- Spotting of Errors
- Vocabulary (Idioms & Phrases)
- Sentence Improvement
- Sentence Completion (Fill in the blanks & Cloze Test)
- Ordering of Words & Sentences
- Active – Passive Voice
- Direct – Indirect Speech or Reported Speech
- One Word Substitution
- Parts of Speech
- Indian Polity
- Defence Specific
- Current Affairs & Static GK
Number System—Natural numbers, Integers, Rational and Real numbers.
Fundamental operations, addition, subtraction, multiplication, division, Square
roots, Decimal fractions. Unitary method, time and distance, time and work,
percentages, applications to simple and compound interest, profit and loss, ratio and
Elementary Number Theory—Division algorithm. Prime and composite numbers.
Tests of divisibility by 2, 3, 4, 5, 9 and 11. Multiples and factors. Factorization
Theorem. H.C.F. and L.C.M. Euclidean algorithm. Logarithms to base 10, laws of
logarithms, use of logarithmic tables.
Basic Operations, simple factors, Remainder Theorem, H.C.F., L.C.M., Theory of
polynomials, solutions of quadratic equations, relation between its roots and
coefficients (Only real roots to be considered). Simultaneous linear equations in two
unknowns—analytical and graphical solutions. Simultaneous linear inequations in
two variables and their solutions. Practical problems leading to two simultaneous
linear equations or inequations in two variables or quadratic equations in one 21
variable & their solutions. Set language and set notation, Rational expressions and
conditional identities, Laws of indices.
Sine ×, cosine ×, Tangent × when 0° < × < 90° Values of sin ×, cos × and tan ×, for ×
= 0°, 30°, 45°, 60° and 90°
Simple trigonometric identities.
Use of trigonometric tables.
Simple cases of heights and distances.
Lines and angles, Plane and plane figures, Theorems on (i) Properties of angles at
a point, (ii) Parallel lines, (iii) Sides and angles of a triangle, (iv) Congruency of
triangles, (v) Similar triangles, (vi) Concurrence of medians and altitudes, (vii)
Properties of angles, sides and diagonals of a parallelogram, rectangle and square,
(viii) Circles and its properties including tangents and normals, (ix) Loci.
Areas of squares, rectangles, parallelograms, triangle and circle. Areas of figures
which can be split up into these figures (Field Book), Surface area and volume of
cuboids, lateral surface and volume of right circular cones and cylinders, surface
area and volume of spheres.
Collection and tabulation of statistical data, Graphical representation frequency
polygons, histograms, bar charts, pie charts etc. Measures of central tendency.