1. State Thales theorem and prove it.
2. AB is a line segment and M is its midpoint. Semicircles are drawn with AM, MB, and AB as diameters on the same side of the line AB. A circle with O as center and r as radius is drawn so that it touches all the three semicricles. Prove that
3. Prove that any four vertices of a regular pentagon are concyclic.
5. Find X and Y if
6. Find the Standard Deviation of the following:-
C.I. 0-10 10-20 20-30 30-40
f 3 4 2 5
7. A number is selcted at random from 40 to 80. Find the probability that it is divisible by 6 or 9.
8. Prove the identity:-
9. Find the area of an isosceles triangle with base 10 cm and vertical angle 47°.
10. The angle of elevation of a jet plane from a point P on the ground is 60°. After 15 seconds, the angle of elevation changes to 30°. If the jet is flying at the speed of 720 km/hour, find the height at which the jet is flying.
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