Seven white balls and three black balls are randomly arranged in a row. The probability that no two black balls are placed adjacently is

• $\frac{1}{2}$

• $\frac{7}{15}$

• $\frac{2}{15}$

• $\frac{1}{3}$

The probability distribution of a random variable X is given below

X = x	0	1	2	3
P(X) = x	$\frac{1}{10}$	$\frac{2}{10}$	$\frac{3}{10}$	$\frac{4}{10}$

Then the variance of X is

• 1

• 2

• 3

• 4

The probability that an individual suffers a bad reaction from an injection is 0.001. The probability that out of 2000 individuals exactly three will suffer bad reaction is

• $\frac{1}{{\mathrm{e}}^2}$

• $\frac{2}{3{\mathrm{e}}^2}$

• $\frac{8}{3{\mathrm{e}}^2}$

• $\frac{4}{3{\mathrm{e}}^2}$

A regular polygon of n sides has 170 diagonals,then n is equal to

• 12

• 17

• 20

• 25

A committee of 12 members is to be formed from 9 women and 8 men. The number of committees in which the women are in majority is

• 2720

• 2702

• 2270

• 2278

A student has to answer 10 out of 13 questions in an examination choosing atleast 5 questions from the first 6 questions. The number of choice available to the student is

• 63

• 91

• 161

• 196

In an entrance test there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student know the answer to a question is 9/10. If he gets the correct answer to a question, then the probability that he was guessing is 

• $\frac{37}{40}$

• $\frac{1}{37}$

• $\frac{36}{37}$

• $\frac{1}{9}$

There are four machines and it is known that exactly two of them are faulty. They are teste done by one, in a random order till both the faulty machines are identified. Then, the probability that only two tests are need is

• $\frac{1}{3}$

• $\frac{1}{6}$

• $\frac{1}{2}$

• $\frac{1}{4}$

A random variable X has the probability distribution given below.

X	1	2	3	4	5
P(X = x)	K	2K	3K	2K	K

Its variance is

• $\frac{16}{3}$

• $\frac{4}{3}$

• $\frac{5}{3}$

• $\frac{10}{3}$

A candidate takes three tests in succession and the probability of passing the first test is p. The probability of passing each succeeding test is p or $\frac{\mathrm{p}}{2}$ according as he passes or fails in the preceding one. The candidate is selected, if he passes atleast two tests. The probability that the candidate is selected, is

• p²(2 - p)

• p(2 - p)

• p + p² + p³

• p²(1 - p)