UGC NET Questions (Paper – 1)

Statements A, B and C give standard definitions of injective, surjective and bijective functions. E is also correct in the finite equal-cardinality case: an injective map from A to B must be surjective. D is false because surjectivity alone does not guarantee injectivity; many onto but not one-to-one functions exist. Therefore A, B, C and E only are correct.

Option A:
Option A is correct as it aggregates all the true statements about these function types, including the finite-set result, while leaving out D, which wrongly treats surjectivity as forcing injectivity.

Option B:
Option B is incorrect because it omits E, and E is a true theorem for finite sets of equal size (injective ⇒ surjective).

Option C:
Option C is incorrect because it omits A (a true definition of injective), so it does not list all correct statements.

Option D:
Option D is incorrect because it omits B (a true definition of surjective), so it does not list all correct statements.

Statements A and B give the standard definitions of injective and surjective functions. Statement C is also correct because a bijection is precisely a function that is both one–one and onto. Statement D is false as there are surjective functions that are not injective when the codomain is smaller than the domain. Statement E is false because the definition of a function requires exactly one output in B for each input in A. Hence, A, B and C only are correct, which matches option C.

Option A:
Option A is incomplete since it omits C and thereby fails to mention bijection, which combines the properties described in A and B and is often tested in NET.

Option B:
Option B is incorrect as it adds D, which wrongly claims that surjectivity implies injectivity, so it contains an incorrect statement along with true ones.

Option C:
Option C is correct because it precisely gathers the three accurate definitions and excludes D and E, which misrepresent either implications between properties or the basic definition of a function.

Option D:
Option D is wrong since it includes E, which permits multiple outputs per input, contradicting the concept of a function, and omits A, so it removes a key correct statement and accepts a false one.