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NCERT Solutions of Class 10th Economics(अर्थशास्त्र) in Hindi

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NCERT Solutions of Class 10th Economics in Hindi (अर्थशास्त्र Social Science - Samajik Vigyan) Aarthik Vikas Ki Samajh  - Free PDF Download

अर्थशास्त्र बताता है कि बाजार कैसे काम करता है और समझाता है कि गरीबी, स्वास्थ्य, शिक्षा और विकास को  किस तरह संख्या में मापा जाए ताकि हम इसमें सुधार ला सकें। NCERT पाठ्यपुस्तक आर्थिक विकास की समझ भारतीय अर्थशास्त्र पर आधारित है जिसमें हम भारतीय अर्थव्यवस्था में विकास की प्रक्रिया के बारे में बात करेंगे। हम अर्थव्यवस्था के विभिन्न क्षेत्रों के बारे में बात करेंगे। विस्तृत और सही तरीके से NCERT Solutions of Class 10th Economicsयहां प्रदान किया गया है। प्रत्येक अध्याय का उत्तर सूची में दिया गया है ताकि आप विभिन्न अध्यायों में आसानी से खोज सकें और किसी एक का चयन कर सकें।

अध्याय 1- विकास
अध्याय 2- भारतीय अर्थव्यवस्था के क्षेत्र
अध्याय 3- मुद्रा और साख
अध्याय 4- वैश्वीकरण और भारतीय अर्थव्यवस्था
अध्याय 5- उपभोक्ता अधिकार

पाठ्यपुस्तक को पाँच अध्यायों में विभाजित किया गया है, जिनमें प्रत्येक विषय के बारे में अधिक विस्तृत तरीके से बताया गया है। पहला अध्याय विकास के दृष्टिकोण और इसे कैसे समायोजित किया जाना चाहिए इसके बारे में बात करता है। दूसरा अध्याय आधुनिक अर्थव्यवस्था में आर्थिक गतिविधियों को वर्गीकृत करने के तरीके से संबंधित है। तीसरा अध्याय पैसे के विकास और आधुनिक अर्थव्यवस्था में इसकी भूमिका के बारे में बात करता है। चौथा अध्याय विभिन्न मामले के अध्ययन के माध्यम से भारतीय अर्थव्यवस्था पर वैश्वीकरण और उसके प्रभावों के बारे में है। अंतिम अध्याय उन तरीकों के बारे में बात करता है जिनके माध्यम से हम उपभोक्ताओं के रूप में नागरिकों के अधिकारों की रक्षा कर सकते हैं।

NCERT Solutions of Class 10th Economics(अर्थशास्त्र) in Hindi

अध्याय 1 - विकास

अध्याय में कुल तेरह प्रश्न हैं। पहले तीन प्रश्न MCQs हैं। शेष प्रश्न लघु उत्तर और दीर्घ उत्तरीय प्रश्न प्रकार के हैं। प्रश्न संख्या सातवें में हमें एक उचित कथन के माध्यम से अपनी बात को सही ठहराना है जबकि प्रश्न संख्या बारह में हमें दिए गए आंकड़ों का विश्लेषण करना है।

अध्याय 2 - भारतीय अर्थव्यवस्था के क्षेत्र

अध्याय में कुल 24 प्रश्न हैं। पहला प्रश्न रिक्त स्थानों को भरने का है। दूसरे प्रश्न संख्या में चार MCQs हैं। तीसरे प्रश्न में मिलान करना है। चौथा प्रश्न odd one out है। पांचवें प्रश्न में, हमें तालिका के आंकड़ों का विश्लेषण करना है और किसी दिए गए शहर में असंगठित क्षेत्र के श्रमिकों के प्रतिशत का पता लगाना है| शेष अन्य प्रश्न लघु और दीर्घ उत्तरीय प्रकार के हैं। अंतिम प्रश्न में हमें दिए गए आंकड़ों का विश्लेषण करना होगा और उससे संबंधित प्रश्नों का उत्तर देना होगा।

अध्याय 3 - मुद्रा और साख

इसमें कुल तेरह प्रश्न दिए गए हैं। प्रश्न संख्या बारह में रिक्त स्थानों को भरना है। अंतिम प्रश्न MCQs है जिसमें हमें सही विकल्प चुनना है। शेष प्रश्न लघु और दीर्घ उत्तरीय प्रकार के हैं।

अध्याय 4 - वैश्वीकरण और भारतीय अर्थव्यवस्था

कुल तेरह प्रश्न हैं। प्रश्न संख्या रिक्त स्थान के प्रकार की है। प्रश्न संख्या बारह निम्नलिखित से मेल खाता है। अंतिम प्रश्न में तीन MCQs होते हैं। शेष दस प्रश्न लघु और दीर्घ उत्तरीय प्रकार के हैं।

अध्याय 5 - उपभोक्ता अधिकार

इस अध्याय में तेरह प्रश्न हैं। पहले ग्यारह प्रश्न लघु और दीर्घ उत्तरीय प्रकार के हैं। प्रश्न संख्या बारह में मिलान करना है। तेरह प्रश्न संख्या में वाक्य को सही/गलत बताना है।

Notes of Ch 7 Directing| Class 12th Business Studies

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Summary and Notes of Ch 7 Directing| Class 12th Business Studies 

Definition of directing (According to Koontz and O’Donnell) 

“Direction is the executive function of guiding and observing subordinates”.

Meaning of directing

It refers to instructing, guiding, communicating and inspiring people in the organisation.

Characteristics of directing

• Directing Initiates action: A manager has to perform this function along with planning, organising, staffing and controlling while discharging his duties in the organisation. While these functions prepare a setting for action, directing initiates action in the organisation.

• Directing takes place at every level of management: The top-managers direct their subordinates who are the middle-level managers and the middle-level managers direct their subordinate who are the supervisory-level managers and supervisory-level direct their subordinate and guide them. The directing takes place wherever superior-subordinate relations exist.

• Directing is a continuous process: Directing takes place throughout the life of the organisation because without direction the organisational activities cannot continue further.

• Directing flows from top to bottom: Directing starts from the top- level management and ends at the supervisory level of management.

Importance of directing

• Directing helps to initiate action by people in the organisation towards attainment of desired objectives.

• Directing integrates employee efforts in the organisation in such a way that every individual effort contributes to the organisational performance.

• The objectives of an organisation can only be achieved by motivated employees. Motivated employees work with full dedication and with a feel of belongingness.

• Often, the employees show resistance to change in their organisational structure. But with the changing demand of time, it needs to be implemented, enforced. Manager through the medium of direction shapes the mind-set of the employees in a manner that they wilfully accept changes.

• Effective directing helps to bring stability and balance in the organisation among employees and work activities.

Principles of Directing

• Maximum individual Contribution: According to this principle directing technique must help every individual in the organisation to contribute to his maximum potential for achievement of organisational objectives.

• Harmony of objectives: According to this principle, there must be full harmony between organisational objectives and individual objectives. Good directing may balance between both objectives.

• Unity of Command: According to this principle a person in the organisation should receive instructions from one superior only. If instructions are received from more than one, it creates confusion.

• Appropriateness of direction technique: According to this principle, appropriate motivational and leadership technique should be used while directing the people based on subordinate needs, attitude and situational variables.

• Managerial Communication: Effective managerial communication across all the levels in the organisation makes direction effective.

• Use of informal organisation: According to this principle, there must be a free flow of information between the seniors and the subordinates and success of direction depends upon effective exchange of information to a great extent.

• Leadership: According to this principle, while directing the subordinates, managers should exercise good leadership as it can influence the subordinates positively without causing dissatisfaction among them.

• Follow through: According to this principle, it must be monitored by management as to what extent the policies framed and issued directions have been enforced.

Elements of Direction

The process of directing involves guiding, Coaching, instructing, motivating, leading the people in an organisation to achieve organisational objectives.

Following function are included in the elements of direction

• Supervision: It refers to monitor the progress of routine work of one’s subordinates and guiding them properly.

Importance of Supervision

• Supervisor maintains day to day contact and maintains friendly relations with workers.

• Supervisor acts as a link between workers and management.

• Supervisor plays a key role in maintaining group unity among workers placed under his control.

• Supervisor provides good on- the –job training to the workers and employees.

• A good supervisor analyses the work performed and gives feedback to the workers.

Motivation

It refers to that process which excites people to work for the attainment of a desired objective.

Motive

A motive is an inner state that energises, activates or moves and directs behaviour towards goals.

Motivators

It refers to that technique which is employed to motivate people, such as bonus, job security, etc.

Features of Motivation

• Motivation is an internal feeling.

• Motivation produces goal directed behaviour.

• Motivation can be either positive or negative.

• Motivation is a complex process as the individuals are heterogeneous in their expectations, perceptions and reactions.

Motivation process: Motivation process is based on human needs.

Robbins and Coulter have presented the following Need-Satisfying Process:

Unsatisfied Need

Tension

Drivers

Search Behaviours

Satisfied Need

Reduction of Tension

Importance of Motivation

Improves Performance Level.
Helps to change Negative or Indifferent Attitudes of Employees.
Reduction in Employee Turnover.
Helps to Reduce Absenteeism in the organisation.
Reduction in Resistance to change.

Maslow’s Need Hierarchy Theory of Motivation

Maslow’s developed the theory of motivation on the basis of sequence of needs. According to him, a man has countless needs and they can be categorised on the basis of priority.

Basic Physiological Needs: These include primary needs Example food, hunger, thirst, sleep. Basic salary helps to satisfy these needs.

Safety or Security Needs: These needs provide security and protection from physical and emotional harm.

Affiliation or social needs: These needs refer to affection, sense of belongingness, acceptance and friendship.

Esteem Needs: These include factors such as self-respect, autonomy status, recognition and attention.

Self- Actualisation Needs: These needs include growth, self-fulfilment and achievement.

Assumpion of Maslow’s Theory

People’s behaviour, being affected by their needs.
There are many needs of people and their order or priority can be made.
Motivation ends with the satisfaction of needs.
People move to next higher need only when the lower level needs are satisfied.

Financial and Non-Financial Incentive

• Incentive: Incentive means all measures which are used to motivate people to improve performance.
Incentive is classified in to Financial and non-Financial:

• Financial Incentive: Financial incentives are those incentives which are evaluated in terms of money example Pay and allowances, Productivity-linked wage incentive, Bonus, Profit sharing, co-partnership, Retirement Benefits, Perquisites.

• Non-Financial Incentive: Non- Financial incentives are not directly related with money. These incentives help in the satisfaction of top hierarchy needs like social, Esteem and self –actualisation examples status, organisational Climate, Career Advancement Opportunity, Job Enrichment, Employee Recognition Programmes, job security, Employee participation, employee Empowerment etc.

Leadership

According to George R. Terry, ‘’ leadership is the ability of influencing people to strive willingly for mutual objectives’’.

Features of leadership

Leadership indicates ability of an individual to influence others.
Leadership tries to bring change in the behaviour of others.
Leadership indicates interpersonal relations between leaders and followers.
Leadership is exercised to achieve common goals of the organisation.
Leadership is a continuous process.

Importance of leadership

Leadership influences the behaviour of people and makes them to positively contribute their energies for the benefit of the organisation.
A leader maintains personal relations and helps followers in fulfilling their needs.
A leader can solve every type of conflict effectively under the weight of his influence.
Leader provides training to their subordinates.
Leader plays a key role in introducing required changes in the organisation.

Qualities of Good Leader

Physical features: Good physical features attract their followers immediately.
Knowledge: A person having good knowledge can instruct subordinate correctly and easily influence them.
Integrity: A leader should have integrity and honesty.
Initiative: A leader should have courage and initiative.
Communication skills: A leader should be a good communicator so, he easily explain his ideas and make people to understand his ideas.
Motivation skills: A leader should be an effective motivator.
Self Confidence: A leader should have high level of self- confidence.
Decisiveness: Leader should be decisive in managing the work.
Social skills: A leader should be sociable and friendly with his colleagues and followers.

Leadership Style

Depending on the use of authority, there are three basic styles of leadership:

Autocratic or Authoritarian leader 

The leader keeps all the authority centred in his hands and the employees have to perform the work exactly as per his hands and the employees have to perform the work exactly as per his orders.

Characteristics of autocratic leader

Centralised Authority
Single -man Decision
Wrong Belief regarding Employees
Only Downward Communication

Democratic or Participative leader

It refers to that leadership style in which the leader consults with his subordinates before making any final decision.

Characteristics of Democratic leader

Cooperative Relations
Belief in Employees
Open communication

Laissez faire or free-rein leader

It refers to that leadership style in which the leader gives his subordinate complete freedom to make decision.

Characteristics of laissez faire leader

Full faith in subordinate.
Independent Decision-making system.
Decentralisation of Authority.
Self-directed, Supervisory and Controlled.

Communication

It refers to an art of transferring facts, ideas, feelings, etc., from one person to another and making him understand them.

Elements of Communication process

Sender: sender means person who conveys his thoughts or ideas to the receiver.
Message: It is the content of ideas, feelings, suggestion, order etc., intended to be communicated.
Encoding: It refers to the process of converting the message in to communication symbols like word, picture, Symbols.
Media: Encoded message is transmitted to receiver.
Decoding: It is the process of converting encoded symbols of the sender.
Receiver: The person who receives communication of the sender.
Feedback: It includes all those actions of receiver indicating that he has received and understood message of sender.
Noise: Noise means some obstruction or hindrance to communication.

Importance of communication

Communication acts as a basis of coordination.
Communication makes possible for the smooth and unrestricted working of the enterprise.
Communication provides needed information for decision making.
Communication is essential for quick and effective performance of managerial functions.
An efficient system of communication enables management to motivate, influence and satisfy the subordinate.
Effective communication helps to influence subordinate.

Types of Communication

Formal communication
Informal communication

Formal communication

It refers to the communication within an organisation that is officially sanctioned. This communication may be take place between a superior and subordinate, a subordinate and superior or among cadre employees or managers. The communications may be oral or written but generally recorded and filed in the office.

Types of formal communication

Vertical communication
Horizontal communication

• Vertical communication: Vertical communication flows vertically example upwards and downwards.

→ Upwards communication: This flow from the subordinates to the superiors. It includes reactions, suggestions, reports, complaints, etc.

→ Downwards communication: The communication by top hierarchy with their subordinates is called downward communication. It includes orders, rules, information, policies, instructions, etc.

• Horizontal communication takes place between one division and another for example a production manager may contact marketing manager to discuss about schedule of product delivery, product design, quality etc.

The different forms of formal communication network are:

Single chain: single chain refers to the communication between superior and subordinate. All the people in an organisation from top to bottom are linked with the help of scalar chain.

Wheel communication: In this form of communication all the subordinates of a superior talk to one another through his medium.

Circular: This communication takes place among the members of a group. Every member of group can communicate with the nearest two members. In this network communication flow is slow.

Free flow: In this network each person can communicate with others freely. The communication flow is slow.

Inverted ‘V’:  In this form of communication a subordinate is permitted to communicate with the boss of his boss. In this form of communication the messages move at a rapid speed.

Informal communication

It refers to the communication within an organisation that is no officially sanctioned. This communication is based on informal relations like friendship, membership of the same club, etc.

Advantage of informal communication
Fast and effective communication
Free environment
Satisfying the social needs of the workers.
Easy solution of the difficult problems.

Limitations of informal communication
It is difficult to detect the source of such communication.
It also leads to generate rumours which are not authentic.
People’s work may also affect due to informal discussion.

Grapevine Network

It refers to the various paths through which informal communication is passed through an organisation. The Following four forms of the grapevine network are:
Single standard
Gossip Chain
Probability
Cluster

Barriers to communication 
Semantic barriers
Psychological or Emotional barriers
Organisational barriers
Personal barriers

Semantic barriers

Semantic barriers may arise due to encoding or decoding of the message into words or impressions. Some semantic barriers are

Badly expressed message:This barrier is created because of the wrong choice of words, inadequate vocabulary, usage of wrong words, omission of needed words etc.

Symbols of words with different meaning: A word may have several meanings. Receiver has to perceive one such meaning for the word used by communicator.

Faulty Translations: A manager receives much information from his superiors and subordinates and he translates it for all the employees according to their level of understanding.

Unclarified assumption: some communications may have certain assumptions which are subject to different interpretations.

Technical jargon- It is usually found that specialists use technical jargon while explaining to persons who are not specialists in the concerned field.

Body language and gesture decoding: when the communication is passed on with the help of body language and gestures, its misunderstanding hinders the proper understanding of the message.

Psychological barriers

The importance of communication depends on the mental condition of both the parties. The state of mind of both sender and receiver of communication reflects in the effective communication. Some of the psychological barriers are:

Premature evaluation: Sometimes the receiver of information tries to dig out meaning without much thinking at the time of receiving or even before receiving information, which can be wrong.

Lack of attention: When the receiver is preoccupied with some important work he/she does not listen to the message attentively.

Loss by transmission and poor retention: When communication passes through various levels, successive transmission of message results in loss of, or transmission of inaccurate information.

Distrust: Distrust between communicator and communicate acts as a barrier.

Organisational barriers

The factors related to organisation structure, authority relationships, rules and regulations may, sometimes as barriers to effective communication.

Some organisational barriers are:

Organisational policy: Some organisational policies which affect the organisational barriers are explicit or implicit, not support free flow communication and some organisation support only written form of communication etc.

Rules and regulations: Rigid rules and cumbersome procedures may be a hurdle to communication. 

Status: sometimes status of superior may create barriers of communication.

Complexity in organisation structure: The greater number of managerial levels in an organisation makes it more complex. It results in delay in communication.

Organisational facilities: if organisational facilities are smooth and sufficient than communication will be clear. In the absence of these facilities communication becomes meaningless.

Personal barriers

The barriers which are directly connected with the sender and receiver some personal barriers are:

Fear of challenge to authority: If a superior perceives that a particular communication may adversely affect his authority.

Lack of confidence of superior on his subordinates: If superiors do not have confidence on the competency of their subordinates, they may not seek their advice or opinions.

Unwillingness to communicate: Sometimes, the subordinates do not want to send any information to their superiors. When the subordinate feel that the information is of negative nature and will adversely affect them, an effort is made to conceal that information.

Lack of proper incentives: If there is no motivation or incentive for communication, subordinate may not take initiative to communicate.

Improving Communication Effectiveness

Clarify the ideas before communication.
Communicate according to the needs of receiver.
Consult others before communicating.
Be aware of languages, tone and content of message.
Convey things of help and value to listeners.
Ensure proper feedback.
Communicate for present as well as future.
Follow up communications.
Be a good listener.

Summary and Quick Revision Notes of A Triumph of Surgery NCERT Class 10th

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Study Material of Chapter 1 A Triumph of Surgery (Summary and Quick Revision Notes) Footprints without Feet Class 10

Summary of the Chapter

Mr. Pumphrey was a rich and emotional lady who has a cute pet . It was a small dog. She named it Tricky. She loved him so much that she usually overfed him. Tricki had put on a lot of weight which made him slow and pathetic. When doctor James Herriot saw the fat dog like a bloated sausage, he was very shocked. He made a plan and told Mrs. Pumphrey that Tricki needed treatment for a disease which was possible only in hospital.

The doctor knew that Mrs. Pumphrey would not be able to keep the dog on a proper diet. When the greedy dog went to the hospital he had to remain hungry if he was slow to approach for food. He was given food at fixed intervals. Soon he shed off a lot of his body weight and became quite active.

When Tricki was at home, he was pampered by Mrs. Pumphrey. He had a luxurious life when he was served with cream cake chocolate and horlicks. But when he came to the doctor he became all right. When Mrs. Pumphrey saw her active dog, she thanked the doctor and felt that it was a triumph of surgery.

Quick Revision Notes

• Tricki was a small dog. It was excessively loved by his mistress, Mrs. Pumphery.

• Tricki was greedy dog who loved food, but do no exercise. As a result he became fat

• Mrs. Pumphery believed that he became lazy due to suffering from malnutrition.

• She was a wealthy woman. She loved her dog so much.

• She also gave him some little foods between the meals to build him up, malt, cod-liver oil and a bowl of Horlicks at night. She gave him lot to eat but no exercise.

• Once he became ill & she was worried. She made a call to James Herriot who was a vet.

• James already had given suggestions regarding Tricki’s balanced diet. But she never followed it.

• He was a vet. He was shocked to see Tricki hugely fat, like a bloated sausage with a leg at each corner. He advised her to cut down on the sweet things.

• He expected call came within a few days & it happened. He was called by Mrs. Pumphery as Tricki refused to eat.

• He told her that Tricki need an immediate hospitalization for keeping under observation at his surgery for a fortnight.

• In the hospital, he gave him no food no medicine but plenty of water.

• Gradually, he mixed with other dogs & started playing with them.

• He had a lot of exercises & fun at the surgery.

• He was completely recovered & transformed into a hard muscled dog.

• James Herriot treated the dog without medicine or surgery.

• Mrs. Pumphrey was happy & filled with gratitude.

• She thanked Herriot & said it was a triumph of surgery. 

Notes of Ch 8 Controlling| Class 12th Business Studies

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Summary and Notes of Ch 8 Controlling| Class 12th Business Studies 

Meaning of Controlling

Controlling ensures that an organisation’s resources are being used effectively and efficiently for the achievement of predetermined goals.

Definition (according to Philip Kotler)

Control is the process of taking steps to bring actual results and desired results closed together.

Importance of controlling
• Accomplish organisational goals: The controlling process is implemented to take care of the plans. With the help of controlling, deviations are immediately detected and corrective action is taken for achievement of organisational goals.

• Judging accuracy of standards: An efficient control system keeps a careful check on the changes taking place in the organisation and in the environment and helps to review and revise the standards in light of such changes.

• Making efficient use of resources: Controlling makes it possible to use human and physical resources efficiently.

• Improving employee motivation: The implementation of controlling makes all the employees to work with complete dedication because they know that their work performance will be evaluated and if the progress report is satisfactory, they will have their identify established in the organisation.

• Ensuring order and discipline: controlling creates an atmosphere of order and discipline in the organisation.

• Facilitating coordination in action: Controlling provides direction to all activities and efforts for achieving organisational goals.

Limitations of Controlling
• Difficulty in setting quantitative standards: The setting of standards is possible if the nature of the work is quantitative but in respect of work which is qualitative in nature, the setting of standard is difficult.

• Little control on external factors: An enterprise cannot control on external factors such as government policies, technological changes, competition etc.

• Resistance from employees: Sometimes, employees think that they have bounded by controlling process.

• Costly affair: Control is a costly affair as it involves a lot of expenditure, time, and effort.

Relationship between Planning and Controlling
• Planning and controlling are inseparable twins of management. Once a plan becomes operational, controlling is necessary to monitor the progress and deviations. Thus planning without controlling is meaningless. Other hand controlling is blind without planning, if the predetermined standards are not set in advance, there is nothing to control.

• Planning is looking Ahead whereas Controlling is Looking Back

• Plans are prepared for future and are based on forecasts about future conditions on the contrary controlling is like a post mortem of past activities to find out deviations from the standards.

Controlling Process
• Setting Performance standards: This is a first step of controlling. Standards are those criteria on the basis of which the actual performance is measured. Standards can be set in both quantitative as well as qualitative terms.

• Quantitative standard: They are the standards which shown with the help figures and standards set in terms of cost to be incurred, revenue to be earned, product units to be produced and sold etc. all represents in terms of quantitative standards.

• Qualitative standards: Some examples of qualitative standards are increasing the morale of the employees, improving goodwill.

• Measurement of Actual performance: Once the performance standards are set, the second step is measurement of actual performance. The measurement of performance is done on the basis of predetermined standards. Some of the techniques for measurement of performance are personal observation, sample checking, Performance checking etc. Measurement of a company’s performance may involve calculation of certain ratios like gross profit ratio, net profit ratio, return on investment, etc., at periodic intervals.

• Comparing Actual Performance with standards: This step involves comparison of actual performance with the standard such comparison will reveal the deviation between actual and desired results.

• Analysing Deviations: Analysing deviations are very important for all the activities done in the organisation but deviations in key areas of business need to be attended more urgently as compared to deviations in certain insignificant areas. Critical point control and management by exception should be used by a manager in this regard.

• Critical Point Control: There is not possible to check each and every activity in an organisation. Managers should focus on key result areas of business which related to goals so, KRAs are set on critical points.

• Management by Exception: It is important principle of management control. Only significant deviations which go beyond the permissible limit should be bought to the notice of management.

• Taking Corrective Action: There is no need of any corrective action required when the deviations are within acceptable limits but when the deviations go beyond the acceptable range especially in the important areas need a special attention so that deviations do not occur again.

Techniques of Managerial Control
Managerial control classified into two categories:
• Traditional Techniques

• Modern Techniques

Traditional technique: This is old technique used by the companies for long time.

• Personal observation: This is traditional method of control. It is time consuming control and cannot effectively used in all kinds of jobs. Employees are observed by the manager personally during job hour.

• Statistical Reports: Statistical Reports provides important information to the managers regarding performance of the organisation in various areas in the form of average, percentage, ratios, correlation, etc.

• Breakeven Analysis: It is useful technique for the managers as it helps in estimating profits at different levels of activities to study the relationship between costs, volume, and profits.

• Budgetary Control: Under this technique all operations are planned in advance in the form of budgets and actual results are compared with budgetary standards.

Advantages of Budgeting
• Budgeting focuses on special and time bound target.

• Budgeting is a source of motivation to the employees.

• Budgeting helps in optimum utilisation of resources by allocating them according to the requirements of different department.

• Budgeting helps in coordination among different departments.

Modern Techniques: New techniques in the field of management which is developed by thinking and new observation of manager.

• Return on investment

• Ratio analysis

• Responsibility accounting

• Management audit

• PERT and CPM

• Management information system

• Return on investment: ROI is usually expressed as a percentage and is typically used for personal financial decisions, to compare a company’s profitability or to compare the efficiency of different investment.
ROI = Net income/Sales × sales/Total investment
Total investment (working capital + fixed capital)

• Ratio Analysis: Ration analysis refers to analysis of financial statements through computation of ratios. The most commonly used ratios are:

• Liquidity Ratios: It is calculated to determine short-term solvency of business and also determines the current position of liquid funds Example-current Ratio, quick Ratio

• Solvency ratios: It is calculated to determine the long-term solvency of business and determine the ability of a business to service its indebtedness, Examples are Debt-Equity Ratio, Proprietary Ratio, Interest Coverage Ratio.

• Profitability Ratios: It is calculated to analyse the profitability position of a business. Examples are Gross Profit Ratio, Net Profit Ratio, Return on Capital Employed.

• Turnover ratios: It is calculated to determine the efficiency of operations based on effective utilisation of resources.

• Responsibility accounting: Under this system different section, divisions, and departments of an organisation are set up as ‘Responsibility Centres.’ The head of the centre is responsible for achieving the target set for this centres.

Types of responsibility centres

• Cost Centre: Cost centre is a segment of an organisation in which managers are responsible for only cost incurred in the centre but not for the revenues.

• Revenue Centre: Revenue Centre is a segment of an organisation in which managers are responsible for only revenue generating.

• Profit Centre: Profit Centre is a segment of an organisation in which managers are responsible for both revenues and costs.

• Investment Centre: An investment centre is responsible not only for profits but also for investments.

• Management Audit: Management Audit means evaluation of the functioning, performance and effectiveness of management of an organisation. This helps to check whether management functions run smoothly or not.

The advantages of management audit are as follows:

• It helps to locate present and potential deficiencies in the performance of management functions.
• It helps to improve the control system of an organisation by continuously monitoring the performance of management.
• It improves coordination in the functioning of various departments.
• It ensures updating of existing managerial policies and strategies in the light of environmental changes.

PERT and CPM

PERT (Programme Evaluation and Review Technique) and CPM (Critical Path Method) are useful in planning and controlling task. These techniques are generally used for planning, scheduling and implementing.

Management Information System

It is a computer based information and support for effective managerial decision making. It is also helpful for control technique because it provides accurate information at right time.



NCERT Solutions for Class 10th: पाठ 6 - राजनीतिक दल लोकतान्त्रिक राजनीति

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NCERT Solutions for Class 10th: पाठ 6 - राजनीतिक दल (Rajnitik Dal) Loktantrik Rajniti

पृष्ठ संख्या:87

अभ्यास

1. लोकतंत्र में राजनीतिक दलों की विभिन्न भूमिकाओं की चर्चा करें।

उत्तर

लोकतंत्र में राजनीतिक दल विभिन्न कार्य करते हैं:

• चुनाव लड़ने के लिए उम्मीदवारों के नामों को राजनीतिक दलों द्वारा आगे किया जाता है। इन उम्मीदवारों का चयन शीर्ष नेताओं या पार्टी के सदस्यों द्वारा किया जाता है।

• पार्टियाँ मतदाताओं को उन्हें चुनने के लिए अपनी नीतियों और कार्यक्रमों प्रस्तुत करते हैं।

• राजनीतिक दल देश के लिए कानून बनाने में प्रमुख भूमिका निभाते हैं। कोई भी कानून तब तक बिल नहीं बन सकता जब तक कि बहुमत वाली दल उसका समर्थन नहीं करते।

• राजनीतिक दल सरकारें बनाते हैं और चलाते हैं।

• चुनाव हारने वाली पार्टियां विपक्ष की भूमिका निभाती हैं। पार्टी सत्ता में।

• पार्टियाँ जनता की राय को एक मूर्त रूप देती हैं।

• राजनीतिक दल सरकार और लोगों के बीच की एक महत्वपूर्ण कड़ी हैं। जनता के लिए सरकारी अधिकारी की तुलना में अपने स्थानीय नेता से संपर्क करना आसान है। स्थानीय नेता को जनता की मांग को सुनना पड़ता है अन्यथा वह अगला चुनाव हार सकता है।

2. राजनीतिक दलों के सामने क्या चुनौतियाँ है?

उत्तर

राजनीतिक दलों के सामने विभिन्न चुनौतियाँ निम्न लिखित हैं:

• आंतरिक लोकतंत्र का अभाव:
→ पार्टी के प्रत्येक सदस्य को निर्णय लेने की प्रक्रिया में भाग लेने का मौका नहीं मिलता है।
→ निर्णय लेने से पहले हर सदस्य से परामर्श नहीं किया जाता है।
→ सदस्यों के पंजीकरण का कोई उचित संगठन या नियम नहीं है।
→ सत्ता कुछ शीर्ष नेताओं के हाथों में होती है, जो सामान्य सदस्यों से परामर्श नहीं लेते हैं।
→ प्राथमिक सदस्यों को पार्टी के आंतरिक कामकाज के बारे में कोई जानकारी नहीं है।
→ वंशवादी उत्तराधिकार: कुछ शीर्ष नेताओं के हाथों में सत्ता होने के साथ ही पार्टी के सभी प्रमुख पदों पर परिवार सदस्य ही आसीन रहते हैं। ये सदस्य योग्य नहीं भी हो सकते हैं या उस पद को धारण करने की क्षमता नहीं रखते हैं।

• धन और ताकत:
→ पार्टी की छवि को सार्वजनिक करने के लिए प्रदर्शनों, सार्वजनिक बैठकों और भाषणों के आयोजन करने के लिए धन की आवश्यकता होती है। पार्टीयॉ उन उम्मीदवारों का चयन करती हैं जो पार्टी के लिए धन जुटा सके हैं और अपने पैसों से चुनाव जीत सकें।
→ कभी-कभी पार्टीयॉ अपराधिक छवि वाले उम्मीदवारों का भी चयन करती हैं क्योंकि ऐसे उम्मीदवारों का चुनाव जीतने की संभावना ज्यादा होती हैं।
→ दूसरों के लिए सार्थक विकल्प: अधिकांश राजनीतिक दलों के मूल और वैचारिक मुद्दे समान होते हैं। मतदाताओं के पास सार्थक विकल्प नहीं होते है। यहां तक कि नेता भी पार्टियों को बदलते रहते हैं इस प्रकार वे मतदाता को भ्रमित करते हैं।

3. राजनीतिक दल अपना कामकाज बेहतर ढंग से करें, इसके लिए उन्हें मजबूत बनाने के कुछ सुझाव दें।

उत्तर

राजनीतिक दलों को मजबूत करने के कुछ सुधार निम्न हैं:

• राजनीतिक दलों के आंतरिक कामकाज को नियमित करने के लिए एक कानून बनाया जाना चाहिए।

• राजनीतिक दलों को महिला उम्मीदवारों को न्यूनतम संख्या लगभग 1 / 3rd टिकट देना अनिवार्य होना करना चाहिए।

• चुनावों का खर्च राज्य वित्त पोषित होना चाहिए। सरकार को चुनाव खर्च के लिए राजनीतिक दलों को पैसा देना चाहिए।

4. राजनीतिक दल का क्या अर्थ होता है?

उत्तर

एक राजनीतिक दल उन लोगों का एक समूह है जो एक विचारधारा को मानते हैं और इस प्रकार चुनाव लड़ने और सरकार में सत्ता में हिस्सेदारी के लिए एकजुट होते हैं।

5. किसी भी राजनीतिक दल के क्या गुण होते हैं?

उत्तर

एक राजनीतिक दल के लक्षण हैं:

• एक राजनीतिक दल लोगों का एक संगठित समूह हैं जो समाज के सामूहिक हितों लिए कुछ नीतियों और कार्यक्रमों पर सहमत होते हैं।

• यह चुनावों के माध्यम से समर्थन जीतकर नीतियों को लागू करना चाहते है।

• एक राजनीतिक दल नेताओं, कार्यकर्ताओं और समर्थकों का समूह है।

• यह ऐसे लोगों का समूह है जो चुनाव लड़ने और सरकार में सत्ता पाने के लिए एकजुट होते हैं।

6. चुनाव लड़ने और सरकार में सत्ता संभालने के लिए एकजुट हुए लोगों के समूह को _____ कहते हैं।

उत्तर

राजनीतिक दल

6. सूची I के साथ सूची II (संगठनों और संघर्ष) का मिलान करें और सूचियों के नीचे दिए गए कोड का प्रयोग करके सही उत्तर का चयन करें।

सूची I
सूची II
1. कांग्रेस पार्टीक. राष्ट्रीय जनतांत्रिक गठबंधन
2. भारतीय जनता पार्टीख. राज्य पार्टी
3. भारतीय कम्युनिस्ट पार्टी (मार्क्सवादी)ग. संयुक्त प्रगतिशील गठबंधन
4. तेलुगु देशम पार्टीघ.  लेफ्ट फ्रंट


1234
(क)
(ख)
(ग)
(घ)

उत्तर


1234
(ग)


9. इनमें से कौन बहुजन समाज पार्टी के संस्थापक हैं?
(क) कांशी राम
(ख) साहू महाराज
(ग़) बी आर अम्बेडकर
(घ) जोतिबा फुले

उत्तर

(क) कांशी राम

10. भारतीय जनता पार्टी का मुख्य प्ररेक सिद्धांत क्या है?
(क) बहुजन समाज
(ख) क्रांतिकारी लोकतंत्र
(ग) समग्र मानववाद
(घ) आधुनिकता

उत्तर

(घ) आधुनिकता

Summary and Quick Revision Notes of The Thief's Story NCERT Class 10th

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Study Material of Chapter 2 The Thief's Story (Summary and Quick Revision Notes) Footprints without Feet Class 10

Summary of the Chapter

Anil was a young writer. He was living his life very carelessly. He was writing for the magazines and earning the money to run his life. One day Anil was watching the wrestling match. Hari best knew how to make unknown person a friend. He used an old formula to flatter the person. Hari stayed with Anil. Anil promised him that he would teach him how to write and add numbers. He also taught him how to cook tasty food. Daily Hari Singh was going to buy daily needs and had profit of one rupee daily. Anil knew it but he did not mind it. Both were living together happily.       
One month passed, Hari Singh did not perform his business. One day he saw Anil had bought a bundle of notes. He saw him to put them under the mattress. As Hari saw the bundle of notes, his evil spirit awakened in his mind and he decided to rob Anil that night. After taking dinner Anil slept peacefully. Hari could not sleep, he woke up. He crept to the bed and slipped his hand under the mattress. He found the notes and ran away on the road. Hari Singh made up his mind that he would directly go to the railway station and would catch the Lucknow Express. He thought that Anil would not catch him if he ran away from the city.  Hari Singh reached the railway station, Lucknow Express was about to go.

Suddenly the good spirit called him. The inner voice told him not to betray the faith of Anil. The train was moving but Hari did not dare to catch it. He was remembering the innocent face of Anil. When Hari Singh thought that what would Anil think about him. Anil would not worry about the money but he might feel bad that a man had broken his faith.  There was conflict in the mind of Hari Singh. He did not want to loose faith of Anil. Because he knew that Anil was a simple man. Moreover Anil was teaching him how to write and add numbers which could change his life. He could become a respected person in the society.

He left the railway station. He came to the maidan and sat on the bench. Just then heavy rain started. It was the month of November. Chill wind started blowing. He felt more uncomfortable as he had cheated an innocent person. His shirt and pyjamas stuck to his body because it were wet due to the rain.

Then he went to the Clock Tower to save from the rain. He sat there under the tower. Suddenly he remembered his notes. He searched for it and found that all the notes were wet. He crept again and secretly put back money under the mattress. The next day Anil woke up, prepared tea for Hari and himself. He handed over fifty rupees note to Hari and told him that he would be regularly paid now. Hari took the note and found that it was still wet. He understood that Anil knew about the last night episode.

NCERT Solutions for Class 10th: पाठ 7 - लोकतंत्र के परिणाम लोकतान्त्रिक राजनीति

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NCERT Solutions for Class 10th: पाठ 7 - लोकतंत्र के परिणाम (Loktantr ke Parinam) Loktantrik Rajniti


पृष्ठ संख्या: 99

अभ्यास

1. लोकतंत्र किस तरह उत्तरदायी, जिम्मेवार और वैध सरकार का गठन करता है?

उत्तर

• जवाबदेह सरकार: लोकतंत्र एक जवाबदेह सरकार का निर्माण करता है क्योंकि लोगों को चुनावी प्रक्रिया के माध्यम से अपने प्रतिनिधियों को चुनने का अधिकार है। ये चुने हुए प्रतिनिधि सरकार बनाते हैं और लोगों की ओर से निर्णय लेने की प्रक्रिया में भाग लेते हैं। यदि ये निर्वाचित प्रतिनिधि ठीक से काम नहीं करते हैं, तो लोगों के पास अगले चुनाव में उन्हें नहीं चुनने का मौका होता है।

• लोकतंत्र उत्तरदायी सरकार का निर्माण करता है: लोकतांत्रिक सरकारें जनता द्वारा चुनी जाती हैं ये सरकार जनता और संसद के प्रति उत्तरदायी होती हैं। ये सरकारें जनमत संग्रह को बढ़ावा देती हैं और लोगों की जरूरतों और अपेक्षाओं का ध्यान रखती हैं।

• लोकतंत्र कानूनी सरकार का निर्माण करता है: एक लोकतांत्रिक सरकार लोगों के द्वारा चुनी हुई सरकार होती है। लोग उनके द्वारा चुने गए प्रतिनिधियों द्वारा शासित होते हैं। वे ये भी मानते हैं कि लोकतंत्र उनके देश के लिए उपयुक्त है। लोकतंत्र अपनी स्वयं की सहायता के लिए उत्पन्न की गई क्षमता ही एक परिणाम है जिसे नजरअंदाज नहीं किया जा सकता है।

2. लोकतंत्र किन स्थितियों में सामाजिक विविधता को सँभालता और उनके बीच सामंजस्य बैठाता है?

उत्तर

लोकतंत्र सामाजिक विविधता को समायोजित करता है जबकी यह अच्छी तरह से समझा जाता है कि लोकतंत्र केवल बहुमत का शासन नहीं है और बहुमत का शासन केवल एक धर्म या सामाजिक समुदाय शासन नहीं होता है।

3. निम्नलिखित कथनों का पक्ष या विपक्ष में तर्क दें:

• औद्योगिक देश ही लोकतांत्रित व्यवस्था का भार उठा सकते हैं पर गरीब देशों को आर्थिक विकास करने के लिए तानाशाही चाहिए। 

• लोकतंत्र अपने नागरिकों के बीच की असमानता को कम नहीं कर सकता।

• गरीब देशों की सरकार को अपने ज्यादा संसाधन गरीबी को कम करने और आहार कपड़ा, स्वास्थ्य तथा शिक्षा पर लगाने की जगह उद्योगों और बुनियादी आर्थिक ढांचे पर खर्च करना चाहिए।

• लोकतंत्र में सभी को एक ही वोट का अधिकार होता है। इसका मतलब है कि लोकतंत्र में किसी तरह का प्रभुत्व और टकराव नहीं होता।

उत्तर

• यह कथन गलत है। उदाहरण के लिए भारत और जिम्बाब्वे को देखा जा सकता है। 1947 में भारत को तीसरे विश्व के देशों में शामिल किया गया था, लेकिन अब यह दुनिया के तेजी से बढ़ती हुई अर्थव्यवस्थाओं में से एक है। दूसरी ओर जिम्बाब्वे जो एक समृद्ध राष्ट्र था, रॉबर्ट मुगाबे के प्रगतिशील शासन के बाबजूद भारी अंतरराष्ट्रीय कर्ज़ में भाग फंस गया है।

• यह कथन गलत है। सरकार और अन्य नीतियों द्वारा लागू न्यूनतम मजदूरी अधिनियम, जो मूल्य को नियंत्रित करती है, जहाँ कृषि उत्पादक और छोटे उद्योग अपना माल बेचते हैं, जिससे देश की प्रति व्यक्ति आय को बढ़ाने में मदद की है इसने नागरिकों को अधिक समृद्ध बनाया गया है।

• गरीब देशों की सरकारें को गरीबी उन्मूलन, स्वास्थ्य, शिक्षा पर कम और उद्योगों और बुनियादी ढांचे पर अधिक खर्च करते हैं। यह एक सही कदम नहीं है क्योंकि गरीब देशों में लोग स्वास्थ्य शिक्षा और सेवाओं का खर्च नहीं उठा सकते हैं।

• लोकतंत्र में सभी नागरिकों के पास एक ही वोट करने का अधिकार होता है जिसका अर्थ है कि किसी भी वर्चस्व और संघर्ष का अभाव है। यह सच नहीं है क्योंकि संघर्ष को केवल एक आदर्श स्थिति में ही समाप्त किया जा सकता है। हालांकि वास्तविक लोकतंत्र में हर व्यक्ति के पास एक वोट का अधिकार होता है, लेकिन लोगों के बीच विभाजन होते हैं। यही विभाजन संघर्ष का कारण बनता हैं।

4. नीचे दिए गए ब्यैारों में लोकतंत्र की चुनौतियों की पहचान करें। ये स्थितियाँ किस तरह नागरिकों के गरिमापूर्ण, सुरक्षित और शांतिपूर्ण जीवन के लिए चुनौती पेश करती हैं। लोकतंत्र को मजबूत बनाने के लिए नीतिगत / संस्थागत उपाय भी सुझाएँ:

• उच्च न्यायालय के निर्देश के बाद उड़ीसा में दलितों और गैर-दलितों के प्रवेश के लिए अलग -अलग दरवाजा रखने वाले एक मंदिर से सबको प्रवेश की अनुमति देनी पड़ी।

• भारत के विभिन्न राज्यों में बड़ी संख्या में किसान आत्महत्या कर रहे हैं।

• जम्मू-कश्मीर पुलिस द्वारा एक फर्जी मुठभेड़ में गांधार में तीन नागरिकों की हत्या के आरोप के बाद, जांच का आदेश दिए गए।

उत्तर

• पहले बयान में लोकतंत्र के लिए चुनौती यह है कि यह अपने सभी नागरिकों को उनकी जाति और धर्म के पूछे वगैर समान अधिकार प्रदान किया जाए।

• दूसरे उदाहरण में लोकतंत्र के लिए चुनौती किसानों को सब्सिडी प्रदान कर रही है जो उन्हें मुनाफा कमाने तथा जीवकोपार्जन करने का संतोषजनक स्तर प्रदान करने में मदद करेगा।

• लोकतंत्र की चुनौती यह है की सरकारी पुलिसतंत्र में लोगों के विश्वास को बनाए रखा जाए।

5. लोकतांत्रिक व्यवस्थाओं के संदर्भ में इनमें से कौन सा विचार सही है - लोकतांत्रिक व्यवस्थाओं ने सफलतापूर्वक-
क. लोगों के बीच टकराव को समाप्त कर दिया है। 
ख. लोगों के बीच की आर्थिक असमानताएँ समाप्त कर दी हैं। 
ग. हाशिए के समूहों से कैसा व्यवहार हो, इस बारे में सारे मतभेद मिटा दिए हैं।  
घ. राजनीतिक गैर बराबरी के विचार को समाप्त कर दिया है।

उत्तर

घ. राजनीतिक गैर बराबरी के विचार को समाप्त कर दिया है।

6. लोकतंत्र के मुल्यांकन के लिहाज से इनमें कोई एक चीज लोकतांत्रिक व्यवस्थाओं के अनुरूप नहीं है। उसे चुनें-
क. स्वतंत्र और निष्पक्ष चुनाव
ख. व्यक्ति की गरिमा
ग. बहुमत का शासन
घ. कानून के समक्ष समानता

उत्तर

ग. बहुमत का शासन

7. लोकतांत्रिक व्यवस्था के राजनीतिक और सामाजिक असमानताओं के बारे में किए गए अध्ययन बताते हैं कि –
क. लोकतंत्र और विकास साथ-साथ ही चलते हैं। 
ख. लोकतांत्रिक व्यवस्था में असमानताएँ बनी रहती है। 
ग. तानाशाही में असमानताएँ नहीं होती है।  
घ. तानाशाहीयोँ लोकतंत्र से बेहतर साबित हुई है।

उत्तर

ख. लोकतांत्रिक व्यवस्था में असमानताएँ बनी रहती है। 


Summary and Quick Revision Notes of Midnight Visitor NCERT Class 10th

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Study Material of Chapter 3 Midnight Visitor (Summary and Quick Revision Notes) Footprints without Feet Class 10

Summary of the Chapter

Fowler is surprised to see a secret agent Ausable who is too fat to be a secret agent. Ausable tells him that he was going to get an important paper for which many men have risked their lives. When both of them reach Ausable’s room.

Fowler is scared to see a man standing in the room.Max who is tall and thin man and is holding an automatic pistol in his hand. He had entered his room by using a key to take the report concerning a new missile. Ausable ,sensing the danger, fabricated a story about the non-existent balcony which Max believed to be true.

Ausable complained that it was due to the balcony that somebody had entered his room the second time. After sometime there was knocking at the door. Ausable again befooled Max by saying that it was the police who wanted to come inside to provide him protection. Max wanted to run away to avoid the police and jumps to his death into that non-existent balcony.

Quick Revision Notes

• Ausable was a secret agent but he didn’t look like that . He was very fat but not much tall but he is much alert in his mind.

• Ausable had a room on the sixth and top floor of a French Hotel.

• Fowler was a writer. Ausable told him that he would get an important report that night concerning some new missiles. This report could change the course of history.

• Fowler saw Max, another secret agent who threatens Fowler with a pistol demanding the report.

• Ausable handled Max cleverly. He told Max that he would complain to the hotel authorities about the balcony Which should be closed immediately.

• There was a loud knocking at the door. Ausable smiled and told that that was the police.

• Max got nervous. His face was black with anger. He asked Ausable to send the police back.In the meantime he would go and wait on the balcony.

• Max jumped into the balcony. In this way Ausable got rid of Max.

Summary and Quick Revision Notes of Mijbil The Otter NCERT Class 10th

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Study Material of Mijbil The Otter (Summary, Quick Revision Notes and Word Meanings) First Flight Class 10

Summary of the Chapter

After the death of the dog, the author thought to have another pet. Early in 1956, he travelled to Southern Iraq. He saw there some Arab people having an otter. Then, he also thought of having an otter. He told this to his friend. His mail was due; therefore, with a friend he went to Basra to receive his mail. His friend collected his mail and went away. After he had left, he received a sack in which there was something. The sack was for the narrator and there was an otter in it. The narrator christened it, Mijbil. First the otter slept on the floor but soon he entered the bed till the servant bought tea. When it went to bathroom it plunged and rolled in the bath tub joyfully. The narrator was extremely surprised when he found it struggling with the water tap. It had learnt how to turn on the tap. It spent most of its time playing with the rubber ball and marbles.

He was staying at Basra while he had to move to England and then to Camusfearna. But the problem was that some of the airlines did not allow transporting animals. Therefore, the narrator had to choose a different flight that allowed animals on board. As a result, Mijbil was packed in a box of its size. Then the narrator went for the meals. When he returned to his room, he noticed blood coming out from the air holes. He got frightened. He hurriedly opened it and saw that Mij was almost unconscious. He removed all the sharp edges from the box and placed it again into the box. The time was passing and he managed to hire a taxi. There were only ten minutes in his flight. So he sat at the back seat of the taxi and placed the box on his lap. Somehow he managed to catch the flight and he boarded the plane. The air hostess was somewhat friendly and she allowed the narrator to place the otter on his lap. But as soon as the narrator opened the box the otter disappeared in the plane. This frightened the passengers. But the airhostess helped him to find out Mij again.

In London people did not recognize otters. They used to make blind guesses to recognize the animal. The most surprising event was when the labourer was digging his hole in the street. On seeing the animal, he placed down his tools and when the narrator neared him, he shouted, what is that supposed to be.

Quick Revision Notes

• In the beginning of 1956, the author was in Iraq. One day on the way to Basra, he casually mentioned to a friend that he would love to have an otter instead of a dog as a pet.

• A few days later, the author got an otter from his friend. Two Arabs brought it for him in a sack.

• The author stayed in Basra for a few days. Very soon the otter became very friendly with the author. It loved to play with water all the time. It played with a rubber ball also.

• The author named his otter Mijbil. He made for it a body-belt. He would take it on a lead to the bathroom. There the otter would go mad playing with water. It could even turn the tap and make the water flow at full pressure.

• After some days, the author was to come back to London. The transporting of Mijbil became a problem.  British airline did not permit animals on its flights. Another airline agreed to take the animal if packed in a box.

• The author made a small box for the otter. He had to face a lot of difficulty and it made him late for the plane.

• While in the plane, the otter escaped from the box. There was a lot of hue and cry. At last, the otter came back and settled on the author’s knees.

• After an eventful journey, the author and his otter at last reached London where he lived in a flat.

• The otter spent most of its time playing with its toys. Sometimes the author took it out for a walk. He would take it on a lead as if it were a dog.

• Opposite to the author’s flat, there was a primary school that had a low outer wall about thirty yards long. The otter would jump on to it and go running all the length of the wall.

• Different people made different guesses as to what animal it was. They would say it was a baby seal, squirrel, a walrus, a hippo, a beaver, a bear cub or even a leopard with spots.

• Very few Londoners had ever seen an otter. They were filled with surprise on seeing such a strange animal.

• One day a labourer was digging a hole in the street. Looking at the author’s otter, he exclaimed, “Here, Mister, what is that supposed to be?”

Summary and Quick Revision Notes of Madam Rides the Bus NCERT Class 10th

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Study Material of Madam Rides the Bus (Summary, Quick Revision Notes and Word Meanings) First Flight Class 10

Summary of the Chapter

This is a sensitive story of an eight year old girl’s whose name is Valliammai. It was story of her first bus journey into the world outside her village. The girl Valli, at a very tender age, tries to understand the mystery of life and death.  The outside world for Valli is charming and fascinating but mysterious. She longs to experience it by herself. 

The talks of the village people about the town added fuel to the fire. She decides to go to the town all by herself without anybody’s support. She asked the bus conductor to take her to the town .She herself paid her fare. She wanted to devour everything with her eyes. She saw the canal, palm tree, grass land, distant mountain and the blue sky. She also saw great stretch of green field as far as the eye could see. 

She was overjoyed when she saw a cow running with her raised tail on the road ahead of the bus. While returning she noticed that the body of the same cow was crushed and bled. She was moved from within. Perhaps she was trying to understand the meaning of life and death in her own terms.  She returned home in time.  None of the family members could know her adventurous journey.


Quick Revision Notes

• The story is about an eight year girl named Valliammai. She was very curious to know about things.

• Her favourite pastime was to stand at the front doorway of her house and see what was happening in the street outside.


• She would watch the bus that passed every half an hour from her village to the nearest town.

She developed a desire to ride the bus. This became her deepest desire.

• Valli found out the details of the bus journey by listening carefully to the conversations between her neighbours and regular bus users.


• She came to know that the town was just six miles from her village and the fare was thirty paise one way. The trip took forty-five minutes.


• Valli planned her visit to the town. She saved sixty paise for the fare. Finally she took the one o’clock bus to the town.


• The conductor was a jolly short of person. He amused Valli with her light hearted remarks. He calls her MADAM by way of joke.


• Valli was very happy to have got into the bus. She saw outside through the window. She could see t6he canal, the palm trees, grassland, distant mountains and the blue sky.


• She met some passengers in the bus. She got annoyed when an elderly man called her a child. She disliked the elderly woman for her shabby look and didn’t prefer to talk to her.


• On the way to the town, Valli saw a frightened cow running right in front of the bus. She clapped gleefully as the cow ran faster.


• Valli did not get off the bus at the town. She did not want to go to the stall and have a drink because she had no money. She also declined the offer of a cold drink by the conductor. It tells u that she is a self-respecting girl and can overcome temptation.


• On the return journey, she saw the same cow lying dead by the roadside. This unpleasant sight made her very sad.


• She was a sensitive girl.


• The bus reached the village at three forty. She got down the bus and reached her home. Her mother did not come to know about her journey.

Summary and Quick Revision Notes of Sermon at Benares NCERT Class 10th

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Study Material of Sermon at Benares (Summary, Quick Revision Notes and Word Meanings) First Flight Class 10

Summary of the Chapter

Sermon is a religious talk delivered by a prophet or Saint. Here we have the journey of Goutam Buddha from prince hood to his saintly life. He left the palace at the age of 25, after seeing the sufferings of the world, to seek enlightenment. He wandered for seven years, here and there, and under a peepal tree at Bodhgaya he got it. His first sermon was delivered at Benaras as it was considered to be the holiest place because of the river Ganga.


He thinks that he who seeks peace should draw out the arrow of lamentation, complaint and grief. He who has drawn out the arrow has become composed, and will obtain peace of mind; he who has overcome all such circumstances will be free from sorrow and be blessed.


Kisa Gautami


Kisa Gautami was grieving over the death of her son. She moved from door to door and at last came to Buddha. She made him a humble request to make her son alive. Buddha said he would do but he asked a handful of mustard seeds. He further commanded it must be taken from a house where no one had lost a child, husband, parent or friend.


She went from house to house but was unable to find one where nobody had died. She was tired and hopeless and sat down at the wayside watching the light of the city as they flickered up. And she realised that these lives flicker up for some time and are extinguished again.


This way she was taught that the lives of mortals in this world are troubled and brief and there is no means by which one can avoid deaths. As all earthen vessels made by the potter are being broken, so is the life of mortals. Death is inevitable.



Quick Revision Notes

• This lesson tells us about the life of Gautama Buddha, who was born in a royal family as Siddhartha.

• Once he saw a funeral processing, and monk begging for the alms.


• These sights moved them a lot and he decided to become a monk and started moving in search of enlightenment.


• He started meditation under a peepal tree and after seven days he got enlightenment and he became known as the Buddha (the Awakened or the Enlightened).


• He preached his first sermon at Benares.


• Once a woman came to him requesting to bring her dead son to life.


• Gautama Buddha asked the lady to bring handful of mustard seeds from the house were there had been no death.


• The lady moved from one house to another but she could not find a single house where no one has lost a child, husband, parents or friend.


• Then she came to know that death common to all and is the ultimate truth.

Summary and Quick Revision Notes of The Proposal NCERT Class 10th

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Study Material of The Proposal (Summary, Quick Revision Notes and Word Meanings) First Flight Class 10

Summary of the Chapter

This story is a drama or play between three characters. They are Stepan Stepanovitch Chubukov who is a landowner, her daughter Natalya Stepanovna who is twenty-five years old and Ivan Vassilevitch Lomov who is a neighbour Chubukov. He is a large and hearty, but very suspicious, landowner.


Lomov enters into the house of Chubukov’s. Chubukov meets him. Chubukov is extremely happy to meet him. He asks him to sit down. He also asks him where he is going in the evening dress.
Lomov tells him that he has come to see him with a request. He wants to say but gets excited. Chubukov feels that he has come to borrow money. Lomov starts speaking. But he talks of this thing or that thing. At last he says that he has come to ask Natalya’s hand. Chubukov is greatly excited to hear it.

Chubukov embraces  and kisses Lomov for it. He says that he always wanted that. Lomov asks him if he should think that he gives his consent. Chubukov okays it. He tells him that Natalya also is in love with him.

Lomov trembles due to great excitement. He says that if he looks for an ideal love he would never get married. He gets cold. He feels that Natalya is a good housekeeper. She is beautiful and well-educated. He is already 35. He should lead a quiet and regular life. But he now has palpitations. He starts jumping like a mad person.

Natalya enters. She asks him why he is in the evening dress. Is he going to a ball?
Lomov tries to tell her the purpose behind the visit. But he  is off the point. He tells that he has known her family for long. He also tells how he inherited his land and how he respects Natalya’s father . He tells her  hat his Oxen Meadows touch Natalya’s birch woods. And over this issue they fight verbally like bull dogs.

Natalya refuses Lomov’s claim. Lomov offers to make a present to them to Natalya. Natalya gets angry. She comes to a low level. She starts accusing Lomov. They start shouting at each other.
Chubukov enters. Natalya asks him to tell Lomov that Oxen Meadows are theirs. Lomov refuses this. Chubukov clarifies that by shouting Lomov won’t prove the ownership. He accuses Lomov of speaking disrespectfully as he is twice his age. Lomov adds that good neighbours don’t behave like that. He calls Chubukov a land grabber.

Lomov threatens to take Chubukov to courts. They exchange abuses calling that Lomov’s grandfather was a drunkard. His younger aunt Nastasya ran away with an architect. Lomov wants to say something. But he feels that he is dying.

Natalya calls Lomov ‘a rascal’. Chubukov calls him the villain and the scare crow. He calls  him a monster who has the courage to propose.

Hearing ‘propose’ Natalya asks what ‘proposal’. Chubukov tells her that Lomov had come to propose her for marriage. She starts weeping. She calls Chubukov to bring him back at once. She is in hysterics. He laments that it is a great burden to be  a father of a grown up daughter.
Lomov enters. He has palpitating heart. Natalya begs to be excused. She tells him that the Meadows are his. Their talk now centers on dogs. Lomov tells Natalya that his best dog Guess costs him 125 roubles. Natalya calls it too much as her father gave 85 roubles for his Squeezer. Squeezer is better than his dog. Lomov refutes it. He states that his lower jaw is shorter than the  upper. Natalya defends saying that their Squeezer is of the finest pedigree.

Both Lomov and Natalya start fighting over their dogs. Lomov calls his Guess better. Natalya calls hers better.  Lomov’s heart gets palpitating. He says that his heart Is going to pieces. Chubukov enters. He asks what the matter is. Chubukov also adds that Lomov’s dog Guess is old and short.

Lomov cites facts for his dog’s superiority. He cites the dog race with the count’s dog. In that Squeezer was left behind. Dogs ran but Squeezer ran after a sheep. Lomov speaks about the condition of his heart. Natalya asks him what sort of hunter he is. He should go to the kitchen and not go after foxes.

Chubukov cites with Natalya. He adds that Lomov should sit at home. He changes the subject to avoid losing his temper. Lomov and he exchange abuses calling ‘intriguer’, ‘pup’, ‘rat’, etc. Lomov tells that Chubukov’s late wife beat him. He falls down.

Natalya asks her father what has happened to Lomov. Chubukov also feels sick as he can’t breathe. Chubukov asks what the matter is. Natalya says that Lomov is ‘dead’. At this Chubukov calls for water and a doctor.

Chubukov starts accusing himself. He calls himself the most unhappy of men. He demands for a knife or a pistol. Lomov is reviving.


Lomov says he sees stars. He asks where he is. Chubukov asks him to hurry up and get married. Natalya is also willing to marry him. Chubukov asks him to kiss each other. Lomov asks whom he should kiss. He then says that he understands. Natalya is also happy. Chubukov feels that a weight has come off his shoulders. He offers some Champaign.


Quick Revision Notes

• Lomov went to Chubukov’s house.

• Lomov tells him the purpose of his visit.


• Chubukov agreed when Lomov tells the purpose.


• Lomov thinks of Natalya as his own life.


• Natalya and Lomov together talk.


• Lomov starts talking of his land.


• Lomov explains the ownership.


• Argument continues.


• Shouting starts.


• Chubukov sides with Natalya.


• Abuses exchanged.


• Accusation exchanged.


• Chubukov tells the purpose behind Lomov’s  visit.


• Fighting over dogs.


• Fighting continues.


• Personal accusation


• Lomov becomes unconscious.


• Chubukov gives her daughter’s hand to Lomov.

R.D. Sharma Solutions Class 10th: Ch 3 Pair of Linear Equations in Two Variables MCQ's

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Chapter 3 Pair of Linear Equations in Two Variables R.D. Sharma Solutions for Class 10th Math MCQ's

Multiple Choice Questions

1. The value of k for which the system of equations has a unique solution, is
kx − y = 2
6x − 2y = 3
(a) = 3
(b) ≠ 3
(c) ≠ 0
(d) = 0

Solution

The given system of equation are 
kx – y = 2 
6x – 2y = 3 
a1/a2 ≠ b1/b2 for unique solution 
Here a1 = k, a2 = 6, b1 = -1, b2 = -2 
k/6 ≠ -1/-2 
By cross multiply we get 
2k ≠ 6 
k ≠ 6/2 
k ≠ 3 
Hence, the correct choice is b . 

2. The value of k for which the system, of equations has infinite number of solutions, is
2x + 3y = 5
4x + ky = 10
(a) 1
(b) 3
(c) 6
(d) 0

Solution

The given system of equations are
2x + 3y = 5
4x + ky = 10
For the equation to have infinite number of solutions a1/a2 = b1/b2 = c1/c2
Here, a1 = 2, a2 = 4, b1 = 3, b2 = k
Therefore 2/4 = 3/k = 5/10
By cross multiplication of a1,a2 = b1/b2 we get ,
2/4 = 3/k
2k = 12
k = 12/2
k = 6
And
b1/b2 = c1/c2
3/k  = 5/10
30 = 5k
30/5 = k
6 = k
Therefore the value of k is 6
Hence the correct choice is c . 

3. The value of k for which the system of equations x + 2y - 3 = 0 and 5x + ky + 7 = 0 has no solution, is 
(a) 10
(b) 6
(c) 3
(d) 1

Solution


The given system of equations are
x + 2y – 3 = 0 
5x + ky + 7 = 0 
For the equations to have no solutions, 
a1/a2 = b1/b2 ≠ c1/c2 
1/5 = 2/k = -3/7 
If we take 
a1a2 = b1/b2 
1/5 = 2/k 
Therefore te value of k is 10 
Hence , correct choice is a .

4. The value of k for which the system of equations 3x + 5y = 0 and kx + 10y = 0 has non-zero solution, is
(a) 0
(b) 2
(c) 6
(d) 8 

Solution

The given system of equations are,
3x + 5y = 0
kx + 10y = 0
Here a1 = 3, a2 = k, b1 = 5, b2 = 10
a1/a2 = b1/b ≠ 0
3/k = 5/10 ≠ 0
By cross multiply we get
30 = 5k
30/5 = k
6 = k
Therefore the value of k is 6,
Hence , the correct choice is c . 

5. If the system of equations has infinitely many solutions, then
2x + 3y = 7
(a + b)x + (2a − b)y = 21
(a) a = 1, b = 5
(b) a = 5, b = 1
(c) a = −1, b = 5
(d) a = 5, b = −1

Solution

The given systems of equations are
2x + 3y = 7
(a+b) x + (2a-b) y = 21

For the equations to have infinite number of solutions , a1/a2 = b1/b
2 = c1/c2
Here a1 = 2, a2 = (a+b), b1 = 3, b2 = 2a – b, c1 = 7, c2 = 21,
2/a+b = 3/2a-b = 7/21

Let us take a1/a2 = b1/b2
2/a+b = 3/2a-b

By cross multilication we get ,
2(2a – b) = 3(a+b)
4a – 2b = 3a + 3b
4a – 3a = 3b + 2b
a = 5b …(i)

Now take b1/b2 = c1/c2
3/2a – b = 7/21
3/2a – b = 1/3
By cross multiplication we get,
3 × 3 = 1 × 2a – b
9 = 2a – b …(ii)
Substitute a = 5b in the above equation
9 = 2 × 5b – b
9 = 10b – b
9 = 9b
9/9 = b
1 = b
Substitute b = 1 in equation (i) we get , a = 5b
a = 5 × 1
a = 5
Therefore a = 5 and b = 1
Hence, the correct choice is b .

6. If the system of equations 3x + y  = 1 and, (2k – 1) x + (k-1) y = 2k + 1 is inconsistent, then k = 1
(a) 1
(b) 0
(c) -1
(d) 2

Solution

The given system of equations is inconsistent,
3x + y = 1
(2k – 1) x + (k-1) y = 2k + 1

If the system of equations is in consistent, we have
a1b2 – a2b1 = 0

3×(k-1)-1(2k-1) = 0
3k – 3 – 2k + 1 = 0
1k – 2 = 0
1k = 2
Therefore, the value of k is 2
Hence, the correct choice is d   

7. If am ≠ bl, then the system of equations ax + by = c and, lx + my = n
(a) has a unique solution
(b) has no solution
(c) has infinitely many solutions
(d) may or may not have a solution

Solution

Given am ≠ bl , the system of equation has
ax + by = c
lx + my = n
We know that intersecting lines have unique solution a1/a2 ≠ b1/b2
a1 × b2 = a2 × b1
Here a1 = a, a2 = 1, b1 = b, b2 = m
a/l ≠ b/m
a × m ≠ l×b
Therefore intersecting  lines, have unique solution
Hence, the correct choice is a .

8. If the system of equations
2x+ 3y = 7
2ax + (a+b)y = 28
has infinitely many solutions , then
(a) a = 2b
(b) b = 2a
(c) a + 2b = 0
(d) 2a + b = 0

Solution

Given the systems of equations are
2x + 3y = 7
2ax + (a+b)y = 28
For the equations to have infinite number of solutions ,
a1/a2 = b1/b2 = c1/c2
a1 = 2, a2 = 2a , b1 = 3, b2 = a + b
2/2a = 3/a+b = 7/28
By cross multiplication we have
2/2a = 3/a+b
2(a+b) = 2a(3)
2a + 2b = 6a
2b = 6a – 2a
2b = 4a
Divide both sides by 2. We get b = 21
Hence, the correct choice is b .


9. The value of k for which the system of equations
 x + 2y = 5
3x + ky + 15 = 0
has no solution is
(a) 6
(b) -6
(c) 3/2
(d) None of these 

Solution

The given system of equation is
x + 2y = 5
3x + ky + 15 = 0
If a1a2 = b1/b2 ≠ c1/c2 then the equation have no solution .
1/3 = 2/k = -5/15
By cross multiply we get
k × 1 = 3 × 2
k = 6
Hence, the correct choice  is a . 

10. If 2x – 3y = 7 and (a+b) x – (a+b-3)y = 4a + b represent coincident lines, then a and b satisfy the equation
(a) a+5b = 0
(b) 5a + b = 0
(c)  a – 5b = 0
(d) 5a – b = 0
Solution

The given system of equations are
2x – 3y = 7
(a+b) x – (a+b-3)y = 4a + b
For coincident lines, infinite number of solution
a1a2 = b1/b2 = c1c2
 2/(a+b) = -3/-(a+b-3) = 7/4a + b
⇒ 2/(a+b) = 3(a+b-3) = 7/(4a+b)
⇒ 2(a+b-3) = 3(a+b)
⇒ 2a + 2b – 6 = 3a + 3b
⇒ 2a + 2b – 3a – 3b = 6
⇒ - a – b = 6
⇒ a + b = -6 …(i)
3(4a + b) = 7 (a+b-3)
⇒ 12a + 3b = 7a + 7b – 21
⇒ 5a – 4b = -21 …(ii)
Multiply equation (i) by 5, we get 5a + 5b = -30 …(iii)
Subtract (ii) from (iii),
(5a + 5b) – (5a – 4b) = -30 + 21
⇒ 5a + 5b – 5a + 4b = -9
⇒ 9b = -9
⇒ b = -1
Substitute b = -1 in equation (1)
a + (-1) = -6
⇒ a = -6 + 1 = -5
Option A :
a + 5b = 0
-5 + 5(-1) = -5-5 = -10 ≠ 0
 Option B :
5a + b = 0
5(-5) + (-1) = - 25 – 1 = -26 ≠ 0
Option C :
a –b = 0
-5-(-1) = -4 ≠ 0
None of the option satisfies the values .

11. If a pair of linear equations in two variables is consistent, then the lines represented by two equations are
(a) intersecting
(b) parallel
(c) always coincident
(d) intersecting or coincident

Solution

If a pair of linear equations in two variables is consistent, then its solution exists.
The lines represented by the equations are either intersecting or coincident.
Hence, the correct choice is d .

12. The area of the triangle formed by the line x/a + y/b = 1 with the coordinate axes is
(a) ab
(b) 2ab
(c) 1/2 ab
(d) 1/4 ab

Solution 

Given the area of the triangle formed by the line x/a + y/b = 1
If in the equation x/a + y/b = 1 either A and B approaches infinity, the line become parallel to either x axis or y axis respectively ,
Therefore
x = a;
y = b
Area of triangle = 1/2 × x × y = 1/2 × a × b
Hence , the correct choice is c .     

13. The area of the triangle formed by the lines y = x, x = 6 and y = 0 is
(a) 36 sq. units
(b) 18 sq. units
(c) 9 sq. units
(d) 72 sq. units

Solution

Given x = 6 , y = 0 and x = y
We have plotting points as (6,0)(0,0)(6,6) when x = y
Therefore , area of ΔABC = 1/2 (Base × Height) = 1/2 (CA × AB) = 1/2 (6×6) = 1/2 × 36 = 18
Area of triangle ABC is 18 square units
Hence, the correct choice is b .

14. If the system of equations 2x + 3y = 5, 4x + ky = 10 has infinitely many solutions, then k =
(a) 1
(b) 1/2
(c) 3
(d) 6

Solution

The given system of equations
2x + 3y = 5
4x + ky = 10
a1a2 = 2/4,  b1/b2 = 3/k , c1c2 = 5/10
For the equations to have infinite number of solutions
a1a2 = b1b2 = c1c2
2/4 = 3/k = 5/10
If we take
2/4 = 3/4
2k = 12
k = 12/2
k = 6
And
3/k = 5/10
30 = 5k
30/5 = k
6 = k
Therefore, the value of k is 6 .
Hence,  the  correct choice is d .

15. If the system of equations kx − 5y = 2, 6x + 2y = 7 has no solution, then k =
(a) −10
(b) −5
(c) −6
(d) −15

Solution

The given systems of equations are 
kx – 5y = 2 
6x + 2y = 7 
a1a2 = b1b2 ≠ c1/c2 
Here a1 = k , a2 = 6, b1 = -5 , b2 = 2 
k/6 = -5/2 
2k = -30 
k = -30/2 
k = -15 
Hence , the correct choice is d .

16. The area of the triangle formed by the lines x = 3, y = 4 and x = y is
(a) 1/2 sq. unit
(b) 1 sq. unit
(c) 2 sq . unit
(d) None of these

Solution

Given  x = 3, y = 4 and x = y
We have plotting points  as (3,4)(3,3)(4,4) when x = y


Therefore,  area of  ΔABC = 1/2 (Base × Height) = 1/2 (AB × AC) = 1/2 (1×1) = 1/2
Area of triangle ABC is 1/2 square units 
Hence, the correct choice is a .

17. The area of the triangle formed by the lines 2x + 3y = 12, x − y − 1 = 0 and x = 0 (as shown in Fig. 3.23), is
(a) 7 sq. units
(b) 7.5 sq. units
(c) 6.5 sq. units
(d) 6 sq. units 

Solution

Given, 2x + 3y = 12, x – y – 1 = 0 and x = 0
If x = 0 we have plotting points as D(0,-1) B(0,4) P(3,2) 



Therefore, area of CBPD = 1/2 (Base × Height) = 1/2 (BP×PM) = 1/2 (5×3) = 1/2(15) = 7.5
Area of triangle ABC is 7.5 square units
Hence, the correct choice is b. 

18. The sum of the digits of a two digit number is 9. If 27 is added to it, the digits of the number get reversed . The number is
(a) 25
(b) 72
(c) 63
(d) 36

Solution

Let the digits at the tens and the ones place be x and y, respectively. So, the two digit number is 10x + y.
Now,
x + y = 9         .....(i)
Also,
10x + y + 27 = 10y + x
 9x − 9y = −27
 x − y = −3            .....(ii)
Adding (i) and (ii), we get
2x = 6
 x = 3
Putting x = 3 in (i), we get
3 + y = 9
 y = 6
Thus, the required number is 10 × 3 + 6 = 36.
Hence, the correct answer is option (d).

19. If x = a, y = b is the solution of the systems of equations x – y = 2 and x + y = 4 , then the values of a and b are respectively
(a) 3 and 1
(b) 3 and 5
( c) 5 and 3
(d) -1 and -3 


Solution

The given equation are
x – y = 2 ….(1)
x + y = 4 ….(2)
Adding (1) and (2) , we get
2x = 6
⇒ x = 3

Putting x = 3 in (1) , we get

3 + y = 4

⇒ y = 1
So, x = a = 3 and y = 1.


20. For what the value k, do the equation 3x – y + 8 = 0 and 6x – ky + 16 = represent coincident lines ?

Solution

The given system of equations  is
3x – y + 8 = 0
6x – ky + 16 = 0
We know that the lines
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
are coinciden if
a1/a2 = b1/b2 = c1/c2
 3/6 = -1/-k = 8/16
⇒ 1/2 = 1/k = 1/2
⇒ k = 2
Thus, the value of k = 2.
Hence the orrect answer is option c. 

21. Arun has only 1 and 2 coins with her . If the toatl number of coins that she has is 50 and the amonut of money with her is 75 , then the number of 1 and 2 coins are , respectively
(a) 35 and 15
(b) 35 and 20
(c) 15 and 35
(d) 25 and 25

Solution

Let the number of ₹1 coins be x and that of ₹2 coins be y.
Now,
Total number of coins = 50
So, x + y = 50 .....(i)
Also,
₹1 × x + ₹2 × y = ₹75
∴ x + 2y = 75 .....(ii)
Subtracting (i) from (ii), we get
y = 25
Putting y = 25 in (i), we get
x + 25 = 50
⇒ x = 25
So, the number of ₹1 coins and ₹2 coins are 25 and 25, respectively.
Hence, the correct answer is option (d).
Note: The answer given in the book does not match with the one obtained.

Notes of Ch 9 Financial Management| Class 12th Business Studies

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Summary and Notes of Ch 9 Financial Management| Class 12th Business Studies 

Meaning of Business Finance
Money required for carrying out business activities smoothly is called Business finance. Finance also helps to run day to day business expenses and purchase assets (Tangible and Intangible).

Financial Management
Financial management is concerned with optimal utilisation of finance.

Aims of Financial Management
• Financial management aims at reducing the cost of funds procured, keeping such fund under control and achieving effective expansion of such funds.

• Financial management also ensure that availability of adequate funds whenever required.

Importance of Financial Management
The financial statements such as Balance Sheet and Profit and Loss Account, reflect a firm’s financial position and its financial health. Some examples of the aspects being affected could be as under:

• The size and the composition of fixed assets of the business.

• The quantum of current assets and its break-up into cash, inventory and receivables.

• The amount of long-term and short-term funds to be used.

• Break-up of long-term financing into debt, equity etc.

• All items in the profit and loss account Example interest, Expense, Depreciation.

• The overall financial health of a business is determined by the quality of its financial management.

Objective of a financial Management
The main objective of the financial management is to maximise shareholder’s wealth. All financial decisions aim at ensuring that each decision is efficient and adds some value. Those decisions which result in increasing the share value known as healthy financial decision and those decisions which result in decline in the share price are poor financial decision.

Financial Decision
Financial decisions depend on three major issues relating to the financial operations of a firm.

• Investment Decision

• Financing Decision

• Dividend Decision

Investment Decision: The investment decision relates to how the firm’s funds invested in different assets. Investment decision can be long term or short term, a decision is long term when managers invest in a new machine to replace old ones this decision is very crucial for any business since they affect its earning capacity of a business. Short-term investment decisions are concerned with the decisions about the level of cash, inventory and receivables.

Factors affecting Capital Budgeting Decision
• Cash flows of the projects: When company takes an investment decision involving huge amount it expects to generate some cash flow.

• The rate of return: During investment time calculations are based on the expected returns from each proposal and the assessment of the risk involved.

• The investment criteria involved: It involved calculations regarding the amount of investment, Interest rate, cash flows and rate of return these terms are considered which investment decisions are taken.

Financing Decision
It refers to the determination as to how the total funds required by the business will be obtained from various long-term sources. Long –term financial sources chiefly include equity share capital, preference share capital, retained earning, debenture, long-term loan, etc.

Factors Affecting Financing Decisions
• Cost: The cost of raising fund in different sources are different, a good financial manager would normally opt for a source which is cheapest.

• Risk: The risk associated with each of the sources is different.

• Floatation Costs: If the floatation cost is higher the sources are less attractive.

• Cash Flow Position of the Company: If the cash flow position of the company is good, the payment of interest on the debt and the refund of capital can be easily made.

• Fixed Operating Costs: There are two types of costs which affect financial decision, fixed operating costs and fixed financial costs.

• Control considerations: When company issues more equity share, the more control of company goes on equity shareholders which are not good situation.

• State of Capital Market: It depends totally on choice of source of fund.

Dividend decision

The decision is that how much of the profit earned by the companies should be retained in the business and how much of the profit distributed to the shareholder.

Factors Affecting Dividend Decision:
• Amount of Earnings: The dividend is paid out of the present and reserved profits. Therefore, greater amount of total profit will ensure greater dividend.

• Stability Earnings: If company having a stable earning is in a better position to declare more Dividends.

• Stability of Dividends: Every companies follow policy of maintaining a dividend. In this condition a little change in profit should not be allowed any increase or decrease in the dividend.

• Growth Opportunities: If the companies have good growth opportunities they pay small amount as a dividend and retain more money for investment.

• Cash Flow Position: The payment of dividend involves an outflow of cash. Availability of enough cash in the company is necessary for declaration of dividend.

• Shareholders’ Preference: While declaring dividends, managements must keep in mind the preferences of the shareholders in this regard.

• Taxation policy: Generally taxation policy is depends on whether company paid less dividend and more if the company has less tax on dividend they paid more and if less tax on dividend they paid more dividend.

• Stock Market Reaction: It means that if the dividend is declared at a higher rate, it is considered to be good news so the price of share increases and market condition related to finance is also good.

• Access to capital Market: In case of need if a company can easily collect finance in the capital market, it should declare dividend at a higher rate otherwise not.

Financial Planning

It refers to the preparation of a financial blueprint of an organisation’s future operations.

Financial planning strives to achieve the following twin objectives:

• To ensure availability of funds whenever required.

• To see that the firm does not raise resources unnecessarily.

Capital Structure
Capital structure refers to the mix between owners and borrowed funds. Capital structure of a company affects both the profitability and the financial risk.

Factors affecting the choice of Capital Structure
• Cash Flow Position

• Interest Coverage Ratio (ICR)

• Debt Service Coverage Ratio

• Return on Investment

• Cost of debt

• Tax Rate

• Cost of Equity

• Floatation costs

• Risk Consideration

• Flexibility

• Control

• Regulatory Framework

• Stock Market Conditions

• Capital Structure of other companies

Fixed Capital

Fixed assets are those which remain in the business for more than one year Example: Plant and Machinery, Furniture and Fixture, Land and building etc., it also helps in to run business.

Management of Fixed Capital
Fixed capital refers to investment in long-term assets. It affects the growth, Profitability and risk of the business in the long-run. It must be financed through long-term source of capital. Investment in these assets would also include expenditure on acquisition expansion, modernisation and their replacement. These decisions include purchase of land, building, plant and machinery.

The management of fixed capital or investment or capital budgeting decisions are important for following reasons:

• These decisions have wearing on the long- term growth.

• When decide to invest in a fixed capital it involves huge amount.

• Investment decision in fixed capital involved a huge amount so, it influence the overall business risk complexion of the firm.

•These decision once taken, are not reversible without incurring heavy losses.

Working capital
• Current assets: A current asset is either cash or an asset that can be converted into cash within a year is often used to pay off current liabilities.

• Current Liabilities: Current liabilities are those payment obligations which are due for payment within one year such as bills payable, creditors, outstanding expenses and advances received from customers.

Factors affecting the Working Capital Requirements
• The requirement of working capital depends on the nature of the business whether it is manufacturing business and trading business.

• There is direct link between the working capital and the scale of operations. More working capital is required in case of big organisation while less working capital is needed in case of small organisation.

• Different phases of business cycles affect the requirement of working capital by a firm.

• Working capital also affect in case of seasonal business.

• Where period of production cycle is more than more working capital needed on the contrary where period of production is little, less working capital will be needed.

• Those enterprises which sell goods on cash payment basis need less working capital but those who provide credit facilities to the customer needs more working capital.

• Firms manage their operations with varied degrees of efficiency.

NCERT Solutions of Chapter 9 Financial Management

Extra Questions of पाठ - 2 दुःख का अधिकार Class 9th Hindi Sparsh

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Extra Questions of पाठ - 2 दुःख का अधिकार Class 9th Hindi Sparsh Important Questions Answer Included

अर्थग्रहण संबंधी प्रश्नोत्तर -

1. मनुष्यों की पोशाकें उन्हें विभिन्न श्रेणियों में बाँट देती हैं। प्रायः पोशाक ही समाज में मनुष्य का अधिकार और उसका दर्जा निश्चित करती है। वह हमारे लिए अनेक बंद दरवाजे खोल देती है, परंतु कभी ऐसी भी परिस्थिति आ जाती है कि हम ज़रा नीचे झुककर समाज की निचली श्रेणियों की अनुभूति को समझना चाहते हैं। उस समय यह पोशाक ही बंधन और अड़चन बन जाती है। जैसे वायु की लहरें कटी हुई पतंग को सहसा भूमि पर नहीं गिर जाने देतीं, उसी तरह खास परिस्थितियों में हमारी पोशाक हमें झुक सकने से रोके रहती है।

प्रश्न –

1. पोशाकें किस प्रकार समाज को श्रेणियों में बाँट देती हैं ? 
2. पोशाक हमारे लिए कब बन्धन और अड़चन बन जाती है?
3. लेखक ने वायु की लहरें और पोशाक में क्या समानता बताई है?
4. पोशाक समाज में मनुष्य का क्या निश्चित करती है?

उत्तर -

1. पोशाकें समाज को विभिन्न श्रेणियों में बाँट देती हैं।
2. जब हम नीचे झुककर समाज की निचली श्रेणियों की अनुभवों को समझना चाहते हैं।
3. वायु की लहरें पतंग को सहसा भूमि पर गिरने से रोकती हैं और और पोशाक व्यक्ति को ख़ास परिस्थितयों में झुकने से रोकती हैं|
4. पोशाक समाज में मनुष्य का अधिकार और उसका दर्जा निश्चित करती है।

2. बाज़ार में, फुटपाथ पर कुछ खरबूज़ डलिया में और कुछ ज़मीन पर बिक्री के लिए रखे जान पड़ते थे।खरबूजों के समीप एक अधेड़ उम्र की औरत बैठी रो रही थी। खरबूजे बिक्री के लिए थे, परंतु उन्हें खरीदने के लिए कोई कैसे आगे बढ़ता? खरबूजों को बेचनेवाली तो कपड़े से मुँह छिपाए सिर को घुटनों पर रखे फफक-फफककर रो रही थी। 
पड़ोस की दुकानों के तख्तों पर बैठे या बाजार में खड़े लोग घृणा से उसी स्त्री के संबंध में बात कर रहे थे। उस स्त्री का रोना देखकर मन में एक व्यथा-सी उठीं, पर उसके रोने का कारण जानने का उपाय क्या था? फुटपाथ पर उसके समीप बैठ सकने में मेरी पोशाक ही व्यवधान बन खड़ी हो गई।

प्रश्न -

1. कोई खरबूजों को खरीदने के लिए आगे क्यों नहीं बढ़ रहा था? 
2. रोती हुई स्त्री को देखकर लेखक को कैसा लगा?
3. लेखक स्त्री के रोने का कारण क्यों न जान सका? 

उत्तर -

1. खरबूजे बेचनेवाली कपड़े में मुँह छिपाए, सिर को घुटनों पर रखे फफक-फफक्कर रो रही थी।
2. रोती हुई स्त्री को देखकर लेखक का मन व्यथित हो उठा और वे उसके रोने का करण जानने को व्याकुल हो उठे|
3. लेखक की सभ्य पोशाक उन्हें फूटपाथ पर स्त्री के समीप बैठने से रोक रही थी इस कारण वे उसके रोने का कारण नहीं जान सके|

लघुउत्तरीय प्रश्नोत्तर -

1. समाज में पोशाक से व्यक्ति का दर्जा क्यों तय किया जाता है? 

उत्तर

समाज में पोशाक से व्यक्ति का दर्जा इसलिए तय किया जाता है क्योंकि हर व्यक्ति अपनी आर्थिक स्थिति के अनुसार अपनी पोशाक का चयन करता है। जिन लोगों की आय कम है वे साधारण कपड़े पहनते हैं और जिनकी आय अधिक हैं वे महँगे कपड़े पहनते हैं।

2. सूतक क्या होता है? उसका दूसरों पर क्या प्रभाव पड़ता है?

उत्तर

किसी व्यक्ति के मृत्यु होने के बाद तेरह दिनों तक घर में सूतक होता है| इस अवधि में घर अशुद्ध माना जाता है। लोग धार्मिक कार्यों में हिस्सा नहीं लेते हैं और घर में रहकर मृत्यु का शोक मनाते हैं|

3. पड़ोस की दुकानों के लोग उस स्त्री की तरफ़ घृणा से क्यों देख रहे थे?

उत्तर

पड़ोस की दुकानों के लोग के अनुसार बुढ़िया को घर पर रहकर अपने बेटे के मृत्यु का शोक मानना चाहिए था| बाज़ार में आकर काम शुरू करना नहीं चाहिए था| उनकी नज़र में ऐसा कर बुढ़िया खुद का धर्म भ्रष्ट करने के साथ-साथ औरों का भी धर्म भ्रष्ट करने का काम कर रही थी इसलिए वे लोग उस स्त्री की तरफ़ घृणा से देख रहे थे|

4. बुढ़िया और संभ्रांत महिला का दुख समान होते हुए भी भिन्न कैसे था?

उत्तर 

दोनों का सुख समान होते हुए भी भिन्न इस तरह था क्योंकि बुढ़िया गरीब थी| वह चाहकर भी अपना दुःख दिखा नहीं सकती थी| दूसरी ओर संभ्रांत महिला पैसे वाली थी। उसके साथ कई लोग थे जो दुःख के समय में उसका देखभाल कर सकते थे| 

दीर्घस्तरीय प्रश्न –

1. ‘शोक करने, गम मनाने के लिए भी सहूलियत चाहिए और... दुखी होने का भी एक अधिकार होता है। लेखक ने ये शब्द किस आधार पर कहे हैं? समझाइए।

उत्तर 

लेखक ने जब देखा कि संभ्रांत महिला के दुख में लोग शामिल हो रहे थे वहीं दूसरी ओर गरीब बूढी औरत के दुख में शामिल होने के बजाय उसे बुरा-भला कह रहे थे तो लेखक ने यह लिखा है कि दुखी होने का भी एक अधिकार होता है। दुख प्रकट करने के लिए और शोक मनाने के लिए भी मनुष्य के पास सुविधा होनी चाहिए अन्यथा वह शोक भी नहीं मना सकता| गरीब होने कि वजह से समाज उसे घृणा की दृष्टि से देखता है|




R.D. Sharma Solutions Class 10th: Ch 4 Triangles Exercise 4.1

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Chapter 4 triangles R.D. Sharma Solutions for Class 10th Math Exercise 4.1

Exercise 4.1

1. Fill in the blanks using the correct word given in brackets :
(i) All circles are ......... (congruent, similar).
(ii) All squares are ........(similar, congruent).
(iii) All .......... triangles are similar (isosceles, equilateral):
(iv) Two triangles are similar, if their corresponding angles are .......... (proportional, equal)
(v) Two triangles are similar, if their corresponding sides are ........... (proportional, equal)
(vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles are and (b) their corresponding sides are ...........(equal, proportional).


Solution

(i) All circles are similar.

(ii) All squares are similar.

(iii) All equilateral triangles are similar.

(iv) Two triangles are similar, if their corresponding angles are equal.

(v) Two triangles are similar, if their corresponding sides are proportional.

(vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles are and (b) their corresponding sides are proportional.

2. Write the truth value (T/F) of each of the following statements:
(i) Any two similar figures are congruent.
⏵False
(ii) Any two congruent figures are similar.
⏵True

(iii) Two polygons are similar, if their corresponding sides are proportional.
⏵False

(iv) Two polygons are similar, if their corresponding angles are proportional.
⏵False

(v) Two triangles are similar if their corresponding sides are proportional.
⏵True

(vi) Two triangles are similar if their corresponding angles are proportional.
⏵True

R.D. Sharma Solutions Class 10th: Ch 4 Triangles Exercise 4.2

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Chapter 4 triangles R.D. Sharma Solutions for Class 10th Math Exercise 4.2

Exercise 4.2

1. In ΔABC, D and E are points on the sides AB and AC respectively such that DE | | BC

(i) AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.
(ii) If AD/DB = 3/4 and AC = 15 cm, find AE
(iii) If AD/DB = 2/3 and AC = 18 cm, find AE
(iv) If AD = 4, AE = 8, DB = x-4, and EC = 3x – 19, find x.
(v) If AD = 8 cm, AB = 12 cm and AE = 12 cm, find CE.
(vi) If AD = 4 cm, DB = 4.5 cm and AE = 8 cm, find AC .
(vii) If AD = 2 cm, AB = 6 cm and AC = 9 cm, find AE.
(viii) If AD/BD = 4/5 and EC = 2.5 cm, find AE .
(ix) If AD = x, DB = x – 2, AE = x+2 and EC = x – 1, find the value of x.
(x) If AD = 8x – 7, DB = 5x – 3, AE = 4x – 3 and EC = (3x -1), find the value of x.
(xi) If AD = 4x – 3, AE = 8x – 7, BD = 3x – 1 and CE = 5x – 3, find the value of x.
(xii) If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75 cm, find the length of AC .


Solution

(i)


(ii)
(iii)

(iv)

(v)


(vi)


(vii)
(viii)

(ix)


(x)
(xi)


(xii)


2. In a ∆ABC, D and E are points on the sides AB and AC respectively. For each of the
following cases show that DE | | BC:
(i) AB = 2cm, AD = 8cm, AE = 12 cm and AC = l8cm.
(ii) AB = 5.6cm, AD = 1.4cm, AC = 7.2 cm and AE = 1.8 cm.
(iii) AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.
(iv) AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm.


Solution
(i)


(ii)

(iii)


(iv)

3. In a ∆ABC, P and Q are points on sides AB and AC respectively, such that PQ || BC. If AP= 2.4 cm, AQ = 2 cm, QC = 3 cm and BC = 6 cm, find AB and PQ.

Solution



4. In a ∆ABC, D and E are points on AB and AC respectively such that DE || BC. If AD = 2.4cm, AE = 3.2 cm, DE = 2cm and BC = 5 cm, find BD and CE.
Solution



5. In below Fig., state if PQ || EF.
Solution



6. M and N are points on the sides PQ and PR respectively of a ∆PQR. For each of the following cases, state whether MN || QR
(i) PM = 4cm, QM = 4.5 cm, PN = 4 cm and NR = 4.5 cm
(ii) PQ = 1.28 cm, PR = 2.56 cm, PM = 0.16 cm, PN = 0.32


Solution
(i)


(ii) For MN | | QR, by Theles theorem the required condition is :
PM/PQ = PN/PR
PM/PQ = 0.16/1.28 = (16/100)/(128/100)
= 16/128 = 1/8

PN/PR = 0.32/2.56 = 32/256 = 1/8
PM/PQ = PN/PR
Therefore MN | | QR.

7. In three line segments OA, OB, and OC, points L, M, N respectively are so chosen that LM || AB and MN || BC but neither of L, M, N nor of A, B, C are collinear. Show that LN || AC.
Solution


8. If D and E are points on sides AB and AC respectively of a ∆ABC such that DE || BC and BD = CE. Prove that ∆ABC is isosceles.

Solution

R.D. Sharma Solutions Class 10th: Ch 4 Triangles Exercise 4.3

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Chapter 4 triangles R.D. Sharma Solutions for Class 10th Math Exercise 4.3

Exercise 4.3

1. In a ∆ABC, AD is the bisector of ∠A, meeting side BC at D.


(i) If BD = 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB = l0 cm, AC =14 cm and BC =6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and 10 cm, find AB
(vi) If AB = 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AD = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC.
(viii) If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC. 


Solution


(i)

(ii)


(iii)


(iv)


(v)


(vi)


(vii)

(viii)


2. In Fig. 4.57, AE is the bisector of the exterior ∠CAD meeting BC produced in E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, and find CE . 
Solution



3. In Fig. 4.58, △ABC is a triangle such that AB/AC = BD/DC, ∠B = 70°, ∠C = 50° . Find ∠BAD.
Solution 



4. In fig. 4.59, check whether AD is the bisector of ∠A of ∆ABC in each of the following:



(i) AB = 5cm, AC = 10cm, BD = 1.5 cm and CD = 3.5 cm
(ii) AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm
(iii) AB = 8 cm, AC = 24 cm, BD = 6 cm and BC = 24cm
(iv) AB = 6 cm, AC = 8cm, BD = l.5 cm and CD = 2 cm
(v) AB = 5 cm, AC = l2 cm, BD = 2.5 cm and BC = 9cm 


Solution



5. In Fig. 4.60, AD bisects ∠A, AB = 12 cm, AC = 20 cm and BD = 5 cm, determine CD. 


Solution

It is given that AD bisects ∠A . Also, AB = 12 cm, AC = 20 cm and BD = 5 cm.
We have to find CD.
Since AD is the bisector of ∠A
Then AD/AC = BD/DC
12cm/20cm = 5cm/DC
12cm × Dc = 20cm × 5 cm
DC = 100/12 cm 
= 8.33 cm
Hence, CD = 8.33 cm

6. In △ABC (Fig., 4.59), if ∠1 = ∠2, prove that AB/AC = BD/DC.


Solution



7. D, E and F are the points on sides BC, CA and AB respectively of ∆ABC such that AD bisects ∠A, BE bisects ∠B and CF bisects ∠C. If AB = 5 cm, BC = 8 cm and CA = 4 cm.
Solution

R.D. Sharma Solutions Class 10th: Ch 4 Triangles Exercise 4.5

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Chapter 4 triangles R.D. Sharma Solutions for Class 10th Math Exercise 4.5

Exercise 4.5

1. In fig. 4.136, ∆ACB ~ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ.

Solution



2. In Fig. 4.137, AB || QR. Find the length of PB. 


Solution


3. In fig. 4.138, XY || BC. Find the length of XY .


Solution


4. In a right angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.

Solution



5. In Fig. 4.139, ∠ABC = 90° and BD ⊥ AC. If BD = 8 cm and AD = 4 cm, find CD .


Solution



6. In Fig. 4.140, ∠ABC = 90° and BD ⊥ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.

Solution



7. In Fig. 4.141, DE || BC such that AE = (1/4) AC. If AB = 6 cm, find AD .


Solution



8. In fig. 4.412, if AB ⟂ BC, DC ⟂ BC and DE ⟂ AC, prove that △CED ~ △ABC.


Solution

Given,
AB ⟂ BC
DC ⟂ BC
So, Both AB and DC are perpendicular to same line BC.
We know that, two lines, perpendicular to same line are parallel.
∴ AB | | DC
Since, AC is transverse (from diagram) (i)
Now, In △ABC and △DCE
∠ABC = ∠DCE = 90° (Given AB⟂BC)
∠BAC = ∠DCE (from i)
Therefore, by AA criteria for similarity
△CED ~ △ABC .

9. Diagonals AC and BD of trapezium ABCD with AB || DC intersect each other at the point O. Using similarity criterion for two triangles, show that OA/OC = OB/OD .

Solution

It is given that trapezium ABCD with AB | | DC.O is the point of intersection of AC and BD .

We have to prove that OA/OC = OB/OD
Now, in △AOB and △COD
∠AOB = ∠COD (Vertically opposite angles)
∠OAB = ∠OCD (Alternate angles)
∴ △AOB ~ △COD (AA Similarity)
Hence, OA/OC = OB/OD (Corresponding sides are proportional)

10. If △ABC and △AMP are two right triangles, triangles, right angled at B and M respectively such that ∠MAP = ∠BAC. Prove that
(i) △ABC ~ △AMP
(ii) CA/PA = BC/MP

Solution



(i) It is given that △ABC and △AMP are two right angle triangles,
Now, in △ABC and △AMP, we have
∠MAP = ∠BAC (Given)
∠AMP = ∠B = 90°
△ABC ~ △AMP (AA Similarity)

(ii) △ABC ~ △AMP
So, CA/PA = BC = MP (corresponding sides are proportional) .

11. A vertical stick 10 cm long casts a shadow 8 cm long. At the same time a shadow 30 m long. Determine the height of the tower.

Solution



12. In below fig., ∠A = ∠CED, Prove that ∆CAB ~ ∆CED. Also, find the value of x.


Solution



13. The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of first triangle is 9 cm, what is the corresponding side of the other triangle?

Solution



14. In ∆ABC and ∆DEF, it is being given that: AB = 5 cm, BC = 4 cm and CA = 4.2 cm; DE =10cm, EF = 8 cm and FD = 8.4 cm. If AL ⊥ BC and DM ⊥ EF, find AL: DM.

Solution



15. D and E are the points on the sides AB and AC respectively of a ∆ABC such that: AD = 8 cm, DB = 12 cm, AE = 6 cm and CE = 9 cm. Prove that BC = 5/2 DE.

Solution


16. D is the mid-point of side BC of a ∆ABC. AD is bisected at the point E and BE produced cuts AC at the point X. Prove that BE : EX = 3 : 1.

Solution



17. ABCD is a parallelogram and APQ is a straight line meeting BC at P and DC produced at Q. Prove that the rectangle obtained by BP and DQ is equal to the AB and BC.

Solution



18. In △ABC, AL and CM are the perpendiculars from the vertices A and C to BC and AB respectively . AL and CM intersect at O, prove that :
(i) △OMA and △OLC
(ii) OA/OC = OM/OL

Solution



19. ABCD is a quadrilateral in which AD = BC. If P, Q, R, S be the mid-points of AB, AC, CD and BD respectively, show that PQRS is a rhombus.

Solution



20. In an isosceles ∆ABC, the base AB is produced both the ways to P and Q such that AP × BQ = AC2. Prove that △APC ~ △BCQ .

Solution


21. A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2m/sec. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.

Solution



22. A vertical stick of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

Solution



23. In below Fig., ∆ABC is right angled at C and DE ⊥ AB. Prove that ∆ABC ~ ∆ADE and Hence, find the lengths of AE and DE .


Solution



24. In fig., 4.142, PA, QB and RC are each perpendicular to AC. Prove that 1/x + 1/z + 1/y .


Solution



25. In Fig below we have AB || CD || EF. If AB = 6 cm, CD = x cm, EF = 10 cm, BD = 4 cm and DE = y cm, calculate the values of x and y.


Solution

R.D. Sharma Solutions Class 10th: Ch 4 Triangles Exercise 4.4

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Chapter 4 triangles R.D. Sharma Solutions for Class 10th Math Exercise 4.4

Exercise 4.4

1. (i) In below fig., If AB || CD, find the value of x.


(ii) In the below fig., If AB || CD, find the value of x.


(iii) In below fig., AB || CD. If OA = 3x – 19, OB = x – 4, OC = x – 3 and OD = 4, find x.


Solution

(i)


(ii)



(iii)
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