**About the Examination and the Conducting Authority** Education is the glorious route through which anyone can attain the goal of success. And if education has been acquired through a renowned institution, it leads to glorious heights in career. National Defense Academy (NDA) is one such institution which propels the students in the arena of life and contributes to a very successful and fulfilled career. But to get enrolled in this institution means goal directed study for passing a competitive examination which is conducted by Union Public Service Commission nationwide. For recruitment to the Indian Army, Navy and Air Force wings of Indian Army, there is prestigious National Defense Academy Entrance Examination. The examination is conducted twice a year and the duration of training is three years.

Though the candidate may give his preference for a particular wing of the Armed Forces, the final selection depends upon his performance and place in the merit list

**Career Building Admission** to the NDA means a golden opportunity for learning, since it has the best of instructors and teachers. The students get phenomenal opportunities to constantly hone and upgrade their skills. On completion of studies, NDA grants its students degrees in Science and Computer Science. Students who opt for technical qualifications have the facility of achieving education through the most prestigious technical institutions. The certificates are awarded by renowned Jawaharlal Nehru University. Some of the most well-known and highly graded institutions teaching engineering, medicine, administration and armament are run by the Indian Army. Students here have the facility to take leave in the middle of the tenure for further studies.

Popularity of the Exam The examination is heid in esteem by the students. lt is a big thing to be enrolled in the National Defense Academy. As soon as a child reaches class Vlll, he begins to aspire for i career as an officer in the Armed Forces. The life of an officer has many amenities. lt is also prestigious to hold an office in the security resource of the country. lt is a noble job to serve the country in this manner. ln a way, one is a confidant of the government which relies heavily on its Armed Forces forth security of the country. As soon as one becomes a partof the NDA, one begins to be treated with awe and respect in the society.

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.

Types of matrices, operations on matrices. Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix, Applications – Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.

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.

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.

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 function at a point, geometrical and physical interpretation 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.

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.

Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors, addition of vectors, scalar multiplication of vector, scalar product or dot product of two-vectors. Vector product and cross product of two vectors. Applications-work done by a force and moment of a force, and in geometrical problems.

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