Question # 1

How many arrangements of the letters of the word MI SSI PPI, taken all together can be made?

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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 domain of a finite sequence is a

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Set of natural numbers

R

Subset of N

Proper subset of N

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

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

The probability that a slip of numbers divisible by 4 is picked from the slips of number 1,2,3,4,......10 is

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1/5

2/5

1/10

3/10

Which one is not defined∀n∈Z+

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-n!

n!

(-n)!

n!+0!=n!+1

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8

1/56

56

None of these

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1 / 2

1 / 3

1 / 4

None of these

Arithmetic mean between 14 and 18 is

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16

17

15

32

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5

10

20

30

There are n seats round a table numbered 1, 2, 3 .... n. The number of ways in which m person can take seats is

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ⁿP_m

ⁿC_mx (m - 1) !

^n-1P_m

None of these

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5 / 12

3 / 8

5 / 8

7 / 4

Number of ways of writing the letters of WORD taken all at a time is

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24

4

12

6

probability of a certain event is

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0

-1

1

∞

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110

220

1320

None of these

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n!

0!

1

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

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

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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

The number of 5-digit number that can be formed from the digits 1,2,4,6,8, when 2 and 8 are never together is

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72

48

144

20

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

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3/8

1/8

1/4

None of these

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Three numbers are chosen random without replacement from {1, 2, 3, ...., 10}. the probability that minimum of the chosen numbering is 3 or their maximum is 7

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7 / 40

5 / 40

11 / 40

None of these

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

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950

760

1230

875

A die is rolled. What is the probability that the dots on the top are greater than 4?

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1/4

1/2

1/3

1/33

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

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1/13

2/13

7/52

None of these

Fifteen girls compete in a race. The first three places can be taken by them in

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3! ways

12! ways

15 x 14 x 13 ways

42 ways

Out of 10, 000 families with 4 children each, the number of families all of whose children are daughters is

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375

500

625

150

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ECAT Pre General Science Mathematics Chapter 9 Permutation, Combination & Probability Online Test MCQs With Answers

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