ECAT Pre Engineering MCQ Test With Answer for Chapter 9 Mathematics

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 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

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

How many 6-Digit number can be formed without repairing any digit from the digits 0,1,2,3,4,5

• 720 A
• 600 B
• 120 C
• 6-5! D

The sample space for tossing a coin once is

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

How many arrangements of the letters of the word PAKISTAN cab be made

• 
  A
• 
  B
• 
  C
• 
  D

Probability of an impossible event is

• 0 A
• -1 B
• 1 C
• ∞ D

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

• 5! A
• 4! B
• 3! C
• 120 D

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

• 
  A
• 
  B
• 
  C
• 
  D

n!/(n-1)!=

• n A
• n! B
• (n-1)! C
• 0! D

• 3 A
• 6 B
• 0 C
• None of these D

The value of n, when ⁿP₂= 20 is

• 3 A
• 4 B
• 6 C
• 5 D

The probability of getting a number between 1 and 100 which is divisible by 1 and itself if only is

• 1 / 4 A
• 1 / 2 B
• 3 / 4 C
• 25 / 98 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

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

In a class of 100 students, 60 drink tea, 50 drink coffee and 30 drink both. A student from his class is selected at takes at last one of 2 drinks is

• 2 / 5 A
• 3 / 5 B
• 4 / 5 C
• None of these D

• 0 A
• 20 B
• 90 C
• 80 D

Which one is not defined∀n∈Z+

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

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

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

• 700 A
• 600 B
• 720 C
• 620 D

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

• 90 A
• 45 B
• 55 C
• 50 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

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

• 6 A
• 1 B
• 1/6 C
• 1/2 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

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 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

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

• 
  A
• 
  B
• 
  C
• 
  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

If n is a negative integer n! is

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