ECAT Pre Engineering MCQ Test With Answer for Chapter 9 Mathematics

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

• 90 A
• 45 B
• 55 C
• 50 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

The sample space for tossing a coin once is

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

A box contains 10 red 30 white and 20 black marbles When a marble is drawn at random the probability that it is either red or white is

• 1/6 A
• 1/3 B
• 1/2 C
• 2/3 D

A key ring is an example of

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

For a positive integer n

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

If n is a negative integer n! is

• 1 A
• 0 B
• Unique C
• Not defined D

The number of permutations of n objects of which there are n₁like of one kind, n₂like of the second kind and n₃like objects of third kind are

• 
  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

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 sum of all positive integral multiple of 5 less than 100 is

• 950 A
• 760 B
• 1230 C
• 875 D

The key for opening a door is in a bunch of 10 keys. A man attempts to open the door by trying the keys at random discarding the wrong key. The probability that the door is opened in the 5th trial is

• 1 / 10 A
• 2 / 10 B
• 3 / 10 C
• 4 / 10 D

8 . 7 . 6. 5 in factorial form is

• 
  A
• 
  B
• 
  C
• 
  D

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangement is

• ⁶C₃x ⁴C₂ A
• ⁴C₂x ⁴P₃ B
• ⁴P₂x ⁶P₃ 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

What is the probability of being born on Wednesday?

• 1/7 A
• 1/2 B
• 1/3 C
• 1/8 D

Product of any n consecutive positive integers is divisible by

• n A
• √n B
• n! C
• None D

Out of 10, 000 families with 4 children each, the number of families all of whose children are daughters is

• 375 A
• 500 B
• 625 C
• 150 D

• 1 / 2 A
• 1 / 3 B
• 1 / 4 C
• None of these D

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

• >0 A
• 1 B
• <1 C
• 0 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

There are 16 point in a plane, in which 6 are collinear. how many lines can be drawn by joining these points?

• 10 A
• 66 B
• 71 C
• 106 D

• 3 A
• 6 B
• 0 C
• None of these D

The domain of a finite sequence is a

• Set of natural numbers A
• R B
• Subset of N C
• Proper subset of N 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

The probability that a person A will be alive 15 years hence is 5/7 and the probability that another person B will be alive 15 years hence is 7/9. Find the probability that both will be alive 15 years hence

• 4/63 A
• 5/9 B
• 45/49 C
• None of these 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

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

• n! A
• 0! B
• 1 C
• None of these D