ECAT Pre Engineering MCQ Test With Answer for Chapter 9 Mathematics

An event having more than one sample point is called

• Certain event A
• Compound event B
• Simple event C
• None 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

Number of permutations of n distinct objects taken r(<n - 3) at a time which exclude 3(<n) particular objects is

• 3! P(n, r - 3) A
• P(n, 3) P(n, r - 3) B
• P(r, r)P(n, r - 3) C
• P(n - 3, r) 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

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

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

The probability that a person A will be alive 15 years hence is 5/7 and the probability that another person B will be alive 15 years hence is 7/9. Find the probability that both will be alive 15 years hence

• 4/63 A
• 5/9 B
• 45/49 C
• None of these D

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

n!/(n-1)!=

• n A
• n! B
• (n-1)! C
• 0! 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

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

• 950 A
• 760 B
• 1230 C
• 875 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

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

• 1/2 A
• 1/6 B
• 1/3 C
• 2 D

If n is a negative integer n! is

• 1 A
• 0 B
• Unique C
• Not defined D

If n is a positive integer then n! is

• (n - 1) (n - 2) .....3,.2.1 A
• n(n - 1) (n - 2) ...3.2.1 B
• n(n - 1 ) ( n -2) ... 3 C
• None of these D

For two events A and B if P(A) = P (A/B) = 1/4 and P(B/A) = 1/2, then

• A is sub-event of B A
• A and B are mutually exclusive B
• A and B are independent and P(A/B) = 3/4 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 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

• 6 A
• 360 B
• 120 C
• 24 D

• 5 / 12 A
• 3 / 8 B
• 5 / 8 C
• 7 / 4 D

The probability of getting a number between 1 and 100 which is divisible by 1 and itself if only is

• 1 / 4 A
• 1 / 2 B
• 3 / 4 C
• 25 / 98 D

Product of any n consecutive positive integers is divisible by

• n A
• √n B
• n! C
• None D

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

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

• 
  A
• 
  B
• 
  C
• 
  D

An unbiased die is thrown. Then the probability of getting a prime is

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

A card is drawn from a pack of cards numbered 2 to 53. the probability that the number on the card is prime number less than 20 is

• 2 / 13 A
• 4 / 13 B
• 5 / 13 C
• 8 / 13 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

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

A key ring is an example of

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