Gears jumping/slipping from the rear cogset on a new bike Its been 1 month since I have bought my new MTB (Kross globate 1.1) with 18 gears (shimano)..
Now the problem is chain has slipped twice while riding. First time my speed was around 25kph and second time it was low around 15kph.

And another point to notice is that my gears are not working properly... chain does not move to other sprocket when I change my gear from rear 6 to rear 5 or vice versa, they start changing afterwards...

What could be the problem?
Parts need a break in time to stretch, flex, and do what they do before they kind of settle in. When I worked at a bikeshop, we told our customers to come in after a month or 2 so that we could go through and get everything tuned up to where it should be after the break in period.

Not only is your situation normal, most bike shops WANT you to bring it back to them, so they can get it running the way it should so you are happy with your purchase. Take it back to the shop and have them tune it up, it should be included in the purchase price.