Real Analysis | Last 5 Years PYQ Discussion | CSIR NET | MH SET | RJ SET | Lec-02 | IFAS

Real Analysis | Last 5 Years PYQ Discussion | CSIR NET | MH SET | RJ SET | Lec-02 | IFAS explained with clear concepts and exam-focused approach. Master Real Analysis PYQs for CSIR NET, MH SET, and RJ SET with problem-solving tricks on uniform continuity, sequences, and limits. 🔥Join India's Best Coaching for CSIR NET and GATE Exams: https://ifasonline.com/csir-net/mathe... 📞 Need Guidance? Call/WhatsApp: 9172266888 ━━━━━━━━━━━━━━━━━━━━━━━━━ ⏳ Lecture Timeline: [00:00:00] – Introduction to Real Analysis PYQs [00:07:27] – Question 1: Subsets with only even integers [00:09:10] – Question 2: Function properties & |f| [00:10:35] – Question 3: limsup & liminf of irrational sets [00:19:44] – Question 4: Preimage under piecewise function [00:20:17] – Concept: Archimedean Property [00:29:32] – Question 5: Cardinality of {0,1,2,3} sequences [00:32:51] – Question 6: Uniform continuity (x², cos x, sin x/x) [00:35:09] – Concept: Uniform Continuity Criteria [00:42:42] – Question 7: Two‑variable limit & continuity [00:47:26] – Trick: Rationalise square‑root differences [00:47:55] – Question 8: Limit with √(x²+3) – √(x²+2) [00:53:04] – Complete Session (Real Analysis PYQs) ━━━━━━━━━━━━━━━━━━━━━━━━━ 📖 Topics Covered in This Lecture: • Real Analysis PYQ Tricks & Pattern • Sequences, Limit Sup/Inf & Cardinality • Uniform Continuity (Compactness & Derivative) • Archimedean Property & Irrational Sets • Functions of Several Variables Limits • Rationalization & Convergence Tests ━━━━━━━━━━━━━━━━━━━━━━━━━ 📚 Lecture Summary: In this session, IFAS Expert Faculty focuses on Real Analysis last 5 years PYQ discussion. Key concepts: limit superior/inferior of irrational sequences, Archimedean property, uniform continuity criteria (compact domain, bounded derivative, sequential criterion), cardinality of sequence spaces, limits of two‑variable functions. Problem‑solving with PYQs reinforces Real Analysis exam techniques for CSIR NET, MH SET, RJ SET. ━━━━━━━━━━━━━━━━━━━━━━━━━ 🎓 This lecture is highly beneficial for students preparing for: ✅ CSIR NET Mathematical Science ✅ GATE Mathematics ✅ SET Mathematics ✅ TIFR Mathematics ✅ PhD Entrance Exams ━━━━━━━━━━━━━━━━━━━━━━━━━ 🏆 Why IFAS is India’s No. 1 Choice for CSIR NET & GATE Mathematics? (Our Results Speak): ✅ CSIR NET Dec 2025: 4000+ Selections (AIR 3, 8, 9.....) ✅ CSIR NET June 2025: 4200+ Selections (AIR 1, 2, 6, 10...) ✅ CSIR NET Dec 2024: 4000+ Selections (AIR 5, 6, 7, 8, 9...) ✅ CSIR NET June 2024: 2000+ Selections (AIR 3, 10, 13...) ✅ CSIR NET Dec 2023: 1200+ Selections (AIR 2, 4, 5...) 📄 View IFAS Result Sheet: 👉 https://drive.google.com/file/d/1THh6... ━━━━━━━━━━━━━━━━━━━━━━━━━ 🔗 Important Links: 🌍 Visit our Website: https://ifasonline.com 📞 Contact for Queries: 9172266888 📘 Free Counselling: https://ifasonline.com/csir-net/mathe... ━━━━━━━━━━━━━━━━━━━━━━━━━ 🔗 India's Best Online Classes and Books: 🔥CSIR NET Mathematical Science Live & Recorded Course: https://ifasonline.com/csir-net/mathe... 🎯 GATE Mathematics Recorded Course: https://ifasonline.com/gate/mathemati... 📘CSIR NET Mathematical Science Books: https://ifasonline.com/csir-net/mathe... ━━━━━━━━━━━━━━━━━━━━━━━━━ 📲 Download IFAS App: Android: https://play.google.com/store/apps/de... IOS: https://apps.apple.com/us/app/ifas/id... ━━━━━━━━━━━━━━━━━━━━━━━━━ Stay Updated Via Other Social Media: ✔Telegram: https://t.me/NET_GATE_SET_Maths_Discu... ✔Instagram:   / csir_net_mathematical_science   #realanalysis #pyq #csirnetmathematicalscience #gatemathematics #csirnetmaths #csirnetjune2026 #csirnetlecture #ifasmathematics