UGC NET Questions (Paper – 1)

Statements A and B correctly distinguish permutations and combinations in terms of the role of order. D is true because permutations can be obtained from combinations by arranging the chosen r objects in r! ways. E is also correct since there is only one way to choose all n objects from n. Statement C is false because nPr generally exceeds nCr when 0 < r < n, so permutations and combinations are not equal in count. Thus the correct combination is A, B, D and E only. Option A: Option A is incomplete as it omits D and E, and hence does not show the quantitative relationship between permutations and combinations or the special case when all objects are chosen. It therefore does not capture the full set of correct statements. Option B: Option B is incorrect because it leaves out E and includes only A, B and D, so it does not mention the important special case nCr = 1 when r = n. This omission makes the combination incomplete. Option C: Option C is correct because it gathers the true distinctions and the exact formula relating nPr and nCr and excludes C, which wrongly claims equality of counts. It therefore matches the combinatorial facts emphasised in NET aptitude. Option D: Option D is wrong as it drops A and includes B, D and E only, failing to state explicitly that permutations take order into account while still not rejecting C. As a result, it does not provide the precise set of correct statements requested.

B is correct: permutations count ordered arrangements. C is correct because nPr = nCr × r! and r! ≥ 1. D is correct since choosing 0 or all items yields one way. E is correct since choosing 1 item from n gives n ways. A is false because combinations ignore order. Hence B, C, D and E only are correct.

Option A:
Option A is incomplete because it omits D and E, which are standard special cases of combinations.

Option B:
Option B is incorrect because it omits E (true).

Option C:
Option C is incorrect because it omits C (true) even though B, D and E are true; it does not list all correct statements.

Option D:
Option D is correct because it includes all true statements and excludes A, which reverses the definition of combinations.