If (P $\cup$ Q) $\cap$ (P $\cup$ R) = P $\cup$ (Q $\cap$ X). Then how many values can $X$ have?

Q.

If every pair of the equations $x^2+px+qr=0,x^2+qx+rp=0,x^2+rx+pq=0$ have a common root, then the sum of three common roots is

Q. If $y=\frac{1}{1+x^{q-p}+x^{r-p}}+\frac{1}{1+x^{r-q}+x^{p-q}}+\frac{1}{1+x^{p-r}+x^{q-r}}$ then $\frac{dy}{dx}=$

Q. If $\left|\begin{array}{ccc}p& q-y& r-z\\ p-x& q& r-z\\ p-x& q-y& r\end{array}\right|=0$, then the value of $\frac{p}{x}+\frac{q}{y}+\frac{r}{z}$ is

Q. If $(p^2-q^2)x^2+(q^2-r^2)x+r^2-p^2=0$ and $(p^2-q^2)y^2+(r^2-p^2)y+q^2-r^2=0$ have a common root for all real values of p, q and r, then find the common root.

Q.

If the roots of the quadratic equation $p(q-r)x^2+q(r-p)x+r(p-q)=0,$ are equal, then find the value of $\frac{2}{q}$ where $p,q,r\in R$