Engineering Mathematics Diploma Syllabus
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Questions and Answers

What is the relationship between the first derivative of a function and its local maxima and minima?

  • The first derivative changes sign at local maxima and minima. (correct)
  • The first derivative is negative at local minima.
  • The first derivative is always positive at local maxima.
  • The first derivative is zero at local minima.

Which method is most suitable for evaluating the integral of a product of two functions?

  • Integration by substitution.
  • Definite integration.
  • Numerical integration.
  • Integration by parts. (correct)

When determining the area enclosed by curves using integration, which of the following steps is essential?

  • Solving simultaneous equations.
  • Calculating the second derivative.
  • Evaluating the limits of integration. (correct)
  • Finding the roots of the functions involved.

What is the main purpose of finding the second derivative of a function?

<p>To determine the concavity and points of inflection. (D)</p> Signup and view all the answers

What is the proper definition of an indefinite integral?

<p>An integral representing an anti-derivative of a function. (A)</p> Signup and view all the answers

During the evaluation of a definite integral, which of the following expressions represents the result?

<p>The net area under the curve from the upper to the lower limit. (A)</p> Signup and view all the answers

When using the substitution method to evaluate an integral, what is a critical first step?

<p>Determining what substitution simplifies the integral. (D)</p> Signup and view all the answers

What is one application of calculus regarding the volume generated by curves?

<p>Finding the volume when a curve rotates about an axis. (D)</p> Signup and view all the answers

Which statement describes the difference between elastic and plastic bodies?

<p>Elastic bodies can return to their original shape after deformation, while plastic bodies cannot. (D)</p> Signup and view all the answers

What is the least count of a micrometer screw gauge typically used for precision measurements?

<p>0.001 mm (A)</p> Signup and view all the answers

Which of the following correctly defines Young's modulus?

<p>The ratio of tensile stress to tensile strain within the elastic limit. (D)</p> Signup and view all the answers

What effect does an increase in temperature generally have on surface tension?

<p>It decreases surface tension. (B)</p> Signup and view all the answers

What is the correct relationship involving pressure, volume, and temperature of a gas?

<p>Pressure is inversely proportional to volume at constant temperature. (C)</p> Signup and view all the answers

Which is a characteristic property of laser light?

<p>Laser light is monochromatic and coherent. (B)</p> Signup and view all the answers

Which of the following is an example of a good conductor of heat?

<p>Copper (B)</p> Signup and view all the answers

What is a common misconception about the statistical nature of error in measurements?

<p>There is a difference between absolute and relative error. (B)</p> Signup and view all the answers

Which of the following components is NOT typically associated with workflows in organizational settings?

<p>Customer interfaces (D)</p> Signup and view all the answers

In the context of Enterprise Resource Planning (ERP), which of the following is considered an essential feature of ERP software tools?

<p>Real-time data processing (C)</p> Signup and view all the answers

Which Cloud service model offers the highest level of control to the user?

<p>IaaS (B)</p> Signup and view all the answers

What is a primary reason for the evolution of ERP systems over time?

<p>To integrate various business functions into a unified system (B)</p> Signup and view all the answers

Which of the following platforms is NOT a recognized tool for creating workflows?

<p>Photoshop (B)</p> Signup and view all the answers

What is the primary function of a biomass power plant in energy generation?

<p>To convert organic materials into fuel (D)</p> Signup and view all the answers

Which of the following best describes a key benefit of biomass energy?

<p>It reduces waste through utilization (A)</p> Signup and view all the answers

In the context of power generation economics, what does 'peak load plants' refer to?

<p>Plants that typically only run during high demand times (D)</p> Signup and view all the answers

What is the significance of a load duration curve in power generation?

<p>It indicates the variability of electrical demand over time (D)</p> Signup and view all the answers

What characteristic defines high voltage transmission lines?

<p>They minimize energy loss over long distances (A)</p> Signup and view all the answers

Which type of biogas plant is primarily used for large-scale biogas production?

<p>Continuous biogas plant (A)</p> Signup and view all the answers

Which combination describes a Hybrid PV system?

<p>Solar and wind energy systems combined (D)</p> Signup and view all the answers

What is one of the common challenges in biomass energy utilization?

<p>It requires a significant amount of space for production (D)</p> Signup and view all the answers

What is the primary objective of application development as outlined in the course content?

<p>To ignite and promote programming skills (A)</p> Signup and view all the answers

Which of the following platforms is intended for creating simple Android applications without prior programming knowledge?

<p>MIT App Inventor (B)</p> Signup and view all the answers

What skill set is NOT listed under Unit 1 regarding computer programming?

<p>Create and write debug scripts (D)</p> Signup and view all the answers

What is an essential tool for developing flowcharts as per the course outline?

<p>Draw.io (D)</p> Signup and view all the answers

Which of the following is an recommended platform to learn coding through hands-on experience?

<p>Scratch (B)</p> Signup and view all the answers

In the context of web page design, what is the primary focus of Unit 2?

<p>Basic web technologies (A)</p> Signup and view all the answers

What kind of problems does the course expect students to solve using flowchart design?

<p>Programmable problems (A)</p> Signup and view all the answers

Which of the following is excluded from the coding platforms suggested for students?

<p>Appy Pie (C)</p> Signup and view all the answers

What distinguishes isotopes from isobars?

<p>Isotopes have different atomic masses but the same atomic number. (B), Isobars have the same atomic mass but different atomic numbers. (C)</p> Signup and view all the answers

Which of the following statements is true regarding the octet rule?

<p>Atoms tend to lose, gain, or share electrons to achieve a full outer shell of eight electrons. (C)</p> Signup and view all the answers

During electrolysis, what occurs at the cathode?

<p>Reduction of cations. (C)</p> Signup and view all the answers

What is the significance of Faraday's second law of electrolysis?

<p>It states that the amount of substance altered at an electrode during electrolysis is proportional to the current used. (B)</p> Signup and view all the answers

Which property distinguishes metals from non-metals?

<p>Conductivity. (D)</p> Signup and view all the answers

What defines an electrovalent compound?

<p>It is composed of oppositely charged ions held together by electrostatic forces. (B)</p> Signup and view all the answers

What explicitly influences the degree of ionization based on Arrhenius Theory?

<p>The strength of the acid or base. (D)</p> Signup and view all the answers

Which of the following is a characteristic property of alloys?

<p>Alloys usually exhibit improved mechanical properties compared to pure metals. (A)</p> Signup and view all the answers

Flashcards

Successive Differentiation

Finding the derivatives of a function multiple times.

Tangent Line

A line that touches a curve at a specific point and has the same slope as the curve at that point.

Maxima/Minima

The highest or lowest points on a function within a specific interval.

Indefinite Integral

The set of all antiderivatives of a function

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Integration by Substitution

A technique to evaluate integrals by changing variables.

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Integration by Parts

A method used for evaluating integrals involving the product of two functions.

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Definite Integral

An integral with bounds to find the area under the curve

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Area Enclosed by Curves

Use integrals to find the area between two curves.

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Atom

The smallest unit of an element that retains its chemical properties.

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Electrovalent Compound

A compound formed by the transfer of electrons between atoms.

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Electrolysis

The process of using an electric current to drive a non-spontaneous chemical reaction.

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Metallurgy

The process of extracting metals from their ores.

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Ore

A naturally occurring solid material from which a metal or valuable mineral can be extracted profitably.

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Alloy

A mixture of two or more metals, or a metal and a nonmetal.

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Electrolyte

A substance that conducts electricity when dissolved in water or melted.

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Covalent Compound

A compound formed by the sharing of electrons between atoms.

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What is a standard unit?

A unit that is universally accepted and used for consistent measurement across different places and times.

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What are fundamental quantities?

Basic quantities that cannot be defined in terms of other quantities. Examples include length, mass, and time.

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What is least count?

The smallest value that an instrument can measure accurately.

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What is the difference between accuracy and precision?

Accuracy refers to how close a measurement is to the true value, while precision refers to how close repeated measurements are to each other.

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What is elastic limit?

The maximum stress a material can withstand before it permanently deforms.

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What is Young's modulus?

A measure of a material's stiffness, representing the ratio of stress to strain in the elastic region.

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What is surface tension?

The force per unit length acting on a liquid surface, tending to minimize the surface area.

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What is viscosity?

A measure of a fluid's resistance to flow, caused by internal friction.

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Municipal Solid Waste (MSW)

Waste generated from homes, businesses, and institutions in urban areas.

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Bio Energy

Energy derived from organic matter, such as plants and animal waste.

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Biomass Conversion Process

Transforming biomass into usable energy, often involving processes like combustion, gasification, or anaerobic digestion.

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Fuel Cell

A device that converts chemical energy directly into electrical energy through an electrochemical reaction.

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Hybrid PV Systems

Systems combining photovoltaic (PV) with other energy sources, such as wind or fuel cells, for a more reliable and stable energy supply.

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Connected Load

The total electrical load that can be connected to a power system.

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Load Curve

A graphical representation of the electrical load demand over a period of time.

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Plant Capacity Factor

The ratio of actual energy generation to the maximum possible generation of a power plant.

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Workflows

A sequence of automated tasks or steps that complete a specific process, often used in business and technology.

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ERP (Enterprise Resource Planning)

Software that integrates and manages all aspects of a business, including finance, human resources, inventory, and production.

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IaaS (Infrastructure-as-a-Service)

A cloud computing model where you rent computing resources like servers, storage, and networking.

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PaaS (Platform-as-a-Service)

A cloud computing model where you get a platform to develop and deploy applications, including tools and environments.

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SaaS (Software-as-a-Service)

A cloud computing model where you access software applications over the internet, without installation or maintenance.

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What is computer programming?

Computer programming is the process of creating instructions for a computer to follow. These instructions, written in a specific programming language, tell the computer what to do and how to do it.

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What is an algorithm?

An algorithm is a step-by-step set of instructions for solving a problem or completing a task. It's like a recipe for a specific problem.

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What is a flowchart?

A flowchart is a visual representation of an algorithm using symbols and arrows to show the order of steps. It helps you visualize the flow of instructions.

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What are coding platforms?

Coding platforms are online or offline tools that provide a space for you to write, execute, and test your code.

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What is application development?

Application development involves creating software programs that can be used on different devices, like smartphones or computers.

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What are the benefits of learning coding?

Learning coding helps you develop problem-solving skills, logical thinking, and creativity. It also opens doors to exciting career opportunities in the tech industry.

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What are some online app builder platforms?

Online app builder platforms like MIT App Inventor, Thunkable, and ibuildapp allow you to create simple Android applications without coding knowledge. They provide a visual interface and drag-and-drop features.

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How to publish and share your Android app?

After creating your Android app, you can publish it on the learning management system or on platforms like Google Play Store, allowing others to download and use it.

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Study Notes

Syllabus Information

  • Document is a syllabus for a Diploma Program in EE/EEE, effective from 2024-2025
  • Location is Jharkhand University of Technology, Ranchi, 834010
  • Branch is EE/EEE
  • Subject: Engineering Mathematics

Engineering Mathematics Course Skill Set

  • Students will be able to solve systems of linear equations in different engineering fields
  • Students will be able to apply knowledge of calculus to support concurrent and subsequent engineering studies
  • Students will be able to solve quantitative problems
  • Students will demonstrate understanding of concrete and abstract problems
  • Students will have proficiency in communicating mathematical ideas
  • Students will be detail-oriented

Details of Mathematics Course Content

  • Topics are taught and assessed to develop unit skill sets for achieving identified skill sets in a cognitive domain
  • Unit 1: Matrices and Determinants
    • Matrix types and examples
    • Matrix operations (addition, subtraction, scalar multiplication, and multiplication)
    • Evaluation of determinants for matrices of order 2 and 3
    • Techniques for solving systems of linear equations (e.g., Cramer's rule)
    • Properties of singular matrices
    • Finding adjoints and inverses of non-singular matrices
  • Other Units:
    • Content outlines detailed topics for subsequent units, including Straight Lines, Trigonometry, Differential Calculus, and Integral Calculus, with subtopics and related problem-solving methods

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Related Documents

Jharkhand University of Technology EE/EEE Syllabus PDF 2024-25

Description

This syllabus outlines the Engineering Mathematics course for the Diploma Program in Electrical Engineering and Electrical & Electronics Engineering at Jharkhand University of Technology. Students will develop skills in solving linear equations, applying calculus, and addressing both concrete and abstract mathematical problems.

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