what will be zero multiplied by infinity or zero divided by infinity or vice versa?

　
Well we can't really multiply or divide 0 and infinity.
The only time these have any meaning is when dealing with limits.

So if you are calculating a limit and get 0*∞, this is indeterminate and you'll need to use other methods to find the actual limit.
Other indeterminate forms are: 0/0, ∞/∞, ∞−∞, 0^0, 1^∞, ∞^0

For purposes of limits: 1/∞ = 0, and 1/0 = ±∞ (depending on whether we are approaching 0 from the right or the left)
Therefore
0/∞ = 0 * 1/∞ = 0*0 = 0
∞/0 = ∞ * 1/0 = ∞*±∞ = ±∞

zero multiplied by infinity is indeterminate

zero divided by infinity is 0