Mathematics - Permutations and Combinations

Question - 1

The number if divisors of 9600 including 1 and 9600 are

  • A 60
  • B 58
  • C 48
  • D 46

Question - 2

Number of divisors of the form \(4n+2(n\ge 0)\) of the integer 240, is

  • A 4
  • B 8
  • C 10
  • D 3

Question - 3

The number of diffrent nine-digit numbers that can be formed from the number 223355888 by re-arranging the digits so that odd digits occupy even positions, is

  • A 16
  • B 36
  • C 60
  • D 180

Question - 4

The total number of ways in which six '+' and four '-' signs can be arranged in a line such that no two '-' signs are together, is

  • A 35
  • B 15
  • C 30
  • D NONE OF THESE

Question - 5

There are five letters and five addressed envelopes, then the number of ways in which no letter is placed in correct envelop, is

  • A 9
  • B 33
  • C 44
  • D 119

Question - 6

Out of n objects p are alike of one kind, q are alike of another kind and r are alike of a third kind and the rest all are different; then number of permutations when all the n objects are taken at a time is

  • A n! p! q! r!
  • B \(n!\over p! q! r!\)
  • C \(p! q! r!\over n!\)
  • D NONE OF THESE

Question - 7

The number numbers greater than 1000 but not greater than 4000 that can be formed with the digits 0, 1, 2, 3, 4, when repetition of digits is allowed is

  • A 375
  • B 625
  • C 125
  • D NONE OF THESE

Question - 8

The sum of all the five-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 (repetition of digits not allowed) is

  • A 3,999,600
  • B 666,000
  • C 366,600
  • D 3,999,960

Question - 9

The number of numbers greater than million that can be formed with the digits 2, 3, 0, 3, 4, 2, 3 is

  • A 380
  • B 420
  • C 360
  • D 960

Question - 10

In a class p girls and q boys (p>q) are to be seated in a row so that no two boys are together. The number of ways in which they can be seated is

  • A \(p!(q+1)!\over (p-q+1)!\)
  • B \((p+1)!\ q!\over (p-q+1)!\)
  • C \((p!)^2\over (p-q+1)!\)
  • D \(p!(p+1)!\over (p-q+1)!\)
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