Question # 1

A bag contains 3 white, 4 black and 2 red balls. If 2 balls are drawn at random, then the probability that both the ball are white is

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1/18

1/12

1/36

None of these

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

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1 / 18

7 / 18

13 / 18

11 / 18

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5

20

9

4

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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

In 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

20

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

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1/2

2/3

3/4

None of these

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

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The sum if 1,3,5,7,9........ up to 20 terms is

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400

472

563

264

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0.9

0.74

0.2016

None of these

How many arrangements of the letters of the word MATHEMATICS can be made

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Number of permutations of n distinct objects taken r(<n - 3) at a time which exclude 3(<n) particular objects is

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3! P(n, r - 3)

P(n, 3) P(n, r - 3)

P(r, r)P(n, r - 3)

P(n - 3, r)

Which one is not defined∀n∈Z+

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-n!

n!

(-n)!

n!+0!=n!+1

Arithmetic mean between 14 and 18 is

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16

17

15

32

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

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

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NAAGI

NAAIG

IAANG

INAGA

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

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90

45

55

50

A combination lock on a suitcase has 3 wheels each labeled with nine digits from 1 to 9. If an opening combination is a particular sequence of three digits with no repeats, the probability of a person guessing the right combination is

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1 / 500

1 / 504

1 / 252

1 / 250

The domain of an infinite sequence is a

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Set of natural numbers

R

Subset of N

None of the above

A bag contains 5 white, 7 red and 5 black balls. If four balls are drawn one by one with replacement, the probability that none is white is

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(11/16)²

(5/16)²

(11/16)⁴

(5/16)⁴

The sum of all even numbers less than 100 is

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2450

2352

2272

2468

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Given two independent event A and B such that P(A) = 0.30 and P(B) = 0.60. Probability of getting neither A nor B is

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0.28

0.13

0.12

0.42

8 . 7 . 6. 5 in factorial form is

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

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

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1 / 32

31 / 32

1 / 16

None of these

0! = ______

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0

1

2

Not defined

If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then the probability that the drawn balls are of different colours is

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1 / 66

3 / 66

19 / 66

47 / 66

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P(A) + P(B)

P(A) - P(B)

P(A) . P(B)

P(A) / P(B)

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

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