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Mathematics Permutations Combinations and Probability Online Test

Maan AliLast Updated: October 15, 2025

Important Math Permutations Combinations and Probability Question and Answer

Total Questions:	74
Time Allowed:	40 Minutes
Total Marks:	74
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Math Permutations Combinations and Probability Practice Test Online With Explanation

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Page 1 of 3

Math

1. ⁶P₃ =

120

360

2. (n + 2)(n + 1) n =

(n – 1)!/(n+2)

(n + 2)!

(n+2)!/(n–1)

3. 1/20.19.18.17 =

20!/16!

1/16!

20!

16!/20!

4. An arrangement of a finite number of objects taken some or all at a time is called their

Sequence

A.P

Combination

Permutation

5. A number is selected at random form the three digit numbers, the probability that the number is divisible by 4 is

1/8

1/16

6. A die is rolled, what is the probability of getting a number which is even and greater than 2?

None of these

1/6

1/3

7. Probability theory was introduced by ___________

American mathematician

German mathematician

French mathematician

British mathematician

8. 5 unbiased coins are tossed simultaneously. The probability of getting at least one head is

31/32

1/16

None of these

1/32

9. A bad contains 3 white, 4 black and 2 red balls. If 2 balls are drawn at random, then the probability that both the balls are white is

1/12

None of these

1/36

1/18

10. The value of ⁵C₂ is

11. If A and Bare mutually exclusive then P(AUB) = ?

P(A) + P(B)

P(A) + P(B) – P(AUB)

P(A) + P(B) – P(A∩B)

P(A) + P(B)+P(AUB)

12.

13. The number of significant numbers which can be formed by using any number of the digits 0, 1, 2, 3, 4 but using each not more than once in each number is

260

356

410

14. The number of words that can be formed out of the letters of the word MATHEMATICS is

11!/2³!

11!/2!2!2!.

11!/2!.2!.2!.

2!2!2!/11!.

15. The probability of getting 5, when one dice is called

1/3

1/5

1/6

16. 19!/19!(19–19)! = ?

None of these

Undefined

17. 6!/8! =

1/56

1/65

18. The letters of the CHORD taken all at a time can be written in

24 ways

720 ways

2 ways

6 ways

19. A function whose domain is the set of natural numbers is called the

Series

Onto function

Identity function

Sequence

20. In different objects can be arranged taken all at a time in

n! Ways

(n – 1)! Ways

(n + 1)! Ways

(2n)! ways

21. There are 25 tickets bearing numbers from 1 to 25. One ticket is drawn at random. The probability that the number on it is a multiple of 5 or 6 is

9/25

None of these

7/25

11/25

22. ⁴C₄ = ?

None of these

124

250

23. n(n–1)/3.2.1 =

(n – 2)!/3!n!

3!(n–2)!/n!

n!/3!(n–2)!

24. ⁶P₄ is equal to

360

25. How many signals can be given with three different flags when any number of them may be used

Page 2 of 3

26. The number of words that can be formed out of the letters of the word MURREE is

2²!/6!

6!/2!.2!

6!.2.2!

6!/2²!

27. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how ways can it be done?

645

756

564

735

28. Three unbiased coins are tossed. Then the probabilities of getting two heads is

None of these

3/8

1/8

29. What is the probability to get a block jack from a well shuffled pack of playing cards?

3/13

1/13

1/26

2/13

30. 8.7.6/3.2.1 =

10!

8!/3!5!

10/2!8!

3!5!/8!

31. 6P1 is equal to

32. If ⁿC₁₂ = ⁿC₆ the value of n is

33. 5 persons can be seated at a round table in

None of these

24 ways

25 ways

20 ways

34. If probability of bulb being defective is 0.2. estimate how many defective bulb there would be in 600 bulbs

120

35. Four cards are drown at random from a pack of 52 playing cards. The probability of getting all the four cards of the same suit is

11/4165

22/4165

None of these

44/4165

36. The number of words that can be formed out of the letters of the word BANNU is

2!/5!

All of these

5!/2!

5!.2!

37.

38. A card is drawn from a pack of cards numbered 1 to 52, the probability that the number on the card is a perfect square is

2/13

1/13

7/52

None of these

39. If n (E₁) = 18 and n (E₂) = 6 and n (5) = 36 also E₁ and E₂ are independent then P(E₁ ∩ E₂) = ?

22/36

1/12

None of these

40. Two unbiased dice are thrown. The probability that the total score is > 5 is

7/18

13/18

11/18

1/18

41. In how many ways can 7 keys be arranged in a circular key ring

1440

720

5040

360

42. From a group of 5 men and 3 women, a committee of 4 persons is to be selected randomly. The probability that there is a majority of men is

1/3

1/6

43. Three dice are thrown together. The probability of getting a total of at least 6 is

None of these

103/108

93/108

10/216

44. The probability that a 3 – digit no. chosen at random divisible by 5 is

1/3

1/10

1/7

1/5

45. The number of permutations of the n objects of which there are p like objects of one kind, q like objects of the second kind nd r like objects of the third kind are

n!/q!ϒ!

p!/q!ϒ!

p!q!r!/n!

n!/q!q!ϒ!

46. If n is any positive integer, then

n! – n (n – 2)!

n! – n(n + 1)!

(n+1)! = (n + 1) n!

(n + 1)! = (n + 1)(n – 1)!

47. Riaz, Saba, Maria, Shehzad are to give speeches in a class. The teacher can arrange the order of their presentation in

12 ways

256 ways

4 ways

24 ways

48. 6.5.4 =

3!/6!

1/6!

6!/3!

49. The number of words that can be formed out of the letters of the word PHYSICS is

7/2

2!/7!

7!/2!

7/2

50. If A is an impossible event then P(A) = ?

-1

∞

Page 3 of 3

51. The sample space for tossing a coin once is

{T}

{H, T}

{H}

{H, H}

52. The letters of the LAHORE taken all at a time can be written in

720 ways

6 ways

2 ways

24 ways

53. A coin is tossed. If head comes up, a die is thrown but if tail comes up, the coin is tossed again. The probability of obtaining a head and an even number is

None of these

1/8

3/8

2/8

54. Factorial of -2 =

40320

-362880

362880

None of these

55. Two dice are thrown simultaneously find the probability that the sum of the dots of the dice is a prime no?

7/36

5/9

5/12

4/9

56. In a class of 100 students, 60 drink tea, 50 drink coffee and 30 drink both. A student from this class is selected at random. The probability that the student takes at last one of 2 drinks is

3/5

2/5

None of these

4/5

57. 4! + 5! = ?

58. There dice are thrown simultaneously find the probability to get greatest sum of dost?

18/216

1/216

1/18

None of these

59. If 4 ⁶Pᵣ = ⁶Pᵣ₊₁, then r is equal to

60. The value of n, when ⁿP₂ = 20 is

61. Two cards are drawn at random from a well shuffled pack of cards. The probability that at least one of them is a face card is

3/17

9/17

7/17

5/17

62. ⁿPᵣ =

(n–r)!/n!

n!/(n–r)!r!

n!/(n–r)!

n!/(n+r)!

63. Events A, B and C are equally likely when

P(A) = P(B) + P(C)

P(A) + P(B) = P(C)

P(A) = P(B) = P(C)

P(B) = P(A) + (PC)

64. If probability of rain today is 1/3 what is probability of not rain today?

1/3

None of these

65. All letters of the word “AGAIN” are permuted in all possible ways and the words so formed (with or without meaning) are written as in dictionary, then the 50th word is:

NAAGI

NAAIG

INAGA

IAANG

66. ⁿPᵣ = ?

n!/(n-r)!

n/(n-r)

n!/(n+r)!

n!/(n+1)!

67. In how many ways can the letters of the word ‘LEADER’ be arranged?

720

144

360

68. (n+1)n(n–1)/3.2.1 =

(n + 1)!

(n+1)/3!(n–2)

3!(n–2)/(n+1)

(n–2)!

69. An unbiased die is thrown. Then the probability of getting a prime is

2/3

None of these

70. Two balanced dice are tossed once, the sample space when the integers on the faces of two dice are the same is

{(1, 1),(2, 2),(3, 3),(4, 4),(5, 5),(6, 6)}

{(1, 1),(2, 2),(3, 3)}

None of these

{(4, 4),(5, 5),(6, 6)}

71. Six boys and 3 girls are to be seated at random, in a row, for a photograph. The probability that no two girls will sit together is

1/6

7/12

1/12

5/12

72. ⁴C₄ has the value equal to

None of these

73. The letters of the JUNE taken all a t a time can be written in

6 ways

24 ways

2 ways

720 ways

M-CAT-Q

74. 0!

-1

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Maan AliLast Updated: October 15, 2025

7 Comments

Anaya says:

February 11, 2022 at 2:28 pm

How i prepare msc math entry test

zohaib says:

July 29, 2017 at 12:37 am

i got 100%

Qasim Ali says:

July 15, 2017 at 11:29 pm

whats the right answer for this mcq’s arrangment of fintite number of objects taken some or all the time??? i have confusion with this

Karan Kumar says:

May 4, 2017 at 1:52 pm

I got 96%. Only 1 mistake.

umair ahmed says:

March 19, 2017 at 1:05 pm

92%

Aunali says:

July 31, 2016 at 11:37 am

i got 96%

AMEER HAMZA says:

July 21, 2016 at 9:01 pm

GREAT PEOPLE DOING THIER JOB IN THEV BEST POSSIBLE WAY

Mathematics Permutations Combinations and Probability Online Test

Important Math Permutations Combinations and Probability Question and Answer

Math Permutations Combinations and Probability Practice Test Online With Explanation

Math

M-CAT-Q

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