ECAT Pre Engineering MCQ Test With Answer for Chapter 9 Mathematics

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• ⁶C₃x ⁴C₂ A
• ⁴C₂x ⁴P₃ B
• ⁴P₂x ⁶P₃ C
• None of these D

How many signals can be given by 5 flags of different colours, using 3 flags at a time

• 120 A
• 60 B
• 24 C
• 15 D

The sum of all odd numbers between 100 and 200 is

• 6200 A
• 7500 B
• 6500 C
• 3750 D

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

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

• 
  A
• 
  B
• 
  C
• 
  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

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

• 6 A
• 1 B
• 1/6 C
• 1/2 D

The sum of all even numbers less than 100 is

• 2450 A
• 2352 B
• 2272 C
• 2468 D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 1/18 A
• 1/12 B
• 1/36 C
• None of these 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

The domain of an infinite sequence is a

• Set of natural numbers A
• R B
• Subset of N C
• None of the above D

A die is thrown 100 times. If getting an odd number is considered a success, the variance of the number of successes is

• 50 A
• 25 B
• 10 C
• 100 D

• n! A
• 0! B
• 1 C
• None of these D

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

• 3/8 A
• 1/8 B
• 1/4 C
• None of these D

Product of any n consecutive positive integers is divisible by

• n A
• √n B
• n! C
• None D

Probability of an impossible event is

• 0 A
• -1 B
• 1 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

Three integers are chosen at random from the first 20 integers. Then probability that their product is even, is

• 2 / 19 A
• 3 / 29 B
• 17 / 19 C
• 4 / 19 D

The number of the diagonals of a 6 sided figure is

• 15 A
• 21 B
• 9 C
• 6 D

In a class of 100 students, 60 drink tea, 50 drink coffee and 30 drink both. A student from his class is selected at takes at last one of 2 drinks is

• 2 / 5 A
• 3 / 5 B
• 4 / 5 C
• None of these 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

Given two independent event A and B such that P(A) = 0.30 and P(B) = 0.60. Probability of getting neither A nor B is

• 0.28 A
• 0.13 B
• 0.12 C
• 0.42 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 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

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

• 400 A
• 472 B
• 563 C
• 264 D