An unbiased coin is tossed to get 2 points forturning up a head and one point for the tail.If three unbiased coins are tossed simultaneously, then the probability of getting a total of odd number of points is

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{1}{8}$

• $\frac{3}{8}$

Suppose E and F are two events of a random experiment. If the probability of occurrence of E is 1/5 and the probability of occurrence of F given E is 1/10, then the probability of non-occurrence of atleast one of the events E and F is

• $\frac{1}{18}$

• $\frac{1}{2}$

• $\frac{49}{50}$

• $\frac{1}{50}$

Six faces of an unbiased die are numbered with 2, 3, 5, 7, 11 and 13. If two such dice are thrown, then the probability that the sum on the upper most faces of the dice is an odd number is

• $\frac{5}{18}$

• $\frac{5}{36}$

• $\frac{13}{18}$

• $\frac{25}{36}$

A person who tosses an unbiased coin gains two points for turning up a head and loses one point for a tail. If three coins are tossed and the total score X is observed, then the range of x is

• {0, 3, 6}

• {- 3, 0, 3}

• {- 3, 0, 3, 6}

• {- 3, 3, 6}

If the distance between the points (acos$\mathrm{\theta }$, asin$\mathrm{\theta }$) and  (acos$\mathrm{\varphi }$, asin$\mathrm{\varphi }$) is 2a, then $\mathrm{\theta }$ is equal to

• $2\mathrm{n\pi } \pm \mathrm{\pi } + \mathrm{\varphi }, \mathrm{n} \in \mathrm{Z}$

• $\mathrm{n\pi } + \frac{\mathrm{\pi }}{2} + \mathrm{\varphi }, \mathrm{n} \in \mathrm{Z}$

• $n\mathrm{\pi } - \mathrm{\varphi }, \mathrm{n} \in \mathrm{Z}$

• $2\mathrm{n\pi } + \mathrm{\varphi }, \mathrm{n} \in \mathrm{Z}$

The number of circles that touch all the three lines x + y - 1 = 0, x - y - 1 = 0 and y + 1 = 0 is

• 2

• 3

• 4

• 1

Suppose A, B are two points on 2x - y + 3 = 0 and P (1, 2) is such that PA = PB. Then, the mid-point of AB is

• $\left(\frac{- 1}{5}, \frac{13}{5}\right)$

• $\left( \frac{- 7}{5}, \frac{9}{5}\right)$

• $\left( \frac{7}{5}, \frac{- 9}{5}\right)$

• $\left( \frac{- 7}{5}, \frac{- 9}{5}\right)$

The angle between the lines represented by

${\mathrm{y}}^2{\sin }^2\left(\mathrm{\theta }\right) - {\mathrm{xysin}}^2\left(\mathrm{\theta }\right) + {\mathrm{x}}^2\left({\cos }^2\left(\mathrm{\theta }\right) - 1\right) = 0 \mathrm{is}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{2}$

Area of the triangle formed by the lines 3x² + 4xy + y² = 0, 2x - y = 6 is

• 16 sq. units

• 25 sq. units

• 36 sq. units

• 49 sq. units

40.

If P₁, P₂, P₃ are the perimeters of the three circles 

x² + y² + 8x - 6y = 0, 4x² + 4y - 4x - 12y - 186 = 0 and x² + y - 6x + 6y - 9 = 0 respectively, then

• ${\mathrm{P}}_1 < {\mathrm{P}}_2 < {\mathrm{P}}_3$

• ${\mathrm{P}}_1 < {\mathrm{P}}_3 < {\mathrm{P}}_2$

• ${\mathrm{P}}_3 < {\mathrm{P}}_2 < {\mathrm{P}}_1$

• ${\mathrm{P}}_2 < {\mathrm{P}}_3 < {\mathrm{P}}_1$