JEE Main - Combinations C(n,r) Question Bank with Options

1. What does C(n, r) represent in terms of sets?

A) The number of ordered arrangements of r elements from n

B) The number of subsets of size r from a set of size n

C) The total number of elements in the set

D) The number of ways to choose r elements with replacement

2. If C(n, 8) = C(n, 4), what is n?

A) 4

B) 8

C) 12

D) 32

3. Evaluate C(5, 0).

A) 0

B) 1

C) 5

D) 25

4. What is C(10, 1)?

A) 0

B) 1

C) 10

D) 100

5. How many ways can a committee of 3 men and 2 women be formed from 7 men and 5 women?

A) C(7, 3) + C(5, 2)

B) C(7, 3) * C(5, 2)

C) P(7, 3) * P(5, 2)

D) C(12, 5)

6. Calculate C(15, 3).

A) 15

B) 45

C) 455

D) 4550

7. If C(n, r) = n! / (r! * (n-r)!), what is the condition for r?

A) r > n

B) r < 0

C) 0 <= r <= n

D) r = n

8. Evaluate C(10, 0).

A) 0

B) 1

C) 10

D) 100

9. What is the value of C(1, 1)?

A) 0

B) 1

C) 2

D) undefined

10. How many ways can a group of 4 students be chosen from a class of 30 students?

A) 30

B) 120

C) 27405

D) 274050

11. If C(n, 10) = C(n, 12), find n.

A) 10

B) 12

C) 22

D) 120

12. Calculate C(6, 5).

A) 1

B) 6

C) 30

D) 720

13. What is C(13, 3)?

A) 13

B) 39

C) 286

D) 1716

14. How many unique combinations of 3 letters can be formed from the letters A, B, C, D, E?

A) 5

B) 10

C) 15

D) 60

15. Evaluate C(10, 7). Using the property C(n, r) = C(n, n-r), this is equal to:

A) C(10, 10)

B) C(10, 3)

C) C(7, 10)

D) C(3, 10)

16. What is C(20, 0)?

A) 0

B) 1

C) 20

D) 400

17. How many ways can a committee of 5 members be selected from 10 men and 8 women if the committee must have exactly 3 men?

A) C(10, 3) * C(8, 2)

B) C(10, 5) * C(8, 5)

C) C(18, 5)

D) P(10, 3) * P(8, 2)

18. If C(n, 5) = C(n, 5), this implies:

A) n must be 5

B) r must be 5

C) No specific conclusion about n or r

D) n = 10

19. Calculate C(7, 7).

A) 0

B) 1

C) 7

D) 5040

20. What is C(11, 4)?

A) 11

B) 44

C) 330

D) 7920

21. The number of ways to choose a subset of size k from a set of size n is given by:

A) P(n, k)

B) C(n, k)

C) n^k

D) k^n

22. How many ways can a president and a vice-president be chosen from a group of 10 people?

A) 10

B) 45

C) 90

D) 100

23. Evaluate C(5, 3).

A) 5

B) 10

C) 15

D) 20

24. What is C(15, 2)?

A) 15

B) 30

C) 105

D) 225

25. How many ways can a hand of 5 cards be dealt from a standard deck of 52 cards?

A) 52

B) 260

C) 2,598,960

D) 311,875,200

26. If C(n, 3) = C(n, 7), find n.

A) 3

B) 7

C) 10

D) 21

27. Calculate C(8, 0).

A) 0

B) 1

C) 8

D) 64

28. What is the value of C(10, 10)?

A) 0

B) 1

C) 10

D) 3628800

29. How many ways can a subset of 3 elements be chosen from a set of 7 elements?

A) 7

B) 21

C) 35

D) 210

30. If C(n, 2) = 28, what is the value of n?

A) 7

B) 8

C) 14

D) 28

31. Evaluate C(6, 3).

A) 6

B) 18

C) 20

D) 30

32. What is C(5, 5)?

A) 0

B) 1

C) 5

D) 120

33. How many distinct teams of 4 players can be formed from a squad of 10 players?

A) 10

B) 40

C) 210

D) 5040

34. Calculate C(12, 5).

A) 792

B) 120

C) 60

D) 240

35. If C(n, r) = C(n, s) and r != s, then what is the relationship between n, r, and s?

A) n = r + s

B) n = r - s

C) n = r * s

D) n = r / s

36. What is the value of C(8, 8)?

A) 0

B) 1

C) 8

D) 40320

37. In how many ways can you choose 2 fruits from a basket containing 5 different fruits?

A) 5

B) 10

C) 20

D) 25

38. Evaluate C(9, 2).

A) 18

B) 36

C) 72

D) 16

39. What is C(n, 1)?

A) 1

B) n

C) n-1

D) n!

40. If a selection does not consider the order of items, it is a problem of:

A) Permutations

B) Combinations

C) Arrangements

D) Variations

41. Calculate C(4, 4).

A) 0

B) 1

C) 4

D) 24

42. What is the value of C(6, 1)?

A) 1

B) 6

C) 36

D) 0

43. How many ways can a committee of 3 people be selected from a group of 8 people?

A) 56

B) 336

C) 24

D) 8

44. If C(n, 4) = C(n, 6), what is the value of n?

A) 4

B) 6

C) 10

D) 24

45. Evaluate C(10, 3).

A) 30

B) 120

C) 240

D) 720

46. Which property of combinations states that C(n, r) = C(n, n-r)?

A) Symmetry property

B) Additive property

C) Multiplicative property

D) Identity property

47. What is the value of C(n, n)?

A) 0

B) 1

C) n

D) n!

48. Calculate C(7, 0).

A) 0

B) 1

C) 7

D) 49

49. What is the value of C(5, 2)?

A) 5

B) 10

C) 20

D) 2

50. In the combination formula C(n,r) = n! / (r! * (n-r)!), what does 'r' represent?

A) The total number of distinct items available

B) The number of items to choose

C) The number of arrangements

D) The factorial of the remaining items

Combinations C(n,r) - Question Bank