(Syllabus) CBSE: All India Engineering Entrance Examination (AIEEE)
Unit 1 : Sets, Relations and Functions:
Sets and their representation; Union, intersection and
complement of sets and their algebraic properties; Power set; Relation, Types of
relations, equivalence relations, functions;. one-one, into and onto functions,
composition of functions.
Unit 2 : Complex Numbers and Quadratic Equations:
Complex numbers as ordered pairs of reals, Representation of
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, triangle inequality, Quadratic
equations in real and complex number system and their solutions. Relation
between roots and co-efficients, nature of roots, formation of quadratic
equations with given roots.
Unit 3 : Matrices and Determinants:
Matrices, algebra of matrices, types of matrices,
determinants and matrices of order two and three. Properties of determinants,
evaluation of determinants, area of triangles using determinants. Adjoint and
evaluation of inverse of a square matrix using determinants and elementary
transformations, Test of consistency and solution of simultaneous linear
equations in two or three variables using determinants and matrices.
Unit 4 : 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 5 : Mathematical Induction:
Principle of Mathematical Induction and its simple applications.
Unit 6 : Binomial Theorem and It's Simple Applications:
Binomial theorem for a positive integral index, general term and middle term,
properties of Binomial coefficients and simple applications.
Unit 7 : Sequences and Series:
Arithmetic and Geometric progressions, insertion of
arithmetic, geometric means between two given numbers. Relation between A.M. and
G.M. Sum upto n terms of special series: S n, S n2, Sn3. Arithmetico – Geometric
Unit 8 : Limit, Continuity and Differentiability:
Real - valued functions, algebra of functions, polynomials,
rational, trigonometric, logarithmic and exponential functions, inverse
functions. Graphs of simple functions. Limits, continuity and differentiability.
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 upto two.
Rolle’s and Lagrange’s Mean Value Theorems. Applications of derivatives: Rate of
change of quantities, monotonic - increasing and decreasing functions, Maxima
and minima of functions of one variable, tangents and normals.
Unit 9 : 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. Evaluation of simple integrals of the type
Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of
definite integrals. Evaluation of definite integrals, determining areas of the
regions bounded by simple curves in standard form.
Unit 10: 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 of the type: dy+ p (x) y = q (x) dx
Unit 11: Co-ordinate Geometry:
Cartesian system of rectangular co-ordinates 10 in a plane,
distance formula, section formula, locus and its equation, translation of axes,
slope of a line, parallel and perpendicular lines, intercepts of a line on the
coordinate axes. Straight lines 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. Circles, conic sections Standard
form of equation of a circle, general form of the equation of a circle, its
radius and centre, 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 a circle, equation of the
tangent. Sections of cones, equations of conic sections (parabola, ellipse and
hyperbola) in standard forms, condition for y = mx + c to be a tangent and point
(s) of tangency.
Unit 12: Three Dimensional Geometry:
Coordinates of a point in space, distance between two points,
section formula, direction ratios and direction cosines, angle between two
intersecting lines. Skew lines, the shortest distance between them and its
equation. Equations of a line and a plane in different forms, intersection of a
line and a plane, coplanar lines.
Unit 13: 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.
Unit 14: Statistics And Probability:
Measures of Dispersion: Calculation of mean, median, mode of
grouped and ungrouped data calculation of standard deviation, variance and mean
deviation for grouped and ungrouped data. Probability: Probability of an event,
addition and multiplication theorems of probability, Baye’s theorem, probability
distribution of a random variate, Bernoulli trials and Binomial distribution.
Unit 15: Trigonometry:
Trigonometrical identities and equations. Trigonometrical functions. Inverse
trigonometrical functions and their properties. Heights and Distances.
Unit 16: Mathematical Reasoning:
Statements, logical operations and, or, implies, implied by, if and only if.
Understanding of tautology, contradiction, converse and contrapositive.