I am a non-native speaker of English with a near-native command of
English but I am weak in a particular area. I often make mistakes in
using the articles/ determiners 'a/an' and 'the'.

I shall be thankful if you could suggest a book that 
1. has a VERY large number of exercises (intermediate and advanced level)
2. has answers to the exercises, which are adequately EXPLAINED

Kindly note I am looking for a SPECIFIC book, not sympathy or a
general lecture etc. Thanks

"Fowler's English Usage" published by Oxford University Press does not
contain excersises but is a very useful book.

Hello aaz-ga,

I'm placing this as a comment, not an answer, because I cannot direct
to a definite purchase of the resource you need.

Unfortunately, I have only been able to find a book that appears to be
out of print:
Collins COBUILD English Guides 3: Articles
Author: Roger Berry
ISBN: 000 370561/7 Paperback
Extent: 128 pages
Format: 181mmx112mm
"Collins COBUILD English Guides provide extensive information on
specific areas of today's English, using the evidence from The Bank of
English to select what is really important. This book is suitable for
upper-intermediate and advanced students and teachers of English. It
focuses on the most frequent words in English: the definite article
the and the indefinite article a or an. Articles are a recognised
problem area for learners of English and this book provides
comprehensive treatment of them. It describes the different uses of
articles, and explains those situations in which no article is used.
Detailed description of the uses of articles  * Hundreds of real
examples * Exercises and answer key"
This is featured on http://www.athel.com/cobuild/eguid3.html at a
price of $14.95.  However, it is not possible to get back to this page
from the site's home page, which makes me suspect the book is no
longer available.  The site is that of Athelstan, a Houston company
that specialises in language learning resources. 
http://www.athel.com/about.html provides contact details.

I did check for this book on the COBUILD pages of the Harper-Collins
site, but it is not listed there.
http://www.collins.co.uk/books.aspx?group=151

You might try contacting some libraries to see if they can obtain it for you. 
 
There is a fairly detailed account of the topic at 
http://www.unc.edu/depts/wcweb/handouts/articles.html (from the
Writing Center, University of North Carolina at Chapel Hill), which
includes a short bibliography. None of these references is to a book
as specific as you require.  One reference is to another article on
the Web, which includes a small number of exercises with explanations
of the answers:
Kohl, John R. "Article Usage." The Writing Center at Rensselaer
Polytechnic Institute. Available at
http://www.rpi.edu/dept/llc/writecenter/web/esl.html

tehuti

What is your native language?  That could have alot to do with your
problem.  I assume it is not a Romance language, for example, as these
have definite and indefinite articles easily translatable to Emnglish.

Written by an ESL teacher for ESL students:

http://www.metaphoricaldwelling.org/Language/index.html#defarticletag