b
\(\begin{array}{l}
R = \frac{{{u^2}\sin 2\theta }}{g} = \frac{{2{u^2}\sin \theta .\cos \theta }}{g}\\
H = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}}\\
\therefore \,\frac{H}{R} = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}} \times \frac{g}{{2{u^2}\sin \theta .\cos \theta }}\\
\,\,\,\,\,\,\,\,\,\,\, = \frac{{\sin \theta }}{{4\cos \theta }}\\
 \Rightarrow \frac{R}{H} = \frac{{4\cos \theta }}{{\sin \theta }}\,or\,,\,\frac{R}{H} = 4\cos \theta 
\end{array}\)