Four circles have areas in the ratio `3:7:11:19`. Four squares are formed whose diagonals are proportional to te radii of the above circles. Find the proportional of the areas of the squares so formed.

Find mid points of the sides of a square of side 1 are joined to form a new square. This procedure is repeated indefinitely. Find the sum of the areas of all the squares

Water is being poured into a vessel in the form of an inverted right circular cone of semi vertical angle 45^@ in such a way that the rate of change of volume at any moment is proportional to the area of the curved surfaces which is wet at that moment.Initially the vessel is full to a height of 1 cm and after 1 second the height is 3 cm.Show that the height of the water after 3 seconds will be 7 cm.

Water is being poured into a vessel in the form of an inverted right circular cone of semi vertical angle 45^@ in such a way that the rate of change of volume at any moment is proportional to the area of the curved surfaces which is wet at that moment.Initially the vessel is full to a height od 2 cm,after 2 seconds the height becomes 10 cm.Show that after 3.5 seconds from the start,the height of water will be 16 cm.

A rectangular Sheet of paper of fixed perimeter with the sides having their length in the ratio 8:15 converted in to an open rectangular box by folding after removing the squares of equal area from all corners. If the total area of the removed squares is 100, the resulting box has maximum volume. Find the lengths of the rectangular sheet of paper.

A wire of length 2 units is cut into two parts which are bent respectively to form a square of s i d e=x units and a circle of radius =r units. If the sum of the areas of the square and the circle so formed is minimum, then :

Select the correct option from the given alternatives.A semi-circle is divided into two sectors whose angles are in the ratio 4:5.Find the ratio of their areas?

The ratio of circumference and area of a circle is 2:7 . Find its circumference.

A block of weight 10 N is fastened to one end of a wire of cross sectional area 3 mm^2 and is rotated in a vertical circle of radius 20 cmk. The speed of the block at the bottom of the circle is 2ms^-1 . Find the elongation of the wire when the block is at the bottom of the circle. Young modulus of the material of the wire =2xx10^11Nm^-2 .