User talk:B.KARTHIK NAYAK

NATIONAL DEFENCE ACADEMY AND NAVAL ACADEMY EXAMINATION Syllabus Kindly note : Date of notification NDA & NA (I) Exam 2015: 27th DECEMBER 2014 Last date of form submissionNDA & NA (I) Exam 2015: 23rdJANUARY 2015 Date of NDA & NA (I) Exam 2015is 19th April 2015 Kindly Note :TestBag now has exclusive microsite for NDA. Please click on nda.testbag.comfor one stop on everything about NDA NATIONAL DEFENCE ACADEMY AND NAVAL ACADEMY EXAMINATION Paper I MATHEMATICS 1. Algebra Concept of a set, operations on sets, Venn diagrams. De Morgan laws. Cartesian product, relation, equivalence relation. Representation of real numbers on a line. Complex numbers - basic properties, modulus, argument, cube roots of unity. Binary system of numbers. Conversion of a number in decimal system to binary system and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its application. Logarithms and their applications. 2.Matrices and Determinants Types of matrices, operations on matrices Determinant of a matrix, basic properties of determinant. Adjoint and inverse of a square matrix, Applications - Solution of a system of linear equations in two or three unknowns by Cramers rule and by Matrix Method.3.Trigonometry Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications - Height and distance, properties of triangles. 4.Analytical Geometry of two and three dimensions Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic. Point in a three dimensional space, distance between two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.5.Differential Calculus Concept of a real valued function - domain, range and graph of a function. Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limits - examples. Continuity of functions - examples, algebraic operations on continuous functions. Derivative of a function at a point, geometrical and physical interpreatation of a derivative - applications. Derivatives of sum, product and quotient of functions, derivative of a function with respect of another function, derivative of a composite function. Second order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima. 6.Integral Calculus and Differential equations Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals - determination of areas of plane regions bounded by curves - applications. Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equation, solution of first order and first degree differential equations of various types - examples. Application in problems of growth and decay.