# Maths

Maths

## (Tutorials) IIT-JEE Mathematics: Algebraic Manipulation

### IIT-JEE Algebraic Manipulation

## (Tutorial) IIT-JEE Mathematics: Integral Limit

### IIT-JEE Integral Limit

## (Tutorial) IIT-JEE Mathematics: Position Vectors

### IIT-JEE Position Vectors

## (Tutorial) IIT-JEE Mathematics: Complex Root Probability (part 2)

### IIT-JEE Complex Root Probability (part 2)

## (Tutorial) IIT-JEE Mathematics: Complex Root Probability (part 1)

### IIT-JEE Complex Root Probability (part 1)

## (Tutorial) IIT JEE Mathematics: Perpendicular Planes (Part- II)

### IIT JEE Perpendicular Plane (Part-II)

## (Tutorial) IIT-JEE Mathematics: Perpendicular Planes (Part-I)

## Perpendicular Planes (Part-I)

## (Tutorials) IIT-JEE Mathematics: Trigonometry Problems

## Trigonometry Problems

## (Tutorials) IIT-JEE Mathematics Video Tutorials

## IIT-JEE Mathematics Video Tutorials

## (Syllabus) BITSAT 2011 Syllabi (Mathematics)

## BITSAT 2011 Syllabus

## MATHEMATICS

**The BITSAT-2011 test will be conducted on the basis of
NCERT syllabus for 11th and 12th class. The detailed syllabus is given in
the Annexure. Candidates may refer to the NCERT textbooks for the contents.
A sample test demonstrating the features of BITSAT will be made available to
the registered candidates at the BITS website on which he/she can practice
as many times as desired.**

## (Syllabus) ISAT 2011 Syllabus - MATHEMATICS

## IIST ISAT 2011 MATHEMATICS SYLLABUS

**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;. one-one, into and onto functions, composition of functions.

**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 co-efficients, nature of roots, formation of quadratic equations with given roots.

**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.

## (Syllabus) IITJEE Syllabus 2011 - MATHEMATICS

## Mathematics Syllabus of IIT-JEE 2011

**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 skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables.

Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations.

## Gujarat Common Entrance Test (GUJCET)

## GUJCET : Gujarat Common Entrance Test

**Gujarat Common Entrance Test (CET) Engineering
Examination
**Gujarat Common entrance Test (CET) is conducted by The Education
Department, Govt of Gujarat and it has assigned The Gujarat Secondary and Higher
Secondary Education to hold CET for admission into various medical, engineering
and pharmacy courses in the state of Gujarat. The information booklet and the
application form prepared by the Board is available on the payment of Rs.
250/-via Demand Draft from any nationalized bank payable at Gandhinagar/Ahmedabad
in favour of

**"Secretary, Gujarat Common Entrance Test (CET) Cell, Gandhinagar"**

**Exam Pattern**

Admission to courses will be based on 40% weightage of GUJCET score and 60% weightage of 12th Marks. For admission to MBBS, 70% marks in 12th are also required. Please note that marks of either PCM (without practicals) or PCB (without practicals) are considered so effective weightage is somewhere between 21-28% for GUJCET Exam.

## (Syllabus) WBJEE: JEM 2010 Mathematics

##

WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

SYLLABUS FOR JEM

## MATHEMATICS

**Algebra**

A.P., G.P., H.P. :Definitions of A. P. and G.P.; General term; Summation of first n-terms; A.M.and G.M.; Definitions of H.P. (only 3 terms) and H.M.; Finite arithmetico-geometric 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 ax2+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.

## (Syllabus) EAMCET : Agriculture & Medicine (AM) Syllabus

## EAMCET : Agriculture & Medicine (AM) Syllabus

## Subject : BOTANY

I. INTRODUCTION: Origin, development and scope of Botany - Classification of plant kingdom - Branches of Botany: Morphology, Cytology, Embryology, Palynology, Taxonomy, Physiology, Ecology, Palaeobotany, Genetics, Phytogeography, Phycology, Mycology,Lichenology, Bryology, Pteriodology, Microbiology, Bacteriology, Virology - Parts of angiospermic plant

II. EXTERNAL MORPHOLOGY: (a)Vegetative morphology: Root: Root system; Types, Functions, Modification of roots (Velamen roots, Photosynthetic roots, Respiratory roots, Parasitic roots, Storage roots and nodular roots) - Stem: characteristics and functions of the stem; Modifications of stem: Aerial: Tendril, Thorn, Hook, Phylloclade, Restiratory roots, Tuberous stem and Bulbil; Sub-aerial: Runner, Stolon, Sucker & Offset, Underground: Rhizome, Corm, Stem tuber & Bulb - Leaf: Parts of Leaf, Types, Functions and Parts of leaves, Venation, Phyllotaxy, Leaf modifications: - tendrils, spines, scale leaves, phyllode,reproductive & trap leaves. (b)Reproductive morphology:Inflorescence: Introduction, Types of Inflorescence - Racemose, Cymose and Special Types Flower: Parts of a typical flower: Structure, Sex distribution and symmetry of flower, position of gynoecium. Detailed description of flower: Prianth, Calyx, Corolla, aestivation, Androecium – Parts, fixation and dehiscence of anther, length of stamens, union of stamens, Gynoecium – number of carpels, fusion of carples, ovary – number of locules , placentation, types of styles, Stigma

III. REPRODUCTION IN ANGIOSPERMS: Introduction – Sporophytic and Gametophytic stages - Structure of an Anther; Microsporogenesis, Structure of a pollen grain and development of male gametophyte Ovule – Structure and Types; megasporogenesis - development and structure of embryosac - Pollination: Types of pollination, self and cross-pollination, contrivances for cross pollination and self pollination, agents of cross pollination. Fertilization – Process, Post - fertilization changes; Seed structure (Dicot & Monocot), and seed germination (epigeal, hypogeal & vivipary) - Fruits: Classification; False fruits and true fruits - Simple fruits (fleshy fruits – berry, pome, pepo, hesperidium, drupe; Dry fruits – dehiscent- legume, septicidal capsule, septifragal capsule, loculicidal capsule; Indehiscent fruits – caryopsis, cypsela, nut; schizocarpic – lomentum, schizocarp); Aggregate and Multiple fruits

IV. PLANT TAXONOMY: Introduction – Alpha and Omega taxonomy; Aspects of taxonomy – Identification – Flora, herbaria, botanical gardens (RBG – Kew, IBG – Kolkata, NBG – Lucknow); Nomenclature, Classification – Types, Units and a brief account of Bentham & Hooker’s system. Study of the following families - Malvaceae - Fabaceae - Solanaceae - Liliaceae.

V. CELL BIOLOGY: Introduction, Techniques of Cell Biology – microscopy (light, electron, fluorescent, phase contrast, SEM, TEM – only uses), Separation techniques - Ultrastructure of plant cell (Eukaryotic cell - Structure of cell wall and cell membrane, Protoplasm, cytoplasm, Plastids, mitochondria, endoplasmic reticulum, ribosomes, golgi complex, lysosomes, peroxisomes and glyoxysomes, vacuoles and Nucleus). – Chromosomes - Introduction, structure (light microscopic study), classification, functions and nucleosome model) - Nucleic acids - Cell Division : Cell Cycle, Mitosis and Meiosis

VI. INTERNAL ORGANIZATION OF PLANTS: Tissues – Types (Meristematic and Permanent ) and functions - Internal structure of Dicot root (Primary) and Monocot root - Internal structure of Dicot stem (Primary) and Monocot stem - Internal structure of leaf (Dicot and Monocot) - Secondary growth in dicot stem.

## (Syllabus) EAMCET Engineering Syllabus

## EAMCET Engineering Syllabus

## Subject : MATHEMATICS

I. ALGEBRA: (a) Functions – Types of functions – Algebra of real valued functions (b) Mathematical induction and applications (c) Permutations and Combinations – linear and circular permutations – combinations.(d) Binomial theorem – for a positive integral index – for any rational index – applications – Binomial Coefficients.(e) Partial fractions (f) Exponential and logarithmic series (g) Quadratic expressions, equations and inequations in one variable.(h) Theory of equations – Relations between the roots and Coefficients in any equation – Transformation of equations – reciprocal equations.(i) Matrices and determinants – Types of matrices – Algebra of matrices – Properties of determinants – simultaneous linear equations in two and three variables – Consistency and inconsistency of simultaneous equations.(j) Complex numbers and their properties – De Moivre’s theorem – Applications – expansions of trigonometric functions.

II. TRIGONOMETRY: (a) Trigonometric functions – Graphs – periodicity (b) Trigonometric ratios of compound angles, multiple and sub-multiple angles.(c) Transformations (d) Trigonometric equations (e) Inverse trigonometric functions (f) Hyperbolic and inverse hyperbolic functions (g) Properties of Triangles (h) Heights and distances (in twodimensional plane)

III. VECTOR ALGEBRA: (a) Algebra of vectors – angle between two non-zero vectors – linear combination of vectors – vector equation of line and plane (b) Scalar and vector product of two vectors and their applications (c) Scalar and vector triple products – Scalar and vector products of four vectors

## (Syllabus) GATE 2011 : Examination Syllabus : (Mathematics)

**GATE 2011 : Examination Syllabus**

## :: MA-Mathematics ::

**Linear Algebra: **Finite dimensional vector spaces; Linear

## (Answer Keys) Karnataka Common Entrance Test (KCET) | Result and Answer Keys of Exam 2010

## Karnataka Common Entrance Test (KCET) | Result and Answer Keys of Exam 2010

*Karnataka Examination Authority
Common Entrance Test
Karnataka
*

Karnataka Common Entrance Test Result 2010 has been announced by Karnataka Examination authority. Answer keys are also published by Karnataka examination authority. There are four subject in Karnataka CET entrance exam - Physics, Chemistry, Biology and Mathematics

**Result: **Click on the following link to check the result

**Answer Keys: **Click on the following buttons to see the answer keys of entrance exam 2010

## (Syllabus) Vellore Institute of Technology Engineering Entrance Examination (VITEEE) Mathematics Syllabus

## Vellore Institute of Technology Engineering Entrance Examination (VITEEE)

## MATHEMATICS SYLLABUS

**MATRICES AND DETERMINANTS:**

Types of matrices, addition and multiplication of matrices-Properties, computation of inverses, solution of system of linear equations by matrix inversion method. Rank of a Matrix – Elementary transformation on a matrix, consistency of a system of linear equations, Cramer’s rule, Non-homogeneous equations, homogeneous linear system, rank method.

**THEORY OF EQUATIONS,
SEQUENCE AND SERIES**

Quadratic equations – Relation between roots and
coefficients – Nature of roots – Symmetric
functions of roots – Diminishing and Increasing
of roots – Reciprocal equations. Arithmetic,
Geometric and Harmonic Progressions-Relation
between A.M., G. M ., and H.M. Special series:
Binomial, Exponential and Logarithmic series –
Summation of Series.

**VECTOR ALGEBRA**

Scalar Product – Angle between two vectors,
properties of scalar product, applications of
dot products. Vector Product – Right handed and
left handed systems, properties of vector
product, applications of cross product. Product
of three vectors – Scalar triple product,
properties of scalar triple product, vector
triple product, vector product of four vectors,
scalar product of four vectors. Lines – Equation
of a straight line passing through a given point
and parallel to a given vector, passing through
two given points, angle between two lines. Skew
lines – Shortest distance between two lines,
condition for

two lines to intersect, point of intersection,
collinearity of three points. Planes – Equation
of a plane, passing through a given point and
perpendicular to a vector, given the distance
from the origin and unit normal, passing through
a given point and parallel to two given vectors,
passing through two given points and parallel to
a given vector, passing through three given
non-collinear points, passing through the line
of intersection of two given planes, the
distance between a point and a plane, the plane
which contains two given lines, angle between
two given planes, angle between a line and a
plane. Sphere – Equation of the sphere whose
centre and radius are given, equation of a
sphere when the extremities of the diameter are
given.

**COMPLEX NUMBERS & TRIGONOMETRY:**

Complex number system, conjugate – properties,
ordered pair representation. Modulus –
properties, geometrical representation meaning,
polar form principal value, conjugate, sum,
difference, product quotient, vector
interpretation, solutions of polynomial
equations, De Moivre’s theorem and its
applications. Roots of a complex number – nth
roots, cube roots, fourth roots. Angle measures-

Circular function-Trigonometrical ratios of
related angles – Addition formula and their
applications – Trigonometric equations – Inverse
trigonometric functions-Properties and solutions

## (Paper) ISAT Mathematics Sample Questions 2010

## ISAT Mathematics Sample Questions 2010

Question 1 :
What is the value of x in the triangle shown?

A. 54

B. 59

C. 49

D. 24

Question 2:
Last year there were 80 students enrolled in the eighth-grade class. This year
the
number of students enrolled in the eighth-grade class increased by 10%.
How many students are enrolled in the eighth-grade class this year?

A. 88

B. 8

C. 90

D. 81

Question 3 :
A company packs its coffee into cylindrical containers. The height of each
container is 6
inches, and the radius of the container is 3 inches.

Which is closest to the volume of one of these cylindrical containers?

A. 36 cubic inches

B. 113 cubic inches

C. 54 cubic inches

D. 170 cubic inches

Question 4 :
The student council is making snack bags for a class trip. Each snack bag will
contain:

• 1 type of drink

• 1 type of cookie

• 1 type of fruit

To make each snack bag, they will choose from 2 types of drinks, 4 types of
cookies,
and 2 types of fruit.
How many combinations of 1 type of drink, 1 type of cookie, and 1 type of fruit
are
possible?

A. 48

B. 8

C. 3

D. 16

Question 5 :
Which is closest to the circumference of this circle?

A. 14 inches

B. 63 inches

C. 20 inches

D. 28 inches

Question 7 :
Which of the following is equivalent to the expression shown?

4x – 5 – 2x – 3

A. 6x + 2

B. 2x + 2

C. 6x – 8

D. 2x – 8

Question 8 :
Between which two consecutive integers is ?

A. 6 and 7

B. 100 and 101

C. 75 and 76

D. 17 and 18

Question 10 :
Amy has of a yard of string to make bracelets. Each bracelet requires of a yard
of string.
What is the greatest number of bracelets Amy can make with this length of
string?

A. 3

B. 6

C. 4

D. 8

Question 11 :
Look at the addition patterns below.

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

1 + 3 + 5 + 7 + 9 = 25

How many consecutive odd integers starting with 1 must be added to produce 64?

A. 8

B. 6

C. 7

D. 9

Question 12 :
Which point on the number line below represents the value ?

A. Point Q

B. Point S

C. Point P

D. Point R

Question 14 :
Paula multiplied a number by 16. Her result is a positive number less than 16.
Which of
these did Paula multiply by 16?

A. A number greater than one

B. A number less than zero

C. A number between zero and one

D. Zero

Question 15 :