Jammu Kashmir BPEE Common Entrance Test 2018 Mathematics Syllabus – Page 1
UNIT 6 : LIMIT, CONTINUITY AND DIFFERENTIATION ( Marks : 08 )
Concept of limit of a function. Theorems on Limits, Evaluation of limits using standard results.
Continuity of a function at a point. Continuity of Sum, product and quotient of functions.
Derivative : definition of a derivative of a function, geometrical interpretation of the derivative.
- Derivative of sum, difference, product and quotient of two or more functions.
- Derivative of algebraic and composite functions.
- Derivative of trigonometric and inverse trigonometric functions.
- Chain rule, derivative of implicit functions.
- Derivative of logarithmic and exponential functions.
- Logarithmic differentiation.
- Derivative of functions expressed in parametric forms. Second order derivatives.
- Rolle‘s and Lagrange‘s Mean Value Theorem and their geometrical interpretation and their simple applications.
Application of Derivative : Rate of change, increasing and decreasing functions, tangents and normals, approximation, maxima and minima ( first derivative and second derivative test ). Simple problems.
UNIT 7 : INTEGRATION AND DIFFERENTIAL EQUATIONS ( Marks : 07 )
Integration as inverse process of differentiation. Integration of variety of functions by Substitution, by parts, by partial fractions.
Simple integrals of the type :
Definite integrals as a Limit of a sum. Fundamental Theorem of calculus. Basic properties of definite integrals Evaluation of definite integrals.
Application of Integrals : Application in finding the area under simple curves, especially lines. Areas of circles, parabolas and ellipses ( in standard form ) Area under the curve y= Sinx, y= Cosx, area between the above two curves.
Differential Equations : Definition, order and degree of a differential equation. General and particular solutions of a differential equation. Formation of a differential equation whose general solution is given. Solution of differentiation equation by method of separation of variables. Solution of Homogeneous differential equation of first order and first degree.
Solution of linear differential equation of the type :
UNIT 8 : STRAIGHT LINES AND CONIC SECTIONS ( Marks : 05 )
Distance between two points, section, slope of a line, angle between two lines, various forms of equations of lines, point- slope form, intercept form, two point form, and normal form. General equation of a line, distance of a point from a line.
Conic Section : Sections of a cone, circles, parabola, ellipse, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of conic section. Standard equation of a circle, parabola, ellipse, and hyperbola and their simple properties.
UNIT 9 : STATISTICS AND PROBABILITY ( Marks : 06 )
STATISTICS : Measure of dispersion, mean, deviation, variance and standard deviation of ungrouped / grouped data. Analysis of frequency distribution with equal means but different variances.
PROBABILITY : Random Experiment: outcome, sample spaces. Events: Mutually exclusive and exhaustive events. Axiomatic ( set theoretic ) probability, probability of an event, probability of ― Not‖ and ― Or‖ events. Multiplication theorem on probability, conditional probability, independent events, total probability, Baye‘s theorem, random variable and its probability, distribution, mean and variance of a random variable. Repeated independent ( Bernouli ) trials and Binomial distribution.
UNIT 10 : VECTORS AND THREE DIMENSIONAL GEOMETRY ( Marks : 06 )
Vectors and scalars, magnitude and direction of a vector Direction Cosines and ratios of a vector. Types of vector, equal, zero, unit, parallel and collinear vectors. Position vector of a point , negative of a vector, components of a vector, addition of vectors, Scalar multiplication, position vector of a point dividing a line segment in a given ratio. Scalar ( dot ) product of vectors, projection of a vector on a line. Vector ( cross ) product of vectors, Scalar triple product. Coordinate axes and Coordinate planes in three dimensions of a point, distance between two points and sectional formula.
STRAIGHT LINES AND SPACE Direction cosines and direction ratios of a line joining two points. Cartesian and vector equation of a line ( in various forms ), coplanar and skew – lines, shortest distance between two lines.
PLANES Cartesian and vector equation of a plane ( in various forms ). Distance of a point from a plane.
Angle between :
- Two lines
- Two planes.
- A line and a plane