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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.
4. If
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.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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