National Defence Academy & Naval
Academy Examination (I), 2012
Scheme of Examination
The subjects of the written examination, the time allowed and the maximum
marks allotted to each subject will be as follows: (Total: 900)
| Subject |
Code |
Duration |
Maximum Marks |
| Mathematics |
01 |
2-½ Hours |
300 |
| General |
02 |
2-½ Hours |
600 |
2. The papers in all the subjects will consist of objective type questions
only. The question papers (Test Booklets) OF MATHEMATICS AND PART "b" OF GENERAL
ABILITY TESTS WILL BE SET BILINGUALLY IN HINDI AS WELL AS English.
3. In the question papers, wherever necessary, questions involving the metric
system of Weights and Measures only will be set.
4. Candidates must write the papers in their own hand. In no circumstances
will they be allowed the help of a scribe to write answers for them.
5. The Commission have discretion to fix qualifying marks in any or all the
subjects at the examination.
6. The candidates are not permitted to use calculator or Mathematical or
logirithmic table for answering objective type papers (Test Booklets). They
should not therefore, bring the same inside the Examination Hall.
B. Syllabus of the Examination
Paper-I Mathematics (Code No. 01)
(Maximum Marks - 300)
1Algebra : 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 Cramer's
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.
