-2x}}, x∈(−1,1)x\in(-1,1), is ______.MediumSingle correct
  2. 9 Jan 2020, Shift 2 · Q51If A={x∈R:∣x∣<2}A=\{x\in\mathbf{R}:|x|<2\} and B={x∈R:∣x−2∣≥3}B=\{x\in\mathbf{R}:|x-2|\ge 3\}; then :EasySingle correct
  3. 2 Sep 2020, Shift 1 · Q51If R={(x,y):x,y∈Z, x2+3y2≤8}R=\{(x, y) : x, y\in \mathbf{Z},\ x^{2}+3y^{2}\le 8\} is a relation on the set of integers Z\mathbf{Z}, then the domain of R−1R^{-1}…EasySingle correct
  4. 6 Sep 2020, Shift 2 · Q51For a suitably chosen real constant a, let a function, f:R−{−a}→Rf:\mathbf{R}-\{-a\}\to\mathbf{R} be defined by f(x)=a−xa+xf(x)=\frac{a-x}{a+x}. Further…MediumSingle correct
  5. 6 Sep 2020, Shift 2 · Q73Suppose that a function f:R→Rf:\mathbf{R}\to\mathbf{R} satisfies f(x+y)=f(x)f(y)f(x+y)=f(x)f(y) for all x,y∈Rx,y\in\mathbf{R} and f(1)=3f(1)=3. If…MediumNumerical value

2017 1 questions

  1. 2 Apr 2017 (offline) · Q61The function f:R→[−12,12]f:\mathbf{R}\rightarrow\left[-\frac{1}{2},\frac{1}{2}\right] defined as f(x)=x1+x2f(x)=\frac{x}{1+x^2}, is :MediumSingle correct

Pattern: Asked most years.