The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2m on the surface of A. What is the height of jump by the same person on the planet B.

The man jumps with the same take-off speed u on both planets, so the kinetic energy he gives himself is the same.
At the highest point this kinetic energy becomes potential energy: $\dfrac{1}{2}mu^2 = mgh$, so $gh$ = constant, i.e. $h \propto \dfrac{1}{g}$.
Height of jump on planet B $= \dfrac{g_A}{g_B} \times$ height of jump on planet A
$h_B = 9 \times 2 = 18$ m
So the man jumps 18 m on planet B.