JEE Main - Combinations C(n,r) Online Test (MCQ Quiz)

1. What is the formula for calculating the number of combinations of choosing 'r' items from a set of 'n' distinct items, denoted as C(n,r) or nCr?

A) n! / (r! * (n-r)!) B) n! / r! C) n! / (n-r)! D) (n!) / r

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

A) The number of items to choose B) The total number of distinct items available C) The number of permutations D) The factorial of the chosen items

3. 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

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

A) 5 B) 10 C) 20 D) 2

5. Calculate C(7, 0).

A) 0 B) 1 C) 7 D) 49

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

A) 0 B) 1 C) n D) n!

7. 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

8. Evaluate C(10, 3).

A) 30 B) 120 C) 240 D) 720

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

A) 4 B) 6 C) 10 D) 24

10. 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

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

A) 1 B) 6 C) 36 D) 0

12. Calculate C(4, 4).

A) 0 B) 1 C) 4 D) 24

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

A) Permutations B) Combinations C) Arrangements D) Variations

14. What is C(n, 1)?

A) 1 B) n C) n-1 D) n!

15. Evaluate C(9, 2).

A) 18 B) 36 C) 72 D) 16

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

A) 5 B) 10 C) 20 D) 25

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

A) 0 B) 1 C) 8 D) 40320

18. 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

19. Calculate C(12, 5).

A) 792 B) 120 C) 60 D) 240

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

A) 10 B) 40 C) 210 D) 5040

21. What is C(5, 5)?

A) 0 B) 1 C) 5 D) 120

22. Evaluate C(6, 3).

A) 6 B) 18 C) 20 D) 30

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

A) 7 B) 8 C) 14 D) 28

24. 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

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

A) 0 B) 1 C) 10 D) 3628800

26. Calculate C(8, 0).

A) 0 B) 1 C) 8 D) 64

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

A) 3 B) 7 C) 10 D) 21

28. 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

29. What is C(15, 2)?

A) 15 B) 30 C) 105 D) 225

30. Evaluate C(5, 3).

A) 5 B) 10 C) 15 D) 20

31. 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

32. 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

33. What is C(11, 4)?

A) 11 B) 44 C) 330 D) 7920

34. Calculate C(7, 7).

A) 0 B) 1 C) 7 D) 5040

35. 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

36. 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)

37. What is C(20, 0)?

A) 0 B) 1 C) 20 D) 400

38. 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)

39. 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

40. What is C(13, 3)?

A) 13 B) 39 C) 286 D) 1716

41. Calculate C(6, 5).

A) 1 B) 6 C) 30 D) 720

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

A) 10 B) 12 C) 22 D) 120

43. 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

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

A) 0 B) 1 C) 2 D) undefined

45. Evaluate C(10, 0).

A) 0 B) 1 C) 10 D) 100

46. 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

47. Calculate C(15, 3).

A) 15 B) 45 C) 455 D) 4550

48. 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)

49. What is C(10, 1)?

A) 0 B) 1 C) 10 D) 100

50. Evaluate C(5, 0).

A) 0 B) 1 C) 5 D) 25

Combinations C(n,r) - Online Test

Test Results