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)

A six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be 7. The probability that the number 3 has appeared atleast once, is

• $\frac{1}{5}$

• $\frac{1}{2}$

• $\frac{1}{3}$

• $\frac{1}{4}$

717.

If A, B and C are mutually exclusive and exhaustive events of a random experiment such that P(B) = $\frac{3}{2}$P(A) and P(C) = $\frac{1}{2}$P(B), then P(A ∪ C) equals to

• $\frac{10}{13}$

• $\frac{3}{13}$

• $\frac{6}{13}$

• $\frac{7}{13}$

Two persons A and B are throwing an unbiased six faced dice alternatively, with the condition that the person who throws 3 first wins the game. If A starts the game, then probabilities of A and B to win the same are, respectively

• $\frac{6}{11}, \frac{5}{11}$

• $\frac{5}{11}, \frac{6}{11}$

• $\frac{8}{11}, \frac{3}{11}$

• $\frac{3}{11}, \frac{8}{11}$

The letters of the word 'QUESTION' are arranged in a row at random. The probability that there are exactly two letters between Q and S is

• $\frac{1}{14}$

• $\frac{5}{7}$

• $\frac{1}{7}$

• $\frac{5}{28}$

$\mathrm{If} \frac{1 + 3\mathrm{P}}{3}, \frac{1 - 2\mathrm{P}}{2} \mathrm{are} \mathrm{probabilities} \mathrm{of} \mathrm{two} \mathrm{mutually} \mathrm{exclusive} \mathrm{events}, \mathrm{then} \mathrm{P} \mathrm{lies} \mathrm{in} \mathrm{the} \mathrm{interval}$

• $\left[- \frac{1}{3}, \frac{1}{2}\right]$

• $\left(\frac{- 1}{2}, \frac{1}{2}\right)$

• $\left[- \frac{1}{3}, \frac{2}{3}\right]$

• $\left(\frac{- 1}{3}, \frac{2}{3}\right)$