**Jammu Kashmir BPEE Common Entrance Test 2021 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

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