The JNU entrance exam for history is usually divided into two parts- one, which is a comprehension section and consists of a passage to read and has questions based on it. This section cannot be planned for very definitely, because the passages are very random. However one thing you can do, is practice from comprehension passages available in bookstores. You should aim at finishing these questions as soon as possible so that you can proceed to the next section.
The second section has a list of about 12–15 questions out of which you will be asked to answer any 3. The questions are overwhelmingly based on history, but are very broad. For example, a comparison between the methods of Gandhi, moderates and extremists; or a review of the scholarship of Mughal administration or even a comparative survey of the differing rates of industrial productivity in England, France and Germany. Popular questions in the past have been on Sufism, Bhakti movements (very broad questions which test your basics rather than ask specific details), ideas of gender in ancient India, factors contributing to the rise of Jainism and Buddhism and relating to European and Indian merchant trade in the Indian Ocean (1200–1700).
Romila Thapar’s, A History of India is great for the basics in Ancient India. She covers the basic field. Upinder Singh’s text on Ancient India is really good too. Satish Chandra’s, A History of Medieval India, and his volume of collected essays cover medieval India and Sekhar Bandopadhyay’s, From Plassey to Partition is a well researches, lucid and does not take a lot of time to read. It covers Modern India. Books such as ‘The Mughal Empire’ by J.F. Richards (published by Cambridge in India, costs rs. 125) cover Mughals pretty well and the Cambridge Economic History of India (volume 1, edited Irfan Habib and Tapan Raychaudhri) is great for economic history questions on trade, revenue and administration.