#1. Ten identical particles are moving randomly inside a closed box. What is the probability that at any given point of time all the ten particles will be lying in the same half of the box? [2005]

#2. There are 10 identical coins and each one of them has ‘H’ engraved on its one face and ‘T’ engraved on its other face. These 10 coins are lying on a table and each one of them has ‘H’ face as the upper face. In one attempt, exactly four (neither more nor less) coins can be turned upside down. What is the minimum total number of attempts in which the ‘T’ faces of all the 10 coins can be brought to be the upper faces? [2005]

#3. A square is divided into 9 identical smaller squares. Six identical balls are to be placed in these smaller square such that each of the three rows gets at least one ball (one ball in one square only). In how many different ways can this be done? [2005]

#4. 2 men and 1 women board a bus in which 5 seats are vacant. One of these five seats is reserved for ladies. A women may or may not sit on the seat reserved for ladies but a man can not sit on the seat reserved for ladies. In how many different ways can the five seats occupied by these passengers? [2005]

#5. On a railway route between two places A and B, there are 20 stations on the way. If 4 new stations are to be added, how many types of new tickets will be required if each ticket is issued for a one way journey? [2005]

#6. Three students are picked at random from a school having a total of 1000 students. The probability that these three students will have identical date and month of their birth, is [2004]

#7. In how many different ways can six players be arranged in a line such that two of them, Ajit and Mukherjee, are never together? [2004]

#8. Nine different letters are to be dropped in three different letter boxes. In how many different ways can this be done? [2004]

#9. In a question of a test paper, there are five items each under List-A and List-B. The examinees are required to match each item under List-A with its corresponding correct item under List-B. Further, it is given that (i) no examinee has given the correct answer. (ii) answers of no two examinees are identical Which is the maximum number of examinees who took this test? [2004]

#10. A two member committee comprising of one male and one female member is to be constituted out of five males and three females. Amongst the females, Mrs. A refused to be a member of the committee in which Mr. B is taken as the member. In how many different ways can the committee be constituted? [2003]

#11. Three flags, each of different colour, are available for a military exercise. Using these flags, different codes can be generated by waving [2003] (i) single flag of different colours or (ii) any two flags in a different sequence of colour Or (iii) three flags in a different sequence of colours. The maximum number of codes that can be generated, is

#12. A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 seconds, yellow for 5 seconds and red for 30 seconds. At a randomly chosen time, the probability that the light will not be green, is [2002]