TS ECET Mathematics Syllabus 2024: Download PDF

TS ECET Mathematics Syllabus 2024 has three sections, the Mathematics section carries 100 marks, and Communicative English and Analytical Ability both carry 50 marks each. All three sections are compulsory, and candidates can download the direct PDF link for TS ECET 2024 Maths syllabus. The TS ECET syllabus is published by the JNTUH authorities on the official website at ecet.tsche.ac.in. 

TS ECET Mathematics Syllabus 2024 PDF

Candidates may refer to the direct link to the official TS ECET 2024 Mathematics Syllabus PDF from the table below.

TS ECET Mathematics Syllabus 2024

TS ECET 2024 syllabus for Maths has been released by the Telangana State Engineering Common Entrance Test on their official website. The syllabus for TS ECET Mathematics Syllabus 2024 is slightly different than other TS ECET subjects as it has only three sections, Mathematics, Communicative English, and Analytical Ability.

Candidates can refer to recommended books such as Competitive Exams Vedic Mathematics or Handbook of Mathematics for exam preparation.

TS ECET Mathematics Syllabus

TS ECET Mathematics Syllabus contains topics such as Partial Differentiation, Curvature and Lengths of Plane Curves, Differential Equations of First Order, Higher order Linear Differential Equations and PDE, Sequences and Series, Continuity, Differentiation and Riemann Integral, Groups, Rings, Vector Spaces, and Diagonalization and Orthogonality.

Unit- I: Partial Differentiation 

• Functions of two variables, Neighborhood of a point(a, b), Continuity of a Function of two variables, Continuity at a point, Limit of a Function of two variables, Partial Derivatives - Geometrical representation of a Function of two Variables - Homogeneous Functions.
• Theorem on Total Differentials, Composite Functions, Differentiation of Composite Functions, Implicit Functions, Equality of fxy(a,b) and fyx(a,b), Taylor’s theorem for function of two variables, Maxima and Minima of functions of two variables, Lagrange’s Method of undetermined multipliers.

Unit- II: Curvature and Lengths of Plane Curves

• Definition of Curvature, Radius of Curvature, Length of Arc as a Function, Derivative of Arc, Radius of Curvature, Cartesian Equations, Newtonian Method, Centre of Curvature, Chord of Curvature.
• Evolutes and Involutes, Properties of the evolutes.
• One Parameter Family of Curves, Definition and Determination of Envelope.
• Lengths of Plane Curves: Expression for the lengths of curves y = f (x), Expressions for the length of arcs x=f(y); x=f(t), y= ϕ(t); r=f(θ).

Unit- III: Differential Equations of First Order

• Variables Separable method, Homogeneous Differential Equations, Differential Equations Reducible to Homogeneous Form, Linear Differential Equations, Differential Equations Reducible to Linear Form, Exact differential equations, Integrating Factors, Change in variables.
• Differential Equations of first order but not first degree: Equations Solvable for p, Equations Solvable for y, Equations Solvable for x, Equations that do not contain x (or y), Equations Homogeneous in x and y, Equations of the First degree in x and y, Clairaut’s equation.

Unit- IV: Higher order Linear Differential Equations and PDE

• 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 Q(x) = eୟ୶, b sin ax, b cos ax, bx୩, Veୟ୶, Method of undetermined coefficients.
• Method of variation of parameters, Linear differential equations with non-constant coefficients, the Cauchy-Euler Equation, Legendre’s Linear Equations, Partial Differential Equations: Formation and solution, Equations easily integrable, Linear equations of the first order.

Unit- V: Sequences and Series

• Sequences: Limits of Sequences, Limit Theorems for Sequences, Monotone Sequences and Cauchy Sequences, Subsequences, Limit Superior and Limit Inferior, Series, Alternating Series and Integral Tests.

Unit- VI: Continuity, Differentiation and Riemann Integral  

• Continuity: Continuous Functions, Properties of Continuous Functions, Uniform Continuity, Limits of Functions, Basic properties of the derivative, the mean value theorems, L-Hospital Rule, Taylor’s theorem.
• The Riemann Integral, Properties of Riemann Integral, Fundamental Theorem of Calculus.

Unit- VII: Groups 

• Definition and Examples of Groups, Elementary Properties of Groups, Finite Groups, Subgroups, Subgroup Tests, Cosets and Lagrange’s Theorem, Properties of Cosets, Cyclic Groups, Properties of Cyclic Groups, Normal Subgroups and Factor Groups, Group Homomorphisms, Properties of Homomorphisms, The First Isomorphism Theorem, Automorphisms, Permutation Groups: Definition and Properties of Permutations, Isomorphisms, Cayley’s Theorem.

Unit- VIII: Rings  

• Rings, Examples of Rings, Properties of Rings, Subrings, Integral Domains, Fields, Characteristics of a Ring. Ideals, Factor Rings, Prime Ideals and Maximal Ideals.
• Ring Homomorphisms and isomorphisms. 

Unit- IX: 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.

Unit- X: Diagonalization and Orthogonality  

• Eigenvalues and Eigenvectors, The Characteristic Equation, Diagonalization, Eigenvectors of Linear Transformations, Inner Product spaces, Length and Orthogonality, Orthogonal Sets, Orthogonal Projections, The Gram-Schmidt Process.

TS ECET Analytical Ability Syllabus

TS ECET Analytical Ability Syllabus consists of topics such as Data Sufficiency, Sequences and Series, Data Analysis, Sequences and Series, Coding and Decoding Problems, and Date, Time and Arrangement Problems

Unit-I: Data Sufficiency  

• A question is given followed by data in the form of two statements labelled I and II. If the data given in I alone is sufficient to answer the question then choice (1) is the correct answer. If the data given in II alone is sufficient to answer the question, then choice (2) is the correct answer. If both I and II put together are sufficient to answer the question but neither of the statements alone is sufficient, then Choice (3) is the correct answer. If both I and II put together are not sufficient to answer the question and additional data is needed, then choice (4) is the correct answer.

Unit-II: Sequences and Series

• Analogies of numbers and alphabets completion of blank spaces following the pattern in A: b:: C:d relationship, odd thing out; Missing number in a sequence or a series.

Unit-III: Data Analysis  

• The data given in a Table, Graph, Bar Diagram, Pie Chart, Venn diagram, or passage is to be analysed and the questions pertaining to the data are to be answered.

Unit-IV: Coding and Decoding Problems

• A code pattern of the English Alphabet is given.
• A given word or a group of letters is to be coded and decoded based on the given code or codes. 

Unit-V: Date, Time, and Arrangement Problems  

• Calendar problems, Clock Problems, Blood Relationships, Arrivals, Departures and Schedules; Seating Arrangements, Symbol and Notation Interpretation.

TS ECET Communicative English Syllabus

TS ECET Communicative English Syllabus has topics such as Vocabulary, Grammar and Reading Comprehension.

Unit-I: Vocabulary

• Synonyms
• Antonyms
• Spelling
• One Word Substitutes
• Words Often Confused
• Idioms
• Phrasal Verbs

Unit-II: Grammar  

• Articles
• Prepositions
• Question Tags
• Active / Passive Voice
• Tenses
• Concord
• Correction of Sentences

Unit-III: Reading Comprehension

• Reading Comprehension (Passage 1)
• Reading Comprehension (Passage 2) 

Recommended Books for TS ECET 2024 Mathematics  

Below are some recommended books TS ECET Mathematics based on analyzing the TS ECET 2024 Mathematics Syllabus. Candidates may refer to the table below for the TS ECET Mathematics books: