APIIT NAT 2021 Mathematics Syllabus

National Admission Test ( NAT ) Entrance Examination Mathematics Syllabus-2015:

For B.Tech:

Admission will be based on JEE Main-2015 Merit Score / NAT Entrance Examination:

Unit 1: Complex Numbers

Complex numbers in the form a + if and their representation in a plane Armand diagram. Algebra of complex numbers, Modulus and Argument (or amplitude) of a complex number, square root of a complex numbers. Cube roots of unity, triangle inequality.

Unit 2: Matrices and Determinants

Determinants and matrices of order two and three, properties of determinants. Evaluation of determinants. Area of triangles using determinants. Addition and multiplication of matrices, adjoin and inverse of matrix. Test of consistency and solution of simultaneous linear equations using determinants and matrices.

Unit 3: Quadratic Equations

Quadratic equations in real and complex number system and their solutions. Relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots; Symmetric functions of roots, equations reducible to quadratic equations-application to practical problems.

Unit 4: Permutations and Combinations

Fundamental principle of counting; Permutation as an arrangement and combination as selection, Meaning of P (n, r) and C (n, r). Simple applications.

Unit 5: Binomial Theorem and Its Applications

Binomial Theorem for a positive integral index; general term and middle term: Binomial Theorem foranyindex. Properties of Binomial coefficient. Simple applications for approximations.

Unit 6: Sequences and Series

Arithmetic, Geometric and Harmonic progressions. Insertion of Arithmetic Geometric and Harmonic means between two given numbers. Relation between A.M., G.M. and H.M. Special series: ?n, ?n2, ?n3. Arithmetic - Geometric Series, Exponential and Logarithmic series.

Unit 7: Differential Calculus

Polynomials, rational, trigonometric, logarithmic and exponential functions. Inverse functions. Graphs of simple functions. Limits, Continuity; differentiation of the sum, difference, product and quotient of two functions, differentiation of trigonometric, inverse trigonometric logarithmic, exponential, composite and implicit functions; derivatives of order up to two. Applications of derivatives: Rate of change of quantities, monotonic increasing and decreasing functions. Maxima and minima of functions of one variable, tangents and normal’s, Role’s and Lagrange's Mean Value Theorems.

Unit 8: Integral Calculus

Integral as an anti-derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Integral as limit of a sum. Properties of definite integrals. Evaluation of definite integrals; Determining areas of the regions bounded by simple curves.

Unit 9: Differential Equations

Ordinary differential equations, their order and degree. Formation of differential equations solution of differential equations by the method of separation of variables. Solution of homogeneous and linear differential equations and those of the type d^y dx3=f(x)

Unit 10: Two Dimensional Geometry

Recall of Cartesian system of rectangular co-ordinates in a plane, distance formula, area of a triangle, condition for the co linearity of three points and section formula, centric and in-centre of a triangle, locus and its equation translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line of the coordinate axes.

The straight line and pair of straight lines

Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line. Equations of intemaland external bisectors of angles between two lines, coordinates of centric, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two tines, homogeneous equation of second degree in x and y, angle between pair of lines through the origin, combined equation of the bisectors of the angles between a pair of lines, condition forth general second degree equation to represent a pair of lines, point of intersection and angle between two lines.

Circles and Family of Circles

Standard form of equation of a circle, generalform of the equation of a circle, its radius and centre, equation of a circle in the parametric form, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to the circle length 0' .he tangent, equation of the tangent, equation of a family of circles through the intersection of two circles, condition for two intersecting circles to be orthogonal..

Unit 11:Three Dimensional Geometry

Coordinates of a point in space, distance between two points; Section formula, direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a tine and a plane in different forms intersection of a line and a plane, coplanar lines, equation of a sphere, its centre and radius. Diameter form of the equation of a sphere.

Unit 12:Vector Algebra

Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products. Scalar and vector triple product. Application of vectors to plane geometry.

Unit 13:Probability

Probability of an event, addition and multiplication theorems of probability and their applications: Conditional probability; Bayes'Theorem, Probability distribution of a random variety; Binomial and Poisson distributions and Their properties.

Unit 14:Trigonometry

Trigonometrically identities and equations, Inverse trigonometric functions and their properties. Properties of triangles, including centric, in centre circum-centre and Roth-centre, solution of triangles. Heights and Distances.

Unit 15:Numerical Methods

Iterative methods of solving equations: False position, Newton Rap son, Numerical Integration Rule: Trapezoidal and Simpsons Rule.

For other details refer,

www.apiit.edu.in