- The pair of equations`(p^2-1)x+(q^2-1)+r=0 and (p+1)x+(q-1)y+r=0` have infinitely many solutions, then which of the following is true?

The pair of equations (p^(2) -1)x + (q^(2) -1) y + r=0 and (p+1) x + (q-1) y + r=0 have infinitely many solutions, then which of the following is true ?

Assertion (A) :Pair of linear equations 9x+3y+12=0 and 18x+6y+24=0 have infinitely many solutions Reason (R ) : Pair of linear equations a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 have infinitely many solutions if (a_(1))/(a_(2))=(b_(1))/(b_(2))=(c_(1))/(c_(2))

Prove that equations (q-r)x^(2)+(r-p)x+p-q=0 and (r-p)x^(2)+(p-q)x+q-r=0 have a common root.

If the roots of the equation (1-q+p^(2)/2)x^(2) + p(1+q)x+q(q-1) +p^(2)/2=0 are equal, then show that p^(2) = 4q

If p and q are the roots of the equation x^2 - 15x + r = 0 and. p - q = 1 , then what is the value of r?

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 the roots of the equation (1)/(x+p)+(1)/(x+q)=(1)/(r) are equal in magnitude and opposite in sign, then (p+q+r)/(r)

If the roots of the equation 1/(x+p)+1/(x+q)=1/r, (x ne -p, x ne -q, r ne 0) are equal in magnitude but opposite in sign, then p + q is equal to :