Since the list does not talk about the books in any specific order, my recommendation would be #9 and #10. John Keay’s book is the perfect concise history of India, that I have come across. For a broad-based introduction to Indian History, this one is very good.
“In our quest to know what books to read to get a better understanding of India’s history, we turned to you, our readers. A few days ago we asked everyone on our Facebook and Twitter pages to recommend a book on Indian history. Many of you responded with some wonderful suggestions. We also received many e-mails suggesting books we had never heard of. Here then, is the list of 10 books (in no particular order) on Indian history that we have compiled based on your responses.”