A corner of a cube of side length 8 m. When cut by a plane which bisects the sides of the cube, we get a pyramid whose volume is : 

A conical vessel of radius 6 cm and height 8 cm. is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. The fraction of water that overflows is? 

In any triangle ABC, AB + BC = 12 cm, BC + CA = 14 cm and CA + AB = 18 cm. What will be length of radius of a circle, if the perimeter of circle is equal to the perimeter of triangle ABC? 

Two partners invest ₹ 1,25,000 and ₹ 85,000 respectively in a business and agree that 60% of the profit should be divided equally between them and the remaining profit is to be divided into ratio of their capitals. If one partner gets 300 more than the other. Find the total profit made in the business. 

An electrician has to repair an electric fault on a pole of height 4 m. He needs to reach a point 1.3 m below the top of the pole to un dertake the repair work the length of ladder that he should use, which when inclined at an angle of 60° to the horizontal would enable him to reach the required positions is :

A wire of length 60 m is used to enclose a field which is in the shape of a right - angled triangle. The area of the field is 150 m² then, the largest side of the field has a length of: 

If a , b , c are in AP and x , y and z are in GP , then $${x^{b-c}.{y^{c-a}.z^{a-b}=?}}$$

What will be the area of thé trapezium formed by x - axis , y - axis , and lines 3x + 12 , 6x + 8y = 60 ?