If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4^th A.M. is equal to 2^nd G.M., then m is equal to _________ .

The total number of 3-digit numbers, whose sum of digits is 10, is __________.

The probability that a randomly chosen 5-digit number is made from exactly two digits is :

If x³dy + xy dx = x²dy + 2y dx; y(2) = e and
x > 1, then y(4) is equal to :