UGC NET Questions (Paper – 1)

This option is correct because combinations count the number of ways to select r objects from n distinct objects when order does not matter. The standard notation for this is nCr. It is also called the binomial coefficient and is given by n!/[r!(n−r)!]. Therefore, nCr represents the required count.

Option A:
nPr is used for permutations, where order of arrangement matters. It counts more cases than combinations because each selection can be arranged in many orders. Since the question specifies "without regard to order," nPr is not suitable.

Option B:
rCn is not the conventional way of writing combinations of r from n. It reverses the parameters and is not used in standard notation. This makes the option incorrect.

Option C:
rPn again refers to permutations but with reversed parameters compared to typical notation. It also considers ordering, which the question explicitly ignores. Thus, this symbol does not answer the question correctly.

Option D:
nCr correctly denotes the number of combinations of n objects taken r at a time. It ignores order and is widely used in probability and counting problems. This precisely matches the description given, so this option is correct.

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.