Ajit has played 50 Test innings and his average is 50. How many runs should Ajit score in his 51st test inning, so that his average moves up to 51? Note: He got dismissed every time.
A tosses a fair coin 50 times. B tosses another fair coin 51 times. What is the probability that B got more heads than A?
Let ABC be an equilateral triangle. Let P be any point on its incircle. Prove that:
AP2 + BP2 + CP2 = k for some constant k
Evaluate the following integral, and use the result to prove that π is less than 22/7.
