The lines `p(p^2+""1)""x""""y""+""q""=""0` and `(p^2+""1)^2x""+""(p^2+""1)""y""+""2q""=""0` are perpendicular to a common line for (1) no value of p (2) exactly one value of p (3) exactly two values of p (4) more than two values of p

The lines quad p(p^(2)+1)x-y+q=0 and (p^(2)+1)^(2)x+(p^(2)+1)y+2q=0 are perpendicular to a common line for (1) no value of p(4) more than two values of p two values of p(4) more than two values of p

The lines p(p^(2)+1)x-y+q=0 and (p^(2)+1)^(2)x+(p^(2)+1)y+2q=0 are perpendicular to a common line for

If P and Q are the points of intersection of the circles x^2+""y^2+""3x""+""7y""+""2p""""5""=""0 and x^2+""y^2+""2x""+""2y""""p^2=""0 , then there is a circle passing through P, Q and (1,""1) for (1) all values of p (2) all except one value of p (3) all except two values of p (4) exactly one value of p

If p and q are distinct reals,then 2{(x-p)(x-q)+(p-x)(p-q)+(q-x)(q-p)}=(p-q)^(2)+(x-p)^(2)+(x-q)^(2) is satisfied by no value of x(B) exactly one value of x(C) exactly two value of x(D) infinite values of x

If the line joining (4,1) and (p,3) is perpendicular to the line joining (1,6) and (-1,-2) then the value of p is

If p and q are positive real numbers such that p^2+q^2=1 , then the maximum value of p+q is