UGC NET Questions (Paper – 1)

Statements A and B are correct because adding the same number or multiplying by a positive number does not change the inequality direction. Statement C is also correct as multiplying by a negative number reverses the inequality sign, a key exam point. Statement E is true since solutions of such inequalities are commonly expressed as intervals or rays on the real line. D is false because if a > b and b > c, then a > c, not a < c. Therefore A, B, C and E only form the correct set. Option A: Option A is incomplete since it leaves out C and E. Without mentioning the effect of multiplying by a negative and the interval representation, it does not give a full picture of inequality properties. Option B: Option B is also incomplete because it omits E and thereby ignores the standard graphical representation of solution sets on the number line. Option C: Option C is correct as it combines the basic algebraic rules for manipulating inequalities with the interval depiction of solutions, while excluding D, which contradicts the transitivity of the “greater than” relation. Option D: Option D is wrong since it includes D, which reverses the transitive relation, and thus mixes a clearly false statement with true ones.

Statements A, B, C and E give standard reasoning techniques for ranking questions. A states the usual formula for total persons when one person’s ranks from top and bottom are known with no ties. B is true because ties disturb this simple formula. C is correct; it uses transitivity of “taller than” to deduce the relation between A and C. E is also correct since drawing a vertical list helps many candidates see the order clearly. D is false because equal scores can lead to shared ranks, so requiring distinct ranks is not correct. Thus, A, B, C and E only form the correct set.

Option A:
Option A is incomplete because it leaves out E, failing to mention the practical diagrammatic strategy that aids in solving ranking questions, even though A, B and C are true.

Option B:
Option B is also incomplete, as it includes only B, C and E and omits A, losing the widely used formula for computing total persons.

Option C:
Option C is correct since it brings together the numerical formula, the effect of ties, transitivity of order and the usefulness of diagrams, while excluding D, which incorrectly denies the possibility of equal ranks.

Option D:
Option D is wrong because it features D, which misstates the treatment of equal scores, and omits B, so it both includes an error and loses a critical observation about ties.