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

Probability of an impossible event is

• 0 A
• -1 B
• 1 C
• ∞ D

The sample space for tossing a coin once is

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

Fifteen girls compete in a race. The first three places can be taken by them in

• 3! ways A
• 12! ways B
• 15 x 14 x 13 ways C
• 42 ways D

An event having more than one sample point is called

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

There are n seats round a table numbered 1, 2, 3 .... n. The number of ways in which m person can take seats is

• ⁿP_m A
• ⁿC_mx (m - 1) ! B
• ^n-1P_m C
• None of these D

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

• nPn A
• nPr B
• nCr C
• 2n D

A card is drawn from a pack of cards numbered 1 to 52, the probability that the number on the card is a perfect square is

• 1/13 A
• 2/13 B
• 7/52 C
• None of these D

• 56 A
• 7 B
• 8 C
• 8/7 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

Which one is not defined∀n∈Z+

• -n! A
• n! B
• (-n)! C
• n!+0!=n!+1 D

8 . 7 . 6. 5 in factorial form is

• 
  A
• 
  B
• 
  C
• 
  D

Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

• 14 / 29 A
• 20 / 39 B
• 1 / 2 C
• n D

• 120 A
• 5 B
• 4 C
• 6 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

When a selection of object is made without paying regard to the order of selection, it is called

• Sequence A
• Series B
• Combination C
• Permutation D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  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

How many 6-Digit number can be formed without repairing any digit from the digits 0,1,2,3,4,5

• 720 A
• 600 B
• 120 C
• 6-5! D

• 5 A
• 10 B
• 20 C
• 30 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

The number of words that can be formed out of the letters of the word ASSASSINATION is

• 
  A
• 
  B
• 
  C
• 
  D

• 8 A
• 1/56 B
• 56 C
• None of these D

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

• 0 A
• -1 B
• 1 C
• 2 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

The number of the diagonals of a 6 sided figure is

• 15 A
• 21 B
• 9 C
• 6 D

If n is a negative integer n! is

• 1 A
• 0 B
• Unique C
• Not defined 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