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Mathematics for NDA

Paper I is worth 300 marks over two and a half hours, broadly at Class 11–12 level. It covers algebra, matrices, trigonometry, coordinate geometry, calculus, vectors, statistics and probability. Recent papers have had 120 questions, and calculators aren’t allowed, so speed matters as much as method.

12 guides·Conducted by Union Public Service CommissionOfficial website

Study in this order

  1. 1A mathematics plan for NDAMathematics is 300 marks in two and a half hours, with a penalty for every wrong answer. The syllabus is Class 11–12 maths; the test is speed and accuracy. The units, an order of study, a 16-week plan, speed techniques with worked examples and exam-day tactics. 6 min read
  2. 2Sets, relations and functions for NDAA scoring topic built on a handful of counting results: union formulas, numbers of subsets, relations and functions, domains, composition and inverses. Key results with conditions, worked NDA-style MCQs and a practice set. 8 min read
  3. 3Complex numbers for NDAPowers of i, modulus and argument, division, square roots, De Moivre's theorem, simple loci and the cube roots of unity. The results NDA tests again and again, with conditions, worked MCQs and a practice set. 7 min read
  4. 4Quadratic equations for NDASum and product of roots, the discriminant, symmetric expressions like α² + β², equations with transformed roots, sign and extreme values of a quadratic, and quadratic inequalities. Results with conditions, worked MCQs and practice. 8 min read
  5. 5Sequences and series for NDAArithmetic, geometric and harmonic progressions, infinite GPs, the three means and standard sums. How each formula is built, the conditions attached, worked NDA-style MCQs and a practice set. 7 min read
  6. 6Permutations and combinations for NDAArrange or choose? The counting principle, nPr and nCr, repeated letters, "together" and "never together", digits, circular arrangements, committees with "at least", and points and lines. Worked NDA-style MCQs and practice. 6 min read
  7. 7The binomial theorem for NDAThe general term solves most NDA binomial questions: a given coefficient, the term independent of x, middle terms. Add sums of coefficients, remainders and approximations, and the chapter is fully covered. Results, worked MCQs and practice. 6 min read
  8. 8Matrices and determinants for NDATypes and operations, determinants and the properties that let you skip calculation, adjoint and inverse, and solving equations by Cramer's rule and the matrix method. Results with conditions, worked NDA-style MCQs and practice. 8 min read
  9. 9Trigonometric ratios and identities for NDARadians, standard and allied angles, the Pythagorean identities, compound, double and triple angles, sum-to-product and the range of a sin θ + b cos θ. Results with conditions, worked NDA-style MCQs and practice. 8 min read
  10. 10Heights and distances for NDAAngles of elevation and depression, one and two observation points, flagstaffs on towers, cliffs, moving boats and shadows. The standard set-ups, shortcut results with their conditions, worked NDA-style MCQs and practice. 7 min read
  11. 11Inverse trigonometric functions for NDADomains and principal value ranges, negative arguments, when sin⁻¹(sin x) = x, the complementary pairs, the tan⁻¹ addition formula with its conditions, and the triangle method. Worked NDA-style MCQs and practice. 6 min read
  12. 12Properties of triangles for NDAThe sine rule, cosine rule and projection formulas, every area formula, the circumradius and inradius, half-angle results and the special triangles. Results with conditions, worked NDA-style MCQs and practice. 7 min read

New Mathematics guides are added regularly. Back to all NDA guides