101.

A committee of two persons is constituted from two men and two women. What is the probability that the committee will have only women ?

• $\frac{1}{2}$

• $\frac{2}{3}$

A question is given to three students A, B and C whose chances of solving it are $\frac{1}{2}, \frac{1}{3} \mathrm{and} \frac{1}{4}$ respectively. What is the probability that the question will be solved ?

• $\frac{1}{24}$

• $\frac{1}{4}$

• $\frac{1}{2}$

• $\frac{23}{24}$

The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys in the class is 70 kg and that of girls is 55 kg. What is the number of boys in the class ?

• 50

• 55

• 60

• 100

For two dependent events A and B, it is given that P(A) = 0.2 and P(B) = 0.5. If AB, then the values of conditional probabilities $\mathrm{P}\left(\overline{)\mathrm{A}}\mathrm{B}\right) \mathrm{and} \mathrm{P}\overline{)(\mathrm{B}}\mathrm{A})$ are respectively

• $\frac{2}{5}, \frac{3}{5}$

• $\frac{2}{5}, 1$

• 1, $\frac{2}{5}$

• Information is insufficient

A point is chosen at random inside a circle. What is the probability that the point is closer to the centre of the circle than to its boundary ?

• $\frac{1}{5}$

• $\frac{1}{4}$

• $\frac{1}{3}$

• $\frac{1}{2}$

If two regression lines between height (x) and weight(y) are 4y - 15x + 410 = 0 and 30x - 2y - 825 = 0,then what will be the correlation coefficient between height and weight ?

• $\frac{1}{3}$

• $\frac{1}{2}$

• $\frac{2}{3}$

• $\frac{3}{4}$

In an examination, 40% of candidates got second class. When the data are represented by a pie chart, what is the angle corresponding to second class ?

• $40°$

• $90°$

• $144°$

• $320°$

For given statistical data, the graphs for less than ogive and more than ogive are drawn. If the point at which the two curves intersect is P, then abscissa of point P gives the value of which one of the following measures of central tendency ?

• Median

• Mean

• Mode

• Geometric mean

If the regression coefficient of x on y and y on x are  $- \frac{1}{2} \mathrm{and} - \frac{1}{8}$ respectively, then what is the correlation coefficient between x and y ?

• $- \frac{1}{4}$

• $- \frac{1}{16}$

• $\frac{1}{16}$

• $\frac{1}{4}$

Consider the following statements : 

1. If $\underset{\mathrm{x}\to \mathrm{a}}{\lim }\mathrm{f}\left(\mathrm{x}\right)$ and $\underset{\mathrm{x}\to \mathrm{a}}{\lim }\mathrm{g}\left(\mathrm{x}\right)$ both exist, then $\underset{\mathrm{x}\to \mathrm{a}}{\lim }\left\{\mathrm{f}\left(\mathrm{x}\right)\mathrm{g}\left(\mathrm{x}\right)\right\} \mathrm{exists}$
2. If $\mathrm{If} \underset{\mathrm{x}\to \mathrm{a}}{\lim }\left\{\mathrm{f}\left(\mathrm{x}\right)\mathrm{g}\left(\mathrm{x}\right)\right\}, \mathrm{then} \mathrm{both} \underset{\mathrm{x}\to \mathrm{a}}{\lim }\mathrm{f}\left(\mathrm{x}\right) \mathrm{and} \underset{\mathrm{x}\to \mathrm{a}}{\lim }\mathrm{g}\left(\mathrm{x}\right)$ must exist.

Which of the above statements is/are correct?

• 1 only

• 2 only

• both 1 and 2

• neither 1 nor 2