The figure below is an equilateral triangle with sides of length 6. What is the area of the triangle?

Waking 3/4 of his normal speed, a man is 24 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and office:

If two complimentary angles are in the ratio of 4:5, find the greater angle.

The volume of the largest right circular cone that can be cut out of a cube of edge 14 cm.

Three numbers are such that the average of first two numbers is 2, the average of the last two numbers is 3 and the average of the first and the last numbers is 4, then the average of three numbers is equal to. 

In a triangle ΔABC, the sides DE parallel to BC and AD = 6 cm, DB = 9 cm, AE = 8 cm, find the value of AC.

A cricketer's average score in 10 innings was 36. In his 11th innings, he scored some runs because of which his average increased to 40. What was his score in 11th innings?

There were two candidates in an election, total 7500 votes were cast, 20% of these votes were declared invalid, if one candidate got 55% of the valid votes then how many valid votes did the other candidate get?