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 (a) no value of p (b) exactly one value of p (c) exactly two values of p (d) 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 vec u , vec v , vec w are noncoplanar vectors and p, q are real numbers, then the equality [3 vec u ,""p vec v , p vec w]-[p vec v ,"" vec w , q vec u]-[2 vec w ,""q vec v , q vec u]=0 holds for (A) exactly one value of (p, q) (B) exactly two values of (p, q) (C) more than two but not all values of (p, q) (D) all values of (p, q)

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

P(A)=p , P(B)=2p , P("exactly one out of A and B occurs")=5/9 then what will be maximum value of p ?

Q57) If the circle x^2+y^2+2ax+cy+a=0 and x^2+y^2-3ax+dy-1=0 intersect at two distinct points Pand Q, then the line 5x+by-a=0 will pass through P and Q for A. No values of a B. Exactly one value of a C. Exactly two values of a D. Infinitely many value of a

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

if exactly one root of equation x^(2)-(p+1)x-p^(2)=0 lie between 1 and 4 then the number of integral value of p is -