21.

If the median of the data 6, 7, x - 2, x, 18 and 21 written in ascending order is 16, then the variance of that data is

• $30\frac{1}{5}$

• $31\frac{1}{3}$

• $32\frac{1}{2}$

• $33\frac{1}{3}$

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

• $\frac{1}{14}$

• $\frac{5}{7}$

• $\frac{1}{7}$

• $\frac{5}{28}$

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

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

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

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

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

The probability that an event does not happen in one trial is 0.8. The probability that the event happens atmost once in three trials is

• 0.896

• 0.791

• 0.642

• 0.592

If the equation to the locus of points equidistant from the points (- 2, 3), (6, - 5) is ax + by + c = 0, where a > 0, then the ascending order of a, b, c is

• a, b, c

• c, b, a

• b, c, a

• a, c, b

The point (2, 3) is first reflected in the straight line y = x and then translated through a distance of 2 units along the positive direction X-axis. The coordinates of the transformed point are

• (5, 4)

• (2, 3)

• (5, 2)

• (4, 5)

If the straight line 2x + 3y - 1 = 0, x + 2y - 1 = 0 and ax + by - 1 = 0 form a triangle with origin as orthocentre, then (a, b) is equal to

• (6, 4)

• ( - 3, 3)

• ( - 8, 8)

• (0, 7)

The point on the line 4x - y - 2 = 0 which is equidistant from the points ( - 5, 6) and (3, 2) is

• (2, 6)

• (4, 14)

• (1, 2)

• (3, 10)

If the slope of one of the lines represented by ax² - 6xy + y² = 0 is the square of the other,then the value of a is

•  - 27 or 8

•  - 3 or 2

•  - 64 or 27

•  - 4 or 3