Two balls are thrown as shown in the figure and they reach the ground in the same time. What is the ratio of the maximum heights attained by them?

$A$ car moving with a linear speed of $72 \ km/h$ has wheels of radius $0.250 \ m$. If the wheels come to rest after $20$ rotations upon applying brakes,the angular retardation produced by the brakes is ....... $rad \ s^{-2}$. (in $.5$)

$A$ charged particle of mass $m = 2 \ kg$ and charge $q = 1 \ \mu C$ is projected from a horizontal ground at an angle $\theta = 45^{\circ}$ with speed $u = 10 \ ms^{-1}$. In space,a horizontal electric field $E = 2 \times 10^7 \ NC^{-1}$ exists in the direction of projection. The range of the projectile is......$m$.

Given that $u_x$ = horizontal component of initial velocity, $u_y$ = vertical component of initial velocity, $R$ = horizontal range, $T$ = time of flight, and $H$ = maximum height of a projectile. Match the following two columns:

Column $I$	Column $II$
$(A)$ $u_x$ is doubled, $u_y$ is halved	$(p)$ $H$ will remain unchanged
$(B)$ $u_y$ is doubled, $u_x$ is halved	$(q)$ $R$ will remain unchanged
$(C)$ $u_x$ and $u_y$ both are doubled	$(r)$ $R$ will become four times
$(D)$ Only $u_y$ is doubled	$(s)$ $H$ will become four times

$A$ projectile can have the same range $(R)$ for two angles of projection. Their initial velocities are same. If $T_1$ and $T_2$ are times of flight in two cases,then the product of two times of flight is directly proportional to

$A$ projectile of mass $200 \ g$ is launched in a viscous medium at an angle $60^{\circ}$ with the horizontal,with an initial velocity of $270 \ m/s$. It experiences a viscous drag force $\vec{F} = -c \vec{v}$,where the drag coefficient $c = 0.1 \ kg/s$ and $\vec{v}$ is the instantaneous velocity of the projectile. The projectile hits a vertical wall after $2 \ s$. Taking $e = 2.7$,the horizontal distance of the wall from the point of projection (in $m$) is