Does buying an expired domain helps in fast ranking on Google?

The first sentence from PaulHoule is 100% spot on. Additionally, you can't just point the expired domain with backlinks at your domain and think its rankings are magically going to boost your rankings.

First off, the domain needs to be somewhat relevant to the topic of the site you are redirecting it to.

Second, make sure you actually reproduce the site to allow Google to understand the domain is online and active again before you simply redirect it.

Basically, to do the "expired domain" tactic right, you are going to need to find one with backlinks worth leveraging, on a topic closely related to yours, and put the site back online for at least 90 days before you redirect.

If you're going to do this (and want to do it right) make sure the juice is worth the squeeze.

If it has a lot of incoming links you get real traffic from them. Any credit you get for links from Google on any web site is hypothetical today.