## VITEEE Syllabus 2016 - Mathematics:

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#### VITEEE 2016 Syllabus:

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## VITEEE Syllabus 2016 For Mathematics:

### 1. Matrices and their Applications

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- Adjoint, inverse – properties, computation of inverses, solution of system of linear equations by matrix inversion method.

- Rank of a matrix – elementary transformation on a matrix, consistency of a system of linear equations, Cramer’s rule, nonhomogeneous equations, homogeneous linear system and rank method.

- Solution of linear programming problems (LPP) in two variables

### 2. Trigonometry and Complex Numbers

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- Definition, range, domain, principal value branch, graphs of inverse trigonometric functions and their elementary properties.

- Complex number system - conjugate, properties, ordered pair representation.

- Modulus – properties, geometrical representation, polar form, principal value, conjugate, sum, difference, product, quotient, vector interpretation, solutions of polynomial equations, De Moivre’s theorem and its applications.

- Roots of a complex number - nth roots, cube roots, fourth roots.

### 3. Analytical Geometry of two dimensions

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- Definition of a conic – general equation of a conic, classification with respect to the general equation of a conic, classification of conics with respect to eccentricity.

- Equations of conic sections (parabola, ellipse and hyperbola) in standard forms and general forms- Directrix, Focus and Latusrectum - parametric form of conics and chords. - Tangents and normals – Cartesian form and parametric form- equation of chord of contact of tangents from a point (x1 ,y1 ) to all the above said curves.

- Asymptotes, Rectangular hyperbola – Standard equation of a rectangular hyperbola.

### 4. Vector Algebra

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- Scalar Product – angle between two vectors, properties of scalar product, and applications of dot product. Vector product, right handed and left handed systems, properties of vector product, applications of cross product.

- Product of three vectors – Scalar triple product, properties of scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors.

### 5. Analytical Geometry of Three Dimensions

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- Direction cosines – direction ratios - equation of a straight line passing through a given point and parallel to a given line, passing through two given points, angle between two lines.

- Planes – equation of a plane, passing through a given point and perpendicular to a line, given the distance from the origin and unit normal, passing through a given point and parallel to two given lines, passing through two given points and parallel to a given line, passing through three given non-collinear points, passing through the line of intersection of two given planes, the distance between a point and a plane, the plane which contains two given lines (co-planar lines), angle between a line and a plane.

- Skew lines - shortest distance between two lines, condition for two lines to intersect, point of intersection, collinearity of three points.

- Sphere – equation of the sphere whose centre and radius are given, equation of a sphere when the extremities of the diameter are given.

6. Differential Calculus
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- Limits, continuity and differentiability of functions - Derivative as a rate of change, velocity, acceleration, related rates, derivative as a measure of slope, tangent, normal and angle between curves.

- Mean value theorem - Rolle’s Theorem, Lagrange Mean Value Theorem, Taylor’s and Maclaurin’s series, L’ Hospital’s Rule, stationary points, increasing, decreasing, maxima, minima, concavity, convexity and points of inflexion.

- Errors and approximations – absolute, relative, percentage errors - curve tracing, partial derivatives, Euler’s theorem.

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7. Integral Calculus and its Applications

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- Simple definite integrals – fundamental theorems of calculus, properties of definite integrals.

- Reduction formulae – reduction formulae for x dx n sin and x dx n cos , Bernoulli’s formula.

- Area of bounded regions, length of the curve.

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8. Differential Equations

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- Differential equations - formation of differential equations, order and degree, solving differential equations (1st order), variables separable, homogeneous and linear equations.

- Second order linear differential equations - second order linear differential equations with constant co-efficients, finding the particular integral if f(x) = emx, sin mx, cos mx, x, x2 .

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9. Probability Distributions

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- Probability – Axioms – Addition law - Conditional probability – Multiplicative law - Baye’s Theorem - Random variable - probability density function, distribution function, mathematical expectation, variance

- Theoretical distributions - discrete distributions, Binomial, Poisson distributions- Continuous distributions, Normal distribution.

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10. Discrete Mathematics

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- Functions – Relations – Basics of counting.

- Mathematical logic – logical statements, connectives, truth tables, logical equivalence, tautology, contradiction.

- Groups-binary operations, semi groups, monoids, groups, order of a group, order of an element, properties of groups.

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RELATED LINKS:

- VITEEE Complete Details - Click Here
- VITEEE 2016 Information Brochure - Click Here

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- Limits, continuity and differentiability of functions - Derivative as a rate of change, velocity, acceleration, related rates, derivative as a measure of slope, tangent, normal and angle between curves.

- Mean value theorem - Rolle’s Theorem, Lagrange Mean Value Theorem, Taylor’s and Maclaurin’s series, L’ Hospital’s Rule, stationary points, increasing, decreasing, maxima, minima, concavity, convexity and points of inflexion.

- Errors and approximations – absolute, relative, percentage errors - curve tracing, partial derivatives, Euler’s theorem.

### 7. Integral Calculus and its Applications

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- Simple definite integrals – fundamental theorems of calculus, properties of definite integrals.

- Reduction formulae – reduction formulae for x dx n sin and x dx n cos , Bernoulli’s formula.

- Area of bounded regions, length of the curve.

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8. Differential Equations

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- Differential equations - formation of differential equations, order and degree, solving differential equations (1st order), variables separable, homogeneous and linear equations.

- Second order linear differential equations - second order linear differential equations with constant co-efficients, finding the particular integral if f(x) = emx, sin mx, cos mx, x, x2 .

### 9. Probability Distributions

####
- Probability – Axioms – Addition law - Conditional probability – Multiplicative law - Baye’s Theorem - Random variable - probability density function, distribution function, mathematical expectation, variance

- Theoretical distributions - discrete distributions, Binomial, Poisson distributions- Continuous distributions, Normal distribution.

### 10. Discrete Mathematics

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- Functions – Relations – Basics of counting.

- Mathematical logic – logical statements, connectives, truth tables, logical equivalence, tautology, contradiction.

- Groups-binary operations, semi groups, monoids, groups, order of a group, order of an element, properties of groups.

### RELATED LINKS:

- VITEEE Complete Details - Click Here
- VITEEE 2016 Information Brochure - Click Here