1. The digits 1, 2, 3, 4, 5, 6, 7, 8, 9 are written in random order to form a nine digit number. Find the probability that this number is divisible by 4 :
A. 4/9
B. 2/9
C. 17/81
D. None of these
Correct Answer : B
2. A four digit number is formed with the digits 1, 3, 4, 5 without repetition. Find the chance that the number is divisible by 5:
A. 3/4
B. 1/4
C. 9/16
D. 1/16
Correct Answer : B
3. Five persons entered the lift cabin on the ground floor of an 8-floor house. Suppose each of them independently and with equal probability can leave the cabin at any floor beginning with the first. Find out the probability that all persons leaving at diff
A. 365/2401
B. 360/2401
C. 35/2410
D. None of these
Correct Answer : B
4. If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is :
A. 13/32
B. 27/32
C. 19/32
D. None of these
Correct Answer : A
5. A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals :
A. 5/12
B. 1/2
C. 5/6
D. 1/6
Correct Answer : B
6. There are four calculators and it is known that exactly two of them are defective. They are tested one by one , in a random order till both the defective calculators are identified. Then the probability that only two tests are required is :
A. 5/6
B. 1/2
C. 1/6
D. 1/3
Correct Answer : C
7. 20 girls, among whom are A and B sit down at a round table. The probability that there are 4 girls between A and B is :
A. 17/19
B. 2/19
C. 13/19
D. 6/19
Correct Answer : B
8. Two integers x and y are chosen with replacement out of the set{0, 1, 2, 3, ...10}. Then the probability that| x - y | > 5 is :
A. 7/11
B. 40/121
C. 35/121
D. 30/121
Correct Answer : D
9. The probability that the birthdays of 4 different persons will fall in exactly two calendar months is :
A. 77/1728
B. 17/87
C. 11/144
D. None of these
Correct Answer : A
10. If 6 objects are distributed at random among 6 persons, the probability that atleast one of them will not get any thing is :
A. 6 x 6!
B. 5
C. (6
D. None of these
Correct Answer : C
11. There is 4 volume encyclopaedia among 40 books arranged on a shelf in a random order. If the volumes are not necessarily kept side by side, the probability that they occur in increasing order from left to right is:
A. 1/24
B. 1/12
C. 1/10
D. None of these
Correct Answer : A
12. Four numbers are multiplied together. Then the probability that the product will be divisible by 5 or 10 is :
A. 169/625
B. 369/625
C. 169/1626
D. None of these
Correct Answer : B
13. 8 couples (husband and wife) attend a dance show ‘Nach Baliye’ in a popular TV channel ; A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is atleast one couple will be selected is :
A. 8/39
B. 15/39
C. 12/13
D. None of these
Correct Answer : B
14. Three persons A, B and C are to speak at a function along with 4 other persons, if they all speak in random order, the probability that A speaks before B and B speaks before C is :
A. 5/6
B. 1/6
C. 1/2
D. 1/3
Correct Answer : B
15. A bag contains 16 coins of which 2 coins are counterfeit with heads on the both sides. The rest are fair coins. One is selected at random from the bag and tossed.The probability of getting a head is :
A. 3/16
B. 13/16
C. 9/16
D. 7/16
Correct Answer : C
16. A committee of five persons is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is :
A. 4/9
B. 5/9
C. 13/18
D. None of these
Correct Answer : A
17. A speaks truth in 60% cases and B speaks truth in 80% cases. The probability that they will say the same thing while describing a single event is :
A. 0.36
B. 0.56
C. 0.48
D. 0.2
Correct Answer : B
18. Two squares are chosen at random on a chessboard, the probability that they have a side in common is :
A. 3/32
B. 1/32
C. 1/18
D. None of these
Correct Answer : C
19. An old person forgets the last two digits of a telephone number, remembering only that these are different dialled at random. The probability that the number is dialled correctly is :
A. 1/90
B. 81/91
C. 2/99
D. None of these
Correct Answer : A
20. Three squares of a chessboard are chosen at random, the probability that two are of one colour and one of another is:
A. 67/992
B. 16/21
C. 31/32
D. None of these
Correct Answer : B
21. The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays, is :
A. 17/53
B. 1/53
C. 3/7
D. None of these
Correct Answer : C
22. In order to get atleast once a head with probability P ≥ 0.9, the number of times a coin needs to be tossed is:
A. 3
B. 2
C. 5
D. 4
Correct Answer : D
23. Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that atleast one of the selected persons will be a woman is :
A. 25/39
B. 31/65
C. 25/69
D. 5/13
Correct Answer : A
24. Nine squares are chosen at random on a chessboard. What is the probability that they form a square of size 3 x 3?
A. 9 / 64C9
B. 36 / 64C9
C. 6 / 64C9
D. None of these
Correct Answer : B
25. Seven digits from the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 are written in random order. The probability that this seven digit number is divisible by 9 is :
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