Permutations and Combinations

Let P be the set of seven digit numbers with sum of their digits equal to 11. If the numbers in P are formed by using the digits 1, 2 and 3 only, then the number of elements in the set P is :

1. 164
2. 158
3. 161
4. 173

The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is .

If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440th position in this arrangement is :

1. PRNAKU
2. PRKAUN
3. PRKANU
4. PRNAUK

Let nCr-1 = 28, nCr = 56 and nCr+1 = 70. Let A(4 t, 4 t), B(2 t, -2 t) and C (3r - n, r2 - n - 1 ) be the vertices of a triangle ABC, where t is a parameter. If (3x - 1)2 + (3y)2 = , is the locus of the centroid of triangle ABC, then equals

1. 18
2. 8
3. 20
4. 6

The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is

1. 5720
2. 5719
3. 4608
4. 4607

The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is .

Let S=\p1,p2 ,p10\ be the set of first ten prime numbers. Let A=S P, where P is the set of all possible products of distinct elements of S. Then the number of all ordered pairs (x,y), x S, y A, such that x divides y, is .

The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is .

Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to :

1. 8925
2. 9100
3. 8575
4. 8750

The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is :

1. 34000
2. 37000
3. 35000
4. 36000

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is .

From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ' M ', is :

1. 6084
2. 5148
3. 14950
4. 4356

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

There are 5 points P1, P2, P3, P4, P5 on the side AB, excluding A and B, of a triangle ABC. Similarly there are 6 points P6, P7, , P11 on the side BC and 7 points P12, P13, , P18 on the side CA of the triangle. The number of triangles, that can be formed using the points P1, P2, , P18 as vertices, is:

1. 751
2. 776
3. 796
4. 771

There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is .

If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to :

1. 47
2. 53
3. 51
4. 43

The number of elements in the set S=\(x, y, z): x, y, z , x+2y+3z=42, x, y, z 0\ equals .

The lines L1, L2, ,L20 are distinct. For n=1,2,3, ,10 all the lines L2n-1 are parallel to each other and all the lines L2n pass through a given point P. The maximum number of points of intersection of pairs of lines from the set \L1, L2, ,L20\ is equal to .

The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to .

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

1. 130
2. 136
3. 142
4. 406

If for some m, n; 6Cm+2 (6Cm+1 )+6Cm+2>8C3 and n-1P3:nP4=1:8, then nPm+1+n+1Cm is equal to

1. 380
2. 376
3. 372
4. 384