All India CA Foundation Group

Sequence & series past year question?

Sounak Jain answered  •  2 hours ago
Understanding Sequences and Series
In the realm of mathematics, sequences and series are foundational concepts that form the basis for more advanced topics. Let’s delve into a typical past year question to clarify these concepts.
Defining Sequences
- A sequence is an ordered list of numbers following a specific pattern.
- Each number in a sequence is termed
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Sequence & series question?

Arnab Nambiar answered  •  2 hours ago
Understanding Sequences and Series
Sequences and series are fundamental concepts in mathematics, particularly in algebra and calculus. They form the backbone of many mathematical analyses and applications.
What is a Sequence?
- A sequence is an ordered list of numbers.
- Each number in a sequence is called a term.
- Sequences can be finite (having a limited n
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A limited liability partnership is:
  • a)
    Not a separate entity from that of its partners
  • b)
    A legal entity separate from that of its partners
  • c)
    A body corporate
  • d)
    Only B and C are correct
Correct answer is option 'D'. Can you explain this answer?

Qudrat Chauhan answered  •  7 hours ago
  • A Limited Liability Partnership (LLP) is a legal entity separate from its partners. It has its own identity and can enter into contracts, own assets, and sue or be sued independently.
  • An LLP is also recognized as a body corporate, much like a company under law.
  • Therefore, statement A is incorrect because an LLP is a separate entity.
Hence, only statements B and C are correct.

When counter offer is made original offer
  • a)
    Lapse.
  • b)
    Change.
  • c)
    Continue.
  • d)
    None of the above.
Correct answer is option 'A'. Can you explain this answer?

Sinjini Gupta answered  •  8 hours ago
Understanding Counter Offers
When a counter offer is made in response to an original offer, it fundamentally alters the original agreement. Here's why the correct answer is "A) Lapse."
Definition of Lapse
- When an original offer is made, it remains valid until it is accepted, rejected, or lapses.
- A counter offer effectively rejects the original offer, causing i
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An unsound person ‘B’ is liable for necessaries provided to him to the extent of:
  • a)
    B’s estate
  • b)
    B personally 
  • c)
    B’s relative 
  • d)
    B’s son 
Correct answer is option 'A'. Can you explain this answer?

Qudrat Chauhan answered  •  13 hours ago
According to Section 68 of the Indian Contract Act, 1872, if necessaries are supplied to a person incapable of entering into a contract (such as an unsound person), the supplier is entitled to be reimbursed from the property of the incapable person. This means the liability is limited to B’s estate and not personal, relative, or son. The law ensures that suppliers of necessaries are protected, but only to the extent of the unsound person’s property.

A minor`s liability for `necessaries` supplied to him
  • a)
    arises after he attains majority age
  • b)
    is against only minor`s property
  • c)
    does not arise at all
  • d)
    arises if minor gives a promise for it
Correct answer is option 'B'. Can you explain this answer?

Qudrat Chauhan answered  •  13 hours ago
According to Section 68 of the Indian Contract Act, 1872, when a minor is supplied with necessaries suitable to his condition in life, the supplier is entitled to be reimbursed from the property of the minor. The liability does not arise personally against the minor, but only against the minor’s property. This ensures that minors are protected from personal liability but also allows suppliers to recover the cost of necessaries from the minor’s assets. Therefore, the correct answer is that the liability is only against the minor’s property.
Jyoti Nair asked a question

Each of the 10 persons namely A, Q, R, Z, M, N, P, B, K and L are wearing a shirt. The colour of each shirt is one out of blue, green and red. There are ten chairs placed in a row. The chairs are consecutively numbered 1, 2, 3, 4...9 and 10 from left to right in that order. These ten persons have to sit on the chairs such that there is only one person in each chair. The number of persons wearing a green and a blue shirt is 2 and 3 respectively.
Additional Information:
1. No two persons wearing blue shirts sit on consecutively numbered chairs.
2. Among the persons wearing red shirts, exactly three persons always are sitting together while the remaining two never.
3. A person wearing a blue shirt and a person wearing a green shirt never is sitting on consecutively numbered chairs.
4. A person wearing a green shirt cannot sit on chairs numbered 2 or 9.
5. Persons wearing red shirts are not sitting at extreme ends.
The following table provides information about the six different seating arrangements namely I, II, III, IV, V and VI of the ten persons done by Mr. Crazy. He observed that out of all the seating arrangements done by him, there is one arrangement that is not consistent with the information stated under "Additional Information".
Q. Which of the arrangements done by Mr. Crazy is not consistent with the information stated under "Additional Information"?
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A machine worth Rs. 490740 is depreciated at 15% on its opening value each year. When its value would reduce to Rs. 200000?
  • a)
    4 years 6 months 
  • b)
    4 years 7 months 
  • c)
    4 years 5 months 
  • d)
    5 years 7 months (appx.) 
Correct answer is option 'D'. Can you explain this answer?

Qudrat Chauhan answered  •  13 hours ago
 
Given
  • Initial value of the machine = Rs. 490740
  • Depreciation rate = 15% per annum on opening value
  • Final value = Rs. 200000
We need to find the time (in years and months) it takes for the value to reduce to or just below Rs. 200000.
Step-by-step:
This is exponential depreciation, so we use the formula:
V = P(1 - r)^t
Where:
  • V = 200000 (final value)
  • P = 490740 (initial value)
  • r = 0.15 (15%)
  • t = time in years
Substitute into the formula:
200000 = 490740 × (0.85)^t 200000 / 490740 ≈ (0.85)^t 0.4076 ≈ (0.85)^t
Taking logarithm on both sides:
log(0.4076) = t × log(0.85) t = log(0.4076) / log(0.85) t ≈ -0.3894 / -0.0706 ≈ 5.51 years
Convert decimal to years and months:
0.51 × 12 ≈ 6.12 months So, t ≈ 5 years 6 months
Correct answer: d) 5 years 7 months (approx.) ✅
(Since depreciation occurs in full months/years, we round to the nearest month.)

The objective of wealth maximization takes into account 
  • a)
     Amount of returns expected
  • b)
     Timing of anticipated returns
  • c)
     Risk associated with uncertainty of returns
  • d)
     All of the above
Correct answer is option 'D'. Can you explain this answer?

Dhruthi Bk answered  •  yesterday
Wealth maximisation means increasing the value of the business by focusing on expected returns, their timing, and the risk involved. It ensures better decisions by considering how much return is earned, when it is received, and how risky it is.

The cost of living index(CLI) is always
(a) Weighted Index
(b) Price Index
(c)Quantity Index
(d)None of these?

Ritika Iyer answered  •  yesterday
Understanding the Cost of Living Index (CLI)
The Cost of Living Index (CLI) is a crucial economic indicator that reflects the relative cost of living in different regions or over time. It helps to assess the changes in the price of goods and services, making it essential for economic analysis, budgeting, and policy-making.
What Type of Index is CLI?
The CLI is categori
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In simple interest, a sum of money amounts to ₹ 6,200 in 2 years and ₹ 6,800 in 3 years. Find the principal and rate of interest.
  • a)
    Rs. 5000, 12%
  • b)
    Rs. 3000, 20%
  • c)
    Rs. 3500, 15%
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Qudrat Chauhan answered  •  yesterday
Let the principal be P and the rate of interest be R%.
Using the simple interest formula: Amount = Principal + (Principal × Rate × Time) / 100
For 2 years: 6,200 = P + (P × R × 2) / 100 6,200 = P(1 + 2R/100)  ... (1)
For 3 years: 6,800 = P + (P × R × 3) / 100 6,800 = P(1 + 3R/100)  ... (2)
Subtract equation (1) from equation (2):
6,800 - 6,200 = P[(1 + 3R/100) - (1 + 2R/100)] 600 = P(R/100) P = 600 × 100 / R P = 60,000 / R  ... (3)
Substitute P from equation (3) into equation (1):
6,200 = (60,000 / R)(1 + 2R/100) 6,200
=(60,000 / R) + 1,200 6,200 - 1,200
= 60,000 / R 5,000
= 60,000 / R
R = 60,000 / 5,000
R = 12% Now, substitute R back into equation (3):
P = 60,000 / 12 P = 5,000 The principal is ₹5,000 and the rate of interest is 12%. 

Graphs of the inequations are drawn below:

L1 : 2x +y = 9 L2 : x + y = 7 L3 : x+2y= 10 L4 : x + 3y = 12
The common region (shaded part) indicated on the diagram is expressed by the set of inequalities
  • a)
  • b)
  • c)
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?

Qudrat Chauhan answered  •  5 days ago
The diagram shows the region which is common of the equations of inequality.
We will select one point from the shaded region and write the equations of inequalities.
Lets the consider the point (6,5) and substitute in equations .
2x + y = 12 + 5 = 17 > 9 , x + y = 6 + 5 = 11 > 7
x + 2y = 6 + 10 = 16 >10 , x + 3y = 6 + 15 = 21 >12.
x = 6 >0, y = 5 >0
So the correct option is c.


L1 : 5x + 3y = 30 L2 : x+y = 9 L3 : y = x/3 L4 : y = x/2 The common region (shaded part) shown in the diagram refers to
  • a)
  • b)
  • c)
  • d)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Qudrat Chauhan answered  •  5 days ago
The diagram shows the region which is common of the equations of inequality.
We will select one point from the shaded region and write the equations of inequalities.
Lets the consider the point (6, 2.5) and substitute in equations .
5x + 3y = 5(6) + 3(2.5) = 30 + 7.5 = 37.5 > 30
x + y = 6 + 2.5 = 8.5 < 9
x / 3 = 6/3 = 2 < 2.5 < y
So the answer is none of these.

The graph to express the inequality y ≤ (½)x is indicated by
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'D'. Can you explain this answer?

Qudrat Chauhan answered  •  5 days ago
To plot the graph of y ≤ (½)x, first plote the graph of y =(½)x
It will be a straight line passing through (0 ,0) and (2, 1) .
The graph of inequality is the region satisfying the inequality.
So it is on one side of a line.
Now we will check any one point of one side , if it satisfy the inequality then the shading is done on that side or on the other side.
As the line passes through origin we can not check (0,0).
Let us check (2,0) , When x = 2, then y = 1. 0 < 1 , So (2,0) satisfy the inequality.
So shading must be towards the point . that is towards x axis.

The graph to express the inequality 5x + 3y ≥ 30 is
  • a)
  • b)
  • c)
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?

Qudrat Chauhan answered  •  5 days ago
To plot the graph of 5x + 3y ≥ 30 , first plote the graph of 5x + 3y = 30.
It will be a straight line passing through (0 ,10) and (6, 0) .
The graph of inequality is the region satisfying the inequality.
So it is one side of a line.
Now we will check any one point of one side , if it satisfy the inequality then the shading is done on that side or on the other side.
Let us check (0, 0) . 0 + 0 = 0 <30, . So the origin does not satisfy the inequality. so the shading has to be done opposite to the origin.

The graph to express the inequality x + y ≤ 9 is
  • a)
  • b)
  • c)
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Qudrat Chauhan answered  •  5 days ago
To plot the graph of x + ≤ 9 , first plote the graph of x + y = 9.
It will be a straight line passing through (0 ,9) and (9, 0) .
The graph of inequality is the region satisfying the inequality.
So it is on side of a line.
Now we will check any one point of one side , if it satisfy the inequality then the shading is done on that side or on the other side.
Let us check (0, 0) . 0 + 0 = 0 < 9, so the shading has to be done towards the origin.

Which of the following statement is true?
  • a)
    Consideration must result in a benefit to both parties.
  • b)
    Past consideration is no consideration in India.
  • c)
    Consideration must be adequate.
  • d)
    Consideration must be something, which a promisor is not already bound to do.
Correct answer is option 'D'. Can you explain this answer?

Qudrat Chauhan answered  •  1 week ago
Consideration in a contract refers to something of value that is exchanged between the parties involved. For consideration to be valid in India:
  • It must be something that the promisor is not already obligated to do. This means the promisor should provide something new or additional.
  • Past consideration, which is something given or promised before the contract is made, is not acceptable. Therefore, it does not count as valid consideration.
  • While consideration should be sufficient and fair, it does not have to be equal in value. The law does not require that the consideration be adequate.
Thus, the statement regarding consideration being something the promisor is not already bound to do is the correct understanding of valid consideration in a contract.

Which Indian state has the lowest density of population?
  • a)
    West Bengal
  • b)
    Delhi
  • c)
    Arunachal Pradesh
  • d)
    Mizoram
Correct answer is option 'C'. Can you explain this answer?

Muskaan Tiwari answered  •  2 weeks ago
Introduction
India is a diverse country with varying population densities across its states. Population density is calculated by dividing the total population by the total area of the state. Among the Indian states, Arunachal Pradesh stands out with the lowest population density.
Reasons for Low Population Density in Arunachal Pradesh
- Geographical Factors: ... more

A agrees to sell to B a horse for Rs. 25,000 if he wins race and for Rs. 15,000 if he does not. The horse wins the race. The agreement is: 
  • a)
    Valid and Enforceable 
  • b)
    Void and enforceable 
  • c)
    Void and wagering 
  • d)
    Voidable and wagering 
Correct answer is option 'C'. Can you explain this answer?

Janhavi Basu answered  •  2 weeks ago
Understanding the Agreement
In this scenario, A agrees to sell a horse to B based on the outcome of a race. The price differs based on whether the horse wins or loses.
Key Components of the Agreement
- The price is contingent on the race outcome:
- Rs. 25,000 if the horse wins.
- Rs. 15,000 if the horse does not win.
Classification of the Agreement
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- This type of agreement is categorized as a wagering agreement.
What is a Wagering Agreement?
- A wagering agreement is defined as one where two parties agree to pay money based on the outcome of an uncertain event.
- In this case, the sale of the horse is not the primary intention; rather, it revolves around the race outcome.
Legal Standpoint
- According to the Indian Contract Act, a wagering agreement is void.
- Since the agreement's enforceability hinges on the outcome of the race, it lacks legal validity.
Conclusion
- The agreement between A and B is classified as "Void and Wagering."
- Therefore, the correct answer is option 'C.'
This understanding is crucial for anyone studying contract law, especially in the context of the CA Foundation.

How many Accounting Standards have been issued by ICAI?
  • a)
    25.
  • b)
    20.
  • c)
    32.
  • d)
    2.
Correct answer is option 'C'. Can you explain this answer?

Pooja Sagar answered  •  2 weeks ago
The Institute of Chartered Accountants of India (ICAI) has issued 28 Accounting Standards (AS) in India. These standards are applicable to companies and other entities that are not required to follow Indian Accounting Standards (Ind AS).
The ICAI has also issued a revised set of Accounting Standards, which are at various stages of formulation. These revised standards, when implemented, will
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DISCOUNT RECEIVED FROM RED & BLACK ₹15 HAS NOT BEEN ENTERED IN THE DISCOUNT COLUMN OF THE CASH BOOK (RECTIFICATION OF ERROR)
I CAN'T UNDERSTAND THE ANSWER
👇👇👇👇👇👇👇👇👇👇👇👇👇👇
RED & BLACK ACC DR.15 ... more

Malavika Basak answered  •  2 weeks ago
Understanding the Error
When a discount received from Red & Black amounting to ₹15 is not recorded in the discount column of the cash book, it results in an understatement of both the cash balance and the discount income. This is a common error in bookkeeping that needs rectification.
Rectification Process
To correct this error, you need to make an adjustment entry in
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 The price of hot-dogs increases by 22% and the quantity demanded falls by 25% this indicates that demand for hot dogs is: 
  • a)
    Elastic 
  • b)
    Inelastic
  • c)
    Unitary elastic 
  • d)
    Perfectly elastic
Correct answer is option 'A'. Can you explain this answer?

Qudrat Chauhan answered  •  2 weeks ago
To determine the type of demand, we calculate the price elasticity of demand (PED) using the formula: PED = (% change in quantity demanded) / (% change in price). Here, PED = (-25%) / (+22%) ≈ -1.14. The absolute value is greater than 1, which means the demand is elastic. Elastic demand means consumers are relatively sensitive to price changes; a small increase in price leads to a larger percentage decrease in quantity demanded.

From the following table by the method of relatives using Arithmetic mean the price Index number is
  • a)
    140.35
  • b)
    148.25
  • c)
    140.75
  • d)
    None of these.
Correct answer is option 'B'. Can you explain this answer?

Qudrat Chauhan answered  •  2 weeks ago
Step 1: Calculate the Price Relative for each commodity 
Formula:
Price Relative = (Current Price / Base Price) × 100
Commodity Base Price Current Price Price Relative
Wheat 5 7 (7/5) × 100 = 140
Milk 8 10 (10/8) × 100 = 125
Fish 25 32 (32/25) × 100 = 128
Sugar 6 12 (12/6) × 100 = 200
Step 2: Calculate the Arithmetic Mean of Price Relatives
Index Number = (140 + 125 + 128 + 200) / 4 = 593 / 4 = 148.25

I have a doubt about the topic allegation in maths?

Maheshwar Sharma answered  •  3 weeks ago
Understanding Allegation in Mathematics
Allegation is a method used in mathematics to determine the average of two or more quantities that are mixed together. It’s particularly useful in problems involving mixtures, ratios, and weighted averages.
Key Concepts of Allegation
- Definition: Allegation is a rule that helps in finding the mean or average of different
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When parties enters into a contract under a mutual mistake of fact the contract is_________ :
  • a)
    Valid 
  • b)
    Voidable 
  • c)
    Void 
  • d)
    None of these 
Correct answer is option 'C'. Can you explain this answer?

Gopal Sen answered  •  3 weeks ago
Understanding Mutual Mistake of Fact
When parties enter into a contract under a mutual mistake of fact, it fundamentally affects the validity of the agreement. A mutual mistake occurs when both parties share a common false belief about a vital fact that influences their decision to enter into the contract.
Nature of the Contract
- A contract is considered void w
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Trial Balance for the financial year ended 31st March 2022 of M/s Deepakshi shows following details?

Rajveer Jain answered  •  3 weeks ago
Understanding Trial Balance
A trial balance is an essential accounting tool that lists all the balances of ledger accounts at a specific point in time, ensuring that total debits equal total credits. For M/s Deepakshi, the trial balance for the financial year ended 31st March 2022 reflects the company's financial position and is crucial for preparing financial statements.
Compo
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- Assets: These are resources owned by the business. Examples include cash, inventory, and accounts receivable.
- Liabilities: These represent obligations that the company owes to outsiders, such as loans and accounts payable.
- Equity: This reflects the owner's interest in the business after deducting liabilities from assets.
Importance of a Trial Balance
- Error Detection: A trial balance helps in identifying errors in the ledgers, ensuring accuracy in financial reporting.
- Financial Analysis: It provides a snapshot of the company's financial health during the accounting period, facilitating analysis.
- Basis for Financial Statements: The trial balance serves as a foundation for preparing the income statement and balance sheet.
Process of Preparing Trial Balance
1. List Accounts: Begin by listing all ledger accounts with their respective balances.
2. Categorize Accounts: Group accounts into debits (assets and expenses) and credits (liabilities, equity, and revenue).
3. Total Balances: Calculate the total of debit and credit columns to ensure they match.
Conclusion
The trial balance for M/s Deepakshi provides crucial insights into the company's finances, highlighting the importance of maintaining accurate accounts. It is a vital step in the accounting cycle, paving the way for sound financial management and reporting.
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