This document contains a pie chart showing the sources of funds collected by the National Highways Authority of India for Phase II projects. It also includes 5 multiple choice questions about the pie chart. The total funds collected were Rs. 57,600 crores. The questions ask about the percentage of funds from different sources, the central angle corresponding to different sources on the pie chart, and calculations involving the data from the pie chart, such as determining amounts based on percentages.
1. The document provides information about pie charts including how to calculate the central angle for each component based on its value as a percentage of the total.
2. It includes 5 examples with pie charts showing distributions of funds, areas under food crops, and student enrollment. Questions test the ability to interpret pie charts and calculate related values.
3. The high-level goal is to assess understanding of how to analyze data presented in pie charts and solve related quantitative problems.
This document is a 16-page exam for the International General Certificate of Secondary Education in Mathematics. It contains 9 questions testing a range of math skills, including algebra, geometry, trigonometry, and statistics. Students are instructed to show working and give answers to an appropriate degree of accuracy. The exam is identified as Paper 4 (Extended) for the May/June 2011 session.
This document is a 16-page exam for the International General Certificate of Secondary Education in Mathematics. It contains 10 multi-part questions testing a variety of math skills, including algebra, geometry, trigonometry, statistics, and functions. The exam is designed to be completed in 2 hours and 30 minutes and includes instructions for candidates and examiners.
A tractor factory established a goal to produce 20,000 tractors by 2025, having produced increasing amounts from 2010 to 2017. Assuming continued growth at the same rate, the goal will be reached and surpassed by 150 tractors. Several word problems are presented involving functions, geometry, trigonometry, and other mathematical concepts. The document provides 20 multiple choice questions with answers for an exam.
This document is a specimen paper for the Cambridge International General Certificate of Secondary Education (IGCSE) Mathematics exam. It consists of 10 multiple-choice questions testing a range of math skills, including algebra, geometry, statistics, and trigonometry. The paper provides the instructions and information students need to correctly answer the questions, such as the time allotted, materials allowed, and how to show working.
This 19-page document contains a mathematics exam with 10 questions and multiple parts per question. The exam covers topics such as algebra, geometry, statistics, and trigonometry. It provides worked examples and questions to solve, with space below each question for showing working. The final page is blank.
This document contains solutions to mathematical simplification problems involving real numbers. It provides step-by-step workings to simplify expressions involving exponents, radicals, fractions, and combinations of variables. The solutions cover simplifying expressions with exponents, rationalizing radicals, combining like radicals, and expanding expressions with polynomials.
This document contains 13 multiple choice questions from the Fuvest 2021 exam. The questions cover topics such as functions, graphs, probability, geometry, numbers, and word problems. Correct answer options are provided for each question.
1. The document provides information about pie charts including how to calculate the central angle for each component based on its value as a percentage of the total.
2. It includes 5 examples with pie charts showing distributions of funds, areas under food crops, and student enrollment. Questions test the ability to interpret pie charts and calculate related values.
3. The high-level goal is to assess understanding of how to analyze data presented in pie charts and solve related quantitative problems.
This document is a 16-page exam for the International General Certificate of Secondary Education in Mathematics. It contains 9 questions testing a range of math skills, including algebra, geometry, trigonometry, and statistics. Students are instructed to show working and give answers to an appropriate degree of accuracy. The exam is identified as Paper 4 (Extended) for the May/June 2011 session.
This document is a 16-page exam for the International General Certificate of Secondary Education in Mathematics. It contains 10 multi-part questions testing a variety of math skills, including algebra, geometry, trigonometry, statistics, and functions. The exam is designed to be completed in 2 hours and 30 minutes and includes instructions for candidates and examiners.
A tractor factory established a goal to produce 20,000 tractors by 2025, having produced increasing amounts from 2010 to 2017. Assuming continued growth at the same rate, the goal will be reached and surpassed by 150 tractors. Several word problems are presented involving functions, geometry, trigonometry, and other mathematical concepts. The document provides 20 multiple choice questions with answers for an exam.
This document is a specimen paper for the Cambridge International General Certificate of Secondary Education (IGCSE) Mathematics exam. It consists of 10 multiple-choice questions testing a range of math skills, including algebra, geometry, statistics, and trigonometry. The paper provides the instructions and information students need to correctly answer the questions, such as the time allotted, materials allowed, and how to show working.
This 19-page document contains a mathematics exam with 10 questions and multiple parts per question. The exam covers topics such as algebra, geometry, statistics, and trigonometry. It provides worked examples and questions to solve, with space below each question for showing working. The final page is blank.
This document contains solutions to mathematical simplification problems involving real numbers. It provides step-by-step workings to simplify expressions involving exponents, radicals, fractions, and combinations of variables. The solutions cover simplifying expressions with exponents, rationalizing radicals, combining like radicals, and expanding expressions with polynomials.
This document contains 13 multiple choice questions from the Fuvest 2021 exam. The questions cover topics such as functions, graphs, probability, geometry, numbers, and word problems. Correct answer options are provided for each question.
This document consists of an examination for the International General Certificate of Secondary Education in mathematics. The exam contains 10 questions testing a variety of math skills including algebra, geometry, trigonometry, statistics, and number patterns. It provides worked examples and questions for students to practice and demonstrate their mathematical abilities.
1) The document discusses altitudes and medians of triangles, explaining that the median of a triangle connects a vertex to the midpoint of the opposite side and is perpendicular to that side.
2) It provides examples of finding the equations of medians and altitudes of various triangles given the vertices.
3) The document also discusses perpendicular bisectors, explaining that they cut a line segment in half at right angles and provides examples of finding the equations of perpendicular bisectors.
This document is an exam paper for the International General Certificate of Secondary Education (IGCSE) mathematics exam. It consists of 9 questions testing a variety of math skills including algebra, geometry, statistics, and trigonometry. Some questions involve word problems related to topics like fish tanks, school data, and diagrams of shapes. The exam is 2 hours and 30 minutes long and contains a total of 130 marks.
Hierarchical matrix approximation of large covariance matricesAlexander Litvinenko
We research class of Matern covariance matrices and their approximability in the H-matrix format. Further tasks are compute H-Cholesky factorization, trace, determinant, quadratic form, loglikelihood. Later H-matrices can be applied in kriging.
This document discusses counting the maximum number of cubes that can fit within parallelepipeds of different dimensions. It provides the formula for counting cubes as the sum of (length x width x height) for each distinct layer, working from the largest dimensions to the smallest. Several examples are worked through applying this formula to find the total number of cubes in parallelepipeds with given dimensions.
This 19-page document consists of examination questions for a mathematics test. It includes 10 questions with multiple parts, covering topics such as ratios, percentages, geometry, probability, statistics, and algebra. Students are asked to show working where necessary and give answers to an appropriate degree of accuracy. The test paper provides space for students to write their answers and includes information about the exam conditions.
The document contains 10 math and word problems involving calculations with fractions, decimals, percentages and equations. It asks the student to simplify expressions, solve equations, calculate areas, means and percentages, construct diagrams and organize data in tables and graphs. The problems cover a range of math concepts including fractions, percentages, averages, equations, geometry and data representation.
This document contains a mock CAT exam with multiple choice questions and explanations. It consists of two pages. The first page lists 60 multiple choice questions with answer options A-D. The second page provides explanations for the questions and solutions to problems. It discusses topics like probability, ratios, geometry, time/speed/distance word problems, and data interpretation from graphs.
This document consists of an International General Certificate of Secondary Education (IGCSE) mathematics exam from May/June 2008. It contains 13 printed pages with questions covering a range of math topics, including:
- Calculating percentages, rates, ratios, and averages from word problems
- Factoring expressions and solving equations
- Working with probability and statistics such as mean, median, and interquartile range
- Geometry questions involving circles, polygons, and coordinate planes
- Graphing compound interest and comparing simple vs. compound interest over time
This document consists of an 11 page mathematics exam with multiple choice and free response questions. The exam covers topics including algebra, geometry, trigonometry, statistics, and financial mathematics. Students are asked to show working for credit and are provided graph paper, calculators, and other tools to aid in solving problems. The exam is designed to test skills and knowledge expected of secondary students in an International General Certificate of Secondary Education (IGCSE) level mathematics course.
This document contains a mock CAT exam with 26 multiple choice questions covering topics in mathematics, data interpretation, and logical reasoning. The questions are from sections including numbers, algebra, geometry, data sufficiency, and data interpretation from tables and graphs. The level of difficulty of the questions ranges from easy to moderate.
This document consists of a 16 page mathematics exam with multiple choice and free response questions covering topics like algebra, trigonometry, calculus, and geometry. The document provides the standard information for exam takers such as instructions, mathematical formulas, worked examples, and blank pages for solutions.
The document contains 20 multiple choice questions about functions. The questions cover topics such as exponential functions, linear functions, quadratic functions, modular functions, and geometric progressions. They involve calculating function values, analyzing function graphs, finding maximums and minimums, and modeling real-world scenarios mathematically.
This document provides solutions to homework problems from Chapter 3 of the textbook Digital Design by M. Mano. It includes solutions for simplifying Boolean functions using maps, sums of products and products of sums. Circuit implementations are also provided for several expressions using NAND gates and half adders.
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The passage discusses the government's expectations for increasing private sector power generation capacity versus the reality of the situation. While the government anticipated over 8000 MW of new private capacity, most current proposals are still in early stages and few new players have entered the sector. Foreign investment, a key part of plans, has also not materialized as hoped. The author believes that actual new private capacity added by the end of the current 5-year plan will be only about 10% of what was planned.
This document contains a question asking for the number of factors of N3 given information about the number of factors of N. It also contains two statements, A and B, that could potentially be used to answer the question. The correct answer is c), as the question can be answered by using both statements together, but neither statement alone provides enough information to determine the number of factors of N3.
For helpful CXC Maths Multiple Choice Videos please click below
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JNU MA Economics Entrance Test Paper (2013)CrackDSE
This document provides instructions for candidates taking an entrance examination for an M.A. in Economics. It outlines details such as the time allowed, maximum marks, instructions for filling out the answer sheet correctly, and guidelines for marking answers. Candidates are informed that the exam contains 100 compulsory questions to be answered in the provided answer sheet by darkening the correct choice with a ballpoint pen. Each correct answer carries 1 mark, while 1/4 of a mark will be deducted for each wrong answer. Candidates are instructed to write their details on the question paper and answer sheet, darken the appropriate question paper series code, and return both items to the invigilator after completing the exam within the allotted 3 hours
Hemant
Eco academy is managed by Harmeet singh (2013 batch) Delhi School of Economics alumni.
Tutors
Apart from the core team, ECO Academy also has a team of tutors, who are graduates from reputed Economics Institutes such as DSE, ISI and JNU.
Assignment Buddy
Apart from ECO Academy, Assignment Buddy is an online education product of Knowledge Spark Consultancy Pvt Ltd, which deals in providing assignment help in Economics, Statistics and Mathematics to students of various universities. As a start-up, Assignment Buddy has successfully done several research projects for student community and has tied-up with several Education Corporations nationally and internationally.
This document contains a solved exam paper for the SSC Graduate Level Tier-II Exam in Arithmetical Ability. The paper contains 49 multiple choice questions covering a range of mathematical topics including ratios, averages, percentages, profit and loss, time and work problems, and geometry. The questions are at a graduate level and assess skills in applying mathematical concepts to word problems.
Placement Papers are published here to help freshers to get themselves prepared for the tests and successfully procure jobs in top companies of India including Infosys, Wipro, TCS, HCL, HP, Accenture, CTS etc. This is the section where you can find previous and latest questions, practice them with the solutions in hand.
This document consists of an examination for the International General Certificate of Secondary Education in mathematics. The exam contains 10 questions testing a variety of math skills including algebra, geometry, trigonometry, statistics, and number patterns. It provides worked examples and questions for students to practice and demonstrate their mathematical abilities.
1) The document discusses altitudes and medians of triangles, explaining that the median of a triangle connects a vertex to the midpoint of the opposite side and is perpendicular to that side.
2) It provides examples of finding the equations of medians and altitudes of various triangles given the vertices.
3) The document also discusses perpendicular bisectors, explaining that they cut a line segment in half at right angles and provides examples of finding the equations of perpendicular bisectors.
This document is an exam paper for the International General Certificate of Secondary Education (IGCSE) mathematics exam. It consists of 9 questions testing a variety of math skills including algebra, geometry, statistics, and trigonometry. Some questions involve word problems related to topics like fish tanks, school data, and diagrams of shapes. The exam is 2 hours and 30 minutes long and contains a total of 130 marks.
Hierarchical matrix approximation of large covariance matricesAlexander Litvinenko
We research class of Matern covariance matrices and their approximability in the H-matrix format. Further tasks are compute H-Cholesky factorization, trace, determinant, quadratic form, loglikelihood. Later H-matrices can be applied in kriging.
This document discusses counting the maximum number of cubes that can fit within parallelepipeds of different dimensions. It provides the formula for counting cubes as the sum of (length x width x height) for each distinct layer, working from the largest dimensions to the smallest. Several examples are worked through applying this formula to find the total number of cubes in parallelepipeds with given dimensions.
This 19-page document consists of examination questions for a mathematics test. It includes 10 questions with multiple parts, covering topics such as ratios, percentages, geometry, probability, statistics, and algebra. Students are asked to show working where necessary and give answers to an appropriate degree of accuracy. The test paper provides space for students to write their answers and includes information about the exam conditions.
The document contains 10 math and word problems involving calculations with fractions, decimals, percentages and equations. It asks the student to simplify expressions, solve equations, calculate areas, means and percentages, construct diagrams and organize data in tables and graphs. The problems cover a range of math concepts including fractions, percentages, averages, equations, geometry and data representation.
This document contains a mock CAT exam with multiple choice questions and explanations. It consists of two pages. The first page lists 60 multiple choice questions with answer options A-D. The second page provides explanations for the questions and solutions to problems. It discusses topics like probability, ratios, geometry, time/speed/distance word problems, and data interpretation from graphs.
This document consists of an International General Certificate of Secondary Education (IGCSE) mathematics exam from May/June 2008. It contains 13 printed pages with questions covering a range of math topics, including:
- Calculating percentages, rates, ratios, and averages from word problems
- Factoring expressions and solving equations
- Working with probability and statistics such as mean, median, and interquartile range
- Geometry questions involving circles, polygons, and coordinate planes
- Graphing compound interest and comparing simple vs. compound interest over time
This document consists of an 11 page mathematics exam with multiple choice and free response questions. The exam covers topics including algebra, geometry, trigonometry, statistics, and financial mathematics. Students are asked to show working for credit and are provided graph paper, calculators, and other tools to aid in solving problems. The exam is designed to test skills and knowledge expected of secondary students in an International General Certificate of Secondary Education (IGCSE) level mathematics course.
This document contains a mock CAT exam with 26 multiple choice questions covering topics in mathematics, data interpretation, and logical reasoning. The questions are from sections including numbers, algebra, geometry, data sufficiency, and data interpretation from tables and graphs. The level of difficulty of the questions ranges from easy to moderate.
This document consists of a 16 page mathematics exam with multiple choice and free response questions covering topics like algebra, trigonometry, calculus, and geometry. The document provides the standard information for exam takers such as instructions, mathematical formulas, worked examples, and blank pages for solutions.
The document contains 20 multiple choice questions about functions. The questions cover topics such as exponential functions, linear functions, quadratic functions, modular functions, and geometric progressions. They involve calculating function values, analyzing function graphs, finding maximums and minimums, and modeling real-world scenarios mathematically.
This document provides solutions to homework problems from Chapter 3 of the textbook Digital Design by M. Mano. It includes solutions for simplifying Boolean functions using maps, sums of products and products of sums. Circuit implementations are also provided for several expressions using NAND gates and half adders.
jstse 2015 question paper with solution,
jstse books,
jstse book for class 9 pdf,
jstse 2016-17,
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jstse 2015 answer key,
jstse exam sample paper for class 9,
jstse official website,
jstse previous year papers,
jstse,
nid coaching classes in hyderabad,Sample Paper for NIFT PG Management GatTakshshila
The passage discusses the government's expectations for increasing private sector power generation capacity versus the reality of the situation. While the government anticipated over 8000 MW of new private capacity, most current proposals are still in early stages and few new players have entered the sector. Foreign investment, a key part of plans, has also not materialized as hoped. The author believes that actual new private capacity added by the end of the current 5-year plan will be only about 10% of what was planned.
This document contains a question asking for the number of factors of N3 given information about the number of factors of N. It also contains two statements, A and B, that could potentially be used to answer the question. The correct answer is c), as the question can be answered by using both statements together, but neither statement alone provides enough information to determine the number of factors of N3.
For helpful CXC Maths Multiple Choice Videos please click below
These videos are very helpful
https://oke.io/dUqlSrd
https://oke.io/UWfOCCP
https://oke.io/FrCDQ
JNU MA Economics Entrance Test Paper (2013)CrackDSE
This document provides instructions for candidates taking an entrance examination for an M.A. in Economics. It outlines details such as the time allowed, maximum marks, instructions for filling out the answer sheet correctly, and guidelines for marking answers. Candidates are informed that the exam contains 100 compulsory questions to be answered in the provided answer sheet by darkening the correct choice with a ballpoint pen. Each correct answer carries 1 mark, while 1/4 of a mark will be deducted for each wrong answer. Candidates are instructed to write their details on the question paper and answer sheet, darken the appropriate question paper series code, and return both items to the invigilator after completing the exam within the allotted 3 hours
Hemant
Eco academy is managed by Harmeet singh (2013 batch) Delhi School of Economics alumni.
Tutors
Apart from the core team, ECO Academy also has a team of tutors, who are graduates from reputed Economics Institutes such as DSE, ISI and JNU.
Assignment Buddy
Apart from ECO Academy, Assignment Buddy is an online education product of Knowledge Spark Consultancy Pvt Ltd, which deals in providing assignment help in Economics, Statistics and Mathematics to students of various universities. As a start-up, Assignment Buddy has successfully done several research projects for student community and has tied-up with several Education Corporations nationally and internationally.
This document contains a solved exam paper for the SSC Graduate Level Tier-II Exam in Arithmetical Ability. The paper contains 49 multiple choice questions covering a range of mathematical topics including ratios, averages, percentages, profit and loss, time and work problems, and geometry. The questions are at a graduate level and assess skills in applying mathematical concepts to word problems.
Placement Papers are published here to help freshers to get themselves prepared for the tests and successfully procure jobs in top companies of India including Infosys, Wipro, TCS, HCL, HP, Accenture, CTS etc. This is the section where you can find previous and latest questions, practice them with the solutions in hand.
1. The document contains instructions for a test with four sections: Section A contains 50 math questions worth 3 marks each, Section B contains 25 general knowledge questions worth 2 marks each, Section C contains 25 language questions worth 2 marks each, and Section D contains 25 intelligence questions to be answered after 2 hours.
2. Candidates must not write their name or roll number on any page of the answer booklet except where indicated. Rough work should only be done on additional sheets, not on the answer sheet.
3. The test has a total of 17 pages and covers topics including numbers, operations, geometry, time, speed, ratios, averages, and general knowledge questions about science, the human body and India's
This document contains a final model test examination for mathematics. It includes questions in four groups - Algebra, Geometry, Trigonometry and Mensuration, and Statistics. The Algebra section contains three multi-part questions on topics like factoring polynomials, solving systems of linear equations, and finding terms in a geometric series. The Geometry section contains two multi-part questions involving constructions related to dividing a line segment into parts and constructing triangles. The Trigonometry and Mensuration section contains one multi-part question on trigonometric ratios and properties or on mensuration formulas. The Statistics section contains one multi-part question involving concepts like frequency distribution, mean, median and mode. The document also includes 40 multiple choice questions testing
The document contains 50 quantitative aptitude questions with multiple choice answers. The questions cover a range of topics including ratios and proportions, averages, percentages, time/work problems, mixtures, profit and loss, and other mathematical concepts. The questions are in a multiple choice format with 4 possible answer choices for each question. The solutions and explanations provided after the questions show the step-by-step working to arrive at the correct answer for each problem.
This document contains 100 numerical aptitude questions and answers from a solved paper for the Railway Recruitment Board (RRB) exam. The questions cover a range of topics including arithmetic, algebra, geometry, time and work, ratios, averages, and data interpretation. The correct answers are provided after each question.
This is GATE 2019 mechanical question paper. The answer key is available at https://prepare.prepleaf.com. For more such content visit- https://www.prepleaf.com.
This document provides an overview of topics and sample questions related to general aptitude tests for undergraduate entrance exams. It begins with an introduction from the presenter Prof. Amul Tamboli. Next, it provides tricks and formulas for topics like alphabets, percentages, simple interest, profit and loss. The document then presents sample multiple choice questions testing these concepts. It concludes by defining general aptitude, listing common tested topics, and encouraging test-takers in their preparation. The overall purpose is to introduce the scope and style of general aptitude questions for undergraduate admissions exams.
This document contains a quantitative aptitude test with 42 multiple choice questions. The questions cover a range of topics including ratios, mixtures, profit and loss, simple and compound interest, time and work problems. The test is designed to evaluate skills in math, problem solving, and logical reasoning. Candidates have 90 minutes to answer the questions, with each correct answer earning 3 marks and an deduction of 1 mark for incorrect answers.
1) The document contains a sample question paper for the GATE 2018 General Aptitude exam, with 10 multiple choice questions covering topics like English grammar, mathematics, data interpretation, and logical reasoning.
2) The questions are either single mark or two mark questions.
3) The paper tests concepts like filling blanks in sentences, number patterns, ratios, data interpretation, and logical inferences.
This document provides a summary of a math quiz with multiple rounds of questions covering various math topics. The quiz is divided into different houses that compete against each other. Rounds include warm up questions, MCQ questions, paper-based questions, mental math questions, and a buzzer round. The questions cover a range of math concepts like geometry, algebra, ratios, percentages, time/work problems, and more. Over 30 multiple choice questions are provided in the buzzer round to test participants' math skills and problem solving abilities.
Grade 10 Math - Second Quarter Summative Testrobengie monera
This document appears to be a summative test for a 10th grade mathematics class covering topics in polynomials and geometry. It contains 45 multiple choice questions testing students' understanding of polynomial functions, properties of circles, coordinate geometry, and solving geometric problems using coordinates. The test includes questions on identifying the degree and leading term of polynomials, graphing polynomial functions, properties of secants, tangents, and circles, finding distances and areas using coordinates, and identifying geometric shapes from their vertices.
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INDIA at a Glance "Glorified Incredible !ndia"Akhilesh Sharma
India is located in South Asia. It has many geographical features including mountain ranges like the Himalayas, rivers like the Ganges and Yamuna, as well as lakes and seas. India has a long and diverse history and culture. It is a federal parliamentary republic with 29 states and 7 union territories. India has a growing economy focused in sectors like services, agriculture, and industry. Tourism is also a major industry in India with many popular destinations.
Ujjain gets direct trains from all over India and is accessible from Indore (60 kms) and therefore an important pilgrim center in India. Ujjain is typically visited along with Omkareshwar as a part of Jyotirlinga Getaway. Situated on the banks of Sacred River Shipra, Ujjain is one of the four places in India where the famous Kumbh Mela takes place. This holy festival is held here every 12 years relating to the position of stars and planets. According to Hindu mythology, the nectar which came out from the ocean during its churning by Gods and Demons, fell at four places and Ujjain was one of them. That is the reason of Ujjain being a venue for the Kumbh Mela.
The document provides information about tabulation questions that may appear in competitive exams. It explains that these questions involve analyzing data presented in a table format regarding topics like production over time, imports/exports, employee incomes, etc. The data is arranged systematically in rows and columns with headings. Example questions are provided based on sales data for different battery types sold by a company each year. The questions test the ability to analyze trends, calculate percentages, and compare values across the table. Overall, the document introduces the concept of tabulation questions and provides a sample table and questions to illustrate the type of data analysis skills required to solve them.
The document provides information and examples regarding trigonometric ratios and their applications to problems involving angles of elevation, depression, and distances. It defines trigonometric ratios for right triangles and gives their values for common angles. It also defines angle of elevation and depression and provides worked examples of problems involving finding heights, distances, widths, and angles using trigonometric ratios and properties of right triangles.
1) Banker's discount is interest charged on the face value of a bill of exchange for the period between the date the bill is discounted by a banker and the legally due date.
2) True discount is the interest charged on the amount received by the holder of the bill for the unexpired period to the legally due date.
3) Banker's gain is the difference between the banker's discount and true discount. It represents the interest earned by the banker on the true discount amount.
1. This document discusses probability and provides examples of calculating probability for random experiments and events.
2. Key concepts explained include sample space, events, and the probability formula of P(E) = n(E)/n(S) where n(E) is the number of outcomes in the event and n(S) is the total number of outcomes in the sample space.
3. Several examples are provided such as calculating the probability of getting a head when tossing a coin, getting a total over 7 when rolling two dice, and the probability of getting cards of the same color or queen when drawing from a deck of cards.
The document discusses permutations and combinations formulas. It defines permutations as arrangements of objects taking some or all at a time. The formula for permutations of n objects taken r at a time is nPr = n!/(n-r)!. Combinations are defined as groups or selections of objects taken some at a time, regardless of order. The formula for combinations of n objects taken r at a time is nCr = n!/(r!(n-r)!). Several examples of calculating permutations and combinations are provided.
1. A company raises funds from the public by dividing its total capital needs into small units called shares. People who buy these shares are shareholders.
2. The company uses the funds raised to start a business or industry. It issues share certificates to shareholders showing the value and number of shares they hold.
3. Profits are distributed annually to shareholders as dividends according to the number and value of shares held.
This document provides information about clocks and time. It includes:
1) Important facts about clock faces being divided into 60 minute spaces and clocks having an hour and minute hand.
2) Examples of calculating time differences between clocks and determining when clock hands will be in certain positions.
3) Explanations and solutions to examples such as finding the angle between hands at a certain time or when hands will be together or perpendicular.
This document provides formulas and examples for calculating the day of the week for any given date by determining the number of odd days. It explains that an ordinary year has 1 odd day while a leap year has 2 odd days. To calculate the odd days for a period, you add the odd days for each year in that period. Several examples are given to demonstrate how to use this method to find the day of the week for different dates. The key points covered are that any date in March will fall on the same day of the week as the corresponding date in November of that year, and the calendar can be reused every 4 years.
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The document provides 27 examples solving problems related to calculating volumes and surface areas of various geometric shapes like cubes, cuboids, cylinders, cones, spheres, and hemispheres. The key formulas used include formulas for volume and surface area of cubes, cuboids, cylinders, cones, spheres, and hemispheres. Sample problems include finding volumes and surface areas given dimensions, number of cubes or balls that can be made from a given volume, and percentage increases in volumes and surface areas when dimensions change.
1. The document provides formulas and concepts related to geometry including triangles, quadrilaterals, circles, and other shapes.
2. It includes formulas for calculating the areas of various shapes such as rectangles, triangles, parallelograms, trapezoids, circles, and composite figures.
3. Several solved examples applying these formulas are given at the end to demonstrate calculations of lengths, widths, areas, and perimeters of different geometric shapes.
This document provides important facts and formulas about logarithms. It defines logarithms and gives examples of evaluating logarithms using properties like loga(xy)=loga(x)+loga(y). It also defines common logarithms as logarithms to base 10, and discusses the characteristic and mantissa of logarithms. Several solved examples are given to illustrate evaluating logarithms and using their properties to simplify logarithmic expressions.
Compound interest is calculated by adding interest to the principal amount in regular intervals called compounding periods. The principal and previously accumulated interest becomes the basis for calculating interest in the next period. Three key formulas are provided for calculating compound interest compounded annually, semi-annually, and quarterly. Several example problems are then solved demonstrating the application of these formulas to calculate compound interest amounts over different time periods and interest rates.
This document provides important facts and formulas for boats and streams, along with sample problems and solutions. It states that the direction of a stream is called downstream, while against the stream is upstream. The speed of a boat downstream equals the boat speed plus the stream speed, while upstream it is the boat speed minus the stream speed. Sample problems are given to calculate boat speed in still water and stream rate based on upstream and downstream times.
1. The document provides 10 examples of problems involving trains passing each other or passing stationary objects while moving at various speeds. It gives the calculations to determine time taken, speed, length of trains/objects from the information provided in each example.
2. Key formulas provided include converting between km/hr and m/sec, calculating relative speed of trains moving in the same or opposite directions, and determining time taken for trains to pass based on their lengths, speeds and direction of motion.
3. The examples use these formulas to solve for values like time taken, speed, length from the data like one value being given in each problem.
1. This document provides important formulas and examples related to time and distance problems. It includes formulas for speed, distance, and time as well as examples of speed, average speed, and time calculations for distances covered at different speeds.
2. Several solved examples demonstrate using the formulas and concepts to calculate speeds, times, distances, and average speeds for scenarios like traveling different distances at different speeds, catching up to another traveler, and missing a train by certain times depending on walking speed.
3. The document serves as a reference for the key formulas and concepts needed to solve time and distance word problems.
1. Ratio and proportion are important concepts involving relationships between quantities. A ratio represents the fraction between two quantities, while a proportion exists when ratios are equal.
2. Key formulas and concepts include: the product of means equals the product of extremes; finding fourth, third, and mean proportionals; comparing and compounding ratios; and direct and inverse variation.
3. Examples demonstrate calculating ratios, proportions, and proportionals from word problems involving money, mixtures, and other real-world scenarios.
The document provides information on profit and loss concepts. It defines key terms like cost price, selling price, profit, gain and loss. It provides formulas to calculate gain, loss, gain/loss percentage. It also includes solved examples like calculating profit/loss percentage when an item is bought and sold at different prices, finding cost price or selling price when other details are given.
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This document provides information on percentage including concepts, formulas, and examples. Some key points:
- Percentage means hundredths, so 20% means 20/100 or 1/5.
- To increase or decrease a number by a certain percentage, the percentage is calculated as a fraction of the original number.
- Population and depreciation problems can be solved using the formula: Current value = Original value × (1 ± Rate of change/100)^Number of years.
- Examples provide calculations for percentage of a number, percentage increase/decrease, and multi-step percentage word problems.
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37. pie charts
1. Free GK Alerts- JOIN OnlineGK to 9870807070
38. PIE-CHARTS
IMPORTANT FACTS AND FORMULAE
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SOLVED EXAMPLES
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The pie-chart or a pie-graph is a method of representing a given numerical data in the form of
sectors of a circle.
The sectors of the circle are constructed in such a way that the area of each sector is proportional
to the corresponding value of the component of the data.
From geometry, we know that the area of a circle is proportional to the central angle.
So, the central angle of each sector must be proportional to the corresponding value of the
component.
Since the sum of all the central angle is 360°, we have
Value of the component
Central angle of the component =
------------------------ * 360
Total value
The procedure of solving problems based on pie-charts will be clear from the following solved
examples.
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Example 1. The following pie-chart shows the sources of funds to be collected by the National
Highways Authority of India (NHAI) for its Phase II projects. Study the pie-chart and answer
the questions that follow.
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SOURCES OF FUNDS TO BE ARRANGED BY NHAI
FOR PHASE II PROJECTS (IN CRORES RS.)
2. Total funds to be arranged for Projects (Phase II) =Rs.57,600 crores.
1. Near about 20% of the funds are to be arranged through:
(a) SPVS
(b) External Assistance
(c) Annuity
(d) Market Borrowing
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2. The central angle corresponding to Market Borrowing is:
(a) 52°
(b) 137.8°
(c) 187.2°
(d) 192.4°
3. The approximate ratio of the funds to be arranged through Toll and that through Market
Borrowing is:
(a) 2:9
(b) 1:6
(c) 3:11
(d) 2:5
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4. If NHAI could receive a total of Rs. 9695 crores as External Assistance, by what percent
(approximately) should it increase the Market Borrowings to arrange for the shortage of funds ?
(a) 4.5%
(b) 7.5%
(c) 6%
(d) 8%
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5.If the toll is to be collected through an outsourced agency by allowing a maximum 10%
commission, how much amount should be permitted to be collected by the outsourced agency, so
that the project is supported with Rs. 4910 crores ?
(a) Rs.6213 crores
(b) Rs. 5827 crores
(c) Rs. 5401 crores
(d) Rs. 5216 crores
SOLUTION
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1. (b): 20% of the total funds to be arranged = Rs.(20% of 57600) crores
= Rs.11520 crores Rs.11486 crores.
Th
2. (c):Central angle corresponding to Market Borrowing = 29952
-------- * 360
57600
= 187.2
3. (b):
4910
1
1
Required ratio = ------- = ---- = ---29952 6.1
6
4. (c):Shortage of funds arranged through External Assistance
=Rs.(11486-9695) crores =Rs. 1791 crores.
therefore, Increase required in Market Borrowings =Rs. 1791 crores.
Percentage increase required =
1791
-------- * 100 % = 5.98 % = 6%
29952
3. 5. (c):Amount permitted = (Funds required from Toll for projects of Phase II ) +
(10 % of these funds)
=Rs. 4910 crores + Rs. (10% of 4910) crores
=Rs. (4910 + 491) crores = Rs. 5401 crores.
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Example 2. The pie-chart provided below gives the distribution of land (in a village) under
various food crops. Study the pie-chart carefully and answer the questions that follow.
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DISTRIBUTION OF AREAS (IN ACRES) UNDER VARIOUS FOOD CROPS
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1.Which combination of three crops contribute to 50% of the total area under the food crops ?
(a) Wheat, Barley and Jowar
(b)Rice, Wheat and Jowar
(c) Rice, Wheat and Barley
(d)Bajra, Maize and Rice
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2.If the total area under jowar was 1.5 million acres, then what was the area (in million acres)
under rice?
(a)6
(b)7.5
(c)9
(d)4.5
3.If the production of wheat is 6 times that of barley, then what is the ratio between the yield per
acre of wheat and barley ?
(a) 3:2
(b) 3:1
(c) 12:1
(d) 2:3
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4.If the yield per acre of rice was 50% more than that of barley, then the production of barley is
what percent of that of rice ?
(a)30%
(b)33 %
(c)35%
(d)36%
5.If the total area goes up by 5%, and the area under wheat production goes up by 12% , then
what will be the angle for wheat in the new pie-chart ?
(a) 62.4
(b) 76.8
(c) 80.6
(d) 84.2
SOLUTIONS
1.(c):The total of the central angles corresponding to the three crops which cover 50% of the
total area ,should be 180.Now, the total of the central angles for the given combinations are:
4. (i) Wheat,Barley and jowar = (72+36+18)=126
(ii) Rice,Wheat and Jowar = (72+72+18)=162
(iii) Rice,Wheat and Barley = (72+72+36)=180
(iv)Bajra,Maize and Rice = (18+45+72) = 135
Clearly:(iii) is the required combination.
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2.(a): The area under any of the food crops is proportional to the angle corresponding to that crop.
Let the area under the rice production be x million acres.
Then, 18:72 = 1.5:x x=(72*15/18)=6
Thus, the area under rice production be = 6 million acres.
3.(b): Let the total production of barley be T tones and let Z acres of land be put under barley
production.
Then, the total production of wheat =(6T) tones.
Also,area under wheat production = (2Z) acres.
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Area Under Wheat Production 72
------------------------------------- = ---- =2
Area Under Barley Production 36
And therefore,Area under wheat = 2*Area under Barley = (2Z)acres
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Now, yield per acre for wheat = (6T/2Z) tones/acre = (3T/Z) tones/acre
And yield per acre for barley = (T/Z) tones/acre.
3T/Z
Required ratio = -------- = 3:1.
T/Z
4. (b):Let Z acres of land be put under barley production.
Area Under Rice Production
72
Then,
----------------------------------- = ---- = 2.
Area Under Barley Production
36
Area under rice production = 2 * area under barley production = (2Z) acres.
Now,if p tones be the yield per acre of barley then ,yield per acre of rice
=(p+50% of p) tones =(3/2 p) tones.
Total production of rice = (yield per acre) * (area under production)
= (3/2 p)*2Z=(3pZ) tones.
And,Total production of barley = (pz) tones.
Percentage production of barley to that rice = (pZ/3pZ *100)%= 33 1/3% .
5.(b): Initially,let t be the total area under considerations.
The area under wheat production initially was =(72/360 * t)acres = (t/5)acres.
Now,if the total area under consideration be increased by 5%,
then the new value of the total area= (105/100 t) acres.
Also,if the area under wheat production be increased by 12%,
t
t
then the new value of area under wheat = -- +(12% of --) acres = (112t/500)acres.
5
5
5. Central angle corresponding to wheat in the pie-chart
Area Under Wheat (new)
=
------------------------------- *360 =
Total area (new)
(112t/500)
------------*360
=76.8
(105t/100)
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Example 3.The following pie-charts show the distribution of students of graduate and post graduate
levels in seven different institute-M,N,P,Q,R,S and T in a town.
DISTRIBUTION OF STUDENTS AT GRADUATE AND POST-GRADUATE
LEVELS IN SEVEN INSTITUTES-M,N,P,Q,R,S AND T.
Number of students of
graduate level
Total Number of students of
post graduate level
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Total
1.How many students of institutes M and S are studying at graduate level?
(a) 7516
(b) 8463
(c) 9127
(d) 9404
2.Total number of students studying at post -graduate level from institutes N and P is:
(a) 5601
(b) 5944
(c) 6669
(d) 7004
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3.What is the total number of graduate and post-graduate level students in institute R?
(a) 8320
(b) 7916
(c) 9116
(d) 8372
4 .What is the ratio between the number of students studying at post graduate and graduate levels
respectively from institute S?
(a) 14:19
(b) 19:21
(c) 17:21
(d) 19:14
5.What is the ratio between the number of students studying post graduate level from institute S and the
number of students studying at graduate level from institute Q?
(a) 13:19
(b) 21:13
(c) 13:8
(d)19:13
6. SOLUTION
1.(b):Students of institute M at graduate level = 17% of 27300 = 4641.
Students of institute S at graduate level = 14% of 27300 = 3822
Total number students at graduate level in institutes M and S = 4641+3822=8463
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2.(c):Required number = (15% of 24700) + (12% of 24700) = 3705 + 2964 = 6669.
3.(d):Required number = (18% of 27300) + (14% of 24700) = 4914 + 3458 = 8372.
4.(d):Required ratio = (21% of 24700) = 21 * 24700 = 19
(14% of 27300) 14 * 27300 14
5.(d):Required ratio = (21% of 24700) = 21 * 24700 = 19
( 13% of 27300) 13 * 27300 13
Example 4.Study the following pie-chart and the table and the answer the questions based on them.
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PROPORTION OF POPULATION OF SEVEN VILLAGES IN 1997
village
Z 11%
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R 16%
S 11%
Y15 %
X 16%
V 10%
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T 21%
% population below
poverty
X
Y
Z
R
S
T
V
38
52
42
51
49
46
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1.Find the population of villages S if the population of village X below poverty line in 1997 is 12160.
(a). 18500
(b) 20500
(c) 22000
(d) 26000
2.The ratio of the population of the village T below poverty line to that of village Z below poverty line in
1997 is:
(a) 11:23
(b) 13:11
(c) 23:11
(d) 11:13
7. 3.If the population of village R in 1997 is 32000,then what will be the population of village Y below
poverty line in that year?
(a) 14100
(b)15600
(c) 16500
(d) 17000
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4.If in 1998, the population of villages Y and V increases by 10% each and the percentage of population
below poverty line remains unchanged for all the villages, then find the population of village V below
poverty line in 1998,given that the population of village Y in 1997 was 30000.
(a) 11250
(b) 12760
(c) 13140
(d) 13780
5.If in 1998,the population of village R increases by 10% while that of village Z reduces by 5% compared
that in 1997 and the percentage of population below poverty line remains unchanged for all the
village,then find the approximate ratio of population of village R below poverty line for the year 1999.
(a) 2:1
(b) 3:2
(c) 4:3
(d) 5:4
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SOLUTION
1.(c):Let the population of village X be x
Then,38% of x=12160 x = 12160 * 100
=3200
38
Now ,if s be the population village S,then
11 * 32000
16:11 = 32000 : s
s=
= 22000.
16
2.(c): Let N be the total population of all the seven villages.
Then ,population of village T below poverty line = 46% of (21% of N) and population of village Z
below poverty line = 42% of (11% of N)
46 * 21 =
42 * 11
23
11
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Required ratio = 46% of (21% of N) =
42% of (11% of N)
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3.(b): Population of village R = 32000(given)
Let the population of village Y be y.
Then, 16:15 = 32000 : y y = 15 * 32000 =30000
16
4.(b): Population of village Y in 1997 = 30000(given) .
Let the population village V in 1997 be v.
Then, 15:10 = 30000:v
v = 30000 * 10
= 20000.
15
Now population of village V in 1998 = 20000 + (10% 0f 20000) = 20000.
Population of village V below poverty line in 1998 = 58% of 22000 = 12760.
5.(a) : Let the total population of all the seven villages in 1997 be N.
Then,population of village R in 1997 = 16% of N = 16/ 100 N
And population of village Z in 1997 = 11% of N =11/100 N
Population of village R in 1999 = 16/100N+10% of 16/100 N)}=1760/10000 N
8. Th
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and population of village Z in 1999 = {11/100 N-(5% of 11/100 N)} = 1045/10000 N.
Now,population of village R below poverty line for 1999 = 51% of(1760/10000 N)
And population of village Z below poverty line 1999 = 42% of (1045/10000 n)
51% of (1760/10000 N)
51 * 1760
2
Required ratio =
-------------------------- = ------------- = -----42% of (1045/10000 N) 42 * 1045
1.