A ball is thrown vertically upward from the top of a building 96m tall with an initial velocity 80m/second. The distances of the ball from the ground after t seconds is s = 96 + 80t - 4.9t². After how may seconds does the ball strike the ground.

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bengaluru (with out taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/h more than that of the passenger train find the average speed of the two trains.

Sum of the areas of two squares is 468m². If the difference of their perimeters is 24m, find the sides of the two squares.

If a polygon of ‘n’ sides has diagonals. How many sides will a polygon having 65 diagonals? Is there a polygon with 50 diagonals?

Find the nature of the roots of the following quadratic equation. If real roots exist, find them:

2x² - 3x + 5 = 0