Maths Yearlong Test Series (MYTS) 2023

Course Fee

For New Students

₹20,000 + 18% GST

      Old Foundation Course Students

                  ₹12,000 + 18% GST

MYTS Objectives

Source of Que.

Exclusive Features


Expectations from Students


Mathematics Yearlong Test Series (MYTS) program is more like a Mini Foundation Course than a test series, focusing on serious aspirants who will appear in the Civil Service examination 2023. The entire syllabus is covered through 15 Sectional Tests and 10 Comprehensive Tests. These periodic tests, followed by discussion, will enhance your understanding of the subject and will also keep your Maths preparation on track throughout the year.


  • 15 Sectional Tests
  • 10 Comprehensive Tests
  • Detailed Classroom / Live Test Discussion.
  • Detailed Solution for Each and Every Question
  • Individual Mentoring & Hand Holding
  • Timely and Multi-level Evaluation within 7 days
  • Flexible Submission of the Tests

UPSC has increased diversity in questions. Relatively new, tricky but easy questions are being asked in the question paper. For example, error analysis in Numerical Analysis, Normal forms in Computer Programming, Cutting and trimming problems in Linear Programming etc. These new questions are not difficult but these are of course unconventional. So, to bring this diversity, the questions are selected/searched from multiple sources, like,

  • Standards books from reputed publications (Krishna publication books, S Chand Publication books, PHI Publication, Pearson Books etc)
  • PYQs (CSE, IFoS, UPPCS, BPSC etc)
  • Questions collected from online platforms and telegram groups/channels
  • College/University Tests papers and Tutorials

The questions in the TEST Series will be a mix of basic to some really hard questions. Easy/fundamental questions will ensure that you have the minimum basic knowledge to score at least 260-270 marks. Preparing hard questions in the test series will give you an edge over others. These are those questions that will push your score beyond 350 marks.

  • Extensive coverage of Physics topics
  • Discussion classes
  • Personal Mentoring
  • Timely and multilevel evaluation and personalized feedback within 7 days
  • Flexible submission of tests.

Schedule & Syllabus
Paper I
Test No.


Test 1



June 2022

Linear Algebra:

Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; Linear transformations, rank and nullity, matrix of a linear transformation. Algebra of Matrices; Row and column reduction, Echelon form, congruence’s and similarity; Rank of a matrix; Inverse of a matrix; Solution of system of linear equations; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues.

Test 2



July 2022


Real numbers, functions of a real variable, limits, continuity, differentiability, mean value theorem, Taylor’s theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing; Functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange’s method of multipliers, Jacobian. Riemann’s definition of definite integrals; Indefinite integrals; Infinite and improper integrals; Double and triple integrals (evaluation techniques only); Areas, surface and volumes.

Test 3



July 2022

Analytic Geometry:

Cartesian and polar coordinates in three dimensions, second degree equations in three variables, reduction to canonical forms, straight lines, shortest distance between two skew lines; Plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties.

Test 4



July 2022

Ordinary Differential Equations:

Formulation of differential equations; Equations of first order and first degree, integrating factor; Orthogonal trajectory; Equations of first order but not of first degree, Clairaut’s equation, singular solution. Second and higher order linear equations with constant coefficients, complementary function, particular integral and general solution. Second order linear equations with variable coefficients, Euler-Cauchy equation; Determination of complete solution when one solution is known using method of variation of parameters. Laplace and Inverse Laplace transforms and their properties; Laplace transforms of elementary functions. Application to initial value problems for 2nd order linear equations with constant coefficients.

Test 5



August 2022


Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; constrained motion; Work and energy, conservation of energy; Kepler’s laws, orbits under central forces.

Test 6



August 2022


Equilibrium of a system of particles; Work and potential energy, friction; common catenary; Principle of virtual work; Stability of equilibrium, equilibrium of forces in three dimensions.

Test 7



October 2022

Vector Analysis:

Scalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence and curl in cartesian and cylindrical coordinates; Higher order derivatives; Vector identities and vector equations. Application to geometry: Curves in space, Curvature and torsion; Serret-Frenet’s formulae. Gauss and Stokes’ theorems, Green’s identities.

Test 8



October 2022

Complete Paper 1 Syllabus
Paper II
Test 9



October 2022

Modern Algebra:

Groups, subgroups, cyclic groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley’s theorem. Rings, subrings and ideals, homomorphisms of rings; Integral domains, principal ideal domains, Euclidean domains and unique factorization domains; Fields, quotient fields.

Test 10



November 2022

Real Analysis:

Real number system as an ordered field with least upper bound property; Sequences, limit of a sequence, Cauchy sequence, completeness of real line; Series and its convergence, absolute and conditional convergence of series of real and complex terms, rearrangement of series. Continuity and uniform continuity of functions, properties of continuous functions on compact sets. Riemann integral, improper integrals; Fundamental theorems of integral calculus. Uniform convergence, continuity, differentiability and integrability for sequences and series of functions; Partial derivatives of functions of several (two or three) variables, maxima and minima.

Test 11



November 2022

Complex Analysis:

Analytic functions, Cauchy-Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, power series representation of an analytic function, Taylor’s series; Singularities; Laurent’s series; Cauchy’s residue theorem; Contour integration.

Test 12



December 2022

Linear Programming:

Linear programming problems, basic solution, basic feasible solution and optimal solution; Graphical method and simplex method of solutions; Duality. Transportation and assignment problems.

Test 13



December 2022

Partial Differential Equations:

Family of surfaces in three dimensions and formulation of partial differential equations; Solution of quasilinear partial differential equations of the first order, Cauchy’s method of characteristics; Linear partial differential equations of the second order with constant coefficients, canonical form; Equation of a vibrating string, heat equation, Laplace equation and their solutions.

Test 14



January 2023

Numerical Analysis:

Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton- Raphson methods; solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss- Seidel(iterative) methods. Newton’s (forward and backward) interpolation, Lagrange’s interpolation. Numerical integration: Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula. Numerical solution of ordinary differential equations: Euler and Runga Kutta-methods.


Computer Programming:

Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimal systems; Conversion to and from decimal systems; Algebra of binary numbers. Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normal forms. Representation of unsigned integers, signed integers and reals, double precision reals and long integers. Algorithms and flow charts for solving numerical analysis problems.

Test 15



January 2023


Generalized coordinates; D’ Alembert’s principle and Lagrange’s equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions.

Test 16



February 2023

Fluid Dynamics:

Equation of continuity; Euler’s equation of motion for inviscid flow; Stream-lines, path of a particle. Potential flow; Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier-Stokes equation for a viscous fluid.

Test 17



February 2023

Complete Paper 2 Syllabus
CSE Prelims – 2023 Examination
8 Comprehensive Full-length Tests*

Note: All the Tests are of 3 Hours duration.

*Schedule will be released after Prelims 2023.


Cracking UPSC is more about developing the right attitude than having great aptitude. Students should stick to routine, attempt tests on the scheduled date, continuously identify gaps and fill these gaps on daily basis.
Follow the famous saying by Swami Vivekanand, “Stop not till the goal is reached.”
Don’t get discouraged if you are not able to score high. The Goal is to score maximum in UPSC not in Test Series. The Test series is for revision purposes and to give you a good compilation of questions. By hook or by crook, prepare all the questions of the Test Series. Once you are done with this, be confident and have faith. You have done what could be done.

Best of Luck!
– Avi Singh (B. Tech IITR, ex IES)

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