UGC NET Questions (Paper – 1)

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.

A is true because absolute value is never negative, so |x| ≥ 0 for all real x. B is true: |x| 0) means x lies within distance a of 0, i.e., −a < x a means x is outside that interval, i.e., x a. D is false because |x| > −2 is true for every real x (since |x| ≥ 0), so it does not force x to be positive. Therefore A, B and C only are correct.

Statements A, B and C are correct: the behaviour of inequalities under multiplication by positive and negative numbers is standard, and solving them parallels solving equations with additional attention to sign changes. Statement D is false because solutions of inequalities are often intervals or ranges of values, not single numbers, and E is false because inequality reasoning has many practical applications and is tested in aptitude sections. Therefore the option that includes A, B and C and excludes D and E is correct.

Option A:
Option A is incomplete as it omits C and thus fails to highlight the close procedural connection between solving equations and inequalities, which is a key conceptual insight in aptitude contexts.

Option B:
Option B is also incomplete because it leaves out A, ignoring the important fact that multiplication by a positive number leaves the inequality direction unchanged. Without A, some fundamental transformation rule is missing.

Option C:
Option C is correct because it gathers all three true statements about manipulation and solution processes for inequalities, while rejecting D and E, which misrepresent the nature and usefulness of inequality solutions. It matches the conceptual level expected in UGC NET.

Option D:
Option D is wrong since it includes D, the false claim that solution sets are always single numbers, and thereby contradicts the idea of intervals. Including this misstatement makes the combination logically incorrect.