Permutations and Combinations

The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:

1. 5040
2. 3050
3. 3410
4. 4320

Let A=\(a, b, c) : a, b, c are non-negative integers and a+b+2c=22\. Then n(A) is equal to :

1. 121
2. 124
3. 144
4. 169

The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is :

1. 15400
2. 17800
3. 16800
4. 29400

Let pn denote the total number of triangles formed by joining the vertices of an n-side regular polygon. If pn+1-pn=66, then the sum of all distinct prime divisors of n is :

1. 7
2. 8
3. 5
4. 6

Let S = \1, 2, 3, 4, 5, 6, 7, 8, 9\. Let x be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let y be the number of 9-digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,

1. 56x = 9y
2. 21x = 4y
3. 45x = 7y
4. 29x = 5y

Three persons enter in a lift at the ground floor. The lift will go up to 10th floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to .

The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0, 1, 2, 5, 9, if the repetition of the digits is allowed, is

The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is

1. 1579
2. 1578
3. 1580
4. 1581

The largest value of n, for which 40n divides 60!, is

1. 14
2. 13
3. 11
4. 12

The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is .