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.

A is correct because x > 5 means any number greater than 5 is allowed. B is also correct since solving 2x + 3 < 11 gives 2x < 8 and hence x < 4. C is wrong because 1 1 and x ≤ 3, not x < 3. D is wrong because multiplying or dividing by a negative number requires reversing the inequality sign. E is correct as x ≥ −2 includes −2 and all greater numbers. Therefore, C and D only are the wrong statements. Option A: Option A lists only C as wrong and overlooks the error in D, which ignores sign reversal when multiplying by a negative number. It thus fails to capture all incorrect statements. Option B: Option B is correct because it selects exactly C and D, the statements that mis-handle combined inequalities and transformation rules, while recognising A, B and E as accurate. It aligns with how inequalities are treated in exam questions. Option C: Option C wrongly labels E as wrong, even though E correctly describes the number line representation of x ≥ −2. Including E makes this option inaccurate. Option D: Option D adds E to the set of wrong statements and so misclassifies a true description of the solution set, making the entire combination invalid.