1. The number of permutations that can be formed by arranging all the letters of word ‘NINETEEN’ in which no two E’s occur together is
2. A man wants to go abroad by ship and return by air. He has a choice of 4 different ships to go and 5 airlines to return. In how many ways, can the man perform his journey?
(a) 20
(b) 18
(c) 24
(d) 16
(e) None of these
Directions (Q.3-4): Read the following information and answer the questions.
In how many ways can 3 prizes be distributed among 4 boys when
3. No boy gets more than one prize?
(a) 36
(b) 24
(c) 64
(d) 48
(e) None of these
4. A boy gets any number of prizes?
(a) 36
(b) 24
(c) 64
(d) 48
(e) None of these
5. Find the number of ways of arranging the host and 8 guests at a circular table so that the host always sits in a particular seat?
(a) 4!
(b) 8!
(c) 6!
(d) 9!
(e) None of these
6. The probability that a man will be alive for 10 more years is 1/4 and the probability that his wife will alive for 10 more years is 1/3. The probability that none of them will be alive for 10 more years, is
(a) 5/12
(b) 1/2
(c) 7/12
(d) 11/12
(e) None of these
7. The probabilities of solving a problem by three students A, B and C are 1/2 ,1/3 and 1/4, respectively. The probability that the problem will be solved is
(a) 1/4
(b) 1/2
(c) 3/4
(d) 1/3
(e) None of these
8. A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. The chance that the first roll was four is
(a) 2/5
(b) 1/5
(c) 1/6
(d) 1/108
(e) 2/3
9. An anti-aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shots are 0.4, 0.3, 0.2 and 0.1, respectively. What is the probability that the plane is hit when all the four shots are fired?
(a) 0.4379
(b) 0.6872
(c) 0.6976
(d) 0.3507
(e) None of these
10. Four boys and three girls stand in queue for an interview. The probability that they stand in alternate position, is
(a) 1/34
(b) 1/35
(c) 1/17
(d) 1/68
(e) 1/5
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