National Defence Academy (NDA) Mathematics | Paper 1

The National Defence Academy (NDA) Paper 1 is a Mathematics examination conducted by the Union Public Service Commission (UPSC) as part of the NDA selection process for the Army, Navy, and Air Force. This paper is aimed at evaluating a candidate’s mathematical aptitude, logical reasoning, and analytical ability. The Mathematics paper carries a total of 300 marks, consists of 120 multiple-choice questions, and is conducted over a duration of two and a half hours. The questions are based on the 10+2 level curriculum and are available in both English and Hindi. A penalty of one-third of the marks allotted to a question is applied for every incorrect answer.

The syllabus for NDA Paper 1 in Mathematics includes several major areas.

Algebra, topics covered are the concept of sets, operations on sets, Venn diagrams, De Morgan’s laws, Cartesian product, relations and functions, complex numbers, quadratic and linear equations, permutations and combinations, the binomial theorem, and basic concepts of matrices and determinants.

Trigonometry includes angles and their measurements in degrees and radians, trigonometric identities and ratios, properties of triangles, the use of trigonometric tables, and applications such as heights and distances. Analytical Geometry in two and three dimensions covers coordinate systems, distance formula, section formula, equations of straight lines and conic sections like circles, parabolas, ellipses, and hyperbolas, as well as three-dimensional geometry involving direction cosines and direction ratios, equations of lines and planes, and angle between two lines.

Differential Calculus includes limits, continuity and differentiability of functions, standard results, derivatives of composite functions, and applications of derivatives in determining maxima, minima, and slopes of curves. Integral Calculus and Differential Equations involve indefinite and definite integrals, standard forms, applications of integration to find areas under curves, and solving first-order differential equations.

Vector Algebra consists of vectors in two and three dimensions, addition and scalar multiplication of vectors, scalar and vector products, and applications of vectors in solving geometrical problems.

The Statistics and Probability section includes the collection and classification of data, frequency distribution, graphical representation, measures of central tendency (mean, median, mode), measures of dispersion (variance, standard deviation), basic probability theory, and concepts such as conditional probability and Bayes’ theorem.

A strong grasp of these mathematical areas is essential for success in NDA Paper 1, along with regular practice and effective time management.