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Mathematics - Mathematical Reasoning

Practise 135 JEE Main previous year questions on Mathematical Reasoning, compiled from papers spanning 2008 to 2023. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Main tests.

Mathematical Reasoning has been asked in 15 of the 25 years of JEE Main papers analysed (2002–2026), with 135 questions in all. 89% of them were easy, 10% moderate and 1% tough. Most of its questions came from 2021, with 25 questions that year. In the last three years (2024–2026) it had 0 questions across 49 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Mathematical Reasoning.

  1. 1Negation of p q ~ p q is15 Apr, 2023 (M)Mathematical Reasoning
  2. 2The negation of the statement ( ( A ( B C ) ) ( A B ) ) A is13 Apr, 2023 (M)Mathematical Reasoning
  3. 3The statement ( p ( ~ q ) ) ( ( ~ p ) q ) ( ( ~ p ) ( ~ q ) ) is equivalent to _ _ _ _ _13 Apr, 2023 (E)Mathematical Reasoning
  4. 4Among the two statements S 1 : p q p ~ q is a contradiction and S 2 : p q ~ p q p ~ q ~ p ~ q is a tautology12 Apr, 2023 (M)Mathematical Reasoning
  5. 5The number of ordered triplets of the truth values of p , q and r such that the truth value of the statement p q p r q r is True, is equal t11 Apr, 2023 (M)Mathematical Reasoning
  6. 6The converse of ~ p q r is11 Apr, 2023 (E)Mathematical Reasoning
  7. 7The negation of the statement p q q ~ r is10 Apr, 2023 (M)Mathematical Reasoning
  8. 8The statement ~ p ~ p q is equivalent to10 Apr, 2023 (E)Mathematical Reasoning
  9. 9Negation of p q q p is08 Apr, 2023 (M)Mathematical Reasoning
  10. 10The negation of ( p ( - q ) ) ( - p ) is equivalent to08 Apr, 2023 (E)Mathematical Reasoning
  11. 11Statement ( P Q ) ( R Q ) is logically equivalent to06 Apr, 2023 (M)Mathematical Reasoning
  12. 12Among the statements S 1 : p q ~ p q is a tautology S 2 : q p ~ p q is a contradiction06 Apr, 2023 (E)Mathematical Reasoning
  13. 13The negation of the expression q ( ( ~ q ) p ) is equivalent to01 Feb, 2023 (M)Mathematical Reasoning
  14. 14Which of the following statements is a tautology?01 Feb, 2023 (E)Mathematical Reasoning
  15. 15Consider: S 1 : p q p ~ q is a tautology. S 2 : ~ p ~ q ~ p q is a contradiction. Then31 Jan, 2023 (M)Mathematical Reasoning
  16. 16The number of values of r p , q , ~ p , ~ q for which p q r q ( p r q is a tautology, is :31 Jan, 2023 (E)Mathematical Reasoning
  17. 17Among the statements: S 1 : p q r p r S 2 : p q r p r q r30 Jan, 2023 (M)Mathematical Reasoning
  18. 18Consider the following statements: P : I have fever Q : I will not take medicine R : I will take rest The statement If I have fever, then I 30 Jan, 2023 (E)Mathematical Reasoning
  19. 19If p , q and r are three propositions, then which of the following combination of truth values of p , q and r makes the logical expression {29 Jan, 2023 (M)Mathematical Reasoning
  20. 20The statement B ~ A B is not equivalent to :29 Jan, 2023 (E)Mathematical Reasoning
  21. 21The statement p ~ q p ~ q is25 Jan, 2023 (M)Mathematical Reasoning
  22. 22Let , { , } be such that ( p q ) ( p q ) is a tautology. Then25 Jan, 2023 (E)Mathematical Reasoning
  23. 23The compound statement ( ~ ( P Q ) ) ( ( ~ P ) Q ) ( ( ~ P ) ( ~ Q ) ) is equivalent to24 Jan, 2023 (M)Mathematical Reasoning
  24. 24Let p and q be two statements. Then ~ ( p ( p ~ q ) is equivalent to24 Jan, 2023 (E)Mathematical Reasoning
  25. 25The statement p q p r is equivalent to29 Jul, 2022 (M)Mathematical Reasoning
  26. 26The statement p q p r is NOT equivalent to:29 Jul, 2022 (E)Mathematical Reasoning
  27. 27Let the operations * , , . If p * q p ~ q is a tautology, then the ordered pair * , is28 Jul, 2022 (M)Mathematical Reasoning
  28. 28Let p : Ramesh listens to music. q : Ramesh is out of his village r : It is Sunday s : It is Saturday Then the statement Ramesh listens to m28 Jul, 2022 (E)Mathematical Reasoning
  29. 29p r p ~ q is equivalent to ~ p when r is27 Jul, 2022 (M)Mathematical Reasoning
  30. 30If the truth value of the statement P ~ R ~ R Q is F , then the truth value of which of the following is F ?27 Jul, 2022 (E)Mathematical Reasoning
  31. 31The statement ~ p ~ q q is:26 Jul, 2022 (M)Mathematical Reasoning
  32. 32Negation of the Boolean expression p q p is26 Jul, 2022 (E)Mathematical Reasoning
  33. 33Which of the following statements is a tautology?25 Jul, 2022 (M)Mathematical Reasoning
  34. 34Consider the following statements: P : Ramu is intelligent. Q : Ramu is rich. R : Ramu is not honest. The negation of the statement Ramu is 25 Jul, 2022 (E)Mathematical Reasoning
  35. 35Let , , , be such that p q p q q is a tautology. Then is equal to29 Jun, 2022 (M)Mathematical Reasoning
  36. 36Negation of the Boolean statement p q ~ r p is equivalent to:29 Jun, 2022 (E)Mathematical Reasoning
  37. 37Let p , q , r be three logical statements. Consider the compound statements S 1 : ~ p q ~ p r and S 2 : p q r Then, which of the following i28 Jun, 2022 (M)Mathematical Reasoning
  38. 38The maximum number of compound propositions, out of p r s , p r ~ s , p ~ q s , ~ p ~ r s , ~ p ~ r ~ s , ~ p q ~ s , q r ~ s , q ~ r ~ s , 28 Jun, 2022 (E)Mathematical Reasoning
  39. 39The boolean expression ~ p q q is equivalent to27 Jun, 2022 (M)Mathematical Reasoning
  40. 40Which of the following statement is a tautology?27 Jun, 2022 (E)Mathematical Reasoning
  41. 41Let , , be such that p q p q r is a tautology. Then p q r is logically equivalent to26 Jun, 2022 (M)Mathematical Reasoning
  42. 42Let r P , q , ~ p , ~ q be such that the logical statement r ~ p p q r is a tautology. Then r is equal to26 Jun, 2022 (E)Mathematical Reasoning
  43. 43Consider the following two propositions : P 1 : ~ p ~ q P 2 : p ~ q ~ p q If the proposition p ~ p q is evaluated as FALSE, then25 Jun, 2022 (M)Mathematical Reasoning
  44. 44The negation of the Boolean expression ~ q p ~ p q is logically equivalent to25 Jun, 2022 (E)Mathematical Reasoning
  45. 45The number of choices for , , , , such that p q p ~ q ~ p q is a tautology, is24 Jun, 2022 (M)Mathematical Reasoning
  46. 46Consider the following statements: A : Rishi is a judge. B : Rishi is honest. C : Rishi is not arrogant. The negation of the statement if Ri24 Jun, 2022 (E)Mathematical Reasoning
  47. 47Which of the following is equivalent to the Boolean expression p ~ q ?01 Sep, 2021 (E)Mathematical Reasoning
  48. 48Let * , { , } be such that the Boolean expression ( p * ~ q ) ( p q ) is a tautology. Then :31 Aug, 2021 (M)Mathematical Reasoning
  49. 49Negation of the statement ( p r ) ( q r ) is :31 Aug, 2021 (E)Mathematical Reasoning
  50. 50The statement ( p ( p q ) ( q r ) ) r is27 Aug, 2021 (M)Mathematical Reasoning

Frequently Asked Questions

1.How many questions are available for Mathematical Reasoning?

This chapter includes 135 questions compiled from JEE Main papers spanning 2008 to 2023.

2.Are these questions only from JEE Main, or from other exams too?

These are JEE Main questions specifically for the Mathematical Reasoning chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Mathematical Reasoning an important chapter for JEE Main Mathematics?

Mathematical Reasoning has appeared in 15 of the 25 years of JEE Main papers covered here, with 135 questions across 133 papers - about one per paper it appears in.

4.What is the difficulty level of Mathematical Reasoning questions in JEE Main?

Of the 135 questions analysed for this chapter, 89% are easy, 10% moderate and 1% tough. 2021 had the most, with 25 questions.

5.Which topics in Mathematical Reasoning should I focus on?

All of this chapter's questions come from a single topic: Mathematical Reasoning.

6.Is Mathematical Reasoning's weightage in JEE Main going up or down?

Across all 133 papers analysed, Mathematical Reasoning has averaged about 1.0 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.