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<\/p>\n\n\n\n
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.<\/p>\n\n\n\n
TS Ed.CET 2020 Exam will be held on 23th May 2020 (Saturday)<\/h4>\n\n\n\n
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.<\/p>\n\n\n\n
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<\/td><\/tr>
100 questions for 100 marks<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
SYLLABUS : MATHEMATICS <\/h4>\n\n\n\n
Mathematics Syllabus (Marks : 100)<\/h5>\n\n\n\n
DIFFERENTIAL CALCULUS<\/strong> 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 \u2013 Lagrange\u2018s Method of multipliers \u2013 Asymptotes – Envelopes. <\/p>\n\n\n\n
DIFFERENTIAL EQUATIONS<\/strong> Differential Equations of first order and first degree: Exact differential equations \u2013 Integrating Factors \u2013 Change in variables \u2013 Total Differential Equations \u2013 Simultaneous Total Differential equations \u2013 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 ) \u2013 Clairaut\u2018s Equation. <\/p>\n\n\n\n
Higher order linear differential equations<\/strong> 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 \uf03d , 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. <\/p>\n\n\n\n
Partial Differential equations<\/strong> Formation and solution- Equations easily integrable – Linear equations of first order – Non linear equations of first order – Charpit\u2018s method – Homogeneous linear partial differential equations with constant coefficient – Non homogeneous linear partial differential equations – Separation of variables. <\/p>\n\n\n\n
REAL ANALYSIS<\/strong> Sequences: Limits of Sequences – A Discussion about Proofs – Limit Theorems for Sequences – Monotone Sequences and Cauchy Sequences. Sub sequences – Lim sup\u2018s and Lim inf\u2018s – 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. <\/p>\n\n\n\n
ALGEBRA<\/strong> 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\u2018s Theorem Properties of Isomorphisms \u2013 Automorphisms – Cosets and Lagrange\u2018s Theorem Properties of Cosets 138 – Lagrange\u2018s 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. <\/p>\n\n\n\n
Introduction to Rings<\/p>\n\n\n\n
Motivation and Definition<\/strong> Examples of Rings – Properties of Rings \u2013 Subrings – Integral Domains: Definition and Examples \u2013Characteristics of a Ring – Ideals and Factor Rings; Ideals – Factor Rings – Prime Ideals and Maximal Ideals. Ring Homomorphisms<\/strong> Definition and Examples – Properties of Ring \u2013 Homomorphisms – The Field of Quotients Polynomial Rings: Notation and Terminology. LINEAR ALGEBRA<\/strong> 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 <\/strong> Eigenvectors and Linear Transformations- Complex Eigen values- Applicationsto Differential Equations- Orthogonality and Least Squares: Inner Product, Length, and Orthogonality – Orthogonal Sets. NUMERICAL ANALYSIS<\/strong> Solutions of Equations in One Variable: The Bisection Method – Fixed-Point Iteration – Newton\u2018s Method and Its Extensions – Error Analysis for Iterative Methods – Accelerating Convergence – Zeros of Polynomials and Mu\u00a8ller\u2018s Method – Survey of Methods and Software. Interpolation and Polynomial Approximation: Interpolation and the Lagrange Polynomial – Data Approximation and Neville\u2018s Method – Divided Differences – Hermite Interpolation – Cubic Spline Interpolation. Numerical Differentiation and Integration<\/strong> Numerical Differentiation – Richardson\u2018s Extrapolation – Elements of Numerical Integration – Composite Numerical Integration \u2013 Romberg Integration – Adaptive Quadrature Methods – GaussianQuadrature. <\/p>\n\n\n\n
Texts:<\/strong><\/p>\n\n\n\n
Shanti Narayan and Mittal, Differential Calculus <\/li>
Zafar Ahsan, Differential Equations and Their Applications<\/li>
Kenneth A Ross, Elementary Analysis-The Theory of Calculus <\/li>
Joseph A Gallian, Contemporary Abstract algebra (9th edition) <\/li>
David C Lay, Linear Algebra and its Applications 4e<\/li>
Richard L. Burden and J. Douglas Faires, Numerical Analysis <\/li><\/ul>\n\n\n\n