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Let 1/x = a and 1/y = b

⇒ 21a +47 b = 110 and 47a + 21b = 162

Adding and subtracting the two equations, 

we get a +b = 4 and a -b = 2

Solving the above two equations, we get a = 3 and b =1

∴ x = 1/3 and y = 1

Given: Three non-collinear points P, Q and R. 

To prove: A circle passes through these three points P, Q and R, and such circle is one and only one.

Construction: Join PQ and QR. Their perpendicular bisectors AL and BM intersect at O. 

Join OP, OQ and OR. 

Proof: ∵ Point O is at the perpendicular bisector of chord PQ. 

∴ OP = OQ …(i) 

Similarly O is at the perpendicular bisector of chord QR 

=> OQ = OR …(ii) 

From Eqn. (i) & (ii) 

OP = OQ = OR = r (Let) 

Now taking O as a centre and r radius if we draw a circle it will pass through all three points P, Q and R, i.e., P, Q and R exist on the circumference of the circle. 

Now let another circle be (O’, s) which pass through points P, Q and R and perpendicular bisectors of PQ and QR i.e., AL and BM passes through the centre O’. 

But the intersection point of AL and BM is O. i.e. 

O’ and O coincide each other or O and O’ are the same point 

∴ OP = r and OP’ = s and O and O’ are coincide => r = s. 

=> C (O, r) = C (O’, s) 

=> There is one and only one circle through which three non-collinear points P, Q and R pass. 

=> There is one and only one circle passing through three given non-collinear points.

Gonadotropins (LH and FSH) are secreted by the anterior lobe of pituitary gland. 

• Gonadotropins (LH and FSH) increases gradually during the follicular phase (proliferative phase) of menstrual cycle and stimulates follicular development as well as secretion of estrogen by the growing follicles. 
• LH and FSH attain a peak level in the middle of the cycle (about 14th day) and rapid secretion of LH induces rupture of Graafian follicle followed by ovulation (release of ovum). 
• LH stimulates transformation of Graafian follicle into corpus luteum.

(i) The alien species become invasive and cause extinction or decline of indigenous species, e.g., the Nile perch introduced into Lake Victoria in east Africa led to the extinction of more than 200 species of cichlid fish in the lake. 

(ii) Loss of habitat and fragmentation drive animals and plants to extinction. E.g., when the Amazon forest is cut and cleared for cultivating soya beans or for conversion of grasslands for raising beef cattle, many species are affected.

(a) Planning reduces creativity. 

(b) (i) Planning involves huge cost. 

(ii) Planning is a time consuming process. 

(c) Growth for all.

Yes, I think that Mr. Ambani should send his son to U.S.A. as it will provide the understanding of environmental content of a business which has the following benefits.

(a) Helps in the identification of threats and early warning signals. Threats refer to the changes in external environment that will have an adverse effect on the firm’s performance. A good knowledge and understanding of the business environment enables managers to identify the various threats and serve as an early warning signal. In fact, they not merely recognize and ward off threats; they convert threats into opportunities. 

(b) Source of intellectual stimulation/Improvement in performance. Environmental scanning provides intellectual stimulation to planners in their decision making. The executive should also lead by empowering people. They have to come forward to make every possible change and transformation in their corporations.

The related component is social environment. Social Environment describes characteristic of the society in which the organization exists. Literacy rate, educational levels, customs, beliefs, value, lifestyle, age, demographic distribution and mobility of population are part of the social environment. It is important for managers to remember that although changes in the attributes of a society may come either slowly or quickly, changes will come inevitably. For example, demand for reservation in jobs for minorities and women, equal pay for equal work for male and female workers.

(a) It refers to first time sale of securities by a company. A company while issuing the securities issues a prospectus to make a direct appeal through advertisement and informs general public about the purpose for which funds are to be raised, background and future prospectus of the company. 

(b) This is the offer of new shares by a company to the existing shareholders. Each shareholder has the right to subscribe to the new shares in the proportion of shares, he already holds. The shareholder may either accept the offer for himself or assign a part or all of his rights to another. Such rights are valuable to shareholders as they are at a price below the current market price. 

(c) This is the practice followed by a company to make preferential allotment of securities to selected persons, who are normally the promoters, etc. at a price unrelated to the prevailing market price. The advantage is that funds are obtained at a minimal cost as compared to the public issue of the private placement method.

(a) Unity of command 

(b) 

(i) It helps in preventing overlapping of activities 

(ii) It promotes coordination 

(c) Values: 

(i) Conflict resolution 

(ii) Harmony

The pre-requisite to selection is recruitment.

Meaning of Financial Management: Financial Management is concerned with efficient acquisition and allocation of funds. In simple words, it refers to the efficient acquisition of finance, efficient utilisation of finance, and efficient distribution and disposal of surplus for smooth working of a business organisation.

Objectives of financial management are as follows:

1. To ensure regular and adequate supply of funds to the concern. 

2. To ensure adequate returns to the shareholders which will depend upon the earning capacity, market price of the share, expectations of the shareholders. 

3. To ensure optimum funds utilization. Once the funds are procured, they should be utilized in maximum possible way at least cost. 

4. To ensure safety on investment, i.e, funds should be invested in safe ventures so that adequate rate of return can be achieved. 

5. To plan a sound capital structure-There should be sound and fair composition of capital so that a balance is maintained between debt and equity capital.

Labour Welfare Officer looks down to both the workers and the owners.

There is a scarcity of right persons to be appointed at right job at the right time, though there is huge availability of workers or personnels.

To curb black money.

(a) Planning is the function of management being discussed in the given para. One of the characteristics of planning is that planning is a mental exercise. Planning implies ability to think out ways to benefit from the opportunities which have yet to arise. Planning is a mental activity. Planning requires application of mind involving foresightedness, intelligent imagination and judgment. Managers have to consider various courses of action, evaluate the merits and demerits of every course of action and then finally decide which course of action may suit them best. The quality of planning will vary according to quality of mind of the manager. 

(b) Following are the limitations of planning :

1. Planning is a time-consuming process – Planning requires collection of information, its analysis and interpretation. These activities take considerable time. Planning is not practicable when quick decisions are to be made. Planning requires time for thinking, collecting data, forecasting, evaluating alternatives and attending other aspects of planning. 

2. Planning results in rigidity – Planning implies prior determination of policies and procedures while business environment is dynamic. This prevents managers from taking initiatives and from doing innovative thinking. Blind conformity with predetermined rules and procedures promotes red tapism and delay in the performance of work. A manager is caught between procedures and formalities where there is a need for quick action. 

3. Planning is an expensive process – Planning depends on effective system of feedback, transmitting necessary data, collection and analysis of data and evaluation of various courses of action. It results in heavy expenditure. Cost of planning may go on increasing if planning becomes more elaborate and formalised. Apart from direct cost involved, such as paper work etc. may also be a costly affair.

Demonetisation is a component of economic environment of business. Economic environment refers to broad characteristics of the economic system in which a business enterprise operates. 

Following are the components of economic environment: 

1. Relative role of private and public sectors. 

2. Growth rate of GNP and per capita income at current and constant prices.

3. Rates of savings and investments. 

4. Volume of imports and exports of different items. 

5. Balance of payment and changes in foreign exchange reserves. 

6. Agricultural and industrial production trends. 

7. Money supply in the economy.

A business enterprise is an economic institution and therefore, economic environment exercises significant influence on business. For example, reduction in rate of interest reduces the cost of capital and thus encourages more investment in business operations. Similarly taxation policy, monetary policy and industrial policy of the government influences the working of the organisation. A rise in the disposable income of people due to increase in national income creates increasing demand for products.

(1) In the given situation, following functions of management are being performed by the firm: 

• Staffing,
• Controlling.

(2) Recruitment is the concept used by the firm to attract more workers for the firm. Joseph Bros, is relying on recommendations of employees of external sources of recruitment.

(3) Following are the merits of external sources of recruitment :

• Wider choice – When an organisation adopts external sources of recruitment, it gets an opportunity to make selection among the large number of candidates. Thus, management has a wider choice.
• Fresh talent – When vacancies are advertised widely, a large number of applicants from outside the organisation apply. As a result, organisation gets fresh talents and new blood available outside the organisation.
• Competitive spirit – When an organisation uses external sources of recruitment, existing employees will have to compete with the outsiders. This promotes competitive spirit in the organisation.

Marketing management refers to planning, organising, directing and controlling of the activities which facilitate exchange of goods and services between producers and consumers or users of products and services. 

Apprenticeship programmes can be used to give training to the plumbers. 

Following is the meaning and difference between Delegation and Decentralization : 

Following are the principles of management highlighted by Rajat in his address : 

(i) Initiative – Initiative is the power of thinking out a plan and ensuring its successful implementation. It stimulates human endeavour. In other words, initiative means eagerness to initiate action without being asked to do so. Employees at all levels should be allowed to take initiative in work related matters. In an organisation, initiative on the part of its employees can become a great source of strength for it. It indicates that subordinates should be encouraged to make and execute plans within the authority given to them. 

(ii) Discipline – Discipline in the context of management means obedience, proper conduct in relation to others and complying with the rules and regulations of the organisation. Smooth running of business requires discipline. Discipline is required not only on the part of workers but also on the part of management. It is facilitated if there are good supervisors at all levels, rules are clear, and penalties are imposed with fairness. 

(iii) Equity – Principle of equity implies that managers should be fair and impartial while dealing with their subordinates. The principle of equity suggests that similar treatment is assured to people in similar positions. For example, workers performing similar jobs should be paid the same wage rate. Equity is essential to create and maintain cordial relations between managers and subordinates. 

(iv) Espirit de corps – “Espirit de corps” is the principle of management according to which a manager replaces “I” with “We” in all his conversation with workers. Fayol’s principle of management “Espirit de corps” means that there should be mutual understanding and team spirit in the workforce. This will promote harmony in the work group and they will contribute to the maximum.

(v) Stability of personnel – “Employee turnover should be minimised to maintain organisational efficiency,” according to Fayol. Personnel should be selected and appointed after due and rigorous procedure. But once selected they should be kept at their post/position for a minimum fixed tenure. 

(vi) Subordination of individual interest to general interest – In all situations the interests of the group/company will supersede the interest of any one individual. This is so because larger interests of the workers and stakeholders are more important than the interest of any one person.

Motivation, as an element of directing, means a technique used to influence the people in an organisation to perform efficiently.

Motivation is the process of stimulating people to take action to accomplish desired goals.

Formal organisation originates as a result of rules and policies of an organisation structure while infprmal organisation originates as a result of personal and social relations within formal organisation.

Employment interview is conducted in the process of selection to have an overview of candidate’s overall personality and suitability for the job.

Employment interview is conducted to evaluate the applicant's suitability for the job.

It is also known as Ternary operator as it requires 3 operands. It checks the condition, if it is evaluated as true it goes to True part else the False part. 

Syntax: 

Condition?True: False

Example:- Ans=(x>y?x:y);

If x=5 and y=3

As x>y i.e. 5>3 condition is true, Ans. is assigned the value of x, else Ans will get the value of y.

(a) The relational operator is >= and the logical operator is !

(b) if(B<=A)

<script language="javascript">

var prod,b;

prod=1;

b=1;

do

{

document.write(b);

prod=prod+b*b;

b+=3;

}while(b<=10);

document.write("the final prod is" & prod);

</script>

<script language=”javascript”>

var sometext = “Bye!”

document.write(strlen()(sometext))

</script>

<SCRIPT LANGUAGE="Javascript">

var count=new Array()

for(i=0;i<=5;i++)

{

if(i%2 == 0)

count[i]=1;

else

count[i]= i *10;

}

</SCRIPT>

The output is :

16

<html>

<head><script language="javascript">

function first()

{

document.f1.img1.src=document.f1.f2.value

}

function second()

{

document.f1.img1.width=document.f1.t2.value

document.f1.img1.height=document.f1.t1.value

}

</script></head>

<body>

<form name =f1>

Select the image that you want to display<br>

<input type=file name=f2><br>

<img width=300 height=300 name=img1>

<br><input type=button name=b1 value=apply onclick=first()><br>

specify the new height<input type=text name=t1><br>

specify the new width<input type=text name=t2><br>

<input type=button name=b2 value=apply onclick=second()><br>

</form>

</body>

</html>

Loop will execute 5 times.

Value of A after the loop terminates is 0.

<html>

<head>

<SCRIPT language="javascript">

function calc()

{

var consm, amount=0;

consm=document.form1.f1.value;

if(consm<=100)

amount=consm*1.0

else if(consm<=200)

amount=100+1.2*(consm-100)

else if(consm<=250)

amount=100+1.2*100+1.5*(consm-200)

else

amount=100+ 1.2*100 + 1.5*50 +2.0 *(consm-250)

document.write("amount payable is " + amount);

}

</SCRIPT>

</head>

<body>

<form name="form1">

NUMBER OF CALLS

<input name=f1 type=text>

<br>

<input type=button name=b1 onclick=calc() value=CALCULATE BILL>

</form>

</body>

</html>

d)You cannot restrict text values using HTML

It is used in electrical cables as it is malleable, ductile and a good conductor of heat and electricity.

1.(a) Stupas are the sacred places related to Buddhism. 

(b) Here, relics of Buddha such as bodily remains and daily object used by him are preserved. 

2.(a) Bharat 

(b) Samath 

(c) Sanchi 

3.(a) They donated money for the maintenance of the stupa. 

(b) Sultan Jehan Begum contributed a lot of money for the erection of a museum and a guest house.

1.(a) Sanskrit was an unfamiliar language. 

(b) Difference in religious beliefs and practices. 

2.(a) The system was not quite rigid in real life. 

(b) The Vaishyas and Shudras mixed together in the same house and lodgings, and were engaged in economic activities. 

3.(a) Al – Biruni’s description of the caste system was influenced by his study of Sanskrit text. 

(b) The highest castes were the Brahmins as they were created from the head of the Brahma. 

(c) The Kshatriyas were next in hierarchy created from the shoulders and hands of Brahma. The Vaishyas and Shudras were created from the thigh and feet of the Brahma respectively.

1.(a) The supply of vegetables in the cities was disrupted. All vegetables were in short supply. 

(b) There was non-availibility of pumpkin and brinjal. Potatoes and yams were available but was stale and rotten; if available were so costly. 

2.(a) The normal life was adversely affected by the revolt of 1857. 

(b) The supply of daily necessities of life got affected and routine activities were broken down. 

3.(a) The supply of vegetables was broken down. The vegetables which were available were stale and rotten. 

(b) The supply of spinach was also disrupted. Kaddu and brinjal were difficult to get. 

(c) Vegetables which were available were beyond the reach of the pool. Middle class and rich only could afford to buy them.

(i) Kamalpuram tank was one of the most important tanks of Vijayanagra. 

(ii) Its water was not only used to irrigate nearby fields but its water was also conducted to the royal center through a channel.

(i) Sudarshana lake was an artificial reservoir which was built by a local governor during the reign of the Mauryas. 

(ii) It was repaired by a Saka ruler, Rudradaman and one of the rulers of the Gupta dynasty.

Considering that a consumer is consuming only two goods X and Y, the conditions of consumer’s equilibrium are : 

(i)  \(\frac{MUpx}{px}=\frac{MUy}{py}\)

(ii) MU of a good falls as more units of the goods are consumed.

If MUx/Px is greater than MUy/Py, it means that the satisfaction a consumer derives from spending a rupee on good X is greater than the satisfaction derived from spending a rupee on good Y. In such situation, a consumer will be motivated to substitute good X for good Y and will relocate his income to satisfy the condition of consumer’s equilibrium. As the consumption of good X increases its marginal utility will fall. As the consumption of good Y decreases, its marginal utility will increase. This is due to the law of diminishing marginal utility. This process will continue till MUx/Px becomes equal to MUy/Py and the consumer is in equilibrium. If MUx/Px is lower than MUy/Py, it means that the satisfaction a consumer derives from spending a rupee on good X is lower than the satisfaction derived from spending a rupee on good Y. In such a situation, a consumer will be motivated to substitute good Y for good X. As the consumption of good Y increases, its marginal utility will fall. As the consumption of good X decreases, its marginal utility will increase.

This process will continue till \(\frac{MUx}{px}=\frac{MUy}{py}\) Unless MU of a good falls, as more units are consumed, the consumer will not reach the equilibrium.

(c) Both (a) and (b).

d) 1-True, 2-False 

Debentures, and Bonds carry a fixed rate of interest and are to be paid off irrespective of the firm’s revenues. 

(x + 1)/x = 2

x + 1 = 2x

x - 2x = -1

-x = -1

x = 1

then,

= (x¹⁰⁰ + 1)/ x¹⁰¹

= 1¹⁰⁰ + 1 / 1¹⁰¹

= 1 +1/1

= 2/1

= 2

The correct option is (d) \(\frac{1}{5}\).

Favourable outcomes are 4, 8, 12, i.e., 3 outcomes and total number of outcomes = 15

Required probability = \(\frac{3}{15}\) = \(\frac{1}{5}\).