(1) Find all positive integers such that is divisible by .
(2) is the orthocentre of , is any point on if a circle described with centre and radius meets produced in , Prove that lies on the circumcircle of .
(3) Suppose is an acute angled triangle with . Let be the midpoint of . Suppose is a point on side such that, if intersects the median at , then .Prove .
(4) Let and y be real numbers such that
(5) Let be number of sequences of n terms formed using the digits and in which occurs an odd number of times. Find
(6) Find all positive integers such that the product of all the positive divisors of is equal to .