TS ECET Syllabus B.Sc Mathematics. TS ECET is the Engineering Common Entrance Test for Diploma holders & B.Sc. (Maths) Degree holders being conducted on behalf of TSCHE. TS ECET [FDH & B.Sc.(Mathematics)] for lateral entry into B.E./ B.Tech./ B.Pharm. courses in the State of Telangana.
TS ECET 2021 will be conducted by JNTUH on behalf of the Telangana State Council of Higher Education for the academic year 2021-2023.
TS ECET 2021 Exam will be on 5th July to 9 July 2021
TS ECET 2021 Computer Based Common Entrance Test, designated as Telangana State Engineering Common Entrance Test for Diploma Holders & B.Sc. (Mathematics) Degree Holders. TS ECET [FDH & B.Sc. (Mathematics)]
TS ECET Syllabus B.Sc Mathematics
TS ECET Syllabus B.Sc Mathematics cover subjects given below
Mathematics, Physics, Chemistry & Electrical and Electronics Engineering
TS ECET Syllabus B.Sc Mathematics
Subject: MATHEMATICS (100 Marks)
Unit – I: Differential Calculus
Mean Value theorems, Taylor‘s Theorem, Partial Differentiation, Euler’s Theorem, Curvature, Evolutes, Envelopes, Maxima & Minima of two variables & Lagrange’s multipliers.
Unit – II: Differential Equations of First Order and First Degree
Linear Differential Equations; Differential Equations Reducible to Linear Form; Exact Differential Equations; Integrating Factors; Change of Variables. Differential Equations of the First Order but not of the 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 – III: Higher Order Linear Differential Equations
Solution of Homogeneous Linear Differential Equations of Order n with Constant Coefficients. Solution of the Non-homogeneous Linear Differential Equations with Constant Coefficients by means of Polynomial Operators. (i)When Q(x) = bxk and P(D) = D – a0, a0 ≠ 0 (ii)When Q(x) =bxk and P(D) = ao D n + a1 D n-1 + … + an (iii)When Q(x) = e ax (iv)When Q(x) = b sin ax or b cos ax (v)When Q(x) = eax V where V is a function of x. (vi)When Q(x) = xV Where V is any function x.
Unit – IV: The Real Numbers
The algebraic and Order Properties of R; Absolute Value and Real Line; The Completeness Property of R; Applications of the Supremum Property; Intervals. Sequences and Series: Sequences and their Limits; Limits Theorems; Monotone Sequences; Subsequences and the Bolzano – Weierstrass Theorem; The Cauchy Criterion; Properly Divergent Sequences. Infinite series: Introduction to series, Test for Convergence of series Absolute convergence, Test for absolute convergence, Leibnitz Test. Limits & Continuity: Limits of Functions, Continuous Functions & Properties, Types of Discontinuities. Uniform Continuity, Uniform Continuity Theorem. The Riemann Integral: The Riemann Integral & properties, the Fundamental theorem.
Unit –V: Binary Operations
Definition and Properties, Tables. Groups: Definition and Elementary Properties; Finite Groups and Group Tables. Subgroups: Subgroups and properties Groups of Cosets: Cosets, Applications, Lagranges Theorem, Normalizer of an element of a group Normal Subgroups and Factor Groups: Criteria for the Existence of a Coset Group; Inner Automorphisms and Normal Subgroups; Factor Groups; Simple Groups Homomorphisms: Definition and Elementary Properties; The Fundamental Theorem on Homomorphism of groups; Applications. Isomorphism: Definition and Elementary Properties, How to show that groups are Isomorphic, How to show that Groups are Not Isomorphic, Cayley‘s Theorem Permutations: Functions and Permutations; Groups of Permutations, Cycles and Cyclic Notation, Even and Odd Permutations, T he Alternating Groups Cyclic Groups: Elementary Properties, The Classification of Cyclic Groups, Subgroups of Finite Cyclic Groups
Unit – VI: Vector Differentiation
Gradient, Divergence, Curl, Differential Operators Vector Integration: Line, Surface, Volume integrals. Theorems of Gauss, Green and Stokes and Problems related to them.
Unit – VII: The Plane
Every equation of the first degree in x, y, z represents a plane, Converse of the preceding Theorem; Transformation to the normal form, Determination of a plane under given conditions. i) Equation of a plane in terms of its intercepts on the axes. ii) Equations of the plane through three given points. Systems of planes; Two sides of a plane; Length of the perpendicular from a given point to a given plane; Bisectors of angles between two planes; Joint equation of two planes; Orthogonal projection on a plane; Volume of a tetrahedron in terms of the co-ordinates of its vertices; Equations of a line; Right Line; Angle between a line and a plane; The condition that a given line may lie in a given plane; The condition that two given lines are coplanar, The shortest distance between two lines. The length and equations of the line of shortest distance between two straight lines; Length of the perpendicular from a given point to a given line; Intersection of three planes; Triangular Prism. The Sphere: Definition and equation of the sphere; Equation of the Sphere through four given points; Plane sections of a sphere. Intersection of two spheres; Equation of a circle. Sphere through a given circle; Intersection of a sphere and a line. Power of a point; Tangent plane. Plane of contact. Polar plane. Angle of intersection of two spheres. Conditions of two spheres. Conditions for two spheres to be orthogonal; Radical plane, coaxial system of spheres; Simplified form of the equation of two spheres.
Unit – VIII: Rings
Definition and Basic Properties Integral Domains: Divisors of zero and cancellation laws, Integral domains, The Characteristic of a Ring, Some Non-Commutative Examples, The Quaternion’s, Fields, Matrices over a field, Sub – Rings, Ideals, Quotient Rings & Euclidean Rings: Ideals, Principal Ideal, Quotient Rings and Euclidean Rings. Homomorphisms of Rings: Definition and Elementary properties, Maximal and Prime Ideals, Principal ideals.
Unit – IX : Vector Spaces
Vector Spaces, Subspaces, General properties of vector spaces, Algebra of subspaces, linear combination of vectors. Linear span, linear sum of two subspaces, Linear Dependence and Linear Independence of vectors, Basis of vector space. Linear Transformation and Matrices: Linear Transformations, Linear operators, Range and null space of linear transformation, Rank and nullity of linear transformations, Linear Transformations as vectors, Product of linear transformations, Invertible linear transformations. Transpose of linear transformations, characteristic values and characteristic vectors, Cayley – Hamilton theorem, Diagonalization method. Inner Product Spaces: Norm of a vector, Inner Product spaces, Euclidean and unitary spaces, Schwartz inequality, Orthogonality, Orthonormal set, complete orthonormal set, Gram – Schmidt orthogonalisation process.
TS ECET Syllabus B.Sc Mathematics
Syllabus: Analytical Ability (50 Marks)
1. Data Sufficiency:-
A question is given followed by data in the form of two statements labeled as 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 by neither statement 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.
2. a. 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.
b.Data Analysis: The data given in a Table, Graph, Bar Diagram, Pie Chart, Venn diagram or a passage is to be analyzed and the questions pertaining to the data are to be answered.
c. Coding and Decoding Problems: A code pattern of English Alphabet is given. A given word or a group of letters are to be coded and decoded based on the given code or codes. d. Date, Time and Arrangement Problems: Calendar problems, Clock Problems, Blood Relationship, Arrivals, Departures and Schedules; Seating Arrangements, Symbol and Notation Interpretation.
TS ECET Syllabus B.Sc Mathematics
Syllabus: Communicative English (50 MARKS)
1. Vocabulary
- Antonyms – 5m Synonyms – 5m
- Single Word Substitute – 3m
- Words often confused – 3m
- Idioms & Phrasal Verbs – 2m
2. Grammar
- Tenses – 2m
- Prepositions – 5m
- Concord – 5m
- Active & Passive Voice – 5m
3. Correction of Sentences – 5m
4. Spelling – 5m
5. Reading Comprehension – 5m
TS ECET 2021 Important Dates
TS ECET 2021 Exam Date, Eligibility & Exam Pattern
TS ECET 2021 Syllabus
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