Let the expression `E=8^(a)+8^(b)-3.2^(a+b)` takes its minimum value `p` at `a=alpha & b=beta,` then perpendicular distance of the point `P(alpha,beta)` from the line `x+y+2p=0` is

The graph of 2x=5-3y cuts the x-axis at the point P(alpha,beta) . The value of (2alpha+beta) is :

The graph of 2x = 5-3y cuts the x-axis at the point P( alpha,beta ). The value of (2alpha+beta) is

If 2x+3y+4=0 is perpendicular bisector of the segment joining the points A(1,2) and B(alpha,beta) then the value of alpha+beta is

If alpha and beta are the roots of the equation x^(2)-px +16=0 , such that alpha^(2)+beta^(2)=9 , then the value of p is

Let alpha, beta and gamma be real numbers such that the system of linear equations x + 2y + 3z = alpha 4x + 5y + 6z = beta 7x + 8y + 9z = gamma-1 Let P be the plane containing all those (alpha, beta, gamma) for which the above system of linear equations is consistent, and D be the square of the distance of the point (0,1,0) from the plane P. The value of absM is ______

Let alpha, beta and gamma be real numbers such that the system of linear equations x + 2y + 3z = alpha 4x + 5y + 6z = beta 7x + 8y + 9z = gamma-1 Let P be the plane containing all those (alpha, beta, gamma) for which the above system of linear equations is consistent, and D be the square of the distance of the point (0,1,0) from the plane P. The value of D is ______

Distance of any point P(x,y) from origin is defined by d=max{|x|,|y|} and if alpha^(2)+beta^(2)-2 alpha+4 beta+5=0, then distance of A(alpha,beta) from origin is .....

P and Q are any two points on the circle x^(2)+y^(2)=4 such that PQ is a diameter.If alpha and beta are the lengths of perpendiculars from P and Q on x+y=1 then the maximum value of alpha beta is