S.No. 
AIEEE
Indian Institutes of Technology
Joint Entrance Examination, IITJEE  2012 (Answer Key)
IITJEE 2012 : PAPER  I & II
CODE0, 1, 2, 3, 4, 5, 6, 7, 8 & 9
Indian Institute of Technology,
Patna
PhD Admission  July 2012
Applications are invited for admission to the Doctor of
Philosophy (Ph.D.) programme, starting in July 2012 in the following
Departments. The areas of research in IIT Patna are as follows:

Computer Science and Engineering

Electrical Engineering

Mechanical Engineering

Chemistry

Mathematics

Physics

Humanities and Social Sciences

InterDisciplinary research
Category of Admission:
Regular and FullTime
A student in this category works fulltime for her/his PhD degree. They can
be classified as
a) Institute Fellows
She/he receives assistantship from the Institute. The qualifying Degree for
Financial Support is:
 BE/ BTech/ MSc/ MA equivalent with valid GATE score above the prescribed
cut off level/ NET /
NBHM/ DBTJRF qualification.
 ME/ MTech or equivalent.
Age Limit: Please refer Eligibility Criteria for Admission into Ph.D.
Programme
b) JRF/SRF Fellows
She/he receives fellowship from any Government recognized funding agencies, such
as CSIR, UGC, DBT, etc.
Sponsored (Full Time)
 A student in this category is sponsored by a recognized R&D
organization, academic institution, government organization or industry for
doing research in the Institute on a fulltime basis. The Institute does not
provide any assistantship/fellowship to such a student.
 Candidate in Sponsored category must be a regular employee of the
sponsoring organization with at least one year of professional experience in
the respective field.
Project Staff
This category refers to a student who is working on a
sponsored project in the Institute and is admitted to the PhD Programme to work
on a fulltime or parttime basis. The remaining duration of the project at the
time of admission should be at least two years. If the project gets completed
before the student completes her/his PhD Programme, her/his category will be
converted to that of SELFFINANCED unless she/he is granted an
assistantship/fellowship from the Institute or any other agency.
Employed & PartTime
 A student in this category is a professionally employed person
(including the staff of IIT Patna), who pursues the PhD Programme while
continuing the duties of her/his service. The Institute does not provide any
assistantship/fellowship to such a student. PhD students registered in
Employed and Part time category, the minimum residential requirement is one
or two semester(s) depending on the completion of mandatory course work
required for PhD students by the respective departments.
 Candidate in Employed and Parttime categories must be a regular
employee of the sponsoring organization with at least one year of
professional experience in the respective field.
Distance requirement: The candidate must reside within 50 km radius
from IIT Patna.
Eligibility Criteria
In all the disciplines, the upper age limit is 28 years (B.Tech./B.E./M.Sc./MA/MCA/MBA)
and 32 years
(M.Tech./M.E./M.S./M.Phil.) to be calculated from 30042012 and is applicable
only for candidates
applying in Regular and Full time category (Institute Fellows). Upper age is
relaxed upto 05 years in case of
candidate belonging to Schedule Castes/Schedule Tribes, Women, Physically
Handicapped, and OBC
applicants.
PhD in Engineering
For admission to the PhD Programme in Engineering Department, a candidate must
satisfy one of the
following criteria:
 Candidates having M.Tech./M.E. degree in a Engineering/Technology, with a
minimum CPI of 6.5 or
60% of marks.
 Bachelor’s degree in Engineering/Technology (from any Institute other than
WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD
JEM 2012  SYLLABUS
MATHEMATICS
Algebra
A.P., G.P., H.P. : Definitions of A. P. and G.P.; General term;
Summation of first nterms; A.M.and G.M.; Definitions of H.P. (only 3 terms) and
H.M.; Finite arithmeticogeometric series.
Logarithms :Definition; General properties; Change of base.
Complex Numbers: Definition and properties of complex numbers; Complex
conjugate; Triangle inequality; Square root of complex numbers; Cube roots of
unity; D’Moivre’s theorem (statement only) and its elementary applications.
Quadratic Equations : Quadratic equations with real coefficients;
Relations between roots and coefficients; Nature of roots; Formation of a
quadratic equation, sign and magnitude of the quadratic expression ax^{2}+bx+c
(a,b,c are rational numbers and a≠0).
Permutation and combination : Permutation of n different things taken
r at a time (r ≤ n). Permutation of n things not all different. Permutation with
repetitions (circular permutation excluded). Combinations of n different things
taken r at a time (r ≤ n). Combination of n things not all different. Basic
properties.
Problems involving both permutations and combinations.
Principle of Mathematical Induction : Statement of the principle.
Proof by induction for the sum of squares, sum of cubes of first n natural
numbers, divisibility properties like 2 2n – 1 is divisible by 3 (n ≥ 1), 7
divides 3^{2n+1}+2 ^{n+2}(n ≥ 1).
Binomial theorem (positive integral index) :Statement of the theorem,
general term, middle term, equidistant terms, properties of binomial coefficients.
All India Engineering Entrance
Examinations (AIEEE) Books
All India Engineering Entrance
Examinations (AIEEE)
About AIEEE:
All India Engineering/Architecture Entrance Entrance
Examinations (AIEEE) is amongst the famous exams for admission in
engineering/architecture bachelor courses throughout most of the leading
engineering/architecture institutes across the country. Therefore AIEEE is the
most popular engineering Entrance examination for BE/BTech aspiring students
across the country. Every year a huge number of students from all over the
country participate in this exam to get admission in the various reputed NIT’s
and state level institutes. Last time nearly 9 lakhs students appeared for AIEEE
exam.
This is given by large number of students from all over the
country. There are large number of top level institutes and universities that
approve AIEEE score. This all includes all the NITs National Institute of
Technology. Although, the number of seats available for admission in all these
institutes are fixed. So one must prepare very well. The competition is quite
tough.
Eligibility Criteria:
The student should be passed in 12th class from a recognized
board with Physics, Chemistry & Mathematics as compulsory subjects. Those who
have to give the final year exams of the qualifying exam can also apply for
AIEEE provided their result has to be out by the time of counseling.
Pattern:
Subject Combinations in Qualifying Examinations:
Course 
Compulsory Subjects 
Any One of the Optional Subjects 
B.E./B.Tech.* 
Physics & Mathematics 
 Chemistry
 BioTechnology
 Computer Science
 Biology

B. Arch./B. Planning** 
Mathematics with 50% marks in aggregate at 10+2 level 

All India Engineering Entrance
Examinations (AIEEE): 2012
AIEEE 2012 Syllabus:
All India Engineering Entrance
Examinations (AIEEE): 2012
About AIEEE:
All India Engineering/Architecture Entrance Entrance
Examinations (AIEEE) is amongst the famous exams for admission in
engineering/architecture bachelor courses throughout most of the leading
engineering/architecture institutes across the country. Therefore AIEEE is the
most popular engineering Entrance examination for BE/BTech aspiring students
across the country. Every year a huge number of students from all over the
country participate in this exam to get admission in the various reputed NIT’s
and state level institutes. Last time nearly 9 lakhs students appeared for AIEEE
exam.
This is given by large number of students from all over the
country. There are large number of top level institutes and universities that
approve AIEEE score. This all includes all the NITs National Institute of
Technology. Although, the number of seats available for admission in all these
institutes are fixed. So one must prepare very well. The competition is quite
tough.
Eligibility Criteria:
The minimum academic qualification for appearing in AIEEE
2012 is that the candidate must have passed in final examination of 10+2 (Class
XII) or its equivalent referred to as the qualifying examination (see Appendix –
IX). Those appearing in 10+2 (Class XII) final or equivalent examination in 2012
may also appear in AIEEE 2012 provisionally.
Scheme of Examination:
Entrance examination would consist of two papers i.e. 1st
paper consisting of three parts of Physics, Chemistry and Mathematics of equal
weight age with objective type questions for B.E/B.Tech courses in
offline/online mode and 2nd paper – consisting of Mathematics, Aptitude Test and
Drawing for B. Architecture and B. Planning in offline mode. The Aptitude Test
is designed to evaluate candidate’s perception, imagination, observation,
creativity and architectural awareness.
Schedule of Examination:

Subjects 
Type of Questions 
Paper 1 
Physics, Chemistry & Mathematics 
Objective type questions with equal weightage to Physics, Chemistry
& Mathematics 
Paper 2 
 Mathematics – Part I
 Aptitude Test – Part II &
 Drawing Test – Part III

 Objective type questions
 Objective type questions
 questions to test Drawing Aptitude

CBSE: All India Engineering
Entrance Examinations (AIEEE)
Syllabus: Mathematics  2012
Unit 1 : Sets, Relations and Functions:
Sets and their representation; Union, intersection and
complement of sets and their algebraic properties; Power set; Relation, Types of
relations, equivalence relations, functions;. oneone, into and onto functions,
composition of functions.
Unit 2 : Complex Numbers and Quadratic Equations:
Complex numbers as ordered pairs of reals, Representation of
complex numbers in the form a+ib and their representation in a plane, Argand
diagram, algebra of complex numbers, modulus and argument (or amplitude) of a
complex number, square root of a complex number, triangle inequality, Quadratic
equations in real and complex number system and their solutions. Relation
between roots and coefficients, nature of roots, formation of quadratic
equations with given roots.
Unit 3 : Matrices and Determinants:
Matrices, algebra of matrices, types of matrices,
determinants and matrices of order two and three. Properties of determinants,
evaluation of determinants, area of triangles using determinants. Adjoint and
evaluation of inverse of a square matrix using determinants and elementary
transformations, Test of consistency and solution of simultaneous linear
equations in two or three variables using determinants and matrices.
Unit 4 : Permutations and Combinations:
Fundamental principle of counting, permutation as an arrangement and
combination as selection, Meaning of P (n,r) and C (n,r), simple applications.
Unit 5 : Mathematical Induction:
Principle of Mathematical Induction and its simple applications.
Unit 6 : Binomial Theorem and It's Simple Applications:
Binomial theorem for a positive integral index, general term and middle term,
properties of Binomial coefficients and simple applications.
Unit 7 : Sequences and Series:
Arithmetic and Geometric progressions, insertion of
arithmetic, geometric means between two given numbers. Relation between A.M. and
G.M. Sum upto n terms of special series: S n, S n2, Sn3. Arithmetico – Geometric
progression.
Unit 8 : Limit, Continuity and Differentiability:
Real  valued functions, algebra of functions, polynomials,
rational, trigonometric, logarithmic and exponential functions, inverse
functions. Graphs of simple functions. Limits, continuity and differentiability.
Differentiation of the sum, difference, product and quotient of two functions.
Differentiation of trigonometric, inverse trigonometric, logarithmic,
exponential, composite and implicit functions; derivatives of order upto two.
Rolle’s and Lagrange’s Mean Value Theorems. Applications of derivatives: Rate of
change of quantities, monotonic  increasing and decreasing functions, Maxima
and minima of functions of one variable, tangents and normals.
Unit 9 : Integral Calculus:
Integral as an anti  derivative. Fundamental integrals
involving algebraic, trigonometric, exponential and logarithmic functions.
Integration by substitution, by parts and by partial fractions. Integration
using trigonometric identities. Evaluation of simple integrals of the type
Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of
definite integrals. Evaluation of definite integrals, determining areas of the
regions bounded by simple curves in standard form.
Indian Institute of Space Science
and Technology
IIST Ph.D. Programme – February 2012
Indian Institute of Space Science and Technology envisions the integration of
Space Technology and Space Science educational programs with basic and applied
research for meeting the national R&D requirements of science and technology in
general and of the Indian Space Programme in particular. The institute provides
a vibrant research atmosphere and offers doctoral and postdoctoral programmes.
IIST: ISAT 2012 Mathematics
Syllabus
PERMUTATIONS AND COMBINATIONS:
Fundamental principle of counting. Permutations and Combinations, derivation
of formulae and their connections and simple applications.
MATHEMATICAL INDUCTION:
Principle of Mathematical Induction and its simple applications.
BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:
Binomial theorem for positive integral indices, general term and middle term,
properties of Binomial coefficients and simple applications.
SEQUENCES AND SERIES:
Arithmetic and Geometric progressions, insertion of arithmetic, geometric
means between two given numbers. Relation between A.M. and G.M. Sum upto n terms
of special series n, n2, n3. Arithmetico  Geometric sequence.
TRIGONOMETRY:
Trigonometric functions. Trigonometrical identities and equations. Inverse
Trigonometric functions, their properties and applications.
COMPLEX NUMBERS AND QUADRATIC EQUATIONS:
Complex numbers as ordered pairs of reals. Representation of
complex numbers in a plane. Argand plane and polar representation of complex
numbers. Algebra of complex numbers, modulus and argument (or amplitude) of a
complex number, square root of a complex number, triangle inequality. Quadratic
equations in real and complex number system and their solutions. Relation
between roots and coefficients, nature of roots, formation of quadratic
equations with given roots.
Indian Institute of Space Science
and Technology
Thiruvananthapuram
Indian Institute of Space Science and Technology (IIST),
Minimum Qualifying Mark for
Ranking (MQMR) and Aggregate Cutoff : JEE2011
Cutoff Marks  JEE2011
Indian Institute of Technology
Ropar
Ph.D. Admission: 20112012
The Indian Institute of Technology Ropar (IIT Ropar) has
invited applications from Indian citizens for Ph.D programs in various
disciplines during second semester of academic year 20112012.
Eligibility criteria and areas of research for each
department are given below:
Sciences:
Chemistry:
Eligibility Criteria: First Class (6.5 grade point out
of 10) or 60% marks (55% marks for SC/ST) in M.Sc. or equivalent degree in
Chemistry.
Candidates meeting this requirement must also fulfill one of the following
additional requirements tenable for the current year:
Area of Research: Organic Chemistry, Organometallics,
Catalysis, Chemical Kinetics and Reaction Dynamics, Electronic Structure
Calculations, Organic polymer synthesis.
Physics:
Eligibility Criteria: First Class (6.5 grade point out
of 10) or 60% marks (55% marks for SC / ST) in M.Sc. Physics/B.Tech. Engineering
Physics.
Candidates meeting this requirement must also fulfill one of the following
additional requirements tenable for the current year:
Areas of Research: (1) Particle/Nuclear Physics, (2)
Quantum Optics and Quantum Information.
Mathematics:
Eligibility Criteria: First class (6.5 grade point out
of 10) or 60% marks (55% marks for SC/ST) in Master's degree in Mathematics,
Statistics, Computer Science, Physical Sciences, Engineering Sciences or
equivalent Master's Degree.
Candidates meeting this requirement must also fulfill one of the following
additional requirements tenable for the current year:
Areas of Research: 1. Fluid Dynamics, 2. Mathematical
Modeling, 3. Differential Equations, 4. Topology
Engineering:
Computer Science and Engineering:
Eligibility Criteria:
1. First class or equivalent Master's Degree in Engineering/Technology (55%
marks for SC/ST) or
2. A first class Master's degree in Science (55 % marks for SC/ST) or a first
class in Bachelor's degree in Engineering / Technology (55 % marks for SC/ST).
Candidates meeting this requirement must also fulfill one of the following
additional requirements:

Valid GATE score

CSIR/UGC/NBHM/DBT award.
Note: MCA degree will be
considered as equivalent to a Master's degree in Science.
Areas of Research: The department is looking for excellent candidates
willing to engage in multidisciplinary research in systems and theory.
Indian Institutes of Technology
Joint Entrance Examination, IITJEE  2012
Mathematics Syllabus
Algebra: Algebra of complex numbers,
addition, multiplication, conjugation, polar representation, properties of
modulus and principal argument, triangle inequality, cube roots of unity,
geometric interpretations.
Quadratic equations with real coefficients, relations between
roots and coefficients, formation of quadratic equations with given roots,
symmetric functions of roots.
Arithmetic, geometric and harmonic progressions, arithmetic,
geometric and harmonic means, sums of finite arithmetic and geometric
progressions, infinite geometric series, sums of squares and cubes of the first
n natural numbers.
Logarithms and their properties.
Permutations and combinations, Binomial theorem for a
positive integral index, properties of binomial coefficients.
Matrices as a rectangular array of real numbers, equality of
matrices, addition, multiplication by a scalar and product of matrices,
transpose of a matrix, determinant of a square matrix of order up to three,
inverse of a square matrix of order up to three, properties of these matrix
operations, diagonal, symmetric and skewsymmetric matrices and their
properties, solutions of simultaneous linear equations in two or three
variables.
IIT Bombay
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