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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. 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

2/5

4/5

3/5

None of these

2. ⁶P₄ is equal to

360

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

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

P(A) + P(B) – P(A∩B)

P(A) + P(B)

P(A) + P(B) – P(AUB)

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

5. 8.7.6/3.2.1 =

3!5!/8!

8!/3!5!

10!

10/2!8!

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

24 ways

6 ways

2 ways

720 ways

7. 5 persons can be seated at a round table in

None of these

20 ways

24 ways

25 ways

8. The value of ⁵C₂ is

9. 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!

10. n(n–1)/3.2.1 =

3!(n–2)!/n!

(n – 2)!/3!n!

n!/3!(n–2)!

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

1/3

1/6

1/5

12. 19!/19!(19–19)! = ?

Undefined

None of these

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

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

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

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

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

14. 1/20.19.18.17 =

20!

16!/20!

1/16!

20!/16!

15. ⁿPᵣ =

n!/(n+r)!

n!/(n–r)!

n!/(n–r)!r!

(n–r)!/n!

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

(2n)! ways

(n – 1)! Ways

n! Ways

(n + 1)! Ways

17. 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

NAAGI

IAANG

INAGA

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

11!/2³!

11!/2!2!2!.

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

2!2!2!/11!.

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

None of these

3/8

1/8

20. 6!/8! =

1/65

1/56

21. 6.5.4 =

6!/3!

3!/6!

1/6!

22. 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

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

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

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

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

(n – 1)!/(n+2)

(n+2)!/(n–1)

(n + 2)!

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

None of these

2/3

25. 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

7/12

1/6

1/12

Page 2 of 3

26. 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

27. 4! + 5! = ?

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

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

-1

∞

30. 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

31. ⁴C₄ = ?

250

124

None of these

32. 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

33. 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

1/13

7/52

2/13

None of these

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. If n is any positive integer, then

n! – n (n – 2)!

n! – n(n + 1)!

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

(n + 1)! = (n + 1)(n – 1)!

36. 5 unbiased coins are tossed simultaneously. The probability of getting at least one head is

1/32

None of these

1/16

31/32

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

1/6

None of these

1/3

38. ⁿPᵣ = ?

n!/(n+1)!

n!/(n-r)!

n/(n-r)

n!/(n+r)!

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

None of these

10/216

103/108

93/108

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

1/18

None of these

1/216

18/216

41. 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

None of these

22/4165

42. Probability theory was introduced by ___________

American mathematician

British mathematician

German mathematician

French mathematician

43. 6P1 is equal to

44. 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

1/18

1/36

None of these

1/12

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

360

144

720

46. If ⁿC₁₂ = ⁿC₆ the value of n is

47. 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

9/17

5/17

3/17

48. 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

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

120

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

p!q!r!/n!

n!/q!ϒ!

p!/q!ϒ!

n!/q!q!ϒ!

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. ⁶P₃ =

120

360

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

Combination

Permutation

A.P

Sequence

54. 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!

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

6 ways

24 ways

720 ways

2 ways

56. 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

57. Factorial of -2 =

None of these

40320

-362880

362880

58. 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

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

Sequence

Onto function

Series

Identity function

60. (n+1)n(n–1)/3.2.1 =

(n + 1)!

3!(n–2)/(n+1)

(n+1)/3!(n–2)

(n–2)!

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

1/18

7/18

11/18

13/18

62.

63.

64. ⁴C₄ has the value equal to

None of these

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

720 ways

2 ways

6 ways

24 ways

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

24 ways

256 ways

12 ways

4 ways

67. 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

68. 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

None of these

1/8

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

1/10

1/3

1/5

1/7

70. The sample space for tossing a coin once is

{H}

{H, T}

{T}

{H, H}

71. 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

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

360

720

5040

1440

73. The value of n, when ⁿP₂ = 20 is

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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