Wednesday, March 28, 2012

Puzzle 43 - Locus of midpoints

Two circles with different radii are given in the plane touching each other externally at . Consider points on and on , such that subtends right angle at . Find the locus of midpoints of all such segments .

Tuesday, March 27, 2012

Puzzle 42


Let is a function such that . Find the value of f(0).

Thursday, March 15, 2012

Wednesday, March 14, 2012

Puzzle 40 - Matrices

Let and are two different matrices such that and . Does the matrix have inverse?

Thursday, March 08, 2012

Puzzle 38 - Point inside the Circle

Find the values of for which the point lies in the larger segment of the circle made by the chord whose equation is x + y – 2 = 0

Tuesday, March 06, 2012

Puzzle 37 - Extreme Values of Integral

Define the function , find the maximum and minimum values of f(x) in the interval