ECAT Pre Engineering MCQ Test With Answer for Chapter 9 Mathematics

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

• nPn A
• nPr B
• nCr C
• 2n 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 combinations of 10 different objects taken 8 objects at a time is

• 90 A
• 45 B
• 55 C
• 50 D

• 6 A
• 360 B
• 120 C
• 24 D

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

• >0 A
• 1 B
• <1 C
• 0 D

• 0.9 A
• 0.74 B
• 0.2016 C
• None of these 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

A sequence is a function whose domain is

• N A
• Subset of N B
• R C
• None of these D

If n is a negative integer n! is

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

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

• 5! A
• 4! B
• 3! C
• 120 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

Cycle tyres are supplied in lots of 10 and there is a chance if 1 in 500 tyres to be defective. Using Poisson distribution, the approximate number of lots containing no defective tyre in a consignment of 10, 0000 lots is

• 9028 A
• 9208 B
• 9802 C
• 9820 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

• 
  A
• 
  B
• 
  C
• 
  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

• 8 A
• 1/56 B
• 56 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

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 card is drawn from a pack of cards numbered 1 to 52, the probability that the number on the card is a perfect square is

• 1/13 A
• 2/13 B
• 7/52 C
• None of these 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

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

A and B throw a dice. The probability that A's throw is not greater then B's is

• 5 / 12 A
• 7 / 12 B
• 1 / 6 C
• 1 / 2 D

A dice is rolled. The probability that the dots on the top are greater than 4 is

• 1/6 A
• 1/3 B
• 1/2 C
• 1 D

If 4 ⁶P_r= ⁶P_r+1, then r is equal to

• 4 A
• 3 B
• 2 C
• 1 D

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

• >0 A
• 1 B
• <1 C
• 0 D

n!/(n-1)!=

• n A
• n! B
• (n-1)! C
• 0! D

n different objects can be arranged taken all at a time in ______

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

Two cards are drawn at random without replacement. the probability that the first is a king and second is not a king is

• 48 / 663 A
• 24 / 663 B
• 12 / 663 C
• None of these D

The factorial of a positive integers is a (an)

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

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