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 V_A/V_B is 

• 1

• 9/4

• 4/9

• 4/9

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

• 385

The 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

• 7/20

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

The probability that a non-leap year selected at random will have 53 Sunday is,

• 0

• 1/7

• 2/7

• 3/7

Out of 7 constants and 4 vowels, words are formed each having 3 constants 2 vowels. The number of such words that can be formed is

• 210

• 25200

• 2520

• 302400

627.

Let A and B be two events such that $\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) = \frac{1}{6}, \mathrm{P}(\mathrm{A} \cup \mathrm{B}) = \frac{31}{45} \mathrm{and} \mathrm{P}\left(\overline{\mathrm{B}}\right) = \frac{7}{10}$ then

• A and B are independent

• A and B are mutually exclusive

• $\mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{B}}\right) < \frac{1}{6}$

• $\mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{A}}\right) < \frac{1}{6}$

If ${}^{\mathrm{n}}\mathrm{C}_{\mathrm{r} - 1} = 36, {}^{\mathrm{n}}\mathrm{C}_{\mathrm{r}} = 84 \mathrm{and} {}^{\mathrm{n}}\mathrm{C}_{\mathrm{r} + 1} = 126, \mathrm{then} \mathrm{the} \mathrm{value} \mathrm{of} {}^{\mathrm{n}}\mathrm{C}_8 \mathrm{is}$

• 10

• 7

• 9

• 8

In a group of 14 males and 6 females. 8 and 3 of the males and females, respectively are aged above 40 yr. The probability that a person selected at random from the group is aged above 40 yr given that the selected person is a female, is

• $\frac{2}{7}$

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{5}{6}$

In a certain town, 60% of the families own a car, 30% own a house and 20% own both car and house. If a family is randomly chosen, then what is the probability that this family owns a car or a house but not both?

• 0.5

• 0.7

• 0.1

• 0.9