a
For same range \(\theta_{1}+\theta_{2}=90^{\circ}\)

\(h _{1} h _{2}=\frac{ u ^{2} \sin ^{2} \theta_{1}}{2 g } \times \frac{ u ^{2} \sin ^{2} \theta_{2}}{2 g }\)

\(\theta_{2}=90-\theta_{1}\)

\(h _{1} h _{2}=\frac{ u ^{2} \sin ^{2} \theta_{1}}{2 g } \cdot \frac{ u ^{2} \cos ^{2} \theta_{1}}{2 g }\)

\(=\left[\frac{ u ^{2} \sin \theta_{1} \cos \theta_{1}}{2 g }\right]^{2}\)

\(=\left[\frac{ u ^{2} \sin \theta_{1} \cos \theta_{1}}{2 g } \times \frac{2}{2}\right]^{2}=\frac{ R ^{2}}{16}\)

\(R =4 \sqrt{ h _{1} h _{2}}\)

So \(R\) is correct explanation of \(A\)