**JEE MAIN 2016 SYLLABUS FOR MATHEMATICS**

**JEE Main Mathematics Syllabus**

**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 ITS 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:**

**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/dx+p(x)y=q(x)

**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.

**JEE Syllabus (Mains)**

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