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

Product of any n consecutive positive integers is divisible by

• n A
• √n B
• n! C
• None 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

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 factorial of a positive integers is a (an)

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

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

• 950 A
• 760 B
• 1230 C
• 875 D

Three numbers are chosen random without replacement from {1, 2, 3, ...., 10}. the probability that minimum of the chosen numbering is 3 or their maximum is 7

• 7 / 40 A
• 5 / 40 B
• 11 / 40 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

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

• >0 A
• 1 B
• <1 C
• 0 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

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

An integer is chosen at random from the number ranging from 1 to 50. the probability that the integer chosen is a multiple of 2 or 3 or 10 is

• 3 / 10 A
• 5 / 10 B
• 7 / 10 C
• 9 / 10 D

• 0 A
• 20 B
• 90 C
• 80 D

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

The domain of a finite sequence is a

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

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

• nPn A
• nPr B
• nCr C
• 2n D

20. 19. 18. 17= _______

• 
  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

Which one is not defined∀n∈Z+

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

Six boys and 3 girls are to be seated at random, in a row, for a photograph. The probability that no two girls will sit together is

• 1/12 A
• 1/6 B
• 5/12 C
• 7/12 D

The number of the diagonals of a 6 sided figure is

• 15 A
• 21 B
• 9 C
• 6 D

The sample space for tossing a coin once is

• {T, T} A
• {H, H} B
• {H, T} 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

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

The number of permutation that can be formed from the letters of the word OBJECT is

• 700 A
• 600 B
• 720 C
• 620 D

Three unbiased coins are tossed. Then the probabilities of getting two heads is

• 3/8 A
• 1/8 B
• 1/4 C
• None of these D