If I want to post solutions of questions from books (with copyrights) on my blog, Is it violation of copyrights?
If there's a particular book you are talking about, check if it has a clause in T&C that explicitly says that you can use the content in it ONLY with author's permission. If there's such a clause, you may obtain necessary permissions by contacting the author before using his/her content. If not, can't really help.
Your post is little unclear, are you wanting to post answers to questions where the question is in the book, or post the answers from the book on your blog? If you are answering questions which are in a book then it shouldn't be a problem BUT if you are posting answers that you found in a book then this would be a blatant copyright infringement. Hope this helps.