JEE Main - Permutations P(n,r) Online Test (MCQ Quiz)

1. What is the formula for calculating the number of permutations of selecting 'r' items from a set of 'n' distinct items?

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

2. The notation P(n, r) represents:

A) The number of combinations of 'n' items taken 'r' at a time. B) The number of permutations of 'n' items taken 'r' at a time. C) The sum of 'n' and 'r'. D) The product of 'n' and 'r'.

3. How many ways can 3 distinct books be arranged on a shelf from a collection of 5 distinct books?

A) 10 B) 60 C) 120 D) 15

4. Calculate P(7, 2).

A) 14 B) 49 C) 42 D) 21

5. If P(n, 4) = 1680, what is the value of 'n'?

A) 5 B) 6 C) 7 D) 8

6. What is P(n, 0)?

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

7. What is P(n, 1)?

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

8. What is P(n, n)?

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

9. Evaluate P(5, 3).

A) 15 B) 60 C) 20 D) 125

10. In how many ways can the letters of the word 'CAT' be arranged?

A) 3 B) 6 C) 9 D) 27

11. How many permutations are possible for 4 distinct items taken 2 at a time?

A) 4 B) 8 C) 12 D) 16

12. If P(n, 2) = 30, find 'n'.

A) 5 B) 6 C) 7 D) 30

13. The number of permutations of 'n' distinct objects taken 'r' at a time is denoted by:

A) C(n, r) B) P(n, r) C) nPr D) Both P(n, r) and nPr

14. What is the value of P(10, 3)?

A) 30 B) 1000 C) 720 D) 10! / 7!

15. How many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repetition?

A) 60 B) 120 C) 15 D) 20

16. Which of the following is equivalent to P(n, r)?

A) n! / r! B) n! / (n-r)! C) n * (n-1) * ... * (n-r+1) D) Both n! / (n-r)! and n * (n-1) * ... * (n-r+1)

17. Calculate P(6, 0).

A) 0 B) 1 C) 6 D) 720

18. If P(n, 3) = 60, find 'n'.

A) 4 B) 5 C) 6 D) 10

19. What does P(n, r) signify in combinatorics?

A) The number of ways to choose 'r' items from 'n' without regard to order. B) The number of ways to arrange 'r' items from 'n' where order matters. C) The number of ways to select 'n' items from 'r' where order matters. D) The total number of items available.

20. How many ways can you arrange 3 letters from the word 'MATH'?

A) 12 B) 24 C) 64 D) 81

21. If P(n, 5) = 720, what is the value of 'n'?

A) 5 B) 6 C) 7 D) 8

22. What is the relationship between P(n, r) and P(n, r-1)?

A) P(n, r) = P(n, r-1) * (n-r+1) B) P(n, r) = P(n, r-1) + (n-r+1) C) P(n, r) = P(n, r-1) / (n-r+1) D) P(n, r) = P(n, r-1) * r

23. Evaluate P(4, 4).

A) 1 B) 4 C) 16 D) 24

24. How many distinct permutations are there of the letters in the word 'GOD'?

A) 3 B) 6 C) 9 D) 27

25. If P(n, 2) = 12, find 'n'.

A) 3 B) 4 C) 5 D) 6

26. What is the value of P(8, 3)?

A) 24 B) 64 C) 336 D) 512

27. The expression n! / (n-r)! represents:

A) The number of combinations of 'n' items taken 'r' at a time. B) The number of permutations of 'n' items taken 'r' at a time. C) The number of ways to arrange 'n' items. D) The number of ways to choose 'r' items from 'n'.

28. How many ways can the first, second, and third prizes be awarded to 10 contestants?

A) 10 B) 30 C) 120 D) 720

29. If P(n, 1) = 5, what is 'n'?

A) 1 B) 4 C) 5 D) 6

30. What is the formula for P(n, r) expanded in terms of factorials?

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

31. Calculate P(5, 5).

A) 1 B) 5 C) 25 D) 120

32. How many different ways can 5 people be seated in a row of 5 chairs?

A) 5 B) 25 C) 60 D) 120

33. If P(n, 3) = 210, find 'n'.

A) 5 B) 6 C) 7 D) 10

34. What is the value of P(6, 3)?

A) 18 B) 120 C) 216 D) 720

35. The number of permutations of 'n' distinct objects taken 'r' at a time is equal to:

A) n * (n-1) * ... * (n-r) B) n * (n-1) * ... * (n-r+1) C) n * (n-1) * ... * (n-r-1) D) n * (n-1) * ... * 1

36. How many ways can you arrange the letters of the word 'GO'?

A) 1 B) 2 C) 3 D) 4

37. If P(n, 2) = 56, find 'n'.

A) 6 B) 7 C) 8 D) 56

38. What is P(7, 7)?

A) 1 B) 7 C) 49 D) 5040

39. How many different 4-letter arrangements can be made from the letters of the word 'COMPUTER'?

A) 24 B) 5040 C) 10400 D) 120

40. If P(n, 3) = 336, find 'n'.

A) 6 B) 7 C) 8 D) 9

41. What is the value of P(10, 0)?

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

42. The number of permutations of 'n' distinct items taken 'r' at a time is given by P(n, r). If r > n, what is P(n, r)?

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

43. How many ways can 4 distinct paintings be arranged on a wall from a collection of 6 distinct paintings?

A) 15 B) 24 C) 360 D) 720

44. If P(n, 2) = 72, find 'n'.

A) 8 B) 9 C) 10 D) 72

45. What is P(5, 2)?

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

46. If P(n, r) = n! / (n-r)!, what is P(n, n-1)?

A) n! B) n! / (n-(n-1))! C) n! / 1! D) n! * n

47. How many permutations are there of the letters in the word 'SEE'?

A) 3 B) 6 C) 3! / 2! D) 3! / (2! * 1!)

48. What is the value of P(1, 1)?

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

49. If P(n, 4) = 5040, find 'n'.

A) 7 B) 8 C) 9 D) 10

50. Which of the following expressions is NOT a valid representation of P(n, r)?

A) n! / (n-r)! B) n * (n-1) * ... * (n-r+1) C) nPr D) n! / r!

Permutations P(n,r) - Online Test

Test Results