SSC CGL - Probability, Permutation and Combination Online Test (MCQ Quiz)

1. What is the probability of an event that is certain to occur?

A) 0 B) 1 C) 0.5 D) Undefined

2. What is the probability of an impossible event?

A) 1 B) 0.5 C) 0 D) Undefined

3. If P(A) = 0.6 and P(B) = 0.7, and P(A ∩ B) = 0.4, what is P(A ∪ B)?

A) 0.9 B) 0.7 C) 0.8 D) 1.0

4. What is the value of 5! (5 factorial)?

A) 120 B) 100 C) 60 D) 24

5. How many ways can the letters of the word 'APPLE' be arranged?

A) 120 B) 60 C) 240 D) 100

6. A fair coin is tossed once. What is the probability of getting a head?

A) 1/2 B) 1/3 C) 1 D) 0

7. A fair die is rolled. What is the probability of getting a number greater than 4?

A) 1/6 B) 2/6 C) 3/6 D) 4/6

8. In how many ways can a committee of 3 people be chosen from a group of 5 people?

A) 10 B) 15 C) 60 D) 5

9. What is the number of permutations of n distinct objects taken r at a time, denoted as nPr?

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

10. What is the number of combinations of n distinct objects taken r at a time, denoted as nCr?

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

11. Two dice are rolled simultaneously. What is the probability of getting a sum of 7?

A) 1/36 B) 6/36 C) 5/36 D) 7/36

12. A bag contains 4 red balls and 6 blue balls. If one ball is drawn at random, what is the probability that it is red?

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

13. What is the value of 0!?

A) 0 B) 1 C) Undefined D) Infinity

14. How many ways can 4 people be arranged in a line?

A) 16 B) 24 C) 12 D) 4

15. From a deck of 52 cards, one card is drawn. What is the probability of drawing an Ace?

A) 1/52 B) 4/52 C) 13/52 D) 1/4

16. If P(A) = 0.3 and P(B) = 0.4, and A and B are independent events, what is P(A ∩ B)?

A) 0.12 B) 0.7 C) 0.1 D) 0.012

17. What is the total number of possible outcomes when tossing three fair coins?

A) 3 B) 6 C) 8 D) 9

18. How many distinct arrangements are there of the letters in the word 'BANANA'?

A) 720 B) 120 C) 60 D) 360

19. In how many ways can the first three positions in a race be filled by 10 contestants?

A) 1000 B) 720 C) 240 D) 120

20. What is the probability that a randomly selected year is a leap year?

A) 1/4 B) 1/3 C) 1/5 D) 1/100

21. If P(A) = 0.5, what is the probability of the complement of A, P(A')?

A) 0.5 B) 0 C) 1 D) 0.25

22. How many ways can a team of 5 players be selected from 12 players?

A) 12C5 B) 12P5 C) 5! * 12 D) 12/5

23. What is the probability of drawing a black card or a king from a standard deck of 52 cards?

A) 32/52 B) 26/52 C) 28/52 D) 30/52

24. How many permutations are possible with the letters of the word 'SUCCESS'?

A) 5040 B) 420 C) 7!/3!2! D) 7!/3!2!1!

25. A bag contains 5 green and 7 yellow balls. If two balls are drawn without replacement, what is the probability that both are green?

A) (5/12) * (4/11) B) (5/12) * (5/11) C) (5/12) * (7/11) D) (5/12) + (4/11)

26. What is the total number of ways to arrange 3 men and 3 women in a row such that all men sit together?

A) 720 B) 144 C) 36 D) 6

27. What is the probability of getting exactly 2 heads in 4 coin tosses?

A) 4C2 * (1/2)^4 B) 4C1 * (1/2)^4 C) 4C2 * (1/2)^2 D) 2/4

28. If nPr = 720 and n = 6, what is r?

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

29. How many ways can 5 distinct books be arranged on a shelf?

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

30. What is the probability of selecting a vowel from the letters of the word 'EDUCATION'?

A) 5/9 B) 4/9 C) 1/9 D) 5/4

31. If nCr = 10 and n = 5, what is r?

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

32. What is the probability of drawing two kings from a deck of 52 cards without replacement?

A) (4/52) * (4/52) B) (4/52) * (3/51) C) (4/52) + (3/51) D) (4/52) * (4/51)

33. How many ways can a president, vice-president, and treasurer be selected from a club of 15 members?

A) 15C3 B) 15P3 C) 15*3 D) 15+3

34. A coin is tossed 5 times. What is the probability of getting at least one head?

A) 1/32 B) 31/32 C) 16/32 D) 1/2

35. What is the probability that a number selected from 1 to 30 is a multiple of 3?

A) 10/30 B) 9/30 C) 3/30 D) 1/3

36. How many diagonals does a polygon with 10 sides have?

A) 45 B) 35 C) 50 D) 10

37. What is the probability of picking a prime number from the integers 1 to 10?

A) 4/10 B) 5/10 C) 3/10 D) 6/10

38. In how many ways can 6 students be seated in a row if two specific students must sit together?

A) 720 B) 120 C) 144 D) 240

39. If P(A) = 0.6, P(B) = 0.5, and P(A ∪ B) = 0.8, what is P(A ∩ B)?

A) 0.3 B) 0.2 C) 0.1 D) 0.4

40. What is the total number of possible outcomes when rolling two distinct dice?

A) 12 B) 36 C) 6 D) 18

41. How many ways can a committee of 4 men and 3 women be formed from 7 men and 5 women?

A) 7C4 * 5C3 B) 7P4 * 5P3 C) (7+5)C(4+3) D) 7C3 * 5C4

42. A letter is chosen at random from the word 'ASSASSINATION'. What is the probability that it is an 'S'?

A) 3/13 B) 4/13 C) 1/13 D) 5/13

43. What is the probability of drawing a red ball or a blue ball from a bag containing 5 red, 3 blue, and 2 green balls?

A) 8/10 B) 5/10 C) 3/10 D) 10/10

44. How many ways can 5 different prizes be distributed among 5 students, if each student gets one prize?

A) 5 B) 25 C) 120 D) 10

45. What is the probability that a year chosen at random contains 53 Sundays?

A) 1/7 B) 2/7 C) 1/4 D) 1/365

46. If nC(r-1) : nCr : nC(r+1) = 1:2:3, find n.

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

47. How many ways can the letters of the word 'ENGINEERING' be arranged?

A) 11! / (3! * 3! * 2!) B) 11! / (3! * 2! * 2!) C) 11! / (3! * 3! * 2! * 1!) D) 11! / (3! * 3!)

48. What is the probability of selecting a number divisible by 7 from the integers 1 to 50?

A) 7/50 B) 6/50 C) 8/50 D) 5/50

49. A fair die is rolled twice. What is the probability of getting a sum of 10?

A) 3/36 B) 1/36 C) 2/36 D) 4/36

50. In how many ways can 5 men and 2 women be seated in a row so that the two women are always together?

A) 1440 B) 720 C) 240 D) 360

Probability, Permutation and Combination - Online Test

Test Results