Understand Of Ratio

   

About Ratio 

  What Is Ratio ?

 👉The Ratio is the when two or more quantity are compared, in this time we can determine the comparison between the quantity's . 

 👉The ratio between A and B can be represented as A : B , where A is called antecedent and B is called consequent 

 ☑ Example :-  For example There can be a ratio between  200 and  400, but there cannot be the ratio between  200 and 400 apples. Hence, the units of quantity for the comparison of ratio should  be same.

                         👉 Ratio should be 200 : 400 = 1:2

 

Types of Ratio : - 

 ➤  Duplicate Ratio : - In this ratio for select that  X is one quantity and another is  Y then the quantity 's squares ratio also same that type ratio is called Duplicate Ratio 

 ☑ Example : the ratio of number 3 and 4 is = 3 : 4 and also squares of the 3 and 4 's ratio is 9:16 that means 3:4 = 9:16 like that X r :Yr 

➤ Sub-duplicate Ratio :-  If two numbers are in ratio, then the ratio of their square roots are  called sub-duplicate ratio. If x and y are two numbers, then the sub-duplicate ratio of x and y would be Vx : Jy.

☑ Example : the ratio of number 3 and 5 is = 3 : 5 and also squares of the 3 and 5 's ratio is 9:25 like that Vx : Jy. 

➤  Triplicate Ratio  If two numbers are in ratio, then the ratio of their cubes is called triplicate ratio. If x and y are two numbers, then the triplicate ratio of x and y would be x^y3 . 

 

 ☑ Example :Triplicate ratio of 2 :3 = 2^3 :3^3 = 8 :27

➤  Sub-triplicate Ratio:- If two numbers are in ratio, then the ratio of their cube roots is called sub-triplicate ratio. If x and y are two numbers, then the sub-triplicate ratio of x and y would be 3/x : ^/y.

  ☑ Example :  Sub-triplicate ratio of 1:125 = 3/1 : 3/125 =1:5 

➤  Inverse Ratio:-  If two numbers are in ratio, then their antecedent and consequent are interchanged and the ratio obtained is called inverse ratio, If X and Y are two numbers and their ratio is X : Y, then its inverse ratio will be Y : X. 

 ☑ Example : Inverse ratio of 4 :5 is 5 :4 . 

➤   Compound Ratio:- If two or more ratios are given, then the antecedent of one is multiplied with antecedent of other and respective consequents are also multiplied. If a : b, c: d and e : / are three ratios, then their compound ratio will be ace: bdf . 

☑ Example : The ratio are 3:5 , 4:7 , 5:7 for the compound Ratio is 

                        (3*4*5)/(5*7*7) = 12/49= 12:49

✅Note   

  ✔✔ If the antecedent is greater than the consequent, then the ratio is known as the ratio of greater inequality, such as 7 : 5 .

 ✔✔ If the antecedent is less than the consequent, then the ratio is called the ratio of less inequality, such as 5 : 7 . 

   Short tricks of LCM

In  previous post we discuss about what is LCM

, who invented LCM in details

Short tricks of LCM 

Now a days there are  many short tricks  available in the internet so  we  discuss the major tricks to solve the LCM  Problem

Trick 1:-

If  all the   is divicible  to the  greatest number

The the LCM is  the greatest number. 

Eg:-

3,6,12,24

Ans :-24

Trick 2:-

If  there  are  4 number  are given  , the greatest number is divicible   two number  then you check  the undivicible number is prime number Or not if  prime  number the simply multiple the 

Greatest and prime number   this multiplication is LCM eg :- the greatest number is 10 and prime number is 7  then 10 x 7=70  is LCM

 Example:-

Q ➤ Find LCM OF 6 , 12,24,3Ans ➤ 24

Q ➤ Find LCM of 5,10,30,20Ans ➤ 60

Q ➤ Find the LCM of 2,4,8,16Ans ➤ 16

Q ➤ Find the LCM of 2,4,7,8Ans ➤ 56

Values and Ethics in Procession(1)

 Unit-3

 Values and Ethics in Procession

Values and Ethics in Procession

 Engineering Ethics - Introduction

 Engineering is the process of developing an efficient mechanism which quickens and eases the work using limited resources, with the help of technology. Ethics are the principles accepted by the society, which also equate to the moral standards of human beings. An engineer with ethics, can help the society in a better way.

 Hence the study of Engineering ethics, where such ethics are implemented in engineering by the engineers, is necessary for the good of the society. Engineering Ethics is the study of decisions, policies and values that are morally desirable in engineering practice and research. 

Morals 

The word “Morality” originates from the Latin word “mos” meaning “custom”. Morals are the principles or habits with respect to right or wrong of one’s own conduct. They are not imposed by anyone. Morals are what you think is good and bad personally. 

Though morals are not imposed, they can be understood as the preaching of our inner self. Depending on a few factors, our mind filters things as good or bad. These are the ideas that help frame our personality so that we can distinguish between what is right and what is wrong.

 A moral is the code of conduct that you develop over time and set for yourself to follow, just like

 • Being good to everyone 

• Speaking only the truth 

• Going against what you know is wrong 

• Having chastity 

• Avoid cheating

• Being a nice human being etc. 

Morals are always defined by one’s own personality. Morals can be changed according to one’s beliefs as they are completely dependent on one’s perception towards the ethical values. 

Ethics 

The word “Ethics” originates from the Greek word “ethos” meaning “character”. Ethics are a set of rules or principles that are generally considered as standards or good and bad or right and wrong, which are usually imposed by an external group or a society or a profession or so.

 Ethics can be understood as the rules of conduct proposed by a society or recognized with respect to a particular class of human actions or a particular group or culture. Ethics are dependent on others definition. They may or may not vary from context to context.

 A person who strictly follows a set of ethical principles, may not have any moral at all while a person who violates ethical principles at times, may maintain a high moral integrity. The ethical theories include duty ethics, right ethics, virtue ethics and so on. A best example that can explain ethics is utilitarianism. 

Utilitarianism is the philosophy which explains that the happiness or pleasure of a greatest number of people in the society is considered as the greatest good. According to this philosophy, an action is morally right if its consequences leads to happiness of the people and wrong if the action leads to their unhappiness. This theory moves beyond the scope of one’s own interests and takes into account the interests of others.

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 Ethics in Engineering 

Ethics are principles followed depending upon the moral responsibility that a person feels. The study of related questions about moral ideals, character, policies and relationships of people and organizations involved in technological activity, can be termed as Engineering ethics.

 An engineer whether he works individually or works for a company, has to go through some ethical issues, mostly under the conditions such as, conceptualization of a product, issues arising in design and testing departments, or may be on the issues involving the manufacturing, sales and services. Questions related to morality also arise during supervision and team works.

 The ethical decisions and moral values of an engineer need to be considered because the decisions of an engineer have an impact the products and services - how safe they are to use, the company and its shareholders who believe in the goodwill of the company, the public and the society who trusts the company regarding the benefits of the people, the law which cares about how legislation affects the profession and industry, the job and his moral responsibilities and about how the environment gets affected, etc. 

Not only an engineer, but everyone has to follow a set of morals in order to keep away from getting morally degraded. 

Our behavior should include the following − 

• Respecting others and ourselves. 

• Respecting the rights of others.

 • Keeping promises.

 • Avoiding unnecessary problems to others.

 • Avoiding cheating and dishonesty. 

• Showing gratitude towards others and encourage them to work. 

Morality commands respect for persons, both others and ourselves. It involves being fair and just, meeting obligations and respecting rights and not causing unnecessary harm by dishonesty and cruelty or by hubris.

 Steps to Deal with Issues 

Whenever there occurs an issue, one should possess a few skills in order to sort out the problem. The issues that engineers face, have to be dealt with patience and few moral goals have to be kept in mind while dealing with such issues. They are as follows − 

• Moral Awareness − One should be able to recognize the moral problems and issues that occur in Engineering. The analysis on the problem is necessary in order to differentiate and judge according to ethics or according to the rules to follow.

 • Cogent Moral Reasoning − In order to come to a conclusion on an issue, the argument has to be assessed and comprehended. The argument on both sides has to be considered with all the probabilities and the nature of the argument should be logical and moral.

 • Moral Coherence − After having gone through all the logical and moral facts, consistent and comprehensive view points are to be formed based upon a consideration of relevant facts.

 • Moral Imagination − The moral issues and the practical issues have to be dealt separately. Alternative responses are to be found out for dealing with moral issues while creative solutions should be found out for practical difficulties.

 • Moral Communication − The language to communicate about one’s moral views should be so precise and clear, that the expression or words should not alter the original meaning. Though one has all these moral goals, the ethical reasoning for achieving moral conduct with responsibility and commitment is obtained by a few skills that are described below.

 Important Skills for Ethical Reasoning 

Let us now discuss the important skills for ethical reasoning − 

• Moral Reasonableness − The ability and willingness to be morally reasonable that one should have while dealing such issues. Unless one is willing and improve such ability, justice cannot be done.

 • Respect for Persons − The persons involved in the issue, should be treated with genuine concern by one. Such concern should also be there with oneself along with being there for others. 

• Tolerance of diversity − One should have a broader perspective towards ethnic and religious differences that the people have. Every person differs with another when compared on grounds of moral reasoning. The acceptance of those differences is really important.

 • Moral hope − The moral conflicts can be resolved by using better communication and having rational dialogue which is evident-based and openended which is acceptable and appreciable by both the parties. • Integrity − The moral integrity has to be maintained. Being honest and having strong moral principles helps one to resolve an issue in an efficient manner. An individual also needs to consider other’s professional life and personal convictions while solving a problem.

 Engineering Ethics - Moral Issues 

A moral issue can be understood as an issue to be resolved not only by considering the technical stuff but also by keeping moral values in mind. To be more precise, let us consider the definition in general. “Moral issue is a working definition of an issue of moral concern is presented as any issue with the potential to help or harm anyone, including oneself.” 

Types of Moral Issues There are mainly two types of Moral issues that we mostly come across while keeping the ethical aspects in mind to respond. They are −

 Micro-ethics 

This approach stresses more on the problems that occur on a daily basis in the field of engineering and its practice by engineers. 

Macro-ethics 

This approach deals with social problems which are unknown. However, these problems may unexpectedly face the heat at both regional and national levels. 

Examples 

Let us now understand a few examples related to moral issues.

 Example 1

 After a recent collapse of a structure in which many people died, an Engineer came to know about a bridge which is marginally safe. He informed his superior who asked him to stay calm and not to discuss with anyone, while waiting for the next year budget sessions to get some financial help for the repair required. What should the engineer do? 

Example 2

 What should an Engineer who observes his colleague copying confidential information unauthorized, do immediately? If he chooses to stop his friend, what if this gets repeated without his notice? If he chooses to report the management, what if his friend loses the job? Which is morally correct?

 Example 3 

An engineer who develops a proto-type for the project, loses it due to a mishap exactly the day before the submission. Is it morally correct to outsource the prototype of the project and reduce the risks of job insecurity? What should he do?

 These are the few examples just to understand the kind of moral dilemmas. There might be one or more correct answers at times. There can be some other way around to deal with the issue, which one can’t easily notice. However, the decisions have to be made by following a slow and clear process in order to avoid further problems and also to solve this in a manner that leads to no regrets.

 Types of Inquiries The issues can be resolved by following an investigation procedure, step by step in order to have a clear understanding towards the issue. Here we have three different types of inquiries. 

Judging the issues has to be followed by a systematic procedure to avoid any flaws. Engineering ethics involves investigations into values, meanings and facts. 

Following are the different types of inquiries made for this. 

• Normative inquiries

 • Conceptual inquiries

 • Factual or descriptive inquiries 

Normative Inquiries 

Normative Inquiry refers to the description that describes what one ought to do under a specific circumstance. This is the expected ideal response, which might differ from what one believes to be right or wrong. 

This list identifies and justifies the morally desirable nature for guiding individuals or groups. This includes the responsibility of engineers to protect the public safety and how they should respond under such dangerous practices. Normative inquiries also quote the laws and procedures that affect the engineering practice on moral grounds. They refer to the thought process where the moral rights are to be implemented in order to fulfill their professional obligations. 

Conceptual Inquiries 

Conceptual Inquiry refers to the description of the meaning of concepts, principles and issues related to engineering ethics. The ethics that an engineer should possess to protect the safety, health and welfare of the public, etc. are described under conceptual inquiries. 

It describes what safety is and mentions the marginal issues of safety along with the precautions an engineer should take to avoid risk. Conceptual inquiries mention the moral aspects of bribery and how its effects, along with the professional ethics and professionalism. 

Factual and Descriptive Inquiries

 Factual Inquiry or the descriptive inquiry help to provide the facts for understanding and finding solutions to the value based issues. The engineer has to conduct factual inquiries by using scientific techniques. 

This helps in providing the information regarding the business realities such as engineering practice, history of engineering profession, the effectiveness of professional societies, the procedures to be adopted when assessing risks and psychological profiles of engineers. 

Let us now go through the concept of Moral dilemma that a person faces when confronted with a situation.

 Engineering Ethics - Moral Dilemmas 

At times, the situations occur where one cannot make immediate decisions as the moral reasons come into conflict. The moral reasons can be rights, duties, goods or obligations, which make the decision making complex. 

Types of Complexities 

The difficulties in arriving to a solution, when segregated, can be divided into the following three sections. 

Vagueness 

This refers to the condition where the doubt lies in whether the action refers to good or bad. This is just like having a thought that following the rules is mandatory. This sometimes includes the unwritten rules like being loyal, having respect, maintaining confidentiality, etc.

Conflicting reasons 

When you know about the solutions you have, the making of better choice among the ones you have, will be the internal conflict. Fixing the priorities depends upon the knowledge and the moral values one has. The reason why the particular choice is being made, makes sense. 

Disagreement 

When there are two or more solutions and none among them is mandatory, the final solution selected should be best suitable under existing and the most probable conditions. The interpretation regarding the moral reasons behind the choice and analysis should be made keeping in mind whether this is the better or the worse solution in the probable aspects. 

Steps in Facing Moral Dilemmas 

Whenever a person is faced with a moral dilemma, the issue is to be solved with a stepwise approach as this will generate a better output. The steps include the following − 

Identification 

The step of identification involves the following − 

• The issue has to be thoroughly understood. 

• The duties and the responsibilities of the persons involved are to be clearly known. 

• The moral factors related to the issue are to be understood.

 • The conflicting responsibilities, the competing rights and the clashing ideas involved are to be identified. 

Ranking 

The considerations in the issue are to be listed down. Then they have to be ranked according to the priorities. The moral aspect has to be considered to rank the issues. The advantages of a single person should never be given any importance unless any moral reason is there behind it. No partiality is allowed. 

Inquiries

 The inquiry of details involved in the issue is to be completely made. All the facts related to the issue are brought into light. Considering the alternative courses of action for resolving and tracing, full implications are also needed. 

Discussions 

Discussions are to be made with other members, as different minds look at the issue in different views to give different solutions. The complete analysis of a problem gives chances to different viewpoints, perspectives and opinions from which a better solution can be drawn. 

Final Solution

 After analyzing different perspectives and considering the facts and reasons on the basis of truths and understanding the flaws which lead to the issue, a final solution has to be drawn out. This solution will add value to the whole analysis, in all aspects.

 Engineering Ethics - Moral Autonomy 

Moral Autonomy is the philosophy which is self-governing or self-determining, i.e., acting independently without the influence or distortion of others. The moral autonomy relates to the individual ideas whether right or wrong conduct which is independent of ethical issues. The concept of moral autonomy helps in improving self-determination.

 Moral Autonomy is concerned with independent attitude of a person related to moral/ethical issues. This concept is found in moral, ethical and even in political philosophy. 

Moral Autonomy – Skills Needed 

In this section, let us discuss the skills needed for moral autonomy. 

• Ability to relate the problems with the problems of law, economics and religious principles − It is essential to have the ability to analyze a problem and finding the relation with the existing law or the topic of issue with the existing principles on that topic. The ability to distinguish between both of them and finding the moral reasons.

 • Skill to process, clarify and understand the arguments against the moral issues − If the issue is against some moral values or the ethical values to be followed in the society, then clarity should be maintained about the differences and similarities. Both of these differences and similarities are to be judged based on why they are a matter of concern and in what aspect.

 • Ability to suggest the solutions to moral issues on the basis of facts − If the moral issues are not fulfilling and needs to be, then the solutions are to be suggested according to the moral issues based on the facts and truths of the issue. These suggestions must be consistent and must include all the aspects of the problem. No partiality is to be allowed in any such aspect. 

• Must have the imaginative skill to view the problems from all the viewpoints − After having known about the facts and illusions of the issue, a clear understanding is attained in viewing the problem in all kinds of viewpoints. This enables one to be able to suggest a proper alternative solution. 

• Tolerance while giving moral judgment, which may cause trouble − When the whole analysis is made considering all the viewpoints of the issue, the final output might be or might not be pleasing to the persons involved. Hence while declaring the judgment or the decisions taken, a detailed description of the actions done should be given, while the actions ought to be done should be presented in a better way, to ensure others that the decisions have been taken without any partialities towards any party. 

• Tolerance while giving moral judgment, which may cause trouble − When the whole analysis is made considering all the viewpoints of the issue, the final output might be or might not be pleasing to the persons involved. Hence while declaring the judgment or the decisions taken, a detailed description of the actions done should be given, while the actions ought to be done should be presented in a better way, to ensure others that the decisions have been taken without any partialities towards any party.   

Skills for Improving Moral Autonomy

 Moral autonomy reflects the concept of individuality. This relates to the idea of building one’s self with the moral values one has while developing psychologically. 

To have moral autonomy in all the aspects, one should have a lot of patience and interest. One should adhere to the basic principles of humanity and should be strict with the Don’ts he has in mind and liberal with his Do’s. The kindness towards his fellow beings is also an important concept to be kept in mind. Inculcation of all these important qualities, enhances the skills of Moral autonomy in a person. 

A Person must have adequate knowledge and understanding about the use of ethical language so as to defend or support his views with others. He must have better knowledge in understanding the importance of suggestions and better solutions while resolving moral problems and also about the importance of tolerance on some critical situations. 

Above all, one must understand the importance of maintaining moral honesty and should be liberal to understand the human behavior under certain circumstances. 

Engineering Ethics - Kohlberg’s Theory

 Lawrence Kohlberg was a professor at Harvard University during the early 1970s and was famous for his works on developmental psychology. He conducted many studies at Harvard’s Center for Moral Development and proposed a theory on moral development which is popularly known as Kohlberg’s theory. 

His theory of moral development was dependent on the thinking of the Swiss psychologist Jean Piaget and the American philosopher John Dewey. He was also inspired by James Mark Baldwin. These men had emphasized that human beings develop philosophically and psychologically in a progressive fashion. 

Lawrence Kohlberg’s Theory 

Kohlberg proposed that people progress in moral reasoning based on their ethical behavior. He postulated this theory based on the thinking of younger children throughout their growing period as adults. He conveyed that younger children make judgment based on the consequences that might occur and the older children make judgment based on their intuitions. 

He believed that there are six stages of moral development which are further classified into three levels. The following illustration shows the different levels. The process being discussed here is about the judgment made by the thinker about the protagonist in a given situation. The steps of the thinking process show the moral development of the thinker. 

Pre-conventional Level

 This can be understood as the first level of moral thinking, which is generally found at Elementary school level. The thinker at this stage tends to think and behave based on the direct consequences that might occur. There are two sub-stages in this.

 Avoid Punishments 

A thinker at this stage generally thinks and believes that the judgment are to be made as per the socially acceptable norms as they are said so by some higher official (a teacher or a parent). This is a child-like obedience, in order to avoid punishments. These thoughts are based on the idea that the protagonist should not disobey the law or rules. 

Self–interest 

A thinker at this stage, shows interest in making decisions according to the rewards they get in exchange. This second stage is characterized by a view that right behavior means acting in one's own best interests. In this stage, they tend to follow the rules of authority because they believe that this is necessary to ensure positive relationships and societal order. 

Conventional Level 

This can be understood as the second level of moral thinking, which is generally found at the primary and high school level. The thinker at this stage tends to think and behave based on the want to please others. There are two sub-stages in this. 

Getting people to like them

 At this stage, the ideas of the society are considered. This level can be that where the protagonist behaves on account of the moral grounds which people decide for decision making. This decision may or may not support the law. Whatever the result is, the thinking process is based on how to impress others or society and on how to please the people around. 

Maintain functioning in society 

A thinker at this stage, considers to follow the rules for the good of the society. The moral grounds on how people in the society will consider the job done will be the priority, because the thinker believes that a social order is maintained by abiding by the rules. Hence a thinker sticks to the idea that the protagonist should follow the moral values. The thinker’s behavior is driven by the authority while his thinking conforms to the social order.

 Post-Conventional Level 

This can be understood as the third level of Moral thinking, which is generally found after the high school level. The thinker at this stage tends to think and behave based on a sense of justice. There are two sub-stages in this. 

Reject rigidity of laws

 In this level, the thinker uses his moral thinking skills at a commendable pace. He starts to feel for the protagonist based on moral grounds. He also might have an opinion that the rules have to be changed according to humanitarian values. The thinker rejects the rigidity of the existing laws and rules at this stage. 

Sense of justice 

This is the pinnacle stage of Moral development where the thinker feels a sense of justice for the protagonist. The thinker has great moral values that he keeps himself free from the external factors that might influence his thinking process. These are the three main sections of moral development proposed by Lawrence Kohlberg. Let us now try to have some detailed idea on this with an example.

 Engineering Ethics - Heinz’s Dilemma 

Lawrence Kohlberg quoted an example for his Moral development theory. This example is popularly called the Heinz’s Dilemma. 

Story of Heinz 

A story of a middle-aged ordinary middle-class man, called Heinz is considered as an example. Heinz is an ordinary man having a wife. His wife suffers from a dreadful disease. Doctors believe that a special drug which was invented recently and is available at the BIG pharma store, can only save his wife. When Heinz went to buy the drug, the drug-seller costed it around $2,000 dollars, while the actual manufacturing cost of the drug is $20 dollars. Heinz borrowed the money from friends and lenders and could finally collect only $1,000 dollars. Though Heinz pleaded a lot, the greedy drug-seller refused to sell the drug at low cost. Now, Heinz had no other option but to steal the drug from the shop to save the life of his wife. Is this a better option to do? What is your judgment? 

Now, to solve this Heinz’s dilemma, a thinker has the following options. 

Options for the Thinker

 In this section, we will discuss the options for the Thinker. 

• Heinz should not steal the drug because it is the disobedience of law. 

• Heinz can steal the drug, but should be punished by the law.

 Heinz can steal the drug and no law should punish him. 

The answer which you choose indicates your moral development. Each answer has its consequences and explanation. Let us go through the answers. 

Heinz should not steal the drug because it is the disobedience of law. 

This decision makes it impossible for Heinz to save his wife. His wife dies and the rich drug-seller becomes richer. Though the law was obeyed, no moral justice was done. This is a pre-conventional level of moral thinking.

 Heinz can steal the drug, but should be punished by the law. 

This decision helps Heinz save his wife, but Heinz will be kept in prison. Though Heinz took a moral decision, he had to undergo the punishment. This is a Conventional level of moral thinking. 

Heinz can steal the drug and no law should punish him.

 This decision lets Heinz save his wife and both of them can live happily. This thinking is based on the thought that the rigidity in law should be rejected and justice should be done on moral grounds. This is a post-conventional level of moral thinking.

Engineering Ethics - Global Issues

                        Engineering Ethics - Global Issues 

 

Engineering Ethics - Global Issues

 In this chapter, let us the discuss the global issues concerning Engineering Ethics. The concept of   globalization increases with the integration of nations through trade, investment, transfer of   technology and exchange of ideas and culture.

 So far as the engineers and companies are concerned, the Multinational Companies play crucial   roles in promoting globalization. The ethics related to business, environment and computer will   also be discussed in this chapter. 

Multinational Companies 

Multinational Companies, also called Transnational Companies are the companies that have a main branch in a country called the Home country and its other branches in different companies called the Host countries, as International Labor Organization (ILO) defines it.

  Multinational Corporations can have a powerful influence in local economies, and even the   world economy, and play an important role in enhancing international relations and   globalization. These MNCs also get tax benefits, pledges of governmental assistance or improved   infrastructure or lax environmental and labor standards enforcement as they help in increasing     the national GDP. MNCs should produce high degree of operational efficiency pertaining to high   standards in the jurisdiction of the place where they are. The wages, safety measures, employee   benefits are all should be taken care of by the MNCs. 

 There have been instances of corporate and government confrontations when governments tried   to force MNCs to make their intellectual property public in an effort to gain technology for local   entrepreneurs. Such an idea paves way for conflicts where either the government has changed its   rules or the companies have withdrawn their investments. Multinational corporate lobbying is   directed at a range of business concerns, from tariff structures to environmental regulations. The   threat of nationalization or changes in local business laws and regulations can limit a MNCs   power.

 Business Ethics

  Ethics are the set of rules of conduct that the concerning persons need to abide by. These ethics      when related to the field of business, are called Business Ethics. Business ethics are similar to          professional ethics. Business ethics are related to the aspects of business dealing with all                  employees in an ethical manner. 

  An organization is expected to follow certain ethical values in its functioning, establishment,          employee welfare, operations, environmental factors, waste management and the issues related      to the people living around, etc. These factors affect the reputation of the company and                    indirectly  affect the value of its shares in the global market. The main principles of admirable        business ethics can be - being trustful, open minded, meeting obligations, having the documents    clear with good accounting control, etc. 

 The general business ethics include the following aspects −

 • Be it any industry or a corporate office, the infrastructure and the working environment                 should  be comfortable and encouraging.

 • The safety precautions and maintenance of the organization are to be taken care of.

 • The work and the skills of the employees are to be identified and encouraged for the                        development of the organization.

 • A hierarchical procedure is to be followed, maintaining the ethical standards for the execution       of work.

 • The product maintenance right from the procurement raw material to the dispatch of product       should be done in a standard procedure uninfluenced by any unethical issues.

 • No tolerance should be there for any kind of unethical behavior or influences that affect the           production and organizational standards.

 • To encourage the activities that promote social good and are environment-friendly. 

Environmental Ethics 

Globalization and industrialization have impacted the environment on a very large scale. The long term effects of the environment are usually neglected unless it is gross and immediate effect.

 We are getting habituated to the ill-effects of pollution and industrial negligence shows on our environment. The aftermath can be seen in acid rains, water and land contamination, effect on crops and food sources, the cattle getting affected, the drying of lakes and canals, floods, drought, tsunamis and earthquakes due to drilling of underground wealth, the effect on marine being, the effect on ozone and the melting of snow mountains due to global warming, etc. The aftermath can be an alarming call for the required environmental changes. 

Engineers need to show some responsibility towards the environment and should be ethical in their approach and find mitigating solutions for the protection of environment. Organizations should support the activities that promote environment protection. 

The environment ethics include − 

• The study of moral issues concerning the environment

 • Moral perspectives, beliefs and attitudes concerning those issues. 

Let us now consider the ethics that need to be followed by a corporation dealing with the manufacture of computers. The organization needs to set priorities for the efficient use of resources, the design of the energy-efficient products, easy disassembly for recycling and waste minimization. The application of high standards throughout its operation and placing priority to companies that have an environmental concern can also extend the support for environmental protection.

 Computer Ethics 

Computers with Internet raise a host of difficult moral issues, many of them connected with basic moral concerns such as free speech, privacy, respect for property, informed consent and harm. To evaluate and deal with these issues, a new area of applied ethics called Computer Ethics has come up. These ethics are related to all the computer professionals such as programmers, analysts, operators, designers, etc. along with the users. 

The ten commandments of Computer Ethics, created in 1992 by the Computer Ethics Institute consists of the following − 

One should never use a computer − 

• To harm the people (anti-social activities) 

• To interfere with other’s work (illegal manipulations)

 • To snoop into other’s files (malware) 

• To steal a computer/data (hacking) 

• To bear false witness (manipulation and morphing) 

• To use/ copy a software you didn’t pay for (like illegal downloads and usages)

 • To use or copy other’s software without compensations (illegal pirated versions)

 • To use other’s intellectual output inappropriately (violating IPR)

 • Doing without thinking of social consequences of the program being written (libeling)

 • Always use a computer ensuring consideration and respect towards fellow beings.

 However, these ethics are facing lax in today’s world. A very small section of concerned individuals seems to be following these ethics. A large section seems to be violating these ethics. With this, there is an unprecedented increase in cybercrime. 

Role of Computers in Technological Development 

In this section, we will discuss the role of Computers in Technological Development. The limitations of Internet usage and free speech are to be known clearly by every netizen. In this digital era, the morals expected from a human being are the basic tools that control the unethical and sleazy manner of handling the internet.

 Internet which is now a global network of networks, initially used the infrastructure of the telephone system and is now being handled by many telecommunication systems by wire, fiber or wireless systems. The Internet provides a spring of new ways to be in contact with other people and with sources of information. It has also created greater convenience in ordering consumer items, paying bills and social experiments trading stocks and bonds. Like other major , it also has raised a host of new issues. One set of issues centers on free speech, including control of obscene forms of pornography, hate speech, spam which is unwanted commercial speech and libel. Computers contribute to greater centralization or decentralization insofar as human decision makers direct them. 

There come issues which call for trouble wherein, computers are used in embezzlement and other forms of stealing money or financial assets. The issues concerning theft of software and information is again a similar one. The computers are centrally involved when an unauthorized person uses a telephone computer system to obtain private phone numbers or when maliciously alters or scrambles the programming of a telephone computer. In today’s world, malicious people have come up with not one but various ways of exploiting money, goods, services, assets, etc. through the computers and internet. The Internet besides easing our work has also paved way to gather an individual’s confidential details easily. 

The two main factors that make computers troublesome are their speed and geographical coverage, which allows the masses to be victimized further. The difficulty lies in tracing the underlying transactions to apprehend the thieves. This problem is compounded when the communication lines linking the computers involved cross national boundaries.

 The most commonly discussed cases of computer abuse are instances such as − 

 • The stealing or cheating by employees at work.

 • The stealing by non-employees or former employees.

 • The stealing from or cheating clients and consumers. 

 • The violation of contracts for computers sales or services. 

 • The many conspiracies to use computer networks to engage in widespread fraud.

 Alarmingly, the Internet has led to an explosion of identity theft, in which personal information is obtained and used to forge documents and commit fraud. 

Privacy Factors 

The misuse of Internet also influences privacy factors. The illegal attackers or hackers get access  to restricted data which is a security threat. 

• The inappropriate access which leads to security breach in an office leads to the leakage of               confidential information which might severely affect the growth of the company.

 • The hackers who crack the security and get unauthorized entry into the highly secured                   information zone, tend to copy the content or they may change the content, delete the content         or  get it affected with virus as soon as the authorized personnel opens the file.

 • The different types of viruses such as Trojan Horse, Memory Resident, Overwrite, Browser            Hijacker, Directory Virus, etc. can create instances wherein, the data on computer system get          affected in various ways. 

• The legitimate access to information is restricted to protect individual privacy, national security     and freedom within a capitalist economy to protect proprietary information essential in                   pursuing corporate goals. 

• The Privacy Act of 1947 prohibits the information contained in government files from being           used for purposes beyond those for which it was originally gathered. 

Weapons Development

 Based on the size of expenditures, direct or indirect involvement of engineers and innovative developments, military technology is an area that calls for serious discussion on engineering ethics. As modern weapons of war progressed through catapults, cannons, machine guns and bombs released from airplanes and missiles to reach further and further, the soldiers firing them were less likely to see the individual human beings, the soldiers as well as citizens, they had as their general target.

 For some engineers, their involvement with weapons develop conflicts with personal conscience, such as knowing that making weapons in a company, is the job which would be done by someone else if he doesn’t do and that cannot change the results. Though working in a toxic chemical manufacturing plant can make you feel guilty, the idea abolishing this disastrous thing once you become the CEO of the company, makes you get the feeling of being in good books, though you might or might not do that when the time comes. 

There can also be instances where an engineer can feel that the development of weapons is an expression of conscientious participation in national defense. An engineer who is a specialist in missile control and guidance, can feel proud that he is being able to help his country through his efforts in the defense industry, especially as part of the “War on terrorism”. In a broader context, weapons include anything used to gain an advantage over an adversary or to place them at a disadvantage. Examples include the use of sieges, tactics, and psychological weapons which reduce the morale of an enemy. 

Engineers as Managers 

An engineer, whether he works individually or works for a company, has to go through some ethical issues, mostly under conditions such as, conceptualization of a product, issues arising in design and testing departments, or may be on the issues involving the manufacturing, sales and services. An Engineer is responsible in promoting ethics in an organization, through framing organizational policies, responsibilities and by personal attitudes and obligations. 

Suppose, an issue occurs which might lead to a conflict, an engineer or say a professional should respond pertaining to specific morals and professional ethics. An engineer should be able to work as a manager in such situations, resolving conflicts according to priorities, keeping the organizational benefits in mind. The issue must be resolved without hurting anyone’s feelings and by developing a mutual understanding with subtlety. Not only the engineers who act as managers or the managers alone will share the responsibility, but there lies some social responsibility to stakeholders, customers and employers of a company. They act to develop wealth as well as the welfare of the society. 

Ethicists project the view that the manager’s responsibility is only to increase the profit of the organization, and only the engineers have the responsibility to protect the safety, health, and welfare of the public. But the manager, though an engineer or not, has the ethical responsibility to produce safe and good products (or useful service), while showing respect for fellow human beings including his employees, customers and the public. Hence, the objective for the managers and engineers is to produce valuable products that are also profitable.

 Managing Conflicts 

A conflict is a result of differences in opinions. Conflicts generally arise where the work is shared among more than one members. In fact, the situations of conflicts should be tolerated with patience, understood impartially and resolved by the participation by all the concerned. 

When a project is distributed among a few members,

 the conflicts that generally occur are − 

• The schedule based conflicts might occur at different levels of execution of a project, depending     upon the priorities and limitations at each level. 

• The prioritizing of projects or departments which can be arrived from end requirements may         change from time to time. 

• The deficiency of personnel availability for certain project completion in due time may also lead     to a conflict. 

• Conflicts that occur over technical, economic, and time factors such as cost, time, and                       performance level. 

• Conflict arising in administration such as authority, responsibility, accountability, and logistics       required.

 • Conflicts of personality, human psychology and ego problems.

 • Conflict over expenditure and its deviations. 

Picking out on the personnel creating may keep others away from the problem and doesn’t affect everyone. Such personnel can be trained again or given precautions. The interest of the personnel doing a project should be focused on the ethical attitudes and morals but not on their positions. In addition, the conflicts between the personnel, can be solved by the manager who has more ways to solve it. The evaluation of the results should be based on certain specified objectives such as efficiency, quality, and customer satisfaction. 

Consulting Engineers 

The consulting engineers differ from the salaried engineers of an organization. These consulting engineers work in private and are paid per advice they offer or for the service they provide in a field of specialized knowledge or training. Consultants are individuals who typically work for themselves but may also be associated with a consulting firm. 

Consultants can play a multi-faceted role; for example, they function as advisors, fixers, bosses, generalists, stabilizers, listeners, advisors, specialists, catalysts, managers or quasi-employees. Bringing in an expert can save time, effort and money. It has been estimated that approximately 3/4 of all companies call upon consultants at one time or another. Many companies claim that they receive a higher return for their invested dollars by using consultants for specific tasks. 

A Consulting Engineer should maintain the ethical values in the profession, such as giving proper information without any ambiguities for advertisements, the allowance of small individual companies to participate in bidding and also maintaining clarity in the contingency fee which is previously agreed. The greater amount of job freedom enjoyed by consulting engineers as opposed to salaried engineers leads to wider areas of responsible decision making concerning safety.

 Engineers as Advisors 

Engineers may accept an assignment requiring education and/or experience outside of their own fields of competence, but their services shall be restricted to other phases of the project in which they are qualified. All other phases of such project shall be performed by qualified associates, consultants, or employees. 

For an engineer to be an advisor, should study the costs and benefits of all alternatives in objective manner, study economic viability, technical feasibility, operational feasibility and social acceptability, follow honesty, and technical complicity leading to moral complicity. Then after analyzing the factors that lead to such things and also the consequences that occur, engineers can work as an advisor.

 There may be various roles or models played by engineers who work as advisors. Let us now see what the roles or models are − 

Human Values (Principles of Harmony)

                                              Unit-2 

Principles of Harmony 

                                       Principles of Harmony

    Compared to the elements of art, the principles of art are challenging to understand. A shape,        for    example, is obviously different from a color. Shape and color are both elements of art. A          person without any art education would immediately recognize how shapes are different from        colors. 

     That same person, however, may struggle to verbalize the differences between some of the               principles of art. Two specific principles – unity and harmony, come to mind. The principles of       art can create a feeling about an artwork and feelings are difficult to quantify. 

     This article explores three of the principles of art. These three principles are best understood         as a group since they are related. The first two, previously mentioned, are harmony and unity.       The third is called variety.

                          Harmony and Variety in Art 

        Harmony

   Harmony is the principle of art that creates cohesiveness by stressing the similarities of                   separate   but related parts. 

   One should note that harmony is not the same as unity. Harmony does, however, enhance unity      in a work of art. Specifically, harmony uses the elements of art (color, line, shape, form, value,        space, texture) as a vehicle to create a sense of togetherness amongst otherwise separate parts.

    A set of colors that relate according to a specific scheme creates harmony. Likewise, a uniform        texture of brush strokes across the surface of a canvas creates harmony. 

     Another way to guarantee harmony is to choose compositional components that are similar in         shape and contour. For example, a composition that utilizes only curvy shapes will have more         harmony than a similar composition that includes both curvy and geometric shapes. The parts       of the image below are in harmony because every contour is a curve. 

 Variety

  For many people, performing the same task or following the same routine over and over again        leads to boredom. That is why vacations are such a pleasure. A vacation is an interruption of          life’s routines. Some people are active when on vacation while others do nothing at all. One            thing  is certain – vacations look different than the routines they interrupt. Vacations are a              measured dose of variety in a person’s life. Art needs variety also.

sor of mine used to say, “Variety is the        spice of life”. He was not life-coaching. He was talking about art. 

   Variety is the principle of art that adds interest to an artwork. 

   Variety works through juxtaposition and contrast. When an artist places different visual                 elements next to one another, he/she is using variety. Straight lines next to curvy lines add               variety. Organic shapes among geometric shapes add variety. Bright colors next to dull colors         add variety.

   Harmony and variety are really opposite expressions of the same nebulous concept. To                     emphasize one is to de-emphasize the other. Harmony and variety play tug-of-war in a                     composition. Too much harmony is boring while too much variety is aimless and                               incomprehensible.

   Unity 

  Unity is the principle of art that gives an artwork a feeling of “oneness”. Unity and harmony are    similar, but unity is more broad. There are numerous ways to create unity in art. Some of those       ways are particular to individual artist’s style. 

   Unity is about separate parts working together. We can better understand unity by thinking           about a car. A car’s purpose is to provide transportation. When the many parts of a car are             working together, it moves. No part of the car, separated from the whole, is capable of                     providing  transportation. When the car functions as it should, the parts are working together       in  unity. 

   Like harmony and variety, unity is not easy to understand at first. Different from the elements       of art, unity is an impression – a feeling the artwork conveys to the viewer. 

  One can imagine a solitary shape and hold that shape in the mind. One cannot, however, simply    imagine unity and hold that concept in the mind. We must evaluate unity by looking and                analyzing. Therefore, developing unity in artworks requires the artist to pay attention to its            development throughout the process of creating.

 Here are some proven methods that ensure a unified composition…

                                                    • Simplicity 

                                                    • Repetition

                                                    • Proximity

 Let’s take a closer look at each of these techniques…

 Simplicity – Simplicity refers to purposely reducing the amount of potential variety. For example,                       a graphite pencil drawing is likely to exhibit some measure of unity, given the lack of                       color. By eliminating color, the image is simpler than it potentially could have been if                       color was introduced.

                     A personal favorite is to make a drawing by hatching with only straight lines.                                     Straight  lines are less complex than curvilinear lines and will unify a composition. 

Repetition – Repetition within a composition will guarantee a feeling of unity. Tessellations are an                       obvious example of how repetition unifies a composition. A tessellation is an                                       arrangement of shapes that fit together in a repeated pattern without gaps.

                     Repetition can also unify an entire series of artworks, like a group of paintings. A                            certain shape, object or texture that is repeated among a group of paintings acts as a                         motif, helping each painting to feel as though it is part of a greater whole.

 Proximity – Proximity refers to the closeness of different components in a work of art. By placing                        parts close together, the mind is able to see the parts as one thing, a mass. 

                      Negative space is the space between elements in a work of art. It can refer to the                                “empty spaces” within a drawing or painting. The more limited the negative space,                          the more unified the areas of a composition may feel.

Human Values

                                        Human Values

                          What are Values, Morals, and Ethics?

Human Values

 

Table of Contain:-   

 # Q.  What are Values ?

 # Q. What are Morals?  

Human Value: 1. Right conduct                              2. Peace                                             3. Truth                                        4. Love                                            5. Co-operation                                  6. Honesty                                7. Trust                                            8. Non-violence                                 9. Wisdom 

Professional Values:   1. Integrity            2. Loyalty             3. Passion           4. Commitment 

                                     5. Valuing Time    6. Attitude            7. Credibility & Responsibility 

Q.  What are Values?

  According to the dictionary,
values are “things that have an intrinsic worth in usefulness or importance to the possessor,” or “principles, standards, or qualities considered worthwhile or desirable.”

 However, it is important to note that, although we may tend to think of a value as something good, virtually all values are morally relative – neutral, really – until they are qualified by asking, “How is it good?” or “Good to whom?” The “good” can sometimes be just a matter of opinion or taste, or driven by culture, religion, habit, circumstance, or environment, etc.

 Again, almost all values are relative. The exception, of course, is the value of life. Life is a universal, objective value. We might take this point for granted, but we all have the life value, or we would not be alive. Life is also a dual value – we value our own life and the lives of others.

  Q. What are Morals?  

Moral values are relative values that protect life and are respectful of the dual life value of self and others. The great moral values, such as truth, freedom, charity, etc., have one thing in common. When they are functioning correctly, they are life protecting or life enhancing for all. But they are still relative values. 

Our relative moral values must be constantly examined to make sure that they are always performing their life-protecting mission. Even the Marine Corps core values of “honor, courage and commitment” require examination in this context. 

 Q. What is Ethics?

 A person who knows the difference between right and wrong and chooses right is moral. A person whose morality is reflected in his willingness to do the right thing – even if it is hard or dangerous – is ethical. Ethics are moral values in action.

 Being ethical id an imperative because morality protects life and is respectful of others – all others. It is a lifestyle that is consistent with mankind’s universal values as articulated by the American Founding Fathers – human equality and the inalienable right to life.

 As warriors it is our duty to be protectors and defenders of the life value and to perform the unique and difficult mission of taking the lives of those acting immorally (against life) when necessary to protect the lives of innocent others.

 Human Value: A human value is defined by our religious Leaders, Gurus and Saviors' teachings and practices, need and judgment of fulfilling individuals need in the society. Human values can be assured of a happy and harmonious human society. We cultivate and inculcate these values among the student and the staff through teaching, co-curricular and extracurricular activities. We as an academic institution believed that along with knowledge, wisdom is essential for sound growth of the society. In this regards, inculcation of human values among the budding citizens of the nation is very important. 

Hence, we are very much concerned to observe the following human values 

1. Right conduct                              2. Peace                                             3. Truth                                        4. Love                                            5. Co-operation                                  6. Honesty                                7. Trust                                            8. Non-violence                                 9. Wisdom 

1. Right Conduct:  a) Self- Help Skills: Care of possessions, diet, hygiene, modesty, posture, self                                               reliance, and tidy appearance.

                               b) Social Skills: Good behavior, good manners, good relationships, helpfulness, no                                       wastage and good environment.

                              c) Ethical Skills: Good conduct, courage, dependability, duty, efficiency, ingenuity,                                      initiative, perseverance, punctuality, resourcefulness, respect for all, and sense of                                      responsibility. 

2. Peace:   Attention, calmness, concentration, contentment, dignity, discipline, equality, equanimity,                        faithfulness, gratitude, happiness, harmony, humility, inner silence, optimism, patience,                            reflection, satisfaction, acceptance, control, self-esteem, tolerance, and understanding. 

3. Truth:    Accuracy, curiosity, fairness, fearlessness, honesty, integrity, intuition, justice, optimism,                        purity, quest for knowledge, reason, self-analysis, sincerity, synthesis, truthfulness, and                            determination. 

4. Love:  "Nothing is impossible for pure Love” says Mahatma Gandhiji. It has immense value.                               Acceptance, affection, care, compassion, consideration, dedication, devotion, forgiveness,                      friendship, generosity, gentleness, interdependence, kindness, patience, patriotism, reverence,                  sacrifice, selflessness, service, sharing, sympathy, tolerance and trust are the segments of love. 5. Co-operation: “Non-cooperation with evil is much a duty as is a cooperation with good” says                                            Mahatma Gandhiji. Co-operation is the process of working together to the same end.                                It is undeniably are of the most vital assets one can have when working through a                                    problem. Having the opinion and voice of another person will not only draw out a                                    discussion of the topic, but also lead to a well rounded solution. Co-operation has                                     been in its high importance and held high in regard.                                                       6. Honesty:    Today, the power of Gandhi's words still inspires us to change the world by changing                                ourselves. “Live as if you were to die tomorrow. Learn as if you were to live forever.”                              Honesty in the realm of human values is extremely important. The idea of staying true to                          oneself can often feel intimidating and impossible, but what most people felt to realize is                          that it is not the act of simply telling the truth that makes someone honest rather the                                  quality of person who is being honest. An honest man is often straight forward, upright,                            sincere and fair. 

7. Trust: Trust can be interpreted in many ways. But ultimately it comes down to reliability and truth.                    Without trust, the world simply would not function. We create documents, money and bullet                     proof glass because we have lost faith which is why the most important human values. Learn                   to trust and be trusted, is not an easy task, but it’s important is beyond measure. In short, one                   cannot serve in a world without trust. 

8. Non -Violence  a) Psychological: Benevolence, compassion, concern for others, consideration,                                             forgiveness, morality, loyalty and happiness.                                                                                           b) Social: Appreciation of other cultures and religions, brotherhood, care of                                                    environment, citizenship, equality, harmlessness, national awareness,                                                         perseverance, respect for property, and social justice. 

9. Wisdom: Wisdom is the most important human value in many ways. Its value is very important                              while  living the lives. Wisdom is often confused with the words like knowledge and                                intelligence. But wisdom is defined as the quality of having experience and good                                       judgment.  Wisdom becomes necessary when society gets cramp with knowledge. In the                        explosion of knowledge based society, wisdom becomes the necessity. 

Professional Values:   1. Integrity            2. Loyalty             3. Passion           4. Commitment 

                                     5. Valuing Time    6. Attitude            7. Credibility & Responsibility 

1. Integrity: Integrity is defined as the unity of thought, word and deed (honesty) and open mindedness.                       It includes the capacity to communicate the factual information so that others can make                           well-informed decisions. It yields the person's "Peace of mind, and hence adds strength                           and consistency in character, decisions, and actions. This paves way to one's success. It is                         one of the self-direction virtues. It enthuses people not only to execute a job well but to                           achieve excellence in performance. It helps them to own the responsibility and earn self-                         respect and recognition by doing the job. Integrity is the quality of being honest and                                 having strong moral principles; moral uprightness. It is generally a personal choice to                               uphold oneself to consistently moral and ethical standards. 

2. Loyalty: Loyalty is faithfulness or a devotion to a person, country, group, or cause. Philosophers                          disagree on what can be an object of loyalty as some argue that loyalty is strictly inter                              personal and only other human beings can be the object of loyalty. 

3. Passion: Passion is a feeling of intense enthusiasm towards or compelling desire for completion of                       the work. Passion defines performance enhancing aspects and work enjoyment. When an                          individual is passionate about their occupation they tend to work more resulting in more                           work satisfaction. 

4. Commitment: Commitment means alignment to goals and adherence to ethical principles during the                               activities. One should have the conviction without an iota of doubt that one will                                       succeed. Holding sustained interest and firmness, in whatever ethical means one                                       follows, with the fervent attitude and hope that one will achieve the goals, is                                             commitment. It is the driving force to realize success. This is a basic requirement for                               any profession. The commitment of top management will naturally lead to committed                               employees, whatever may be their position or emoluments. This is bound to add                                       wealth to oneself, one's employer, society, and the nation at large. Target oriented                                     efforts are put to reap efficiency. 

Height and Distance Mathematic

Height and Distance Mathematic

Height and Distance Mathematic

Important information:- It is an important application of trigonometry which helps us to find the height of any object and distance of that object from any point which are not directly measurable. If the angle of elevation/ depression from a point is known.

Line of Sight:-  A line of sight is the line drawn from the eye of an observer to the point, where the object is viewed by the observer.

Horizontal Line:- The line of sight which is parallel to ground level is known as horizontal line.

Angle of Elevation:- The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal, when the point being viewed is above the horizontal level.

Angle of Depression:- When the line of sight is below the horizontal level, the angle so formed by the line of sight with the horizontal is called the angle of depression . 

 

Table of Contain:-   

# The shadow of a tower is 15 m, when the Sun's elevation is 30°. What is the length of the                   shadow, when the Sun's elevation is 60° ? 

#The tops of two poles of height 24 m and 36 m are connected by a wire. If the wire makes an           angle of 60° with the horizontal, then the length of the wire is ?

#The angle of elevation of the top of an unfinished pillar at a point 150 m from its base is 30°. If        the angle of elevation at the same point is to be 45°, then the pillar has to be raised to a height        of  how many meters?  

 1. What is the angle of elevation of the Sun when the shadow of a pole is √3 times the length of           the  pole ?  

       (a) 30°

       (b) 45° 

        (c) 60°

        (d) None of these 

 Answer :-  (a) 30°

2. The shadow of a tower is 15 m, when the Sun's elevation is 30°. What is the length of the                   shadow, when the Sun's elevation is 60° ?  

      (a) 3 m 

      (b) 4 m

      (c) 5 m

       (d) 6 m 

   Answer :- (c) 5 m

3. What is the angle of elevation of the Sun, when the shadow of a pole of height x m is —m√3 ?

     (a) 30°

     (b) 45° 

     (c) 60° 

     (d) 75°

Answer :-   (c) 60° 

 4. A vertical stick 12 m long casts a shadow 8 m long on the ground. At the same time, a tower            casts a shadow of 40 m long on the ground. The height of the tower is [SSCCGL2012]

    (a) 60 m

    (b) 65 m

    (c) 70 m

    (d) 72 m

Answer :-  (a) 60 m

 5. The tops of two poles of height 24 m and 36 m are connected by a wire. If the wire makes an           angle of 60° with the horizontal, then the length of the wire is [SSCCCL2012]

    (a) 8√3 m

    (b) 8 m 

    (c) 6√3 m

    (d) 6 m 

Answer :-  (a) 8√3 m

6. The shadow of a tower standing on a level plane is found to be 50 m longer when the Sun's              elevation is 30°. When it is 60°, then what is the height of the tower? [CDS 2014]

     (a)  25m

     (b) 25√3m

     (c) 25/√3m

     (d) 30m

Answer :-  (c) 25/√3m

 7. The angle of elevation of the tip of a tower from a point on the ground is 45°. Moving 21 m              directly towards the base of the tower, the angle of elevation changes to 60°. What is the                  height  of the tower, to the nearest meter?  

      (a) 48 m 

      (b) 49 m 

      (c) 50 m

      (d) 51 m 

Answer :-  (c) 50 m

8. The angles of depression from the top of a light house of two boats are 45° and 30° towards the      west. If the two boats are 5 m apart, then the height of the light house is [SSCFCI2012] 

    (a) (2.5√3 - 1) m

    (b) 2.5(√3 - 1) m

    (c) (2.5√3 + 1) m

   (d) 2.5(√3 + 1) m 

Answer :-   (d) 2.5(√3 + 1) m 

9. The angle of elevation of the top of an unfinished pillar at a point 150 m from its base is 30°. If        the angle of elevation at the same point is to be 45°, then the pillar has to be raised to a height        of  how many meters?  

    (a) 59.4 m 

    (b) 61.4 m 

    (c) 62.4 m

    (d) 63.4 m 

Answer :-  (d) 63.4 m 

10. From the top of a cliff 200 m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 45°, respectively. What is the height of the tower? [CDS 2012] 

(a) 200 m 

(b) 200{(√3 - 1)/ √3} m 

(c) 200√3 m 

(d) None of these 

Answer :- (b) 200{(√3 - 1)/ √3} m