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SCRA Mathematics Syllabus

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Here you will find SCRA Mathematics Syllabus 2015.

1. Algebra :-

Concept of a set, Union and Intersection of sets, Complement of a set, Null set, Universal set and Power set, Venn diagrams and simple applications. Cartesian product of two sets, relation and mapping — examples, Binary operation on a set examples. Representation of real numbers on a line. Complex numbers: Modulus, Argument, Algebraic operations on complex numbers. Cube roots of unity. Binary system of numbers, Conversion of a decimal number to a binary number and vice-versa. Arithmetic, Geometric and Harmonic progressions. Summation of series involving A.P., G.P., and H.P.. Quadratic equations with real co-efficients. Quadratic expressions: extreme values. Permutation and Combination, Binomial theorem and its applications.

Matrices and Determinants: Types of matrices, equality, matrix addition and scalar multiplication - properties. Matrix multiplication — non-commutative and distributive property over addition. Transpose of a matrix, Determinant of a matrix. Minors and Cofactors. Properties of determinants. Singular and non-singular matrices. Adjoint and Inverse of a square-matrix, Solution of a system of linear equations in two and three variables-elimination method, Cramers rule and Matrix inversion method (Matrices with m rows and n columns where m, n < to 3 are to be considered).Idea of a Group, Order of a Group, Abelian Group. Identitiy and inverse elements Illustration by simple examples.

2. Trigonometry :-

Addition and subtraction formulae, multiple and sub-multiple angles. Product and factoring
formulae. Inverse trigonometric functions — Domains, Ranges and Graphs. DeMoivre's the-
orem, expansion of Sin n0 and Cos n0 in a series of multiples of Sines and Cosines.
Solution of simple trigonometric equations. Applications: Heights and Distance.

3. Analytic Geometry (two dimensions):
Rectangular Cartesian. Coordinate system, distance between two points, equation of a
straight line in various forms, angle between two lines, distance of a point from a line.
Transformation of axes. Pair of straight lines, general equation of second degree in x
and y — condition to represent a pair of straight lines, point of intersection, angle
between two lines. Equation of a circle in standard and in general form, equations of
tangent and normal at a point, orthogonality of two cricles. Standard equations of
parabola, ellipse and hyperbola — parametric equations, equations of tangent and nor-
mal at a point in both cartesian and parametric forms.

4. Differential Calculus: Concept of a real valued function — domain, range and graph. Composite functions, one to one, onto and inverse functions, algebra of real functions, examples of polynomial, rational, trigonometric, exponential and logarithmic functions. Notion of limit, Standard limits - examples. Continuity of functions - examples, algebraic operations on continuous functions. Derivative of a function at a point, geometrical and physical interpretation of a derivative - applications. Derivative of sum, product and quotient of functions, derivative of a function with respect to another function, derivative of a composite function, chain rule. Second order derivatives. Rolle's theorem (statement only), increasing and decreasing functions. Application of derivatives in problems of maxima, minima, greatest and least values of a function.

5. Integral Calculus and Differential equations :

Integral Calculus :-

Integration as inverse of differential, integration by substitution and by parts, standard integrals involving algebraic expression, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals-determination of areas of plane regions bounded by curves - applications.

Differential equations :-

Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equation, solution of first order and first degree differential equation of various types - examples. Solution of second order homogeneous differential equation with constant co-efficients.

6. Vectors and its applications :-

Magnitude and direction of a vector, equal vectors, unit vector, zero vector, vectors in two and three dimensions, position vector. Multiplication of a vector by a scalar, sum and difference of two vectors, Parallelogram law and triangle law of addition. Multiplication of vectors — scalar product or dot product of two vectors, perpendicularity, commutative and distributive properties. Vector product or cross product of two vectors. Scalar and vector triple products. Equations of a line, plane and sphere in vector form - simple problems. Area of a triangle, parallelogram and problems of plane geometry and trigonometry using vector methods. Work done by a force and moment of a force.

7. Statistics and probability :

Statistics :-

Frequency distribution, cumulative frequency distribution - examples. Graphical representation - Histogram, frequency polygon - examples. Measure of central tendency - mean, median and mode. Variance and standard deviation - determination and comparison. Correlation and regression.

Probability :-

Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary and composite events. Definition of probability : classical and statistical - examples. Elementary theorems on probability - simple problems. Conditional probability, Bayes' theorem - simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binomial distribution.

Birla Institute of Technology and Science is a higher educational institute that is known for its excellent pedagogy in engineering and sciences.

Birla Institute of Technology and Science BITS Pilani Courses Offered

Address : Vidya Vihar Campus, Pilani, Rajasthan, India Ph : 01596 -242090

Vellore Institute of Technology in Vellore is considered to be one of the leading technical training institutes in the state of Tamil Nadu.

VIT (Vellore Institute of Technology) Vellore Courses Offered

National Institute of Technology Suratkal is a public engineering institute that was set up in the year 1960.

NIT (National Institute of Technology) Surathkal Courses Offered

Address : Surathkal, Srinivasnagar, Mangalore - 575025, India. Ph : +91-824-2474000 Fax :+91-824-2474033

College of Engineering Anna University Chennai is one of the pioneer engineering institutes in the state of Tamil Nadu, which was established in the year 1794.

College of Engineering Anna University Guindy Courses Offered

Address : Sardar Patel Road, Guindy, Chennai, Tamil Nadu, India Ph : 044 - 22351723, 22351126 Email: deanceg@annauniv.edu

Coimbatore

PSG College of Technology is located in Coimbatore in Tamil Nadu.

PSG College of Technology Courses Offered

Address : Post Box No. 1611 Peelamedu Coimbatore - 641 004 Tamil Nadu INDIA Ph : 422-2572177, 2572477, 2580455, 2578455, 4344777 Email: principal@psgtech.edu

National Institute of Technology in Tiruchirappalli is a public engineering institute that was set up in the year 1964.

NIT (National Institute of Technology) Trichy Courses Offered

NIT (National Institute of Technology) in Calicut is a public engineering institute that was set up in the year 1961.

NIT (National Institute of Technology) Calicut Courses Offered

Address : Kettangal Koduvally Road, Kozhikode, Kerala, India Ph : 0495 228 6118

NIT (National Institute of Technology) in Rourkela is a public engineering institute that was set up in the year 1964.

NIT (National Institute of Technology) Rourkela Courses Offered

Address : Orissa, Rourkela Pin - 769008.

Patiala

Thapar Inst of Engg & Tech Patiala, which is also known as Thapar University is one of the leading engineering institutes in the state of Punjab that was established by Karam Chand Thapar in the year 1956.

Thapar University Patiala Courses Offered

Address : P.O Box 32, Patiala, Pin -147004 Ph : +91-175-2393021 Fax : +91-175-2364498, 2393020 Email :  registrar@thapar.edu

Veermata Jijabai Technological Institute is one of the oldest technical institutes in Asia that was established in the year 1887.

Veermata Jijabai Technological Institute Courses Offered

Address : Nathalal Parekh Road, Matunga East, Mumbai, MH, India Ph : 022 2419 8102

Bangalore

BMS College of Engineering is a technical school that is known for offering excellent education to those students who aspire to become an engineer or aim of achieving higher position in the field of IT.

BMS College of Engineering Bangalore Courses Offered

Address : P.O. Box No.: 1908 Bull Temple Road Bangalore - 560 019 Karnataka, India. Phone : +91-80-26622130-35 (6 lines) Fax : +91-80-26614357

Bangalore

Bangalore Institute of Technology in Bangalore is an educational institute for engineering and information technology that was set up in 1979 by Vokkaligara Sangha.

Bangalore Institute of Technology Courses Offered

Address : K.R. Road , V V Puram, India Ph : +91-080-26615865 , 26613237 Fax :+91-080-26526796

Bengal Engineering and School University (BESU) is the second oldest technical institute in India that was established in the year 1856.

Bengal Engineering and Science University Courses Offered

Address : PO: Botanic Garden, Dist: Howrah, West Bengal, India - 711103

Visakhapatnam

Gayatri Vidya Parishad College of Engineering is a technical institute in Vishakapatnam, Andhra Pradesh that was established in the year 1996.

College of Engineering Visakhapatnam Courses Offered

Address : Andhra University, Visakhapatnam, Andhra Pradesh, India Ph : 0891-2844771 Email : principal@aucevizag.ac.in

Dhirubhai Ambani Institute of Information & Communication Technology is a technical institute nestled in Gandhinagar, Gujarat.

Dhirubhai Ambani Institute of Information and Communication Technology (DAIICT) Gandhinagar Courses Offered

Address : Near Indroda Circle Gandhinagar Pin - 382 007 Gujarat (India) Tel. : (+91) 079-3052-0000 Fax : (+91) 079-3052-0010 Email : info[at]daiict[dot]ac[dot]in

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