Permutations and Combinations

In a group of 3 girls and 4 boys, there are two boys B1 and B2. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but B1 and B2 are not adjacent to each other, is :

1. 120
2. 96
3. 72
4. 144

The number of integers, between 100 and 1000 having the sum of their digits equal to 14, is .

The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3 , is equal to .

The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to:

1. 179
2. 177
3. 175
4. 181

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

1. 56
2. 16
3. 24
4. 48

If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at 315th position in this arrangement is :

1. NRAPUG
2. NRAGUP
3. NRAPGU
4. NRAGPU

Let 0 r n. If n+1Cr+1 : nCr : n-1Cr-1 = 55 : 35 : 21, then 2n + 5r is equal to :

1. 62
2. 60
3. 55
4. 50

The number of ways of getting a sum 16 on throwing a dice four times is .

Let the set S = \2, 4, 8, 16, , 512\ be partitioned into 3 sets A, B, C with equal number of elements such that A B C = S and A B = B C = A C = . The maximum number of such possible partitions of S is equal to:

1. 1640
2. 1520
3. 1710
4. 1680

60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the 50th word is:

1. OBBJH
2. HBBJO
3. OBBHJ
4. JBBOH