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

Two balanced dice are tossed once, the sample space when the integers on the faces of two dice are the same is

• {(1, 1), (2, 2), (3, 3)} A
• {(4, 4), (5, 5), (6, 6)} B
• {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)} C
• None of these 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

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

• 
  A
• 
  B
• 
  C
• 
  D

A dice is rolled. The probability that the dots on the top are greater than 4 is

• 1/6 A
• 1/3 B
• 1/2 C
• 1 D

Form a group of 5 men and 3 women, a committee of 4 persons is to be selected randomly. The probability that there is a majority of men is

• 1/4 A
• 1/3 B
• 1/2 C
• 1/6 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

• 
  A
• 
  B
• 
  C
• 
  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

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

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

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

• 1/2 A
• 1/6 B
• 1/3 C
• 2 D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D

Riaz, Saba. Maria, Shehzad are to give speeches in a class. The teacher can arrange the order of their presentation in

• 4 ways A
• 12 ways B
• 256 ways C
• 24 ways D

A sequence is a function whose domain is

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

A die is thrown, the probability that the dots on the top are prime numbers or odd numbers is

• 1/2 A
• 2/3 B
• 1/3 C
• 2/5 D

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  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

If 4 ⁶P_r= ⁶P_r+1, then r is equal to

• 4 A
• 3 B
• 2 C
• 1 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

Three integers are chosen at random from the first 20 integers. Then probability that their product is even, is

• 2 / 19 A
• 3 / 29 B
• 17 / 19 C
• 4 / 19 D

• 3 A
• 6 B
• 0 C
• None of these D

How many arrangements of the letters of the word MI SSI PPI, taken all together can be made?

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D

If n is a negative integer n! is

• 1 A
• 0 B
• Unique C
• Not defined 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