Gre arithmetic iii
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The document contains 4 math problems with solutions: 1) Finding the sum of the unique prime factors of 198 (16) 2) Finding the sum of the distinct primes that are the product of all positive 11 multiples below 120 (28) 3) Finding the sum of the least and greatest of 5 consecutive integers with an average of 11 (22) 4) Converting 6 miles per hour to feet per second (8.8 feet per second)
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chap 5 ex: 5b
1) The document discusses addition and multiplication rules for integers. It provides examples of adding and multiplying integers with the same and different signs.
2) It then provides 10 questions with solutions that apply these integer rules. The questions involve adding, subtracting, multiplying and dividing integers.
3) The document aims to teach students how to perform basic arithmetic operations like addition, subtraction, multiplication and division on integers by following rules about sign changes when integers have the same or different signs.
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The document defines several types of numbers:
1) Natural numbers (counting numbers like 1, 2, 3)
2) Integers (natural numbers and their negatives)
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4) Real numbers (rational numbers and numbers that cannot be written as fractions like pi)
It also defines factors, prime numbers, and prime factors. Prime factors are factors of a number that are also prime numbers. The document provides examples of writing numbers as products of their prime factors and converting terminating decimals to fractions.
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2) It then provides 10 questions with solutions that apply these integer rules. The questions involve adding, subtracting, multiplying and dividing integers.
3) The document aims to teach students how to perform basic arithmetic operations like addition, subtraction, multiplication and division on integers by following rules about sign changes when integers have the same or different signs.
Types of number
The document defines several types of numbers:
1) Natural numbers (counting numbers like 1, 2, 3)
2) Integers (natural numbers and their negatives)
3) Rational numbers (integers and fractions)
4) Real numbers (rational numbers and numbers that cannot be written as fractions like pi)
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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
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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
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Gre arithmetic iii
- 2. What is the sum of the unique prime factors of 198 198 = 2 × 32 × 11 Sum of the unique prime factors = 2+3 + 11= 16 mathews.suman@gmail.com
- 3. mathews.suman@gmail.com P is the product of all positive multiples of 11 < 120 , What is the sum of the distinct primes of P Possible multiples of 11< 120 are 11,22,33,-----110 𝑃 = 11 × 22 × 33 ×−−−−− −110
- 4. mathews.suman@gmail.com P= 11(1 × 2 × 3 ×−−− − 10) Distinct primes of P are 2,3, 5, 7, 11 Sum = 28
- 5. mathews.suman@gmail.com If the average of 5 consecutive integers is 11, what is the sum of the least and greatest integer Let the integers be a, a+1, a+2, a+3, a+4 Average = 5𝑎+10 5 = 11
- 6. mathews.suman@gmail.com 5a+10 = 55 a= 9 Least integer = 9, greatest integer = 13 Sum = 22
- 7. mathews.suman@gmail.com Convert 6 miles per hour to feet per second 1 mile = 5280 feet 6 miles = 6(5280) feet 6 miles per hour = 6(5280) 3600 = 8.8 𝑓𝑒𝑒𝑡 𝑝𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑