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11.

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

12.

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

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

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

13.

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

14.

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

$\frac{2}{7}$

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{5}{6}$

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15.

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

16.

If the letters of the word 'PROBABILITY' are written down at random in a row, then probability that two B's are together, is

$\frac{2}{11}$

$\frac{10}{11}$

$\frac{3}{11}$

$\frac{6}{11}$

17.

A person goes to office by car, scooter, bus and train, probability of which are 1/7, 3/7, 2/7 and 1/7, respectively. Probability that he reaches office late, if he takes car, scooter, bus or train is 2/9, 1/9, 4/9, and 1/9, respectively. Given that he reached office in time, the probability that he travelled by a car, is

1/7

2/7

3/7

4/7

18.

Ram is visiting a friend. Ram knows that his friend has 2 children and 1 of them is a boy. Assuming that a child is equally likely to be a boy or a girl, then the probability that the other child is a girl, is

1/2

1/3

2/3

7/10

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19.

Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels is,

24800

25100

25200

25400

20.

A fair six-faced die is rolled 12 times. The probability that each face turns up twice is equal to

$\frac{12!}{6!6!{6}^{12}}$

$\frac{{2}^{12}}{{2}^{6}{6}^{12}}$

$\frac{12!}{{2}^{6}{6}^{12}}$

$\frac{12!}{{6}^{2}{6}^{12}}$

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