SRMEE 2014 Mathematics Syllabus

PART 3 – MATHEMATICS (35 Questions)

UNIT 1: Sets, Relations and Functions

 Sets and their representations, union, intersection and  complements of sets and their algebraic properties, relations,  equivalence relations, mappings, one-one, into and onto  mappings, composition of mappings.

UNIT 2: Complex Numbers

Complex numbers in the form a+ib and their representation  in a plane. Argand diagram. Algebra of complex numbers,  modulus and argument (or amplitude) of a complex number,  square root of a complex number. Cube roots of unity,  triangle inequality.

UNIT 3: Matrices and Determinants

 Determinants and matrices of order two and three,  properties of determinants, evaluation of determinants.  Addition and multiplication of matrices, adjoint and inverse  of matrix.

UNIT 4: Applications of Matrices and Determinants

Computing the rank of a matrix-test of consistency and  solution of simultaneous linear equations using determinants and matrices.

UNIT 5: Quadratic Equations

 Quadratic equations in real and complex number system and  their solutions. Relation between roots and coefcients,  nature of roots, formation of quadratic equations with given  roots; symmetric functions of roots, equations reducible to  quadratic equations.

UNIT 6: Permutations and Combinations

Fundamental principle of counting: permutation as an  arrangement and combination as selection, meaning of  P(n,r) and C(n,r). Simple applications.

UNIT 7: Mathematical Induction and its Applications

 Stating and interpreting the principle of mathematical  induction. Using it to prove formula and facts.

UNIT 8: Binomial Theorem and its Applications

Binomial theorem for a positive integral index; general term  and middle term; Binomial theorem for any index.  Properties of binomial coefficients. Simple applications for approximations.

UNIT 9: Sequences and Series

 Arithmetic, geometric and harmonic progressions. Insertion  of arithmetic, geometric and harmonic means between two  given numbers. Relation between A.M., G.M. and H.M.  arithmetic, geometric series, exponential and logarithmic  series.

UNIT 10: Differential Calculus

Polynomials, rational, trigonometric, logarithmic and  exponential functions. Inverse functions. Graphs of simple  functions. Limits, continuity, differentiation of the sum,  difference, product and quotient of two functions.  differentiation of trigonometric, inverse  trigonometric, logarithmic, exponential, composite  and implicit functions, derivatives of order up to  two.

UNIT 11: Applications of Differential Calculus

 Rate of change of quantities, onotonic – increasing  and decreasing functions, maxima and minima of  functions of one variable, tangents and normals,  Rolle’s and Lagrange’s mean value theorems.

UNIT 12: Integral Calculus

Integral as an anti-derivative. Fundamental  integrals involving algebraic, trigonometric,  exponential and logarithmic functions. Integration  by substitution, by parts and by partial fractions.  Integration using trigonometric identities. Integral  as limit of a sum. Properties of denite integrals.  Evaluation of denite integrals; Determining areas  of the regions bounded by simple curves.

UNIT 13: Differential Equations

Ordinary differential equations, their order and  degree. Formation of differential equations.  Solution of differential equations by the method of  separation of variables. Solution of homogeneous  and linear differential equations and those of the type d2y / dx2 = f(x).

UNIT 14: Straight Lines in Two Dimensions

Cartesian system of rectangular co-ordinates in  plane, distance formula, area of a triangle,  condition for the collinearity of three points and  section formula, centroid and in-centre of a  triangle, locus and its equation, translation of axes,  slope of a line, parallel and perpendicular lines,  intercepts of a line on the coordinate axes. Various  forms of equations of a line, intersection of lines,  angles between two lines, conditions for  concurrence of three lines, distance of a point from  a line. Equations of  internal and external bisectors  of angles between two lines, coordinates of  centroid, orthocentre and circumcentre of a  triangle, equation of family of lines passing  through the point of intersection of two lines,  homogeneous equation of second degree in x and  y, angle between pair of lines through the origin,  combined equation of the bisectors of the angles  between a pair of lines, condition for the general  second degree equation to represent a pair of lines,  point of intersection and angle between two lines.

UNIT 15: Circles in Two Dimensions

 Standard form of equation of a circle, general  form of the equation of a circle, its radius and  centre, equation of a circle in the parametric form,  equation of a circle when the end points of a  diameter are given, points of intersection of a line  and a circle with the centre at the origin and  condition for a line to be tangent to the circle,  length of the tangent, equation of the tangent,  equation of a family of circles through the  intersection of two circles, condition for two  intersecting circles to be orthogonal.

UNIT 16: Conic Sections in Two Dimensions

Sections of cones, equations of conic sections  (parabola, ellipse and hyperbola) in standard form,  condition for y = mx+c to be a tangent and  point(s) of tangency.

UNIT 17: Vector Algebra

Vectors and scalars, addition of vectors,  components of a vector in two dimensions and  three dimensional  space, scalar and vector  products, scalar and vector triple product.  Application of vectors to plane geometry.

UNIT 18: Measures of Central Tendency and  Dispersion

Calculation of mean, median and mode of  grouped and ungrouped data.  Calculation of  standard deviation, variance and mean deviation  for grouped and ungrouped data.

UNIT 19: Probability

Probability of an event, addition and  multiplication theorems of probability and their  applications; Conditional probability; Baye’s  theorem, probability distribution of a random  variate; binomial and poisson distributions and  their properties.

UNIT 20: Trigonometry

Trigonometrical identities and equations. Inverse  trigonometric functions and their properties.  Properties of triangles, including, incentre,  circumcentre and orthocenter, solution of  triangles.

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