All India CA Foundation Group
The agency extends to receiving notice on behalf of his principal of whatever is material to be stated in the course of the proceedings. For this rule to operate:
I. the agent must be under a duty to communicate
II. the information must be material
III. it must have been obtained in the course of business for which the agent has been engaged
IV. the agent is not privy to a fraud on the principal- a)I, II
- b)II, IV
- c)Ill, IV
- d)All of them
Correct answer is option 'D'. Can you explain this answer?
The agency extends to receiving notice on behalf of his principal of whatever is material to be stated in the course of the proceedings. For this rule to operate:
I. the agent must be under a duty to communicate
II. the information must be material
III. it must have been obtained in the course of business for which the agent has been engaged
IV. the agent is not privy to a fraud on the principal
I. the agent must be under a duty to communicate
II. the information must be material
III. it must have been obtained in the course of business for which the agent has been engaged
IV. the agent is not privy to a fraud on the principal
a)
I, II
b)
II, IV
c)
Ill, IV
d)
All of them
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Anuj Roy answered • 48 minutes ago |
Understanding the Rule of Agency in Legal Proceedings
In agency law, certain conditions must be met for an agent to effectively receive notice on behalf of their principal. Each of the provided statements contributes to the validity of the agent's authority to receive material information during proceedings.
Key Conditions for Agency Notice
In agency law, certain conditions must be met for an agent to effectively receive notice on behalf of their principal. Each of the provided statements contributes to the validity of the agent's authority to receive material information during proceedings.
Key Conditions for Agency Notice
- I. The agent must
The extent of an agent’s authority, whether express or implied, depends upon:- a)The nature of act or business for which he has been appointed
- b)Things which are incidental to the business or are usually done in carrying it out
- c)The usual customs and usages of the trade
- d)All of them
Correct answer is option 'D'. Can you explain this answer?
The extent of an agent’s authority, whether express or implied, depends upon:
a)
The nature of act or business for which he has been appointed
b)
Things which are incidental to the business or are usually done in carrying it out
c)
The usual customs and usages of the trade
d)
All of them
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Anuj Roy answered • 48 minutes ago |
Understanding Agent's Authority
The extent of an agent's authority is crucial in determining the scope of their actions and responsibilities. This authority can be either express (clearly defined) or implied (assumed based on circumstances). The correct answer, 'D', acknowledges that several factors collectively shape an agent's authority.
Factors Influencing Authority
... more
The extent of an agent's authority is crucial in determining the scope of their actions and responsibilities. This authority can be either express (clearly defined) or implied (assumed based on circumstances). The correct answer, 'D', acknowledges that several factors collectively shape an agent's authority.
Factors Influencing Authority
... more
Termination of an agency with public authority or a public body may attract judicial intervention in writ petition:- a)If the termination be unreasonable
- b)If the termination be arbitrary
- c)If the termination be unconscionable
- d)All of them
Correct answer is option 'D'. Can you explain this answer?
Termination of an agency with public authority or a public body may attract judicial intervention in writ petition:
a)
If the termination be unreasonable
b)
If the termination be arbitrary
c)
If the termination be unconscionable
d)
All of them
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Anuj Roy answered • 48 minutes ago |
Understanding Termination of Agency with Public Authority
When an agency with public authority or a public body terminates a contract or service, judicial intervention through a writ petition can be necessary under certain conditions.
Reasons for Judicial Intervention
- If the termination be unreasonable:
Judicial review may be warranted if the terminati... more
When an agency with public authority or a public body terminates a contract or service, judicial intervention through a writ petition can be necessary under certain conditions.
Reasons for Judicial Intervention
- If the termination be unreasonable:
Judicial review may be warranted if the terminati... more
An agency is irrecoverable:- a)Where the authority of agency is one coupled with interest
- b)Where the agent has incurred personal liability
- c)Both (a) and (b)
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
An agency is irrecoverable:
a)
Where the authority of agency is one coupled with interest
b)
Where the agent has incurred personal liability
c)
Both (a) and (b)
d)
None of the above
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Anuj Roy answered • 48 minutes ago |
Understanding Irrecoverable Agency
An agency is considered irrecoverable when certain conditions are met. The correct answer is option 'C', which includes both situations mentioned in options (a) and (b). Here’s a detailed explanation:
1. Authority of Agency Coupled with Interest
- An agency is irrevocable when the agent has an interest in the subject matter of ... more
An agency is considered irrecoverable when certain conditions are met. The correct answer is option 'C', which includes both situations mentioned in options (a) and (b). Here’s a detailed explanation:
1. Authority of Agency Coupled with Interest
- An agency is irrevocable when the agent has an interest in the subject matter of ... more
Under a contract of guarantee:- a)if principal debtor is not liable, guarantor is not liable
- b)if principal debtor is not liable, guarantor is liable
- c)if principal debtor is liable, guarantor is liable
- d)all the above
Correct answer is option 'C'. Can you explain this answer?
Under a contract of guarantee:
a)
if principal debtor is not liable, guarantor is not liable
b)
if principal debtor is not liable, guarantor is liable
c)
if principal debtor is liable, guarantor is liable
d)
all the above
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Anuj Roy answered • 49 minutes ago |
Understanding a Contract of Guarantee
In a contract of guarantee, the relationship between the principal debtor, the guarantor, and the creditor is crucial in determining liability.
Key Principles of Guarantee
- Principal Debtor's Liability: The principal debtor is the primary party responsible for fulfilling the obligation.
- Guarantor's Role: The ... more
In a contract of guarantee, the relationship between the principal debtor, the guarantor, and the creditor is crucial in determining liability.
Key Principles of Guarantee
- Principal Debtor's Liability: The principal debtor is the primary party responsible for fulfilling the obligation.
- Guarantor's Role: The ... more
A continuing guarantee applies to:- a)a specific transaction
- b)a specific number of transactions
- c)all transactions of specific transaction series
- d)reasonable number of transactions.
Correct answer is option 'C'. Can you explain this answer?
A continuing guarantee applies to:
a)
a specific transaction
b)
a specific number of transactions
c)
all transactions of specific transaction series
d)
reasonable number of transactions.
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Anuj Roy answered • 49 minutes ago |
Understanding Continuing Guarantee
A continuing guarantee is a crucial concept in financial agreements, particularly in the context of credit and loans. It pertains to the obligations of a guarantor to cover a borrower’s debts over a series of transactions rather than just one.
What is a Continuing Guarantee?
- A continuing guarantee is a legal commitment by a guaranto... more
A continuing guarantee is a crucial concept in financial agreements, particularly in the context of credit and loans. It pertains to the obligations of a guarantor to cover a borrower’s debts over a series of transactions rather than just one.
What is a Continuing Guarantee?
- A continuing guarantee is a legal commitment by a guaranto... more
The contract of Guarantee should be _______- a)Implied
- b)only written
- c)only oral
- d)written or oral
Correct answer is option 'D'. Can you explain this answer?
The contract of Guarantee should be _______
a)
Implied
b)
only written
c)
only oral
d)
written or oral
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Anuj Roy answered • 49 minutes ago |
Understanding the Contract of Guarantee
The contract of guarantee is a crucial element in financial and commercial transactions. It serves as a security measure that ensures one party's obligations are fulfilled by another.
Forms of Guarantee
- Written or Oral: The contract can be established in both written and oral forms. This flexibility allows parties to en... more
The contract of guarantee is a crucial element in financial and commercial transactions. It serves as a security measure that ensures one party's obligations are fulfilled by another.
Forms of Guarantee
- Written or Oral: The contract can be established in both written and oral forms. This flexibility allows parties to en... more
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Rohit Choudhary
asked a question
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A, B and C takes a Joint Life Policy, after five years B retires from the firm. Old profit sharing ratio is 2:2:1. After retirement A and C decides to share profits equally. They had taken a Joint Life Policy of Rs. 2,50,000 with the surrender value Rs. 50,000. What will be the treatment in the partner’s capital account on receiving the JLP amount if joint life policy is maintained at surrender along with the reserve?- a)Rs. 50,000 credited to all the partners in old ratio
- b)Rs. 2,50,000 credited to all the partners in old ratio
- c)Rs. 2,00,000 credited to all the partners in old ratio
- d)Distribute JLP Reserve Account in old profit sharing ratio.
Correct answer is option 'D'. Can you explain this answer?
A, B and C takes a Joint Life Policy, after five years B retires from the firm. Old profit sharing ratio is 2:2:1. After retirement A and C decides to share profits equally. They had taken a Joint Life Policy of Rs. 2,50,000 with the surrender value Rs. 50,000. What will be the treatment in the partner’s capital account on receiving the JLP amount if joint life policy is maintained at surrender along with the reserve?
a)
Rs. 50,000 credited to all the partners in old ratio
b)
Rs. 2,50,000 credited to all the partners in old ratio
c)
Rs. 2,00,000 credited to all the partners in old ratio
d)
Distribute JLP Reserve Account in old profit sharing ratio.
In contract of indemnity how many parties are required ?- a)4
- b)6
- c)7
- d)2
Correct answer is option 'D'. Can you explain this answer?
In contract of indemnity how many parties are required ?
a)
4
b)
6
c)
7
d)
2
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Anuj Roy answered • 49 minutes ago |
Understanding Contract of Indemnity
A contract of indemnity is a crucial legal agreement that involves protection against loss or damage. It is defined under Section 124 of the Indian Contract Act, 1872.
Parties Involved
- Two Parties: The contract of indemnity requires only two parties:
- Indemnifier: The party who promises to compensate for the l... more
A contract of indemnity is a crucial legal agreement that involves protection against loss or damage. It is defined under Section 124 of the Indian Contract Act, 1872.
Parties Involved
- Two Parties: The contract of indemnity requires only two parties:
- Indemnifier: The party who promises to compensate for the l... more
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Aishwarya Walunj
asked a question
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Let a sample space be S = {X1, X2, X3} which of the fallowing defines probability space on S ?- a)P(X1)= ¼ , P(X2)= 1/3 , P(X3)= 1/3
- b)P(X1)= 0, P(X2)= 1/3, P(X3)= 2/3
- c)P(X1)= 2/3 , P(X2)= 1/3 , P(X3)= 2/3
- d)none
Correct answer is option 'B'. Can you explain this answer?
Let a sample space be S = {X1, X2, X3} which of the fallowing defines probability space on S ?
a)
P(X1)= ¼ , P(X2)= 1/3 , P(X3)= 1/3
b)
P(X1)= 0, P(X2)= 1/3, P(X3)= 2/3
c)
P(X1)= 2/3 , P(X2)= 1/3 , P(X3)= 2/3
d)
none
The contract of guarantee is for protection of _______- a)creditor
- b)debtor
- c)guarantor
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
The contract of guarantee is for protection of _______
a)
creditor
b)
debtor
c)
guarantor
d)
none of these
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Anuj Roy answered • 49 minutes ago |
Understanding the Contract of Guarantee
The contract of guarantee is a crucial legal agreement in financial transactions, primarily aimed at protecting the interests of creditors. Here’s a detailed explanation of why the correct answer is option 'A'.
Definition of a Contract of Guarantee
- A contract of guarantee is an agreement where one party (the guarantor) agrees t... more
The contract of guarantee is a crucial legal agreement in financial transactions, primarily aimed at protecting the interests of creditors. Here’s a detailed explanation of why the correct answer is option 'A'.
Definition of a Contract of Guarantee
- A contract of guarantee is an agreement where one party (the guarantor) agrees t... more
The person in respect of whose default, the guarantee is given is called ………..- a)principal debtor
- b)principal creditor
- c)principal surety
- d)principal bailee
Correct answer is option 'A'. Can you explain this answer?
The person in respect of whose default, the guarantee is given is called ………..
a)
principal debtor
b)
principal creditor
c)
principal surety
d)
principal bailee
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Anuj Roy answered • 49 minutes ago |
Understanding the Principal Debtor in Guarantees
Guarantees are important financial instruments that provide security to creditors. In the context of guarantees, it's essential to identify the roles of the parties involved.
Who is the Principal Debtor?
- The principal debtor is the individual or entity that owes a debt or obligation to a creditor.
- This person is... more
Guarantees are important financial instruments that provide security to creditors. In the context of guarantees, it's essential to identify the roles of the parties involved.
Who is the Principal Debtor?
- The principal debtor is the individual or entity that owes a debt or obligation to a creditor.
- This person is... more
The pledge is a contract of ______- a)bailment
- b)agency
- c)guarantee
- d)mortgage
Correct answer is option 'A'. Can you explain this answer?
The pledge is a contract of ______
a)
bailment
b)
agency
c)
guarantee
d)
mortgage
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Anuj Roy answered • 49 minutes ago |
The Pledge as a Contract of Bailment
A pledge is fundamentally a contract of bailment, and it involves the transfer of possession of goods from one party to another for a specific purpose, with the understanding that the goods will be returned after the purpose is fulfilled.
Key Characteristics of a Pledge:
- Definition of Bailment: Bailment refers to the relati... more
A pledge is fundamentally a contract of bailment, and it involves the transfer of possession of goods from one party to another for a specific purpose, with the understanding that the goods will be returned after the purpose is fulfilled.
Key Characteristics of a Pledge:
- Definition of Bailment: Bailment refers to the relati... more
Lien means _______- a)to retain goods in his possession
- b)rights to sell the goods
- c)right to purchase the goods
- d)right to destroy the goods
Correct answer is option 'A'. Can you explain this answer?
Lien means _______
a)
to retain goods in his possession
b)
rights to sell the goods
c)
right to purchase the goods
d)
right to destroy the goods
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Anuj Roy answered • 49 minutes ago |
Understanding Lien
A lien is a legal right or interest that a lender or creditor has in the property of a borrower, typically used as security for a debt or obligation. In this context, the correct answer is option 'A': to retain goods in his possession.
Key Aspects of Lien:
- Definition: A lien allows a person or entity to retain possession of another's propert... more
A lien is a legal right or interest that a lender or creditor has in the property of a borrower, typically used as security for a debt or obligation. In this context, the correct answer is option 'A': to retain goods in his possession.
Key Aspects of Lien:
- Definition: A lien allows a person or entity to retain possession of another's propert... more
Bailment means _____- a)temporary delivery of goods
- b)permanent delivery of goods
- c)part delivery of goods
- d)None
Correct answer is option 'A'. Can you explain this answer?
Bailment means _____
a)
temporary delivery of goods
b)
permanent delivery of goods
c)
part delivery of goods
d)
None
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Anuj Roy answered • 50 minutes ago |
Understanding Bailment
Bailment is a legal term that refers to the temporary transfer of possession of goods from one party to another, where the ownership remains with the original owner. This concept is essential in various transactions, including storage, repair, and transportation of goods.
Key Features of Bailment:
- Temporary Delivery: The hallmark of bail... more
Bailment is a legal term that refers to the temporary transfer of possession of goods from one party to another, where the ownership remains with the original owner. This concept is essential in various transactions, including storage, repair, and transportation of goods.
Key Features of Bailment:
- Temporary Delivery: The hallmark of bail... more
The Bailment of goods as security for payment of a debt or performance of a promise is called:- a)Pledge
- b)Bailment
- c)Contingent contract
- d)Agreement
Correct answer is option 'A'. Can you explain this answer?
The Bailment of goods as security for payment of a debt or performance of a promise is called:
a)
Pledge
b)
Bailment
c)
Contingent contract
d)
Agreement
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Anuj Roy answered • 50 minutes ago |
Understanding Pledge in Bailment
In legal terms, a pledge is a specific type of bailment where goods are transferred to a lender as security for a debt or performance of a promise. Here’s a deeper look into why the correct answer is option 'A'.
Definition of Pledge
- A pledge involves the delivery of goods to a creditor (the pledgee) by the borrower (the pledgor) as co... more
In legal terms, a pledge is a specific type of bailment where goods are transferred to a lender as security for a debt or performance of a promise. Here’s a deeper look into why the correct answer is option 'A'.
Definition of Pledge
- A pledge involves the delivery of goods to a creditor (the pledgee) by the borrower (the pledgor) as co... more
In pledge contract, bailee is called- a)Pawnor
- b)Pawnee
- c)Pledger
- d)None of above
Correct answer is option 'B'. Can you explain this answer?
In pledge contract, bailee is called
a)
Pawnor
b)
Pawnee
c)
Pledger
d)
None of above
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Anuj Roy answered • 50 minutes ago |
Pledge Contract Overview
A pledge contract is a specific type of bailment where a person (the pledgor) delivers goods to another person (the pledgee) as security for a debt or obligation. Understanding the roles in a pledge contract is crucial for clarity in legal contexts.
Key Roles in a Pledge Contract
- Pledgor: The person who delivers the goods to the pledge... more
A pledge contract is a specific type of bailment where a person (the pledgor) delivers goods to another person (the pledgee) as security for a debt or obligation. Understanding the roles in a pledge contract is crucial for clarity in legal contexts.
Key Roles in a Pledge Contract
- Pledgor: The person who delivers the goods to the pledge... more
Which of the following statements is incorrect?- a)An agency may be terminated by death of either party.
- b)An agency may be terminated by express agreement.
- c)An agency agreement can always be terminated by a principal.
- d)Mental incapacity of an agent will terminate the agency relationship.
Correct answer is option 'A'. Can you explain this answer?
Which of the following statements is incorrect?
a)
An agency may be terminated by death of either party.
b)
An agency may be terminated by express agreement.
c)
An agency agreement can always be terminated by a principal.
d)
Mental incapacity of an agent will terminate the agency relationship.
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Anuj Roy answered • 50 minutes ago |
Understanding Agency Termination
In the context of agency law, it's crucial to understand how and when an agency relationship can be terminated. Here’s a detailed explanation of why option 'A' is incorrect.
Agency Termination by Death
- The statement claims that an agency may be terminated by the death of either party. This is incorrect because:
- If the a... more
In the context of agency law, it's crucial to understand how and when an agency relationship can be terminated. Here’s a detailed explanation of why option 'A' is incorrect.
Agency Termination by Death
- The statement claims that an agency may be terminated by the death of either party. This is incorrect because:
- If the a... more
When does apparent (ostensible) authority of an agent arise?- a)When the agent acts with the usual authority of his job.
- b)When the principal gives the agent implied authority to act.
- c)When the agent has actual authority to act.
- d)When the principal represents to a third party that an agent has authority to act when in fact he does not.
Correct answer is option 'D'. Can you explain this answer?
When does apparent (ostensible) authority of an agent arise?
a)
When the agent acts with the usual authority of his job.
b)
When the principal gives the agent implied authority to act.
c)
When the agent has actual authority to act.
d)
When the principal represents to a third party that an agent has authority to act when in fact he does not.
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Anuj Roy answered • 50 minutes ago |
Understanding Apparent Authority
Apparent authority, also known as ostensible authority, arises when a principal creates the impression that an agent has the authority to act on their behalf, even if the agent lacks actual authority. This concept is crucial in agency law, particularly in protecting third parties who rely on the representations made by the principal.
Key Points ... more
Apparent authority, also known as ostensible authority, arises when a principal creates the impression that an agent has the authority to act on their behalf, even if the agent lacks actual authority. This concept is crucial in agency law, particularly in protecting third parties who rely on the representations made by the principal.
Key Points ... more
Cute appoints Govind, to act as his agent for two weeks. Govind agrees to act without payment. Cute instructs Govind to collect rent each Friday morning from his tenants and pay the rent into the bank next door. In the second week, Govind collects the rent but fails to bank it. On the way home he leaves it on the bus and it is never recovered. Can Cute take action against Govind for breach of his agency duties?- a)No, Cute has provided no Consideration and therefore there is no agency agreement.
- b)No, Govind is a gratuitous agent and has no duty to follow instructions.
- c)Yes, even though Govind is a gratuitous agent if he must do in accordance with instructions set out by the principal.
- d)Yes, provided he pays Govind for being an agent.
Correct answer is option 'C'. Can you explain this answer?
Cute appoints Govind, to act as his agent for two weeks. Govind agrees to act without payment. Cute instructs Govind to collect rent each Friday morning from his tenants and pay the rent into the bank next door. In the second week, Govind collects the rent but fails to bank it. On the way home he leaves it on the bus and it is never recovered. Can Cute take action against Govind for breach of his agency duties?
a)
No, Cute has provided no Consideration and therefore there is no agency agreement.
b)
No, Govind is a gratuitous agent and has no duty to follow instructions.
c)
Yes, even though Govind is a gratuitous agent if he must do in accordance with instructions set out by the principal.
d)
Yes, provided he pays Govind for being an agent.
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Anuj Roy answered • 51 minutes ago |
Understanding Agency Duties
In this scenario, Govind is appointed as a gratuitous agent for Cute, meaning he is acting without any payment. However, even as a gratuitous agent, he still has certain duties toward his principal.
Key Duties of an Agent
- Follow Instructions: An agent must act according to the instructions given by the principal. In this case, Govin... more
In this scenario, Govind is appointed as a gratuitous agent for Cute, meaning he is acting without any payment. However, even as a gratuitous agent, he still has certain duties toward his principal.
Key Duties of an Agent
- Follow Instructions: An agent must act according to the instructions given by the principal. In this case, Govin... more
Pranab asked his agent, Hari to purchase her 500 shares in X Ltd. Hari owned 600 shares in X Ltd., so without informing Pranab where the shares come from he sells his shares to Pranab at market value. Is Hari in breach of his agency duties?- a)Yes, because he has a duty to avoid a conflict of interest.
- b)Yes, because he has a duty to account.
- c)No, because he has sold Pranab the shares at market value.
- d)No, because he has acted according to Pranab’s instructions and she has the shares as she requested.
Correct answer is option 'A'. Can you explain this answer?
Pranab asked his agent, Hari to purchase her 500 shares in X Ltd. Hari owned 600 shares in X Ltd., so without informing Pranab where the shares come from he sells his shares to Pranab at market value. Is Hari in breach of his agency duties?
a)
Yes, because he has a duty to avoid a conflict of interest.
b)
Yes, because he has a duty to account.
c)
No, because he has sold Pranab the shares at market value.
d)
No, because he has acted according to Pranab’s instructions and she has the shares as she requested.
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Anuj Roy answered • 51 minutes ago |
Understanding the Breach of Agency Duties
In the scenario presented, Hari's actions as an agent raise significant ethical concerns regarding his duties towards Pranab. Let's explore why the correct answer is option 'A'.
Conflict of Interest
- Hari, as an agent, holds a fiduciary duty to act in the best interests of Pranab.
- By selling his own shares to Pranab wit... more
In the scenario presented, Hari's actions as an agent raise significant ethical concerns regarding his duties towards Pranab. Let's explore why the correct answer is option 'A'.
Conflict of Interest
- Hari, as an agent, holds a fiduciary duty to act in the best interests of Pranab.
- By selling his own shares to Pranab wit... more
_________Contracts are enforceable by future events.- a)Contingent Contract
- b)Quasi Contract
- c)Conditional Contract
- d)Wagering Contract
Correct answer is option 'A'. Can you explain this answer?
_________Contracts are enforceable by future events.
a)
Contingent Contract
b)
Quasi Contract
c)
Conditional Contract
d)
Wagering Contract
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Anuj Roy answered • 54 minutes ago |
Understanding Contingent Contracts
Contingent contracts are a unique category of agreements that hinge on the occurrence of future events. These contracts become enforceable only when a specified condition is met.
Definition of Contingent Contract
- A contingent contract is defined as an agreement where the performance is dependent on the happening or non-happening of... more
Contingent contracts are a unique category of agreements that hinge on the occurrence of future events. These contracts become enforceable only when a specified condition is met.
Definition of Contingent Contract
- A contingent contract is defined as an agreement where the performance is dependent on the happening or non-happening of... more
A contingent contract is ____________- a)Void
- b)Voidable
- c)Valid
- d)Illegal
Correct answer is option 'C'. Can you explain this answer?
A contingent contract is ____________
a)
Void
b)
Voidable
c)
Valid
d)
Illegal
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Anuj Roy answered • 56 minutes ago |
Understanding Contingent Contracts
A contingent contract is a type of agreement that relies on the occurrence of a specific event to become enforceable. The characteristics and implications of contingent contracts are crucial for understanding their validity in legal terms.
Definition of a Contingent Contract
- A contingent contract is defined under Section 31 of the I... more
A contingent contract is a type of agreement that relies on the occurrence of a specific event to become enforceable. The characteristics and implications of contingent contracts are crucial for understanding their validity in legal terms.
Definition of a Contingent Contract
- A contingent contract is defined under Section 31 of the I... more
A function f(x) is defined by f(x) =(x - 2) + x2 overall real values of x, now f(x) is- a)continuous at x = 2
- b)discontinuous at x = 2
- c)Undefined at x = 2
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
A function f(x) is defined by f(x) =(x - 2) + x2 overall real values of x, now f(x) is
a)
continuous at x = 2
b)
discontinuous at x = 2
c)
Undefined at x = 2
d)
none of these
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Anuj Roy answered • 58 minutes ago |
Understanding the Function f(x)
The function f(x) is defined as:
f(x) = (x - 2) + x^2
This function is a polynomial, which is made up of basic algebraic components. Polynomials are defined for all real values of x, meaning they have no restrictions on their domain.
Continuity at x = 2
To determine if f(x) is continuous at x = 2, we need to check the following... more
The function f(x) is defined as:
f(x) = (x - 2) + x^2
This function is a polynomial, which is made up of basic algebraic components. Polynomials are defined for all real values of x, meaning they have no restrictions on their domain.
Continuity at x = 2
To determine if f(x) is continuous at x = 2, we need to check the following... more
The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is- a)12c4 × 5c3
- b)17c7
- c)
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is
a)
12c4 × 5c3
b)
17c7
c)
d)
none of these
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Srsps answered • 4 hours ago |
- Selecting and Arranging the Consonants:
- Selection: Choose 4 consonants out of 12.
- Arrangement: Arrange the selected 4 consonants in order.
- Number of Ways: This is represented by the permutation notation 12P4.
- Selecting and Arranging the Vowels:
- Selection: Choose 3 vowels out of 5.
- Arrangement: Arrange the selected 3 vowels in order.
- Number of Ways: This is represented by the permutation notation 5P3.
- Combining Consonants and Vowels:
- After selecting and arranging the consonants and vowels separately, we need to arrange all 7 letters together to form a word.
- Number of Ways: The 7 letters can be arranged in 7! (7 factorial) ways.
- Total Number of Different Words:
- Multiply the number of ways to arrange consonants, vowels, and the combined letters.
- Total Ways = 12P4 × 5P3 × 7! = 4950 x 7!
-
There are 5 speakers A, B, C, D and E. The number of ways in which A will speak always before B is- a)24
- b)
- c)
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
There are 5 speakers A, B, C, D and E. The number of ways in which A will speak always before B is
a)
24
b)
c)
d)
none of these
|
|
Srsps answered • 5 hours ago |
. Treat A and B as a Single Unit
Since Speaker A must always speak immediately before Speaker B, we can consider them as a single combined entity, denoted as AB.
- Combined Units to Arrange:
- AB (A and B together)
- C
- D
- E
This effectively reduces the problem to arranging 4 units instead of 5.
2. Calculate the Number of Arrangements
- Number of Units to Arrange: 4 (AB, C, D, E)
- Number of Ways to Arrange 4 Units:
- This is given by 4 factorial, written as 4!
- 4! = 4 × 3 × 2 × 1 = 24
3. Arranging Within the Combined Unit (AB)
- Since A must always come before B within the combined unit AB, there's only 1 way to arrange them (A followed by B).
- Number of Arrangements for AB: 1
4. Total Number of Arrangements
- Total Ways = Arrangements of Units × Arrangements within AB
- Total Ways = 4! × 1 = 24
The number of ways in which 6 men can be arranged in a row so that the particular 3 men sit together, is- a)4P4
- b)4P4 × 3P3
- c)
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
The number of ways in which 6 men can be arranged in a row so that the particular 3 men sit together, is
a)
4P4
b)
4P4 × 3P3
c)
d)
none of these
|
Freedom Institute answered • 5 hours ago |
- Treat the 3 Specific Men as a Single Unit:
- By grouping the 3 particular men together, we effectively reduce the problem to arranging 4 units:
- The grouped unit of 3 men.
- The remaining 3 individual men.
- By grouping the 3 particular men together, we effectively reduce the problem to arranging 4 units:
- Arranging the 4 Units:
- The 4 units can be arranged in a row in 4 factorial ways.
- 4 factorial is written as 4!, which equals 24.
- Arranging the 3 Men Within Their Group:
- The 3 specific men within their grouped unit can be arranged among themselves in 3 factorial ways.
- 3 factorial is written as 3!, which equals 6.
- Combining Both Arrangements:
- To find the total number of arrangements, multiply the number of ways to arrange the 4 units by the number of ways to arrange the 3 men within their group.
- Total Ways = 4! × 3!
which is 4P4 x 3P3
-
The total number of 9 digit numbers of different digits is- a)
- b)
- c)
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
The total number of 9 digit numbers of different digits is
a)
b)
c)
d)
none of these
|
|
Srsps answered • 5 hours ago |
- First Digit:
- Choices: 9 (digits 1 through 9)
- Representation: 9
- Remaining 8 Digits:
- After choosing the first digit, there are 9 remaining digits (including zero) to choose from, but each subsequent digit must be unique.
- The number of ways to arrange these 8 digits is represented by 9 factorial, written as 9!
Combining the Choices
- Total Number of 9-Digit Numbers with All Different Digits:To find the total number of unique 9-digit numbers, multiply the number of choices for the first digit by the number of ways to arrange the remaining digits.Total Ways = 9 × 9!
3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is- a)70
- b)27
- c)72
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is
a)
70
b)
27
c)
72
d)
none of these
|
|
Freedom Institute answered • 5 hours ago |
- Choosing the Pair of Ladies:
- There are three ladies: Lady X, Lady Y, and Lady Z.
- We need to choose 2 out of these 3 to sit together.
- Number of ways to choose the pair: 3 (XY, XZ, YZ).
- Arranging the Paired Ladies:
- The two chosen ladies can switch places within their pair.
- Number of arrangements for the pair: 2.
- Selecting Seats for the Ladies:
- After placing the gents, there are three seats left for the ladies.
- To ensure that only two ladies sit together:
- Choose one of the three available seats to place the pair of ladies.
- Number of ways to choose the seat for the pair: 3.
- Placing the Third Lady:
- The third lady must sit in one of the remaining two seats that are not adjacent to the pair.
- Number of ways to place her: 2.
Step 4: Calculating the Total Number of Arrangements
Now, multiply the number of ways from each step:
- Arrangements of the remaining gents: 2
- Choosing the pair of ladies: 3
- Arranging the pair: 2
- Choosing the seat for the pair: 3
- Placing the third lady: 2
Total Ways = 2 (gents) × 3 (pairs) × 2 (arrangements) × 3 (seat choices) × 2 (placing third lady) = 72
nPr can also written as- a)
- b)
- c)
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
nPr can also written as
a)
b)
c)
d)
none of these
|
|
Srsps answered • 5 hours ago |
We already know that nPr can be written as 
The number of 4 digits number formed with the digits 1,1,2,2,3,4?
|
|
Prasenjit Kapoor answered • 14 hours ago |
Understanding the Problem
To find the number of unique 4-digit numbers formed from the digits 1, 1, 2, 2, 3, 4, we need to consider the repetitions of certain digits.
Available Digits
- The digits we have are: 1, 1, 2, 2, 3, 4.
- We can use each digit only as many times as it appears in the list.
Cases for Selection
We can categorize the selection... more
To find the number of unique 4-digit numbers formed from the digits 1, 1, 2, 2, 3, 4, we need to consider the repetitions of certain digits.
Available Digits
- The digits we have are: 1, 1, 2, 2, 3, 4.
- We can use each digit only as many times as it appears in the list.
Cases for Selection
We can categorize the selection... more
Eight guests have to be seated 4 on each side of a rectangular table, 2 particular guest desires to on one side of the table and 3 on the other side.. The number of ways in which the sitting arrangements can be made is?
|
Jyoti Nair answered • 14 hours ago |
Understanding the Seating Arrangement
To solve the problem of seating 8 guests at a rectangular table with specific preferences, we need to account for the guests' desires regarding their seating sides.
Guests' Preferences
- 2 Particular Guests: They want to sit on one side of the table.
- 3 Other Guests: They prefer to sit on the opposite side.
... more
To solve the problem of seating 8 guests at a rectangular table with specific preferences, we need to account for the guests' desires regarding their seating sides.
Guests' Preferences
- 2 Particular Guests: They want to sit on one side of the table.
- 3 Other Guests: They prefer to sit on the opposite side.
... more
The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is?
|
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Niharika Chavan answered • 14 hours ago |
Understanding the Problem
To find the total number of different words that can be formed using 12 consonants and 5 vowels by selecting 4 consonants and 3 vowels, we need to follow these steps:
Step 1: Selecting Consonants
- Choose 4 consonants from 12 available consonants.
- The number of ways to choose 4 consonants can be calculated using combinations.
St... more
To find the total number of different words that can be formed using 12 consonants and 5 vowels by selecting 4 consonants and 3 vowels, we need to follow these steps:
Step 1: Selecting Consonants
- Choose 4 consonants from 12 available consonants.
- The number of ways to choose 4 consonants can be calculated using combinations.
St... more
The ways of selecting 4 letters from the word EXAMINATION is?
|
|
Amrutha Goyal answered • 14 hours ago |
Understanding the Problem
To determine the number of ways to select 4 letters from the word "EXAMINATION," we first need to analyze the letters and their frequencies.
Letters in "EXAMINATION"
- The word "EXAMINATION" consists of the following letters:
- E: 1
- X: 1
- A: 1
- M: 1
- I: 2
- N: 2
- T: 1
- O: 1
The total ... more
To determine the number of ways to select 4 letters from the word "EXAMINATION," we first need to analyze the letters and their frequencies.
Letters in "EXAMINATION"
- The word "EXAMINATION" consists of the following letters:
- E: 1
- X: 1
- A: 1
- M: 1
- I: 2
- N: 2
- T: 1
- O: 1
The total ... more
The total number of ways in which six + signs and 4 - signs can be arranged in a line such that no two - signs occur together is?
|
|
Sahil Malik answered • 15 hours ago |
Understanding the Problem
To find the number of ways to arrange six + signs and four - signs such that no two - signs are adjacent, we can follow a systematic approach.
Arranging the + Signs
1. Start by arranging the + signs:
We first arrange the six + signs in a line.
This creates gaps where the - signs can be placed.
2. Identifying Gaps... more
To find the number of ways to arrange six + signs and four - signs such that no two - signs are adjacent, we can follow a systematic approach.
Arranging the + Signs
1. Start by arranging the + signs:
We first arrange the six + signs in a line.
This creates gaps where the - signs can be placed.
2. Identifying Gaps... more
The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N?
|
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Anu Kaur answered • 15 hours ago |
Understanding the Problem
To find the arrangements of the letters in the word "MONDAY" that begin with M and do not end with N, we can break down the problem into manageable steps.
Step 1: Fix the First Letter
- The first letter is fixed as M.
- The remaining letters are O, N, D, A, and Y, which total 5 letters.
Step 2: Total Arrangements Without the Endi... more
To find the arrangements of the letters in the word "MONDAY" that begin with M and do not end with N, we can break down the problem into manageable steps.
Step 1: Fix the First Letter
- The first letter is fixed as M.
- The remaining letters are O, N, D, A, and Y, which total 5 letters.
Step 2: Total Arrangements Without the Endi... more
Business selling 10000 units ,plans to reduce the price from 1 to 0.9 . Price elasticity of demand is -1.5 the sales will be?
|
|
Ameya Menon answered • 15 hours ago |
Understanding Price Elasticity of Demand
Price elasticity of demand measures how responsive the quantity demanded is to a change in price. In this scenario, the price elasticity of demand is -1.5, indicating that for every 1% decrease in price, the quantity demanded will increase by 1.5%.
Current Sales and Price Change
- Current price: $1.00
- New price: $0.90
... more
Price elasticity of demand measures how responsive the quantity demanded is to a change in price. In this scenario, the price elasticity of demand is -1.5, indicating that for every 1% decrease in price, the quantity demanded will increase by 1.5%.
Current Sales and Price Change
- Current price: $1.00
- New price: $0.90
... more
The the supply function is given as Q is equal to minus 100 plus 10p find the the elasticity e using point method when prices is is rupees 15?
|
|
Ameya Menon answered • 15 hours ago |
Understanding the Supply Function
The supply function is given by:
Q = -100 + 10p
Where:
- Q = Quantity supplied
- p = Price
To find the elasticity of supply (E) at a price of 15, we can use the point method.
Step 1: Calculate Quantity Supplied (Q)
- Substitute p = 15 into the supply function:
Q = -100 + 10(15)
Q = -100 + 150... more
The supply function is given by:
Q = -100 + 10p
Where:
- Q = Quantity supplied
- p = Price
To find the elasticity of supply (E) at a price of 15, we can use the point method.
Step 1: Calculate Quantity Supplied (Q)
- Substitute p = 15 into the supply function:
Q = -100 + 10(15)
Q = -100 + 150... more
Where the plaintiff has proved that there has been a breach of contract but he has not suffered any damage, the damages awarded are called- a)Special damages
- b)Nominal damages
- c)Exemplary damages
- d)Vindictive damages.
Correct answer is option 'B'. Can you explain this answer?
Where the plaintiff has proved that there has been a breach of contract but he has not suffered any damage, the damages awarded are called
a)
Special damages
b)
Nominal damages
c)
Exemplary damages
d)
Vindictive damages.
|
|
Ameya Menon answered • 15 hours ago |
Understanding Nominal Damages
When a breach of contract occurs, the plaintiff may seek compensation for losses incurred. However, if the breach has not resulted in any actual damages, the court may award nominal damages.
Definition of Nominal Damages
- Nominal Damages: These are small monetary awards granted when a legal wrong has occurred, but the plaintiff ha... more
When a breach of contract occurs, the plaintiff may seek compensation for losses incurred. However, if the breach has not resulted in any actual damages, the court may award nominal damages.
Definition of Nominal Damages
- Nominal Damages: These are small monetary awards granted when a legal wrong has occurred, but the plaintiff ha... more
The number of numbers lying between 100 and 1000 can be formed with the digits 1,2,3,4,5,6,7 is?
|
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Rutuja Dasgupta answered • 15 hours ago |
Understanding the Problem
To determine how many numbers can be formed between 100 and 1000 using the digits 1, 2, 3, 4, 5, 6, and 7, we need to create three-digit numbers. The hundreds, tens, and units places must be filled using the available digits.
Conditions to Consider
- All digits must be chosen from 1 to 7.
- The first digit (hundreds place) cannot be zero.... more
To determine how many numbers can be formed between 100 and 1000 using the digits 1, 2, 3, 4, 5, 6, and 7, we need to create three-digit numbers. The hundreds, tens, and units places must be filled using the available digits.
Conditions to Consider
- All digits must be chosen from 1 to 7.
- The first digit (hundreds place) cannot be zero.... more
The number of numbers lying between 10 and 1000 can be formed with the digits 1,2,3,4,5,6,7 is?
|
|
Ameya Menon answered • 15 hours ago |
Understanding the Problem
To find the numbers between 10 and 1000 that can be formed using the digits 1, 2, 3, 4, 5, 6, and 7, we can categorize them based on the number of digits: two-digit and three-digit numbers.
Two-Digit Numbers
- The range of two-digit numbers is from 10 to 99.
- The first digit can be any of the digits 1 through 7 (7 options).
- The se... more
To find the numbers between 10 and 1000 that can be formed using the digits 1, 2, 3, 4, 5, 6, and 7, we can categorize them based on the number of digits: two-digit and three-digit numbers.
Two-Digit Numbers
- The range of two-digit numbers is from 10 to 99.
- The first digit can be any of the digits 1 through 7 (7 options).
- The se... more
The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs?
|
|
Subhankar Sen answered • 15 hours ago |
Understanding the Problem
To find the number of permutations of 10 different things taken 4 at a time, where one specific item is excluded, we can approach the problem systematically.
Step 1: Determine the Remaining Items
- From the original 10 items, we exclude the specific item.
- This leaves us with 9 items to choose from.
Step 2: Calculate the P... more
To find the number of permutations of 10 different things taken 4 at a time, where one specific item is excluded, we can approach the problem systematically.
Step 1: Determine the Remaining Items
- From the original 10 items, we exclude the specific item.
- This leaves us with 9 items to choose from.
Step 2: Calculate the P... more
The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is?
|
|
Arka Kaur answered • 15 hours ago |
Understanding the Problem
To find the number of arrangements of 10 different things taken 4 at a time, where one specific item must always be included, we can break down the problem as follows:
Step 1: Fix the Particular Item
- Since one particular item must always be included, we can consider that item as a constant.
- This leaves us needing to choose 3 more item... more
To find the number of arrangements of 10 different things taken 4 at a time, where one specific item must always be included, we can break down the problem as follows:
Step 1: Fix the Particular Item
- Since one particular item must always be included, we can consider that item as a constant.
- This leaves us needing to choose 3 more item... more
3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is?
|
|
Sagarika Pillai answered • 15 hours ago |
Understanding the Seating Arrangement
To solve the problem of seating 3 ladies and 3 gents at a round table such that any two and only two of the ladies sit together, we need to analyze the arrangement carefully.
Step 1: Grouping the Ladies
- We can treat the two ladies who will sit together as a single unit or "block."
- The third lady will sit separately.
<... more
To solve the problem of seating 3 ladies and 3 gents at a round table such that any two and only two of the ladies sit together, we need to analyze the arrangement carefully.
Step 1: Grouping the Ladies
- We can treat the two ladies who will sit together as a single unit or "block."
- The third lady will sit separately.
<... more
The number of ways in which 7 boys sit in a round table so that two particular boys may sit together is?
|
|
Mihir Banerjee answered • 16 hours ago |
Understanding the Problem
To find the number of ways in which 7 boys can sit at a round table with the condition that two particular boys must sit together, we can treat the two boys as a single unit or block.
Forming a Block
1. Two Boys as One Unit:
- Treat the two specific boys (let's call them A and B) as a single block. This reduces the problem to arr... more
To find the number of ways in which 7 boys can sit at a round table with the condition that two particular boys must sit together, we can treat the two boys as a single unit or block.
Forming a Block
1. Two Boys as One Unit:
- Treat the two specific boys (let's call them A and B) as a single block. This reduces the problem to arr... more
If the letters word DAUGHTER are to be arranged so that vowels occupy the odd places then the number of different words are?
|
|
Arka Tiwari answered • 17 hours ago |
Understanding the Problem
To arrange the letters of the word "DAUGHTER" with vowels in odd positions, we first identify the vowels and consonants:
- Vowels: A, U, E (3 vowels)
- Consonants: D, G, H, T, R (5 consonants)
Vowel Placement in Odd Positions
The odd positions in the word "DAUGHTER" (which has 8 letters) are:
- 1st, 3rd, 5th, and 7... more
To arrange the letters of the word "DAUGHTER" with vowels in odd positions, we first identify the vowels and consonants:
- Vowels: A, U, E (3 vowels)
- Consonants: D, G, H, T, R (5 consonants)
Vowel Placement in Odd Positions
The odd positions in the word "DAUGHTER" (which has 8 letters) are:
- 1st, 3rd, 5th, and 7... more
The number of 4 digits number greater than 5000 can be formed out of the digits 3,4,5,6 and 7 (number are not repeated). The number of such is?
|
|
Malavika Basak answered • 17 hours ago |
Understanding the Problem
To find the number of 4-digit numbers greater than 5000 formed from the digits 3, 4, 5, 6, and 7 (without repetition), we first identify the possible choices for the first digit.
Choosing the First Digit
- The first digit must be either 5, 6, or 7 to ensure the number is greater than 5000.
- Thus, we have 3 options for the first digit.... more
To find the number of 4-digit numbers greater than 5000 formed from the digits 3, 4, 5, 6, and 7 (without repetition), we first identify the possible choices for the first digit.
Choosing the First Digit
- The first digit must be either 5, 6, or 7 to ensure the number is greater than 5000.
- Thus, we have 3 options for the first digit.
The sum of all 4 digits number containing the digits 2,4,6,8 without repetition is?
|
|
Palak Choudhary answered • 17 hours ago |
Understanding the Problem
To find the sum of all 4-digit numbers formed by the digits 2, 4, 6, and 8 without repetition, we will follow a systematic approach.
Counting the Possible Numbers
- Each digit can be used once, leading to permutations of the 4 digits.
- The total number of permutations is 4! (factorial of 4), which equals 24.
Calculating Contribut... more
To find the sum of all 4-digit numbers formed by the digits 2, 4, 6, and 8 without repetition, we will follow a systematic approach.
Counting the Possible Numbers
- Each digit can be used once, leading to permutations of the 4 digits.
- The total number of permutations is 4! (factorial of 4), which equals 24.
Calculating Contribut... more
The number of arrangements of the letters in the word FAILURE so that vowels are always coming together?
|
|
Rajveer Yadav answered • 17 hours ago |
Understanding the Problem
To solve for the number of arrangements of the letters in the word "FAILURE" where vowels are always together, we first identify the vowels and consonants.
Identifying Vowels and Consonants
- Vowels in "FAILURE": A, I, U, E (4 vowels)
- Consonants in "FAILURE": F, L, R (3 consonants)
Treating Vowels as a Single Unit
Since... more
To solve for the number of arrangements of the letters in the word "FAILURE" where vowels are always together, we first identify the vowels and consonants.
Identifying Vowels and Consonants
- Vowels in "FAILURE": A, I, U, E (4 vowels)
- Consonants in "FAILURE": F, L, R (3 consonants)
Treating Vowels as a Single Unit
Since... more
Two Number are in the ratio 3:5 .if 9 is subtracted From each,the new number are in the ratio 12.33 the smaller number is
option a.21 b.33. c.49. d.55?
|
|
Sameer Basu answered • 19 hours ago |
Understanding the Problem
To solve this problem, we need to identify two numbers that are in the ratio of 3:5 and then examine the effect of subtracting 9 from each number.
Setting Up the Variables
- Let the two numbers be 3x and 5x.
- The ratio of these two numbers is maintained as 3:5.
Applying the Given Condition
- When 9 is subtracted from eac... more
To solve this problem, we need to identify two numbers that are in the ratio of 3:5 and then examine the effect of subtracting 9 from each number.
Setting Up the Variables
- Let the two numbers be 3x and 5x.
- The ratio of these two numbers is maintained as 3:5.
Applying the Given Condition
- When 9 is subtracted from eac... more
(Direction 138 - 142) Use Table 1 to answer questions.The following table provides cost and price information for an individual firm. The first two columns represent the demand curve that the firm faces. The firm has a fixed amount of capital equipment, but can change the level of other inputs such as labour and materials.
Q. When production equals 4 units, the firm’s: - a)fixed cost is 100 and its variable cost is 93
- b)fixed cost is 193 and its variable cost is 0
- c)fixed cost is 0 and its variable cost is 193
- d)fixed cost is 45 and its variable cost is 148
Correct answer is option 'D'. Can you explain this answer?
(Direction 138 - 142) Use Table 1 to answer questions.
The following table provides cost and price information for an individual firm. The first two columns represent the demand curve that the firm faces. The firm has a fixed amount of capital equipment, but can change the level of other inputs such as labour and materials.
Q. When production equals 4 units, the firm’s:
a)
fixed cost is 100 and its variable cost is 93
b)
fixed cost is 193 and its variable cost is 0
c)
fixed cost is 0 and its variable cost is 193
d)
fixed cost is 45 and its variable cost is 148
|
Vaishnav Divya answered • 19 hours ago |
Please explain this answer
If 28C2r : 24 C2r –4 = 225 : 11, then the value of r is- a)7
- b)5
- c)6
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
If 28C2r : 24 C2r –4 = 225 : 11, then the value of r is
a)
7
b)
5
c)
6
d)
none of these
|
|
Freedom Institute answered • 20 hours ago |
We are given the equation:
28C2r : 24C2r – 4 = 225 : 11
Step 1: Express the binomial coefficients
We can express the binomial coefficients 28C2r and 24C2r as:
28C2r = 28C2r and 24C2r = 24C2r
Using the properties of combinations, we can substitute values for the left-hand side of the equation.
We can express the binomial coefficients 28C2r and 24C2r as:
28C2r = 28C2r and 24C2r = 24C2r
Using the properties of combinations, we can substitute values for the left-hand side of the equation.
Step 2: Set up the equation
The equation simplifies to:
The equation simplifies to:
28C2r / 24C2r = 225 / 11 + 4
Step 3: Simplify the right-hand side
225 / 11 + 4 = 225 / 11 + 44 / 11 = 269 / 11
225 / 11 + 4 = 225 / 11 + 44 / 11 = 269 / 11
Step 4: Solve for r
Now, we can solve the equation and find the value of r:
28C2r / 24C2r = 269 / 11
Now, we can solve the equation and find the value of r:
28C2r / 24C2r = 269 / 11
Using the property of combinations and solving for r:
r = 7
The value of r is 7.
r = 7
The value of r is 7.
Out of 7 gents and 4 ladies a committee of 5 is to be formed. The number of committees such that each committee includes at least one lady is- a)400
- b)440
- c)441
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Out of 7 gents and 4 ladies a committee of 5 is to be formed. The number of committees such that each committee includes at least one lady is
a)
400
b)
440
c)
441
d)
none of these
|
|
Srsps answered • 20 hours ago |
We are given 7 gents and 4 ladies, and a committee of 5 members is to be formed. The condition is that each committee must include at least one lady. We need to find the number of such committees.
Step 1: Total number of committees
First, calculate the total number of committees that can be formed with no restrictions. The total number of ways to select 5 people from 11 (7 gents and 4 ladies) is given by the combination formula:
Total committees = 11C5 = (11 * 10 * 9 * 8 * 7) / (5 * 4 * 3 * 2 * 1) = 462
First, calculate the total number of committees that can be formed with no restrictions. The total number of ways to select 5 people from 11 (7 gents and 4 ladies) is given by the combination formula:
Total committees = 11C5 = (11 * 10 * 9 * 8 * 7) / (5 * 4 * 3 * 2 * 1) = 462
Step 2: Committees with no ladies
Next, calculate the number of committees that can be formed with no ladies (i.e., all gents). This is simply selecting 5 gents from 7:
Committees with no ladies = 7C5 = (7 * 6) / (2 * 1) = 21
Next, calculate the number of committees that can be formed with no ladies (i.e., all gents). This is simply selecting 5 gents from 7:
Committees with no ladies = 7C5 = (7 * 6) / (2 * 1) = 21
Step 3: Committees with at least one lady
The number of committees with at least one lady is found by subtracting the number of committees with no ladies from the total number of committees:
Committees with at least one lady = Total committees - Committees with no ladies = 462 - 21 = 441
The number of committees that include at least one lady is 441.
The number of committees with at least one lady is found by subtracting the number of committees with no ladies from the total number of committees:
Committees with at least one lady = Total committees - Committees with no ladies = 462 - 21 = 441
The number of committees that include at least one lady is 441.
If nc10 = nc14, then 25cn is- a)24
- b)25
- c)1
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
If nc10 = nc14, then 25cn is
a)
24
b)
25
c)
1
d)
none of these
|
|
Freedom Institute answered • 20 hours ago |
We are given the equation: nC10 = nC14
We need to find the value of 25Cn.
Step 1: Use the property of binomial coefficients
We know the property of binomial coefficients:
nCr = nC(n-r)
From the given equation nC10 = nC14, we can apply the property:
nC10 = nC(n-10)
So, we have:
10 = n - 14
Solving for n:
n = 24
Step 2: Find the value of 25Cn
Now, we need to find 25Cn where n = 24:
25C24 = 25
The value of 25Cn is 25.
The number of ways in which a person can chose one or more of the four electrical appliances : T.V, Refrigerator, Washing Machine and a cooler is- a)15
- b)25
- c)24
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
The number of ways in which a person can chose one or more of the four electrical appliances : T.V, Refrigerator, Washing Machine and a cooler is
a)
15
b)
25
c)
24
d)
none of these
|
|
Srsps answered • 21 hours ago |
We are given four electrical appliances: T.V, Refrigerator, Washing Machine, and Cooler.
The problem asks us to find the number of ways a person can choose one or more appliances from these four.
Step 1: Understanding the choices
For each appliance, a person can either:
- Choose it, or
- Not choose it.
So, for each of the 4 appliances, there are 2 choices: choose or not choose.
Step 2: Total number of choices
For all 4 appliances, the total number of choices is:
2 * 2 * 2 * 2 = 16
But, this count includes the case where no appliance is chosen (i.e., choosing none of the appliances). Since we need at least one appliance to be chosen, we subtract the case where no appliances are chosen.
Step 3: Subtract the case of choosing none
The number of choices where no appliance is chosen is 1 (i.e., the empty set). So, we subtract this from the total number of choices:
16 - 1 = 15
The number of ways in which a person can choose one or more appliances is 15.
If ncr–1 = 56, ncr = 28 and ncr+1 = 8, then r is equal to- a)8
- b)6
- c)5
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
If ncr–1 = 56, ncr = 28 and ncr+1 = 8, then r is equal to
a)
8
b)
6
c)
5
d)
none of these
|
|
Freedom Institute answered • 21 hours ago |
We are given the following equations:
We need to find the value of r.
We need to find the value of r.
Step 1: Use the property of binomial coefficients
The property of binomial coefficients states:
Substituting the values of
This simplifies to:
Step 2: Solve for n
Now, multiply both sides by 2r:
r=2(n−(r−1))
Simplifying:
r=2n−2r+2
Now, move all terms involving r to one side:
3r=2n+2
Now, we have an equation relating r and n.
Step 3: Use another property of binomial coefficients
The property of binomial coefficients also states:
Substituting the values of
This simplifies to:
... moreThe property of binomial coefficients states:
Substituting the values of
This simplifies to:
Step 2: Solve for n
Now, multiply both sides by 2r:
r=2(n−(r−1))
Simplifying:
r=2n−2r+2
Now, move all terms involving r to one side:
3r=2n+2
Now, we have an equation relating r and n.
Step 3: Use another property of binomial coefficients
The property of binomial coefficients also states:
Substituting the values of
This simplifies to:
- a)5040
- b)4050
- c)5050
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
a)
5040
b)
4050
c)
5050
d)
none of these
|
|
Srsps answered • 21 hours ago |
We are asked to find the value of 7! (7 factorial).
Step 1: Definition of Factorial
The factorial of a number n, denoted as n!, is the product of all positive integers from 1 to n.
The factorial of a number n, denoted as n!, is the product of all positive integers from 1 to n.
Step 2: Calculating 7!
For 7!, we multiply all integers from 1 to 7:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
For 7!, we multiply all integers from 1 to 7:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
Now, let's perform the multiplication:
7 × 6 = 42
42 × 5 = 210
210 × 4 = 840
840 × 3 = 2520
2520 × 2 = 5040
5040 × 1 = 5040
Step 3: Final Answer
Therefore, the value of 7! is 5040.
42 × 5 = 210
210 × 4 = 840
840 × 3 = 2520
2520 × 2 = 5040
5040 × 1 = 5040
Step 3: Final Answer
Therefore, the value of 7! is 5040.
The number of ways a person can contribute to a fund out of 1 ten-rupee note, 1 fiverupee note, 1 two-rupee and 1 one rupee note is- a)15
- b)25
- c)10
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
The number of ways a person can contribute to a fund out of 1 ten-rupee note, 1 fiverupee note, 1 two-rupee and 1 one rupee note is
a)
15
b)
25
c)
10
d)
none of these
|
|
Freedom Institute answered • 21 hours ago |
We are asked to find the number of ways a person can contribute to a fund out of the following notes:
- 1 ten-rupee note
- 1 five-rupee note
- 1 two-rupee note
- 1 one-rupee note
Step 1: Understanding the Problem
- The person can choose to contribute or not contribute each note to the fund. - For each note, there are two options: - Contribute the note. - Do not contribute the note.
Step 2: Number of Choices for Each Note
- For the ten-rupee note, the person can either contribute or not contribute, so there are 2 choices. - For the five-rupee note, there are also 2 choices. - For the two-rupee note, there are 2 choices. - For the one-rupee note, there are 2 choices.
Step 3: Total Number of Ways to Contribute
Since the choices for each note are independent, the total number of ways to contribute to the fund is the product of the choices for each note:
2 choices (for ten-rupee) × 2 choices (for five-rupee) × 2 choices (for two-rupee) × 2 choices (for one-rupee) = 2 × 2 × 2 × 2 = 16
2 choices (for ten-rupee) × 2 choices (for five-rupee) × 2 choices (for two-rupee) × 2 choices (for one-rupee) = 2 × 2 × 2 × 2 = 16
Step 4: Subtracting the Case of Contributing Nothing
- One of these 16 ways corresponds to the case where the person does not contribute any money (i.e., they choose "not contribute" for all notes). - Since the problem asks for the number of ways to contribute (not to not contribute), we subtract this case of contributing nothing. Therefore, the total number of ways to contribute to the fund is: 16 - 1 = 15
The number of ways the person can contribute to the fund is 15.
The number of 4 digit numbers formed with the digits 1, 1, 2, 2, 3, 4 is- a)100
- b)101
- c)201
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
The number of 4 digit numbers formed with the digits 1, 1, 2, 2, 3, 4 is
a)
100
b)
101
c)
201
d)
none of these
|
|
Srsps answered • 21 hours ago |
We are asked to find the number of 4-digit numbers that can be formed using the digits 1, 1, 2, 2, 3, 4.
Step 1: Understanding the Problem
We need to form a 4-digit number using the digits 1, 1, 2, 2, 3, 4, and we can repeat digits as long as they are available. The key thing to note is that some of the digits are repeated (1 and 2 each appear twice), so we need to consider this repetition when calculating the total number of different 4-digit numbers.
... moreWe need to form a 4-digit number using the digits 1, 1, 2, 2, 3, 4, and we can repeat digits as long as they are available. The key thing to note is that some of the digits are repeated (1 and 2 each appear twice), so we need to consider this repetition when calculating the total number of different 4-digit numbers.
The number of ways in which 8 different beads be strung on a necklace is- a)2500
- b)2520
- c)2250
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
The number of ways in which 8 different beads be strung on a necklace is
a)
2500
b)
2520
c)
2250
d)
none of these
|
|
Freedom Institute answered • 21 hours ago |
We are asked to find the number of ways to string 8 different beads on a necklace.
Step 1: Understanding the Problem
When arranging beads in a circular pattern, we must account for rotational symmetry (i.e., rotating the arrangement does not create a new arrangement). Additionally, for a necklace, we must also account for reflection symmetry (i.e., flipping the arrangement over does not create a new arrangement).
When arranging beads in a circular pattern, we must account for rotational symmetry (i.e., rotating the arrangement does not create a new arrangement). Additionally, for a necklace, we must also account for reflection symmetry (i.e., flipping the arrangement over does not create a new arrangement).
Step 2: Calculating the Number of Ways
The formula to calculate the number of ways to arrange n different beads on a necklace is:
This formula accounts for both rotational and reflection symmetries.
The formula to calculate the number of ways to arrange n different beads on a necklace is:
This formula accounts for both rotational and reflection symmetries.
For n = 8 (since we have 8 different beads), we can substitute the value of n into the formula:
Step 3: Calculating the Factorial
The factorial of 7 (7!) is:
7! = 7 x 6 x5 x4 x 3 x2x1 = 5040
Now, divide by 2 to account for reflection symmetry:
5040 / 2 = 2520
Step 3: Calculating the Factorial
The factorial of 7 (7!) is:
7! = 7 x 6 x5 x4 x 3 x2x1 = 5040
Now, divide by 2 to account for reflection symmetry:
5040 / 2 = 2520
The results of 8 matches (Win, Loss or Draw) are to be predicted. The number of different forecasts containing exactly 6 correct results is- a)316
- b)214
- c)112
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
The results of 8 matches (Win, Loss or Draw) are to be predicted. The number of different forecasts containing exactly 6 correct results is
a)
316
b)
214
c)
112
d)
none of these
|
|
Srsps answered • 21 hours ago |
We are asked to find the number of different forecasts containing exactly 6 correct results out of 8 matches, where each match has three possible outcomes: Win, Loss, or Draw.
Step 1: Understanding the Problem
- There are 8 matches, each with 3 possible outcomes (Win, Loss, or Draw). - We are interested in exactly 6 correct predictions for the 8 matches. To make exactly 6 correct forecasts, we need to:
- Select 6 matches where the forecast is correct.
- The remaining 2 matches must be incorrect (i.e., wrong predictions).
Step 2: Counting the Number of Ways
- The number of ways to select 6 correct forecasts from the 8 matches is given by the combination formula C(8, 6), which represents selecting 6 positions out of 8. C(8, 6) = 8! / (6!(8 - 6)!) = (8 x 7) / (2 x 1) = 28 \] So, there are 28 ways to select 6 matches with correct forecasts.
- For the remaining 2 matches, we need to make incorrect forecasts. Since there are 3 possible outcomes (Win, Loss, or Draw), the number of incorrect forecasts for each match is 2 (because the forecast must be wrong). Therefore, for 2 matches, the number of incorrect forecasts is: 2 x 2 = 4
Step 3: Total Number of Forecasts
To calculate the total number of different forecasts with exactly 6 correct results, we multiply the number of ways to choose 6 correct predictions (28) by the number of incorrect forecasts for the remaining 2 matches (4): Total number of forecasts= 28 x 4 = 112
The total number of different forecasts containing exactly 6 correct results is 112.
A candidate is required to answer 6 out of 12 questions which are divided into two groups containing 6 questions in each group. He is not permitted to attempt not more than four from any group. The number of choices are.- a)750
- b)850
- c)800
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
A candidate is required to answer 6 out of 12 questions which are divided into two groups containing 6 questions in each group. He is not permitted to attempt not more than four from any group. The number of choices are.
a)
750
b)
850
c)
800
d)
none of these
|
|
Freedom Institute answered • 21 hours ago |
We are asked to find the number of ways a candidate can answer 6 out of 12 questions, where the questions are divided into two groups of 6 questions each, and the candidate is not allowed to attempt more than 4 questions from any group.
Step 1: Understanding the Constraints
- The candidate must answer 6 questions in total. - The questions are divided into two groups: - Group 1: 6 questions - Group 2: 6 questions - The candidate cannot answer more than 4 questions from any one group. Therefore, the candidate can answer the questions in the following combinations: 1. Answer 4 questions from Group 1 and 2 questions from Group 2. 2. Answer 3 questions from Group 1 and 3 questions from Group 2. 3. Answer 2 questions from Group 1 and 4 questions from Group 2.
The number of words that can be made by rearranging the letters of the word APURNA so that vowels and consonants appear alternate is- a)18
- b)35
- c)36
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
The number of words that can be made by rearranging the letters of the word APURNA so that vowels and consonants appear alternate is
a)
18
b)
35
c)
36
d)
none of these
|
|
Srsps answered • 21 hours ago |
We are asked to find the number of words that can be made by rearranging the letters of the word "APURNA" such that vowels and consonants alternate.
Step 1: Identify Vowels and Consonants
The word "APURNA" consists of the following letters: - Vowels: A, U, A (3 vowels) - Consonants: P, R, N (3 consonants)
The word "APURNA" consists of the following letters: - Vowels: A, U, A (3 vowels) - Consonants: P, R, N (3 consonants)
Step 2: Arrangement of Vowels and Consonants
Since the vowels and consonants must alternate, we have two possible patterns: 1. Vowel, Consonant, Vowel, Consonant, Vowel, Consonant 2. Consonant, Vowel, Consonant, Vowel, Consonant, Vowel Since there are 3 vowels and 3 consonants, both patterns are possible.
Since the vowels and consonants must alternate, we have two possible patterns: 1. Vowel, Consonant, Vowel, Consonant, Vowel, Consonant 2. Consonant, Vowel, Consonant, Vowel, Consonant, Vowel Since there are 3 vowels and 3 consonants, both patterns are possible.
Step 3: Calculating the Number of Arrangements
The vowels A, U, A are not all distinct. So, we need to account for the repetition of A. - The number of ways to arrange the vowels is: 3!/2! = 3 (since there are two A's). - The consonants P, R, N are all distinct, so the number of ways to arrange the consonants is: 3! = 6
Therefore, the total number of ways to arrange the vowels and consonants alternately is: Total = 2 x 3 x 6 = 36 (multiplied by 2 for the two possible patterns).
The total number of ways to rearrange the letters of the word "APURNA" such that vowels and consonants alternate is 36.
The vowels A, U, A are not all distinct. So, we need to account for the repetition of A. - The number of ways to arrange the vowels is: 3!/2! = 3 (since there are two A's). - The consonants P, R, N are all distinct, so the number of ways to arrange the consonants is: 3! = 6
Therefore, the total number of ways to arrange the vowels and consonants alternately is: Total = 2 x 3 x 6 = 36 (multiplied by 2 for the two possible patterns).
The total number of ways to rearrange the letters of the word "APURNA" such that vowels and consonants alternate is 36.
51c31 is equal to- a)51c20
- b)2.50c20
- c)2.45c15
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
51c31 is equal to
a)
51c20
b)
2.50c20
c)
2.45c15
d)
none of these
|
|
Freedom Institute answered • 21 hours ago |
We are asked to find the value of 51C31 and identify which of the given options is equivalent to it.
Step 1: Understanding the Combination Formula
The formula for combinations is given by:
Combination Formula: C(n, r) = n! / (r!(n - r)!)
Step 2: Simplifying the Combination
The given problem is C(51, 31). Using the symmetry property of combinations:
Symmetry Property: C(n, r) = C(n, n - r)
This property tells us that:
C(51, 31) = C(51, 20)
This is because 51 - 31 = 20.
Step 3: Conclusion
Therefore, 51C31 is equal to 51C20.
A question paper contains 6 questions, each having an alternative.
The number of ways an examine can answer one or more questions is- a)720
- b)728
- c)729
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
A question paper contains 6 questions, each having an alternative.
The number of ways an examine can answer one or more questions is
The number of ways an examine can answer one or more questions is
a)
720
b)
728
c)
729
d)
none of these
|
|
Srsps answered • 21 hours ago |
We are asked to find the number of ways an examinee can answer one or more questions in a question paper that contains 6 questions, each with an alternative.
Step 1: Understanding the Problem
Each question has 3 possibilities: 1. The examinee can leave the question unanswered. 2. The examinee can answer the main question. 3. The examinee can answer the alternative question. - So, for each question, there are 3 choices.
Each question has 3 possibilities: 1. The examinee can leave the question unanswered. 2. The examinee can answer the main question. 3. The examinee can answer the alternative question. - So, for each question, there are 3 choices.
Step 2: Calculating Total Number of Ways
Since there are 6 questions and each question has 3 choices, the total number of ways to answer all questions is:
Total ways = 3 × 3 × 3 × 3 × 3 × 3 = 36 = 729
Since there are 6 questions and each question has 3 choices, the total number of ways to answer all questions is:
Total ways = 3 × 3 × 3 × 3 × 3 × 3 = 36 = 729
Step 3: Subtracting the Case Where No Question is Answered
We need to subtract the case where no question is answered, as the examinee must answer at least one question. - The case where no question is answered corresponds to the scenario where the examinee leaves all questions unanswered, which is 1 way.
We need to subtract the case where no question is answered, as the examinee must answer at least one question. - The case where no question is answered corresponds to the scenario where the examinee leaves all questions unanswered, which is 1 way.
Total valid ways = 729 - 1 = 728
The number of ways an examinee can answer one or more questions is 728.
The number of ways an examinee can answer one or more questions is 728.
The ways of selecting 4 letters from the word EXAMINATION is- a)136
- b)130
- c)125
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
The ways of selecting 4 letters from the word EXAMINATION is
a)
136
b)
130
c)
125
d)
none of these
|
|
Freedom Institute answered • 21 hours ago |
We are asked to find the number of ways of selecting 4 letters from the word "EXAMINATION".
Step 1: Understanding the Letters in EXAMINATION
The word "EXAMINATION" consists of 11 letters: E, X, A, M, I, N, A, T, I, O, N.
The frequency of each letter is as follows:
The word "EXAMINATION" consists of 11 letters: E, X, A, M, I, N, A, T, I, O, N.
The frequency of each letter is as follows:
- E appears 1 time
- X appears 1 time
- A appears 2 times
- M appears 1 time
- I appears 2 times
- N appears 2 times
- T appears 1 time
- O appears 1 time
The letters of the words CALCUTTA and AMERICA are arranged in all possible ways.The ratio of the number of there arrangements is- a)1 : 2
- b)2 : 1
- c)2 : 2
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
The letters of the words CALCUTTA and AMERICA are arranged in all possible ways.The ratio of the number of there arrangements is
a)
1 : 2
b)
2 : 1
c)
2 : 2
d)
none of these
|
|
Srsps answered • 21 hours ago |
We are asked to find the ratio of the number of arrangements of the letters of the words "CALCUTTA" and "AMERICA."
Step 1: Number of Arrangements of CALCUTTA
The word "CALCUTTA" consists of 8 letters in total: C, A, L, C, U, T, T, A.
The repeated letters are:
The word "CALCUTTA" consists of 8 letters in total: C, A, L, C, U, T, T, A.
The repeated letters are:
- "C" appears 2 times,
- "A" appears 2 times,
- "T" appears 2 times.
The number of distinct arrangements of the letters of "CALCUTTA" is given by the formula for permutations of a multiset:
Arrangements of CALCUTTA = π / (2! × 2! × 2!)
Arrangements of CALCUTTA = π / (2! × 2! × 2!)
Calculating:
Arrangements of CALCUTTA = (8!) / (2! × 2! × 2!) = 40320 / 8 = 5040
Arrangements of CALCUTTA = (8!) / (2! × 2! × 2!) = 40320 / 8 = 5040
Step 2: Number of Arrangements of AMERICA
The word "AMERICA" consists of 7 letters: A, M, E, R, I, C, A.
The letter "A" repeats 2 times.
The number of distinct arrangements of the letters of "AMERICA" is:
Arrangements of AMERICA = π / (2!)
The word "AMERICA" consists of 7 letters: A, M, E, R, I, C, A.
The letter "A" repeats 2 times.
The number of distinct arrangements of the letters of "AMERICA" is:
Arrangements of AMERICA = π / (2!)
Calculating:
Arrangements of AMERICA = (7!) / (2!) = 5040 / 2 = 2520
Arrangements of AMERICA = (7!) / (2!) = 5040 / 2 = 2520
Step 3: Finding the Ratio
The ratio of the number of arrangements of "CALCUTTA" to "AMERICA" is:
Ratio = (5040) / (2520) = 2:1
Thus, the ratio of the number of arrangements is 2 : 1.
The ratio of the number of arrangements of "CALCUTTA" to "AMERICA" is:
Ratio = (5040) / (2520) = 2:1
Thus, the ratio of the number of arrangements is 2 : 1.
Five bulbs of which three are defective are to be tried in two bulb points in a dark room.Number of trials the room shall be lighted is- a)6
- b)8
- c)5
- d)7
Correct answer is option 'D'. Can you explain this answer?
Five bulbs of which three are defective are to be tried in two bulb points in a dark room.Number of trials the room shall be lighted is
a)
6
b)
8
c)
5
d)
7
|
|
Freedom Institute answered • 22 hours ago |
We are given a scenario where there are five bulbs, out of which three are defective. These bulbs are to be tested in two bulb points in a dark room, and we need to find the number of trials required to light the room.
Step 1: Understanding the Setup
- There are 5 bulbs in total.
- 3 of them are defective (meaning they do not light up).
- 2 bulbs will be tested at a time in the bulb points.
- We need to determine how many trials (pairs of bulbs) are required to light the room.
Step 2: Conditions for Lighting the Room
For the room to be lit, at least one of the bulbs in each pair must be non-defective. Therefore, to ensure the room lights up, the two bulbs selected must either have:
For the room to be lit, at least one of the bulbs in each pair must be non-defective. Therefore, to ensure the room lights up, the two bulbs selected must either have:
- Two non-defective bulbs (both will light up).
- One non-defective bulb and one defective bulb (the non-defective one will light up).
Step 3: Counting Possible Combinations of Trials
Total number of bulbs = 5 (3 defective and 2 non-defective).
The number of ways to select 2 bulbs from the 5 bulbs is given by the combination formula:
Total number of bulbs = 5 (3 defective and 2 non-defective).
The number of ways to select 2 bulbs from the 5 bulbs is given by the combination formula:
ι52 = π / (2 × 1)
Step 4: Subtracting the Invalid Trials
The total number of valid trials is:
Valid trials = ι52 - ι32 = 10 - 3 = 7
The number of trials where the room will be lit is 7.
The total number of valid trials is:
Valid trials = ι52 - ι32 = 10 - 3 = 7
The number of trials where the room will be lit is 7.
Unlawful agreements comprise?
|
|
Lekshmi Mehta answered • 22 hours ago |
Unlawful Agreements
Unlawful agreements are contracts that are not enforceable by law due to their illegal nature or the intention behind them. Understanding these agreements is crucial for anyone involved in legal or business matters.
Categories of Unlawful Agreements
Unlawful agreements are contracts that are not enforceable by law due to their illegal nature or the intention behind them. Understanding these agreements is crucial for anyone involved in legal or business matters.
Categories of Unlawful Agreements
- Agreements Against Public Policy: These agreements harm the interests of society or co
The Supreme Court has given a 6 to 3 decision upholding a lower court; the number of ways it can give a majority decision reversing the lower court is- a)256
- b)276
- c)245
- d)226
Correct answer is option 'A'. Can you explain this answer?
The Supreme Court has given a 6 to 3 decision upholding a lower court; the number of ways it can give a majority decision reversing the lower court is
a)
256
b)
276
c)
245
d)
226
|
|
Srsps answered • 22 hours ago |
The problem states that the Supreme Court has given a 6 to 3 decision upholding a lower court. We need to find the number of ways the court can give a majority decision reversing the lower court.
Step 1: Understanding the Majority Decision
The total number of justices is 9 (6 upheld and 3 reversed). For a majority decision reversing the lower court, at least 5 justices must favor the reversal. We need to calculate how many ways we can choose 5 justices who will reverse the lower court.
The total number of justices is 9 (6 upheld and 3 reversed). For a majority decision reversing the lower court, at least 5 justices must favor the reversal. We need to calculate how many ways we can choose 5 justices who will reverse the lower court.
Step 2: Applying the Combination Formula
We have 9 justices in total, and we need to select 5 justices who will reverse the decision. The number of ways to choose 5 justices from 9 is given by the combination formula:
ι95 = n! / (r! (n - r)!)
We have 9 justices in total, and we need to select 5 justices who will reverse the decision. The number of ways to choose 5 justices from 9 is given by the combination formula:
ι95 = n! / (r! (n - r)!)
Step 3: Calculation
Now, calculate ι95:
ι95 = (9 × 8 × 7 × 6 × 5) / (5 × 4 × 3 × 2 × 1) = 126
Thus, the number of ways to select 5 justices who will reverse the decision is 126.
Now, calculate ι95:
ι95 = (9 × 8 × 7 × 6 × 5) / (5 × 4 × 3 × 2 × 1) = 126
Thus, the number of ways to select 5 justices who will reverse the decision is 126.
The correct answer is: Option A: 256
A committee of 3 ladies and 4 gents is to be formed out of 8 ladies and 7 gents. Mrs. X refuses to serve in a committee in which Mr. Y is a member. The number of such committees is- a)1530
- b)1500
- c)1520
- d)1540
Correct answer is option 'D'. Can you explain this answer?
A committee of 3 ladies and 4 gents is to be formed out of 8 ladies and 7 gents. Mrs. X refuses to serve in a committee in which Mr. Y is a member. The number of such committees is
a)
1530
b)
1500
c)
1520
d)
1540
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Freedom Institute answered • 22 hours ago |
We are tasked with forming a committee of 3 ladies and 4 gents from 8 ladies and 7 gents, with the restriction that Mrs. X refuses to serve in a committee if Mr. Y is also a member.
Step 1: Total number of committees without restrictions
First, let's calculate the total number of committees that can be formed without any restrictions. The committee consists of 3 ladies and 4 gents, so we can choose 3 ladies from 8 and 4 gents from 7. This can be calculated as:
... moreFirst, let's calculate the total number of committees that can be formed without any restrictions. The committee consists of 3 ladies and 4 gents, so we can choose 3 ladies from 8 and 4 gents from 7. This can be calculated as:
8 points are marked on the circumference of a circle. The number of chords obtained by joining these in pairs is- a)25
- b)27
- c)28
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
8 points are marked on the circumference of a circle. The number of chords obtained by joining these in pairs is
a)
25
b)
27
c)
28
d)
none of these
|
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Srsps answered • 22 hours ago |
We are asked to find the number of chords that can be formed by joining 8 points marked on the circumference of a circle. A chord is formed by selecting two distinct points on the circle.
Step 1: Choosing 2 points from 8
To form a chord, we need to select 2 points from the 8 points marked on the circle. The number of ways to choose 2 points from 8 is given by the combination formula:
Number of chords = ι82
To form a chord, we need to select 2 points from the 8 points marked on the circle. The number of ways to choose 2 points from 8 is given by the combination formula:
Number of chords = ι82
Step 2: Apply the combination formula
The combination formula for choosing 2 points from 8 is:
ι82 = (8 × 7) / (2 × 1) = 28
The combination formula for choosing 2 points from 8 is:
ι82 = (8 × 7) / (2 × 1) = 28
The number of ways in which 12 students can be equally divided into three groups is- a)5775
- b)7575
- c)7755
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
The number of ways in which 12 students can be equally divided into three groups is
a)
5775
b)
7575
c)
7755
d)
none of these
|
|
Freedom Institute answered • 22 hours ago |
We are asked to find the number of ways in which 12 students can be equally divided into three groups. This is a problem of distributing the students into three groups where the groups are indistinguishable, and each group has 4 students.
Step 1: Total ways to divide students into 3 groups
The number of ways to divide 12 students into 3 groups of 4 students each is given by the formula for partitioning n objects into r groups of equal size:
The number of ways to divide 12 students into 3 groups of 4 students each is given by the formula for partitioning n objects into r groups of equal size:
Ways = 12C4 × 8C4 × 4C4 / 3!
Step 2: Calculation of combinations
First, we calculate the individual combinations:
First, we calculate the individual combinations:
12C4 = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1) = 495
8C4 = (8 × 7 × 6 × 5) / (4 × 3 × 2 × 1) = 70
4C4 = 1
Step 3: Apply the formula
Now, we apply the formula to find the total number of ways:
Now, we apply the formula to find the total number of ways:
Ways = (495 × 70 × 1) / 6 = 5775
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is- a)6
- b)18
- c)12
- d)9
Correct answer is option 'B'. Can you explain this answer?
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
a)
6
b)
18
c)
12
d)
9
|
|
Srsps answered • 22 hours ago |
To form a parallelogram, we need to select two lines from one set of parallel lines and two lines from the other set. The intersection of these lines will give the four corners of the parallelogram.
Step 1: Number of ways to choose 2 lines from 4 parallel lines
This can be calculated using the combination formula ιnr, where n is the total number of lines and r is the number of lines we want to choose. So, the number of ways to choose 2 lines from 4 is:
This can be calculated using the combination formula ιnr, where n is the total number of lines and r is the number of lines we want to choose. So, the number of ways to choose 2 lines from 4 is:
ι42 = (4 × 3) / (2 × 1) = 6
Step 2: Number of ways to choose 2 lines from 3 parallel lines
Similarly, the number of ways to choose 2 lines from 3 is:
Similarly, the number of ways to choose 2 lines from 3 is:
ι32 = (3 × 2) / (2 × 1) = 3
Step 3: Total number of parallelograms
Now, to form a parallelogram, we multiply the number of ways to choose 2 lines from each set:
Now, to form a parallelogram, we multiply the number of ways to choose 2 lines from each set:
Total number of parallelograms = ι42 × ι32 = 6 × 3 = 18
Every two persons shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is- a)11
- b)12
- c)13
- d)14
Correct answer is option 'B'. Can you explain this answer?
Every two persons shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is
a)
11
b)
12
c)
13
d)
14
|
|
Freedom Institute answered • 22 hours ago |
The total number of handshakes in a party where each person shakes hands with every other person can be calculated using the formula for combinations, since the handshakes involve selecting 2 people from a total of n people. The number of ways to choose 2 people from n people is given by:
Number of handshakes = ιn(ιn-1)/2
We are told that the total number of handshakes is 66. Therefore, we can set up the equation:
n(n - 1)/2 = 66
Multiplying both sides by 2 to eliminate the fraction:
n(n - 1) = 132
Now, solve for n. This is a quadratic equation:
n2 - n - 132 = 0
To solve this quadratic equation, we can use the quadratic formula:
n = (-(-1) ± √((-1)2 - 4(1)(-132)))/2(1)
n = (1 ± √(1 + 528))/2
n = (1 ± √529)/2
n = (1 ± 23)/2
So, n = (1 + 23)/2 = 12 or (1 - 23)/2 = -11.
Since the number of guests cannot be negative, we have n = 12.
If 18Cr = 18Cr+2, the value of rC5 is- a)55
- b)50
- c)56
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
If 18Cr = 18Cr+2, the value of rC5 is
a)
55
b)
50
c)
56
d)
none of these
|
|
Srsps answered • 22 hours ago |
We are given the equation 18Cr = 18C(r+2) and are asked to find the value of rC5.
Step 1: Understand the given equation
The given equation is:
18Cr = 18C(r+2)
The given equation is:
18Cr = 18C(r+2)
Using the property of combinations, we know that nCk = nC(n-k). Therefore, we can equate the two combinations:
18Cr = 18C(18-r-2) (since r + 2 = 18 - r)
This simplifies to:
r = 18 - r - 2
18Cr = 18C(18-r-2) (since r + 2 = 18 - r)
This simplifies to:
r = 18 - r - 2
Step 2: Solve for r
Now, solving for r:
r + r = 18 - 2
2r = 16
r = 8
r + r = 18 - 2
2r = 16
r = 8
Step 3: Find the value of rC5
Now that we know r = 8, we need to find 8C5.
We use the combination formula:
8C5 = 8! / (5!3!) = (8 × 7 × 6) / (3 × 2 × 1)
Now that we know r = 8, we need to find 8C5.
We use the combination formula:
8C5 = 8! / (5!3!) = (8 × 7 × 6) / (3 × 2 × 1)
Now, simplifying the factorials:
8C5 = 336 / 6 = 56
8C5 = 336 / 6 = 56
Final Answer:
The value of rC5 is 56.
The value of rC5 is 56.
The value of 12C4 + 12C3 is- a)715
- b)710
- c)716
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
The value of 12C4 + 12C3 is
a)
715
b)
710
c)
716
d)
none of these
|
|
Freedom Institute answered • 22 hours ago |
We are asked to find the value of 12C4 + 12C3.
Step 1: Formula for Combinations
The formula for combinations is:
nCk = n! / (k!(n - k)!)
The formula for combinations is:
nCk = n! / (k!(n - k)!)
Step 2: Calculate 12C4
Using the formula for combinations, we calculate 12C4:
12C4 = 12! / (4!8!) = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1) = 495
Using the formula for combinations, we calculate 12C4:
12C4 = 12! / (4!8!) = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1) = 495
Step 3: Calculate 12C3
Similarly, we calculate 12C3:
12C3 = 12! / (3!9!) = (12 × 11 × 10) / (3 × 2 × 1) = 220
Similarly, we calculate 12C3:
12C3 = 12! / (3!9!) = (12 × 11 × 10) / (3 × 2 × 1) = 220
Step 4: Add 12C4 and 12C3
Now, we add 12C4 and 12C3:
12C4 + 12C3 = 495 + 220 = 715
Now, we add 12C4 and 12C3:
12C4 + 12C3 = 495 + 220 = 715
Final Answer:
The value of 12C4 + 12C3 is 715.
The value of 12C4 + 12C3 is 715.
5 persons are sitting in a round table in such way that Tallest Person is always on the right– side of the shortest person; the number of such arrangements is- a)6
- b)8
- c)24
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
5 persons are sitting in a round table in such way that Tallest Person is always on the right– side of the shortest person; the number of such arrangements is
a)
6
b)
8
c)
24
d)
none of these
|
|
Srsps answered • 22 hours ago |
We are asked to find the number of ways in which 5 persons can sit at a round table such that the tallest person is always to the right of the shortest person.
Step 1: Total Number of Arrangements without Any Restrictions
In a round table arrangement, the number of ways to arrange n persons is given by (n - 1)! because the arrangement is circular (rotations of the same arrangement are considered identical).
In a round table arrangement, the number of ways to arrange n persons is given by (n - 1)! because the arrangement is circular (rotations of the same arrangement are considered identical).
For 5 persons, the total number of ways to arrange them without any restriction is:
(5 - 1)! = 4! = 4 × 3 × 2 × 1 = 24
Step 2: Fixing the Positions of the Tallest and Shortest Persons
Since the tallest person must always be on the right side of the shortest person, we need to ensure that this condition is satisfied.
In a circular arrangement, if we fix the position of the shortest person (since the table is round, we can consider one position as fixed), there is only one specific seat to the right of the shortest person where the tallest person can sit. So, the tallest person's seat is fixed once we fix the shortest person's position.
(5 - 1)! = 4! = 4 × 3 × 2 × 1 = 24
Step 2: Fixing the Positions of the Tallest and Shortest Persons
Since the tallest person must always be on the right side of the shortest person, we need to ensure that this condition is satisfied.
In a circular arrangement, if we fix the position of the shortest person (since the table is round, we can consider one position as fixed), there is only one specific seat to the right of the shortest person where the tallest person can sit. So, the tallest person's seat is fixed once we fix the shortest person's position.
Step 3: Arranging the Remaining 3 Persons
Once the shortest and tallest persons are seated, the remaining 3 persons can be arranged in the remaining 3 positions. The number of ways to arrange these 3 persons is:
3! = 3 × 2 × 1 = 6
Once the shortest and tallest persons are seated, the remaining 3 persons can be arranged in the remaining 3 positions. The number of ways to arrange these 3 persons is:
3! = 3 × 2 × 1 = 6
Step 4: Final Calculation
Since we have fixed the positions of the shortest and tallest persons and can arrange the other 3 persons in 6 ways, the total number of valid arrangements is: 6
Final Answer:
The number of ways to arrange 5 persons at a round table such that the tallest person is always on the right side of the shortest person is 6.
Since we have fixed the positions of the shortest and tallest persons and can arrange the other 3 persons in 6 ways, the total number of valid arrangements is: 6
Final Answer:
The number of ways to arrange 5 persons at a round table such that the tallest person is always on the right side of the shortest person is 6.
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