Quantitative Ab...

From a solid cube of side 8cm, a portion is cut out such that the cutting plane touches the midpoints of three adjacent sides of the cube. Find the surface area of the cut out portion.

The selling price of a cycle varies with the number of cycles sold. The selling price S, is given by S = 200 - 4x, where x is the number of cycles sold. If the shopkeeper wants to maximize his revenue, how many cycles should he sell?

Triangle PQR is an equilateral triangle with side 8 cm. The triangle is rotated about a line passing through Q and parallel to PR by 180°. What would be the volume of the figure generated?

Raghu, Raghav and Raja ran on a racetrack at their respective constant speed. Raghu finished the race when Raghav was 200m behind and Raja was 350m behind. Raghav finished the race when Raja was 180 m behind. What is the length of the race track in meters?

Two points are selected at random on the curve x² + y² = 49x. Find the probability that the length of the minor arc between the two points is not greater than 11 units.

A shopkeeper cheated a wholesaler, from whom he buys the goods, both in terms of quantity and price (by fraudulently paying less than market price for a given quantity) by 20% each. The same shopkeeper cheated the customer both in terms of quantity and price by 40% each. The shopkeeper claims to sell at no profit - no loss. What is the actual profit percentage for the shopkeeper?

Ram earned Rs. 20000 as an additional allowance. 25% of this income will have to be deducted as income tax. But if Ram deposit Rs. 12000 in the tax saving instrument which fetches 14% interest he would get a tax rebate of 11% on the original tax amount thus reducing his tax liability. What will be the approx. effective interest rate earned by Ram on the tax saving instrument?

What will be the remainder when 761376137613…..(578 digits) is divided by 625?

Find the area enclosed by the curves, given by (x - a)² + (y - b)² = 49(x−a) , where a² = 49

Assume that π =22/7

Four points are arranged in space such that distance between any two of the points is 6m. Find the volume of the solid formed by joining all the four points. (in cubic metres)