Write the empirical relationship among mean, median and mode.

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground where it makes an angle 30°. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree from where it is broken.

If the perimeter and the area of a circle are numerically equal, then find the radius of the circle.

For what values of p does the pair of equations 4x + py + 8 = 0 and 2x + 2y + 2 = 0 has unique solution?

OR

What type of straight lines will be represented by the system of equations 2x + 3y = 5 and 4x + 6y = 7?

A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is red?

OR

A die is thrown once. What is the probability of getting a prime number?