This book has been written by a pioneer teacher associated with JEE (Main & Advanced) coaching, Dr. G.S.N. Murti, along with Dr. U.M. Swamy who had an illustrious career as a renowned mathematician. The topics covered in this book - Trigonometry, Vector Algebra, and Probability - are of utmost importance to engineering students. An additional chapter on Inequalities has been included. The book has a two-fold advantage: (a) Conceptual strength provided by accurate, precise but sufficient coverage of topics; (b) solved and unsolved problems as per JEE (Main & Advanced) pattern for strengthening concepts. The main idea is to make students understand the theory behind to enable them to strategize a given problem and tactically solve it.