Mathematics Objective Questions and Answers: Mathematical Reasoning
Access targeted multiple-choice questions for Mathematical Reasoning designed to align with the latest JEE academic syllabus for JEE Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.
Download Mathematical Reasoning MCQs with Answers
Access the complete set of multiple-choice questions for Mathematical Reasoning below. This focused format allows students to isolate specific topics for thorough review and uninterrupted practice alongside official JEE textbooks.
Multiple Choice Questions
(a) I and II are correctly stated forms of the contrapositive and converse
(b) Only I is correctly stated
(c) Only II is correctly stated
(d) Neither I nor II is correctly stated
Show Answer & Explanation
Answer: (a) I and II are correctly stated forms of the contrapositive and converse
Explanation:
1. With p: x is prime and q: x is odd, the contrapositive is ~q → ~p and the converse is q → p.
2. I is ~q → ~p and II is q → p, so both are correctly formed.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) Both I and II are true
(b) Only I is true
(c) Only II is true
(d) Both I and II are false
Show Answer & Explanation
Answer: (a) Both I and II are true
Explanation:
1. I is the definition of a statement.
2. 'Today is a windy day' can be true on one day and false on another, so it is not a statement.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) I is the converse of II but II is not the converse of I
(b) II is the converse of I but I is not the converse of II
(c) I and II are converses of each other
(d) Neither is the converse of the other
Show Answer & Explanation
Answer: (c) I and II are converses of each other
Explanation:
1. Swapping the hypothesis and conclusion of I gives II.
2. Swapping those of II gives I, so each is the converse of the other.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) Only II is a statement
(b) Only I is a statement
(c) Both are statements
(d) Neither I nor II is a statement
Show Answer & Explanation
Answer: (a) Only II is a statement
Explanation:
1. In I, 'she' is not identified, so it is neither true nor false.
2. II is false, but definite, so it is a statement.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) I and II
(b) I and III
(c) II and III
(d) I, II and III
Show Answer & Explanation
Answer: (a) I and II
Explanation:
1. I and II are false, but definite, so they are statements.
2. III is a command.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) Only III is false
(b) Only I is false
(c) Only II is false
(d) All of I, II and III are false
Show Answer & Explanation
Answer: (a) Only III is false
Explanation:
1. I and II are true.
2. III is false because 2 is an even prime.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) p: The sky is blue; q: The sky is not blue
(b) p: The sky is blue; q: The grass is green
(c) Neither of the pairs is a pair of component statements
(d) Both pairs are component statements
Show Answer & Explanation
Answer: (b) p: The sky is blue; q: The grass is green
Explanation:
1. The compound statement is joined by 'or'.
2. Its components are the two simple statements on either side of 'or'.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) I, II and III are true
(b) Only I and II are true
(c) Only II and III are true
(d) Only I and III are true
Show Answer & Explanation
Answer: (a) I, II and III are true
Explanation:
1. Converse swaps the parts, contrapositive swaps and negates, inverse negates.
2. All three descriptions are correct.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) Both are correct
(b) Both are incorrect
(c) Only I is correct
(d) Only II is correct
Show Answer & Explanation
Answer: (a) Both are correct
Explanation:
1. 'If p then q' means 'p implies q'.
2. It also means 'p is a sufficient condition for q'; II states exactly that.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
(c) Assertion is true but Reason is false
(d) Assertion is false but Reason is true
Show Answer & Explanation
Answer: (a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion
Explanation:
1. The truth table of 'and' gives T only when all components are T.
2. So the Reason states exactly the same table from the false side and explains the Assertion.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
(c) Assertion is true but Reason is false
(d) Assertion is false but Reason is true
Show Answer & Explanation
Answer: (d) Assertion is false but Reason is true
Explanation:
1. 'Mathematics is difficult' is a matter of opinion, so it is not definitely true or false: the Assertion is false.
2. The Reason is the correct definition of a statement.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
(c) Assertion is true but Reason is false
(d) Assertion is false but Reason is true
Show Answer & Explanation
Answer: (a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion
Explanation:
1. '8 is less than 6' is false, but definitely false, so it is a statement.
2. The Reason gives the definition that justifies this.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
(c) Assertion is true but Reason is false
(d) Assertion is false but Reason is true
Show Answer & Explanation
Answer: (c) Assertion is true but Reason is false
Explanation:
1. Contrapositive: ~r → ~(p ∨ q) = ~r → (~p ∧ ~q), so the Assertion is true.
2. For the conditional to be false, p ∧ ~q = T and ~p ∨ r = F, giving p = T, q = F, r = F, not F, T, T: the Reason is false.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
(c) Assertion is true but Reason is false
(d) Assertion is false but Reason is true
Show Answer & Explanation
Answer: (d) Assertion is false but Reason is true
Explanation:
1. A conditional is false only for antecedent T and consequent F: p = T, q = F, so the Assertion is false.
2. ~(p → r) = p ∧ ~r, here ~(~p ∨ q) = p ∧ ~q, so the negation is p ∧ (p ∧ ~q) = p ∧ ~q: the Reason is true.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
(c) Assertion is true but Reason is false
(d) Assertion is false but Reason is true
Show Answer & Explanation
Answer: (c) Assertion is true but Reason is false
Explanation:
1. The first sentence is the definition of negation: true.
2. A compound statement can be broken into component statements; it is a simple statement that cannot be broken down: the Reason is false.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) is true
(b) is false
(c) has a false contrapositive
(d) cannot be decided
Show Answer & Explanation
Answer: (a) is true
Explanation:
1. If x = y then 2x = 2y, so 2x + a = 2y + a for any a.
2. Hence the statement is true (and so is its contrapositive).
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) x is a real number.
(b) 6 is a natural number.
(c) Switch off the fan.
(d) Let me go.
Show Answer & Explanation
Answer: (b) 6 is a natural number.
Explanation:
1. '6 is a natural number' is definitely true.
2. 'x is a real number' depends on x, and the other two are commands or requests.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) The number of ways of seating 2 persons in two chairs out of n persons is P(n, 2).
(b) The cube roots of unity are in G.P.
(c) A quadratic equation has always a real root.
(d) The sum of the angles of a triangle is 180°.
Show Answer & Explanation
Answer: (c) A quadratic equation has always a real root.
Explanation:
1. x² + 1 = 0 is a quadratic equation with no real root, so the first statement is false.
2. The other three are true: the roots 1, ω, ω² form a G.P. with ratio ω.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) If Chandigarh is not in India, then Chandigarh is not the capital of Punjab.
(b) If Chandigarh is in India, then Chandigarh is the capital of Punjab.
(c) If Chandigarh is the capital of Punjab, then Chandigarh is not in India.
(d) If Chandigarh is not the capital of Punjab, then Chandigarh is not in India.
Show Answer & Explanation
Answer: (a) If Chandigarh is not in India, then Chandigarh is not the capital of Punjab.
Explanation:
1. The contrapositive of p → q is ~q → ~p.
2. ~q: Chandigarh is not in India; ~p: it is not the capital of Punjab.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) p ∧ q
(b) ~(p ∧ q)
(c) ~p ∨ ~q
(d) ~p ∧ ~q
Show Answer & Explanation
Answer: (d) ~p ∧ ~q
Explanation:
1. 'Neither ... nor' means both are false.
2. So it is ~p ∧ ~q.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) false
(b) true
(c) false only if p is true
(d) cannot be determined
Show Answer & Explanation
Answer: (a) false
Explanation:
1. p ∧ ~r = T ∧ T = T, so the disjunction (p ∧ ~r) ∨ (~q ∨ s) is T.
2. Its negation is F.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) ~Q ⇔ ~P ∧ R
(b) ~(Q ⇔ (P ∧ ~R))
(c) ~(P ∧ ~R) ⇔ Q
(d) ~P ∧ (Q ⇔ ~R)
Show Answer & Explanation
Answer: (b) ~(Q ⇔ (P ∧ ~R))
Explanation:
1. The statement is (P ∧ ~R) ⇔ Q.
2. Its negation is ~((P ∧ ~R) ⇔ Q), which equals ~(Q ⇔ (P ∧ ~R)).
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) There is no rational number x ∈ S such that x ≤ 0.
(b) Every rational number x ∈ S satisfies x ≤ 0.
(c) x ∈ S and x ≤ 0 ⇒ x is not rational.
(d) There is a rational number x ∈ S such that x ≤ 0.
Show Answer & Explanation
Answer: (b) Every rational number x ∈ S satisfies x ≤ 0.
Explanation:
1. The negation of 'there exists x with x > 0' is 'for all x, x is not > 0'.
2. That is: every rational x in S satisfies x ≤ 0.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) F
(b) both T and F
(c) 54
(d) T
Show Answer & Explanation
Answer: (d) T
Explanation:
1. 3 + 3 = 33 is F and 1 + 2 = 12 is F, so the 'or' statement is F.
2. Its negation, 'it is false that ...', is T.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) (p ∨ q) ∧ (p ∨ r) is T
(b) (p ∧ q) ∨ r is F
(c) (p ∧ q) → r is T
(d) (p → q) ↔ (p → r) is T
Show Answer & Explanation
Answer: (a) (p ∨ q) ∧ (p ∨ r) is T
Explanation:
1. (p ∨ q) = T and (p ∨ r) = T, so their conjunction is T.
2. (p ∧ q) ∨ r = T; (p ∧ q) → r = F; (p → q) ↔ (p → r) = T ↔ F = F.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
(a) p ∧ ~p ≡ T
(b) p ∨ ~p ≡ F
(c) p → q ≡ (~q) → (~p)
(d) p → q ≡ q → p
Show Answer & Explanation
Answer: (c) p → q ≡ (~q) → (~p)
Explanation:
1. A conditional is equivalent to its contrapositive.
2. p ∧ ~p is always F, p ∨ ~p is always T, and p → q is not equivalent to its converse.
Teacher's Note:
1. Write the statement in symbols and use a truth table or the standard laws: p to q is equivalent to not p or q, and the negation of p to q is p and not q.
2. Remember: the converse swaps the parts, the contrapositive swaps and negates them, and the inverse only negates them.
Free study material for Mathematics
Practice MCQs for JEE Mathematics Mathematical Reasoning
Download Multiple Choice Questions: Mathematical Reasoning (JEE Mathematics)
Explore reliable practice questions for Mathematical Reasoning tailored for JEE Mathematics learners. Use these multiple-choice formats to evaluate preparedness and strengthen problem-solving skills.
Concept Clarification for Mathematical Reasoning
Each question includes structured solution keys mapped directly to standard JEE textbooks, helping students evaluate their reasoning and correct mistakes early in their revision.
Additional Study Resources for JEE Mathematics
Explore our broader library of printable assignments, chapter notes, and mock tests designed to support continuous revision and secure higher marks in JEE assessments.
FAQs
You can get most exhaustive JEE Mathematics Mathematical Reasoning MCQs Set 12 for free on StudiesToday.com. These MCQs for JEE Mathematics are updated for the 2026-27 academic session as per JEE examination standards.
Yes, our JEE Mathematics Mathematical Reasoning MCQs Set 12 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the JEE paper is now competency-based.
By solving our JEE Mathematics Mathematical Reasoning MCQs Set 12, JEE students can improve their accuracy and speed which is important as objective questions provide a chance to secure 100% marks in the Mathematics.
Yes, Mathematics MCQs for JEE have answer key and brief explanations to help students understand logic behind the correct option as its important for 2026 competency-focused JEE exams.
Yes, you can also access online interactive tests for JEE Mathematics Mathematical Reasoning MCQs Set 12 on StudiesToday.com as they provide instant answers and score to help you track your progress in Mathematics.