a tankis filled up to a height 2H WITH A LIQUID and is placed on a platform of height H from the ground .the distance x from the ground where a small hole is punched to get maximum range R is?

H/2.

let the distance be x.

then range(R)=2 . [(3H-x).x]^1/2 ......................... [ since t=(2x/g)^1/2 and v={2g(3H-x)}^1/2  ]

 R^2 = 4.(3Hx-x^2)

 for R to be max...R^2 should be max.

hence differentiating and putting d(R^2)/dx=0.
we get 3H-2x=0

x=3H/2 (ANS).                                                   

you have to differentiate it

3h/2

use torcellies law to find the horizontal velocity then as projectile motin calcute the range

then diffrentiate to get the desired result