WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD
SYLLABUS FOR JEM
M A T H E M A T I C S
A.P., G.P., H.P. :Definitions of A. P. and G.P.; General term; Summation of first n–terms; A.M.and
G.M.; Definitions of H.P. (only 3 terms) and H.M.; Finite arithmetico-geometric series.
Logarithms: Definition; General properties; Change of base
Complex Numbers: Definition and properties of complex numbers; Complex conjugate; Triangle inequality; Square root of complex numbers; Cube roots of unity; De Moivre’s theorem (statement only) and its elementary applications. Solution of quadratic equation in complex number system.
Quadratic Equations : Quadratic equations with real coefficients; Relations between roots and coefficients; Nature of roots; Formation of a quadratic equation.
Binomial theorem (positive integral index): Statement of the theorem, general term, middle term, equidistant terms, properties of binomial coefficients.
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Sets, Relations and Mappings: Idea of sets, subsets, power set, complement, union, intersection and difference of sets, Venn diagram, De Morgan’s Laws, Inclusion / Exclusion formula for two or three finite sets, Cartesian product of sets
Statistics and Probability: Measure of dispersion, mean, variance and standard deviation, frequency distribution. Addition and multiplication rules of probability, conditional probability and Bayes’ Theorem, independence of events, repeated independent trails and Binomial distribution.Statistics and Probability: Measure of dispersion, mean, variance and standard deviation, frequency distribution. Addition and multiplication rules of probability, conditional probability and Bayes’ Theorem, independence of events, repeated independent trails and Binomial distribution.
Trigonometry : Trigonometric functions,addition and subtraction formulae general solution of trigonometric equationsProperties of triangles,Inverse trigonometric functions and their properties.
Coordinate geometry of two dimensions : Distance formula, section formula,area of a triangle,Condition of collinearity of three points in a plane.Polar coordinates,Transformation from Cartesian to polar coordinates and vice versa. Parallel transformation of axes, the concept of locus,elementary locus problems Slope of a line. Equation of lines in different forms,Angle between two lines.Condition of perpendicularity and parallelism of two linesDistance of a point from a line Distance between two parallel lines.Lines through the point of intersection of two lines.Equation of a circle with a given center and radius.Equation of a circle in terms of endpoints of a diameter Equation of tangent,normal and chord Parametric equation of a circle Intersection of a line with a circle Equation of common chord of two intersecting circles. Definition of conic section, Directrix
Co-ordinate geometry of three dimensions : Direction cosines and direction ratios, distance between two points and section formula, equation of a straight line, equation of a plane, distance of a point from a plane.
Calculus Differential calculus: Functions, composition of two functions and inverse of a function, limit, continuity, derivative, chain rule, derivative of implicit functions and functions defined parametrically. Their geometric interpretation and elementary application. L’Hospital’s rule (statement only) and applications. Integral calculus: Integration as a reverse process of differentiation, indefinite integral of standard functions. Integration by parts. Integration by substitution and partial fraction. Definite integral as a limit of a sum with equal subdivisions. Fundamental theorem of integral calculus and its applications. Properties of definite integrals.
Differential Equations : Formation of ordinary differential equations,solution of homogeneous differential equations,separation of variables method,linear first order differential equations.
Application of Calculus: Tangents and normals, conditions of tangency. Determination of monotonicity, maxima and minima. Differential coefficient as a measure of rate. Motion in a straight line with constant acceleration. Geometric interpretation of definite integral as area, calculation of area bounded by elementary curves and Straight lines. Area of the region included between two elementary curves
Vectors : Addition of vectors, scalar multiplication, dot and cross products, scalar triple product.
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