1 Three persons A1, A2 and A3 are to speak at a function along with 5 other persons. If the persons speak in random order, the probability that A1 speaks before A2 and A2 speaks before A3 is’

(A) 1/6

(B) 3/5

(C) 3/8

(D) none of these

2. Two persons A, and B, have respectively n + 1 and n coins, which they toss simultaneously. Then probability P that A will have more heads than B

(A) P >1/2

(B) P = 1/2

(C) 1/4 < P < 1/2

(D) 0 < P < 1/4

3. On a toss of two dice, A throws a total of 5, then the probability that he will throw another 5 before he throws 7, is

(A) 1/9

(B) 1/6

(C) 2/5

(D) 5/36

4. One of two events must occur. If the chance of one is of the other, then odd in favour of the other are

(A) 1 : 3

(B) 3 : 1

(C) 2 : 3

(D) none of these

5. In a convex polygon of 6 sides two diagonals are selected at random. The probability that they intersect at an interior point of the polygon is

(A)2/5

(B)5/12

(C)7/12

(D)3/5

6. A and B are two events such that P(A) = 0.2 and P(AB) = 0.7. If A and B are independent events then P(B) equals

(A) 2/7

(B) 7/9

(C) 3/8

(D) none of these

7. A fair coin is tossed 99 times. Let X be the number of times heads occurs. Then P(X=r) is maximum when r is

(A) 49

(B) 52

(C) 51

(D) None of these

8. The numbers 1, 2, 3,…, n are arranged in random order. The probability that the digits 1, 2, 3…k (k < n) appear as neighbours in that order is (A) 1/n!

(B) k!/n!

(C) (n-k)!/n!

(D) None of these

9. Entries of a 2 x 2 determinant are chosen from the set {1, 1}. The probability that determinant has zero value is

(A) 1/4

(B) 1/3

(C) 1/2

(D) none of these

10. A bag contains 14 balls of two colours, the number of balls of colour being equal, seven balls are drawn at random one by one. The ball in hand is returned to the bag before each new draw. The probability that at least 3 balls of each colour are drawn, is

(A) 1/2

(B) >1/2

(C) < 1/2

(D) none of these

**Answer :**

1. A 2. B 3. C

4. D 5. B 6. C

7. A 8. D 9. C

10. A