JEE Advanced Syllabus 2016 for Maths

JEE ADVANCED 2016 Syllabus:

Jee Advanced Syllabus covers all the topics required to be studied by aspirants who wish to avail admissions in IIT's via the Jee Advanced 2016 Examination. Students will have to study topics as prescribed for Mathematics in the Jee Advanced 2016.

Check All the Subjects Syllabus For Jee Advanced 2016:

• Physics Syllabus

• Chemistry Syllabus

• Mathematics Syllabus

Jee Advanced 2016 - Mathematics Syllabus:

1. Algebra

• Algebra of complex numbers, addition, multiplication, conjugation, polar

representation, properties of modulus and principal argument, triangle
inequality, cube roots of unity, geometric interpretations.

• Quadratic equations with real coefficients, relations between roots and

coefficients, formation of quadratic equations with given roots, symmetric
functions of roots.

• Arithmetic, geometric and harmonic progressions, arithmetic, geometric and

harmonic means, sums of finite arithmetic and geometric progressions, infinite
geometric series, sums of squares and cubes of the first n natural numbers.

• Logarithms and their properties.

Permutations and combinations, binomial theorem for a positive integral
index, properties of binomial coefficients.

• Matrices as a rectangular array of real numbers, equality of matrices, addition,

multiplication by a scalar and product of matrices, transpose of a matrix,
determinant of a square matrix of order up to three, inverse of a square matrix
of order up to three, properties of these matrix operations, diagonal,
symmetric and skew-symmetric matrices and their properties, solutions of
simultaneous linear equations in two or three variables.

• Addition and multiplication rules of probability, conditional probability, Bayes

Theorem, independence of events, computation of probability of events using
permutations and combinations.

2. Trigonometry:

• Trigonometric functions, their periodicity and graphs, addition and subtraction

formulae, formulae involving multiple and sub-multiple angles, general
solution of trigonometric equations.

• Relations between sides and angles of a triangle, sine rule, cosine rule, halfangle

formula and the area of a triangle, inverse trigonometric functions
(principal value only).

3. Analytical geometry

• Two dimensions: Cartesian coordinates, distance between two points, section

formulae, shift of origin.

• Equation of a straight line in various forms, angle between two lines, distance

of a point from a line; Lines through the point of intersection of two given
lines, equation of the bisector of the angle between two lines, concurrency of
lines; Centroid, orthocentre, incentre and circumcentre of a triangle.

• Equation of a circle in various forms, equations of tangent, normal and chord.

Parametric equations of a circle, intersection of a circle with a straight line or a
circle, equation of a circle through the points of intersection of two circles and
those of a circle and a straight line.

• Equations of a parabola, ellipse and hyperbola in standard form, their foci,

directrices and eccentricity, parametric equations, equations of tangent and
normal.

• Locus problems.

• Three dimensions: Direction cosines and direction ratios, equation of a straight

line in space, equation of a plane, distance of a point from a plane.

4. Differential calculus:

• Real valued functions of a real variable, into, onto and one-to-one functions,

sum, difference, product and quotient of two functions, composite functions,
absolute value, polynomial, rational, trigonometric, exponential and
logarithmic functions.

• Limit and continuity of a function, limit and continuity of the sum, difference,

product and quotient of two functions, L’Hospital rule of evaluation of limits of
functions.

• Even and odd functions, inverse of a function, continuity of composite

functions, intermediate value property of continuous functions.
Derivative of a function, derivative of the sum, difference, product and
quotient of two functions, chain rule, derivatives of polynomial, rational,
trigonometric, inverse trigonometric, exponential and logarithmic functions.

• Derivatives of implicit functions, derivatives up to order two, geometrical

interpretation of the derivative, tangents and normals, increasing and
decreasing functions, maximum and minimum values of a function, Rolle’s
theorem and Lagrange’s mean value theorem.

5. Integral calculus

• Integration as the inverse process of differentiation, indefinite integrals of

standard functions, definite integrals and their properties, fundamental
theorem of integral calculus.

• Integration by parts, integration by the methods of substitution and partial

fractions, application of definite integrals to the determination of areas
involving simple curves.

• Formation of ordinary differential equations, solution of homogeneous

differential equations, separation of variables method, linear first order
differential equations.

6. Vectors

• Addition of vectors, scalar multiplication, dot and cross products, scalar triple

products and their geometrical interpretations.

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