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The given equation is x² + m²xy - xy - my² = 0. That is, mx(x + my)- y(x + my) = 0 Therefore, the lines are x + my = 0 and mx - y = 0 . The angle bisectors of the coordinates are y = x = -x and y = -x . Hence, m = ±1 or |m| = 1.

Correct option  (A)  2

Explanation :

Solving the given equations, the x-coordinate of their point of intersection is

5/3 + 4m = -5, -1

when m = -1 and 2, respectively. That is for m = -1 and  -2, the x-coordinate is also an integer. Hence, the number of integral values is 2.

Solving the above equations taken two by two, the vertices of the triangle are

A(-3/5,8/5), B(-3,4), and C(-3/7, 16/7)

 The equation of the altitude drawn from A to the side BC is

y - 8/5 = 3/2(x + 3/5)

3x - 2y = -5 ....(1)

 Again the equation of the altitude from B onto CA is

y - 4 = -1/4(x + 3)

⇒ x + 4y = 13  ...(2)

 Solving Eqs. (1) and (2), the coordinates of the orthocentre are

(3/7,22/7)

which lies in quadrant number 1.

The correct option (2) 200   

Explanation:

1C.S.d = 5 x 10^-6 = (1 x 10^-3)/N

N = 1000/5 = 200

The proposal of marriage from Daulat Singhji’s wife upset Geeta. She angrily said “Bhabhi, whatever happens, Vijay cannot be engaged at this age.” After the outburst, she went up to her room. She felt that she had ruined her life but would not let the children ruin theirs. As Ajay Singh, her husband came into her room, she shouted that she would never agree to the criminal act of child marriage.

दौलत सिंह जी की पत्नी की ओर से विवाह के प्रस्ताव ने गीता को व्यथित कर दिया। उसने क्रोध से कहा, * भाभी चाहे कुछ भी हो विजय की सगाई (विजय का रिस्ता पक्का करना) इस उम्र में नहीं हो सकती।” इस विस्फोट के बाद वह अपने कमरे में चली गई। उसे महसूस हुआ कि उसने अपना जीवन तो नष्ट कर लिया है पर बच्चों का जीवन बर्बाद नहीं होने देगी। जैसे ही उसके पति अजय सिंह कमरे में आये उसने चिल्ला कर कहा कि वह बाल विवाह जैसे अपराधी कार्य से सहमत नहीं होगी।

(i) b) 78.57m² 

Cloth material required = 2 X S A of hemispherical dome

= 2 x 2πr² 

= 2 x 2 x \(\frac{22}{7}\) x (2.5)² m² 

= 78.57 m²

(ii) a) πr²h

Volume of a cylindrical pillar = πr²h

(iii) b) = 123.2 m²

Lateral surface area = 2 x 2πrh 

= 4 x \(\frac{22}{7}\) x 1.4 x 7 m² 

= 123.2 m²

(iv) d) 89.83 m³

Volume of hemisphere = \(\frac{2}{3}\)πr³ 

= \(\frac{2}{3}\frac{22}{7}\) (3.5)³ m³ 

= 89.83 m³

(v) b) 1:8

Sum of the volumes of two hemispheres of radius 1cm each = 2 x \(\frac{2}{3}\pi1^3\)

Volume of sphere of radius 2cm = \(\frac{4}{3}\pi2^3\)

So, required ratio is \(\frac{2\times\frac{2}{3}\pi1^3}{\frac{4}{3}\pi2^3}\)

= 1:8

When Sita was stopped from going to school, Geeta was very upset. She ran to her room sad and sullen. She sat there with her chin resting on her knees. At the sight of Dhapu, the maid, she could not contain herself. She asked her “What is the idea of stopping Sita from going to school when she will remain in the haveli for two years even after her marriage ?”

जब सीता को स्कूल जाने से रोक दिया गया तो गीता बहुत व्यथित हो गई। वह अपने कमरे में मुँह बनाये और दुखी होकर भाग गई। अपने घुटनों पर ठोड़ी रखकर वह बैठ गई। धापू नौकरानी को देखते ही वह स्वयं पर काबू नहीं कर सकी। गीता ने उससे पूछा, “सीता को स्कूल जाने से रोकने में क्या विचार है जब शादी के बाद उसे दो वर्ष तक हवेली में रहना ही है ?”

A stability test for time invariant linear systems can also be derived in the frequency domain. It is known as Nyquist stability criterion. 

It is based on the complex analysis result known as Cauchy’s principle of argument.

(c) (I) and (IV)

Correct answer is (a) increases

The correct answer is ​the Feasibility of the business.

• The conclusion part of the business plan will identify the Feasibility of the business.
  • Business plans explain what a company does, who runs the company and how the company plans on hitting revenue goals, based on competitive advantages and marketing strategies.
  • Business plans are also used to seek investor loans or to finance their business.

• The key components of a business plan are:
• Executive Summary
  • It should appear first in the business plan.
  • It should summarize what the business seeks to accomplish.
  • Since it’s meant to highlight the intentions of the rest of the plan, it is recommended by some to write it in the end.
  • It reveals the company’s mission statement, along with a short description of its products and services.
  • Investors are looking for reasons why they should risk money in the venture; this is achieved by highlighting the unique ways in which the company solves problems and how an influx of funding will yield success.
• Company Description
  • It includes key information about the business, goals and the target customers.
  • It also explains why the company stands out from other competitors.
• Market Analysis
  • It should help visualize the target customers, how much money they make, what their buying habits are, which services do they want and need, etc.
• Competitive Analysis
  • It presents a clear comparison of the business vs direct and indirect competitors.
• Description of Management and Organization
• Breakdown of Your Products and Services
  • It includes a detailed breakdown of the products and services.
• Marketing Plan
  • It includes promotional and marketing strategies.
• Sales Strategy
• Request for Funding
  • It focuses on the amount of money that you need to set up your business and how you plan to use the capital that you are raising.
• Financial Projections
  • It breaks down the financial goals and expectations that you’ve set based on market research.

The correct answer is Strategy.

• The strategy entails specifying the organization‘s mission, vision, and objectives; developing policies and plans to execute the vision; and allocating resources to implement those policies and plans.
  • Strategy is largely about using internal assets to create a value-added proposition.
  • This helps to capture opportunities in the competitive environment while avoiding threats.

• In the context of management, a mission is a quest, a journey to a destination in which the whole organization is engaged.
  • The mission statement tells what the goal of the company is and where is it going.
• Goals are outcome statements that define what an organization is trying to accomplish, both programmatically and organizationally.
• Objectives are the goals, aims, or purposes that organizations wish to achieve over varying periods of time

Community is a circle of interwoven relationships. Within the ranges of a community, the members may carry on their economic, political, religious, educational and other activities. The social relationship involves some degree of reciprocity as well as awareness of mutuality. Friendship, Relationship, Relatives are not exclusively private entities; they are constantly influenced by outside forces. 

• A group may have a strong influence upon the individual in that the individual gladly accepts the activities of the group. Each and every human being has own personal interest, attitudes, values etc. 

• If you carefully analyse friendship groups in your school, you would be able to identify Going to School patterns. Though friendships appear to be simple matters of liking and striking a chord with a particular group of children, they involve a complex matrix of social norms and stratification.
• A child has varied kinds of experiences in these relationships, both good and bad, which form a part of the understanding of the world and ways of relating to others. All these play a formative role in the personality development of the child (including physical, social, emotional, cognitive and language).
• In this society neither personal attachment nor traditional rights and duties are important. The relationships between people are determined by bargaining and defined in written agreements. Relatives are often separated because people move about and live among strangers.

Thus from the above-mentioned points, it is clear that all of the above are not exclusively private entities; they are constantly influenced by outside forces.

• Famous for their social-psychological contribution, the three social psychologists defined psychological group “ as two or more persons who meet the following conditions, viz., (i) the relations among the members are independent (ii) each member’s behaviour influences the behaviour of each of the others, (iii) the members ‘share an ideology’ – a set of beliefs, values and norms which regulate their mutual conduct.” 

Social influence is defined as the change in an individual’s thoughts, feelings, attitudes, or behaviours that results from interaction with another individual or group. It refers to the change in behaviour that one person causes in another, intentionally or unintentionally. As a result, the changed person perceives himself in relationship to the influencer, other people and society in general. Because of the social factor, people are what they are.

• Social influence can also be defined as the process by which individuals make real changes to their feelings and behaviours as a result of interaction with others who are perceived to be similar, desirable, or expert. People adjust their beliefs with respect to others to whom they feel similar in accordance with psychological principles such as balance. 

Thus from the above-mentioned points, it is clear that "People are the way they are" because of social factor.

Three areas of social influence are conformity, compliance and obedience. Conformity is changing how you behave to be more like others. This plays to belonging and esteem needs as we seek the approval and friendship of others. Conformity can run very deep, as we will even change our beliefs and values to be like those of our peers and admired superiors.

The correct answer is Managerial Approach

1. Managerial Approach

• The managerial approach thus entails the study of marketing at the micro-level- level of a business firm, of the managerial functions of analysis, planning, execution, coordination, and control in relation to the marketing functions of creating, stimulating, facilitating, and valuing transactions.

2. Commodity approach

• The commodity approach involves the examination of the marketing system for each of a number of specific commodities. It takes as its focal points individual products. 

3. Functional approach

• The functional approach is one of the methods used in the classification of activities that occur in the marketing processes by breaking down the processes into functions.

4. Institutional approach

• The institutional approach to the study of marketing is a system whereby a detailed description and analysis are made for each segment of the marketing mechanism.

Human society has made a long journey in this; so is the concept of development. Human society has progressed and developed through several stages. The social system prevalent in any society or country at any point in time is a sum total of several sub-systems such as political system, economic system, educational system, etc. 

• In every society, no matter how simple or complex, there exist standards, norms, customs, values, beliefs and conventional ways of behaving which shape the behaviour and preferences of its members.
• These behaviours may differ from society to society and from era to era, but they represent a process through which the social heritage or the culture, is passed on from generation to generation.  
• Man is the only living creature capable of'co~nmunicating symbolically and storing his social heritage for transmission to the new generation.
• Therefore, 'culture' refers to the attitudes, values, beliefs and ways of acting and interacting that characterize a social group.
• Neither a single individual nor a group, nor an entire society can be understood without reference to culture. 

Thus from the above-mentioned points, it is clear that society gains potency as it is handed down from generation to generation.

Business environment refers to those aspects of the surroundings of business enterprise which affect or influence its operations and determine its effectiveness. The business environment is always changing and is uncertain. It is because of this that it is said that the business environment is the sum of all the factors outside the control of management of a company those are depended to each other—the factors which are constantly changing and they carry with them both opportunities and risks or uncertainties which can make or mar the future of business.

Time Series

• The arrangement of data in accordance with their time of occurrence is a time series.
• It is the chronological arrangement of data. 
• A time series depicts the relationship between two variables. 

Mathematical Model for Time Series Analysis

1. Additive Model for Time Series Analysis
   • If yt is the time series value at time t. Tt, St, Ct, and Rt are the trend value, seasonal, cyclic and random fluctuations at time t respectively. According to the Additive Model, a time series can be expressed as
   • yt = Tt + St + Ct + Rt.
   • This model assumes that all four components of the time series act independently of each other.
2. Multiplicative Model for Time Series Analysis
   • The multiplicative model assumes that the various components in a time series operate proportionately to each other. According to this model
   • yt = Tt × St × Ct × Rt
   • Multiplicative model is used when all four components of the time series act dependently of each other as in case of Economy and Business.

The Correct option is A. s ⁄r

Correct option: a) Cryoprecipitate bath

Correct option: a) 2-6 degree

Correct option: c) Hot air Oven

(i) The basis of similarities between metallic and ionic crystals is that both these crystal types are held by the electrostatic force of attraction. In metallic crystals, the electrostatic force acts between the positive ions and the electrons. In ionic crystals, it acts between the oppositely-charged ions. Hence, both have high melting points. The basis of differences between metallic and ionic crystals is that in metallic crystals, the electrons are free to move and so, metallic crystals can conduct electricity. However, in ionic crystals, the ions are not free to move. As a result, they cannot conduct electricity. However, in molten state or in aqueous solution, they do conduct electricity. 

(ii) The constituent particles of ionic crystals are ions. These ions are held together in three-dimensional arrangements by the electrostatic force of attraction. Since the electrostatic force of attraction is very strong, the charged ions are held in fixed positions. This is the reason why ionic crystals are hard and brittle. 

Correct density order is (1) Li < K < Na < Rb < Cs

Correct option is (A) Li < K < Na < Rb < Cs

The volume of 2.8g of CO at 27°C and 0.821 atm pressure is 3L.