What are pull-ups?
Grab a Horizontal Bar above you and pull yourself to the Point where your nose is parallel to the Iron rod. You should literally be able to smell the iron rod Or Taste the iron if it is fine with you.
That's "Pull ups" for you .
If you want to have a tight squeeze in the back, recruiting those lats or having a sound mind muscle connection then try to drive your elbows into your hips and hold it for couple of moments.
If you want to yank out Multiple pushups which is the hardest thing to do, work on your secondary muscles forearms, grip strength, core strength ..