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Mathematical Reasoning — JEE Previous Year Questions

Every Mathematical Reasoning question asked in JEE Main and JEE Advanced across the last 186 papers — 26 questions, each with its correct answer. Free to read, no account needed.

Questions

26

Papers it appeared in

26/186

Appearance rate

14%

All 26 Mathematical Reasoning questions

Most recent papers first.

Q1·MathematicsSingle correctJEE Main 2020
Consider the statement: “For an integer n, if n3−1n^3 - 1n3−1 is even, then n is odd.” The contrapositive statement of this statement is:
  1. (A)For an integer n, if n is even, then n3−1n^3 - 1n3−1 is odd.
  2. (B)For an integer n, if n3−1n^3 - 1n3−1 is not even then n is not odd.
  3. (C)For an integer n, if n is even, then n3−1n^3 - 1n3−1 is even.
  4. (D)For an integer n, if n is odd, then n3−1n^3 - 1n3−1 is even.

Correct answer: (A)

Step-by-step solution →
Q2·MathematicsSingle correctJEE Main 2020
The negation of the Boolean expression p ∨ (~p ∧ q) is equivalent to:
  1. (A)p ∧ ~q
  2. (B)~p ∧ ~q
  3. (C)~p ∨ ~q
  4. (D)~p ∨ q

Correct answer: (B)

Step-by-step solution →
Q3·MathematicsSingle correctJEE Main 2020
The negation of the Boolean expression x↔∼yx \leftrightarrow \sim yx↔∼y is equivalent to
  1. (A)(x∧∼y)∨(∼x∧y)(x \wedge \sim y) \vee (\sim x \wedge y)(x∧∼y)∨(∼x∧y)
  2. (B)(∼x∧y)∨(∼x∧∼y)(\sim x \wedge y) \vee (\sim x \wedge \sim y)(∼x∧y)∨(∼x∧∼y)
  3. (C)(x∧y)∧(∼x∨∼y)(x \wedge y) \wedge (\sim x \vee \sim y)(x∧y)∧(∼x∨∼y)
  4. (D)(x∧y)∨(∼x∧∼y)(x \wedge y) \vee (\sim x \wedge \sim y)(x∧y)∨(∼x∧∼y)

Correct answer: (D)

Step-by-step solution →
Q4·MathematicsSingle correctJEE Main 2020
The statement (P→(q→p))→(p→(p∨q))(P \to (q \to p)) \to (p \to (p \vee q))(P→(q→p))→(p→(p∨q)) is:
  1. (A)a tautology
  2. (B)equivalent to (p∧q)∨(∼q)(p \wedge q) \vee (\sim q)(p∧q)∨(∼q)
  3. (C)equivalent to (p∨q)∧(∼p)(p \vee q) \wedge (\sim p)(p∨q)∧(∼p)
  4. (D)a contradiction

Correct answer: (A)

Step-by-step solution →
Q5·MathematicsSingle correctJEE Main 2020
Contrapositive of the statement: 'If a function f is differentiable at a, then it is also continuous at a', is:
  1. (A)If a function f is not continuous at a, then it is not differentiable at a.
  2. (B)If a function f is continuous at a, then it is differentiable at a.
  3. (C)If a function f is not continuous at a. then it is differentiable at a.
  4. (D)If a function f is continuous at a, then it is not differentiable at a.

Correct answer: (A)

Step-by-step solution →
Q6·MathematicsSingle correctJEE Main 2020
Given the following two statements: (S1):(q∨p)→(p↔∼q)(S_{1}) : (q \vee p) \rightarrow (p \leftrightarrow \sim q)(S1​):(q∨p)→(p↔∼q) is a tautology. (S2):∼q∧(∼p↔q)(S_{2}) : \sim q \wedge (\sim p \leftrightarrow q)(S2​):∼q∧(∼p↔q) is a fallacy. Then:
  1. (A)both (S1)(S_{1})(S1​) and (S2)(S_{2})(S2​) are correct
  2. (B)only (S2)(S_{2})(S2​) is correct
  3. (C)both (S1)(S_{1})(S1​) and (S2)(S_{2})(S2​) are incorrect
  4. (D)only (S1)(S_{1})(S1​) is correct

Correct answer: (C)

Step-by-step solution →
Q7·MathematicsSingle correctJEE Main 2020
The proposition p→∼(p∧∼q)p \rightarrow \sim (p \wedge \sim q)p→∼(p∧∼q) is equivalent to:
  1. (A)(∼p)∧q(\sim p) \wedge q(∼p)∧q
  2. (B)qqq
  3. (C)(∼p)∨q(\sim p) \vee q(∼p)∨q
  4. (D)(∼p)∨(∼q)(\sim p) \vee (\sim q)(∼p)∨(∼q)

Correct answer: (C)

Step-by-step solution →
Q8·MathematicsSingle correctJEE Main 2020
Let p, q, r be three statements such that the truth value of (p∧q)→(∼q∨r)\left( p \wedge q \right) \rightarrow \left( \sim q \vee r \right)(p∧q)→(∼q∨r) is F. Then the truth values of p, q,r are respectively:
  1. (A)T, F, T
  2. (B)T, T, F
  3. (C)F, T, F
  4. (D)T, T, T

Correct answer: (B)

Step-by-step solution →
Q9·MathematicsSingle correctJEE Main 2020
If p→(p∧∼q)p \rightarrow (p \wedge \sim q)p→(p∧∼q) is false, then the truth values of p and q are respectively:
  1. (A)F, T
  2. (B)F, F
  3. (C)T, T
  4. (D)T, F

Correct answer: (C)

Step-by-step solution →
Q10·MathematicsSingle correctJEE Main 2020
Negation of the statement: 5\sqrt{5}5​ is an integer or 5 is irrational' is:
  1. (A)5\sqrt{5}5​ is an integer and 5 is irrational
  2. (B)5\sqrt{5}5​ is not an integer or 5 is not irrational
  3. (C)5\sqrt{5}5​ is not an integer and 5 is not irrational
  4. (D)5\sqrt{5}5​ is irrational or 5 is an integer

Correct answer: (C)

Step-by-step solution →
Q11·MathematicsSingle correctJEE Main 2020
Which of the following statement is a tautology?
  1. (A)∼(p∧∼q)→p∨q\sim(p \wedge \sim q) \to p \vee q∼(p∧∼q)→p∨q
  2. (B)∼(p∨∼q)→p∨q\sim(p \vee \sim q) \to p \vee q∼(p∨∼q)→p∨q
  3. (C)p∨(∼q)→p∧qp \vee (\sim q) \to p \wedge qp∨(∼q)→p∧q
  4. (D)∼(p∨∼q)→p∧q\sim(p \vee \sim q) \to p \wedge q∼(p∨∼q)→p∧q

Correct answer: (B)

Step-by-step solution →
Q12·MathematicsSingle correctJEE Main 2020
Which one of the following is a tautology?
  1. (A)P∧(P∨Q)P\wedge(P\vee Q)P∧(P∨Q)
  2. (B)P∨(P∧Q)P\vee(P\wedge Q)P∨(P∧Q)
  3. (C)(P∧(P→Q))→Q(P\wedge(P\rightarrow Q))\rightarrow Q(P∧(P→Q))→Q
  4. (D)Q→(P∧(P→Q))Q\rightarrow(P\wedge(P\rightarrow Q))Q→(P∧(P→Q))

Correct answer: (C)

Step-by-step solution →
Q13·MathematicsSingle correctJEE Main 2020
Let A, B, C and D be four non-empty sets. The contrapositive statement of "If A⊆BA \subseteq BA⊆B and B⊆DB \subseteq DB⊆D, then A⊆CA \subseteq CA⊆C" is:
  1. (A)If A⊆CA \subseteq CA⊆C, then B⊂AB \subset AB⊂A or D⊂BD \subset BD⊂B
  2. (B)If A⊈CA \not\subseteq CA⊆C, then A⊈BA \not\subseteq BA⊆B or B⊆DB \subseteq DB⊆D
  3. (C)If A⊈CA \not\subseteq CA⊆C, then A⊈BA \not\subseteq BA⊆B or B⊈DB \not\subseteq DB⊆D
  4. (D)If A⊈CA \not\subseteq CA⊆C, then A⊆BA \subseteq BA⊆B or B⊆DB \subseteq DB⊆D

Correct answer: (C)

Step-by-step solution →
Q14·MathematicsSingle correctJEE Main 2020
The logical statement (p⇒q)∧(q⇒∼p)(p\Rightarrow q)\wedge(q\Rightarrow\sim p)(p⇒q)∧(q⇒∼p) is equivalent to:
  1. (A)∼q\sim q∼q
  2. (B)p
  3. (C)q
  4. (D)∼p\sim p∼p

Correct answer: (D)

Step-by-step solution →
Q15·MathematicsSingle correctJEE Main 2019
The Boolean expression ∼(p⇒(∼q))\sim(p \Rightarrow (\sim q))∼(p⇒(∼q)) is equivalent to:
  1. (A)(∼p)⇒q(\sim p) \Rightarrow q(∼p)⇒q
  2. (B)p∨qp \vee qp∨q
  3. (C)p∧qp \wedge qp∧q
  4. (D)q⇒∼pq \Rightarrow \sim pq⇒∼p

Correct answer: (C)

Step-by-step solution →
Q16·MathematicsSingle correctJEE Main 2019
If the truth value of the statement p→(∼q∨r)p \rightarrow (\sim q \vee r)p→(∼q∨r) is false (F), then the truth values of the statement p, q, r are respectively :
  1. (A)T, T, F
  2. (B)F, T, T
  3. (C)T, F, T
  4. (D)T, F, F

Correct answer: (A)

Step-by-step solution →
Q17·MathematicsSingle correctJEE Main 2019
Which one of the following Boolean expressions is a tautology?
  1. (A)(p ∨ q) ∧ (p∨∼q)
  2. (B)(p ∧ q) ∨ (p∧∼q)
  3. (C)(p ∨ q) ∧ (∼p∨∼q)
  4. (D)(p ∨ q) ∨ (p∨∼q)

Correct answer: (D)

Step-by-step solution →
Q18·MathematicsSingle correctJEE Main 2019
The negation of the Boolean expression ∼s∨(∼r∧s)\sim s \vee (\sim r \wedge s)∼s∨(∼r∧s) is equivalent to
  1. (A)s∨rs \vee rs∨r
  2. (B)∼s∧∼r\sim s \wedge \sim r∼s∧∼r
  3. (C)rrr
  4. (D)s∧rs \wedge rs∧r

Correct answer: (D)

Step-by-step solution →
Q19·MathematicsSingle correctJEE Main 2019
For any two statements p and q, the negation of the expression p∨(∼p∧q)p\vee(\sim p\wedge q)p∨(∼p∧q) is:
  1. (A)p↔qp\leftrightarrow qp↔q
  2. (B)∼p∨∼q\sim p\vee \sim q∼p∨∼q
  3. (C)∼p∧∼q\sim p\wedge \sim q∼p∧∼q
  4. (D)p∧qp\wedge qp∧q

Correct answer: (C)

Step-by-step solution →
Q20·MathematicsSingle correctJEE Main 2019
If P⇒(q∨r)P\Rightarrow\left(q\vee r\right)P⇒(q∨r) is false, then the truth values of p, q, r are respectively
  1. (A)F, T, T
  2. (B)T, F, F
  3. (C)T, T, F
  4. (D)F, F, F

Correct answer: (B)

Step-by-step solution →
Q21·MathematicsSingle correctJEE Main 2019
The contrapositive of the statement "If you are born in India, then you are a citizen of India", is:
  1. (A)If you are a citizen of India, then you are born in India
  2. (B)If your are not a citizen of India, then you are not born in India
  3. (C)If you are no born in India, then you are not a citizen of India
  4. (D)If you are born in India, then you are not a citizen of India

Correct answer: (B)

Step-by-step solution →
Q22·MathematicsSingle correctJEE Main 2019
The Boolean expression ((p∧q)∨(p∨∼q))∧(∼p∧∼q)((p \wedge q) \vee (p \vee \sim q)) \wedge (\sim p \wedge \sim q)((p∧q)∨(p∨∼q))∧(∼p∧∼q) is equivalent to:
  1. (A)p∧qp \wedge qp∧q
  2. (B)p∧(∼q)p \wedge (\sim q)p∧(∼q)
  3. (C)(∼p)∧(∼q)(\sim p) \wedge (\sim q)(∼p)∧(∼q)
  4. (D)p∨(∼q)p \vee (\sim q)p∨(∼q)

Correct answer: (C)

Step-by-step solution →
Q23·MathematicsSingle correctJEE Main 2019
The expression ∼(∼p→q)\sim(\sim p \rightarrow q)∼(∼p→q) is logically equivalent to :
  1. (A)∼p∧∼q\sim p \wedge \sim q∼p∧∼q
  2. (B)p∧∼qp \wedge \sim qp∧∼q
  3. (C)∼p∧q\sim p \wedge q∼p∧q
  4. (D)p∧qp \wedge qp∧q

Correct answer: (A)

Step-by-step solution →
Q24·MathematicsSingle correctJEE Main 2019
Contrapositive of the statement “If two numbers are not equal, then their squares are not equals” is:
  1. (A)If the squares of two numbers are not equal, then the numbers are equal
  2. (B)If the squares of two numbers are equal, then the numbers are not equal
  3. (C)If the squares of two numbers are equal, then the numbers are equal
  4. (D)If the squares of two numbers are not equal, then the numbers are not equal

Correct answer: (C)

Step-by-step solution →
Q25·MathematicsSingle correctJEE Main 2019
If q is false and p∧q↔rp \wedge q \leftrightarrow rp∧q↔r is true, then which one of the following statements is a tautology?
  1. (A)(p∨r)→(p∧r)(p \vee r) \rightarrow (p \wedge r)(p∨r)→(p∧r)
  2. (B)(p∧r)→(p∨r)(p \wedge r) \rightarrow (p \vee r)(p∧r)→(p∨r)
  3. (C)p∧rp \wedge rp∧r
  4. (D)p∨rp \vee rp∨r

Correct answer: (B)

Step-by-step solution →
Q26·MathematicsSingle correctJEE Main 2019
Consider the statement: \"P(n): n2−n+41n^2 - n + 41n2−n+41 is prime.\" Then which one of the following is true?
  1. (A)Both P(3) and P(5) are true
  2. (B)P(3) is false but P(5) is true
  3. (C)Both P(3) and P(5) are false
  4. (D)P(5) is false but P(3) is true

Correct answer: (A)

Step-by-step solution →

Mathematical Reasoning — frequently asked

How many questions from Mathematical Reasoning appear in JEE?

Mathematical Reasoning has appeared in 26 of the last 186 JEE Main and JEE Advanced papers — about 14% of them — contributing 26 questions in total across those papers.

Is Mathematical Reasoning an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 14% of papers. Chapters above about 50% are effectively guaranteed to show up every session, so they repay thorough preparation; lower-frequency chapters are better treated as targeted revision.

Where do these Mathematical Reasoning questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.

Other Mathematics chapters

  • Three Dimensional Geometry 344
  • Matrices and Determinants 342
  • Sets, Relations and Functions 313
  • Sequence and Series 287
  • Definite Integration 267
  • Vector Algebra 245
  • Differential Equations 240
  • Probability 226

All 26 Mathematics chapters →

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