how many steps 2 take2 checkmate when king alone.

in india we use only 16 steps.

I think that you are asking about the fifty move rule.

There's no special rule concerning a bare King.

For example:

What do you mean by steps?  Do you mean moves?

The "rule" in both USCF and FIDE is you get 50 moves (by each player) to either mate the King or else have something of yours captured (since there is nothing left to capture of his) or else for you to move a pawn.  Once you move a pawn, or any piece or pawn is captured, the count starts over.

Of course, against a lone king, it depends on what you have left how many moves it should take in the worst case scenario.

If White actually proceeds to think about it, if my memory serves me right, in the absolute worst case scenario for each, the follow can be done with "best play":

K+Q vs Lone K - Mate in 9

K+R vs Lone K - Mate in 13

K+2B vs Lone K - Mate in 17

K+B+N vs Lone K - Mate in 33

Again, these may each be off by a move.

I thought King couldn't mate alone, he could only try and bring a draw by breaking the fifty move rule.

You've missed the point, see posts 2 & 3.

idk