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One ticket is selected at random from 50 tickets numbered 00, 01, 02, ... , 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals
1/14
1/7
5/14
1/50
A.
1/14
A = Events that sum of the digits on selected ticket is 8
= {08, 17, 26, 35, 44}
n(A) = 5
Event that product of digits is zero
= {00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 20,30, 40}
⇒ n(B) = 14
=P(A/B) = (5/14)
The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is
40
20
80
60
C.
80
52x + 42y = 50
(x + y) 2x = 8y
Suppose a population A has 100 observations 101, 102, … , 200, and another population B has 100 observations 151, 152, … , 250. If VA and VB represent the variances of the two populations, respectively, then VA/VB is
1
9/4
4/9
2/3
A.
1
(Here deviations are taken from the mean) Since A and B both have 100 consecutive integers, therefore both have same standard deviation and hence the variance. 
At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is
5040
6210
385
1124
C.
385
10C1 + 10C2 + 10C3 + 10C4The probability that A speaks truth is 4/ 5 , while this probability for B is 3/ 4 . The probability that they contradict each other when asked to speak on a fact is
3/20
1/20
7/20
4/5
C.
7/20
The probability of speaking truth of A, P(A) = 4/5.
The probability of not speaking truth of A, P(
) =1− 4./ 5 = 1/5.
The probability of speaking truth of B, P(B) = 3/4.
The probability of not speaking truth of B,P(
) =1/4.
The probability of that they contradict each other
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is
At least 750 but less than 1000
At least 1000
Less then 500
At least 500 but less than 750
B.
At least 1000
Number of ways of selecting 4 novels from 6 novels
= 6C4
Number of ways of selecting 1 dictionary from
3 dictionaries = 3C1
Required arrangements = 6C4 × 3C1 × 4! = 1080
=> At least 1000
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