In a competition A, B, C are participating the probability that A wins is twice that of B, the probability that B wins is twice that of C, then probability that A loses is

• $\frac{1}{7}$

• $\frac{2}{7}$

• $\frac{4}{7}$

• $\frac{3}{7}$

The probability that a number selected at random from the set of numbers (1, 2, 3, ... , 100) is a cube, is

• $\frac{1}{25}$

• $\frac{2}{25}$

• $\frac{3}{25}$

• $\frac{4}{25}$

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number, is

• $\frac{5}{12}$

• $\frac{7}{12}$

• $\frac{9}{12}$

• 0.25

The events A andB have probabilities 0.25 and 0.50, respectively. The probability that both A and B occur simultaneously is 0.14, then the probability that neither A nor B occurs, is

• 0.39

• 0.29

• 0.11

• 0.25

For all values of a and b the line (a + 2b)x + (a - by + (a + 5b) = 0 passes through the point.

• (- 1, 2)

• (2, - 1)

• (- 2, 1)

• (1, - 2)

The lines 2x + 3y = 6 , 2x + 3y = 8 cut the X-axis at A and B, respectively. A line L drawn through the point (2, 2) meets the X-axis as C in such away that abscissae of A, B and C are in arithmetic progression. Then, the equation of the line L is

• 2x + 3y = 10

• 8x + 2y = 10

• 2x - 3y = 10

• 8x - 2y = 10

The number of circles that touch all the straight lines x + y = 4,x - y = - 2 and y = 2 is

• 1

• 2

• 3

• 4

The incentre of triangle formed by the lines x + y = 1, x =1, y = 1 is

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

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

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

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

9.

The orthocentre of triangle formed by the lines x + 3y = 10 and 6x² + xy - y² = 0 is

• (1, 3)

• (3, 1)

• (- 1, 3)

• (1, - 3)

If one of the lines of pair of straight lines ax² + 2hxy + by²  = 0 bisects the angle between the coordinate axes, then

• a² + b² = h²

• (a + b)² = 4h²

• a² + b² = 4h²

• (a + b)² = h²