#NDA/ NA 17 year Topic-wise Solved Papers (2006 - 2022) consists of last 17 years from 2006 - 2022 solved papers of Mathematics distributed into 24 topics. #In all there are 31 Question papers (2006 April - 2022 April). #The book is distributed into 24 topics containing 3720 MCQ’s from the above 31 Question papers. #The strength of the book lies in the originality of its question papers and Errorless Solutions. #The solution of each and every question is provided in detail (step-by-step) so as to provide 100% concept clarity to the students.

Knowledge updating is a never-ending process and so should be the revision of an effective textbook. The book originally written fifty years ago has, during the intervening period, been revised and reprinted several times. The authors have, however, been thinking, for the last few years that the book needed not only a thorough revision but rather a substantial rewriting. They now take great pleasure in presenting to the readers the twelfth, thoroughly revised and enlarged, Golden Jubilee edition of the book. The subject-matter in the entire book has been re-written in the light of numerous criticisms and suggestions received from the users of the earlier editions in India and abroad. The basis of this revision has been the emergence of new literature on the subject, the constructive feedback from students and teaching fraternity, as well as those changes that have been made in the syllabi and/or the pattern of examination papers of numerous universities. Knowledge updating is a never-ending process and so should be the revision of an effective textbook. The book originally written fifty years ago has, during the intervening period, been revised and reprinted several times. The authors have, however, been thinking, for the last few years that the book needed not only a thorough revision but rather a substantial rewriting. They now take great pleasure in presenting to the readers the twelfth, thoroughly revised and enlarged, Golden Jubilee edition of the book. The subject-matter in the entire book has been re-written in the light of numerous criticisms and suggestions received from the users of the earlier editions in India and abroad. The basis of this revision has been the emergence of new literature on the subject, the constructive feedback from students and teaching fraternity, as well as those changes that have been made in the syllabi and/or the pattern of examination papers of numerous universities. Knowledge updating is a never-ending process and so should be the revision of an effective textbook. The book originally written fifty years ago has, during the intervening period, been revised and reprinted several times. The authors have, however, been thinking, for the last few years that the book needed not only a thorough revision but rather a substantial rewriting. They now take great pleasure in presenting to the readers the twelfth, thoroughly revised and enlarged, Golden Jubilee edition of the book. The subject-matter in the entire book has been re-written in the light of numerous criticisms and suggestions received from the users of the earlier editions in India and abroad. The basis of this revision has been the emergence of new literature on the subject, the constructive feedback from students and teaching fraternity, as well as those changes that have been made in the syllabi and/or the pattern of examination papers of numerous universities. Some prominent additions are given below: 1. Variance of Degenerate Random Variable 2. Approximate Expression for Expectation and Variance 3. Lyapounov’s Inequality 4. Holder’s Inequality 5. Minkowski’s Inequality 6. Double Expectation Rule or Double-E Rule and many others

"The ongoing COVID-19 pandemic marks the most significant, singular global disruption since World War II, with health, economic, political, and security implications that will ripple for years to come." -Global Trends 2040 (2021) Global Trends 2040-A More Contested World (2021), released by the US National Intelligence Council, is the latest report in its series of reports starting in 1997 about megatrends and the world's future. This report, strongly influenced by the COVID-19 pandemic, paints a bleak picture of the future and describes a contested, fragmented and turbulent world. It specifically discusses the four main trends that will shape tomorrow's world: - Demographics-by 2040, 1.4 billion people will be added mostly in Africa and South Asia. - Economics-increased government debt and concentrated economic power will escalate problems for the poor and middleclass. - Climate-a hotter world will increase water, food, and health insecurity. - Technology-the emergence of new technologies could both solve and cause problems for human life. Students of trends, policymakers, entrepreneurs, academics, journalists and anyone eager for a glimpse into the next decades, will find this report, with colored graphs, essential reading.

1. Pathfinder NDA/NA Entrance Examination - prescribed under UPSC Guidelines. 2. The Self Study Guide divides the entire syllabus in 4 Major Sections 3. Provides 5 Previous Years' Solved Papers for practice 4. More than 8000 MCQs for quick revision of topics 5. Chapterwise division of Previous Years' Questions. 6. Gives deep insight of the paper pattern, its types and weightage in the exam. Mark Twain once said, “Patriotism is supporting your country all time and government when it deserves it”. The Union services commission or UPSC has released the notification of about 413 seats for the NDA/NA exam 2022. Here comes the updated edition of the Pathfinder series “NDA/NA Entrance Examination” comprehensively complete syllabus of entrance examination as prescribed by UPSC. The book has been divided into chapters that are categorized under 4 major subjects; Mathematics, General English, General Science, General Studies providing a complete coverage. Each chapter of every section has been well explained with proper theories for better understanding. More than 8000 MCQs and Previous Years’ Solved Papers are providing a deep insight for examination patterns and types of questions asked in the exam. Chapterwise Division of Previous Years’ Solved Papers are provided with well detailed answers to clarify all the doubts. This book a must have for those who aim to score high for upcoming NDA/NA Exam. TOC NDA/NA Solved Paper 2021 – 2017 (I & II), , General English, General Science, General Studies.