Hey aspirant

The Dayalbagh Educational Institute holds its DEI entrance Examination for admission to all Bachelor's courses, including B.Sc. Maths (H).Its syllabus is:

UNIT 1

1.1 SETS

1.2 RELATIONS AND FUNCTIONS

1.3 TRIGONOMETRIC FUNCTIONS: Positive and negative angles. Measuring angles in radians and in degrees and conversion from-one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2x+cos2x=1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin(x±y) one cos (x±y) in terms of sin x, sin y, cos x and cos y. Identities related to sin 2x, cos 2x, six 3x, cos 3x and tan 3x. General solution of trigonometric equations of the type sinθ = sinα, cosθ = cosα, and tanθ = tanα. Proof and simple application of sine and cosine rules only.

1.4 INVERSE TRIGONOMETRIC FUNCTIONS: Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

1.5 SEQUENCE AND SERIES

UNIT 2:

2.1 COMPLEX NUMBERS AND QUADRATIC EQUATIONS: Need for complex numbers, especially−1 to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex_ numbers: Argand plane and polar representation of complex numbers, Statement of fundamental theorem of algebra, solution of quadratic equations in the complex number system. Square root of a complex number, Cube roots of unity and their properties.

2.2 LINEAR INEQUALITIES: Linear inequalities, Algebraic solutions of linear inequalities in one-variable and their representation: on the number line. Graphical solution of linear inequalities in two variables. Solution of system of linear inequalities in- two variable graphically, 'Inequalities involving modulus function.

2.3 PERMUTATIONS AND COMBINATIONS: Fundamental principle of counting, Factorial n(n!), Permutations and combinations, derivation of formulae and their connections, simple applications.

2.4 BINOMIAL THEOREM: History, statement and proof of the binomial theorem for positive integral indices. Pascal's triangle, general and middle term in binomial expansion, simple applications.

2.5 MATHEMATICAL REASONING

UNIT 3:

3.1 MATRICES: Concept, notation, order, equality, types of matrices, zero matrix; transpose of a matrix symmetric and skew symmetric matrices, addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication, Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations; Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

3.2 DETERMINANTS: Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix, Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix. Cramer's Rule and its applications.

3.3 LIMITS, DERIVATIVES, CONTINUITY: Derivative introduced as rate of change and as that of distance function, Definition of derivative, relate it to slope of tangent of the curve derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric function. Continuity

3.4 DIFFERENTIABILITY: Differentiability, derivative of composite functions, Chain rule, derivative of inverse trigonometric functions, derivative of implicit functions, concept of exponential and logarithmic functions to the base e. Logarithmic functions as inverse of exponential functions.

Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle’s and Largrange’s Mean value theorems (without proof) and the geometric interpretation and simple applications.

3.5 APPLICATIONS OF DERIVATIVES: Applications of derivatives: rate of change, increasing / decreasing functions, tangent and normals, approximation, maxima and minima (first derivative test, integrate geometrically and second derivative test given as a provable tool). Simple problem (that illustrate basic principle and understanding of the subject as well as real- life situations)

5.3 Vectors : Vectors and scalars, magnitude and direction of a vector, Direction cosines/ ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, 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.

5.4 THREE DIMENSIONAL GEOMETRY :Co-ordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula. Direction cosines/ ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines, Cartesian and vector equation of a plane, Angle between (i) two lines, (ii) two planes, (iii) a line and a plane, Distance of a point from a plane.

5.5 LINEAR PROGRAMMING: Introduction, definition of related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints)

All the best.