Google Nexus 5 — Unwanted contact from LinkedIn & Google account are still in the memory.

Hi,

I have recently bought Nexus 5. I am having 2 issues in reference to the unwanted contacts from LinkedIn & Google account.

1. Linked Contact:- I have around 500+ connection on my linked in when I have downloaded this app it has asked me to sync the contacts which I have synced than I thought I shouldn't be having so many contacts in my phone. To overcome that I have removed all the unwanted connection from the Linked and kept all the necessary one. But when I am searching contact in phone it still shows the old contacts but when I go to the contact app of android it doesn't have those contacts.
2. Google Contact:- Same as above I have also deleted the contact from my gmail account; although there are no contacts showing in the contact app; but when I search from the 'dialpad' it displays those earlier removed contact.

What could be the possible cause of this and how to overcome the same and remove all the unnecessary contacts from my phone even while searching from dialpad.

Note:- Sync has been turned on for contacts for both the apps.

Thanks for your help

Regards,
Nitesh Sharma