ECAT Pre Engineering MCQ Test With Answer for Chapter 9 Mathematics

How many arrangements of the letter of the word PAKPATTAN can be made

• 
  A
• 
  B
• 
  C
• 
  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

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

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

Form a group of 5 men and 3 women, a committee of 4 persons is to be selected randomly. The probability that there is a majority of men is

• 1/4 A
• 1/3 B
• 1/2 C
• 1/6 D

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

• 6 A
• 1 B
• 1/6 C
• 1/2 D

In school there are 150 students Out of these 80 students enrolled for mathematics class 50 enrolled for English class and 60 enrolled for Physics class The student enrolled for English cannot attend any other class but the students of mathematics and Physics can take two courses at a time Find the number of students who have taken both physics and mathematics.

• 40 A
• 30 B
• 50 C
• 20 D

• 0 A
• 20 B
• 90 C
• 80 D

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

• >0 A
• 1 B
• <1 C
• 0 D

• 56 A
• 7 B
• 8 C
• 8/7 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

n!/(n-1)!=

• n A
• n! B
• (n-1)! C
• 0! 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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D

All letters of the word "AGAIN" are permuted in all possible ways and the words so formed (with or without meaning) are written as in dictionary, then the 50th word is

• NAAGI A
• NAAIG B
• IAANG C
• INAGA D

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

• 120 A
• 60 B
• 24 C
• 15 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

• 120 A
• 5 B
• 4 C
• 6 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
• 
  B
• 
  C
• 
  D

5 unbiased coins coins are tossed simultaneously. The probability of getting at least one head is

• 1 / 32 A
• 31 / 32 B
• 1 / 16 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

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

• 36 A
• 360 B
• 24 C
• 6 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

probability of a certain event is

• 0 A
• -1 B
• 1 C
• ∞ 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

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

• 
  A
• 
  B
• 
  C
• 
  D

• P(A) + P(B) A
• P(A) - P(B) B
• P(A) . P(B) C
• P(A) / P(B) D