ECAT Pre Engineering MCQ Test With Answer for Chapter 9 Mathematics

Product of any n consecutive positive integers is divisible by

• n A
• √n B
• n! C
• None D

• 
  A
• 
  B
• 
  C
• 
  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

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

probability of a certain event is

• 0 A
• -1 B
• 1 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

n!/(n-1)!=

• n A
• n! B
• (n-1)! C
• 0! 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

• 0 A
• -1 B
• 1 C
• 2 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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

Which one is not defined∀n∈Z+

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

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

9. 8. 7. 6= ______

• 
  A
• 
  B
• 
  C
• 
  D

A box containing 10 mangoes out of which 4 are rotter. Two mangoes are taken together from the box. If one of them is found to be good, the probability that the other is also good is

• 1 / 3 A
• 8 / 15 B
• 5 / 13 C
• 5 / 9 D

• 6 A
• 360 B
• 120 C
• 24 D

nCn-r is equal to

• n! A
• n-1Cr B
• nCr C
• None of these D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 5 / 12 A
• 3 / 8 B
• 5 / 8 C
• 7 / 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 machine operates if all of its three components function. The probability that the first component fails during the year is 0.14, the second component fails is 0.10 and the third component fails is 0.05. the probability that the machine will fail during the year is

• 0.2647 A
• 0.2692 B
• 0.3647 C
• None of these D

• 110 A
• 220 B
• 1320 C
• None of these D

If for two events A and B , P(A∪B)=1,then events A and B are

• Certain events A
• Mutually exclusive B
• Complementary events C
• Independent 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 factorial of a positive integers is a (an)

• Rational number A
• Positive integer B
• Real number C
• None D

An experiment yields 3 mutually exclusive and exhaustive events A, B, C, if P(A) =2 and P(B) = 3. then P(C) =

• 1 / 11 A
• 2 / 11 B
• 3 / 11 C
• 6 / 11 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

Four cards are drawn at random from a pack of 52 playing cards. The probability of getting all the four cars of the same suit is

• 44/4165 A
• 22/4165 B
• 11/4165 C
• None of these D