UGC NET Questions (Paper – 1)

A is correct because each element of the domain must be assigned exactly one image. B is true as many-one mappings allow different domain elements to share a common image. C correctly describes surjective functions where every codomain element is hit by at least one domain element, and D is correct that a mapping both one-one and onto is a bijection. E is false because that condition describes surjectivity; a function in general does not require every codomain element to have a pre-image. Hence A, B, C and D only are correct.

Option A:
Option A omits D and so fails to name bijection explicitly, even though the other statements are true. Because it does not list all correct statements, it is incomplete.

Option B:
Option B leaves out A and therefore does not include the basic definition of a function as a mapping with single-valued images. This omission makes the combination insufficient.

Option C:
Option C drops B and thus ignores the many-one possibility, which is an important non-injective behaviour, even though A, C and D are true. The set is therefore not fully representative.

Option D:
Option D is correct in collecting all accurate statements about functions, surjections and bijections, while excluding E, which confuses general functions with onto functions. It matches the functional concepts tested in NET.

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.