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

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

• 0 A
• -1 B
• 1 C
• 2 D

• 
  A
• 
  B
• 
  C
• 
  D

• 120 A
• 5 B
• 4 C
• 6 D

Probability of an impossible event is

• 0 A
• -1 B
• 1 C
• ∞ 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

The number of words that can be formed out of the letters of the word ASSASSINATION is

• 
  A
• 
  B
• 
  C
• 
  D

Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

• 14 / 29 A
• 20 / 39 B
• 1 / 2 C
• n D

How many arrangements of the letters of the word PAKISTAN cab be made

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

How many 3 digit numbers can be formed by using each one of the digit 2, 3, 5, 7, 9 only once?

• 15 A
• 24 B
• 60 C
• 120 D

20. 19. 18. 17= _______

• 
  A
• 
  B
• 
  C
• 
  D

There are 16 point in a plane, in which 6 are collinear. how many lines can be drawn by joining these points?

• 10 A
• 66 B
• 71 C
• 106 D

A and B throw a dice. The probability that A's throw is not greater then B's is

• 5 / 12 A
• 7 / 12 B
• 1 / 6 C
• 1 / 2 D

9. 8. 7. 6= ______

• 
  A
• 
  B
• 
  C
• 
  D

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

• 1 / 18 A
• 7 / 18 B
• 13 / 18 C
• 11 / 18 D

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

• 1/8 A
• 2/8 B
• 3/8 C
• None of these D

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

• (11/16)² A
• (5/16)² B
• (11/16)⁴ C
• (5/16)⁴ D

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

• 1/13 A
• 2/13 B
• 7/52 C
• None of these D

A key ring is an example of

• Permutation A
• Circular permutation B
• Combination C
• None D

The key for opening a door is in a bunch of 10 keys. A man attempts to open the door by trying the keys at random discarding the wrong key. The probability that the door is opened in the 5th trial is

• 1 / 10 A
• 2 / 10 B
• 3 / 10 C
• 4 / 10 D

8 . 7 . 6. 5 in factorial form is

• 
  A
• 
  B
• 
  C
• 
  D

Number of selections of n different things out of n

• 1 A
• nPr B
• n! C
• nPr 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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  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

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