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. 1/20.19.18.17 =

1/16!

16!/20!

20!/16!

20!

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

6!/2!.2!

6!/2²!

6!.2.2!

2²!/6!

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

12 ways

4 ways

24 ways

256 ways

4. 5 unbiased coins are tossed simultaneously. The probability of getting at least one head is

31/32

1/32

1/16

None of these

5. The value of ⁵C₂ is

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

1/26

2/13

3/13

1/13

7. n(n–1)/3.2.1 =

3!(n–2)!/n!

(n – 2)!/3!n!

n!/3!(n–2)!

8. 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

11/25

7/25

None of these

9/25

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

5/9

5/12

4/9

7/36

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

(n – 1)! Ways

(2n)! ways

n! Ways

(n + 1)! Ways

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

11!/2!2!2!.

11!/2³!

2!2!2!/11!.

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

12. 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!q!ϒ!

n!/q!ϒ!

p!q!r!/n!

p!/q!ϒ!

13. 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

7/12

1/6

5/12

1/12

14. 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

7/17

3/17

5/17

9/17

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

1440

5040

720

360

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

(n + 2)!

(n+2)!/(n–1)

(n – 1)!/(n+2)

17. If n is any positive integer, then

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

(n + 1)! = (n + 1)(n – 1)!

n! – n(n + 1)!

n! – n (n – 2)!

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

∞

-1

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

24 ways

2 ways

6 ways

720 ways

20. 6P1 is equal to

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

Series

Sequence

Identity function

Onto function

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

None of these

1/12

22/36

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

Permutation

A.P

Sequence

Combination

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

25. If ⁿC₁₂ = ⁿC₆ the value of n is

Page 2 of 3

26. ⁿPᵣ =

n!/(n–r)!

n!/(n+r)!

n!/(n–r)!r!

(n–r)!/n!

27. 8.7.6/3.2.1 =

10/2!8!

10!

3!5!/8!

8!/3!5!

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

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

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

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

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

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

6 ways

2 ways

720 ways

24 ways

30. 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

31. (n+1)n(n–1)/3.2.1 =

3!(n–2)/(n+1)

(n + 1)!

(n+1)/3!(n–2)

(n–2)!

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

1/18

13/18

11/18

7/18

33. $Math 7. 02$

34. ⁴C₄ has the value equal to

None of these

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

1/7

1/5

1/3

1/10

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

144

360

720

37. Factorial of -2 =

40320

-362880

None of these

362880

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

120

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

93/108

10/216

None of these

103/108

40. ⁶P₃ =

120

360

41. ⁴C₄ = ?

None of these

250

124

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

1/216

None of these

1/18

18/216

43. 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

410

260

356

44. The value of n, when ⁿP₂ = 20 is

45. 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)}

None of these

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

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

46. 19!/19!(19–19)! = ?

None of these

Undefined

47. Probability theory was introduced by ___________

American mathematician

German mathematician

British mathematician

French mathematician

48. ⁿPᵣ = ?

n!/(n-r)!

n!/(n+1)!

n!/(n+r)!

n/(n-r)

49. The sample space for tossing a coin once is

{T}

{H, H}

{H, T}

{H}

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

None of these

1/3

Page 3 of 3

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

5!/2!

5!.2!

2!/5!

All of these

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

1/6

1/3

1/5

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

None of these

2/3

54. 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:

NAAIG

INAGA

NAAGI

IAANG

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

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

P(A) + P(B) – P(AUB)

P(A) + P(B) – P(A∩B)

P(A) + P(B)

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

24 ways

720 ways

6 ways

2 ways

57. 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?

756

645

564

735

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

2!/7!

7!/2!

7/2

59. 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

2/8

3/8

60. 4! + 5! = ?

61. $Math 7. 01$

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

63. ⁶P₄ is equal to

360

64. 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

None of these

7/52

1/13

65. 6.5.4 =

1/6!

3!/6!

6!/3!

66. 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

22/4165

11/4165

None of these

44/4165

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

1/8

3/8

None of these

68. 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

1/18

1/36

69. 6!/8! =

1/65

1/56

70. 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

71. 5 persons can be seated at a round table in

None of these

24 ways

20 ways

25 ways

72. 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

4/5

None of these

3/5

2/5

73. 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

M-CAT-Q

74. 0!

-1

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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

Important Math Permutations Combinations and Probability Question and Answer

Math Permutations Combinations and Probability Practice Test Online With Explanation

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