TSCHE ECET 2021 Syllabus : Telangana State Engineering Common Entrance Test

Organisation : TSCHE Telangana State Council of Higher Education
Exam Name : Telangana State Engineering Common Entrance Test
Announcement : TS ECET 2021 Syllabus
Website : https://ecet.tsche.ac.in/

TS ECET Exam

A Common Entrance Test designated in full as Engineering Common Entrance Test for Diploma and for B.Sc.(Mathematics) Degree Candidates in short as TS ECET [FDH & B.Sc. (Mathematics)] will be conducted by Jawaharlal Nehru Technological University Hyderabad on behalf of the Telangana State Council of Higher Education

Related / Similar Syllabus : TSCHE TSICET 2021 Syllabus

TSECET Syllabus

Computer Science & Engineering
Syllabus: Mathematics (50 Marks)

Unit-I:
Matrices Matrices: Definition of Matrix, Types of matrices-Algebra of matrices-Transpose of a matrix-Symmetric, skew symmetric matrices-Minor, cofactor of an element-Determinant of a square matrix-Properties-Laplace‘s expansion-singular and nonsingular matrices-Adjoint and multiplicative inverse of a square matrix-System of linear equations in 3 variables-Solutions by Crammer‘s rule, Matrix inversion method-Gauss-Jordan method.-Partial Fractions: Resolving a given rational function into partial fractions.Logarithms: Definition of logarithm and its properties, meaning of ‘e’ exponential function and logarithmic function.

Unit–II:
Trigonometry Properties of Trigonometric functions– Ratios of Compound angles, multiple angles, sub multiple angles – Transformations of Products into sum or difference and vice versa.Properties of triangles: sine rule, cosine rule, tangent rule and projection rule. Solving a triangle when (i) three sides (SSS), (ii) two sides and an included angle(SAS), (iii) one side and two angles are given(SAA).

Inverse Trigonometric functions, Hyperbolic functions. Complex Numbers: Properties of Modulus, amplitude and conjugate of complex numbers, arithmetic operations on complex numbers—Modulus-Amplitude form (Polar form) – Euler form (exponential form)-Properties.

Unit–III:
Analytical Geometry Straight Lines–different forms of Straight Lines, distance of a point from a line, angle between two lines, intersection of two non-parallel lines and distance between two parallel lines.

Circles-Equation of circle given center and radius, given ends of diameter-General equation- finding center and radius, center and a point on the circumference, 3 non-collinear points, center and tangent, equation of tangent and normal at a point on the circle.

Unit–IV:
Differentiation and its Applications Functions and limits – Standard limits – Differentiation from the First Principle – Differentiation of sum, product, quotient of functions, function of function, trigonometric, inverse trigonometric, exponential, logarithmic, Hyperbolic functions, implicit, explicit and parametric functions–Derivative of a function with respect to another function-Second order derivatives – Geometrical applications of the derivative(angle between curves, tangent and normal)–Increasing and decreasing functions–Maxima and Minima(single variable functions) using second order derivative only – Partial Differentiation–Partial derivatives up to second order–Euler‘s theorem.

Unit–V:
Integration and its Applications Indefinite Integral – Standard forms – Integration by decomposition of the integrand, integration of trigonometric, algebraic, exponential, logarithmic and Hyperbolic functions– Integration by substitution –Integration of reducible and irreducible quadratic factors – Integration by parts– Definite Integrals and properties, Definite Integral as the limit of a sum – Application of Integration to find areas under plane curves and volumes of Solids of revolution– Mean and RMS values, Trapezoidal rule and Simpson’s 1/3 Rule for approximation integrals

Unit–VII:
Laplace Transforms (LT) of elementary functions-Linearity property, first shifting property, change of scale property multiplication and division by t – LT of derivatives and integrals, Unit step function, LT of unit step function, second shifting property, evaluation of improper integrals, Inverse Laplace transform (I LT)-shifting theorem, change of scale property, multiplication and division by s, ILT by using partial fractions and convolution theorem. Applications of LT to solve linear ordinary differential equations up to second order on

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