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.

Statements A, B, C and E correctly describe geometric aspects of inequalities. A states that a single linear inequality shades a half-plane. B and C distinguish between including and excluding the boundary line based on the inequality sign. E is true because shading regions on the Cartesian plane is a standard way to solve systems of inequalities. D is false because the intersection of inequalities means satisfying all of them, not just at least one. Thus A, B, C and E only are correct.

Option A:
Option A is incomplete as it excludes E and therefore misses the point that these inequalities are often solved graphically in exam problems.

Option B:
Option B is also incomplete since it omits C and thereby fails to stress the difference between strict and non-strict inequalities with respect to boundary lines.

Option C:
Option C is wrong because it omits A, which states the key half-plane interpretation.

Option D:
Option D is correct because it includes every true statement about the geometric representation and graphical solution of inequalities, while excluding D, which confuses intersection with union.

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.

Statements A and B correctly describe linear inequalities in two variables as half-planes bounded by straight lines, and D accurately notes the convention of using dashed lines for strict inequalities. Statement E is also true because many optimisation and allocation problems, such as resource constraints, are modelled with systems of inequalities. Statement C is false because solution sets are typically infinite regions rather than single points. Therefore, the combination A, B, D and E only is correct.

Option A:
Option A is correct as it includes all true statements and excludes C, which wrongly restricts solutions to a single point. It reflects the graphical interpretation used for inequality questions at the NET level.

Option B:
Option B is incomplete since it omits E and thus does not emphasise that such inequalities can model practical constraints in optimisation problems like linear programming. Without E, the application aspect is missing.

Option C:
Option C is wrong because it contains C, the claim about a single point, and also omits A, so it both admits a false statement and leaves out a key concept about half-planes. This combination does not represent the topic accurately.

Option D:
Option D is incorrect because it includes C and therefore endorses a misunderstanding of the size of solution sets, even though some of the other statements in the option are correct. The presence of C makes the option unacceptable.