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

Two cards are drawn at random from a well shuffled pack of cards. The probability that at least one of them is a face card is

• 3 / 17 A
• 5 / 17 B
• 7 / 17 C
• 9 / 17 D

• 
  A
• 
  B
• 
  C
• 
  D

How many terms of the A.P 3,6,9,12,15...........must be taken to make the sum 108

• 8 A
• 6 B
• 7 C
• 36 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

probability of a certain event is

• 0 A
• -1 B
• 1 C
• ∞ D

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

A bag contains 7 whit, 5 black and 4 rd balls. If two balls are drawn at random from the bag, the probability that they are not of the same color is

• 73 / 120 A
• 83 / 120 B
• 67 / 120 C
• 43 / 120 D

A sequence is a function whose domain is

• N A
• Subset of N B
• R C
• None of these 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

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

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

The number of ways of arranging the letter AAAAA BBB CCC D EE F in a row when no two C's are together is

• 
  A
• 
  B
• 
  C
• 
  D

5 unbiased coins coins are tossed simultaneously. The probability of getting at least one head is

• 1 / 32 A
• 31 / 32 B
• 1 / 16 C
• None of these 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

The number of 5-digit number that can be formed from the digits 1,2,4,6,8, when 2 and 8 are never together is

• 72 A
• 48 B
• 144 C
• 20 D

20. 19. 18. 17= _______

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  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

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 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
• 
  B
• 
  C
• 
  D

n(n - 1) (n - 2) .... (n - r + 1) = ______

• 
  A
• 
  B
• 
  C
• 
  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 sample space for tossing a coin twice is

• {H, T} A
• {HH, HT, TH, TT} B
• {H, T, HH} C
• {HH, HT, TT} D

• P(A) + P(B) A
• P(A) - P(B) B
• P(A) . P(B) C
• P(A) / P(B) D

The number of combinations of 10 different objects taken 8 objects at a time is

• 90 A
• 45 B
• 55 C
• 50 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

The probability that a slip of numbers divisible by 4 is picked from the slips of number 1,2,3,4,......10 is

• 1/5 A
• 2/5 B
• 1/10 C
• 3/10 D

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

• 
  A
• 
  B
• 
  C
• 
  D

Cycle tyres are supplied in lots of 10 and there is a chance if 1 in 500 tyres to be defective. Using Poisson distribution, the approximate number of lots containing no defective tyre in a consignment of 10, 0000 lots is

• 9028 A
• 9208 B
• 9802 C
• 9820 D