Take timed practice tests on Mathematical Reasoning for JEE Main and JEE Advanced with session-wise drills, score review, and explanation-led revision.
Six 20-question timed sessions plus one 60-question module test. Each question is original and calibrated from the uploaded material pattern without copying PDF wording.
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1. A tautology is a compound statement that is:
Explanation: Tautology: a compound statement true for ALL possible truth value combinations. Example: p ∨ ¬p. Contradiction: always false (p ∧ ¬p). Contingency: sometimes true, sometimes false.
2. The truth table for p → q (implication) shows it is FALSE only when:
Explanation: p → q (if p then q) is FALSE only in the case where the hypothesis (p) is TRUE but the conclusion (q) is FALSE. In all other cases it is TRUE.
3. The contrapositive of 'If p then q' (p → q) is:
Explanation: For p → q: Converse: q → p. Inverse: ¬p → ¬q. Contrapositive: ¬q → ¬p. The contrapositive is logically equivalent to the original statement.
4. The negation of 'Some students are intelligent' is:
Explanation: Negation of 'Some A are B' = 'No A is B' (¬∃x: B(x) = ∀x: ¬B(x)). Negation of 'All A are B' = 'Some A are not B'.
5. p ↔ q (biconditional) is TRUE when:
Explanation: p ↔ q is TRUE when p and q are both TRUE or both FALSE. It is FALSE when they have different truth values. Equivalently: p ↔ q = (p → q) ∧ (q → p).
6. Which of the following is a tautology?
Explanation: (p ∧ q) → p: If p AND q are true, then p must be true — this is always valid (tautology). The truth of the conjunction implies the truth of each conjunct.
7. Which symbol represents 'AND' in logic?
Explanation: ∧ = AND (conjunction). ∨ = OR (disjunction). ¬ = NOT (negation). → = IMPLIES (conditional). ↔ = IF AND ONLY IF (biconditional).
8. If p: 'It rains' and q: 'Roads are wet', then 'If it rains then roads are wet' in symbolic form is:
Explanation: 'If p then q' = p → q. The converse would be q → p (if roads are wet, it rained), which is not necessarily true.