If the equation $\mathrm{k} x y+10 x+8 y+16=0$ represents a pair of lines, then

If the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{x}{y}=\frac{\mathrm{a}}{y}$ where a is constant, represents a family of circles then the radius of the circle is $\qquad$

If $2 \mathrm{f}(x)+3 \mathrm{f}\left(\frac{1}{x}\right)=x^2+1, x \neq 0$ and $y=5 x^2 \mathrm{f}(x)$, then $y$ is strictly increasing in

The possible values of $\theta \in(0, \pi)$ such that $\sin \theta+\sin (4 \theta)+\sin (7 \theta)=0$ are