### 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 $p!(p+1)!\over (p-q+1)!$