Maths For CBSE class 12th

There are problems for the students appearing in class 12th exam. Solutions may be sent at rprsto@gmail.com. Best solution will be appreciated. For the solution or answer also you may send the request at the same e-mail address.
Below the symbol ^ means raised to the power.
Problem : A line l intersects the parabola y = x^2 at P and another line y - x -2=0 at Q so that the segment PQ is shortest. What is the equation of line l and the length PQ?
Difficult : Inside a right triangle with sides 3, 4 and 5 units length, a point O is taken. Find the least value of the sum OA+OB+OC, where A, B, C are vertices of the triangle.

Easy : Minimum and maximum values of the expression (sin x)^6 + (cos x)^6 are ...

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