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

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

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

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

• 3 A
• 6 B
• 0 C
• None of these D

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

• 950 A
• 760 B
• 1230 C
• 875 D

Probability of an impossible event is

• 0 A
• -1 B
• 1 C
• ∞ D

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

• 
  A
• 
  B
• 
  C
• 
  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

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

• 0 A
• -1 B
• 1 C
• 2 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

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

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

• 36 A
• 360 B
• 24 C
• 6 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

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

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 sum of all even numbers less than 100 is

• 2450 A
• 2352 B
• 2272 C
• 2468 D

• 
  A
• 
  B
• 
  C
• 
  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

For a positive integer n

• n! = n(n + 1) A
• n! = n(n+1)! B
• n! = n(n - 1 ) C
• n! = n(n - 1)! 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

• 
  A
• 
  B
• 
  C
• 
  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

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

• 
  A
• 
  B
• 
  C
• 
  D

Product of any n consecutive positive integers is divisible by

• n A
• √n B
• n! C
• None D

In a school there are 150 students Out of these 80 students enrolled for mathematics class.50 enrolled for English class and 60 enrolled for Physics class The student enrolled for English cannot attend any other class but the students of mathematics and Physics can take two courses at a time find the number of students who have taken both physics and mathematics.

• 40 A
• 30 B
• 50 C
• 60 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

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

An event having more than one sample point is called

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