ECAT Pre Engineering MCQ Test With Answer for Chapter 9 Mathematics

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

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

• 
  A
• 
  B
• 
  C
• 
  D

Five engineering, four mathematics, two chemistry books are placed on a table at random.The probability that the books of each kind are all together is

• 
  A
• 
  B
• 
  C
• 
  D

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

• 6 A
• 1 B
• 1/6 C
• 1/2 D

• 5 A
• 10 B
• 20 C
• 30 D

How many comittees of 5 numbers can be chosen from a group of 8 players person when each committee must include 2 particular persons

• 8! A
• 5!3! B
• 5! C
• 20 D

An integer is chosen at random from the number ranging from 1 to 50. the probability that the integer chosen is a multiple of 2 or 3 or 10 is

• 3 / 10 A
• 5 / 10 B
• 7 / 10 C
• 9 / 10 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

A key ring is an example of

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

The value of n, when ⁿP₂= 20 is

• 3 A
• 4 B
• 6 C
• 5 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

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

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

• 24 A
• 4 B
• 12 C
• 6 D

• 
  A
• 
  B
• 
  C
• 
  D

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

• 72 A
• 48 B
• 144 C
• 20 D

How many terms of the A.P 3,6,9,12,15...........must be taken to make the sum 108

• 8 A
• 6 B
• 7 C
• 36 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

Two balanced dice are tossed once, the sample space when the integers on the faces of two dice are the same is

• {(1, 1), (2, 2), (3, 3)} A
• {(4, 4), (5, 5), (6, 6)} B
• {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)} C
• None of these D

9. 8. 7. 6= ______

• 
  A
• 
  B
• 
  C
• 
  D

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

• 1 / 500 A
• 1 / 504 B
• 1 / 252 C
• 1 / 250 D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

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

• 7 / 40 A
• 5 / 40 B
• 11 / 40 C
• None of these D

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

• 375 A
• 500 B
• 625 C
• 150 D

• 
  A
• 
  B
• 
  C
• 
  D

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

• 400 A
• 472 B
• 563 C
• 264 D

8 . 7 . 6. 5 in factorial form is

• 
  A
• 
  B
• 
  C
• 
  D

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

• 90 A
• 45 B
• 55 C
• 50 D

n different objects can be arranged taken all at a time in ______

• (n + 1)! ways A
• (n - 1)! ways B
• n! ways C
• n ways D

The sample space for tossing a coin twice is

• {H, T} A
• {HH, HT, TH, TT} B
• {H, T, HH} C
• {HH, HT, TT} D