ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 9 (Permutation, Combination and Probability)

20. 19. 18. 17= _______

• 
  A
• 
  B
• 
  C
• 
  D

In how many ways can 5 persons be seated at a round table

• 5! A
• 4! B
• 3! C
• 120 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

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

• 44/4165 A
• 22/4165 B
• 11/4165 C
• None of these D

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

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

• 
  A
• 
  B
• 
  C
• 
  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

probability of a certain event is

• 0 A
• -1 B
• 1 C
• ∞ D

A dice is rolled. The probability that the dots on the top are greater than 4 is

• 1/6 A
• 1/3 B
• 1/2 C
• 1 D

Form 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

• 1/4 A
• 1/3 B
• 1/2 C
• 1/6 D

How many different 5-digit even numbers are possible form digit 1,2,4,6,8

• 4 : 4! A
• 4! B
• 5! C
• 4!+4! D

(n + 2) (n + 1) n= ______

• 
  A
• 
  B
• 
  C
• 
  D

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

Number of combination of zero or more things out of n different things

• nPn A
• nPr B
• nCr C
• 2n D

• 56 A
• 7 B
• 8 C
• 8/7 D

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

• 1 / 66 A
• 3 / 66 B
• 19 / 66 C
• 47 / 66 D

Probability of an impossible event is

• 0 A
• -1 B
• 1 C
• ∞ D

The sample space for tossing a coin once is

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

• 36 A
• 360 B
• 24 C
• 6 D

The probability to get an odd number in a dice thrown once is

• 6 A
• 1 B
• 1/6 C
• 1/2 D

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

• 120 A
• 60 B
• 24 C
• 15 D

0! = ______

• 0 A
• 1 B
• 2 C
• Not defined 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

Which one is not defined∀n∈Z+

• -n! A
• n! B
• (-n)! C
• n!+0!=n!+1 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

A sequence is a function whose domain is

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

A box contains 10 red 30 white and 20 black marbles When a marble is drawn at random the probability that it is either red or white is

• 1/6 A
• 1/3 B
• 1/2 C
• 2/3 D

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

• 
  A
• 
  B
• 
  C
• 
  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

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

• 950 A
• 760 B
• 1230 C
• 875 D