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.
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

Please wait...

Page 1 of 3

Math

1. 8.7.6/3.2.1 =

8!/3!5!

10/2!8!

3!5!/8!

10!

2. 4! + 5! = ?

3. ⁴C₄ = ?

None of these

124

250

4. 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

IAANG

INAGA

NAAGI

5. 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

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

7/18

13/18

11/18

1/18

7. 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

356

410

260

8. ⁶P₄ is equal to

360

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

720

360

144

10. 5 persons can be seated at a round table in

20 ways

None of these

25 ways

24 ways

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

1440

720

5040

360

12. If n is any positive integer, then

(n + 1)! = (n + 1)(n – 1)!

n! – n (n – 2)!

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

n! – n(n + 1)!

13. 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

1/18

1/36

None of these

14. 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

15. 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

2/5

3/5

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

(n+2)!/(n–1)

(n – 1)!/(n+2)

(n + 2)!

17. The sample space for tossing a coin once is

{H}

{H, H}

{H, T}

{T}

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

Identity function

Onto function

Sequence

Series

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

5/9

4/9

5/12

7/36

20. 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

None of these

1/13

7/52

2/13

21. ⁿPᵣ =

(n–r)!/n!

n!/(n+r)!

n!/(n–r)!

n!/(n–r)!r!

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

2 ways

6 ways

24 ways

720 ways

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

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

1/7

1/5

1/3

1/10

25. 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

None of these

9/25

7/25

11/25

Page 2 of 3

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

1/13

1/26

3/13

2/13

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

2/3

None of these

28. 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

44/4165

22/4165

11/4165

None of these

29. The value of ⁵C₂ is

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

120

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

6 ways

24 ways

720 ways

2 ways

32. ⁿPᵣ = ?

n!/(n-r)!

n!/(n+r)!

n/(n-r)

n!/(n+1)!

33. If ⁿC₁₂ = ⁿC₆ the value of n is

34. Factorial of -2 =

None of these

40320

362880

-362880

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

93/108

None of these

103/108

10/216

36. $Math 7. 02$

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

P(A) + P(B) – P(A∩B)

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

P(A) + P(B) – P(AUB)

P(A) + P(B)

38. 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

39. ⁶P₃ =

360

120

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

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

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

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

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

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

∞

-1

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

Permutation

Sequence

Combination

A.P

43. (n+1)n(n–1)/3.2.1 =

(n+1)/3!(n–2)

(n–2)!

(n + 1)!

3!(n–2)/(n+1)

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

1/16

1/8

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

3/8

None of these

1/8

46. 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

2/8

1/8

3/8

None of these

47. 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!/2!2!2!.

11!/2³!

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

None of these

1/3

1/6

49. 19!/19!(19–19)! = ?

Undefined

None of these

50. 6!/8! =

1/65

1/56

Page 3 of 3

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

1/3

None of these

52. 6P1 is equal to

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

6!/2!.2!

6!/2²!

2²!/6!

6!.2.2!

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

55. 1/20.19.18.17 =

20!/16!

20!

1/16!

16!/20!

56. 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!ϒ!

p!q!r!/n!

57. Probability theory was introduced by ___________

French mathematician

American mathematician

British mathematician

German mathematician

58. 5 unbiased coins are tossed simultaneously. The probability of getting at least one head is

1/16

1/32

31/32

None of these

59. n(n–1)/3.2.1 =

3!(n–2)!/n!

n!/3!(n–2)!

(n – 2)!/3!n!

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

(n – 1)! Ways

(n + 1)! Ways

(2n)! ways

n! Ways

61. 6.5.4 =

6!/3!

1/6!

3!/6!

62. The value of n, when ⁿP₂ = 20 is

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

18/216

1/216

None of these

1/18

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

256 ways

12 ways

4 ways

24 ways

65. 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

5/12

1/6

1/12

7/12

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

720 ways

24 ways

6 ways

2 ways

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

1/6

1/3

1/5

68. 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

69. 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

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)}

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

None of these

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

71. 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?

735

564

756

645

72. ⁴C₄ has the value equal to

None of these

73. $Math 7. 01$

M-CAT-Q

74. 0!

-1

More Related Resources

PPSC Syllabus for Mathematics Lectu...

Can't find what you're looking for? Search below:

Latest Updates

PPSC Syllabus for Mathematics Lecturer 2026 Sample Test Pattern

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

Important Math Permutations Combinations and Probability Question and Answer

Math Permutations Combinations and Probability Practice Test Online With Explanation

Math

M-CAT-Q

More Related Resources

Latest Updates

Maan Ali

7 Comments

Leave a Reply Cancel reply