Uploaded September 2026 | Updated September 2026, 3 weeks ago
UPSC CSE Mains 2026 Mathematics Optional โ Paper 1 aur Paper 2 dono ka complete question-wise analysis by Rajneesh Kumar Srivastava (Unacademy). Is video mein har question ka solution approach, method, aur ye batatey hain ki kaise saare questions unke class notes se hi aaye the โ koi bhi question out of syllabus ya out of trend nahi tha.
๐ฅ Join the 10th Batch on Unacademy โ
Complete Course Of Mathematics Optional Paper-1: unacademy.app.link/jc65sFr525b
~~~~~~~~~~~~~
โฑ๏ธ TIMESTAMPS
00:00 โ Introduction
02:58 โ Paper 1 Begins
02:58 โ Q1: System of Linear Equations (Matrices)
08:38 โ Q1: Diagonalizable & Similar Matrices
14:25 โ Q1: Maclaurin's Theorem
25:05 โ Q1: Equation of Sphere
39:36 โ Q1: Subspace, Basis & Direct Sum
42:14 โ Q2: Matrix of Linear Transformation
35:34 โ Q2: Maxima-Minima of One Variable
37:46 โ Q2: Shortest Distance Between Two Lines
42:14 โ Q3: Subspace, Direct Sum
42:14 โ Q3: Double Integral (Change of Order of Integration)
46:32 โ Q3: Region Bounded by Triangle/Tetrahedron
50:47 โ Q3: Cone โ Perpendicular Generators
58:24 โ Q3: Curve Tracing
1:11:04 โ Section B (Paper 1) Begins
1:11:04 โ Q5: Linear Differential Equation (2nd Order)
1:12:32 โ Q5: Laplace Transform + ODE
1:16:31 โ Q5: Mechanics โ Friction
1:22:23 โ Q5: Catenary
1:22:01 โ Q5: Stokes' Theorem
1:25:03 โ Q6: Homogeneous Linear DE with Constant Coefficients
1:27:28 โ Q6: Projectile Motion
1:30:53 โ Q6: Friction (Statics)
1:37:37 โ Q6: Curvature & Torsion
1:38:19 โ Q7: Elastic String
1:38:24 โ Q7: Gauss Divergence Theorem
1:39:03 โ Q7: Integrating Factor + Laplace/Convolution
1:41:28 โ Q8: Variation of Parameters
1:42:41 โ Q8: Stable & Unstable Equilibrium
1:46:46 โ Q8: Curl of A + Scalar Triple Product
1:47:18 โ Paper 2 Begins
1:47:36 โ Section A Topics Overview
1:48:06 โ Q1: Group Theory (Order of Subgroups)
1:48:49 โ Q1: Prime Ideal & Maximal Ideal
1:49:38 โ Q1: Continuity & Differentiability
1:50:41 โ Q1: Complex Analysis (Analytic Function)
1:57:41 โ Q1: Duality (LPP)
1:53:02 โ Q2: Isomorphism/Homomorphism
1:53:18 โ Q2: Sequence & Series
1:54:40 โ Q2: Contour Integration
1:56:22 โ Q2: Residue Theorem
1:57:41 โ Q3: Riemann Integral
1:58:33 โ Q3: Assignment Problem (LPP)
1:59:56 โ Q4: Galois Theory (Z/nZ)
2:00:48 โ Q4: Improper Integral
2:01:41 โ Q4: Simplex Method (LPP)
2:15:19 โ Section B (Paper 2) Begins
2:15:19 โ Q5: Lagrange's Method (PDE)
2:03:05 โ Q5: Newton-Raphson Method
2:04:30 โ Q5: Boolean Expression / Logic Gates
2:05:26 โ Q5: Velocity Potential (Fluid Dynamics)
2:06:21 โ Q5: Motion in Two Dimensions (Rigid Body)
2:07:19 โ Q6: Canonical Form (PDE)
2:07:48 โ Q6: Number System Conversion
2:08:14 โ Q6: Milne-Thomson (Fluid Dynamics)
2:09:00 โ Q7: Linear PDE with Constant Coefficients
2:09:45 โ Q7: Simpson's 1/3 & 3/8 Rule
2:10:04 โ Q7: Lagrangian Method
2:11:00 โ Q8: PDE โ Polar Form
2:11:43 โ Q8: Euler's Method
2:12:12 โ Q8: Dynamics โ Motion in Vertical Circle
2:15:20 โ Closing Remarks
๐ Subscribe for more UPSC CSE Mathematics Optional strategy, paper analysis, and daily prep tips.
~~~~~~~~~~~
#UPSC #UPSCCSE #MathematicsOptional #UPSCMains #UPSCMains2026 #MathsOptional #UPSCPreparation #IAS #CivilServices #UPSCStrategy #Unacademy #UPSCMotivation #MathsForUPSC #UPSCAnswerWriting
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UPSC CSE Mains 2026 Mathematics Optional โ Paper 1 aur Paper 2 dono ka complete question-wise analysis by Rajneesh Kumar Srivastava (Unacademy). Is video mein har question ka solution approach, method, aur ye batatey hain ki kaise saare questions unke class notes se hi aaye the โ koi bhi question out of syllabus ya out of trend nahi tha.
๐ฅ Join the 10th Batch on Unacademy โ
Complete Course Of Mathematics Optional Paper-1: unacademy.app.link/jc65sFr525b
~~~~~~~~~~~~~
โฑ๏ธ TIMESTAMPS
00:00 โ Introduction
02:58 โ Paper 1 Begins
02:58 โ Q1: System of Linear Equations (Matrices)
08:38 โ Q1: Diagonalizable & Similar Matrices
14:25 โ Q1: Maclaurin's Theorem
25:05 โ Q1: Equation of Sphere
39:36 โ Q1: Subspace, Basis & Direct Sum
42:14 โ Q2: Matrix of Linear Transformation
35:34 โ Q2: Maxima-Minima of One Variable
37:46 โ Q2: Shortest Distance Between Two Lines
42:14 โ Q3: Subspace, Direct Sum
42:14 โ Q3: Double Integral (Change of Order of Integration)
46:32 โ Q3: Region Bounded by Triangle/Tetrahedron
50:47 โ Q3: Cone โ Perpendicular Generators
58:24 โ Q3: Curve Tracing
1:11:04 โ Section B (Paper 1) Begins
1:11:04 โ Q5: Linear Differential Equation (2nd Order)
1:12:32 โ Q5: Laplace Transform + ODE
1:16:31 โ Q5: Mechanics โ Friction
1:22:23 โ Q5: Catenary
1:22:01 โ Q5: Stokes' Theorem
1:25:03 โ Q6: Homogeneous Linear DE with Constant Coefficients
1:27:28 โ Q6: Projectile Motion
1:30:53 โ Q6: Friction (Statics)
1:37:37 โ Q6: Curvature & Torsion
1:38:19 โ Q7: Elastic String
1:38:24 โ Q7: Gauss Divergence Theorem
1:39:03 โ Q7: Integrating Factor + Laplace/Convolution
1:41:28 โ Q8: Variation of Parameters
1:42:41 โ Q8: Stable & Unstable Equilibrium
1:46:46 โ Q8: Curl of A + Scalar Triple Product
1:47:18 โ Paper 2 Begins
1:47:36 โ Section A Topics Overview
1:48:06 โ Q1: Group Theory (Order of Subgroups)
1:48:49 โ Q1: Prime Ideal & Maximal Ideal
1:49:38 โ Q1: Continuity & Differentiability
1:50:41 โ Q1: Complex Analysis (Analytic Function)
1:57:41 โ Q1: Duality (LPP)
1:53:02 โ Q2: Isomorphism/Homomorphism
1:53:18 โ Q2: Sequence & Series
1:54:40 โ Q2: Contour Integration
1:56:22 โ Q2: Residue Theorem
1:57:41 โ Q3: Riemann Integral
1:58:33 โ Q3: Assignment Problem (LPP)
1:59:56 โ Q4: Galois Theory (Z/nZ)
2:00:48 โ Q4: Improper Integral
2:01:41 โ Q4: Simplex Method (LPP)
2:15:19 โ Section B (Paper 2) Begins
2:15:19 โ Q5: Lagrange's Method (PDE)
2:03:05 โ Q5: Newton-Raphson Method
2:04:30 โ Q5: Boolean Expression / Logic Gates
2:05:26 โ Q5: Velocity Potential (Fluid Dynamics)
2:06:21 โ Q5: Motion in Two Dimensions (Rigid Body)
2:07:19 โ Q6: Canonical Form (PDE)
2:07:48 โ Q6: Number System Conversion
2:08:14 โ Q6: Milne-Thomson (Fluid Dynamics)
2:09:00 โ Q7: Linear PDE with Constant Coefficients
2:09:45 โ Q7: Simpson's 1/3 & 3/8 Rule
2:10:04 โ Q7: Lagrangian Method
2:11:00 โ Q8: PDE โ Polar Form
2:11:43 โ Q8: Euler's Method
2:12:12 โ Q8: Dynamics โ Motion in Vertical Circle
2:15:20 โ Closing Remarks
๐ Subscribe for more UPSC CSE Mathematics Optional strategy, paper analysis, and daily prep tips.
~~~~~~~~~~~
#UPSC #UPSCCSE #MathematicsOptional #UPSCMains #UPSCMains2026 #MathsOptional #UPSCPreparation #IAS #CivilServices #UPSCStrategy #Unacademy #UPSCMotivation #MathsForUPSC #UPSCAnswerWriting
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