APEX INSTITUTE has been established with sincere and positive resolve to do something rewarding for ENGG. / PRE-MEDICAL aspirants. For this the APEX INSTITUTE has been instituted to provide a relentlessly motivating and competitive atmosphere.
As It is very important to discover the basic weaknesses and problems of students not succeeding in IIT-JEE / PRE-MEDICAL exams. In fact, as question patterns are changing, now you need to have a different approach for these exams. As far as ENGG. / PRE-MEDICAL preparations is concerned, students have been wasting time and energy, studying Physics, Chemistry and Maths at different places. At APEX INSTITUTE, the scope of the subject has been deliberately made all- inclusive to free them of this burden. APEX INSTITUTE offers you complete preparation for IIT-JEE/PRE-MED. exams under one roof.
The document provides definitions for mathematical terms that students in 5th/6th class primary school and junior cycle secondary school may encounter. It includes over 50 terms defined with diagrams and examples. The glossary is designed to inform students, parents, and teachers about the vocabulary and meanings of key mathematical terms as students transition between primary and post-primary education in Ireland.
This document provides an overview of matrices including:
- How to describe matrices using m rows and n columns
- Common types of matrices such as row, column, zero, square, diagonal, and unit matrices
- Basic matrix operations including addition, subtraction, scalar multiplication
- Rules for matrix multiplication including that matrices must be conformable
- The transpose of a matrix which is obtained by interchanging rows and columns
- Properties of transposed matrices including (A+B)T = AT + BT and (AB)T = BTAT
- The document discusses how to multiply matrices, including defining when multiplication is valid based on the number of columns and rows of the matrices.
- It provides an example of multiplying two matrices, showing the step-by-step process of multiplying corresponding elements and summing them.
- It also discusses properties of matrix multiplication, including associativity, distributivity, and the existence of an identity matrix.
- Examples are provided to illustrate verifying these properties by calculating different matrix multiplications.
The document provides information on geometry topics including angles, distance, area, and volume. It defines key concepts such as perpendicular lines, parallel lines, interior and exterior angles, circumference, arc length, perimeter, area of triangles, circles, quadrilaterals, and strategies for finding areas of irregular shapes. Examples are provided to illustrate formulas and problem-solving approaches for finding distances, midpoints, areas, and perimeters in various geometric figures.
It contains the basics of matrix which includes matrix definition,types of matrices,operations on matrices,transpose of matrix,symmetric and skew symmetric matrix,invertible matrix,
application of matrix.
A matrix is a rectangular array of numbers arranged in rows and columns. There are several types of matrices including square, rectangular, diagonal, identity, and triangular matrices. Operations that can be performed on matrices include addition, subtraction, multiplication by a scalar, and determining the transpose, determinant, and inverse of a matrix. A C program is shown that uses nested for loops to input and output the elements of a matrix.
This document provides definitions and explanations of various mathematical concepts. It defines linear and simultaneous equations, quadratic equations, matrices including types of matrices. It also discusses sequences and series, percentages, discounts, commission, and interest. Key terms are defined such as determinant, properties of addition and multiplication for matrices, and formulas for arithmetic and geometric progressions.
The document provides definitions for mathematical terms that students in 5th/6th class primary school and junior cycle secondary school may encounter. It includes over 50 terms defined with diagrams and examples. The glossary is designed to inform students, parents, and teachers about the vocabulary and meanings of key mathematical terms as students transition between primary and post-primary education in Ireland.
This document provides an overview of matrices including:
- How to describe matrices using m rows and n columns
- Common types of matrices such as row, column, zero, square, diagonal, and unit matrices
- Basic matrix operations including addition, subtraction, scalar multiplication
- Rules for matrix multiplication including that matrices must be conformable
- The transpose of a matrix which is obtained by interchanging rows and columns
- Properties of transposed matrices including (A+B)T = AT + BT and (AB)T = BTAT
- The document discusses how to multiply matrices, including defining when multiplication is valid based on the number of columns and rows of the matrices.
- It provides an example of multiplying two matrices, showing the step-by-step process of multiplying corresponding elements and summing them.
- It also discusses properties of matrix multiplication, including associativity, distributivity, and the existence of an identity matrix.
- Examples are provided to illustrate verifying these properties by calculating different matrix multiplications.
The document provides information on geometry topics including angles, distance, area, and volume. It defines key concepts such as perpendicular lines, parallel lines, interior and exterior angles, circumference, arc length, perimeter, area of triangles, circles, quadrilaterals, and strategies for finding areas of irregular shapes. Examples are provided to illustrate formulas and problem-solving approaches for finding distances, midpoints, areas, and perimeters in various geometric figures.
It contains the basics of matrix which includes matrix definition,types of matrices,operations on matrices,transpose of matrix,symmetric and skew symmetric matrix,invertible matrix,
application of matrix.
A matrix is a rectangular array of numbers arranged in rows and columns. There are several types of matrices including square, rectangular, diagonal, identity, and triangular matrices. Operations that can be performed on matrices include addition, subtraction, multiplication by a scalar, and determining the transpose, determinant, and inverse of a matrix. A C program is shown that uses nested for loops to input and output the elements of a matrix.
This document provides definitions and explanations of various mathematical concepts. It defines linear and simultaneous equations, quadratic equations, matrices including types of matrices. It also discusses sequences and series, percentages, discounts, commission, and interest. Key terms are defined such as determinant, properties of addition and multiplication for matrices, and formulas for arithmetic and geometric progressions.
This document provides an overview of different types of functions that may be assessed on the ACT exam, including linear, quadratic, trigonometric, logarithmic, and exponential functions. It discusses key concepts for each type of function such as domain and range, asymptotes, amplitude and period for trig functions, and properties of logarithmic and exponential growth/decay functions. Examples are provided to illustrate how to work with each function type, including solving equations, finding features of graphs, and recognizing standard forms.
The document discusses matrices and their operations. It defines what a matrix is, provides examples of different types of matrices, and covers key matrix operations like addition, subtraction, scalar multiplication, and matrix multiplication. It also defines important matrix concepts such as the transpose of a matrix, inverse of a matrix, and properties related to these operations and concepts.
The document provides an overview of key algebra concepts covered on the ACT exam, including expressions, equations, inequalities, functions, and quadratic equations. It discusses how to simplify and combine like terms in expressions, solve different types of equations (linear, quadratic, absolute value), factor expressions using techniques like greatest common factor and difference of squares, work with fractions and systems of equations. Example problems and step-by-step explanations are provided for many of the concepts. The document is intended as a review of essential algebra skills and strategies for tackling related questions that may appear on the ACT.
- The document discusses determinants of square matrices, including how to calculate the determinant of matrices of various orders, properties of determinants, and some applications of determinants.
- Key concepts covered include minors, cofactors, expanding determinants in terms of minors and cofactors, properties such as how determinants change with row/column operations, and using determinants to solve systems of linear equations.
- Examples are provided to demonstrate calculating determinants and using properties to simplify or prove identities about determinants.
The document discusses operations with integers. It defines absolute value and covers addition, subtraction, multiplication, and division of integers through examples. Rules for integer operations are that the sign of the product is the product of the signs of the factors, and the sign of the quotient is the sign of the dividend. Division by zero is undefined.
This document contains problems related to discrete-time signals and systems. It asks the student to:
1. Determine if various signals are periodic and calculate their fundamental frequencies.
2. Graph a sampled analog sinusoidal signal, calculate the discrete-time signal's frequency, and compare it to the original analog signal.
3. Graph a piecewise defined discrete-time signal, derive transformed versions of it, and express it using unit step and impulse functions.
The document defines matrices and provides examples of different types of matrices. It discusses key concepts such as rows, columns, dimensions, entries, addition, subtraction, and multiplication of matrices. It also covers special matrices like identity matrices, inverse matrices, transpose of matrices, and using matrices to solve systems of linear equations. The document is a comprehensive overview of matrices that defines fundamental terms and concepts.
Please go through the slides. It is very interesting way to learn this chapter for 2020-21.If you like this PPT please put a thanks message in my number 9826371828.
The document discusses matrix algebra and operations on matrices. It defines a matrix as a rectangular table of numbers with rows and columns. A matrix with R rows and C columns is denoted as an R x C matrix. Individual entries in a matrix are denoted by their row and column position, such as a32 for the entry in the 3rd row and 2nd column. There are two main types of operations on matrices - adding/subtracting same-sized matrices entry by entry, and multiplying matrices. Matrix multiplication involves multiplying corresponding entries of a row and column and summing the products.
The document provides information about a test for candidates applying for M.Tech in Computer Science. It consists of two parts - Test MIII in the morning and Test CS in the afternoon. Test CS has two groups - Group A containing questions on analytical ability and mathematics, and Group B containing subject-specific questions in one of several sections according to the candidate's choice. The document then provides sample questions for Group A (mathematics-based) and Group B (subject-specific for various domains like mathematics, statistics, physics, computer science, and engineering).
Business mathematics is a very powerful tools and analytic process that resul...mkrony
Business mathematics is a powerful analytical tool that can result in optimal solutions despite limitations. The document lists the names and IDs of 7 group members working on topics related to permutations, combinations, number systems, set theory, and linear programming. It provides examples and definitions of permutations, combinations, and the differences between them.
Matrices can be added, subtracted, and multiplied under certain conditions.
Addition and subtraction require matrices to be the same size.
Matrix multiplication requires the number of columns of the first matrix to equal the number of rows of the second matrix.
Matrices can also be multiplied by scalars.
Algebraic Mathematics of Linear Inequality & System of Linear InequalityJacqueline Chau
A brief, yet thorough look into the Linear Inequality & System of Linear Inequality and how these Math Concepts would be useful in solving our everyday life problems.
The document outlines various formulae that students are expected to know, understand, or be able to use for the GCSE Mathematics exam. It presents formulae for the quadratic formula, circumference and area of a circle, Pythagoras' theorem, and trigonometry. It also lists formulae for perimeter, area, surface area, volume, compound interest, and probability that students should understand but won't be provided. Finally, it mentions kinematics formulae and calculators that may be provided or useful for questions involving various required formulae.
This presentation describes Matrices and Determinants in detail including all the relevant definitions with examples, various concepts and the practice problems.
The document describes the cofactor method for finding the inverse of a matrix A. It defines the cofactor Cij as the signed determinant of the matrix made by removing row i and column j from A. The inverse is then given by the transpose of the matrix of cofactors divided by the determinant of A. An example calculates the inverse of the 2x2 matrix A = [a, c; b, d] using this method.
Matrices are widely used in business, economics, and other fields. They allow problems to be represented with distinct finite numbers rather than infinite gradations as in calculus. Sociologists, demographers, and economists use matrices to study groups, populations, industries, and social accounting. [/SUMMARY]
This document provides an overview of linear models and matrix algebra concepts that are important for economics. It discusses the objectives of using mathematics for economics, including understanding problems by stating the unknown and known variables. The document then covers key topics in linear algebra like the history of matrices, what matrices are, basic matrix operations, and properties of matrix addition and multiplication. It also introduces concepts like the inverse and transpose of a matrix. Finally, it provides an example of how matrices and vectors can represent systems of linear equations used in economic models.
The document provides a list of formulae for the ICSE Mathematics (Class 10) exam. It covers topics like commercial arithmetic, algebra, coordinate geometry, geometry, mensuration, trigonometry, and statistics. For each topic, relevant formulae are listed along with explanations. The exam will have one 2-hour paper divided into two sections carrying 80 marks total. Section I will consist of short answer questions and Section II will require answering 4 out of 7 questions.
There are so many mathematical symbols that are important for students. To make it easier for you we’ve given here the mathematical symbols table with definitions and examples
This document provides an overview of different types of functions that may be assessed on the ACT exam, including linear, quadratic, trigonometric, logarithmic, and exponential functions. It discusses key concepts for each type of function such as domain and range, asymptotes, amplitude and period for trig functions, and properties of logarithmic and exponential growth/decay functions. Examples are provided to illustrate how to work with each function type, including solving equations, finding features of graphs, and recognizing standard forms.
The document discusses matrices and their operations. It defines what a matrix is, provides examples of different types of matrices, and covers key matrix operations like addition, subtraction, scalar multiplication, and matrix multiplication. It also defines important matrix concepts such as the transpose of a matrix, inverse of a matrix, and properties related to these operations and concepts.
The document provides an overview of key algebra concepts covered on the ACT exam, including expressions, equations, inequalities, functions, and quadratic equations. It discusses how to simplify and combine like terms in expressions, solve different types of equations (linear, quadratic, absolute value), factor expressions using techniques like greatest common factor and difference of squares, work with fractions and systems of equations. Example problems and step-by-step explanations are provided for many of the concepts. The document is intended as a review of essential algebra skills and strategies for tackling related questions that may appear on the ACT.
- The document discusses determinants of square matrices, including how to calculate the determinant of matrices of various orders, properties of determinants, and some applications of determinants.
- Key concepts covered include minors, cofactors, expanding determinants in terms of minors and cofactors, properties such as how determinants change with row/column operations, and using determinants to solve systems of linear equations.
- Examples are provided to demonstrate calculating determinants and using properties to simplify or prove identities about determinants.
The document discusses operations with integers. It defines absolute value and covers addition, subtraction, multiplication, and division of integers through examples. Rules for integer operations are that the sign of the product is the product of the signs of the factors, and the sign of the quotient is the sign of the dividend. Division by zero is undefined.
This document contains problems related to discrete-time signals and systems. It asks the student to:
1. Determine if various signals are periodic and calculate their fundamental frequencies.
2. Graph a sampled analog sinusoidal signal, calculate the discrete-time signal's frequency, and compare it to the original analog signal.
3. Graph a piecewise defined discrete-time signal, derive transformed versions of it, and express it using unit step and impulse functions.
The document defines matrices and provides examples of different types of matrices. It discusses key concepts such as rows, columns, dimensions, entries, addition, subtraction, and multiplication of matrices. It also covers special matrices like identity matrices, inverse matrices, transpose of matrices, and using matrices to solve systems of linear equations. The document is a comprehensive overview of matrices that defines fundamental terms and concepts.
Please go through the slides. It is very interesting way to learn this chapter for 2020-21.If you like this PPT please put a thanks message in my number 9826371828.
The document discusses matrix algebra and operations on matrices. It defines a matrix as a rectangular table of numbers with rows and columns. A matrix with R rows and C columns is denoted as an R x C matrix. Individual entries in a matrix are denoted by their row and column position, such as a32 for the entry in the 3rd row and 2nd column. There are two main types of operations on matrices - adding/subtracting same-sized matrices entry by entry, and multiplying matrices. Matrix multiplication involves multiplying corresponding entries of a row and column and summing the products.
The document provides information about a test for candidates applying for M.Tech in Computer Science. It consists of two parts - Test MIII in the morning and Test CS in the afternoon. Test CS has two groups - Group A containing questions on analytical ability and mathematics, and Group B containing subject-specific questions in one of several sections according to the candidate's choice. The document then provides sample questions for Group A (mathematics-based) and Group B (subject-specific for various domains like mathematics, statistics, physics, computer science, and engineering).
Business mathematics is a very powerful tools and analytic process that resul...mkrony
Business mathematics is a powerful analytical tool that can result in optimal solutions despite limitations. The document lists the names and IDs of 7 group members working on topics related to permutations, combinations, number systems, set theory, and linear programming. It provides examples and definitions of permutations, combinations, and the differences between them.
Matrices can be added, subtracted, and multiplied under certain conditions.
Addition and subtraction require matrices to be the same size.
Matrix multiplication requires the number of columns of the first matrix to equal the number of rows of the second matrix.
Matrices can also be multiplied by scalars.
Algebraic Mathematics of Linear Inequality & System of Linear InequalityJacqueline Chau
A brief, yet thorough look into the Linear Inequality & System of Linear Inequality and how these Math Concepts would be useful in solving our everyday life problems.
The document outlines various formulae that students are expected to know, understand, or be able to use for the GCSE Mathematics exam. It presents formulae for the quadratic formula, circumference and area of a circle, Pythagoras' theorem, and trigonometry. It also lists formulae for perimeter, area, surface area, volume, compound interest, and probability that students should understand but won't be provided. Finally, it mentions kinematics formulae and calculators that may be provided or useful for questions involving various required formulae.
This presentation describes Matrices and Determinants in detail including all the relevant definitions with examples, various concepts and the practice problems.
The document describes the cofactor method for finding the inverse of a matrix A. It defines the cofactor Cij as the signed determinant of the matrix made by removing row i and column j from A. The inverse is then given by the transpose of the matrix of cofactors divided by the determinant of A. An example calculates the inverse of the 2x2 matrix A = [a, c; b, d] using this method.
Matrices are widely used in business, economics, and other fields. They allow problems to be represented with distinct finite numbers rather than infinite gradations as in calculus. Sociologists, demographers, and economists use matrices to study groups, populations, industries, and social accounting. [/SUMMARY]
This document provides an overview of linear models and matrix algebra concepts that are important for economics. It discusses the objectives of using mathematics for economics, including understanding problems by stating the unknown and known variables. The document then covers key topics in linear algebra like the history of matrices, what matrices are, basic matrix operations, and properties of matrix addition and multiplication. It also introduces concepts like the inverse and transpose of a matrix. Finally, it provides an example of how matrices and vectors can represent systems of linear equations used in economic models.
The document provides a list of formulae for the ICSE Mathematics (Class 10) exam. It covers topics like commercial arithmetic, algebra, coordinate geometry, geometry, mensuration, trigonometry, and statistics. For each topic, relevant formulae are listed along with explanations. The exam will have one 2-hour paper divided into two sections carrying 80 marks total. Section I will consist of short answer questions and Section II will require answering 4 out of 7 questions.
There are so many mathematical symbols that are important for students. To make it easier for you we’ve given here the mathematical symbols table with definitions and examples
This document provides an overview of linear equations and graphs. It introduces the Cartesian coordinate system and defines linear equations in two variables. It discusses using intercepts and graphing calculators to graph lines. Special cases of vertical and horizontal lines are covered. The concepts of slope, slope-intercept form, and point-slope form of a line are explained. An example of using a linear equation to model the depreciation of office equipment is provided. Finally, the relationship between supply and demand is discussed and an example of finding the equilibrium point using supply and demand equations is worked through.
This document discusses the real number system and its properties. It begins by describing how the set of real numbers is constructed by successive extensions of the natural numbers to include integers, rational numbers, and irrational numbers. It then establishes a one-to-one correspondence between real numbers and points on the real number line. Key properties of real numbers discussed include algebraic properties like closure under addition/multiplication, as well as properties of order and completeness. The document also covers intervals, inequalities, and the absolute value of real numbers.
This document provides an overview of graphing linear equations. It defines key terms like solutions, intercepts, and linear models. Examples are given to show how to graph equations by finding intercepts or using a table of points. Horizontal and vertical lines are discussed as special cases of linear equations. The document concludes with an example of using a linear equation to model a real-world situation involving monthly phone costs.
The document discusses three forms of quadratic equations - standard form, vertex form, and intercept form. It provides the definitions and formulas for each form. It then explains how to graph each form by identifying key features of the equation, finding important points like the vertex, axis of symmetry, intercepts, and connecting points to sketch the parabolic curve. Graphing techniques include using the value of a to determine the opening direction, using b and c for standard form, using h and k for vertex form, and using p and q for intercepts form.
This document provides a summary of topics related to algebra, functions, and calculus including: linear and quadratic expressions, simultaneous equations, completing the square, trigonometric ratios, differentiation, tangents, normals, and finding stationary points through higher derivatives. It outlines key steps and methods for solving various types of problems within these topics.
The document provides definitions and explanations of key concepts in algebra including:
1. Types of numbers such as complex, rational, irrational, and integer numbers.
2. Properties of real numbers like commutative, associative, and distributive properties.
3. Exponents, radicals, logarithms, progressions, the binomial theorem, and word problems.
This document defines and explains various sets of numbers including natural numbers, integers, rational numbers, irrational numbers, and real numbers. It provides properties and examples of operations like addition, subtraction, multiplication, and division on real numbers. Key points covered include:
- The definitions of natural numbers, integers, rational numbers, irrational numbers, and real numbers as sets.
- Properties of addition, subtraction, multiplication, and division for real numbers like commutativity, associativity, identity elements, and opposites.
- Absolute value and inequalities involving absolute value.
Mathematics important points and formulas 2009King Ali
This document contains a table of contents for a mathematics reference book. It lists 58 topics covered in the book, ranging from natural numbers to symmetry, along with the page number for each topic. The document also includes sections on important points and formulas for various mathematical concepts such as algebraic expressions, quadratic equations, trigonometry, geometry, and statistics. The sections provide definitions, properties, and formulas for key concepts in mathematics.
The document provides lecture notes for a course on matrix algebra for engineers. It covers topics such as the definition of matrices, addition and multiplication of matrices, special matrices like the identity and zero matrices, transposes, inverses, orthogonal matrices, and systems of linear equations. The notes are intended to teach the basics of matrix algebra at a level appropriate for engineering students who have taken calculus. They include video links, examples, problems at the end of each section, and solutions to the problems in an appendix.
The document describes functions and exercises for basic simulation and matrix manipulation in MATLAB. It covers creating vectors and matrices, arithmetic operations, matrix manipulations like concatenation and indexing, sorting, shifting, reshaping and flipping matrices. It also discusses generating random sequences, plotting functions, solving differential equations, and creating and accessing structures and arrays of structures. The key topics are functions for vector/matrix creation and manipulation, common mathematical operations, plotting and solving differential equations in MATLAB.
An algebraic expression is a combination of letters and numbers linked by operation signs: addition, subtraction, multiplication, division and exponentiation. Algebraic expressions allow us, for example, to find areas and volumes. Some examples given are the circumference of a circle (2πr), the area of a square (s=l2), and the volume of a cube (V=a3). The document then provides examples and explanations of algebraic addition, subtraction, multiplication, division, and factorization.
This document provides an overview and definitions of key concepts from Chapter 1 of a college mathematics textbook, including: linear equations and inequalities in standard form and how they are solved; the Cartesian coordinate system and how graphs of linear equations form lines; determining the slope and equations of lines in slope-intercept and point-slope form; the relationship between supply and demand curves; and using linear regression to fit a line to scatter plot data and make predictions.
The document provides instructions and worked examples for solving various math problems involving straight lines, composite functions, limits of recurrence relations, trigonometric equations, graphs of functions, and finding maximums and minimums. It includes step-by-step workings for finding the equation of a line, angle between two points, perpendicular bisector of a line, composite functions, limits of recurrence relations, solving trig equations, sketching transformed graphs, and minimizing cost functions.
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The document defines key concepts in real numbers and the number plane. It discusses the sets of natural numbers, integers, rational numbers, irrational numbers and their properties. It also covers operations like addition, subtraction, multiplication and distribution. Graphical representations of conic sections like circles, ellipses, parabolas and hyperbolas are shown. Examples of distance and midpoint on the number plane are provided, along with inequalities and absolute value exercises.
Vectors have both magnitude and direction, represented by arrows. The sum of two vectors is obtained by placing the tail of one vector at the head of the other. If the vectors are at right angles, their dot product is zero, while their cross product is maximum. Scalar multiplication scales the magnitude but not the direction of a vector.
This document provides information on mathematical concepts and formulas relevant to economics, including:
- Exponential functions such as y=ex and their graphs showing exponential growth and decay
- Quadratic functions of the form y=ax2+bx+c and total cost functions
- Differentiation rules for common functions like exponentials, logarithms, and the product, quotient and chain rules
- Integration basics and formulas for integrating common functions
- Concepts like inverse functions, the mean, variance and standard deviation in statistics
- Information is also provided on fractions, ratios, percentages, and algebraic rules involving exponents, logarithms and sigma notation.
Similar to ICSE class X maths booklet with model paper 2015 (20)
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Crash-Course for AIPMT & Other Medical Exams 2016(Essentials heart)APEX INSTITUTE
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Crash-Course for AIPMT & Other Medical Exams 2016Target pmt (2)APEX INSTITUTE
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Crash-Course for AIPMT & Other Medical Exams 2016 (Essentials cockroach)APEX INSTITUTE
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
The document provides information about an educational institute called APEX that offers coaching for various competitive exams like IIT-JEE, AIPMT, and NTSE. It highlights some of APEX's strengths such as having experienced and qualified faculty, small student-teacher ratios, regular testing and feedback, and good historical results. It also mentions some questions students should ask before choosing a coaching institute like student-teacher ratios, faculty qualifications, and selection processes.
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
I.S.C. Class XII MATHEMATICS Sample Papers 2016APEX INSTITUTE
This document provides information about a crash course for IIT-JEE, BITS, UPTU and AIPMT exams, including details about faculty, study material, practice problems, mock tests, and registration. It mentions that the course includes over 240 hours of training by experienced faculty, concise chapter-wise theory, 3000 practice problems, 10 full-length tests, and a 30% discount on registration until March 10th. The batch is scheduled to commence on March 15th, 22nd, and 29th.
The document provides information about a crash course for IIT-JEE, BITS, UPTU and AIPMT exams, including details about the course structure, faculty, study material, practice problems, and test series. It mentions that the course provides over 240 hours of training by experienced faculty, concise chapter-wise theory, 3000 practice problems, expert time management tips, and 10 full-length tests on the IIT-Main exam pattern. It also provides information about course features, registration fees and dates.
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
APEX INSTITUTE has been established with sincere and positive resolve to do something rewarding for ENGG. / PRE-MEDICAL aspirants. For this the APEX INSTITUTE has been instituted to provide a relentlessly motivating and competitive atmosphere.
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
APEX INSTITUTE has been established with sincere and positive resolve to do something rewarding for ENGG. / PRE-MEDICAL aspirants. For this the APEX INSTITUTE has been instituted to provide a relentlessly motivating and competitive atmosphere.
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
APEX INSTITUTE has been established with sincere and positive resolve to do something rewarding for ENGG. / PRE-MEDICAL aspirants. For this the APEX INSTITUTE has been instituted to provide a relentlessly motivating and competitive atmosphere.
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
APEX INSTITUTE has been established with sincere and positive resolve to do something rewarding for ENGG. / PRE-MEDICAL aspirants. For this the APEX INSTITUTE has been instituted to provide a relentlessly motivating and competitive atmosphere.
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
Communicating effectively and consistently with students can help them feel at ease during their learning experience and provide the instructor with a communication trail to track the course's progress. This workshop will take you through constructing an engaging course container to facilitate effective communication.
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In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Gender and Mental Health - Counselling and Family Therapy Applications and In...PsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
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ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ICSE class X maths booklet with model paper 2015
1. Mock Test Paper
Apex Institute for IIT-JEE / PMT
Head Office : 62 Nitikhand -3 Indirapuram Cont. +91-9990495952, +91-9910817866, www.apexiit.co.in
Mathematics
2. 1
ICSE MATHEMATICS (X)
There will be one paper of 2 hours duration carrying 80 marks and Internal Assessment of 20 marks.
The paper will be divided into two Sections. Section I (40 marks), Section II (40 marks).
Section I: It will consist of compulsory short answer questions.
Section II: Candidates will be required to answer four out of seven questions.
UNITS & CHAPTERS
1. COMMERCIAL ARITHMETIC
Compound Interest (Paying back in equal installments not included)
Sales Tax and Value Added Tax
Banking (Saving Bank Accounts and Recurring Deposit Accounts)
Shares and Dividends (Brokerage and fractional shares not included)
2. ALGEBRA
Linear Inequations
Quadratic Equations and Solving Problems
Ratio and Proportion
Remainder and Factor Theorems (f(x) not to exceed degree 3)
Matrices
3. CO-ORDINATE GEOMETRY
Reflection
Distance and Section Formulae
Equation of a Straight Line
4. GEOMETRY
Symmetry
Similarity
Loci (Locus and Its Constructions)
Circles
Tangents and Intersecting Chords
Constructions (tangents to circle, circumscribing & inscribing circle on & reg. hexagon)
5. MENSURATION
Circumference and Area of a circle (Area of sectors of circles other than semi-circle and
quarter-circle not included)
Surface Area and Volume (of solids)
6. TRIGONOMETRY
Trigonometrical Identities and Trigonometrical Tables
Heights and Distances (Cases involving more than 2 right angled excluded)
7. STATISTICS
Graphical Representation (Histogram and Ogives)
Measures of Central Tendency (Mean, Median, Quartiles and Mode)
Probability
3. 2
COMMERCIAL ARITHMETIC
Compound Interest:
A = P ; when the interest is compounded half-yearly.
A = P , If the time is 2 years and the rate is compounded yearly.
For Growth: V = V0 , V0 = Initial Value, V = Final Value
For Depreciation: V = V0
Sales Tax and Value Added Tax:
The price at which an Article is marked : List Price/Marked Price/Printed Price/Quoted Price
Sale Price = M.P. – Discount, Discount is calculated on M.P.
Sales Tax is calculated after deducting the discount (on the discounted price).
Sales Tax =
Sale-price = C.P.
Sale-price = C.P.
Sale-price = M.P.
VAT paid by a person =
VAT = Tax recovered(charged) on the sale – Tax paid on the purchase
A = P + I
S.I. =
S.I. for 1st
year = C.I. for 1st
year
C. I. for (n + 1) year = C.I. of nth
year + Int. on it for 1 year ; R% = %, where T = 1yr
Amount in (n + 1) year = Amount in nth
year + Int. on it for 1 year; R% = %
A = P
C.I. = P
A = P ; when rates for successive years are different.
4. 3
Banking:
1. SB Account:
a. Withdrawal = Debit
b. Deposit = Credit
c. Steps for calculation of interest:
i. Find the minimum balance of each month between 10th
day and the last day.
ii. Add all the balances. This is the Equivalent Monthly Principal for 1 month.
iii. Calculate the SI on the Equivalent Monthly Principal with T = years.
iv. No interest is paid for the month in which the account is closed.
v. If the Amount Received on closing is asked, add the interest to the LAST BALANCE
and not to the Equivalent Monthly Principal.
2. RD Account:
a. I = ; T = years ; P = monthly deposit, n = no. of months, r = rate%
b. M.V. = P ; Maturity Value = Total deposit (monthly deposit nterest
Shares and Dividend:
The total money invested by the company is called its capital stock.
The capital stock is divided into a number of equal units. Each unit is a called a share.
Nominal Value is also called Register Value, Printed Value, and Face Value.
The FV of a share always remains the same, while its MV goes on changing.
The part of the profit of a company which is distributed amongst the shareholders is known as
dividend.
If the MV of the share is same as its NV, the share is said to be at par.
If the MV of the share is greater than NV, the share is said to be at premium.
If the MV of the share is less than NV, the share is said to be at discount.
No. of shares =
Dividend = NV No. of shares ; total annual income = DNN or DFN
Return % = 100 %
Rate of dividend% NV = Return % MV ; DN = PM
% increase in return on original investment = 100 %
% increase in return = 100 %
5. 4
ALGEBRA
Linear Inequations:
The signs are called signs of inequality.
On transferring +ve term becomes –ve and vice versa.
If each term is multiplied or divided by +ve number, the sign of inequality remains the same.
The sign of inequality reverses:
If each term is multiplied or divided by same negative number.
If the sign of each term on both the sides of an inequation is changed.
On taking reciprocals of both sides, in case both the sides are positive or negative.
Always, write the solution set for the inequation, e.g.,{x : x 3, x N}, solution set = {1, 2, 3}
To represent the solution on a number line:
Put arrow sign on both the ends of the line and keep extra integers beyond the range.
Use dark dots on the line for each element of N, W and Z.
For Q, R: mark range with solid circle (for ), hollow circle (for < and >.)
“and” means Intersection ( only common elements of the sets).
“or” means Union(all elements of the sets without repetition).
Quadratic Equations:
1. Quadratic equation is an equation with one variable, the highest power of the variable is 2.
2. Some useful results:
a) (a + b)2
= a2
+ b2
+ 2ab
b) (a - b)2
= a2
+ b2
- 2ab
c) a 2
– b2
= (a + b) (a – b)
d) (a + b)2
- (a - b)2
= 4ab
e) (a + b)3
= a3
+ b3
+ 3ab(a + b)
f) (a - b)3
= a3
- b3
- 3ab(a - b)
6. 5
Ratio and Proportion:
A ratio is a comparison of the sizes of two or more quantities of the same kind by division. Since ratio
is a number, so it has no units.
To find the ratio between two quantities, change them to the same units.
To compare two ratios, convert them into like fractions.
In the ratio, a : b, a is called antecedent and b is called consequent.
= = =
Compound ratio of a : b and c : d is (a × c) : (b × d)
Duplicate ratio of a : b is a2
: b2
Triplicate ratio of a : b is a3
: b3
Sub-duplicate ratio of a : b is :
g) (a + b + c)2
= a2
+ b2
+ c2
+ 2ab + 2bc + 2ca
h) a3
+ b3
+ c3
– 3abc = (a + b + c) (a2
+ b2
+ c2
– ab – bc – ca)
3. Steps for solving quadratic equation by factorization:
a. Clear all fractions and brackets if necessary.
b. Bring it to the form ax2
+ bx + c = 0 by transposing terms.
c. Factorize the expression by splitting the middle term as a sum of product of a and c.
4. Discriminant (D) =
a. if D 0, then the roots are real and unequal
b. if D = 0, then the roots are real and equal
c. if D 0, then the roots are not real (imaginary).
5. The roots of the quadratic equation ax2
+ bx + c = 0 ; a 0 can be obtained by using the formula:
x =
7. 6
Matrices:
A rectangular arrangement of numbers, in the form of horizontal (rows) and vertical lines (columns)
is called a matrix. Each number of a matrix is called its element. The elements of a matrix are
enclosed in brackets [ ].
The order of a matrix = No. of rows × No. of columns
Row matrix: Only 1 row.
Column matrix: Only 1 column.
Sub-triplicate ratio of a : b is :
Reciprocal ratio of a : b is b : a
Proportion- An equality of two ratios is called a proportion. Written as: a : b :: c : d or =
Product of extreme terms = product of middle terms, if a, b, c, d are in proportion then ad = bc
Continued Proportion- a : b :: b : c or a : b = b : c ; mean proportion (b) =
Invertendo - If a : b = c : d, then b : a = d : c
Alternendo - If a : b = c : d, then a : c = b : d
Componendo - If a : b = c : d, then a + b : b = c + d : d
Dividendo - If a : b = c : d, then a - b : b = c - d : d
Componendo and Dividendo - If a : b = c : d, then a + b : a – b = c + d : c – d
Remainder and Factor Theorem:
1. If f (x) is a polynomial, which is divisible by (x – a), a R, then the remainder is f (a).
2. If the remainder on dividing a polynomial f (x) by (x – a), f (a) = 0, then (x - a) is a factor of f (x).
3. When f (x) is divided by (ax + b), then remainder is f , a 0
4. When f (x) is divided by (ax - b), then remainder is f , a 0
8. 7
Square matrix: No. of rows = No. of columns.
Rectangular matrix: No. of rows No. of columns.
Zero matrix: All elements are zero.
Diagonal matrix: A square matrix with all the elements zero except the elements on the leading
diagonal.
Unit matrix (I): A diagonal matrix with all the elements on the leading diagonal = 1; I =
Transpose of a matrix: If A = then At
=
Addition or subtraction of matrices is possible iff they are of the same order.
Addition of two matrices: + =
Multiplication of matrix by a real number: i =
Multiplication of 2 matrices: x × y × b× a , y = b , order of the product matrix = ( x × a) ,
Multiplication process: = , run & fall
9. 8
COORDINATE GEOMETRY
Reflection:
Mx (x, y) = (x, -y)
My (x, y) = (-x, y)
Mo (x, y) = (-x, -y)
X- axis: y = 0
Y- axis : x = 0
Any point that remains unaltered under a given transformation is called an invariant point.
(x, y) (2a – x, y )
(x, y) (x, 2a - y)
More Coordinate Geometry:
Equation of a Line:
Every straight line can be represented by a linear equation.
Any point, which satisfies the equation of a line, lies on that line.
Distance formula: Distance between 2 given points (x1, y1) and (x2, y2) =
Distance between the origin (0, 0) and any point (x, y) =
To show the quadrilateral as a parallelogram or rhombus, find all four sides.
To show the quadrilateral as a rectangle or square, find all four sides and both the diagonals.
Section formula: Coordinates of a point P(x, y) = ; ratio = m1 : m2
Midpoint formula: Coordinates of the midpoint M(x, y) of a line segment =
The co-ordinates of the centroid of a triangle G(x, y) =
10. 9
Inclination of a line is the angle which the part of the line makes with x-axis.
Inclination is positive in anti-clockwise direction and negative in clockwise direction.
Slope or gradient of any inclined plane is ratio of vertical rise and horizontal distane.
Slope of a line (m) = = tan
Inclination of x-axis and every line parallel to it is 0 .
Inclination of y-axis and every line parallel to it is 90 .
Slope of a line which passes through any two points P(x1, y1) and Q(x2, y2) = .
Slopes of two parallel lines are equal or m1 = m2.
Product of the slopes of two perpendicular line = - 1 or m1 m2 = -1.
Equation of a line:
o y = mx + c : (Slope-intercept form : m = slope, c = y-intercept)
o (y – y1) = m(x – x1) : (Slope-point form : (x1, y1) = co-ordinates of the point)
o (y – y1) = m(x – x1) : (Two point form – where m = ).
11. 10
GEOMETRY
Symmetry:
A figure is said to have line symmetry if on folding the figure about this line, the two parts of the
figure exactly coincide.
Geometrical Name Line(s) of Symmetry
Line segment
2 lines of symmetry – line midway and perpendicular bisector of them.
A Rhombus 2 – the diagonals
A rectangle 2 - the lines joining midpoints of the opposite sides.
A square 4 – the diagonals , lines joining midpoints of the opposite sides.
A kite 1 – the diagonal that bisects the pair of angles contained by equal sides.
A circle Infinite – all the diameters
A semicircle 1 – the bisector of the diameter
A regular pentagon 5 - the angle bisectors or the bisectors of the sides.
A regular hexagon 6 - the angle bisectors, the bisectors of the sides.
2 lines of symmetry – line itself and perpendicular bisector of it.
Angle with equal arms 1 line of symmetry – the angle bisector
A pair of equal parallel
line segments
A scalene triangle Nil
An isosceles triangle 1– the bisector of the vertical angle which is bisector of the base.
An equilateral triangle 3 – the angle bisectors which are also side bisectors.
An isosceles trapezium 1 – the line joining midpoints of the two parallel sides.
A parallelogram Nil
12. 11
Similarity:
Criteria for similarity – 1. AA or AAA 2. SAS 3. SSS
A drawn from vertex of a rt- d divides the into 2 similar , also to original triangle.
BPT – A line drawn || to any side of a divides other two sides proportionally.
The areas of 2 similar are proportional to the square of their corresponding sides.
Median divides a triangle into 2 of equal area.
If have common vertex & are between same ||, ratio of their areas = ratio of bases.
Scale factor = k, k = ; k2
= ; k3
= .
Loci:
Circle:
A line drawn from centre of a circle to bisect the chord is to the chord.
A perpendicular line drawn to a chord from the centre of the circle bisects the chord.
The bisector of a chord passes through the centre of the circle.
One and only one circle can be drawn passing through 3 non-collinear points.
Equal chords are equidistant from the centre.
The locus is the set of all points which satisfy the given geometrical condition.
Locus of a point equidistant from 2 fixed points is bisector of line segment joining them.
Locus of a point equidistant from 2 intersecting lines is angle bisector between the lines.
Locus of a point at a constant distance from a fixed point is circle.
Locus of a point equidistant from a given line is a pair of lines parallel to the given line and at the
given distance from it.
For equilateral triangle, centroid = incentre = circumcentre = orthocentre
13. 12
Chords which are equidistant from the centre are equal in length.
If the parallel chords are drawn in a circle, then the line through the midpoints of the chords passes
through the centre.
Greater the size of chord, lesser is its distance from the centre.
Angle at the centre = 2 × angle on the circumference.
Angles in the same segment are equal.
Angle in a semicircle is a right angle.
The opposite angles of a cyclic quadrilateral are supplementary.
If the opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic.
Angle in the major segment is acute and in the minor segment is obtuse.
Exterior angle of a cyclic quadrilateral = Interior opposite angle.
In equal or same circle. If two arcs subtend equal angle at the centre, then they are equal.
In equal circle, if two arcs are equal, then they subtend equal angle at the centre.
In equal circle, if two chords are equal, they cut off equal arcs.
In equal circle, if two arcs are equal, the chords of the arcs are also equal.
The tangent at any point of a circle & the radius through this point are to each other.
If two tangents are drawn to a circle from an exterior point,
o The tangents are equal,
o They subtend equal angle at the centre of the circle,
o They are equally inclined to the line joining the point and the centre of the circle.
If two chords of a circle intersect internally/externally, the product of their segments is equal.
Angle in the alternate segment are equal.
Tangent2
= product of the lengths of the segments of the chord.
Incentre – Point of intersection of the angle bisectors.
Cicumcentre - Point of intersection of the bisectors of the sides.
14. 13
MENSURATION
Circumference and Area of a Circle:
Circumference of a circle = 2 r
Circumference of a semi-circle = r + 2r
Circumference of a quarter-circle = r + 2r
Area of a circle = r2
Area of a circular ring = (R2
– r2
)
Area of a semi-circle = r2
Area of a quarter-circle = r2
Distance travelled by a wheel in one revolution = Its circumference
No. of Revolutions =
Area of a triangle = × b × h
Area of scalene triangle = , s =
Area of equilateral triangle = a2
Surface Area and Volume:
Volume of a cuboid = l × b × h
Area of 4 walls of a cuboid = 2(l + b) × h
T.S.A. of a cuboid = 2(lb + bh + hl)
Diagonal a cuboid =
Volume of a cube = a3
15. 14
Area of 4 walls of a cube = 4 a2
T.S.A. of a cube = 6 a2
Diagonal of a cube = a
Volume of a solid cylinder = r2
h
C.S.A. of a solid cylinder = 2 rh
T.S.A. of a solid cylinder = 2 r(h + r)
Volume of a hollow cylinder = R2
- r2
)h
T.S.A. of a hollow cylinder = 2 rh + 2 Rh + 2 R2
- r2
)
Slant height of a right circular cone, l =
Volume a right circular cone = r2
h
C.S.A. of a right circular cone = rl
T.S.A. of a right circular cone = r(l + r)
Volume a sphere = r3
Surface area a sphere = 4 r2
Volume a hemisphere = r3
Curved Surface area a hemisphere = 2 r2
Total Surface area a hemisphere = 3 r2
Volume a hollow sphere = (R3
- r3
)
16. 15
TRIGONOMETRY
Trigonometry:
OR ; SOH CAH TOA or OSH ACH OTA
Trigonometric ratios of standard angles
0 30 45 60 90
sin
= 0 = = = = 1
cos 1 0
tan 0 1 n.d.
= , =
= , =
= , =
= , =
2
+ 2
= 1 ( mutual understanding)
2
- 2
= 1 or 1 + 2
= 2
( cosec is big brother)
2
- 2
= 1 or 1 + 2
= 2
( sec is big brother)
= , =
= , =
= , =
17. 16
STATISTICS
Statistics:
–
Mode is the variate which has the maximum frequency.
The class with maximum frequency is called the modal class.
To estimate mode from histogram: draw two straight lines from the corners of the rectangles on either
sides of the highest rectangle to the opposite corners of the highest rectangle. Through the point of
intersection of the two straight lines, draw a vertical line to meet the x-axis at the point M (say). The
variate at the point M is the required mode.
Arithmetic mean on non tabulated data: =
Arithmetic mean on tabulated data(Direct Method): = ; x = mid value (C.I.)
Arithmetic mean by Short-cut Method: = + A ; A = assumed mean , d = x – A
Arithmetic mean by Step-deviation Method: = + A ; i = class width , t =
If n is odd, Median = term
For raw data, if n is even, Median =
For tabulated data, Median = if n is even and Median = if n is odd.
Lower quartile, Q1 = term if n is odd and term if n is even
Upper quartile, Q3 = term if n is odd and term if n is even
Inter Quartile Range, IQR = Q3 – Q1
Semi Inter Quartile Range =
18. 17
Probability:
Probability is a measure of uncertainty.
An Experiment is an action which results in some (well-defined) outcomes.
Sample space is the collection of all possible outcomes of an experiment. n(S)
An Event is a subset of the sample space associated with a random experiment. n(E)
An Event occurs when the outcome of an experiment satisfies the condition mentioned in the event.
The outcomes which ensure the occurrence of an event are called favourable outcomes to that event.
The probability of an event E, written as P(E), is defined as P (E) =
P(E) =
The value of probability is always between 0 and 1.
The probability of sure (certain) event is 1.
The probability of an impossible event is 0.
An elementary event is an event which has one (favourable) outcome from the sample space.
A Compound event is an event which has more than one outcome from the sample space.
If E is an event, then the event „not E‟ is complementary event of E and denoted by .
0 1
P(E) + P( ) = 1
In a pack (deck) of playing cards, there are 52 cards which are divided into 4 suits of 13 cards each –
spades ( ), hearts ( ), diamonds ( ) and clubs ( ). Spades and clubs are black in colour,
while hearts and diamonds are of red colour. The cards in each suit are ace, king, queen, jack, 10, 9,
8, 7, 6, 5, 4, 3, 2. Kings, queens and jacks are called face (picture/court) cards. The cards bearing
number 10, 9, 8, 7, 6, 5, 4, 3, 2 are called numbered cards. Thus a pack of playing cards has 4 aces, 12
face cards and 36 numbered cards. The aces together with face cards (= 16). are called cards of
honour.
When a coin is tossed, it may show head (H) up or tail (T) up. Thus the outcomes are: {H, T}.
When two coins are tossed simultaneously, then the outcomes are: {HH, HT, TH, TT}. [n(S) = 2n
]
When a die is thrown once the outcomes are: {1, 2, 3, 4, 5, 6}. [n(S) = 6n
]
When two dice are thrown simultaneously, then the outcomes are: {(1, 1),(1, 2)…….(6, 6)}.
19. Page: 1
ICSE March-2015
(MATHEMATICS)
SAMPLE MODEL PAPER
Time: 2 hours M.M.: 80
Instructions: You will not be allowed to write during the first 15 minutes.
This time is to be spent in reading the Question Paper.
The time given at the head of this Paper is the time allowed for writing the answers.
Section I is compulsory. Attempt any four questions from Section II.
The intended marks for questions or the parts of questions are given in brackets [ ].
SECTION I (40 Marks)
Attempt all questions from this Section
Question 1
A. If (x + 1) is a factor of (5x + 8)3
– (a – x) 3
, find a. [3 Marks]
B. Find the value of x, given A2
= B, A = and B = [3 Marks]
C. The difference of C.I. payable half-yearly and S.I. on a sum of money lent out at 10% p.a. for
one year was Rs 25. Find the sum. [4 Marks]
Question 2
A. Solve for x : + = [3Marks]
20. Page: 2
B. A die is rolled once. Find the probability of getting:
i. a perfect square
ii. an even prime number
iii. a number < 5
iv. not an even number. [3 Marks]
C. In the given figure, AD is diameter of the circle with
centre ‘O’. If BCD = 125 , calculate:
i) DAB
ii) ADB [4 Marks]
Question 3
A. Mr. Prakash Nagaria opened a Recurring Deposit Account in a bank and deposited Rs. 300 per
month for two years. If he received Rs. 7725 at the time of maturity, find the rate of interest per
annum. [3 Marks]
B. A bicycle wheel whose diameter is 77 cm makes 50 revolutions in 20 seconds. Find the speed in
km/h. [Take π = 22/7] [3 Marks]
C. KM is a straight line of 13 units. If K has the coordinates (2, 5) and M has coordinates (x, -7), find
the possible values of x. [4 Marks]
Question 4
A. Solve: x + , x W and graph the solution set. [3 Marks]
B. Without using tables, find the value of: - - 2sin2
45°
. [3 Marks]
C. IQ of 50 students was recorded as follows:
IQ Score 80 - 90 90 - 100 100 - 110 110 - 120 120 - 130 130 - 140
No. of Students 6 9 16 13 4 2
Draw a histogram for the above data and estimate the mode. [4 Marks]
OA
B
C
D.
21. Page: 3
SECTIONII (40 Marks)
Attempt any four questions from this Section
Question 5
A. A purchases an article for Rs. 3,100 and sells it to B for Rs. 4,250. B in turn sells it to C for Rs.
5,000. If VAT is 10%, find the VAT levied on A and B. [3 Marks]
B. Find the volume of a right circular conical tent, whose vertical height is 8 m and the area of
whose base is 156 m2
. [3 Marks]
C. ABCD is a rhombus. The coordinates of A and C are (3, 6) and (-1, 2) respectively. Write down
the equation of BD. [4 Marks]
Question 6
A. Use a graph paper to answer the following questions:
i. Plot A (4, 4), B (4, -6) and C (8, 0), the vertices of a triangle ABC.
ii. Reflect ABC on the y-axis and name it as A B C .
iii. Write the coordinates of the images A , B and C .
iv. Give the geometrical name for the figure AA C B BC.
v. Identify the line of symmetry of AA C B BC. [5 Marks]
B. The rate of interest decreases from 5 % to 4% with effect from 01.06.2013. Compute the
interest at the end of the year on a saving bank account for the entries shown in the table if the
interest is payable yearly.
[5 Marks]Date , Year 2013 Balance (in Rs.)
January 1 600
February 9 1,200
March 11 2,500
June 25 3,500
September 10 1,500
November 5 4,000
December 23 500
22. Page: 4
Question 7
A. Find the numbers such that their mean proportion is 14 and third proportion is 112. [3 Marks]
B. Find x and y, if = . [3 Marks]
C. In the figure, name three pairs of similar triangle.
If AB = 2 cm, BC = 4 cm and CD = 9 cm,
calculate EB and AF. [4 Marks]
Question 8
A. Calculate the mean of the following frequency distribution by step-deviation method:
Classes 80 – 85 85 – 90 90 – 95 95 - 100 100 - 105 105 -110 110 - 105
Frequency 5 8 10 12 8 4 3
[5 Marks]
B. Draw a cumulative frequency curve (ogive) for the following distribution and determine the
median.
Marks 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100
No. of Students 4 8 12 6 10
[5 Marks]
Question 9
A. Mr. Nilesh holds 150 shares of face value Rs. 50 each. The company declares a dividend of 15%.
Find his income. [3 Marks]
B. Construct a circle in a hexagon of side 3.6 cm. [3 Marks]
C. Prove that: + = sin A + cos A [4 Marks]
F
E
D
CBA
23. Page: 5
Question 10
A. Solve for x : = 3. [3 Marks]
B. A certain sum of money compounded annually becomes Rs 6750 after 1 year and Rs 7873.20
after 3 years. Find the sum. [3 Marks]
C. A vertical pole and a vertical tower are on the same level ground. From the top of the pole the
angle of elevation of the top of the tower is 60°
and the angle of depression of the foot of the
tower is 30°
. Find the height of the tower if the height is of the pole is 20 m. [4 Marks]
Question 11
A. The sum of squares of two consecutive natural numbers is 313. Find the numbers. [3Marks]
B. In the given figure, AP is a tangent to the circle [3 Marks]
at P. ABC is a secant such that PD is bisector of BPC.
Prove that: BPD = [ ABP - APB].
C. Find the equation of the altitude AD of the triangle whose vertices are A (7, -1), B (-2, 8) and
C (1, 2). [4 Marks]
**************
C D B A
P
24. Admission cum Scholarship Test
29th March,5th & 12th April 2015
60%
Scholarship
Upto
100%
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University in Asia. she was our two years classroom
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classroom program Student
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He was our One year Dropper Batch Student
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from BITS Goa.He was our Three years Classroom
Program Student.
AIR 427(GE)
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Patna. She was our Two years classroom
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