What is the area (in cm²) of the circumcircle of a triangle whose sides are 6 cm, 8 cm and 10 cm respectively?

The top of two poles of height 24m and 36 m are connected by a wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire is 

$$ {3tan^{2}30°}-{4\over 3}{sin^{2}60°}- {1\over2}{cosec^{2}45°}+{4\over3}{sin^{2}90°=?}$$

A solid metallic cylinder of base radius 3 cm. and height 5 cm. is melted to form cones, each of height 1 cm. and base radius 1 mm. The number of cones is -

If ABC is an equilateral triangle and P, Q, R respectively denote the middle points of AB, BC, CA, then 

The number of sides in two regular polygons are in the ratio of 5 : 4. The difference between their Interior angles of the polygon is 6⁰ . Then the number of sides are 

In a mixture 25 litres, the ratio of milk and water is 4:1. How many litres of milk must be added to make the ratio 16:1?

In what ratio does the point T (x, 0) divide the segment joining the points S ( -4, -1 ) and U ( 1,4 )?