1. A boy has 3 library cards and 8 books of his interest in the library. Of these 8, he does not want to borrow chemistry part II unless Chemistry part I is also borrowed. In how many ways can he choose the three books to be borrowed?
(a) 56
(b) 27
(c) 26
(d) 41
(e) None of these
2. In how many ways can 7 persons be seated at a round table if 2 particular persons must not sit next to each other?
(a) 5040
(b) 240
(c) 480
(d) 720
(e) None of these
3. In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?
(a) 10080
(b) 4989600
(c) 120960
(d) 12960
(e) None of these
4. There are 4 candidates for the post of a lecturer in Mathematics and one is to be selected by votes of 5 men. The number of ways in which the votes can be given is
(a) 24
(b) 36
(c) 40
(d) 48
(e) None of these
5. The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
(a) 6 ! × 5 !
(b) 5 ! × 4 !
(c) 30
(d) 7 ! × 5 !
(e) None of these
6. A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
(a) 140
(b) 280
(c) 196
(d) 346
(e) None of these
7. There are 100 students in a college class of which 36 are boys studying statistics and 13 girls not studying statistics. If there are 55 girls in all, then the probability that a boy picked up at random is not studying statistics, is
(a) 3/5
(b) 2/5
(c) 1/5
(d) 4/5
(e) None of these
8. The number of ways in which a team of eleven players can be selected from 22 players including 2 of them and excluding 4 of them is:
(a) 16C11
(b) 16C5
(c) 16C9
(d) 20C9
(e) None of these
9. In how many different ways can the letters of the word ‘PRETTY’ be arranged?
(a) 120
(b) 36
(c) 360
(d) 720
(e) None of these
10. A box contains 3 Green balls, 4 Red balls, 2 Blue balls and 2 Orange balls. If two balls are drawn at random, what is the probability that both are red?
(a) 3/7
(b) 1/2
(c) 2/11
(d) 1/6
(e) None of these
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MAHENDRA GURU