Most Probable Questions | L04 | CSIR NET Jul 2026 | IFAS

Описание: In this session, IFAS Expert Faculty focuses on Most Probable Questions for CSIR NET Jul 2026, solving high-yield problems from Complex Analysis, PDE, Group Theory, and Linear Algebra. Key tricks covered: residue theorem for contour integrals, recurrence for ROC, PDE formation/solving, Sylow theorems, class equations. The approach links concepts to PYQ patterns, enhancing exam readiness. This Most Probable Questions session boosts retention with derivations and elimination strategies.

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⏳ Video Timeline:
[00:00:00] – Introduction to Most Probable Question L04
[00:02:10] – Question 1: Complex Integration (|z-1|=1)
[00:07:27] – Question 2: Residue Theorem for |z|=2
[00:15:41] – Question 3: ROC from Recurrence Relation
[00:23:41] – Question 4: Cauchy Integral (Zero)
[00:28:14] – Question 5: Argument Principle (tan z)
[00:31:56] – Question 6: Taylor Coefficient (sin z)
[00:36:45] – Concept: Removable Singularity (Bounded)
[00:38:24] – Concept: Entire Function, Range Restriction
[00:41:17] – Question 7: Removable Singularity (Limit)
[00:43:40] – Question 8: Contour Integral (Parametric)
[00:47:16] – Question 9: PDE Formation (Arbitrary Fns)
[00:52:12] – Question 10: First-Order PDE Solution
[00:57:17] – Question 11: General Solution (MSQ)
[01:03:03] – Question 12: Integral Surface of PDE
[01:10:26] – Question 13: PDE with Initial Data
[01:16:59] – Question 14: Cauchy Problem for PDE
[01:27:10] – Question 15: Particular Integral
[01:31:39] – Question 16: Number of Particular Integrals
[01:36:42] – Question 17: Classification of 2nd Order PDE
[01:43:27] – Question 18: Parabolic PDE Domain
[01:48:40] – Question 19: Basis of Subspace
[01:51:05] – Question 20: Sylow-2 Order in SL(3,7)
[01:56:44] – Question 21: Homomorphisms S3 to S4
[02:00:05] – Question 22: Normal Subgroups (A4 × D3)
[02:05:33] – Question 23: Group of Order 57
[02:12:47] – Question 24: Group of Order 1001
[02:19:24] – Question 25: Homomorphism Z → Z8×Z10
[02:26:05] – Question 26: Class Equation (Order 30)
[02:30:23] – Question 27: Matrix Multiplication Transform
[02:36:24] – Question 28: Idempotent Matrix Properties
[02:40:01] – Question 29: Column-Constrained Matrix
[02:48:02] – Question 30: 1-1 Homomorphisms Q8, D4
[02:52:23] – Question 31: Embedding into GL2(C)
[03:00:37] – Question 32: Minimal Polynomial via GCD
[03:05:40] – Question 33: Matrix with A³ = I
[03:10:11] – Question 34: Polynomial to Matrix Mapping
[03:16:52] – Complete Session (Most Probable Question L04)
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