Automatically list all tags along with all post titles of particular category

On a page I want to automatically display following result of a particular category:
 
Tag 1:

• Post 01
• Post 05
• Post 12
• Post 121

Tag 6:

• Post 06
• Post 12
• Post 30
• Post 70

Tag 10:

• Post 07
• Post 09
• Post 81
• Post 70

******************************************************
I want all the tags of particular category automatically displayed.
I also want all post title to be displayed under each tag.
Please give me the PHP code to achieve this result on a page.

[duplicate topic moderated – please start only one topic per problem]