ECAT Pre Engineering MCQ Test With Answer for Chapter 9 Mathematics

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

• 
  A
• 
  B
• 
  C
• 
  D

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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  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

A key ring is an example of

• Permutation A
• Circular permutation B
• Combination C
• None D

• 0 A
• -1 B
• 1 C
• 2 D

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• 20 B
• 90 C
• 80 D

In how many ways can 5 persons be seated at a round table

• 5! A
• 4! B
• 3! C
• 120 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

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

How many signals can be given by 5 flags of different colours, using 3 flags at a time

• 120 A
• 60 B
• 24 C
• 15 D

How many necklaces can be made from 6 beads of different colours?

• 120 A
• 60 B
• 24 C
• 15 D

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

• 
  A
• 
  B
• 
  C
• 
  D

If S is a sample space and event set E =Φ then P(E) is

• >0 A
• 1 B
• <1 C
• 0 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

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

• 1/5 A
• 1/4 B
• 1/3 C
• 1/2 D

• 3 A
• 6 B
• 0 C
• None of these D

A class contains nine boys and three girls, in how many ways can the teacher choose a committee of four?

• 60 A
• 460 B
• 495 C
• 272 D

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

• nPn A
• nPr B
• nCr C
• 2n D

• 
  A
• 
  B
• 
  C
• 
  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

A sequence is a function whose domain is

• N A
• Subset of N B
• R 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

A card is drawn from a pack of cards numbered 2 to 53. the probability that the number on the card is prime number less than 20 is

• 2 / 13 A
• 4 / 13 B
• 5 / 13 C
• 8 / 13 D

Which one is not defined∀n∈Z+

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

The value of n, when ⁿP₂= 20 is

• 3 A
• 4 B
• 6 C
• 5 D