Maths

Maths

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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.

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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.

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GUJCET : Gujarat Common Entrance Test

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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. 

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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.

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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.

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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

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GATE 2011 : Examination Syllabus

:: MA-Mathematics ::

Linear Algebra: Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of

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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

Karnataka CET 2010 Result

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

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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

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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 :

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With just a few more days to go for the joint entrance exams for India's premier Institutes of Technology, popularly known as IIT JEE, students are in for the final push. Here rediff.com in collaboration with TCYonline present mock papers for mathematics, physics and chemistry for JEE students to improve their speed and sharpen their skills.

Just click on the links below, take a print-out and get cracking!

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Karnataka Common Entrance Test (KCET) Previous Papers & Answer Keys (2009)

Download KCET Solved Papers

Papers : Chemistry, Mathematics, Biology & Answer Keys of Year 2009

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Karnataka Common Entrance Test (KCET) Previous Papers & Answer Keys (2008)

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Papers : Physics, Chemistry, Mathematics, Biology & Answer Keys of Year 2008

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Karnataka Common Entrance Test (KCET) Previous Papers & Answer Keys (2007)

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Papers : Physics, Chemistry, Mathematics, Biology & Answer Keys of Year 2007

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Karnataka Common Entrance Test (KCET) Previous Papers & Answer Keys (2006)

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Papers : Physics, Chemistry, Mathematics, Biology & Answer Keys of Year 2006

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Karnataka Common Entrance Test (KCET) Previous Papers & Answer Keys (2005)

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Papers : Physics, Chemistry, Mathematics, Biology & Answer Keys of Year 2005

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Karnataka Common Entrance Test (KCET) Previous Papers & Answer Keys (2004)

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Papers : Physics, Chemistry, Mathematics, Biology & Answer Keys of Year 2004

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Download BITSAT 2009 Exam Paper (Math, Physics, Chemistry English And Logical Resoning)

Q1. A boat takes time t to go downstream from point A to point B and time 2t to go upstream from point B to point A . If the speed of the stream is v and the speed of the boat with respect to the stream is u , then which of the following gives the correct relationship between u & v ?
a) u = v
b) u = 3v
c) v = 2u
d) v=3u

Q2. Which of the following is correct about the acceleration of a particle describing a uniform circular motion ?
a) The acceleration is constant both in magnitude and direction
b) The acceleration is constant in direction but not in magnitude
c) The acceleration is constant in magnitude but not in direction
d) The acceleration is neither constant in magnitude nor in direction

Q3. Five identical resistors of resistance 1 each, are connected along the four edges and one of the diagonals of a square. A potential difference of 1 V is applied across the other diagonal. What will be the current in the resistor along the diagonal ?
a) 0.5A
b) 1 A
c) 5A
d) zero ... [..]

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IIT JEE 2010 Study Plan | Physics

IIT JEE 2010 entrance exam is to be held on coming days. So it is necessary to make the schedule of study for different subjects which will help you to prepare in suitable discipline.

Study Plan for Photoelectric Effect and Wave- particle Duality

Sections of the chapter
42.1 Photon theory of light
42.2 Photoelectric effect
42.3 Matter waves

Day 1

  • 42.1 Photon theory of light
  • 42.2 Photoelectric effect
  • 42.3 Matter waves

Day 2

  • Worked out examples 1 to 10

Day 3

  • WOE 11 to 13
  • Exercises 1 to 5

Day 4

  • Exercises 6 to 15

Day 5

  • Exercises 16 to 25

Day 6

  • Exercises 26 to 35

Day 7

  • Objective I and II, Questions for short answer

Day 8

  • Concept review and Formula review

Study Plan for Bohr's Model and Physics of Atom

Day 1

  • 43.1 Early atomic models
  • 43.2 Hydrogen spectra
  • 43.3 Difficulties with Rutherford Model
  • 43.4 Bohr's model

Day 2

  • Worked out examples 1 to 5
  • Exercises 1 to 5

Day 3

  • 43.5 Limitations of Bohr's model
  • 43.6 The wave function of an electron
  • 43.7 Quantum mechanics of the hydrogen atom

Day 4

  • WOE 6 to 10
  • Exercises 6 to 10

Day 5

  • 43.8 Nomenclature in atomic physics
  • 43.9 Laser
  • WOE 11 to 15
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