Preface to the New Edition It is very heartening that the new edition of our book “MATHEMATICS –IV” fully revised, is out to reach the B.Tech. Students of AKTU, Lucknow. It is as per the latest syllabi of all these university. Latest papers of these university have been included at the end and have been solved in the book. We sincerely thank all our valued readers for their time to time suggestion for the improvement of the book. The readers are requested to extend their suggestions to us which will be thankfully acknowledged.