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

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

Equation 1+x^2+2x"sin"(cos^(-1)y)=0 is satisfied by exactly one value of x exactly two value of x exactly one value of y exactly two value of y

If 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 the same line, then the value of p is

If p^(2)-p+1=0 , then the value of p^(3n) can be

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)

The random variable X can take only the values 0,1,2. If P(X=0)=P(X=1)=p and E(X^(2))=E[X] , then find valu of p.

If y+ (2p + 1) x + 3=0 and 8y- (2p-1)x=5 are mutually perpendicular, find the value of p.

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

If the solution to 2x^(2)-8x-5=0 are p and q with pgtq , what is the value of p-q?

Find the value of : 1/2 p^(2) xx 4p^(2)q xx(-3 p)