Indian Institutes of Technology
Joint Entrance Examination, IIT-JEE - 2012
Algebra: Algebra of complex numbers,
addition, multiplication, conjugation, polar representation, properties of
modulus and principal argument, triangle inequality, cube roots of unity,
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
Addition and multiplication rules of probability, conditional
probability, Bayes Theorem, independence of events, computation of probability
of events using permutations and combinations.
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, half-angle formula and the area of a triangle, inverse
trigonometric functions (principal value only).
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.
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.
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.
Integral calculus: Integration as the
inverse process of differentiation, indefinite integrals of standard functions,
definite integrals and their properties, Fundamental Theorem of Integral
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.
Vectors: Addition of vectors, scalar
multiplication, dot and cross products, scalar triple products and their