1. A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?
Answer
Correct Answer:
168
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2. From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to include at least one lady?
Answer
Correct Answer:
246
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3. In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?
Answer
Correct Answer:
8*9!
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4. A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?
Answer
Correct Answer:
15
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5. In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?
Answer
Correct Answer:
43200
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6. How many diagonals can be drawn in a pentagon?
Answer
Correct Answer:
5
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7. After every get-together every person present shakes the hand of every other person. If there were 105 handshakes in all, how many persons were present in the party?
Answer
Correct Answer:
15
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8. The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?
Answer
Correct Answer:
242
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9. The number of positive integers which can be formed by using any number of digits from 0,1,2,3,4,5 without repetition.
Answer
Correct Answer:
1630
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10. Three gentlemen and three ladies are candidates for two vacancies. A voter has to vote for two candidates. In how many ways can one cast his vote?
Answer
Correct Answer:
15
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11. 12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done.
Answer
Correct Answer:
384
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12. How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?
Answer
Correct Answer:
24
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13. Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct.
Answer
Correct Answer:
65000
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14. A class photograph has to be taken. The front row consists of 6 girls who are sitting. 20 boys are standing behind. The two corner positions are reserved for the 2 tallest boys. In how many ways can the students be arranged?
Answer
Correct Answer:
18! × 1440
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15. In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
Answer
Correct Answer:
18
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16. There are 6 equally spaced points A,B,C,D,E and F marked on a circle with radius R. How many convex pentagons of distinctly different areas can be drawn using these points as vertices?
Answer
Correct Answer:
None
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17. How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?
Answer
Correct Answer:
4!
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18. In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?
Answer
Correct Answer:
3! 4! 8! 4!
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19. In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party.
Answer
Correct Answer:
15
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