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 $P\equiv (\frac{1}{x_p},p);Q\equiv (\frac{1}{x_q},q);R\equiv (\frac{1}{x_r},r),$ where $x_k(\ne 0)$ denotes the $k^{th}$ term of an HP for $kϵN$, then

Q. If $P\equiv (\frac{1}{x_p},p);Q=(\frac{1}{x_q},q);R=(\frac{1}{x_r},r)$ where $x_k\ne 0$ denotes the kth term of an HP for $kϵN$ then

Q. Calculate $\underset{x\to 1}{lim}(\frac{p}{1-x^p}-\frac{q}{1-x^q});p,q\in N$

Q. Let $P=(\frac{1}{x_p},p),Q=(\frac{1}{x_q},q)$ and $R=(\frac{1}{x_r},r)$, where $x_k\ne 0$ denotes the $k^{th}$term of an H.P. for $k\in N$. If the area formed by the points $P,Q$ and $R$ is $\lambda pqr$ sq. units, then the value of $\lambda$ is

Q. If $p$ and $q$ are positive integers, then the absolute difference of the coefficients of $x^p$ and $x^q$ in the expansion of $(1+x{)}^{p+q}$ is