The number of three digit numbers of the form xyz such that `x lt y , z le y and x ne0`, is

If lamda be the number of 3-digit numbers are of the form xyz with x lt y, z le y and x ne0 , the value of (lamda)/(30) is

If the number of solutions of the equation x+y+z=20, where 1 le x lt y lt z and x, y, z in I is k, then (k)/(10) is equal to

Let x and y be two different digits. If the sum of the two digit numbers formed by using both the digits is a perfect square, then value of x+y is

For any positive real number x , prove that there exists an irrational number y such that 0 lt y lt x .

The number of the positive integral solutions (x,y, z) of the equation xyz = 24 is t, then the number of all possible factors of t is

The number of integral solutions of the inequation x+y+z le 100, (x ge 2, y ge 3, z ge 4) , is

The number of all possible values of theta , where 0 lt theta lt pi , for which the system of equations (y+z)cos 3 theta =(xyz) sin 3 theta ,x sin 3 theta =(2cos3theta)/y+(2sin3theta)/z and (x y z)sin3theta=(y+2z)cos3theta+ysin3theta have a solution (x_0,y_0,z_0) wiith y_0 z_0 !=0 is

Let N be the number of integral solution of the equation x+y+z+w=15" where " x ge 0, y gt 5, z ge 2 and w ge 1 . Find the unit digit of N.

If x,y and z are three different numbers, then prove that : x^(2) + y^(2) + z^(2)- xy - yz- zx is always positive

The number of solutions of equations x + y - z=0, 3x - y - z= 0,x - 3y + z = 0 is