If `x+y = p and x -y =q`, then `y` is ________.
(where `p ltq`)(positive/negative)

Given that q^2-p r ,0,\ p >0, then the value of |p q p x+q y q r q x+r y p x+q y q x+r y0| is- a. zero b. positive c. negative \ d. q^2+p r

Let x and y be the positive real numbers such that log_x y=-(1)/(4) , then value of the expression log_x(xy^5)-log_y""((x^(2))/(sqrt(y))) is (p)/(q) then q is _____________. { where p , q in N and are coprime to each other }

Let x and y be the positive real numbers such that log_x y=-(1)/(4) , then value of the expression log_x(xy^5)-log_y""((x^(2))/(sqrt(y))) is (p)/(q) then q is _____________. { where p , q in N and are coprime to each other }

If (x,2p+q)=(y,p+2q) then p-q=_______

If x^(p) . y^(q) = (x+y)^(p+q) , then dy/dx is equal to

If x^(p) + y^(q) = (x + y)^(p+q) , " then" (dy)/(dx) is

If (p)/(x) +(q)/(y) =m and (q)/(x) +(p)/(y) =n , then what is (x)/(y) equal to ?

If p and q are positive integers, f is a function defined for positive number and attain only positive value such that f(xf(y)) = x^p y^q , prove that q = p^2