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

• 1.5 A
• 1.2 B
• 8 C
• None of these D

If A is an event then which of the following is true

• P(A)<0 A
• 0≥P(A)≤1 B
• P(A)>0 C
• None D

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

• 
  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

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

The sample space for tossing a coin once is

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

How many arrangements of the letter of the word PAKPATTAN can be made

• 
  A
• 
  B
• 
  C
• 
  D

nCn-r is equal to

• n! A
• n-1Cr B
• nCr C
• None of these 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

If n is a negative integer n! is

• 1 A
• 0 B
• Unique C
• Not defined 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

All letters of the word "AGAIN" are permuted in all possible ways and the words so formed (with or without meaning) are written as in dictionary, then the 50th word is

• NAAGI A
• NAAIG B
• IAANG C
• INAGA 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

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 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

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

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

• 5! A
• 4! B
• 3! C
• 120 D

A box containing 10 mangoes out of which 4 are rotter. Two mangoes are taken together from the box. If one of them is found to be good, the probability that the other is also good is

• 1 / 3 A
• 8 / 15 B
• 5 / 13 C
• 5 / 9 D

• 56 A
• 7 B
• 8 C
• 8/7 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

• 5 A
• 10 B
• 20 C
• 30 D

• 
  A
• 
  B
• 
  C
• 
  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

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

• 
  A
• 
  B
• 
  C
• 
  D

Arithmetic mean between 14 and 18 is

• 16 A
• 17 B
• 15 C
• 32 D

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

• nPn A
• nPr B
• nCr C
• 2n D

• 
  A
• 
  B
• 
  C
• 
  D

The sum of all even numbers less than 100 is

• 2450 A
• 2352 B
• 2272 C
• 2468 D

The probability that the sum of dots appearing in two successive thrown of two dice, in every time 7 is

• 1/5 A
• 1/36 B
• 1/7 C
• 1/63 D

The domain of a finite sequence is a

• Set of natural numbers A
• R B
• Subset of N C
• Proper subset of N D