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ECAT Mathematics Permutations Combinations and Probability Online Test

Maan AliLast Updated: April 18, 2025

Mathematics Permutations Combinations and Probability MCQS Online Test

ECAT Math Permutations Combinations and Probability Online Test

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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ECAT Math Permutations Combinations and Probability Chapter Online Test

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Page 1 of 3

Math

1. 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

2. (n+1)n(n–1)/3.2.1 =

(n–2)!

(n+1)/3!(n–2)

3!(n–2)/(n+1)

(n + 1)!

4. 1/20.19.18.17 =

1/16!

20!

16!/20!

20!/16!

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

Permutation

A.P

Sequence

Combination

6. 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

3/8

2/8

1/8

None of these

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

Onto function

Sequence

Series

Identity function

8. 6P1 is equal to

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

18/216

1/18

None of these

1/216

10.

11. 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

12. 6!/8! =

1/65

1/56

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

2/3

None of these

14. 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!.

15. 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

3/17

7/17

5/17

16. 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)}

17. 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

p!q!r!/n!

n!/q!ϒ!

n!/q!q!ϒ!

p!/q!ϒ!

18. 6.5.4 =

3!/6!

1/6!

6!/3!

19. 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

20. 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

7/25

11/25

None of these

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

1/3

1/7

1/10

1/5

22. 19!/19!(19–19)! = ?

None of these

Undefined

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

∞

-1

24. 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

44/4165

22/4165

None of these

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

7/18

13/18

11/18

1/18

Page 2 of 3

26. ⁿPᵣ =

n!/(n–r)!

n!/(n+r)!

(n–r)!/n!

n!/(n–r)!r!

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

2 ways

720 ways

24 ways

6 ways

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

29. ⁶P₃ =

360

120

30. 5 persons can be seated at a round table in

25 ways

None of these

24 ways

20 ways

31. If ⁿC₁₂ = ⁿC₆ the value of n is

32. 8.7.6/3.2.1 =

8!/3!5!

3!5!/8!

10!

10/2!8!

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

120

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

5/9

7/36

4/9

5/12

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

7!/2!

7/2

2!/7!

7/2

36. 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

4/5

None of these

37. 4! + 5! = ?

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

1/3

1/5

1/6

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

720 ways

24 ways

6 ways

2 ways

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

6!/2²!

2²!/6!

6!.2.2!

6!/2!.2!

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

None of these

3/8

1/8

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

360

144

720

43. ⁴C₄ has the value equal to

None of these

44. 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

1/12

1/6

5/12

7/12

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

5040

360

1440

720

46. If n is any positive integer, then

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

(n + 1)! = (n + 1)(n – 1)!

n! – n (n – 2)!

n! – n(n + 1)!

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

2 ways

6 ways

720 ways

24 ways

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

(n – 1)! Ways

(n + 1)! Ways

n! Ways

(2n)! ways

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

5!/2!

2!/5!

5!.2!

All of these

50. The value of n, when ⁿP₂ = 20 is

Page 3 of 3

51. ⁶P₄ is equal to

360

52. 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

53. 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)

54. n(n–1)/3.2.1 =

3!(n–2)!/n!

n!/3!(n–2)!

(n – 2)!/3!n!

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

1/3

None of these

56. 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

57. 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

22/36

1/12

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

1/26

1/13

3/13

2/13

59. Probability theory was introduced by ___________

American mathematician

German mathematician

French mathematician

British mathematician

60. 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:

INAGA

IAANG

NAAIG

NAAGI

61. 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) + P(B) – P(A∩B)

62. The value of ⁵C₂ is

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

64. ⁴C₄ = ?

124

250

None of these

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

(n+2)!/(n–1)

(n + 2)!

(n – 1)!/(n+2)

66. 5 unbiased coins are tossed simultaneously. The probability of getting at least one head is

1/16

1/32

None of these

31/32

67. Factorial of -2 =

362880

None of these

40320

-362880

68. 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

260

410

69. ⁿPᵣ = ?

n!/(n-r)!

n/(n-r)

n!/(n+r)!

n!/(n+1)!

70. 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

None of these

1/12

1/18

1/36

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. The sample space for tossing a coin once is

{T}

{H}

{H, H}

{H, T}

73. 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

M-CAT-Q

74. 0!

-1

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Maan AliLast Updated: April 18, 2025

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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

ECAT Mathematics Permutations Combinations and Probability Online Test

Mathematics Permutations Combinations and Probability MCQS Online Test

ECAT Math Permutations Combinations and Probability Online Test

ECAT Math Permutations Combinations and Probability Chapter Online Test

Math

M-CAT-Q

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Mathematics Permutations Combinations and Probability MCQS Online Test

ECAT Math Permutations Combinations and Probability Online Test

ECAT Math Permutations Combinations and Probability Chapter Online Test

Math

M-CAT-Q

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