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Merits: 

• Ease of formation and closure: Like sole proprietorship, the partnership business can be formed easily without any legal formalities.
• More funds: In a partnership, the capital is contributed by a number of partners. This makes it possible to raise larger amount of funds as compared to a sole proprietor and undertake additional operations when needed.
• Sharing risks: The risks involved in running a partnership firm are shared by all the partners. This reduces the anxiety, burden and stress on individual partners.
• Secrecy: A partnership firm is not legally required to publish its accounts and submit its reports. Hence it is able to maintain confidentiality of information relating to its operations. 

Demerits: 

• Limited capital: Since the total number of partners cannot exceed 20, the capital to be raised is always limited. It may not be possible to start a very Large business in partnership form.
• Lack of continuity of business: A partnership firm comes to an end in the event of death, lunacy or retirement of any partner. Even otherwise, it can discontinue its business at the will of the partners. At any time, they may take a decision to end their relationship.
• Lack of public confidence: There is no governmental supervision over the affairs of the business of a partnership and publishing accounts is also not necessary. Hence, public may not have full confidence in them.
• Unlimited liability: The liability of each partner is not limited to the amount invested but his private property is also liable to pay the business obligations.

Company generally does not distribute all its earnings amongst the shareholders as dividends. A portion of the net earnings may be retained in the business for use in the future. This is known as retained earnings.

Merits: 

• Retained earnings is a permanent source of funds available to an organisation. 
• It does not in involve any explicit cost in the form of interest, dividend or flotation cost. 
• As the funds are generated internally, there is a greater degree of operational freedom and flexibility.
• It enhances the capacity of the business to absorb unexpected losses. 
• It may lead to increase ¡n the market price of the equity shares of a company.

Demerits: 

• Excessive ploughing back may cause dissatisfaction amongst the shareholders as they would get lower dividends. 
• It is an uncertain source of funds as the profits of business are fluctuating. 
• The opportunity cost associated with these funds is not recognized by many firms. This may lead to sub-optimal use of the funds.

(B) Old profit sharing ratio.

1. Transportation or interstate movement of goods: The Chambers of Commerce and Industry help in many activities concerning interstate movement of goods which includes registration of vehicles, surface transport policies, construction of highways and roads.

2. Marketing of agro products and related issues: The associations of agriculturists and other federations play an important role in the marketing of agro products. Streamlining of local subsidies and marketing policies of organisations selling agro products are some of the areas where the Chambers of  Commerce and Industry can really intervene and interact with concerned agencies like farming cooperatives.

3. Weights and measures and prevention of duplication brands: Laws relating to weights and Measures and protection of brands are necessary to protect the interest of the consumers as well as the traders. They need to be enforced strictly. The Chambers of Commerce and Industry interact with the government to formulate such laws and take action against those who violate rules and regulations.

4. Promoting sound infrastructure: A sound infrastructure like road, port, electricity, railways, etc. plays a catalytic role in promoting trade. The Chambers of Commerce and Industry in collaboration with the government needs to take up heavy investment projects.

5. Labour legislation: A simple and flexible labour legislation is helpful in running industries, maximising production and generating employment. The Chambers of Commerce and Industry and the government are constantly interacting on issues like labour laws, retrenchment. etc.

6. Octroi and other local levies: Octroi and local taxes are the important sources of revenue of the local government. These are collected on the goods and from people entering the state or the municipal limits. The government and Chambers of Commerce should ensure that their imposition is not at the cost of smooth transportation and local trade.

7. Harmonisation of sales tax structure and value added tax: The Chambers of Commerce and Industry play an important role in interacting with the government to harmonise the sales tax structure in different states.

8. Excise duty: Central excise is the chief source of the government revenue levied across states by the central government. The excise policy plays an important role in pricing mechanism and hence the associations need to interact with the government to ensure streamlining of excise duties.

The usage of time series models is twofold: Obtain an understanding of the underlying forces and structure that produced the observed data. Fit a model and proceed to forecasting, monitoring or even feedback and feedforward control.

Correct option is 

1 a. ₹ 33,000

2 c. ₹ 80,000

3 a. ₹ 44,000

4 a. Dr. C’s capital a/c ₹25,000; Cr. A’s capital a/c ₹ 25,000

Merits: 

• The deposits that are raised by organisations directly from the public are known as public deposits.
• The procedure of obtaining deposits is simple and does not contain restrictive conditions as are generally there in a loan agreement. 
• Cost of public deposits is generally lower than the cost of borrowings from banks and financial institutions. 
• Public deposits do not usually create any charge on the assets of the company. The assets can be used as security for raising loans from other sources. 
• As the depositors do not have voting rights, the control of the company is not diluted.

Demerits: 

• New companies generally find it difficult to raise funds through public deposits. 
• It is an unreliable source of finance as the public may not respond when the company needs money. 
• Collection of public deposits may prove difficult, particularly when the size of deposits required is large.

The usage of time series models is twofold: Obtain an understanding of the underlying forces and structure that produced the observed data. Fit a model and proceed to forecasting, monitoring or even feedback and feedforward control.

Correct option is 

1 a. Dr. A’s Capital A/c ₹6,000; Cr. B’s Capital A/c ₹ 6,000

2 b. Cr. A’s Capital A/c ₹9,000 ;Dr. B’s Capital A/c ₹ 9,000

3 c. ₹ 1,35,000

4 a. A-₹1,53,000; B-₹87,000

Principle: The principle of Insurable interest is an essential part of every insurance contract and is considered as legal prerequisite for getting insurance.

 Explanation of Principle: Therefore, you can buy a life insurance policy on someone else’s life, provided you have an interest in that person remaining alive, or expect an emotional or financial loss from that person’s death. This is the condition of the life insurance company will look for, that is, if you have a true relationship with the person, you have insured and whether there will be an emotional loss or a financial loss in case that person dies. 

So, a person can take a policy on his own life, his spouse, his children, his parents as he has an Insurable interest in the continuing wellbeing and also stands to face a financial loss in the case of death or if they fall ill. But a person cannot take a life insurance policy in the name of his friend or neighbour as there is no Insurable interest present.

1. Principle of utmost good faith: According to this principle, the insurance contract must be signed by both parties (i.e. insurer and insured) in an absolute good faith or belief or trust. The person getting insured must willingly disclose and surrender to the insurer his complete true information regarding the subject matter of insurance.

Example: If any person has taken a life insurance policy by hiding the fact that he is a cancer patient and later on if he dies because of cancer then Insurance Company can refuse to pay the compensation as the fact was hidden by the insured.

2. Principle of insurable interest: As per this principle, the insured must have insurable interest in the subject matter of insurance. It means insured should gain by the existence or safety and lose by the destruction of the subject matter of insurance.

Example: If a person has taken the loan against the security of a factory premises then the lender can take fire insurance policy of that factory without being the owner of the factory because he has financial interest in the factory premises.

3. Principle of indemnity: According to the principle of indemnity, an insurance contract is signed only for getting protection against unpredicted financial losses arising due to future uncertainties. Insurance contract is not made for making profit else its sole purpose is to give compensation in case of any damage or loss.

Example: A person insured a car for 5 lakhs against damage or an accident case. Due to accident he suffered a loss of 3 lakhs. then the insurance company will compensate him 3 lakhs not only the policy amount i.e., 5 lakhs as the purpose behind it is to compensate not to make profit. 

4. Principle of contribution: According to this principle, the insured can claim the compensation only to the extent of actual loss either from all insurers in a proportion or from any one insurer.

Example: A person gets his house insured against fire for 50,000 with insurer A and for 25,000 with insurer B. A loss of 37,500 occurred. Then A is liable to pay 25,000 and B is liable to pay 12,500.

5. Principle of subrogation: According to the principle of subrogation, when the insured is compensated for the losses due to damage to his insured property, then the ownership right of such property shifts to the insurer.

Example: If a person receives Rs. 1 lakh for his or her damaged stock, then the ownership of the stock will be transferred to the insurance company and the person will hold no control over the stock.

6. Principle of mitigation of loss: According to the Principle of mitigation of loss, insured must always try his level best to minimize the loss of his insured property, in case of uncertain events like a fire outbreak or blast, etc. The insured must not neglect and behave irresponsibly during such events just because the property is insured.

Example: If a person has insured his house against fire, then, in case of fire, he or she should take all possible measures to minimise the damage to the property exactly in the manner he or she would have done in absence of the insurance,

7. Principle of Causa Proxima: Principle of Causa Proxrna (a Latin phrase), or in simple English words, the Principle of Proximate (i.e. Nearest) Cause, means when a loss is caused by more than one causes, the proximate or the nearest cause should be taken into consideration to decide the liability of the insurer.

Example: If an individual suffers a loss in A fire accent, then this should already he a part of the contract in order for this person to claim the insurance amount.

Merits:

• It is preferred by investors who want fixed income at lesser risk. 
• Debentures are fixed charge funds and do not participate in profits of the company. 
• The issue of debentures is suitable in the situation when the sales and earnings are relatively stable. 
• As debentures do not carry voting rights, financing through debentures does not dilute control of equity shareholders on management. 
• Financing through debentures is less costly as compared to cost of preference or equity capital as the interest payment on debentures is tax deductible.

Demerits: 

• As fixed charge instruments, debentures put a permanent burden on the earnings of a company. There is a greater risk when earnings of the company fluctuate. 
• In case of redeemable debentures, the company has to make provisions for repayment on the specified date, even during periods of financial difficulty. 
• Each company has certain borrowing capacity. With the issue of debentures, the capacity of a company to further borrow funds reduces. 

1. Principle of utmost good faith: According to this principle, the insurance contract must be signed by both parties (i.e. insurer and insured) in an absolute good faith or belief or trust. The person getting insured must willingly disclose and surrender to the insurer his complete true information regarding the subject matter of insurance.

Example: If any person has taken a life insurance policy by hiding the fact that he is a cancer patient and later on if he dies because of cancer then Insurance Company can refuse to pay the compensation as the fact was hidden by the insured.

2. Principle of insurable interest: As per this principle, the insured must have insurable interest in the subject matter of insurance. It means insured should gain by the existence or safety and lose by the destruction of the subject matter of insurance. 

Example: If a person has taken the loan against the security of a factory premises then the lender can take fire insurance policy of that factory without being the owner of the factory because he has financial interest in the factory premises.

3. Principle of indemnity: According to the principle of indemnity, an insurance contract is signed only for getting protection against unpredicted financial losses arising due to future uncertainties. Insurance contract is not made for making profit else its sole purpose is to give compensation in case of any damage or loss. 

Example: A person insured a car for 5 lakhs against damage or an accident case. Due to accident he suffered a loss of 3 lakhs. then the insurance company will compensate him 3 lakhs not only the policy amount i.e., 5 lakhs as the purpose behind it is to compensate not to make profit.

4. Principle of contribution: According to this principle, the insured can claim the compensation only to the extent of actual loss either from all insurers in a proportion or from any one insurer. 

Example: A person gets his house insured against fire for 50,000 with insurer A and for 25,000 with insurer B. A loss of 37,500 occurred. Then A is liable to pay 25,000 and B is liable to pay 12,500.

5. Principle of subrogation: According to the principle of subrogation, when the insured is compensated for the losses due to damage to his insured property, then the ownership right of such property shifts to the insurer. 

Example: If a person receives Rs. 1 lakh for his or her damaged stock, then the ownership of the stock will be transferred to the insurance company and the person will hold no control over the stock.

6. Principle of mitigation of loss: According to the Principle of mitigation of loss, insured must always try his level best to minimize the loss of his insured property, in case of uncertain events like a fire outbreak or blast, etc. The insured must not neglect and behave irresponsibly during such events just because the property is insured. 

Example: If a person has insured his house against fire, then, in case of fire, he or she should take all possible measures to minimise the damage to the property exactly in the manner he or she would have done in absence of the insurance,

7. Principle of Causa Proxima: Principle of Causa Proxrna (a Latin phrase), or in simple English words, the Principle of Proximate (i.e. Nearest) Cause, means when a loss is caused by more than one causes, the proximate or the nearest cause should be taken into consideration to decide the liability of the insurer.

Example: If an individual suffers a loss in A fire accent, then this should already he a part of the contract in order for this person to claim the insurance amount.

Explain the types of co-operative societies.

1. Consumer’s cooperative societies: 

• The consumer cooperative societies are formed to protect the interests of consumers. 
• The members comprise of consumers desirous of obtaining good quality products at reasonable prices. 
• The society aims at eliminating middlemen to achieve economy in operations. 
• It purchases goods in bulk directly from the wholesalers and sells goods to the members directly. 
• Profits, if any, are distributed on the basis of either their capital contributions to the society or purchases made by individual members.

2. Producer’s cooperative societies:

• These societies are set up to protect the interest of small producers. 
• The members comprise of producers desirous of procuring inputs for production of goods to meet the demand of consumers. 
• The society aims to fight against the big capitalists and enhance the bargaining power of the small producers. 
• It supplies raw materials, equipment and other inputs to the members and also buys their output for sale. 
• Profits among the members are generally distributed on the basis of their contributions to the total pool of goods produced or sold by the society.

3. Marketing cooperative societies: 

• Such societies are established to help small prices in selling their products. 
• The members consist of producers who wish to obtain reasonable prices for their output. 
• The society aims to eliminate middlemen and improve competitive position of its members by securing a favorable market for the products. 
• It pools the output of individual members and performs marketing functions like transportation, warehousing, packaging, etc. 
• Profits are distributed according to each member’s contribution to the pool of output.

4. Farmer’s cooperative societies: 

• These societies are established to protect the interests of farmers by providing better inputs at a reasonable cost. 
• The members comprise of farmers who wish to jointly take up farming activities. 
• The aim is to gain the benefits of large scale farming and increase the productivity.
• Such societies provide better quality seeds, fertilizers, machinery and other modern techniques.

5. Credit cooperative societies: 

• Credit cooperative societies are established for providing easy credit on reasonable terms to the members. 
• The members comprise of persons who seek financial help in the form of loans. 
• The aim of such societies is to protect the members from the exploitation of lenders who charge high rates of interest on loans. 
• Such societies provide loans to members out of the amounts collected as capital and deposits from the members and charge low rates of interest.

6. Cooperative housing societies: 

• To help people with limited income to construct houses at reasonable costs. 
• The members of these societies consist procuring residential accommodation at lower costs.
• The aim is to solve the housing problems of the members by constructing houses and giving the option of paying in installments. 
• These societies construct flats or provide plots to members on which the members themselves can construct the houses as per their choice.

1. Ease of formation and closure: Like sole proprietorship, the partnership business can be formed easily without any legal formalities. 

2. More funds: In a partnership, the capital is contributed by a number of partners. This makes it possible to raise larger amount of funds as compared to a sole proprietor and undertake additional operations when needed. 

3. Sharing risks: The risks involved in running a partnership firm are shared by all the partners. This reduces the anxiety, burden and stress on individual partners. 

4. Secrecy: A partnership firm is not legally required to publish its accounts and submit its reports. Hence it is able to maintain confidentiality of information relating to its operations.

Demerits: 

1. Limited capital: Since the total number of partners cannot exceed 20, the capital to be raised is always limited. It may not be possible to start a very large business in partnership form. 

2. Lack of continuity of business: A partnership firm concerns to an end in the event of death, lunacy or retirement of any partner. Even otherwise, it can discontinue its business at the partners. At any time, they may take a decision to end their relationship. 

3. Lack of public confidence: There is no governmental supervision over the affairs of the business of a partnership and publishing accounts is also not necessary. Hence, public may not have full confidence in them. 

4. Unlimited liability: The liability of each partner is not limited to the amount invested but his private property is also liable to pay the business obligations.

c² cos²B + b² cos² C + bc cos (B-C)

= (cos B + b cos C)² - 2 bc cos B cos C + bc cos (B-C) (∵ a²+b² = (a+b)² - 2ab)

= a² - bc (cos(B+C) + cos(B-C)) + bc cos (B-C) (∵ 2 cosB cosC = cos(B+C) + cos(B-C))

And b cos C + c cos B = a

= a² - bc cos (B+C)

= a² - bc cos(180° - A) (∵ A+B+C = 180°, therefore B+C = 180° - A)

= a² + bc cos A

= a² + bc x \(\frac{b^2+c^2-a^2}{2bc}\) (∵ cos A \(=\frac{b^2+c^2-a^2}{2bc})\)

= a² + 1/2 (b²+c²-a²)

= 1/2 (2a²+b²+c²-a²)

= 1/2 (a²+b²+c²)

Hence proved.

The different ways of online payment are:

1. Cash-On Delivery: As is clear from the name, payment for the goods ordered online may be made in cash at the time of physical delivery of goods. 

2. Cheque: The buyer may send a cheque to the online vendor. In this case, the goods are delivered upon realisation of the cheque. 

3. Net-banking transfer: The buyer may instruct his bank to electronically transfer the amount from his account to account of online vendor.

4. Debit Card or Credit Card: Popularly referred to as ‘plastic money,’ these cards are the most widely used medium for online transactions. Credit card allows its holder to make purchase on credit. Later the issuing bank transfers the amount to the online vendors account and buyers account is debited.

5. Digital Cash: This is a form of electronic currency that exists only in cyberspace. This type of currency has no real physical properties, but offers the ability to use real currency in an electronic format.

Services of wholesale sellers to retailers are:

1. Availability of goods: Retailers have to maintain adequate stock of varied commodities so that they can offer variety to their customers. The wholesalers make the products of various manufacturers readily available to the retailers. This relieves the retailers of the work of collecting goods from several producers.

2. Marketing support: The wholesalers perform various marketing functions and provide Support to the retailers. They undertake advertisements and other sales promotional activities to induce customers to purchase the goods.

3. Grant of credit: The wholesalers generally extend credit facilities to their regular customers. This enables the retailers to manage their business with relatively small amount of working capital.

4. Specialized knowledge: The wholesalers specialize in one line of products and know the pulse of the market. They pass on the benefit of their specialized knowledge to the retailers. They inform the retailers about the new products. their uses, quality, prices, etc.

The different type of pollution are: 

1. Air Pollution: Air pollution refers to the presence of any unwanted gases, dust particles, etc. in the air, that can cause damage to people as well as nature.

Causes of Air Pollution: 

• Emission of fumes from vehicles. 
• Emission of smoke, dust and chemicals from manufacturing plants. 
• Emission of gases and dust arising from atomic plants. 
• Emission of smoke from oil refineries,burning of trees and plants in forests, burning of coal, etc.

Effects of Air Pollution: 

• Presence of gases in air, which are not required by human beings, animals and birds, creates serious health problems. It can create diseases like asthma, cough and cold, blindness, hearing loss, skin disease, etc. 
• It reduces natural visibility and irritates the eyes and respiratory tract.
• Ozone layer gets depleted because of air pollution and thereby causes gene mutation, genetic defects and skin cancer.

2. Water Pollution: Water pollution refers to contamination of water due to presence of unwanted and harmful substances thus, making water unfit for use.

Causes of Water Pollution:

• Drainage of human excreta into rivers, canals etc. 
• Improper sanitation and sewage system. 
• Dumping of wastes and effluents by various industrial units into the rivers and canals. 
• Drainage of toxic substances like chemicals and fertilizers used in cultivation, into streams and rivers.

Effects of Water Pollution: 

• It can create health hazards among human beings, animals and birds. Diseases like typhoid, jaundice, cholera, gastroenteritis, etc. are common. 
• It can endanger lives of various aquatic species. 
• It can lead to scarcity of drinking water as the water of rivers and canals as well as underground water get polluted.

3. Land Pollution: Land Pollution refers to dumping of useless, unwanted as well as hazardous substances on the land that degrades the quality of soil we use.

Causes of Land Pollution: 

• Excessive use of fertilizers, chemicals and pesticides in cultivation. 
• Disposal of solid waste of industries mines and quarries. 
• Disposal of solid waste from construction of roads, buildings, etc.
• Effluents of some plants like paper, sugar, etc. which are not absorbed by soil. 
• Excessive use of plastic bags, which are non-biodegradable.

Effects of Land Pollution: 

• Reduces the quantum of cultivable land area. 
• Causes health hazards as it contaminates the sources of food. 
• Causes damage to the landscape. 
• Leads to water and air pollution.

4. Noise Pollution: Noise simply means an unwanted sound that causes irritation. It is caused by modem machines and gadgets such as rail engines, loud speakers, generators, aeroplanes, vehicles, machineries, telephones, televisions, etc. Noise pollution can cause loss of hearing, headache, irritation, high blood pressure, neurological or psychological disorders, etc.

1. Commercial Banks: Commercial banks all over the world extend foreign currency loans for business purposes. They arc an important source of financing non-trade international operations. The types of loans and services provided by banks vary from country to country. 

2. International Agencies and Development Banks: A number of international agencies and development banks have emerged over the years to finance international trade and business. These bodies provide long and medium term loans and grants to promote the development of economically backward areas in the world. These bodies were set up by the Governments of developed countries of the world at national, regional and international levels for funding various projects. The more notable among them include International Finance Corporation (IFC), EXIM Bank and Asian Development Bank.

3. International Capital Markets: Modern organizations including multinational companies depend upon sizable borrowings in rupees as well as in foreign currency. 

Prominent financial instruments used for this purpose are:

(i) Global Depository Receipts (GDR’s): 

• Global depository receipts or certificate created by the overseas bank outside India dominated in dollars and issued to non-resident investors against the issue of ordinary shares of issuing company. 
• The depository receipts are marketed in Europe and United States of America or both.

(ii) American Depository Receipts (ADR’s): 

• The depository receipts which are issued by a United States of America Bank for trading only in American Stock markets are known as American Depository Receipts. 
• Securities of a non-U.S. company that traded in the U.S. financial markets. 

(iii) Foreign Currency Convertible Bonds (FCCB’s): 

• Foreign currency convertible bonds are equity linked debt securities that are to be converted into equity or depository receipts after a specific period. Thus, a holder of FCCB has the option of either converting them into equity shares at a predetermined price or exchange rate, or retaining the bonds.
• The FCCB’s are issued in a foreign currency and carry a fixed interest rate which is lower than the rate of any other similar non convertible debt instrument. FCCB’s are listed and traded in foreign stock exchanges.

Company generally does not distribute all its earnings amongst the shareholders as dividends. A portion of the net earnings may be retained in the business for use in the future. This is known as retained earnings.

Merits:

• Retained earnings is a permanent source of funds available to an organisation. 
• It does not involve any explicit cost in the form of interest, dividend or float at ion cost. 
• As the funds are generated internally, there is a greater degree of operational freedom and flexibility. 
• It enhances the capacity of the business to absorb unexpected losses. 
• It may lead to increase in the market price of the equity shares of a company.

(a) The main sources of income of the government are taxes which are of two types:

1. Direct taxes
2. Indirect taxes

1. Direct taxes: Direct tax is that which is paid by the same person on whom tax has been imposed legally. For example income tax, gift tax, corporate tax, wealth tax etc.

2. Indirect taxes: Indirect tax is defined as that form of taxes which are imposed on goods and services. These taxes are imposed indirectly on Public. Examples of indirect taxes are sale tax, excise duty, entertainment tax, export, import duty, GST etc.

(b) Following are the main objectives of Public Finance:

1. Price Stabilization. Public Finance maintains stability in the prices of goods and services thereby, preventing constant fluctuations and inflation and deflation that tend to destabilize the economy of a country.
2. Equitable Distribution of Wealth. Public Finance is also concerned with equitable distribution of income and wealth among individuals and various sections of the country. „
3. Satisfaction of Needs. The satisfaction of collective needs is another main objective of Public Finance.
4. Allocation of Resources. Public Finance performs the function of allocating resources among public and private sectors.
5. Provision of full employment. Provision of full employment opportunities to citizens of a country is another aim to public finance.

1. b) Maintaining internal law and order

2. c) Prof. Hugh Dalton

3. (1) a, b and d

Q3. indirect tax

Correct answer is (d) 39 cm

60 minutes = 360 degrees.

1 minutes = 6 degrees. 

40 minutes = 240 degrees

240° = 240 × \(\frac{\pi}{180} = \frac{4 \pi}{3}\)

The required distance travelled = l = rθ

1.5 x \(\frac{4 \pi}{3} = 2 x 3.14 = 6.28 cm\)

Correct option is: (c) 132 cm

Given:

The number 892547x2 is divisible by 9

Concept used:

If the number is divisible by 9, then sum of its digits is also divisible by 9.

Calculation:

As the number is divisible by 9 then,

8 + 9 + 2 + 5 + 4 + 7 + x + 2 is divisible by 9

 is divisible by 9

Nearest number to 37 which is divisible by 9 is 45

37 + x = 45

⇒ x = 45 – 37 = 8

Next nearest number is 54

37 + x = 54

⇒ x = 54 – 37 = 17

x cannot be 17 as it’s a two digit number

∴ x is 8

Answer is (c) iii , iv

Given:

The given number = 675x797

Concept used:

If the sum of all digits of a number is divisible by 3 then the number is divisible by 3.

Calculation:

Our number = 675x797

Sum of digits of the number = 41 + x

∴ Least number in place of x is 1

Given

Difference between age of man and woman = 6 years

12 years after the marriage, man's age was 6/5 times the age of his wife

Calculation

Let the age of wife at the time of marriage be 'x'

Then the age of husband at the time of marriage was 'x + 6'

After 12 years of marriage,

(x + 6) + 12 = (6/5)(x + 12)

⇒ 5(x + 18) = 6(x + 12)

⇒ 5x + 90 = 6x + 72

⇒ x = 18

So, Age of wife = 18

∴ Age of husband = 18 + 6 = 24

So, their ages at the time of marriage were 24 years and 18 years

Answer is c. i and iv

(c) Halo effect

Correct option  (1)  (i)

Explanation:

 (i)  (P ∨  q) ∨ (p ∨ ~ q) = p ∨ (q ∨ ~ q) = P ∨ t = t

(ii)  (P ∨ q) ∧ (p  ~  q)

(iii)  (P ∨  q) ∧ (p  ∨ ~  q) =  p ∨ (q ∨ ~ q) = P ∨ f = p

(iv)  (P ∨  q) ∨ (p  ∧ ~  q)

(P ∧ q) ∧ (p  ∨ ~  q)

(2) If you are not citizen of India then you are not born in India.

Correct option (2)  Stratosphere

Explanation:

Stratosphere  lies between 10 to 50 km.from sea level.

The correct option 

(1) Troposphere and troposphere

The correct option is (1) (B), (C) and (D).

Explanation:

(B) is anti-aromatic with 4 πe^–. 

(C) is anti-aromatic with 8 πe^–. 

(D) is non aromatic, because of sp³ carbon in the ring.