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

2!/7!

7/2

7!/2!

7/2

2. Factorial of -2 =

40320

None of these

362880

-362880

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

1/10

1/3

1/5

1/7

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

(n + 1)! Ways

(2n)! ways

n! Ways

(n – 1)! Ways

6. 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

7/25

None of these

7. 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

8. ⁶P₄ is equal to

360

9. 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

5/17

3/17

9/17

7/17

10. 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?

645

564

756

735

11. 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)

12. 6P1 is equal to

13. If ⁿC₁₂ = ⁿC₆ the value of n is

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

6!.2.2!

6!/2!.2!

2²!/6!

6!/2²!

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

4 ways

256 ways

24 ways

12 ways

16. 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!ϒ!

p!q!r!/n!

n!/q!q!ϒ!

n!/q!ϒ!

17. Probability theory was introduced by ___________

British mathematician

French mathematician

American mathematician

German mathematician

18. ⁿPᵣ = ?

n!/(n+1)!

n/(n-r)

n!/(n-r)!

n!/(n+r)!

19. 8.7.6/3.2.1 =

3!5!/8!

10/2!8!

8!/3!5!

10!

20. 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

21. 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

2/13

7/52

None of these

1/13

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

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

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

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

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

None of these

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

A.P

Permutation

Sequence

Combination

Page 2 of 3

26. 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

NAAIG

NAAGI

IAANG

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

None of these

2/3

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

11/18

1/18

7/18

13/18

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

6 ways

2 ways

720 ways

24 ways

30. (n+1)n(n–1)/3.2.1 =

3!(n–2)/(n+1)

(n–2)!

(n+1)/3!(n–2)

(n + 1)!

31. ⁴C₄ has the value equal to

None of these

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

1/3

1/6

1/5

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

1/3

None of these

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

1/8

None of these

3/8

35.

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

103/108

None of these

93/108

10/216

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

360

720

144

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

(n – 1)!/(n+2)

(n+2)!/(n–1)

(n + 2)!

39. 5 unbiased coins are tossed simultaneously. The probability of getting at least one head is

31/32

1/32

1/16

None of these

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

24 ways

720 ways

2 ways

6 ways

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

5!/2!

5!.2!

All of these

2!/5!

42. 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

None of these

1/18

1/12

43. 5 persons can be seated at a round table in

None of these

24 ways

25 ways

20 ways

44. The sample space for tossing a coin once is

{H, H}

{H}

{H, T}

{T}

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

360

720

5040

1440

46. ⁶P₃ =

120

360

47. The value of n, when ⁿP₂ = 20 is

48. 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

49. 4! + 5! = ?

50. ⁴C₄ = ?

None of these

250

124

Page 3 of 3

51. The value of ⁵C₂ is

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

2!2!2!/11!.

11!/2³!

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

11!/2!2!2!.

53. 19!/19!(19–19)! = ?

None of these

Undefined

54. 1/20.19.18.17 =

20!/16!

20!

1/16!

16!/20!

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

∞

-1

56. ⁿPᵣ =

n!/(n–r)!r!

n!/(n–r)!

n!/(n+r)!

(n–r)!/n!

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

1/3

None of these

1/6

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

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

P(A) + P(B) – P(A∩B)

P(A) + P(B) – P(AUB)

P(A) + P(B)

59. n(n–1)/3.2.1 =

n!/3!(n–2)!

(n – 2)!/3!n!

3!(n–2)!/n!

60. If n is any positive integer, then

n! – n (n – 2)!

(n + 1)! = (n + 1)(n – 1)!

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

n! – n(n + 1)!

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

120

62. 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

63. 6.5.4 =

3!/6!

6!/3!

1/6!

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

3/13

1/26

1/13

2/13

65. 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

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

Series

Sequence

Onto function

Identity function

67. 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

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

6 ways

24 ways

2 ways

720 ways

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

70. 6!/8! =

1/65

1/56

71. 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

7/12

1/6

5/12

72. 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

None of these

2/5

4/5

3/5

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

None of these

1/216

1/18

18/216

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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