UGC NET Questions (Paper – 1)

Statements A, B, D and E accurately summarise key ideas about linear equations: they have a standard form, a solution makes the equation true, a common solution satisfies each equation in a system and many word problems can be translated into such equations. Statement C is false because an equation true for all values is an identity, whereas an inconsistent equation has no solution at all. Thus, the combination A, B, D and E only is correct.

Option A:
Option A is correct as it gathers all four true statements and omits C, which confuses the notions of identity and inconsistency. It presents the conceptual framework used in NET aptitude questions about simple equations.

Option B:
Option B is incomplete since it omits E, failing to mention the important modelling role linear equations play in real-life aptitude contexts like age and mixture problems. Without E, the practical side is under-emphasised.

Option C:
Option C is wrong because it excludes A and thus lacks the canonical ax + b = 0 form that defines linear equations in one variable, while also not addressing the error in C. The combination is therefore incomplete and inaccurate.

Option D:
Option D is incorrect because it includes C, the misdefinition of inconsistent equations, even though A, D and E are true. The presence of C makes the overall set logically inconsistent.