#1. In how many ways can four children be made to stand in a line such that two of them, A and B are always together? [2010]

#2. When ten persons shake hands with one another, in how many ways is it possible? [2010]

#3. A person X has four notes of Rupee 1, 2, 5 and 10 denomination. The number of different sums of money she can form from them is [2010]

#4. A question paper had ten questions. Each question could only be answered as True (T) or False (F). Each candidate answered all the questions. Yet, no two candidates wrote the answers in an identical sequence. How many different sequences of answers are possible? [2010]

#5. In a carrom board game competition, m boys and n girls (m > n > 1) of a school participate in which every student has to play exactly one game with every other student. Out of the total games played, it was found that in 221 games one player was a boy and the other player was a girl. [2009] Consider the following statements: 1. The total number of students that participated in the competition is 30. 2. The number of games in which both players were girls is 78. Which of the statements given above is/are correct?

#6. How many three-digit numbers can be generated from 1, 2, 3, 4, 5, 6, 7, 8, 9 such that the digits are in ascending order? [2009]

#7. How many numbers lie between 300 and 500 in which 4 comes only one time? [2009]

#8. A person has 4 coins each of different denomination. What is the number of different sums of money the person can form (using one or more coins at a time)? [2009]

#9. There are two identical red, two identical black and two identical white balls. In how many different ways can the balls be placed in the cells (each cell to contain one ball) shown below such that balls of the same colour do not occupy any two consecutive cells? [2008]

#10. There are 6 different letters and 6 correspondingly addressed envelopes. If the letters are randomly put in the envelopes, what is the probability that exactly 5 letters go into the correctly addressed envelopes? [2008]

#11. In how many different ways can all of 5 identical balls be placed in the cells shown below such that each row contains at least 1 ball? [2008]

#12. A schoolteacher has to select the maximum possible number of different groups of 3 students out of a total of 6 students. In how many groups any particular student will be included? [2008]

#13. In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position? [2008]

#14. Groups each containing 3 boys are to be formed out of 5 boys - A, B,C, D and E such that no one group contains both C and D together. What is the maximum number of such different groups? [2007]

#15. In how many maximum different ways can 3 identical balls be placed in the 12 squares (each ball to be placed in the exact centre of the squares and only one ball is to be placed in one square) shown in the figure given below such that they do not lie along the same straight line? [2007]

#16. Three dice (each having six faces with each face having one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one dice shows the number 2? [2007]

#17. All the six letters of the name SACHIN are arranged to form different words without repeating any letter in any one word. The words so formed are then arranged as in a dictionary. What will be the position of the word SACHIN in that sequence? [2007]

#18. Five balls of different colours are to be placed in three different boxes such that any box contains at least one ball. What is the maximum number of different ways in which this can be done? [2007]

#19. Amit has five friends: 3 girls and 2 boys. Amit’s wife also has 5 friends: 3 boys and 2 girls. In how many maximum number of different ways can they invite 2 boys and 2 girls such that two of them are Amit’s friends and two are his wife’s? [2007]

#20. In the figure shown below, what is the maximum number of different ways in which 8 identical balls can be placed in the small triangles 1, 2, 3 and 4 such that each triangle contains at least one ball? [2007]

#21. Each of the 3 persons is to be given some identical items such that product of the numbers of items received by each of the three persons is equal to 30. In how many maximum different ways can this distribution be done? [2007]

#22. Each of eight identical balls is to be placed in the squares shown in the figures given below in a horizontal direction such that one horizontal row contains six balls and the other horizontal row contains two balls. In how many maximum different ways can this be done? [2006]

#23. In a question paper, there are four multiple choice type questions. Each question has five choices with only one choice for its correct answer. What is the total number of ways in which a candidate will not get all the four answers correct? [2006]

#24. 3 digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without repeating any digit. What is the probability that their product is odd? [2006]

#25. A mixed doubles tennis game is to be played between two teams (each team consists of one male and one female.) There are four married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played? [2006]

#26. There are three parallel straight lines. Two points, 'A' and 'B', are marked on the first line, points, 'C' and 'D' are marked on the second line; and points, 'E' and 'F', are marked on the third line. Each of these 6 points can move to any position on its respective straight line. [2006] Consider the following statements: 1. The maximum number of triangles that can be drawn by joining these points is 18. 2. The minimum number of triangles that can be drawn by joining these points is zero. Which of the statement(s) given above is/are correct?

#27. In a tournament, each of the participants was to play one match against each of the other participants. Three players fell ill after each of them had played three matches and had to leave the tournament. What was the total number of participants at the beginning, if the total number of matches played was 75? [2006]

#28. Each of two women and three men is to occupy one chair out of eight chairs, each of which numbered from 1 to 8. First, women are to occupy any two chairs from those numbered 1 to 4; and then the three men would occupy any, three chairs out of the remaining six chairs. What is the maximum number of different ways in which this can be done? [2006]