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Language: ENGLISH
Instructors: SuccessClap
Valid Till: 20241101
Weekly Test Series for UPSC CSE 2024
Total 45 TESTS for Practice
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Test No 
Date 
Topic Covered 
References 






Linear Algebra 

1 
July 2 2023 
Matrix: Find Rank of Matrices Given Matrix, Find Inverse and Express High order Matrix Polynomial in terms of A Find Inverse using ONLY ELEMENTART ROW OPERATION Given Matrices, find Eigen Values and eigen Vectors State and Prove Cayley Hamilton theorem Given Matrix A, Find A(power of 300 ) using Cayley Hamilton Given Homogeneous Equation, Find Dimension and Basis Linear Eqn , Find Condition for No Solution , Unique Solution ,Infinite Solutions Theorems and Problems from Krishna Series Book
Eigen Values, Vectors Orthogonality Similarity Diagonalizable Quadratic Form 
MatricesKrishna Series 
2 
July 9 2023 
Vector Spaces, Subspaces Basis, Dimensions, Nullity
Linear Transformation: Given Linear Transformation, Find a) Rank, b) Nullity c) Range Space d) Null Space Given Matrix Form of Linear Transformation, Find a) Rank, b) Nullity c) Range Space d) Null Space Given Linear Transformation with Two Different Bases Sets, Find Matrix Given Linear Transformation with Standard Basis. Find Matrix relative to New Basis Set 
Any Graduation Text Book covers this Syllabus Schaum Series Linear Algebra : Selected Problem Solving SuccessClap Free Study material on Linear Algebra 






Calculus 

3 
July 16 2023 
Limits: Continuity, Types of Discontinuity, Heine Continuity method, Bolzano Intermediate Value Theorem, Uniform Continuity Differentiability, Indeterminants Max/ Min Single Variable Find Max/Min of function. Problems to find Max/Min Area, Surface, Height
Max Min TWO Variables Find Max/Min of function Max/Min Multiple Variables Lagrange Multiplier Length of Arc Areas: Cartesian, Polar, Loop/Asymptotes Volumes: Cartesian, Polar , Spherical System Surface Areas Asymptote: General Method, Inspection method, Intersection of Curve and Asymptote Curve Tracing

Krishna Series : 1)Differential Calculus, 2)Integral Calculus 
4 
July 23 2023 
Mean Value theorem: MVT, Taylor Maclurin Expansion, Generalized MVT Rolle Theorem Lagrange Theorem (Also proof) Cauchy MVT Function Increasing/Decreasing
Jacobians Partial Differentiation Formation, Eulers Total Differentiation

Krishna Series : 1)Differential Calculus, 2)Integral Calculus 
5 
July 30 2023 
Beta Gamma Properties Relation between Beta and Gamma Legendre Duplication Formula and Properties
Beta Gamma Several Variables Evaluation of Integrals
Definite Integral as Sum
Differentiation under Integral Sign
Multiple Integrals Change of Order of Integration Evaluation of Integrals 
Krishna Series : 1)Differential Calculus, 2)Integral Calculus 






REAL ANALYSIS 

6 
Aug 6 2023 
Riemann Integrals Summation of Series Theorems : Continuous is integrable Bounded and Finite Set of Discontinuity is integrable Bounded and Discontinuity point has fixed limit point is integrable Monotonic is integrable Integral Inequality Eqn First Mean Value Theorem Generalised Mean Value Theorem Second Mean Value Theorem
Improper Integrals Limit Test Cauchy Test Absolute Convergence and conditional convergence Abel Test Dirichlet Test

Real Analysis by Raisinghania S.Chand 
7 
Aug 13 2023 
Sequence BolzanoWeistress Theorem Cauchy First Theorem on Limit Cauchy second Theorem on Limit Caseros Theorem Cauchy sequence Monotone Convergence Theorem
Series Necessary Condition Comparison Test Comparison Test of Second Kind D Alembert Ratio Test Cauchy nTH Root Test Raabe Test Logarithmic Test DE Morgan and Bertrand Test Second Logarithmic Ratio Test Kummer Test Gauss Test Cauchy Integral Test Cauchy Condensation Test

Real Analysis by Raisinghania S.Chand 
8 
Aug 20 2023 
Uniform Convergence Cauchy Principle Mn Test Weir strass Test Abel Test Dirichlet Test Properties on a) Sum b) Differentiability c) Integrability
Functions of Several Variables Limit Continuity Differentiability Maxima and Minima

Real Analysis by Raisinghania S.Chand 






VECTOR ANALYSIS 

9 
Aug 27 2023 
Directional Derivative : Max/Min ,Angle made, Vector Identities: Proof Curl (A XB), Div (A X ,Grad (A.B) ,Curl(curl A) Invariance under Transformation Green Theorem Stoke Theorem Divergence Theorem Work done. Differential Geometry: Derive Serret Frennet formula, Show curve lie in Plane, Find Curvature Vector, Problems on finding Radius of Curvature, Torsion 
Krishna Series Vector Analysis Differential Geometry by Paramanda Gupta 






ODE 

10 
Sep 3 2023 
Formation of DE Eqn of 1^{st} Order, 1^{st} Degree Integrating Factors Linear Differential Eqns Eqn reducible to Linear form Bernauli Eqn List of Important Results like Subnornal,subtangent, length of normal and tangent, Eqn of Tangent and Normal Tangent and Normal X and Y intercept Polar subtangent, subnormal, length of tangent, normal Orthogonal Trajectory/Oblique Trajectory Eqn Eqn of First Order but not of first degree Solvable for p, x, y Lagrange form Eqn in Claurait Form Eqn reducible to Claurait form Singular Solution 
Ordinary and Partial Differential Equations by Raisinghania

11 
Sep 10 2023 
Linear Differential Equations with Constant Coefficients Method of variation of parameter Linear Equation of Second Order Euler Cauchy Reduction with One known integral Reduction to Normal Changing independent variable 
Ordinary and Partial Differential Equations by Raisinghania

12 
Sep 17 2023 
Laplace, Inverse Laplace Application to initial value problem for 2^{nd} order linear equations with constant coefficients 
Ordinary and Partial Differential Equations by Raisinghania







PDE 

13 
Sep 24 2023 
Formation of PDE of a given function Lagrange Equations: Various Methods Surface Orthogonal to a given Surface Charpit method Clairaut equations Jacobi method 
Ordinary and Partial Differential Equations by Raisinghania
Advance PDE by Raisinghania 
14 
Oct 1 2023 
Homogeneous Linear PDE with Constant Coefficient Linear PDE of Second Order with Constant Coefficient
Cauchy Method of Characteristic Strip (Total 10 Qns ) Canonical Form 
Ordinary and Partial Differential Equations by Raisinghania
Advance PDE by Raisinghania 
15 
Oct 8 2023 
Wave Eqn Initial Velocity is zero, Initial Displacement is Given Initial Velocity is Given, Initial Displacement is Zero
Heat Eqn a) Initial Temperature f(x) .Both Ends suddenly changed to Zero Temperature b) Initial Tempearature (T1 , T2 ) , suddenly change to ( T3 , T4) c)Initial Temperature f(x). Both Ends Insulated suddenly d)At t=0 distribution is f(x). Suddenly One end is kept at T1 and other end Insulated Laplace Eqns a) Three sides Temperature is 0, Other side f(x) b) Two sides Temperature is 0, One side f(x), Other side at Infinite Long c)One side Insulated (XAxis) d)One Side Insulated (Opposite side of XAxis) e) Two sides Insulated , Xaxis side f(x), Other side 0 f) Two sides Insulated, Xaxis side 0, Other side f(x) g) Three sides Insulated
Laplace in Polar Coordinate Sysytem a) Semicircular Plate b) Circular Arc c) Circular Place d) Circular Annulus 
Advance PDE by Raisinghania 






Complex Analysis 

16 
Oct 15 2023 
Analytic Function: Cauchy Riemann Equation Given Function and Given Point a) Show it satisfy Cauchy Riemann eqn b) Show Analytic or NonAnalytic c) Show Existence of Derivative or Not Given U or V as Harmonic Function, find its Conjugate and also Function
Complex Integration: Cauchy Integrals, Zeroes, Singularity, Poles, Rouche theorem

Krishna Series Complex Analysis 
17 
Oct 22 2023 
Series Expansion Expand in Taylor Series Expand in Laurent Series Power Series representation Use Cauchy Residue Theorem, to Evaluate the Integral Contour Integrations 
Krishna Series Complex Analysis 






Analytic Geometry 

18 
Oct 29 2023 
Straight Lines Find coordinate the foot of perpendicular from given point to a plane. And also find distance Plane and St line: Parallel/ Perpendicular / Coincide Projection of Line on Plane Condition for Coplanar Lines Determine Eqn of St Line intersecting two given Lines Find Perpendicular distance of a point from line and its foot coordinate. Intersection of 3 Planes
Shortest Distance Find SD between two lines and obtain eqn of SD (Very Imp) Projection Method Two Lines in Symmetric Form Oneline General, Other Symmetric Form Two lines in General Form Skew Lines Find locus of line, which intersects set of lines or function. Planes Eqn of plan through 3 points Angle between planes Variable Plane Problems Bisecting Planes Combined Eqn of Planes Projection of planes

Krishna Series 3D Geometry 
19 
Nov 5 2023 
Spheres Sphere touching plane. Sphere through Circle Eqn of tangent plane to sphere and its condition Polar plane eqn and find pole. Intersection of Spheres and orthogonality condition
Cylinder Eqn parallel to line and guiding curve Right Circular Cylinder Tangent Plane Enveloping Cylinder
Cone Find eqn of cone with Vertex origin cone Find cone, with non origin vertex Condition for second degree to represent cone and find coordinates Tangent Line and Tangent Plane of Cone Condition for Tangency Reciprocal cone Angle between lines in which plane cuts Cone Condition for 3 mutually perpendicular generators Condition for 3 mutually perpendicular tangent planes Right Circular Cone Enveloping Cone

Krishna Series 3D Geometry 
20 
Nov 12 2023 
Central Conicoids Find Eqn of Tangent plane Condition for Tangency Director Sphere Polar Planes, Pole Locus of Chord Bisected at a given point Normal to Conicoid Prove 6 normal to ellipsoid Find cubic curve through feet of normal Diametral Plane Problems on Semi conjugate diameter properties Paraboloid Generating Lines 
Krishna Series Analytic Geometry (Slim Book) 






LPP 

21 
Nov 19 2023 
Formulation of LPP Graphical Method of Solution Simplex Method Big M Method Construct Dual and Solve 
Operation Research by Taha
ANY BOOK 
22 
Nov 26 2023 
Transportation Problem Assignment Problem 
Operation Research by Taha 






Numerical Analysis 

23 
Dec 3 2023 
Obtain derivation (a)Quadrature Formula, (b)Trapezoid Rule, (c)Simpson 1/3, (d) Simpson3/8. Rule and also (e)derive their Error Formula for ALL RULES.
Newton Raphson Method a)Derivation, b) Find Condition for its convergence c) Show rate of convergence is quadratic d) Explain its merits and demerits
Bisection Method Regula Falsi Method Secant Method Iteration Method and its Convergence Derive Newton Gregory Forward interpolation formula, and its Error.
Derive Newton Gregory’s Backward Interpolation formula and its Error
Lagrange Interpolation Derivation of formula and derive its Error formula Prove that Lagrange’s formula can be put in the form of
Show that the sum of Lagrangian coefficient is unity. Use Lagrange’s interpolation formula to express the function
as sums of partial fractions. Find the parabola passing through points (0,1) (1,3) and (3,55) using Lagrange’s formula
Gauss Quadrature Formula. Derive formula for n=3,4,5
Solve ODE Problems a) Euler b) Euler Modified c)Runge Kutta Order 1, 4
Solve Linear Eqns a) Gauss Elimination b) Gauss Jordan c) Gauss Seidel d) Gauss Jacobi
Use Gauss Jordan to Find Inverse Conversion Decimal to Octogonal and Vice versa Decimal to Hexadeceimal and vice versa Solve Boolean Expression
Algorithms and Flow Chart 
Krishna Series Numerical Analysis
Numerical Analysis by Iyenger (Few Questions)
Numerical Analysis by Sastry
Flow Charts: Free Study Material by SuccessClap 






Mechanics 

24 
Dec 10 2023 
Solving Problems on Lagrange Eqns Solving Problems on Hamilton Eqns 
Classical Mechanics by JC Upadhyay,
Krishna: Rigid Dynamics Vol1 
25 
Jan 21 2024 
D Alembert Principle Problems Moment of Inertia Fixed Axis Motions( Important questions Only) Motion in 2Dimension ( Important questions Only)

Krishna : Rigid Dynamics Vol 1 and Vol 2 






Fluid Dynamics 

26 
Jan 28 2024 
Learn Basics: Del,div,curl in catesian, spherical, cylindrigal, general coordinate system Kinematics Continuity Equation of motion Boundary Problems Path Line Vector Potential Vortex Line, vector Euler Eqns Energy Conservation Bernoulli Eqns and Application Stream Fns Source Sink problem

Fluid Dynamics: Raisinghania Chapter 1,2,3,4,5 
27 
Feb 4 2024 
Irrotational Motion Circular Cylinder Motion Irrotational 3D Vortex Navier Stoke Laminar Flow 
Fluid Dynamics: Raisinghania Chapter 6, 7,10,11,14,16 






Dynamics 

28 
Feb 11 2024 
Rectilinear Motion SHM Projectile Motion Constrained Motion Motion in a Plane, Circle Work, Energy, Impulse

Krishna Series Dynamics 
29 
Feb 18 2024 
Kepler Laws, Problems on Central Forces Planetary Motion Motion in resisting medium

Krishna Series Dynamics 






STATICS 

30 
Feb 25 2024 
Force Eqns, Moments Equilibrium of Rigid Body Frictions Catenary

Krishna Series Statics 
31 
Mar 3 2024 
Virtual Work Stable and Unstable Equilibrium

Krishna Series Statics 


Abstract Algebra 

32 
Mar 10 2024 
Group Theory Groups SubGroups Cosets, Lagrange Theorem Cyclic Group Normal Subgroups Quotient Groups Homomorphism Fundamental Theorem of Homomorphism 1,2,3 Permutation Groups Cayley’s theorem 
Any State B.Sc Text Book
Group Theory by R Kumar
SuccessClap Free Study material on Algebra
Don’t waste time on Galian, Khanna Bhambri or any book 
33 
Mar 17 2024 
Ring Theory Rings SubRings Ring Homomorphism Embedness Max Ideal Prime Ideal PID Divisibility in Rings, prime, Irreducible element Euclidean Domain, UFD, Einstein criteria 
Any State B.Sc Text Book Ring Theory by R Kumar
SuccessClap Free Study material on Algebra







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FLT1 
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37 
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42 43 
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44 45 
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FLT11 FLT12 
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