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Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Department of Mathematics G. M. College Sambalpur Reviewed by Dr. C K Mohapatra P G Separtment of Mathematics Sambalpur University Published by Vaidik Anusandhan Parishad Ujalpur 770011 Orissa Printed at Satyabrata Printing Press Sambalpur Utkal Bharati Room Number 3 Eastern Tower Bhubaneswar 751009 Orissa The BEST E/29 B N A C Market New Station Road Rourkela 769011 The Authors of this book did not cover RMS ≥ AM ≥ GM ≥ HM For positive numbers RMS ≥ AM ≥ GM ≥ HM ( Recall AM is Arithmetic Mean, GM is Geometric Mean, HM is Harmonic Mean, and RMS is Root Mean Square ) (cid:3028)(cid:2878)(cid:3029) (cid:2870) (cid:3028)(cid:3118)(cid:2878)(cid:3029)(cid:3118) For positive numbers a and b AM is , GM is √𝑎𝑏, HM is and RMS is (cid:3495) (cid:2870) (cid:3117)(cid:2878)(cid:3117) (cid:2870) (cid:3159) (cid:3160) For positive numbers a, b and c AM is (cid:3028)(cid:2878)(cid:3029)(cid:2878)(cid:3030) , GM is (cid:3119)√𝑎𝑏𝑐, HM is (cid:2871) and RMS is (cid:2871) (cid:3117)(cid:2878)(cid:3117)(cid:2878)(cid:3117) (cid:3159) (cid:3160) (cid:3161) (cid:3028)(cid:3118)(cid:2878)(cid:3029)(cid:3118)(cid:2878)(cid:3030)(cid:3118) (cid:3495) (cid:2871) You will observe authors wrote only AM ≥ GM ≥ HM Contents 1 – Foreword (i) 2 – Acknowledgements (iii) 3 – Introduction (iv) 4 – Tool kit (x) 5 – Specimen Questions (xxiv) 6 – Examples – 1 Number Theory, Inequality, Logarithm, Trigonometry, Algebra, Arithmetic, Combinatorics, Set Theory, Logic 7 – Solutions to Examples - 15 8 – Problems for Practice – 67 Number Theory 72 Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Inequality – 76 Algebra – 82 Logarithm – 84 Arithmetic – 85 Combinatorics – 94 Set Theory & Logic – 99 Geometry – 101 Puzzles – 109 9 – Hints with Answers – 113 10 – Appendix – 211 11 – Problem set for practice – 259 Introduction Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions

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Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions PDF

310 Pages·1999·174.601 MB·English
by  Dr. Ujagar Patel Dr. Shishir Kumar Sahoo
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Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Department of Mathematics G. M. College Sambalpur Reviewed by Dr. C K Mohapatra P G Separtment of Mathematics Sambalpur University Published by Vaidik Anusandhan Parishad Ujalpur 770011 Orissa Printed at Satyabrata Printing Press Sambalpur Utkal Bharati Room Number 3 Eastern Tower Bhubaneswar 751009 Orissa The BEST E/29 B N A C Market New Station Road Rourkela 769011 The Authors of this book did not cover RMS ≥ AM ≥ GM ≥ HM For positive numbers RMS ≥ AM ≥ GM ≥ HM ( Recall AM is Arithmetic Mean, GM is Geometric Mean, HM is Harmonic Mean, and RMS is Root Mean Square ) (cid:3028)(cid:2878)(cid:3029) (cid:2870) (cid:3028)(cid:3118)(cid:2878)(cid:3029)(cid:3118) For positive numbers a and b AM is , GM is √𝑎𝑏, HM is and RMS is (cid:3495) (cid:2870) (cid:3117)(cid:2878)(cid:3117) (cid:2870) (cid:3159) (cid:3160) For positive numbers a, b and c AM is (cid:3028)(cid:2878)(cid:3029)(cid:2878)(cid:3030) , GM is (cid:3119)√𝑎𝑏𝑐, HM is (cid:2871) and RMS is (cid:2871) (cid:3117)(cid:2878)(cid:3117)(cid:2878)(cid:3117) (cid:3159) (cid:3160) (cid:3161) (cid:3028)(cid:3118)(cid:2878)(cid:3029)(cid:3118)(cid:2878)(cid:3030)(cid:3118) (cid:3495) (cid:2871) You will observe authors wrote only AM ≥ GM ≥ HM Contents 1 – Foreword (i) 2 – Acknowledgements (iii) 3 – Introduction (iv) 4 – Tool kit (x) 5 – Specimen Questions (xxiv) 6 – Examples – 1 Number Theory, Inequality, Logarithm, Trigonometry, Algebra, Arithmetic, Combinatorics, Set Theory, Logic 7 – Solutions to Examples - 15 8 – Problems for Practice – 67 Number Theory 72 Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Inequality – 76 Algebra – 82 Logarithm – 84 Arithmetic – 85 Combinatorics – 94 Set Theory & Logic – 99 Geometry – 101 Puzzles – 109 9 – Hints with Answers – 113 10 – Appendix – 211 11 – Problem set for practice – 259 Introduction Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions Mathematics Olympiad A Problem Solution Set Dr. Ujagar Patel Dr. Shishir Kumar Sahoo RMO INMO IMO Questions and Solutions

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