A Common Entrance Test, designated as Telangana State Education Common Entrance Test through Computer Based Test -2020 (TS Ed.CET-2020 (CBT) will be conducted by the convener, TS Ed.CET-2020, Osmania University on behalf of the Telangana State Council of Higher Education for admission into B.Ed.(Two years)Regular Course in the Colleges of Education in Telangana for the academic year 2020-2021
TS Ed.CET-2020 is a CBT test will be conducted by the convener of Osmania University on behalf of the Telangana State Council of Higher Education.
TS Ed.CET 2020 Exam will be held on 23th May 2020 (Saturday)
Students should satisfy the following requirements shall be eligible to appear for TS Ed.CET-2020 (CBT) for admission into 2-year B.Ed Course.
Part-A
| General English | 25 questions for 25 marks |
Part-B
| General English | 15 questions for 15 marks |
| Teaching Aptitude | 10 questions for 10 marks |
Part-C
Methodology: Candidate has to choose one of the following subjects. It consists of 100 Questions for 100 marks . Each carry one marks
| Mathematics | 100 questions for 100 mark |
| Physical Sciences 1. Physics 2. Chemistry | 100 questions for 100 marks 1. 50 questions for 50 marks 2. 50 questions for 50 marks |
| Biological Sciences 1. Botany 2. Zoology | 100 questions for 100 marks 1. 50 questions for 50 marks 2. 50 questions for 50 marks |
| Social Studies 1. Geography 2. History 3. Civics 4. Economics | 100 questions for 100 marks 1. 35 questions for 35 marks 2. 30 questions for 30 marks 3. 15 questions for 15 marks 2. 20 questions for 20 marks |
| English | 100 questions for 100 marks |
SYLLABUS : MATHEMATICS
Mathematics Syllabus (Marks : 100)
DIFFERENTIAL CALCULUS
Successive Differentiation – Expansions of Functions- Mean value theorems. Indeterminate forms – Curvature and Evolutes. Partial differentiation – Homogeneous functions – Total derivative. Maxima and Minima of functions of two variables – Lagrange‘s Method of multipliers – Asymptotes – Envelopes.
DIFFERENTIAL EQUATIONS
Differential Equations of first order and first degree: Exact differential equations – Integrating Factors – Change in variables – Total Differential Equations – Simultaneous Total Differential equations – Equations of the form dx dy dz P Q R Differential Equations first order but not first degree: Equations solvable for y – Equations solvable for x – Equations that do not contain x ( or y ) – Clairaut‘s Equation.
Higher order linear differential equations
Solution of homogeneous linear differential equations with constant coefficients – Solution of non-homogeneous differential equations P(D)y = Q(x) with constant coefficients by means of polynomial operators when ( ) ax Q x be , b ax b ax Sin / Cos , k bx , ax Ve . Method of undetermined coefficients – Method of variation of parameters – Linear differential equations with non constant coefficients – The Cauchy- Euler Equation.
Partial Differential equations
Formation and solution- Equations easily integrable – Linear equations of first order – Non linear equations of first order – Charpit‘s method – Homogeneous linear partial differential equations with constant coefficient – Non homogeneous linear partial differential equations – Separation of variables.
REAL ANALYSIS
Sequences: Limits of Sequences – A Discussion about Proofs – Limit Theorems for Sequences – Monotone Sequences and Cauchy Sequences. Sub sequences – Lim sup‘s and Lim inf‘s – Series – Alternating Series and Integral Tests. Sequences and Series of Functions: Power Series – Uniform Convergence – More on Uniform Convergence – Differentiation and Integration of Power Series. Integration: The Riemann Integral – Properties of Riemann Integral – Fundamental Theorem of Calculus.
ALGEBRA
Groups: Definition and Examples of Groups- Elementary Properties of Groups – Finite Groups; Subgroups -Terminology and Notation -Subgroup Tests – Examples of Subgroups Cyclic
Groups:Properties of Cyclic Groups – Classification of Subgroups Cyclic Groups – Permutation Groups: Definition and Notation – Cycle Notation -Properties of Permutations – A Check Digit Scheme Based on D5. Isomorphisms: Motivation – Definition and Examples – Cayley‘s Theorem Properties of Isomorphisms – Automorphisms – Cosets and Lagrange‘s Theorem Properties of Cosets 138 – Lagrange‘s Theorem and Consequences – An Application of Cosets to Permutation Groups – The Rotation Group of a Cube and a Soccer Ball – Normal Subgroups and Factor Groups ; Normal Subgroups – Factor Groups – Applications of Factor Groups – Group Homomorphisms – Definition and Examples – Properties of Homomorphisms – The First Isomorphism Theorem.
Introduction to Rings
Motivation and Definition
Examples of Rings – Properties of Rings – Subrings – Integral Domains: Definition and Examples –Characteristics of a Ring – Ideals and Factor Rings; Ideals – Factor Rings – Prime Ideals and Maximal Ideals.
Ring Homomorphisms
Definition and Examples – Properties of Ring – Homomorphisms – The Field of Quotients Polynomial Rings: Notation and Terminology.
LINEAR ALGEBRA
Vector Spaces: Vector Spaces and Subspaces – Null Spaces, Column Spaces, and Linear Transformations – Linearly Independent Sets; Bases – Coordinate Systems – The Dimension of a Vector Space. Rank-Change of Basis – Eigen values and Eigenvectors – The Characteristic Equation.
Diagonalization
Eigenvectors and Linear Transformations- Complex Eigen values- Applicationsto Differential Equations- Orthogonality and Least Squares: Inner Product, Length, and Orthogonality – Orthogonal Sets.
NUMERICAL ANALYSIS
Solutions of Equations in One Variable: The Bisection Method – Fixed-Point Iteration – Newton‘s Method and Its Extensions – Error Analysis for Iterative Methods – Accelerating Convergence – Zeros of Polynomials and Mu¨ller‘s Method – Survey of Methods and Software.
Interpolation and Polynomial Approximation: Interpolation and the Lagrange Polynomial – Data Approximation and Neville‘s Method – Divided Differences – Hermite Interpolation – Cubic Spline Interpolation.
Numerical Differentiation and Integration
Numerical Differentiation – Richardson‘s Extrapolation – Elements of Numerical Integration – Composite Numerical Integration – Romberg Integration – Adaptive Quadrature Methods – GaussianQuadrature.
Texts:
- Shanti Narayan and Mittal, Differential Calculus
- Zafar Ahsan, Differential Equations and Their Applications
- Kenneth A Ross, Elementary Analysis-The Theory of Calculus
- Joseph A Gallian, Contemporary Abstract algebra (9th edition)
- David C Lay, Linear Algebra and its Applications 4e
- Richard L. Burden and J. Douglas Faires, Numerical Analysis
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