The number of integral solutions of `1/x+1/y=1/6 " with " x le y " is " 'alpha'`. The value of `'alpha-6'` is ……….. .

The number of solutions to x+y+z=10 , where 1le x, y, z le 6 and x, y, z in N , is equal to

If x alpha 1/y then

The number of integral values of alpha for which the quadratic expression alpha x^(2)+|2 alpha-3|x-6 is positive for exactly two integral values of x is equal to

If 1/x-1/y alpha 1/(y-x) , show that x alpha y .

The plane 2x – 3y + 6z - 11 = 0 makes an angle sin^(-1)alpha with X- axis. The value of alpha is equal to …............

The Plane 2x - 3y + 6z - 11 = 0 makes an angle sin^(-1) (alpha) with x-axis. The value of alpha is equal to

If the plane 2x-3y+6z=11 makes an angle sin^(-1) (alpha) with the x-axis , then the value of alpha is

The system of equations alpha x + y + z = alpha - 1 x + alpha y + = alpha - 1 , x + y + alpha z = alpha - 1 has infinite solutions, if alpha is

If x=2alpha+1\ a n d\ y=alpha-1 is a solution of the equation 2x-3y+5=0 , find the value of alpha