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

120

2. ⁶P₃ =

120

360

3. 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

7/52

1/13

2/13

4. 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

11/25

7/25

9/25

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

2 ways

6 ways

24 ways

720 ways

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

1/5

1/6

1/3

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

Permutation

Combination

Sequence

A.P

8. 1/20.19.18.17 =

1/16!

20!

20!/16!

16!/20!

9. 4! + 5! = ?

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

(n+2)!/(n–1)

(n – 1)!/(n+2)

(n + 2)!

11. Probability theory was introduced by ___________

German mathematician

British mathematician

American mathematician

French mathematician

12. The value of ⁵C₂ is

13. 8.7.6/3.2.1 =

3!5!/8!

10/2!8!

8!/3!5!

10!

14. 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

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

5/12

7/36

4/9

5/9

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

5!/2!

All of these

5!.2!

2!/5!

17. 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

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

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

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

(n + 1)! Ways

(n – 1)! Ways

(2n)! ways

n! Ways

19. 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!

p!q!r!/n!

n!/q!ϒ!

p!/q!ϒ!

20. 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)

21. n(n–1)/3.2.1 =

n!/3!(n–2)!

3!(n–2)!/n!

(n – 2)!/3!n!

22. 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

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

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

11/18

1/18

7/18

13/18

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

1/10

1/5

1/7

1/3

Page 2 of 3

26. 6P1 is equal to

27. 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)

28. 6!/8! =

1/56

1/65

29. 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

645

564

756

30. The value of n, when ⁿP₂ = 20 is

31. (n+1)n(n–1)/3.2.1 =

3!(n–2)/(n+1)

(n–2)!

(n+1)/3!(n–2)

(n + 1)!

32. 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

1/8

2/8

None of these

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

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

None of these

1/216

1/18

18/216

35. 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

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

24 ways

6 ways

720 ways

2 ways

37. 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

44/4165

22/4165

11/4165

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

720 ways

24 ways

6 ways

2 ways

39. ⁿPᵣ =

n!/(n–r)!r!

(n–r)!/n!

n!/(n+r)!

n!/(n–r)!

40. 19!/19!(19–19)! = ?

Undefined

None of these

41. 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

42. 5 unbiased coins are tossed simultaneously. The probability of getting at least one head is

None of these

31/32

1/16

1/32

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

-1

∞

44. ⁴C₄ = ?

None of these

124

250

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

Identity function

Onto function

Series

Sequence

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

2!2!2!/11!.

11!/2!2!2!.

11!/2³!

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

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

1/8

None of these

3/8

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

None of these

2/3

49. 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

None of these

4/5

2/5

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

1/3

None of these

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. ⁿPᵣ = ?

n!/(n+r)!

n!/(n+1)!

n/(n-r)

n!/(n-r)!

53. 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

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

1440

720

5040

360

55. If ⁿC₁₂ = ⁿC₆ the value of n is

56. 6.5.4 =

3!/6!

1/6!

6!/3!

57. 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

NAAGI

IAANG

NAAIG

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

1/6

1/3

None of these

59.

60.

61. The sample space for tossing a coin once is

{T}

{H}

{H, T}

{H, H}

62. 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

5/17

3/17

7/17

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

144

720

360

64. 5 persons can be seated at a round table in

24 ways

None of these

25 ways

20 ways

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

4 ways

24 ways

12 ways

256 ways

66. ⁴C₄ has the value equal to

None of these

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

2/13

1/26

1/13

3/13

68. 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!

69. ⁶P₄ is equal to

360

70. 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

1/12

7/12

5/12

71. Factorial of -2 =

-362880

362880

40320

None of these

72. If n is any positive integer, then

n! – n(n + 1)!

n! – n (n – 2)!

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

(n + 1)! = (n + 1)(n – 1)!

73. 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

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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