Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$,but different maximum heights,$h_1$ and $h_2$. Which of the following is correct?

$A$ projectile is projected from the ground with an initial velocity $\vec{u} = u_0 \hat{i} + v_0 \hat{j}$. If the acceleration due to gravity $g$ is along the negative $y$-direction,find the maximum displacement in the $x$-direction (horizontal range).

Two projectiles are fired with the same initial speed from the same point on the ground at angles of $(45^{\circ}-\alpha)$ and $(45^{\circ}+\alpha)$,respectively,with the horizontal direction. The ratio of their maximum heights attained is:

$A$ projectile is thrown at an angle $\theta$ with the horizontal and its range is $R_1$. It is then thrown at an angle $\theta$ with the vertical and the range is $R_2$. Then:

$A$ particle is projected in air at some angle to the horizontal and moves along a parabola as shown in the figure,where $x$ and $y$ indicate horizontal and vertical directions,respectively. The diagram shows the direction of velocity and acceleration at points $A$,$B$,and $C$.

Given below are two statements. One is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: Two identical balls $A$ and $B$ thrown with the same velocity '$u$' at two different angles with the horizontal attain the same range $R$. If $A$ and $B$ reach maximum heights $h_{1}$ and $h_{2}$ respectively,then $R = 4 \sqrt{h_{1} h_{2}}$.
Reason $R$: The product of the said heights is $h_{1} h_{2} = \left(\frac{u^{2} \sin^{2} \theta}{2g}\right) \cdot \left(\frac{u^{2} \cos^{2} \theta}{2g}\right)$.
Choose the $CORRECT$ answer.