The following distribution gives the daily income of 50 workers of a factory

Convert this distribution to less than type of cumulative frequency distribution and draw its ogive.

If the sum of first 14 terms of an A.P. is 1050 and its first term is 10, find the 20^th term.

OR

The first term of an A.P. is 5, the last term is 45 and sum is 400. Find the number of terms and common difference.

As observed from the top of a 75m high light house above the sea level, the angles of depression of two ships are 30° and 45° respectively. If one ship is exactly behind the other on the same side of the light house and in the same straight line, find the distance between the two ships. (use √3 = 1.732)

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.

OR

State and prove the Pythagoras theorem.

A copper rod of diameter 1 cm and length 8 cm is drawn in to a wire of length 18 m of uniform thickness. Find the thickness of wire.

OR

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.