OJEE 2011 Syllabus MATHEMATICS Download Odisha JEE

OJEE 2011 Syllabus MATHEMATICS Download Odisha JEE

MATHEMATICS

Logic : Statement, Negation, Implication, Converse, Contraposititves, Conjuction, Disjunction, Truth Table. Algebra of sets : Set operation, Union, Intersection, Difference, Symmetric difference, Complement, Venn diagram, Cartesian product of sets, Relation and functions, Composite function, Inverse of a function, Equivalence relation, Kinds of function.

Number system : Real numbers (algebraic and order properties, rational and irrational numbers), Complex numbers, Algebra of complex numbers, Conjugate and square root of a complex number, Cube roots of unity, De Moivre’s theorem with simple application. Permutations and combinations-simple applications, Mathematical induction, Binomial theorem.

Determinants and matrices : Determinants of third order, Minors and cofactors, Properties of determinants, Matrices upto third order, Types of matrices, algebra of matrix, adjoint and inverse of matrix, Application of determinants and matrices to the solution of linear equations (in three unknowns).

Trigonometry : Compound angles, Multiple and Submultiple angles, Solution of trigonometric equations, Properties of triangles, Inverse circular function, Sum and product of sine and cosine functions.

Co-ordinate geometry of two dimensions : Straight lines, Pairs of straight lines, Circles, Equations of tangents and normals to a circle, Equations of parabola, Ellipse and hyperbola in simple forms and their tangents (focus, directrix, eccentricity and latus rectum in all cases).

Coordinate geometry of three dimensions : Distance and Division formulae, Direction cosines and direction ratios, Projection, Angle between two planes, Angle between a line and a plane. Distance of a point from a line and a plane. Equation of a sphere – general equation).

Vectors : Fundamentals, Dot and cross product of two vectors, Scalar triple product, Simple applications (to geometry, work and moment).

Differential calculus: Concept of limit, Continuity and derivative of standard functions, Successive differentiation (simple cases), Leibnitz theorem, Partial differentiation (simple cases), Derivative as a rate measure, Maxima and Minima, Indeterminate forms, Geometrical application such as tangent and normals to plane curves.

Integral calculus: Standard methods of integration (substitution, by parts, by partial fraction, etc), Definite integrals and properties of definite integrals. Areas under plane curves.

Differential equations (only simple cases)

(i) dy/dx = f(x)

(ii) dy/dx = f(x) .g(y)

(iii) d2y/dx2= f(x) and applications to motions in a straight line.

Probability and statistics: Average (mean, median and mode). Dispersion (standard deviation and variance), Definition of probability, Mutually exclusive events, Independent events, Addition theorem.

Computer and computing : Computer arithmetic, decimal, binary, octal, hexadecimal and their conversion and operation, Simple programmes in BASIC.

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