The Union Public Service Commission will hold the National Defence Academy and Naval Academy Examination (II), 2011 on 21st August 2011, for admission to Army, Navy and Air Force Wings of NDA for 128th Course and for the 90th Indian Naval Academy Course (INAC) commencing from June 2012.
features of the examination are published herein for general
information of candidates. For details regarding the Syllabus and
Scheme of the examination, Centres of examination, Guidelines for
filling up application form etc. aspirants must refer to the Detailed
Notice of the examination published in the Employment News/Rozgar Samachar dated 9th April, 2011.
1. The subjects of the written examination, the time allowed and the
maximum marks allotted to each subject will be as follows :–
General Ability Test
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
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.
should note that there will be penalty (negative marking) for wrong
answers marked by a candidate in the Objective Type Question Papers.
Nationality : A candidate must either be :
(i) a citizen of India, or
a subject of Bhutan, or
a subject of Nepal, or
(iv) a Tibetan refugee who came over to India
before the 1st January, 1962 with the intention of permanently settling in
a person of Indian origin who has migrated from Pakistan, Burma, Sri Lanka and
East African Countries of Kenya, Uganda, the United Republic of Tanzania,
Zambia, Malawi, Zaire and Ethiopia and Vietnam with the intention of permanently
settling in India.
Provided that a candidate belonging to categories
(ii), (iii), (iv) and (v) above shall be a person in whose favour a certificate
of eligibility has been issued by the Government of India.
Certificate of eligibility will not, however, be
necessary in the case of candidates who are Gorkha subjects of Nepal.
Age Limits, Sex and Marital Status : "Only
unmarried male candidates born not earlier than 2nd
July, 1993 and not later
than 1st January, 1996 are eligible".
The date of birth accepted by the Commission is
that entered in the Matriculation or Secondary School Leaving Certificate or in
a certificate recognised by an Indian University as equivalent to Matriculation
or in an extract from a Register of Matriculates maintained by a University
which must be certified by the proper authority of the University or in
the Higher Secondary or an equivalent examination certificates. These
certificates are required to be submitted only after the declaration of the
result of the written part of the examination. No other document relating to age
like horoscopes, affidavits, birth extracts from Municipal Corporation, service
records and the like will be accepted. The expression Matriculation/Higher
Secondary Examination Certificate in this part of the instruction includes the
alternative certificates mentioned above.
Educational Qualifications :
(i) For Army wing of National Defence Academy :- 12th Class pass of the 10+2 pattern of School Education or equivalent examination conducted by a State Education Board or a University.
(ii) For Air Force and Naval Wings of National Defence Academy and for the 10+2 Cadet Entry Scheme at the Indian Naval Academy :- 12th Class pass of the 10+2 pattern of School Education or equilvalent with Physics and Mathematics conducted by a State Education Board or a University.
(iii) Candidates who are appearing in the 12th exam can also apply.
Physical Standards: Candidates must be physically fit according to the Regulations given in notice.
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.
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.
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.
6.Integral Calculus and Differential equations:
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.
7. Vector Algebra :_
8.Statistics and Probability :-
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
of data, Frequency distribution, cumulative frequency distribution -
examples Graphical representation - Histogram, Pie Chart, Frequency
Polygon - examples. Measures of Central tendency - mean, median and
mode. Variance and standard deviation - determination and comparison.
Correlation and regression.
Probability : Random
experiment, outcomes and associated sample space, events, mutually
exclusive and exhaustive events, impossible and certain events. Union
and Intersection of events. Complementary, elementary and composite
events. Definition of probability - classical and statistical -
examples. Elementary theorems on probability - simple problems.
Conditional probability, Bayes' theorem - simple problems. Random
variable as function on a sample space. Binomial distribution,
examples of random experiments giving rise to Binominal distribution.
Part ‘A’ - ENGLISH
(Maximum Marks 200). The question paper in English will be designed to
test the candidate’s understanding of English and workman like use of
words. The syllabus covers various aspects like : Grammar and usage,
vocabulary, comprehension and cohesion in extended text to test the
candidate’s proficiency in English.
Part ‘B’ - GENERAL KNOWLEDGE