UGC NET Questions (Paper – 1)

Statements A and B correctly define closure and commutativity for binary operations, D notes that exams introduce custom operations to test rule-following rather than standard arithmetic and E emphasises the need to use the given definition faithfully. Statement C is false because associativity means (a * b) * c = a * (b * c), not that the results are always different. Hence, the combination A, B, D and E only is correct.

Option A:
Option A is incomplete as it omits E and thus fails to stress that candidates must not revert to usual addition or multiplication when a custom rule is specified. This omission makes the description less helpful for exam strategy.

Option B:
Option B is also incomplete because it leaves out A, so it does not explicitly mention closure, the idea that combining elements of S stays within S, which is often implied when operations are defined.

Option C:
Option C is wrong since it includes C, which reverses the meaning of associativity by saying results are always different, and omits B, thereby ignoring the commutative law. This mixture of an error and an omission makes the option invalid.

Option D:
Option D is correct because it captures closure, commutativity, exam usage of custom operations and the necessity of following the definition, while excluding C, which misstates associativity. It reflects the way NET questions check conceptual clarity about operations.