JEE MAIN 2013
JEE Main 2013 Mathematics Syllabus
JEE Main 2013 Mathematics Syllabus
The careful JEE Main 2013
arithmetic programme is as follows:
UNIT one : SETS, RELATIONS AND
FUNCTIONS:
Sets and their representation;
Union, intersection and complement of sets and their algebraical properties;
Power set; Relation, styles of relations, equivalence relations, functions;.
one-one, into and onto functions, composition of functions.
UNIT two : advanced NUMBERS ANDQUADRATIC EQUATIONS:
Complex numbers as ordered pairs
of reals, illustration of advanced numbers within the kind a+ib and their
illustration during a plane, Argand diagram, pure mathematics of advanced
numbers, modulus and argument (or amplitude) of a posh range, root of a posh
range, triangle difference, Quadratic equations in real and complicated system
of numeration and their solutions. Relation between roots and co-efficients,
nature of roots, formation of quadratic equations with given roots.
UNIT three : MATRICES AND
DETERMINANTS:
Matrices, pure mathematics of
matrices, styles of matrices, determinants and matrices of order 2 and 3.
Properties of determinants, analysis of determinants, space of triangles
mistreatment determinants.
Adjoint and analysis of inverse
of a matrix mistreatment determinants and elementary transformations, take a
look at of consistency and resolution of coinciding linear equations in 2 or 3
variables mistreatment determinants and matrices.
UNIT four : PERMUTATIONS AND
COMBINATIONS:
Fundamental principle of
reckoning, permutation as a meeting and combination as choice, that means of P
(n,r) and C (n,r), easy applications.
UNIT five : MATHEMATICAL
INDUCTION:
Principle of Mathematical
Induction and its easy applications.
UNIT vi : theorem AND ITS easy
APPLICATIONS:
Binomial theorem for a positive
integral index, general term and term, properties of Binomial coefficients and
easy applications.
UNIT seven : SEQUENCES AND
SERIES:
Arithmetic and Geometric
progressions, insertion of arithmetic, geometric suggests that between 2 given
numbers. Relation between A.M. and G.M. total upto n terms of special series: S
n, S n2, Sn3. Arithmetico – patterned advance.
UNIT eight : LIMIT, CONTINUITY
AND DIFFERENTIABILITY:
Real – valued functions, pure
mathematics of functions, polynomials, rational, pure mathematics, exponent and
exponential functions, inverse functions. Graphs of easy functions. Limits,
continuity and differentiability. Differentiation of the total, difference,
product and quotient of 2 functions. Differentiation of pure mathematics,
inverse pure mathematics, exponent, exponential, composite and implicit
functions; derivatives of order upto 2. Rolle’s and Lagrange’s norm Theorems.
Applications of derivatives: Rate of modification of quantities, monotonic –
increasing and decreasing functions, Maxima and minima of functions of 1
variable, tangents and normals.
UNIT nine : INTEGRAL CALCULUS:
Integral as associate degree
opposing – spinoff. basic integrals involving algebraical, pure mathematics,
exponential and exponent functions. Integration by substitution, by elements
and by partial fractions. Integration mistreatment pure mathematics identities.
Evaluation of easy integrals of
the sort Integral as limit of a total. basic Theorem of Calculus. Properties of
definite integrals. analysis of definite integrals, deciding areas of the
regions delimited by easy curves in customary kind.
UNIT 10: DIFFERENTIAL EQUATIONS:
Ordinary differential equations,
their order and degree. Formation of differential equations. resolution of
differential equations by the strategy of separation of variables, resolution
of consistent 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 ten during 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 sorts of equations of a
line, intersection of lines, angles between 2 lines, conditions for concurrence
of 3 lines, distance of some extent from a line, equations of internal and
external bisectors of angles between 2 lines, coordinates of centre of mass,
orthocentre and circumcentre of a triangle, equation of family of lines passing
through the purpose of intersection of 2 lines.
Circles, conic sections
Standard kind of equation of a
circle, general kind of the equation of a circle, its radius and centre,
equation of a circle once the top points of a diameter ar 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, conic section and hyperbola) in
customary forms, condition for y = magnetic flux unit + c to be a tangent and
purpose (s) of tangency.
UNIT 12: 3 DIMENSIONAL GEOMETRY:
Coordinates of some extent in
house, distance between 2 points, section formula, direction ratios and
direction cosines, angle between 2 crossed
lines. Skew lines, the shortest distance between them and its equation.
Equations of a line and a plane in numerous forms, intersection of a line and a
plane, two-dimensional lines.
UNIT 13: VECTOR ALGEBRA:
Vectors and scalars, addition of
vectors, elements of a vector in 2 dimensions and 3 dimensional house, scalar
and vector merchandise, scalar and vector triple product.
UNIT 14: STATISTICS AND
PROBABILITY:
Measures of Dispersion: Calculation
of mean, median, mode of sorted and ungrouped information calculation of
ordinary deviation, variance and deviation for sorted and ungrouped
information.
Probability: likelihood of an
occasion, addition and multiplication theorems of likelihood, Baye’s theorem,
likelihood distribution of a random variable, Bernoulli trials and
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 on condition that. Understanding of tautology,
contradiction, converse and contrapositive and JEE Main 2013 Mock Test. 