Let a, b, x, y be real numbers such that `a^2 + b^2=81`, `x^2 + y^2 = 121` and `ax + by = 99`, Then the set of all possible values of `ay -bx` is

Let x, y be real numbers such that x gt 2y gt 0 and 2log (x-2y) = log x + log y . Then the possible values (s) of (x)/(y)

Let a, x, y, z be real numbers satisfying the equations ax+ay=z x+ay=z x+ay=az, where x, y, z are not all zero, then the number of the possible values of a is

Let a, x, y, z be real numbers satisfying the equations ax+ay=z x+ay=z x+ay=az, where x, y, z are not all zero, then the number of the possible values of a is

Let a, b, c be three distinct real numbers such that each of the expressions ax^+bx +c, bx^2 + cx + a and ax^2 + bx + c are positive for all x in R and let alpha=(bc +ca+ab)/(a^2+b^2+c^2) then (A)alpha 1/4 (D) alpha>1

If the lines ax+y=0,x+ay+2=0 and x+y+a=0 (a in R) are concurrent lines,then sum of all possible value(s) of a is

If ax + by = a^(2)-b^(2) and bx + ay = 0, find the value of x + y .

If a and b are positive numbers and eah of the equations x^(2)+ax+2b=0 and x^(2)+2bx+a=0 has real roots,then the smallest possible value of (a+b) is

If (ax+2)(bx+7)=15x^(2)+cx+14 for all values of x, and a+b=8 , what are the two possible values for c ?