ECAT Mathematics Chapter 9 Permutation, Combination and Probability Online Test

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

• 1/2 A
• 2/3 B
• 3/4 C
• None of these D

• 110 A
• 220 B
• 1320 C
• None of these D

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

• 1 / 729 A
• 1 / 24 B
• 1 / 21 C
• 2 / 7 D

An experiment yields 3 mutually exclusive and exhaustive events A, B, C, if P(A) =2 and P(B) = 3. then P(C) =

• 1 / 11 A
• 2 / 11 B
• 3 / 11 C
• 6 / 11 D

What is the probability of being born on Wednesday?

• 1/7 A
• 1/2 B
• 1/3 C
• 1/8 D

• 8 A
• 1/56 B
• 56 C
• None of these D

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.

• 40 A
• 30 B
• 50 C
• 60 D

An event having more than one sample point is called

• Certain event A
• Compound event B
• Simple event C
• None D

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

• 103 / 108 A
• 10 / 216 B
• 93 / 108 C
• None of these D

The sample space for tossing a coin once is

• {T, T} A
• {H, H} B
• {H, T} C
• None of these D

A class contains nine boys and three girls, in how many ways can the teacher choose a committee of four?

• 60 A
• 460 B
• 495 C
• 272 D

The number of permutation that can be formed from the letters of the word OBJECT is

• 700 A
• 600 B
• 720 C
• 620 D

• 
  A
• 
  B
• 
  C
• 
  D

Probability of an impossible event is

• 0 A
• -1 B
• 1 C
• ∞ D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 4 ways A
• 12 ways B
• 256 ways C
• 24 ways D

In a country 55% of the male population has houses in cities while 30% have houses both in cities and in villages find the percentage of the population that has houses only in villages

• 45 A
• 30 B
• 25 C
• 50 D

0! = ______

• 0 A
• 1 B
• 2 C
• Not defined D

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

• 1 / 32 A
• 31 / 32 B
• 1 / 16 C
• None of these D

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

• 73 / 120 A
• 83 / 120 B
• 67 / 120 C
• 43 / 120 D

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

• 260 A
• 356 B
• 410 C
• 96 D

• 120 A
• 5 B
• 4 C
• 6 D

A sequence is a function whose domain is

• N A
• Subset of N B
• R C
• None of these D

The value of n, when ⁿP₂= 20 is

• 3 A
• 4 B
• 6 C
• 5 D

Two coins are tossed twice each. The probability that the head appears on the first toss and the same forces appear in the two tosses is

• 1/4 A
• 1/2 B
• 1/3 C
• 1/7 D

There are 25 tickets bearing number 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

• 7 / 25 A
• 9 / 25 B
• 11 / 25 C
• None of these D

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

• >0 A
• 1 B
• <1 C
• 0 D

If for two events A and B , P(A∪B)=1,then events A and B are

• Certain events A
• Mutually exclusive B
• Complementary events C
• Independent D

Arithmetic mean between 14 and 18 is

• 16 A
• 17 B
• 15 C
• 32 D

A machine operates if all of its three components function. The probability that the first component fails during the year is 0.14, the second component fails is 0.10 and the third component fails is 0.05. the probability that the machine will fail during the year is

• 0.2647 A
• 0.2692 B
• 0.3647 C
• None of these D