A survey was conducted among 300 students. It was found that 125 students like to play cricket, 145 students like toplay football and 90 students like to play tennis. 32 students like to play exactly two games out of the three games.

How many students like to play all the three games ?

• 14

• 21

• 28

• 35

A survey was conducted among 300 students. It was found that 125 students like to play cricket, 145 students like toplay football and 90 students like to play tennis. 32 students like to play exactly two games out of the three games. How many students like to play exactly only one game?

How many students like to play all the three games ?

• 196

• 228

• 254

• 268

If two dice are thrown and at least one of the dice shows 5, then the probability that the sum· is 10 or more is

• $\frac{1}{6}$

• $\frac{4}{11}$

• $\frac{3}{11}$

• $\frac{2}{11}$

The average age of a combined group of men and women is 25 years. If the average age of the group of men is 26 years and that of the group of women is 21 years, then the percentage of men and women inthe group is respectively

• 20, 80

• 40, 60

• 60, 40

• 80, 20

In a bolt factory, machines X, Y, Z manufacture bolts that are respectively 25%, 35% and 40% of the factory's total output. The machines X, Y, Z respectively produce 2%, 4% and 5% defective bolts. A bolt is drawn at random from tlie product and is found to be defective. What is the probability that it was manufactured by machine X ?

• $\frac{5}{39}$

• $\frac{14}{39}$

• $\frac{20}{39}$

• $\frac{34}{39}$

$8 \mathrm{coins} \mathrm{are} \mathrm{tossed} \mathrm{simultaneously}. \mathrm{The} \mathrm{probability} \mathrm{of} \mathrm{getting} \mathrm{at} \mathrm{least} 6 \mathrm{heads} \mathrm{is}$

• $\frac{7}{64}$

• $\frac{57}{64}$

• $\frac{37}{256}$

• $\frac{229}{256}$

Three groups of children contain 3 girls and 1 boy; 2 girls and 2 boys; 1 girl and 3 boys. One child is selected at random rom each group. The probability that the three selected consist of 1 girl and 2 boys is

• $\frac{13}{32}$

• $\frac{9}{32}$

• $\frac{3}{32}$

• $\frac{1}{32}$

Let A, B and C be three mutually exclusive and exhaustive events associated with a random experiment. If P(B) = 1.5 P(A) and P(C) = 0.5 P(B), then P(A) is equal to

• $\frac{3}{4}$

• $\frac{4}{13}$

• $\frac{2}{3}$

• $\frac{1}{2}$

If the probability of simultaneous occurrence of two events A and B is p and the probability that exactly one of A, B occurs is q, then which of the following is/are correct ?

$$\begin{gathered} 1. \mathrm{P}\left(\overline{\mathrm{A}}\right) + \mathrm{P}\left(\overline{\mathrm{B}}\right) = 2 - 2\mathrm{p} - \mathrm{q} \\ 2.\mathrm{P}\left(\overline{\mathrm{A}} \cap \overline{\mathrm{B}}\right) = 1 - \mathrm{p} - \mathrm{q} \end{gathered}$$

Select the correct answer using the code given below :

• 1 only

• 2 only

• both 1and 2

• neither 1 nor 2

$$\begin{gathered} \mathrm{If} \mathrm{the} \mathrm{regression} \mathrm{coefficient} \mathrm{of} \mathrm{Y} \mathrm{on} \mathrm{X} \mathrm{is} - 6, \mathrm{and} \mathrm{the} \mathrm{correlation} \mathrm{coefficient} \\ \mathrm{between} \mathrm{X} \mathrm{and} \mathrm{Y} \mathrm{is} - \frac{1}{2} \mathrm{then} \mathrm{the} \mathrm{regression} \mathrm{coefficient} \mathrm{of} \mathrm{X} \mathrm{on} \mathrm{Y} \mathrm{would} \mathrm{be} \end{gathered}$$

• $\frac{1}{24}$

• $- \frac{1}{24}$

• $- \frac{1}{6}$

• $\frac{1}{6}$