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GATE 2025 Mathematics (MA) previous year question solved in detail with complete conceptual clarity and exam-oriented approach. ➡️ Website Login / Sign-Up 👉 https://www.aingmathematics.com ➡️ Buy TIFR Mathematics Solutions E-Book 👉 https://www.aingmathematics.com/learn... 📌 Aing Mathematics Telegram Group 👉 https://t.me/aingmaths 📌 Lalit Sir & Basant Sir’s Telegram Group 👉 https://t.me/lalitthuw 🎥 Interviews & Exam Experience Playlist (NBHM / CSIR-NET / TIFR / PhD) 👉 • Interview Experiences Join this channel to get access to perks: / @aingmathematics Are you preparing for NET, GATE, TIFR, NBHM, JAM, ISI, CMI, or any other competitive exam, or even a PhD interview? Join Aing Mathematics and take your preparation to the next level! How to reach us: 📞 WhatsApp/Call: 7483062013 📧 Email: aingmathematics@gmail.com Join our active Telegram communities for updates, study materials, and discussions: 📌 Aing Mathematics Group: https://t.me/aingmaths 📌 Lalit and Basant Sir’s Group: https://t.me/lalitthuw Meet our Faculty: • Lalit Sir (NET JRF AIR 4, GATE, TIFR, IISc, NBHM HRI) • Basant Sir (NET, GATE, INSPIRE, JRF, USET) Don’t miss out on expert guidance and comprehensive solutions to ace your exams. Subscribe now for more detailed solutions to challenging problems, and stay updated on new content and resources! This video contains the complete solution of Question Number 50 from GATE 2025 (Mathematics – MA). The problem is based on the concept of Orthogonal Projection in Functional Analysis. In this video, we explain the solution step-by-step with proper mathematical reasoning and standard exam-oriented methodology. Such problems are very important for: • GATE Mathematics • CSIR-NET (Mathematical Sciences) • NBHM • TIFR / CMI / ISI • PhD entrance examinations These solution videos are aimed at helping students understand concepts deeply, not just memorize formulas. GATE 2025 MA question 50 GATE 2025 mathematics solution GATE 2025 orthogonal projection Orthogonal projection GATE GATE linear algebra questions GATE MA solved questions GATE 2025 MA solutions GATE mathematics linear algebra CSIR NET linear algebra NBHM mathematics TIFR mathematics preparation PhD entrance maths Orthogonal projection problems #GATE2025 #GATEMathematics #GATEMA #OrthogonalProjection #LinearAlgebra #GATEQuestion50 #GATESolution #CSIRNET #NBHM #TIFR #MathsPreparation