$\int \frac{\log \sqrt{x}}{3 x} \mathrm{dx}$ is equal to

The negation of contrapositive of the statement $\mathrm{p} \rightarrow(\sim \mathrm{q} \wedge \mathrm{r})$ is

If $\mathrm{F}(x)=\left(\mathrm{f}\left(\frac{x}{2}\right)\right)^2+\left(\mathrm{g}\left(\frac{x}{2}\right)\right)^2$, where $\mathrm{f}^{\prime \prime}(x)=-\mathrm{f}(x)$ and $\mathrm{g}(x)=\mathrm{f}^{\prime}(x)$ and given by $\mathrm{F}(5)=5$, then $F(10)$ is equal to

Let $P$ be the image of the point $(3,1,7)$ with respect to the plane $x-y+z=3$. Then the equation of the plane passing through $P$ and containing the straight line $\frac{x}{1}=\frac{y}{2}=\frac{z}{1}$ is