Group Theory | CUET PG Mathematics | Top 250 Questions Practice | MSQ & NAT Series | L-1

Group Theory | CUET PG Mathematics | Top 250 Questions Practice | MSQ & NAT Series | L-1 explained with clear concepts and exam-focused approach. This session covers Group Theory question practice for CUET PG Mathematics with MSQ and NAT series. Master PYQ-based problem-solving, order of elements, homomorphisms, and normal subgroups for competitive exams. 🔥 Join India's Best Mathematics Coaching for IIT JAM and CUET PG Exams: https://ifasonline.com/iit-jam/mathem... 📞 Need Guidance? Call/WhatsApp: 9172266888 ━━━━━━━━━━━━━━━━━━━━━━━━━ ⏳ Lecture Timeline: [00:00:00] – Introduction of Group Theory L-1 [00:01:40] – Question 1: Order of Element Divides n [00:06:58] – Question 2: Self-Inverse Elements Count [00:09:20] – Question 3: Elements of Order 9 in Z3×Z9 [00:11:30] – Question 4: Order of Disjoint Cycles (LCM) [00:13:20] – Question 5: Elements of Order 2 in 2n Group [00:15:10] – Question 6: Subgroups of Group Order 61 [00:17:00] – Question 7: Order of GL(2,Z2) [00:19:00] – Question 8: Group of Order 29 is Cyclic [00:21:00] – Question 9: {±1,±i} is Cyclic (Z4) [00:23:00] – Question 10: Direct Product Cyclic Condition [00:25:00] – Question 11: Number of r-Cycles in S_n [00:27:00] – Question 12: Same Cycle Type ⇒ Conjugate [00:29:00] – Question 13: Sylow p-Subgroup Statements [00:31:00] – Question 14: Finite Group in S_n (Cayley) [00:33:00] – Question 15: Aut(Z7) Isomorphic to Z6 [00:35:00] – Question 16: Homomorphisms Z12 to Z8 [00:37:00] – Question 17: Homomorphisms Z8 to Z20 [00:39:00] – Question 18: Normality & Product HN [00:41:00] – Question 19: Cayley Theorem: Permutation Group [00:43:00] – Question 20: Homomorphism Z onto Z2 [00:45:00] – Question 21: Inner Automorphism is Automorphism [00:47:00] – Question 22: Every Group to Permutation Group [00:49:00] – Question 23: Surjective Homomorphism & Cyclic Image [00:51:00] – Question 24: Z5 Homomorphism φ(2)=3 → φ(1) [00:52:43] – Complete Session (Group Theory L-1) ━━━━━━━━━━━━━━━━━━━━━━━━━ 📖 Topics Covered in This Lecture: • Order of Elements: a^n=e Concepts & Divisibility Tricks • Self-Inverse Elements: Cardinality & Group Order Relations • Counting Elements of Specific Order: Zn×Zm Product Methods • Disjoint Cycles: LCM Formula & Order of Permutation PYQ • Prime Order Groups: Cyclic & Simple Group Properties • Homomorphism Counting: gcd Method for Zn to Zm Problems • Normal Subgroups: Normality Transitivity & Product of Subgroups • Conjugacy Classes: Same Cycle Decomposition Criteria • Cayley Theorem: Embedding Groups into Permutation Groups • Inner Automorphism: f(x)=axa^-1 Properties & Counterexamples ━━━━━━━━━━━━━━━━━━━━━━━━━ 📚 Lecture Summary: In this session, IFAS Expert Faculty focuses on Group Theory important questions for CUET PG Mathematics. Key concepts include order of elements, self-inverse subsets, prime order groups, homomorphism counting, normal subgroups, conjugacy classes, and Cayley theorem. Problem-solving with PYQ relevance and counterexample-based tricks makes this Group Theory question practice session highly exam-oriented. ━━━━━━━━━━━━━━━━━━━━━━━━━ 🎓 This lecture is highly beneficial for students preparing for: ✅ IIT JAM Mathematics ✅ CUET PG Mathematics ✅ TIFR Mathematics ✅ NBHM Mathematics ━━━━━━━━━━━━━━━━━━━━━━━━ 🏆 Why IFAS is India’s No. 1 Choice for IIT JAM Chemistry & CUET PG? (Our Results Speak): 🌟 IIT JAM 2026 - Total Selections: 1100+ (AIR 2,3,6,....)  🌟 IIT JAM 2025 - Total Selections: 1000+ (AIR 1,3,4,6,7,8....)  🌟CUET PG 2025 - Total Selections: 1500+  🌟IIT JAM 2024: Total Selections: 800+ (AIR 1, 2, 3, 4, 8, 10...)  🌟CUET PG 2024: Total Selections: 500+  🌟IIT JAM 2023: Total Selections: 600+ (AIR 1, 2, 8, 9...)  🌟IIT JAM 2022: Total Selections: 500+ (AIR 1, 4, 7, 10...)  📄 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/iit-jam/mathem... ━━━━━━━━━━━━━━━━━━━━━━━━━ 🔗 India's Best Online Classes and Books: 🔥 IIT JAM Mathematics Live & Recorded Course: https://ifasonline.com/iit-jam/mathem... 🔥 CUET PG Mathematics Live & Recorded Course: https://ifasonline.com/cuet-pg/mathem... 📘IIT JAM Mathematics Books: https://ifasonline.com/iit-jam/mathem... ━━━━━━━━━━━━━━━━━━━━━━━━━ 📲 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 Discussion Group: https://t.me/IITJAM_NBHM_MScEntranceM... ✔ Instagram:   / ifas_maths__iit_jam_cuet_nbhm   #grouptheory #iitjammathematics #cuetpgmaths #ifas