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Sunday, 25 October

JEE Main · Maths · Class 11

Mathematical Reasoning: JEE Main previous year questions

This chapter is not in NTA's JEE Main 2026 syllabus. It had 64 questions in the shifts Lumi analysed; they are kept here for reference.

Questions
64
in 63 of 108 shifts · 5 of 8 years
Average a shift
0.5
of 25 Maths · 0.0 since 2024 -0.8
Typical range
0.0–0.8
questions a shift; fewest 0.0, most 0.9
Syllabus
Dropped
NTA JEE Main 2026 syllabus
  • Typical range (fact)
  • Average a shift (fact)
  • Weighted estimate (model)

Questions are counted per shift, out of the 25 each subject has, in the shifts Lumi analysed; papers that offered 30 a subject (2017, 2021–2024) are scaled to 25. Typical range: the middle six of the eight years (2017, 2020–2026), leaving out the single highest and lowest year. The average and the range are historical fact. The weighted estimate is a model: each year's share, with recent years counting more (half-life three years), and chapters NTA dropped from the syllabus set near zero. It is a guide to effort, not a forecast of the paper.

Key findings

Mathematical Reasoning at a glance

  1. 01

    3%

    of its questions asked for a numerical answer, 0.1 times the Maths average.

  2. 02

    2%

    of its questions were rated hard, against 26% across all Maths questions in the same shifts.

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

0240.9’170.8’200.7’210.7’220.8’230’240’250’26

Raw count: 2017: 1 in 1 shift · 2020: 10 in 12 shifts · 2021: 20 in 24 shifts · 2022: 21 in 24 shifts · 2023: 12 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Conceptual44%
  • Application44%
  • Recall, single correct6%
  • Numerical answer3%
  • Two statements3%

Most common asks: negation of compound statement (11); logical equivalence of compound statements (9); tautology check of compound statement (6).

Profile

This chapter in numbers

Where it ranks, how steady it is, and what it costs to study.

Syllabus
Dropped
NTA JEE Main 2026
Last asked
2023
Share of Maths
2.0%
of its questions, all shifts analysed
Busiest year
2017
0.9 questions a shift
Year to year
Swings a lot
varies by about 0.4 questions a shift
Long-run direction
-0.12
questions a shift, per year
Easy questions
50%
2% rated hard
Numerical answer
3%
0.1× the Maths rate
With a figure
0%
graph, diagram or structure
Foundation for others
50%
of its ideas are used in other chapters

Difficulty, year by year

Each question rated easy, medium or hard. Each bar is that year’s split, so years compare directly; the number is the questions in that year’s analysed shifts (1 to 24 shifts a year).

  • 20171
  • 202010
  • 202120
  • 202221
  • 202312
  • 2024
  • 2025
  • 2026
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Application47%
  • Conceptual45%
  • Recall6%
  • Multi-step2%

Every question

All 64 Mathematical Reasoning questions

Newest first, shift by shift. The newest 40 show their opening words; older ones name the idea they tested. Each opens with its options and the official answer.

JEE Main 202312 questions

  1. 6 Apr 2023, Shift 1 · Q20Statement (P⇒Q)∧(R⇒Q)(P\Rightarrow Q)\wedge(R\Rightarrow Q) is logically equivalent toEasySingle correct
  2. 6 Apr 2023, Shift 2 · Q20Among the statements (S1): (p⇒q)∨((∼p)∧q)(p\Rightarrow q)\vee\left((\sim p)\wedge q\right) is a tautology (S2):…MediumTwo statements
  3. 8 Apr 2023, Shift 1 · Q20Negation of (p⇒q)⇒(q⇒p)(p\Rightarrow q)\Rightarrow(q\Rightarrow p) isMediumSingle correct
  4. 8 Apr 2023, Shift 2 · Q20The negation of (p∧(∼q))∨(∼p)(p \wedge (\sim q)) \vee (\sim p) is equivalent toEasySingle correct
  5. 10 Apr 2023, Shift 1 · Q20The negation of the statement (p∨q)∧(q∨(∼r))(p\vee q)\wedge(q\vee(\sim r)) isEasySingle correct
  6. 10 Apr 2023, Shift 2 · Q20The statement ∼[p∨(∼(p∧q))]\sim[p \vee (\sim(p \wedge q))] is equivalent toEasySingle correct
  7. 11 Apr 2023, Shift 1 · Q23The number of ordered triplets of the truth values of pp, qq and rr such that the truth value of the statement…EasyNumerical value
  8. 11 Apr 2023, Shift 2 · Q20The converse of ((∼p)∧q)⇒r((\sim p) \wedge q) \Rightarrow r isEasySingle correct
  9. 12 Apr 2023, Shift 1 · Q20Among the two statements (S1) : (p⇒q)∧(p∧(∼q))(p\Rightarrow q)\wedge(p\wedge(\sim q)) is a contradiction and (S2) :…MediumSingle correct
  10. 13 Apr 2023, Shift 1 · Q20The negation of the statement ((A∧(B∨C))⇒(A∨B))⇒A((A\wedge(B\vee C))\Rightarrow(A\vee B))\Rightarrow A isMediumSingle correct
  11. 13 Apr 2023, Shift 2 · Q20The statement (p∧(∼q))∨((∼p)∧q)∨((∼p)∧(∼q))(p\wedge(\sim q))\vee((\sim p)\wedge q)\vee((\sim p)\wedge(\sim q)) is equivalent to ______EasySingle correct
  12. 15 Apr 2023, Shift 1 · Q20Negation of p∧(q∧∼(p∧q))p\wedge\left(q\wedge\sim(p\wedge q)\right) isMediumSingle correct

JEE Main 202221 questions

  1. 25 Jul 2022, Shift 1 · Q20Which of the following statements is a tautology ?EasySingle correct
  2. 25 Jul 2022, Shift 2 · Q20Consider the following statements : PP : Ramu is intelligent. QQ : Ramu is rich. RR : Ramu is not honest. The negation of the statement…MediumOther
  3. 26 Jul 2022, Shift 2 · Q17Negation of the Boolean expression p⇔(q⇒p)p\Leftrightarrow(q\Rightarrow p) isEasySingle correct
  4. 27 Jul 2022, Shift 1 · Q16(p∧r)⇔(p∧(∼q))(p \wedge r) \Leftrightarrow (p \wedge (\sim q)) is equivalent to (∼p)(\sim p) when rr isMediumSingle correct
  5. 27 Jul 2022, Shift 2 · Q20If the truth value of the statement (P∧(∼R))→((∼R)∧Q)(P \wedge (\sim R)) \rightarrow ((\sim R) \wedge Q) is F, then the truth value of which of the…MediumSingle correct
  6. 28 Jul 2022, Shift 1 · Q5Let the operations ∗,⊙∈{∧,∨}*,\odot\in\{\wedge,\vee\}. If (p∗q)⊙(p⊙∼q)(p*q)\odot(p\odot\sim q) is a tautology, then the ordered pair (∗,⊙)(*,\odot) is :MediumSingle correct
  7. 28 Jul 2022, Shift 2 · Q80Let p : Ramesh listens to music. q : Ramesh is out of his village. r : It is Sunday. s : It is Saturday. Then the statement "Ramesh…EasySingle correct
  8. 29 Jul 2022, Shift 1 · Q12The statement (p∧q)⇒(p∧r)(p \wedge q) \Rightarrow (p \wedge r) is equivalent to :MediumSingle correct
  9. 29 Jul 2022, Shift 2 · Q20The statement (p⇒q)∨(p⇒r)(p\Rightarrow q)\vee(p\Rightarrow r) is NOT equivalent toMediumSingle correct
  10. 30 Jul 2022, Shift 2 · Q80Which of the following is a contradiction?MediumSingle correct
  11. 24 Jun 2022, Shift 1 · Q20The number of choices for Δ∈{∧,∨,⇒,⇔}\Delta\in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}, such that…MediumSingle correct
  12. 25 Jun 2022, Shift 1 · Q7Consider the following two propositions : P1 : ∼(p→∼q)\sim(p\to\sim q) P2 : (p∧∼q)∧((∼p)∨q)(p\wedge\sim q)\wedge((\sim p)\vee q) If the proposition…MediumSingle correct
  13. 25 Jun 2022, Shift 2 · Q17The negation of the Boolean expression ((∼q)∧p)⇒((∼p)∨q)((\sim q) \wedge p) \Rightarrow ((\sim p) \vee q) is logically equivalent to :EasySingle correct
  14. 26 Jun 2022, Shift 1 · Q20Let Δ,∇∈{∧,∨}\Delta, \nabla \in \{\wedge, \vee\} be such that p ∇ q⇒((p Δ q) ∇ r)p \,\nabla\, q \Rightarrow ((p \,\Delta\, q) \,\nabla\, r) is a tautology. Then…MediumSingle correct
  15. 27 Jun 2022, Shift 1 · Q20The boolean expression (∼(p∧q))∨q(\sim(p\wedge q))\vee q is equivalent to :EasySingle correct
  16. 27 Jun 2022, Shift 2 · Q20Which of the following statement is a tautology ?EasySingle correct
  17. 28 Jun 2022, Shift 1 · Q20Let p,q,rp, q, r be three logical statements. Consider the compound statements S1:((∼p)∨q)∨((∼p)∨r)S_1:((\sim p)\vee q)\vee((\sim p)\vee r) and…MediumSingle correct
  18. 28 Jun 2022, Shift 2 · Q30The maximum number of compound propositions, out of p∨r∨sp\vee r\vee s, p∨r∨∼sp\vee r\vee\sim s, p∨∼q∨sp\vee\sim q\vee s, ∼p∨∼r∨s\sim p\vee\sim r\vee s,…HardNumerical value
  19. 29 Jun 2022, Shift 1 · Q9Let Δ∈{∧,∨,⇒,⇔}\Delta \in \{\wedge, \vee, \Rightarrow, \Leftrightarrow\} be such that (p∧q) Δ ((p∨q)⇒q)(p \wedge q)\,\Delta\,((p \vee q) \Rightarrow q) is a…EasySingle correct
  20. 29 Jun 2022, Shift 2 · Q19Negation of the Boolean statement (p∨q)⇒((∼r)∨p)(p \vee q) \Rightarrow ((\sim r) \vee p) is equivalent toMediumSingle correct
  21. 30 Jun 2022, Shift 1 · Q20The conditional statement ((p∧q)→((∼p)∨r))∨(((∼p)∨r)→(p∧q))((p \wedge q) \rightarrow ((\sim p) \vee r)) \vee (((\sim p) \vee r) \rightarrow (p \wedge q)) is :MediumSingle correct

JEE Main 202120 questions

  1. 3 Aug 2021, Shift 1 · Q80If □, ◊ ∈{∧,∨}\in \{\wedge, \vee\} such that (∼q∧p)(\sim q \wedge p) □ (q(q ◊ ∼p)\sim p) is a tautology, thenMediumSingle correct
  2. 3 Aug 2021, Shift 2 · Q80The statement ∼(p↔∼q)\sim(p \leftrightarrow \sim q) is equivalent toEasySingle correct
  3. 4 Aug 2021, Shift 1 · Q80If r∈{p,q,∼p,∼q}r\in\{p, q, \sim p, \sim q\} such that the Boolean expression (∼(p∨q))∨(p∧r)(\sim(p\vee q))\vee(p\wedge r) is equivalent to rr, then rr is…MediumSingle correct
  4. 4 Aug 2021, Shift 2 · Q80Consider the following statements : p : Amit plays cricket q : Amit is out of Delhi. r : It is Sunday Then the statement “Amit plays…EasySingle correct
  5. 26 Aug 2021, Shift 1 · Q78If the truth value of the Boolean expression ((p∨q)∧(q→r)∧(∼r))→(p∧q)((p \vee q) \wedge (q \rightarrow r) \wedge (\sim r)) \rightarrow (p \wedge q) is false,…EasySingle correct
  6. 27 Aug 2021, Shift 1 · Q79The statement (p∧(p→q)∧(q→r))→r(p \wedge (p \rightarrow q) \wedge (q \rightarrow r)) \rightarrow r is :MediumSingle correct
  7. 27 Aug 2021, Shift 2 · Q79The Boolean expression (p∧q)⇒((r∧q)∧p)(p \wedge q) \Rightarrow ((r \wedge q) \wedge p) is equivalent to :MediumSingle correct
  8. 31 Aug 2021, Shift 1 · Q80Open the question · Medium · Single correct
  9. 31 Aug 2021, Shift 2 · Q80Open the question · Easy · Single correct
  10. 24 Feb 2021, Shift 1 · Q80Open the question · Easy · Single correct
  11. 24 Feb 2021, Shift 2 · Q66Open the question · Easy · Single correct
  12. 24 Feb 2021, Shift 2 · Q77Open the question · Medium · Other
  13. 25 Feb 2021, Shift 1 · Q80Open the question · Medium · Single correct
  14. 26 Feb 2021, Shift 2 · Q72Open the question · Medium · Single correct
  15. 22 Jul 2021, Shift 2 · Q66Open the question · Easy · Single correct
  16. 25 Jul 2021, Shift 1 · Q77Open the question · Easy · Single correct
  17. 25 Jul 2021, Shift 2 · Q65Open the question · Medium · Single correct
  18. 17 Mar 2021, Shift 1 · Q77Open the question · Medium · Single correct
  19. 17 Mar 2021, Shift 2 · Q62Open the question · Easy · Single correct
  20. 18 Mar 2021, Shift 2 · Q62Open the question · Easy · Single correct

JEE Main 202010 questions

  1. 8 Jan 2020, Shift 1 · Q70Open the question · Easy · Single correct
  2. 8 Jan 2020, Shift 2 · Q70Open the question · Medium · Single correct
  3. 9 Jan 2020, Shift 1 · Q70Open the question · Easy · Single correct
  4. 9 Jan 2020, Shift 2 · Q70Open the question · Easy · Single correct
  5. 2 Sep 2020, Shift 1 · Q70Open the question · Easy · Single correct
  6. 3 Sep 2020, Shift 1 · Q70Open the question · Easy · Single correct
  7. 3 Sep 2020, Shift 2 · Q70Open the question · Easy · Single correct
  8. 4 Sep 2020, Shift 1 · Q70Open the question · Medium · Two statements
  9. 5 Sep 2020, Shift 1 · Q70Open the question · Easy · Single correct
  10. 6 Sep 2020, Shift 2 · Q70Open the question · Easy · Single correct

JEE Main 20171 question

  1. 2 Apr 2017 (offline) · Q90Open the question · Medium · Single correct

Questions from the official JEE Main papers published by NTA. Chapter, topic and idea tags, counts and notes are Lumi’s. Pattern: Asked most years.

More Maths, Class 11

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