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Opsc PGT Mathematics 2026 Free Mock Test Practice
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Opsc PGT Mathematics 2026 Exam Free Online Question Bank
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OPSC PGT Mathematics Combo Packages
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Combo Package
OPSC PGT Mathematics
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2. Question Bank - 1000 Questions with Answer.
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OPSC PGT Mathematics
Combo - 2 Paper 1 (English)
1. Online Mock Test Series in English - 20 Tests
2. Question Bank - 1500 Questions with Answer.
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Combo Package
OPSC PGT Mathematics
Combo - 3 Paper 2 & 3 (English)
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2. Question Bank - 1000 Questions with Answer.
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Combo - 4 Paper 1 (English)
1. Online Mock Test Series in English = 20 Tests.
2. Question Bank - 1500 Questions with Answer.
3. Printed Material 10 Mock Test Papers with OMR Sheet.
4. EBook of OPSC PGT Mathematics Exam (1000 MCQ) in PDF Format in English
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Combo Package
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Combo - 5 Paper 2 & 3 (English)
1. Online Mock Test Series in English = 10 Tests.
2. Question Bank - 1500 Questions with Answer.
3. Printed Material 10 Mock Test Papers with OMR Sheet.
4. EBook of OPSC PGT Mathematics Exam (1000 MCQ) in PDF Format in English
2. Question Bank - 1500 Questions with Answer.
3. Printed Material 10 Mock Test Papers with OMR Sheet.
4. EBook of OPSC PGT Mathematics Exam (1000 MCQ) in PDF Format in English
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OPSC PGT Mathematics Syllabus 2026 & Exam Pattern
OPSC PGT Mathematics Syllabus 2026, Exam Pattern, Exam Date 2026
Detail Information about OPSC has published notification 2026 for the recruitment of PGT Mathematics vacancies. Those Candidates who are Interested to the following vacancy and completed all Eligibility Criteria can read the Notification & Apply Online. In this page we provide the Complete Syllabus of this Recruitment with Latest Update Exam Pattern and the Exam Date also.
OPSC PGT Syllabus 2026 - Overview
OPSC PGT Syllabus 2026 - Overview
| Recruiting Body | OPSC |
| Full-Form | Odisha Public Service Commission |
| Post | Post Graduate Teacher |
| Number of Vacancies | Notified Soon |
| Category | Syllabus and Exam Pattern |
| Mode | Online |
| Official website | www.opsc.gov.in |
OPSC PGT (Mathematics) Syllabus 2026
Paper 1 Syllabus :-
General English :
1. Spotting Errors
2. Antonyms
3. Homonyms
4. synonyms
5. Word Formation
6. Spelling Test
7. Sentence Arrangement
8. Error Correction (Underlined Part)
9. Transformation
10. Passage Completion
11. prepositions
12. Sentence Improvement
13. Joining Sentences
14. Theme Detection
15. Topic rearrangement of passage
16. Error Correction (Phrase in Bold)
17. Fill in the blanks
18. Data Interpretation
19. Direct and Indirect speech
20. Active and Passive Voice
General Knowledge :
1. About India
2. Indian Constitution
3. National News (current)
4. Indian Culture
5. Economy
6. History – India & World
7. Cultural Heritage
8. General Science
9. Space & IT
10. Political Science
11. Indian National Movement
12. Indian Polity & Governance
13. Science & Technology
14. Scientific observations
15. Important Days
16. General Knowledge of Karnataka
17. Important Financial & Economic News
18. Current Affairs – National & International
19. Indian Constitution
20. International issues
21. Abbreviations
22. Economic Scene
23. Everyday Science
24. Sports and Games
25. Science – Inventions & Discoveries
26. History
27. General Politics
28. Awards and Honors
29. Culture
30. Books and Authors
31. Current events
32. Geography
33. Current Affairs
34. Social Science
35. Inventions in the World
36. Indian Economy
37. Indian Parliament
38. Botany
39. Chemistry
40. Indian Politics
Concerned Subject (Mathematics)
PAPER – I :-
UNIT – I ALGEBRA AND NUMBER THEORY
Group Theory : Groups, Subgroups, Normal Subgroups and Quotient Groups, Homomorphisms and applications, Permutation groups, Conjugacy and Class equation, Simple group, Sylow Theorms.
Ring Theory : Rings, Special Classes of rings, Homomorphisms, Ideals and Quotient rings, Maximal and Prime ideals, Polynomial rings, Principal Ideal Domain, Unique Factorization Domain.
Field : Field of Quotients of an Integral Domain, Polynomials over the rational field, Algebraic Extension of Fields: Irreducible polynomials and Eisenstein:
Criterion, roots of Polynomial, Splitting field and its degree of extension, Multiple roots, Ruler and Compass Constructions, Symmetric function of roots, Solution of Cubic and Biquadratic Equations.
Number Theory : Integers, g.c.d., Fundamental Theorem of Arithmetic, Euclidean Alogorithm, Arithmetical functions (Euler-function, Mobius function), Dirichlet multiplication, Linear Congruences, Euler-Fermat Theorem, Linear Diophantine Equations, Fermat’s Theorem, Fermat Little Theorem, Polynomial Congruence, Lagrange’s Theorem, Chinese Remainder Theorem, Wilson’s Theorem and Applications.
UNIT –II ANALYSIS –I
Basic Topology : Finite, Countable and Uncountable sets, Metric Spaces, Topological Spaces, Basis, Closed sets, Open Sets, Limit Points, Properties of Connected Spaces and Compact Spaces, Heine Boril Theorem.
Sequence and Series : Convergent Sequences, Subsequences, Convergence of Monotone Sequences, Couchy Sequences, Upper and Lower limits of Sequences, Bolzano Weirstrass Theorem, Series of non-negative terms, Convergence tests, Power Series, Couchy Convergence Criterion, Absolute Convergence, Alternating Series.
Continuity and Differentiability : Properties of Continuous Function, Continuity and Compactness, Continuity and Connectedness, Discontinuity, Monotonic functions, Mean Value Theorem, Taylor Series.
Function of Several Variables : Continuity Differentiability, Extreme Values, Maxima and Minima, Line Integral, Surface Integral, Volume Integral, Applications of Green’s Theorem, Stokes Theorem and Gauss Theorem.
UNIT – III COMPLEX ANALYSIS :
Analytical Functions : Continuity, Differentiability, Couchy-Reimenn Equations, Analytic Functions, Harmonic Functions.
Bilinear Transformation : Elementary Transformations, Bilinear Transformation, Mapping by Elementary Functions.
Complex Integration : Couch’s Theorem, Couchy’s Integral Formula, Maximum Modulus Theorem, Liouville’s Theorem, Morera’s Theorem, Related Problems.
Singularities and Calculus of residues : Series Expansion, Taylor’s Series, Laurent’s Series, Zeros of Analytic Function, Singularities, Residues, Councy’s Residue Theorem, Evaluation of Definite Integrals.
UNIT – IV OPERATIONS RESEARCH
Linear Programming : Simpler Method, Computational Procedure, Use of Artificial Variables.
Duality in Linear Programming : General Primal-dual pair, Duality Theorems, Complementary Slackness Theorem, Duality and Simplex Method, Dual Simplex Method.
Games and Strategies : Two-person-Zero Sum Games, Minimax-Maximin Principle, Games with Saddle Points, Mixed Strategies, Graphical Solutions, Dominance Property, Arithmetic Method of nxn Games, General Solution of nxn rectangular Games.
Transportation and Assignment : General Transportation Problem, Finding Initial Basic Feasible Solution, Test of Optionality, Transportation Algorithm,
Transhipment Problems.
Mathematical Formulation of Assignment Problem, Method of Solution of Assignment Problem, Travelling Salesman Problem.
UNIT – V NUMERICAL ANALYSIS
Root Finding for Non-Linear Equations : Newton’s Method, Secant Method, One-point Iteration Method, Multiple Roots, Newton Methods of Non-Linear Systems.
Interpolation Theory : Finite Differences, Newton’s Forward and Backward differences, Newton’s Divided differences, Lagrange’s Interpolation, Errors in data
and Forward differences, Hermite Interpolation, Piece-wise linear Interpolation.
Numerical Integration : Newton-cote integration formula, trapezoidal rule, Simpsons’ rule, Gaussian quadrature, Asymptotic error formulas and their applications.
Numerical Methods for Ordinary Different Equations : Euler’s Method, Multistep Methods, Midpoint Method, Trapezoidal Method, Single Step Method and Runge-Kutta Method.
PAPER-II :-
UNIT-I ANALYSIS
Riemann stieltjes integral Existence of the integral, Properties of the integral, Fundamental theorem of calculus, change of variables in on integral, Differentiation of integral.
Sequence and series of functions :
Uniform convergence of sequence of functions, Cauchy criterion for uniform convergence, weierstrass test for uniform convergence, uniform convergence and continuity, uniform convergence and differentiation, construction of continuous function on the real line which is nowhere differentiable.
Measure Theory :
Lebesgue outer measure , Properties of outer measure, Measurable sets, Cantor set, Borel set, and sets, Non measurable sets, Measurable functions, Properties of measurable functions.
Lebesgue integration and lp spaces comparison of Lebesgue and Riemann integral, Lebesgue integral of bounded measurable functions over sets of finite measure, Bounded convergence theorem, Lebesgue integral for nonnegative measurable function. Fatou’s Lemma, Monotone convergence theorem, lp spaces, essential supremum of a function, Minkowski and Holder inequalities, Absolute summable and summable series in a normal linear space completeness in lp.
UNIT-II FUNCTIONAL ANALYSIS
Normed Linear space :
Linear spaces, Subspaes, Quotient spaces, properties of norm, Riesz Lemma, Continuity of linear maps, Bounded linear operations, Equivalent norms, Hahn Banach theorem and its consequences.
Banach spaces :
Uniform boundedness principle, closed graph theorem and its consequences, open mapping theorem and its consequences.
Spaces of Bounded linear functional :
Duals and transposes, Duals of lp, Lp[a,b], C[a,b], Weak convergence, weak convergence, Reflexivity. Hilbert space Inner product spaces, Orthonormal sets, Gram Schmidt Orthonormalisation, Bessel’s Inequality, Riesz. Fischer theorem, Projection theorem, Riesz representation theorem.
UNIT-III LINEAR ALGEBRA
Vectorspace, Subspace, Linear Dependence , Independence, Dimension and Basis , Linear Transformation, Range and Kernel, Rank and Nullity, Inverse of Linear Transformation, Linear Map associated with matrix.
Elementary Row Operations, Rank and Nullity of Matrix, Inverse of a Matrix, Determinants and product of Determinats, Eigen values, Eigen vectors, Characteristic roots.
Canonical forms, Tringular form, Nilpotent Transformations, Similarity of Matrices, Quadratic form.
UNIT- IV DISCRETE MATHEMATICS
Logic- Fundamentals of logic, Normal forms, Logical Inferences, Methods of proof, Mathematical Induction, Rules of Inferences for quantified propositions.
Lattice and Boolean Algebra – Binary relations, Equivalence relations, prset, Lattice, Hasse Diagram, Algebraic properties of Lattice, Paths and closures, Directed graphs and adjacency matrix, Boolean Algebra, Boolean functions, Minimization of Boolean functions.
Recurrence relation – Generating functions of sequences, Calculating co-efficients of generating functions, Recurrence relation, solving recurrence relations by substitution and generating functions. Solution by the method of characteristic roots.
Graph Theory – Trees and their properties, spanning trees, Binary trees, Euler’s formula, Euler’s circuits, Hamiltanian Graphs
UNIT – V DIFFERENTIAL EQUATIONS :
Linear Differential Equations with constant coefficients and variable coefficients, system of Linear Differential Equations. Laplace Transformation : Linearity of the Laplace transformation. Laplace transforms of derivatives and integrals, shifting theorems. Differentiation and integration of transforms. Convolution theorem. Solution of integral equations and systems of differential equations using Laplace Transformation.
Series Solution of differential equations: Power series method, Bessel, Legendre and Hypergeometirc equations. Bessel, Legendre functions and their properties . SturmLiouville problem, Orthogonality of eigen functions. Orthogonality of Bessel fuctions and Legendre polynomials.
Partial Differential Equations of the 1st order. Lagrange’s solution some special types of equations, their solution, Charpit’s general method of solution.
Partial Differential Equations of second and Higher orders. Classification of linear partial differential equations of second order. Homogeneous and non-homogeneous equations with constant colffficients, Monge’s method.
Fourier Series and Fourier Transform, Convergence of Fourier series, Application of Fourier series and Fourier Transforms to Boundary value problems. Solution of Laplace equation, wave equation and heat conduction equations.
Group Theory : Groups, Subgroups, Normal Subgroups and Quotient Groups, Homomorphisms and applications, Permutation groups, Conjugacy and Class equation, Simple group, Sylow Theorms.
Ring Theory : Rings, Special Classes of rings, Homomorphisms, Ideals and Quotient rings, Maximal and Prime ideals, Polynomial rings, Principal Ideal Domain, Unique Factorization Domain.
Field : Field of Quotients of an Integral Domain, Polynomials over the rational field, Algebraic Extension of Fields: Irreducible polynomials and Eisenstein:
Criterion, roots of Polynomial, Splitting field and its degree of extension, Multiple roots, Ruler and Compass Constructions, Symmetric function of roots, Solution of Cubic and Biquadratic Equations.
Number Theory : Integers, g.c.d., Fundamental Theorem of Arithmetic, Euclidean Alogorithm, Arithmetical functions (Euler-function, Mobius function), Dirichlet multiplication, Linear Congruences, Euler-Fermat Theorem, Linear Diophantine Equations, Fermat’s Theorem, Fermat Little Theorem, Polynomial Congruence, Lagrange’s Theorem, Chinese Remainder Theorem, Wilson’s Theorem and Applications.
UNIT –II ANALYSIS –I
Basic Topology : Finite, Countable and Uncountable sets, Metric Spaces, Topological Spaces, Basis, Closed sets, Open Sets, Limit Points, Properties of Connected Spaces and Compact Spaces, Heine Boril Theorem.
Sequence and Series : Convergent Sequences, Subsequences, Convergence of Monotone Sequences, Couchy Sequences, Upper and Lower limits of Sequences, Bolzano Weirstrass Theorem, Series of non-negative terms, Convergence tests, Power Series, Couchy Convergence Criterion, Absolute Convergence, Alternating Series.
Continuity and Differentiability : Properties of Continuous Function, Continuity and Compactness, Continuity and Connectedness, Discontinuity, Monotonic functions, Mean Value Theorem, Taylor Series.
Function of Several Variables : Continuity Differentiability, Extreme Values, Maxima and Minima, Line Integral, Surface Integral, Volume Integral, Applications of Green’s Theorem, Stokes Theorem and Gauss Theorem.
UNIT – III COMPLEX ANALYSIS :
Analytical Functions : Continuity, Differentiability, Couchy-Reimenn Equations, Analytic Functions, Harmonic Functions.
Bilinear Transformation : Elementary Transformations, Bilinear Transformation, Mapping by Elementary Functions.
Complex Integration : Couch’s Theorem, Couchy’s Integral Formula, Maximum Modulus Theorem, Liouville’s Theorem, Morera’s Theorem, Related Problems.
Singularities and Calculus of residues : Series Expansion, Taylor’s Series, Laurent’s Series, Zeros of Analytic Function, Singularities, Residues, Councy’s Residue Theorem, Evaluation of Definite Integrals.
UNIT – IV OPERATIONS RESEARCH
Linear Programming : Simpler Method, Computational Procedure, Use of Artificial Variables.
Duality in Linear Programming : General Primal-dual pair, Duality Theorems, Complementary Slackness Theorem, Duality and Simplex Method, Dual Simplex Method.
Games and Strategies : Two-person-Zero Sum Games, Minimax-Maximin Principle, Games with Saddle Points, Mixed Strategies, Graphical Solutions, Dominance Property, Arithmetic Method of nxn Games, General Solution of nxn rectangular Games.
Transportation and Assignment : General Transportation Problem, Finding Initial Basic Feasible Solution, Test of Optionality, Transportation Algorithm,
Transhipment Problems.
Mathematical Formulation of Assignment Problem, Method of Solution of Assignment Problem, Travelling Salesman Problem.
UNIT – V NUMERICAL ANALYSIS
Root Finding for Non-Linear Equations : Newton’s Method, Secant Method, One-point Iteration Method, Multiple Roots, Newton Methods of Non-Linear Systems.
Interpolation Theory : Finite Differences, Newton’s Forward and Backward differences, Newton’s Divided differences, Lagrange’s Interpolation, Errors in data
and Forward differences, Hermite Interpolation, Piece-wise linear Interpolation.
Numerical Integration : Newton-cote integration formula, trapezoidal rule, Simpsons’ rule, Gaussian quadrature, Asymptotic error formulas and their applications.
Numerical Methods for Ordinary Different Equations : Euler’s Method, Multistep Methods, Midpoint Method, Trapezoidal Method, Single Step Method and Runge-Kutta Method.
PAPER-II :-
UNIT-I ANALYSIS
Riemann stieltjes integral Existence of the integral, Properties of the integral, Fundamental theorem of calculus, change of variables in on integral, Differentiation of integral.
Sequence and series of functions :
Uniform convergence of sequence of functions, Cauchy criterion for uniform convergence, weierstrass test for uniform convergence, uniform convergence and continuity, uniform convergence and differentiation, construction of continuous function on the real line which is nowhere differentiable.
Measure Theory :
Lebesgue outer measure , Properties of outer measure, Measurable sets, Cantor set, Borel set, and sets, Non measurable sets, Measurable functions, Properties of measurable functions.
Lebesgue integration and lp spaces comparison of Lebesgue and Riemann integral, Lebesgue integral of bounded measurable functions over sets of finite measure, Bounded convergence theorem, Lebesgue integral for nonnegative measurable function. Fatou’s Lemma, Monotone convergence theorem, lp spaces, essential supremum of a function, Minkowski and Holder inequalities, Absolute summable and summable series in a normal linear space completeness in lp.
UNIT-II FUNCTIONAL ANALYSIS
Normed Linear space :
Linear spaces, Subspaes, Quotient spaces, properties of norm, Riesz Lemma, Continuity of linear maps, Bounded linear operations, Equivalent norms, Hahn Banach theorem and its consequences.
Banach spaces :
Uniform boundedness principle, closed graph theorem and its consequences, open mapping theorem and its consequences.
Spaces of Bounded linear functional :
Duals and transposes, Duals of lp, Lp[a,b], C[a,b], Weak convergence, weak convergence, Reflexivity. Hilbert space Inner product spaces, Orthonormal sets, Gram Schmidt Orthonormalisation, Bessel’s Inequality, Riesz. Fischer theorem, Projection theorem, Riesz representation theorem.
UNIT-III LINEAR ALGEBRA
Vectorspace, Subspace, Linear Dependence , Independence, Dimension and Basis , Linear Transformation, Range and Kernel, Rank and Nullity, Inverse of Linear Transformation, Linear Map associated with matrix.
Elementary Row Operations, Rank and Nullity of Matrix, Inverse of a Matrix, Determinants and product of Determinats, Eigen values, Eigen vectors, Characteristic roots.
Canonical forms, Tringular form, Nilpotent Transformations, Similarity of Matrices, Quadratic form.
UNIT- IV DISCRETE MATHEMATICS
Logic- Fundamentals of logic, Normal forms, Logical Inferences, Methods of proof, Mathematical Induction, Rules of Inferences for quantified propositions.
Lattice and Boolean Algebra – Binary relations, Equivalence relations, prset, Lattice, Hasse Diagram, Algebraic properties of Lattice, Paths and closures, Directed graphs and adjacency matrix, Boolean Algebra, Boolean functions, Minimization of Boolean functions.
Recurrence relation – Generating functions of sequences, Calculating co-efficients of generating functions, Recurrence relation, solving recurrence relations by substitution and generating functions. Solution by the method of characteristic roots.
Graph Theory – Trees and their properties, spanning trees, Binary trees, Euler’s formula, Euler’s circuits, Hamiltanian Graphs
UNIT – V DIFFERENTIAL EQUATIONS :
Linear Differential Equations with constant coefficients and variable coefficients, system of Linear Differential Equations. Laplace Transformation : Linearity of the Laplace transformation. Laplace transforms of derivatives and integrals, shifting theorems. Differentiation and integration of transforms. Convolution theorem. Solution of integral equations and systems of differential equations using Laplace Transformation.
Series Solution of differential equations: Power series method, Bessel, Legendre and Hypergeometirc equations. Bessel, Legendre functions and their properties . SturmLiouville problem, Orthogonality of eigen functions. Orthogonality of Bessel fuctions and Legendre polynomials.
Partial Differential Equations of the 1st order. Lagrange’s solution some special types of equations, their solution, Charpit’s general method of solution.
Partial Differential Equations of second and Higher orders. Classification of linear partial differential equations of second order. Homogeneous and non-homogeneous equations with constant colffficients, Monge’s method.
Fourier Series and Fourier Transform, Convergence of Fourier series, Application of Fourier series and Fourier Transforms to Boundary value problems. Solution of Laplace equation, wave equation and heat conduction equations.
OPSC PGT Mathematics Exam Pattern 2026
Negative Marking : 0.25
| Paper | Subject | No.of Question | Marks | Duration |
| Paper 1 | Part-I General English | 50 | 50 | 2 Hour |
| Part-II General Knowledge | 50 | 50 | ||
| Paper 2 | Concerned Subjects (Mathematics) | 100 | 100 | 2 Hour |
| Paper 3 | Concerned Subjects (Mathematics) | 100 | 100 | 2 Hour |
Exam Date : Update Soon
Starting Date of Application Form : Notified Soon
Last Date of Application Form : Notified Soon
FAQs
Opsc PGT Mathematics 2026 Exam Syllabus Frequently Asked Questions (FAQ's)
Here at Toppersexam.com , you can practice a complete set of Imporatnt Questions (MCQ) along with a Free OPSC PGT Mathematics MCQ designed by our expert faculty.
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Being familiar with OPSC PGT Mathematics Exam Pattern will help you understand the types of questions asked, difficulty level of the exam and important topics that require your keen attention. It will also acquaint you with the marking scheme and time allotted to each Topics.
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