**MPESB High School Teacher Selection Test , Syllabus , Application Form , Exam Date , Eligibility Criteria , Pattern**

**Join the Group :**

MP High School Teacher Exam Application form Released Date **:** ** 18 / 05 / 2023**

Last Date for submission of the application form **:** **01 / 06 / 2023**

Admit Card Release **:** **Before the Exam **

Exam Date **:** **02 / 08 / 2023**

Conduct Agency **:** **MPESB **(Madhya Pradesh Employee Selection Board)

Exam Pattern **:** **Online Mode** (CBT)

Exam Type **:** **MCQ **

Result **: Notified Soon**

**Selection Process : **

**Written Exam****Interview / Document Verification**

**MP High School Teacher Selection Test (HSTST) Exam Eligibility Criteria : –**

The condinates who Qualify MP HSTST shall have to fullfill the following Eligibility Requirement for Application form.

- Post – Graduate Degree in the concerned subject with second division from a recognized university.
- B.Ed. from a recognized university.
- HSTET Qualified.

**MP High School Teacher Selection Test ****(HSTST) Exam ****Age Limit & Relaxation :- **

- Minimum Age : 21 Year
- Maximum Age : 40 Year.
- Age Relaxation Extra as Per Rules .

Category |
Age Relaxation |

Male | 40 Years |

Female | 45 Years |

MP Government Employee | 45 Years |

SC / ST / OBC | 45 Years |

PwD | 45 Years |

**MP High School Teacher Selection Test Pattern : – **

- MP High School Teacher Selection Test will conducted Online Mode (CBT) .

The MP High School Teacher Selection Test will be a written test is of **100 marks** ( **100 objective type multiple choice questions**) carrying **01 mark **for each question. The duration of Written test will be **120 minutes** without any time limit for each part individually.

**MP High School Teacher Selection Test Marking Pattern of the Paper :-**

- The MP High School Teacher Selection Test will be a written test is of 100 marks ( 100 objective type multiple choice questions).
- There will be a total of 100 questions that will carry 1 mark eachquestion.
- The duration of written test will be 120 minutes without any time limit for each part individually.
- The questions will be of the objective type with four options per question.
- Each incorrect answer will result in a deduction of No Negative Marks .
- There is no negative marking for questions that have been left unanswered.
- Also after the process of Challenges of the Answer Key, in case there are

multiple correct options or change in key, only those candidates who have attempted

it correctly as per the revised Answer key will be awarded marks. - In case a Question is dropped due to some technical error, full marks shall be given

to all the candidates irrespective of the fact who have attempted it or not .

5. Charts , Graph Sheets , Tables , Cellular Phone or Other Electronic Gadgets are NOT allowes in the examination hall.

**MP High School Teacher Selection Test ****(HSTST) Exam ****Subject Wise Expected Cut Off 2023 : –**

Knowing the cutoff helps candidates to know the minimum marks they must score to clear the written test and qualify the recruitment process. The MP High School Teacher Selection Test (HSTST) Exam cut-off 2023 will be released after the commencement of the examination till then have a look at the expected marks.

Category |
Expected Cut Off Marks |

General | 90 |

OBC | 85 |

SC | 80 |

ST | 75 |

**MP High School Teacher Selection Test (HSTST) Exam Selection Process 2023 :- **

The Selection for the Post of MPESB High School Teacher Selection Test (HSTST) Exam will be done on the basis of the following stages :

**Written Exam****Interview / Document Verification**

**Salary :- **

- MP High School Teacher Selection Test (HSTST) Pay Salary : 36200 Rs + DA.

**MPESB High School Teacher Selection Test (HSTST) : **

**MP HSTST Mathematics Syllabus :**

**Unit – 1 **

**Arithmetic :**

Numbers (natural numbers, whole numbers, integers, rational numbers, rational numbers, irrational numbers and real numbers, complex numbers), unitary method, average, profit & loss, simple interest, compound interest, length, mass, capacity, time, simple fractions, decimal, percentage, ratio & proportion, multiple & factor, lowest common multiple & highest common factor.

**Mensuration : **

Perimeter and area of triangle and quadrilateral. Surface area and volume of cubs, cuboids, cones, spheres,and cylinders.

**Unit – 2**

**Elementary Number Theory : **

Piano’s Axioms, Principle of Induction; First Principle, Second Principle, Third Principle, Basis, Representation Theorem, Greatest Integer Function Test of Divisibility, Euclid’s algorithm, The Unique Factorisation Theorem, Congruence, Sum of divisors of a number. Euler’s totient function, Theorems of Fermat, and Wilson.

**Unit – 3**

**Matrices and Determinants : **

Definition and Types of Matrices. Addition and Product of Matrices up to order 3 x 3,Transpose Matrices, Symmetric and Skew-symmetrical Matrices, Definition of determinant, Minors and Cofactor of a Matrix, Inverse of a Matrix, Solution of the simultaneous equation of three unknown quantities with the help of the Inverse of a Matrix. expansion of determinants up to order 3 × 3, Camer’s rule.

**Unit – 4**

**Relations & Functions : **

Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the reals with itself (upto R × R × R). Definition of relation, pictorial diagrams, domain. co- domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation a function, domain, co-domain & range of a function.

Real valued function of the real variable, domain, and range of these functions, constant, identity, polynomial, rational, modulus signum and greatest integer functions with their graphs. Sum. difference, product, and quotients of functions. Sets and their Representations. Union, intersection and complements of sets, and their algebraic properties, Relations, equivalence relations, mappings, one-one, into and onto mappings, composition of mappings. Binary operations.

**Unit – 5**

**Geometry and Coordinate Geometry : **

Angle & their types, parallel lines. triangle -types & properties, congruency of triangles, quadrilateral – types & properties, parallel lines, theorems on triangle, quadrilateral & circle, and questions based on theorems, geometrical shapes, constructions & properties.

**Three-dimensional Coordinate Geometry : **

Coordinate axes and coordinate planes in three-dimensional space. Coordinates of a point in space. Distance between two points. Section formula. Direction cosines and direction ratios of a line. Equation of a line in a space. Angle between two lines. Shortest distance between two lines. Plane. Coplanarity of two lines. Distance of a point from a plane. Angle between a line and a plane Coordinates of a point, line, pairs of lines, circle and family of circles, conic section, three-dimensional geometry, sphere.

**Unit – 6**

**Mathematical Reasoning : **

Statements, New statement from Old, Special Words/Phrases, Implications, Validating Statements.

**Mathematical Induction and Binomial Theorem : **

The principle of mathematical induction, Binomial theorem, General and Middle terms.

**Permutation and Combination : **

Fundamental principle of counting. Permutations, Combinations.

**Unit – 7**

**Linear Algebra :**

Linear independence & dependence of row & column matrices, Row rank, column rank and rank of a matrix, Equivalence of column and row ranks. Eigen values, eigen vectors and characteristics equation of a matrix. Cayley Hamilton theorem and its use in finding inverse of a matrix.Definition and examples of vector spaces. Subspaces. Sum and direct sum of subspaces. Linear span. Linear dependence, independence, and their basic properties. Basis. Finite dimensional vector spaces, existence theorem for bases, invariance of the number of elements of a basis set, dimension, existence of complementary subspace of a finite dimensional vector space, dimension of sums of subspaces, quotient space and its dimension.

Linear transformations and their representation as matrices, the Algebra of linear transformations, the rank nullity theorem. change of basis, dual space, bidual space and natural isomorphism, adjoint of a linear transformation, eigen values and eigen vectors for a linear transformation, diagonalisation, bilinear, quadratic, and Hermitian forms. Inner product spaces- Cauchy- Schwarz inequality, orthogonal vectors, orthogonal complements, orthonormal sets and, bases,Bessel’s inequality for finite dimensional spaces, Gram-Schmidt orthogonalization process.

**Unit – 8**

**Abstract Algebra :**

Definition of a group with examples and simple properties, Sub groups, Cyclic groups, Coset decomposition, Lagrange’s theorem, Fermat’s, and Euler’s theorems. Homomorphism and isomorphism. Normal subgroups. Quotient groups.

The fundamental theorem of homomorphism. Permutation groups. Even and odd permutations, rings, sub-rings, integral domains, and fields. Characteristics of ring. Group Automorphisms, inner automorphism. Automorphism groups. Conjugacy relation and centraliser, normaliser. counting principle and the class equation of a finite group, Cauchy’s theorem and Sylow’s theorems for finite abelian groups and non-abelian groups.

**Ring theory :**

Ring homomorphism, Ideals and Quotient Rings, field of quotients of an integral domain, Euclidean rings. polynomial rings, polynomials over the rational field, polynomial rings over commutative rings, unique factorization domain.

**Unit – 9**

**Discrete Mathematics :**

**Boolean functions –** separable and combinatorial normal forms (canonical and end canonical), theorem relations – bipartite relations, inverse relations, conjugate relations, equivalence relations, equivalence classes and division of sets. Partially ordered set, partially ordered set, completely ordered set, Hemukh diagram, Maximum and last elements, First and last elements.

**Lattice –** Definition and examples, Dual lattice. Bounded lattice, Distributive complementary lattice.

**Graph –** Definition and types of subgraphs, locomotion, path, and circuit, connected and unconnected graphs, path, and circuit connected and unconnected, graphs circuit. **Tree** and its attributes, fixed tree, bivariate tree, parent tree, caste, and emptiness of graph, Kuskal and I’s algorithm.Matrix representation of graphs, incidence, and adjacency matrices, cutsets and their properties, planar graphs (definition). Kuratovsky bigraphs Unit.

**Unit – 10**

**Differentiation & Integration : **

Function, limit and continuity, differentiation, successive differentiation, application of derivatives, integration, fundamental theorem on integration, definite integration differential equation.

**Calculus : **

Leibnitz theorem. Maclaurin and Taylor series expansions. Linear equations and equations reducible to the linear form. Exact differential equations. Linear differential equations with constant coefficients. Homogeneous linear ordinary differential equations. Linear differential equations of second order.

**Unit – 11**

**Advanced Calculus : **

Advanced Calculus of a sequence, Theorems on limits of sequences. Bounded and monotonic sequences. Cauchy’s convergence criterion. Series of non-negative terms. Comparison tests. Cauchy’s integral test. Ratio tests. Raabe’s, logarithmic, de Morgan and Bertrand’s tests (without proofs). Alternating series. Leibnitz’s theorem. Absolute and conditional convergence. Continuity of single variable, Sequential continuity. Properties of continuous functions. Uniform continuity. Chain, rule of differentiability. Mean value theorems and their geometrical interpretations. Darboux’s intermediate value theorem for derivatives.

Limit and continuity of functions of two variables. Partial differentiation. Change of variables. Euler’s theorem on homogeneous functions. Taylor’s theorem for functions of two variables. Jacobians, Envelopes, Evolutes. Maxima, minima, and saddle points of functions of two variables, Lagrange’s multiplier method. Indeterminate forms. Beta and Gamma functions. Double and triple integrals. Dirichlet’s integrals. Change N of order of integration in double integrals.

**Unit – 12**

**Differential Equations : **

Series solutions of differential equations Power series method, Bessel and Legendre equations, Bessel’s & Legendre’s functions, and their properties. recurrence and generating relations, Orthogonality of functions. Sturm- Liouville problem. Orthogonality of eigen-functions. Reality of eigen-values. Laplace Transformation-Linearity of the Laplace transformation.

Existence theorem for Laplace transforms. Laplace transforms of derivatives and integrals. Shifting theorems. Differentiation and integration of transforms. Inverse Laplace transforms. Convolution theorem. Application of Laplace transformation in solving linear differential equations with constant coefficients. Partial differential equations of first order. Lagrange’s solution. Some special types of equations, which can be solved easily by methods other than the general method. Charpit’s general method of solution.

Partial differential equations of second & higher orders. Classification of linear partial differential equations of second order. Homogeneous and non- homogeneous equations with constant coefficients. Partial differential equation reducible to equations with constant coefficients. Calculus of Variations- Variational problems with fixed boundaries Euler’s equation for functionals containing first order derivative and one independent variable. Extremals, Functionals dependent on higher order derivatives. Functionals dependent on more than one independent variable. Variational problems in parametric form. Invariance of Euler’s equation under coordinates transformation.

**Unit – 13**

**Vector Analysis and Geometry : **

Magnitude and direction of vector, position vector, two dimensional & three-dimensional vector, scalar & vector products of vector and their properties, moment of couple, ‘application of vectors in three-dimensional geometry, to find out the distance between two skew lines. Scalar and vector product of three vectors, Reciprocal vectors, Vector differentiation. Gradient, divergence, and curl. Vector integration. Theorems of Gauss, Green, Stokes. Equation of cone with given base, right circular cone, Equation of cylinder and its properties.

**Unit – 14**

**Linear Inequalities and Linear Programming :**

Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of system of linear inequalities in two variables- graphically. Absolute value, Inequality of means, Cauchy-Schwarz Inequality, Chebyshev’s Inequality.

**Linear Programming :**

Related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions.

**Unit – 15**

**Trigonometry : **

Angle ; Degree measure Radian measure, Relation between degree and radian, Trigonometrical functions, Identities and equations of trigonometrical functions, Properties of triangle, Solution of triangles, Height, and Distances.

**Inverse trigonometrical functions : **

Basic concepts, Properties of Inverse Trigonometric Functions.

**Unit – 16**

**Basic Algebra : **

Algebraic expressions and their factors, linear equations in one and two variables and their applications, sets and operations on them, quadratic equations, symmetric functions of the roots.

**Sequence and Series : **

Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), Geometric mean (G.M.), Relation between A.M. and G.M.

**Unit – 17**

**Metric Spaces : **

Definition and examples of spaces. Neighbourhoods. Limit points. Interior points. Open and closed sets. Closure and interior. Boundary points. Sub-space of a metric space. Cauchy sequences. Completeness. Cantor’s intersection theorem. Contraction principle.

Real numbers as a complete ordered field, dense subsets, Baier Category theorem, separable, second countable and first countable spaces. Continuous functions, extension theorem, uniform continuity. Compactness, sequential compactness, totally bounded spaces, finite intersection property, continuous functions and compact sets, connectedness.

**Unit – 18**

**Real Analysis : **

Riemann integral. Integrability of continuous and monotonic functions. The fundamental theorem of integral calculus. Mean value theorems of integral calculus. Partial derivation and differentiability of real-valued functions of two variables.

Schwarz and the Young’s theorem. Implicit function theorem. Improper integrals and their convergence. Comparison tests, Abel’s and Dirichlet’s tests, Frullani’s integral, integral as a function of parameter, continuity, derivability, Fourier series of half & full intervals.

**Unit – 19**

**Complex Analysis :**

The Complex Numbers and Quadratic Equations : Complex numbers, Algebra of the complex numbers, The modulus and the conjugate of a complex numbers, Argand plain and polar representation.Quadratic equations. Complex numbers as ordered pairs. Geometric of Complex numbers. Stereographic projection. Continuity & differentiability of Complex functions, Analytic functions, Cauchy- Riemann equations, harmonic functions. Mobius transformations, fixed points, cross ratio, inverse points and critical mapping, Conformal mapping.

**Unit – 20**

**Statistics and Probability :**

Statistics Measures of dispersion, Range, Mean deviation, Variance, and standard deviations Probability Random experiment, Event, Axiomatic approach to probability, Conditional probability, Multiplication theorem on probability, independent events, Bayes’ theorem, Random variables and its probability distributions, Bernoulli trials and Binomial distributions.

**MP High School Teacher Selection Test (HSTST) Exam Syllabus Download :- **

MPESB HSTST Syllabus

**MP High School Teacher Selection Test (HSTST) Exam Application Fees : –**

- General / Other State Fees :
**Rs 560 /-**only - SC / ST / OBC Category Fees :
**Rs 310 / –**only.

**Steps To Check MP High School Teacher Selection Test (HSTST) Exam Result :-**

- Visit the Official Website of KVS PRT Exam 2023 i.e http://esb.mp.gov.in
- On the Home Page, Search for the MPESB High School Teacher Selection Test (HSTST)
**Exam Result.** - Click on the
**Result link.** - Enter your
**Roll No**and**Password.** - Click on
**Submit Button.** - Check the
**Result.** - Download and take the Printout of the Result.

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**FAQs : – **

Question : What is MP High School Teacher Selection Test (HSTST) Teacher Salary ?

Answer : The MP High School Teacher Selection Test (HSTST) Teacher Salary is 36200 Rs + DA.

Question : What is the selection Process for MP High School Teacher Selection Test (HSTST)Teacher Recruitment 2023 ?

Answer : Written , & Interview / Document Verification.

Question : Is there any negative marking for the Wrong Answers ?

Answer : There is no negative marking for the wrong answers.

Question : When willl be MP High School Teacher Selection Test (HSTST) Exam Held ?

Answer : MP High School Teacher Selection Test (HSTST) Exam will be held soon.

Question : Is B.Ed compulsory for MP High School Teacher Selection Test (HSTST) Exam ?

Answer : Yes

Question : Is there any Interview in MP High School Teacher Selection Test (HSTST) Exam ?

Answer : Yes