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Let the three given points are A(1, -1, 3), B(2, -4, 5) & C(5, -13, 11). The direction ratios of the line AB joining the points A and B :

2 - 1, -4 - (-1), 5 - 3 = 2 - 1, -4 + 1, 5 - 3, 2 ...(1)

Similarly, the direction ratios of the line BC joining the points B and C:

5 - 2, -13 - (-4), 11 - 5 = 3, -9 ,6 ...(2)

It is clear from (1) and (2) that direction ratios of AB and BC are proportional i.e. AB is parallel to BC. But the point B is common to both AB and BC. Therefore A, B and C are co-linear points. 

Given equation of half plane is 2x + 3y − 12 ≤ 0.

Then, point on half plane 2x + 3y − 12 > 0 does not lie in the given half plane.

⇒ 2x + 3y > 12.

Points which satisfies inequality 2x + 3y > 12 does not lie on the given half plane.

Point (1, 4) satisfies inequality 2x + 3y > 12.

Therefore, the point (1, 4) does not lie on the given half plane.

Given that is square matrix of order 3 and |A| = 3.

We know that |adj A| = |A|^{n - 1} , where A is square matrix of order n.

Therefore, |adj A| = |A|³⁻¹ = |A|² = 3² = 9. (Because, A is square matrix of order 3)

Hence, |adj A| = 9.

Personal income = Net domestic product at factor cost + Net factor income from abroad + (Interest received by households – Interest paid by households) + Transfer income – Corporate tax – Undisbursed profit.

Therefore, – PI = 8000 + 200 + (1500 – 1200) + 300 – 500 -1000 

= 8000 + 200 + 300+300-500-1000 

= 7300

Personal Disposable Income = Personal Income – Personal Tax Therefore PDI 

= 7300 – 500 

= 6800.

1. 5 Bananas (20/4). 

2. 4 Mangoes (20/5). 

3. Slope of budget line is downward. 

4. Yes, the bundles on the budget line are equal to the consumer’s income. 

5. True, if we want to have more of banana we have to give up mangoes.

The government imposed upper limit on the price of a good or service is called price ceiling. Example, price ceiling on necessary items like selected medicines, kerosene, wheat, etc. Imposition of price ceiling below the equilibrium leads to an after excess demand.

1. 5 Bananas (20/4). 

2. 4 Mangoes (20/5). 

3. Slope of budget line is downward. 

4. Yes, the bundles on the budget line are equal to the consumer’s income. 

5. True, if we want to have more of banana we have to give up mangoes.

Revenue deficit = Revenue expenditure minus Revenue Receipts.

In reality all economies are Mixed Economies.

The revenue received by the firm per unit of commodity sold is called Average Revenue.

Correct option: (b) Both assertion and reason are correct

The point of minimum AVC where the SMC curve cuts the AVC curves is called as Shut down point.

Discharge lamp, Fluorescent lamp, LED, Arc lamp.

Kinds of Elasticity of supply – The kinds of elasticity of supply can be divided into five categories. 

I. Perfectly Elastic supply (e_s = x ) 

II. Greater than unit Elastic supply (e_s > 1) 

III. Unitary Elastic supply (e_s = 1) 

IV. Less than unitary elastic supply (Inelastic supply)(e_s < 1).

V. Perfectly Inelastic supply (e_s = 0).

In equilibrium, a perfectly competitive firm will equate marginal revenue with marginal cost.

An economy is in equilibrium when intended investment equals intended investment.

The existence of a Parallel Economy or Black Money makes the monetary policies less effective.

(D) Above all

a. All 1,2,3 and 4 are correct 

1. (i)-(C), (ii) -(A), (iii)-(B), (iv)-(D) 

Business class groups suffer the most from inflation.

• Tax is paid by the person on whom it is imposed
• Tax is imposed on one and paid by another.

• Tax revenue 
• Non-tax revenue

1. (i)-(B), (ii) -(A), (iii)-(D), (iv)-(C) 

1. (i)-(D), (ii) -(C), (iii)-(B), (iv)-(A) 

2. (i)-(C), (ii) -(D), (iii)-(A), (iv)-(B) 

An athletic runs some distance before taking a jump to gain some initial momentum. It helps the athlete to jump more.

(a) Variable Cost: Variable costs are those costs which vary in amount with changes in the level of output or activity. Such costs increase or decrease in the same proportion in which the level of output increases or decreases. Variable costs vary in total amount but remain constant per unit of production. 

(b) Tidal Energy: The energy possessed by rising and falling water in tides is known as tidal energy. Tidal energy is harnessed for producing electricity by constructing a dam across a narrow opening to the sea. This is not a major source of energy. 

(c) Four main reasons: 

1. Communication gap. 

2. Population growth. 

3. Recognition of social responsibility. 

4. Education in Public Relations. 

(d) Balance Sheet: Balance sheet means a statement which shows the assets and liabilities of the organisation (including capital fund and other fund) on a particular date. It is a statement which reports the property values owned by the organisation and the claims of creditors and owners against these proper-ties. It depicts the financial position of the organisation on specified date. 

(e) The two essentials of a good advertisement: 

1. Prestige: This theme is used to popularize luxurious items like motor cars, refrigerators and furniture. Their possession acts as a symbol of prestige to their holders. 

2. Comfort: This theme is used to advertise products like fans, air conditioners, refrigerators etc., as such products help to make life comfortable.

Primary Succession can be defined as the process of growth in an area that was previously uninhabited, barren, unoccupied and there was no initial vegetation. On the other hand, Secondary Succession can be defined as the growth of the community in such area which was previously occupied, inhabited and that has primary vegetation but got disturbed or damaged due to some external or internal factors.

The example of Primary Succession is the newly formed bare rock, desert, ponds, etc., while the area covered under deforestation, or affected by natural calamities such as flood, earthquake, etc. are the examples of Secondary Succession.

 Sustainable development is development that meets the needs of the present without compromising the ability of future generations to meet their own needs. It contains within it two key concepts:

• The concept of 'needs,' in particular the essential needs of the world's poor, to which overriding priority should be given; and
• The idea of limitations imposed by the state of technology and social organization on the environment's ability to meet present and future needs.

1. The satisfaction of human needs and aspirations is the major objective of development. The essential needs of vast numbers of people in developing countries for food, clothing, shelter, jobs – are not being met, and beyond their basic needs these people have legitimate aspirations for an improved quality of life. 
2. A world in which poverty and inequity are endemic will always be prone to ecological and other crises. Sustainable development requires meeting the basic needs of all and extending to all the opportunity to satisfy their aspirations for a better life.
3. A society may in many ways compromise its ability to meet the essential needs of its people in the future – by overexploiting resources, for example. The direction of technological developments may solve some immediate problems but lead to even greater ones. Large sections of the population may be marginalized by ill-considered development.
4. Sustainable development involves more than growth, it requires a change in the content of growth, to make it less material- and energy-intensive and more equitable in its impact. These changes are required in all countries as part at a package of measures to maintain the stock or ecological capital, to improve the distribution of income, and to reduce the degree of vulnerability to economic crises.

This is when a request from a prospective guest is received for some future day arrival and the hotel blocks the room for this guest provisionally in the hotel records such as charts and diaries and racks or computer and sends a letter of offer to the prospective guest. The offer has a cutoff date by which the guest should send his confirmation which may be in the form of a letter, guarantee by company, credit card or deposit and whichever the hotel may require. Once the confirmation from the guest is received by the hotel till the cutoff date the hotel makes the tentative booking into confirmed booking otherwise the tentative booking is cancelled and records updated.

The tradition of assigning room numbers goes back to the pre-computer days where hotels used a large book or wall mounted room rack, sometimes known as a Whitney rack, to track their reservations.

This poem is about a bom spectator who confesses about his views on Sports and sportsmen. He says that they injure each other as they prance and feel happy on others heroic deeds. His limp and bashful spirit feeds on the heroism of other players. He has seen zealous athletes playing so rough that they never consider the feelings of fellow players. He watches with a palpitating heart when ‘A’ runs ninety yards to bag a medal. He watches with obvious alarm when ‘B’ knocks another boxer down cracking his vertebrae and spines.

They are insensitive to the cracking wrist and snapping knees of fellow players. When his ego and prudence clashed, ego told him to seek glory in sports, but his prudence always ignored it. Thus common sense prevailed, he remained a cheerful life-time fan of successful athletes. He was contented as a spectator of all kinds of games and sports and world famous athletes. The crazy desire for championship titles and the light of fame on them leads them to ignore swollen eyes, snapping of knee joints or cracking of wrists.

An organization who buys individual travel components, separately from their suppliers and combines them into a package tour, which is sold with their own price tag to the public directly or through middlemen, is called a tour operator.

Macavity is an elusive master criminal who leaves no evidence after he commits a crime. He baffles Scotland Yard police and the flying squad as he disappears before their arrival to the scene of crime. He is called a “Hidden paw“ because even Scotland Yard is unable to arrest him after he commits any crime. He does not leave his foot prints in the spot of crime. He defies law of gravity and his powers of levitation make the fakir stare with wonder.

Other cats are lazy and just stay in the kitchen and take the food offered by their master. But Macavity is agile and defies law of the land and laws of gravity. Despite doing all wicked things, he pretends to be innocent. So, the poet claims one can never come across such a cat of “Deceitfulness and suavity”. When he appears to be half-asleep with his half-closed eyes, he would be wide-awake.

He is an enigma to everyone. Macavity is indeed a mystery.