Question # 1

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

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1/12

1/6

5/12

7/12

A bag contains 7 whit, 5 black and 4 rd balls. If two balls are drawn at random from the bag, the probability that they are not of the same color is

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73 / 120

83 / 120

67 / 120

43 / 120

n(n - 1) (n - 2) in factorial form is

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If S is a sample space and event set E = S then P(E) is

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>0

1

<1

0

For two events A and B if P(A) = P (A/B) = 1/4 and P(B/A) = 1/2, then

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A is sub-event of B

A and B are mutually exclusive

A and B are independent and P(A/B) = 3/4

None of these

Four cards are drawn at random from a pack of 52 playing cards. The probability of getting all the four cars of the same suit is

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44/4165

22/4165

11/4165

None of these

The sum of all positive integral multiple of 5 less than 100 is

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950

760

1230

875

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An integer is chosen at random from the number ranging from 1 to 50. the probability that the integer chosen is a multiple of 2 or 3 or 10 is

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3 / 10

5 / 10

7 / 10

9 / 10

How many necklaces can be made from 6 beads of different colours?

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120

60

24

15

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8

1/56

56

None of these

If 4 ⁶P_r= ⁶P_r+1, then r is equal to

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4

3

2

1

A key ring is an example of

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Permutation

Circular permutation

Combination

None

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The factorial of a positive integers is a (an)

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Rational number

Positive integer

Real number

None

For a positive integer n

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n! = n(n + 1)

n! = n(n+1)!

n! = n(n - 1 )

n! = n(n - 1)!

6! = ______

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360

720

6.5.4

None of these

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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

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1/8

2/8

3/8

None of these

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangement is

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⁶C₃x ⁴C₂

⁴C₂x ⁴P₃

⁴P₂x ⁶P₃

None of these

The value of n, when ⁿP₂= 20 is

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3

4

6

5

probability of a certain event is

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0

-1

1

∞

In a school there are 150 students Out of these 80 students enrolled for mathematics class.50 enrolled for English class and 60 enrolled for Physics class The student enrolled for English cannot attend any other class but the students of mathematics and Physics can take two courses at a time find the number of students who have taken both physics and mathematics.

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40

30

50

60

Arithmetic mean between 14 and 18 is

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16

17

15

32

A committee consists of 9 experts taken from three institutions A, B, and C, of which 2 are from, A, 3 form B and 4 from C. If three experts resign, then the probability that they belong to different institutions is

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1 / 729

1 / 24

1 / 21

2 / 7

The number of combinations of 10 different objects taken 8 objects at a time is

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90

45

55

50

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6

360

120

24

n(n - 1) (n - 2) .... (n - r + 1) = ______

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5

10

20

30

Cycle tyres are supplied in lots of 10 and there is a chance if 1 in 500 tyres to be defective. Using Poisson distribution, the approximate number of lots containing no defective tyre in a consignment of 10, 0000 lots is

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9028

9208

9802

9820

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ECAT Mathematics Chapter 9 Permutation, Combination and Probability Online Test MCQs With Answers

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