Mathematics Permutations Combinations and Probability Online Test

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Maan AliLast Updated: October 15, 2025

Start your preparation for Mathematics Permutations Combinations and Probability Online Test. This online test contains important MCQs from past papers. Attempting this test will help you prepare for Annual Exams and Entry Tests. Read the questions carefully and select the correct option below to see your result.

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.
Test Helpful For:	ECAT Entry Test Math Online Test Interview Questions about Math All Universities Entrance Test Recruitments Tests

Math Permutations Combinations and Probability Practice Test Online With Explanation

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Page 1 of 3

Math

1. 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:

IAANG

NAAIG

NAAGI

INAGA

2. The sample space for tossing a coin once is

{H, H}

{H, T}

{H}

{T}

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

2/13

1/26

3/13

1/13

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

1/32

None of these

31/32

1/16

5. Probability theory was introduced by ___________

American mathematician

British mathematician

German mathematician

French mathematician

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

4/9

7/36

5/9

5/12

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

8. 6!/8! =

1/56

1/65

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

P(A) + P(B)

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

P(A) + P(B) – P(AUB)

P(A) + P(B) – P(A∩B)

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

6 ways

720 ways

2 ways

24 ways

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

120

12. ⁴C₄ has the value equal to

None of these

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

None of these

103/108

10/216

93/108

14. 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

24 ways

4 ways

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

720 ways

2 ways

6 ways

24 ways

16. The value of n, when ⁿP₂ = 20 is

17. ⁴C₄ = ?

124

250

None of these

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

None of these

1/3

19. 19!/19!(19–19)! = ?

Undefined

None of these

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

Identity function

Series

Sequence

Onto function

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

720

144

360

22. 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

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

3/8

1/8

None of these

24. 5 persons can be seated at a round table in

24 ways

25 ways

None of these

20 ways

25. 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

Page 2 of 3

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

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

2!2!2!/11!.

11!/2³!

11!/2!2!2!.

27. ⁶P₃ =

120

360

28. The value of ⁵C₂ is

29. 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

None of these

11/4165

22/4165

44/4165

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

13/18

7/18

11/18

1/18

31. 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

11/25

None of these

7/25

32. 4! + 5! = ?

33. 6.5.4 =

6!/3!

1/6!

3!/6!

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

1/5

1/6

1/3

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

(n + 2)!

(n+2)!/(n–1)

(n – 1)!/(n+2)

36.

37. If n is any positive integer, then

(n + 1)! = (n + 1)(n – 1)!

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

n! – n (n – 2)!

n! – n(n + 1)!

38. 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

1/36

1/18

1/12

None of these

39. 1/20.19.18.17 =

20!/16!

1/16!

16!/20!

20!

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

Combination

Permutation

A.P

Sequence

41. 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

735

564

645

42.

43. 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

9/17

7/17

3/17

5/17

44. Factorial of -2 =

362880

40320

-362880

None of these

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

(2n)! ways

(n + 1)! Ways

(n – 1)! Ways

n! Ways

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

47. 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

1/6

1/3

48. If ⁿC₁₂ = ⁿC₆ the value of n is

49. ⁿPᵣ = ?

n!/(n-r)!

n!/(n+1)!

n!/(n+r)!

n/(n-r)

50. 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!r!/n!

n!/q!q!ϒ!

p!/q!ϒ!

Page 3 of 3

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

2!/7!

7/2

7!/2!

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

1/18

None of these

1/216

18/216

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

2/3

None of these

54. (n+1)n(n–1)/3.2.1 =

(n + 1)!

(n–2)!

(n+1)/3!(n–2)

3!(n–2)/(n+1)

55. 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

7/52

2/13

1/13

None of these

56. n(n–1)/3.2.1 =

n!/3!(n–2)!

(n – 2)!/3!n!

3!(n–2)!/n!

57. 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

1/8

None of these

3/8

2/8

58. 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

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

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

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

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

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

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

1/3

1/10

1/5

1/7

61. 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

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

None of these

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

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

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

63. 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

64. ⁶P₄ is equal to

360

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

5!/2!

2!/5!

All of these

5!.2!

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

∞

-1

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

5040

720

360

1440

68. 6P1 is equal to

69. 8.7.6/3.2.1 =

10/2!8!

8!/3!5!

3!5!/8!

10!

70. ⁿPᵣ =

(n–r)!/n!

n!/(n–r)!r!

n!/(n+r)!

n!/(n–r)!

71. 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

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

2 ways

24 ways

6 ways

720 ways

73. 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!

M-CAT-Q

74. 0!

-1

How to Score High in Mathematics Permutations Combinations and Probability Online Test?

Mastering scientific subjects requires conceptual clarity.

Key Preparation Tips:

Concepts First: Ensure you understand the underlying theories before attempting the MCQs.
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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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M-CAT-Q

How to Score High in Mathematics Permutations Combinations and Probability Online Test?

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