If $$R=\left\{\left(x,y\right):y=2x\right\}$$ is a relation in $$A=\left\{1,2,3,4,6,7,8\right\}$$ then write all the elements of $$R$$

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Subjective Type
Sharma brothers inherited some ancestoral property. They decided to form a Hindu undivided family consisting of four male members. Mr. Raman Sharma was eldest brother so he became 'Karta'. The business took a loan of Rs. 20 lac from Canara Bank, which was to be returned within 5 years. Due to poor financial position of the business, they were unable to repay the loan. Brothers sold the ancestoral property for Rs. 10 lac and paid the amount to Canara Bank. The bank filed a case for recovery of balance amount. Mr. Raman Sharma pleaded the court that the loan was taken for the purpose of Business; so all members of business are liable to repay. The court said all members are responsible only to the extent of their share in business and business property is already sold, but you being Karta will have to repay whole amount even by selling your personal property. (a) In this case who has unlimited liability? (b) Was the decision of court to claim only from Raman is justified?
Solution
(a)Mr. Raman Sharma has unlimited liability in this case. This is so because he is the Karta, i.e. ,he is the senior most male member of the family and as a head or manager of the family, he is the representative of the family and acts for or on behalf of the family. A Karta is a person in whom, others in the family repose confidence, so between the Karta and the family members there is a fiduciary relation because there is always a need for a manager to look after the welfare of minor members and females in a joint Hindu family. Such manager of the joint Hindu Family is known as the Karta of family and he enjoys immense powers in respect of the management of the affairs of family and its property. A Karta incurs unlimited liability and is representative of the family in all the affairs. It has been said regarding the position of Karta that no one else is equivalent to him in the family. The position and powers are wider than anyone. If the business suffers from losses then the amount can be recovered from the Karta's personal property. (b) The decision of court to claim only from Raman is justified. This is so because in the case of HUF, if the business suffers from losses, then the losses can be recovered from the Karta's personal property. The co-partners are responsible to bear the losses upto the extent of share in the profit.They are not liable to pay from their personal property and since the business property is already sold, Karta will have to repay whole amount even by selling his personal property.
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