Linear inequalities in two variables – UGC NET Question

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.