Category: Class 12

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 9 Applications of Integration Ex 9.1 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.1

Question 1.
Find an approximate value of \(\int_{1}^{1.5}\) x dx by applying the left – end rule with the partition {1.1, 1.2, 1.3, 1.4, 1.5}
Solution:
Here a = 1, b = 1.5, n = 5, f(x) = x
So, the width of each subinterval is

The left hand rule for Riemann sum,
S = [f(x₀) + f(x₁)) + f(x₂) + f(x₃) + f(x₄)] ∆x
= [f(1) + f(1.1) + f(1.2) + f(1.3) + f(1.4)] (0.1)
= [1 + 1.1 + 1.2 + 1.3 + 1.4] (0.1)
= [6] (0.1)
= 0.6.

Question 2.
Find an approximate value of \(\int_{1}^{1.5}\) x² dx by applying the right – end rule with the partition {1.1, 1.2, 1.3, 1.4, 1.5}
Solution:
Here a = 1, b = 1.5, n = 5, f(x) = x²
So, the width of each subinterval is
h = Δx = \(\frac{b-a}{n}\) = \(\frac{1.5- 1}{5}\) = 0.1
The partition of the interval is given by
x₁ = 1.1
x₂ = 1.2
x₃ = 1.3
x₄ = 1.4
x₅ = 1.5
The right – end rule for Riemann sum with equal width Δx is
S = [f(x₁) + f(x₂) + ….. + f(x_n)] Δx
∴ S = [f(1.1) + f(1.2) + f(1.3) + f(1.4) + f(1.5)](0.1)
= (1.21 + 1.44 + 1.69 + 1.96 + 2.25) × 0.1
= 8.55 × 0.1
= 0.855

Question 3.
Find an approximate value of \(\int_{1}^{1.5}\) (2 – x) dx by applying the mid – point rule with the partition {1.1, 1.2, 1.3, 1.4, 1.5}
Solution:
Here a = 1, b = 1.5, n = 5, f(x) = 2 – x
So, the width of each subinterval is
h = Δx = \(\frac{b-a}{n}\) = \(\frac{1.5- 1}{5}\) = 0.1
The partition of the interval is given by
The partition of the interval is given b.y
x₀ = 1, x₁ = 1.1, x₂=1.2, x₃ = 1.3, x₄ = 1.4, x₅ = 1.5
The mid – point rule for Riemann sum with equal width Δx is

∴ S = (0.95 + 0.85 + 0.75 + 0.65 + 0.55) × 0.1
= 3.75 × 0.1
= 0.375

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Accountancy Guide Pdf Chapter 10 Computerised Accounting System-Tally Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Accountancy Solutions Chapter 10 Computerised Accounting System-Tally

12th Accountancy Guide Computerised Accounting System-Tally Text Book Back Questions and Answers

I Multiple Choice Questions

Choose the correct answer
Question 1.
Accounting report prepared according to the requirements of the user is
(a) Routine accounting report
(b) Special purpose report
(c) Trial balance
(d) Balance sheet
Answer:
(b) Special purpose report

Question 2.
Function key F 11 is used for
(a) Company Features
(b) Accounting vouchers
(c) Company Configuration
(d) None of these
Answer:
(a) Company Features

Question 3.
Which sub menu displays groups, ledgers and voucher type in tally?
(a) Inventory vouchers
(b) Accounting vouchers
(c) Company Info
(d) Account Info
Answer:
(d) Account Info

Question 4.
What are the predefined Ledger(s) in Tally?
(i) Cash
(ii) Profit & Loss A/c
(iii) Capital A/c
(a) Only (i)
(b) Only (ii)
(c) Both (i) and (ii)
(d) Both (ii) and (iii)
Answer:
(c) Both (i) and (ii)

Question 5.
Contra voucher is used for
(a) Master entry
(b) Withdrawal of cash from bank for office use
(c) Reports
(d) Credit purchase of assets
Answer:
(b) Withdrawal of cash from bank for office use

Question 6.
Which is not the default group in Tally
(a) Suspense account
(b) Outstanding expense
(c) Sales account
(d) Investments
Answer:
(b) Outstanding expense

Question 7.
Salary account comes under which of the following head?
(a) Direct Incomes
(b) Direct Expenses
(c) Indirect Incomes
(d) Indirect Expenses
Answer:
(d) Indirect Expenses

Question 8.
₹ 25,000 withdrawn from bank for office use. In which voucher type, this transaction will be recorded
(a) Suspense account
(b) Outstanding expense
(c) Sales account
(d) Investment
Answer:
(a) Suspense account

Question 9.
In which vouchers type credit purchase of furniture is recorded in Tally
(a) Receipt voucher
(b) Journal voucher
(c) Purchase voucher
(d) Payment voucher
Answer:
(b) Journal voucher

Question 10.
Which of the following options is used to view Trial Balance from Gateway of Tally?
(a) Gateway of Tally → Reports → Trial Balance
(b) Gateway of Tally → Trial Balance
(c) Gateway of Tally → Reports → Display → Trial Balance
(d) None of these
Answer:
(c) Gateway of Tally → Reports → Display → Trial Balance

II Very Short Answer Questions

Question 1.
What is automated accounting system?
Answer:
Automated accounting is an approach to maintain up-to-date accounting records with the aid of accounting software.

Question 2.
What are accounting reports?
Answer:
Accounting report is a compilation of accounting information that are derived from the accounting records of a business concern. Accounting reports may be classified as routine reports and special purpose reports.

Question 3.
State any five accounting reports.
Answer:

1. Daybooks/Joumal
2. Ledger
3. Trial Balance
4. Income statement
5. Balance sheet

Question 4.
What is Accounting Information System (AIS)?
Answer:
Accounting Information System (AIS) collects financial data, processes them, and provides information to the various users. To provide information AIS requires data from another information system that is manufacturing, marketing, and human resources. Similarly, other information systems require data from Ais in order to provide information.

Question 5.
What is a group in Tally.ERP 9?
Answer:
A group is a collection of ledgers of the same nature. There are predefined groups of accounts which are widely used in accounts of any organization. Groups are categorized as primary groups and subgroups.

III Short Answer Questions

Question 1.
Write a brief note on accounting vouchers.
Answer:
A voucher is a document which contains details of transactions. Transactions are to be recorded through voucher entries. Tally has a set of predefined vouchers such as Purchase, Sales, Payment, Receipt and Contra.

To view the list of voucher types:
Gateway of Tally → Masters Accounts Info → Voucher Type →Display
As per the requirements of users, additional voucher type can be created.

Following are some of the major accounting vouchers used in an organisation:

• Receipt Voucher
• Payment Voucher
• Contra Voucher
• Purchase Voucher
• Sales Voucher
• Journal Voucher

Question 2.
What are the pre-defined ledgers available in Tally.ERP 9?
Answer:
Tally has two predefined ledgers, cash and profit and loss A/c. The user has to create various other ledgers based on their requirements. Predefined group/ledger cannot be deleted.

Question 3.
Mention the commonly used voucher types in Tally.ERP 9?
Answer:
Following are some of the major accounting vouchers used in an organization:

1. Receipt Voucher
2. Payment Voucher
3. Contra Voucher
4. Purchase Voucher
5. Sales Voucher
6. Journal Voucher

Question 4.
Explain how to view profit and loss statement in Tally ERP 9?
Answer:
F10: A/c Reports > Profit & Loss A/c > AltF1 (detailed)
(or)
Gateway of Tally > Reports > Profit & Loss A/c > AltF1 (detailed)

Question 5.
Explain any five applications of computerized accounting system.
Answer:
Application of accounting software – Tally

(1) Starting Tally:
Tally can be started in either of the ways given below:
Click on Start > All programs . Tally.ERP 9 > Tally.ERP 9 icon
(Or)
Click Tally.ERP. 9 icon (shortcut) on the desktop

(2) Creation of a company:
It is essential to enter the particulars of the company for which accounts are to be maintained in Tally. In order to create a company, the following steps are to be followed:
Company Info>Create Company

(3) Gateway of Tally:
After creation of a company and whenever Tally is started a screen Gateway of Tally appears. It shows the company selected under List of Selected Companies on the left pane.

Gateway of Tally is shown on the right pane which contains menu options such as Transactions and Reports. The shortcut key for each menu option is a letter from the option’s name, which will be highlighted in red.

Vertical button bar is placed on the extreme right of screen which contains buttons such as F1 and F2 for quick interaction with Tally.ERP 9.

Bottom horizontal information panel displays details of product, version, licence, configuration and calculator.

(4) Closing Tally
The following are the two ways for closing Tally:
Press Esc Key > Press Enter or Y or Click on yes
(or)
Press Ctrl + Q

(5) Select a company
If multiple companies are created, to choose a particular company, after opening Tally, click F1 (Select Cmp) on the vertical button bar. Tally.ERP 9 displays the Select Company screen, with a list of companies that are already created. Select the company for which accounting has to be done.

IV Exercises

Question 1.
Record the following transactions in Tally.
(a) Devi commenced a business with a capital of ₹ 4,00,000
(b) An account was opened with Indian Bank and deposited ₹ 60,000
(c) Purchased furniture by paying cash ₹ 15,000
(d) Goods purchased on credit from Sumathy for ₹ 50,000
(e) Cash sales made for ₹ 10,000
(f) Goods purchased from Raja for ₹ 5,000 and paid by cheque
(g) Goods sold to Arun on credit for ₹ 70,000
(h) Money is withdrawn from bank for office use ₹ 25,000
(i) Part payment of ₹ 30,000 made to Sumathy by cheque
(j) Arun made part payment of ₹ 10,000 by cash
(k) Salaries paid to staff through ECS ₹ 36,000
(l) Carriage on purchases of ₹ 6,000 paid by cash
(m) Purchased computer from Muthu Ltd. on credit ₹ 44000
Solution

Question 2.
The following balance sheet has been prepared from the books of pearl on 1 – 4- 2018,

During the year the following transactions took place.

(a) Wages paid by cash ₹ 4,000
(b) Salaries paid by cheque ₹ 10,000
(c) Cash purchases made for ₹ 4,000
(d) Good purchased on credit from Yazhini ₹ 30,000
(e) Goods sold on credit to Jothi ₹ 40,000
(f) Payment made to Yazhini through NEFT ₹ 6,000
(g) Cash received from Peter ₹ 10,000
(h) Cash sales made for ₹ 4,000
(i) Depreciate buildings at 20%
(j) Closing stock on 31.03.2013 ₹ 9,000

You are required to prepare trading and profit and loss account for the year ended 31-03-2019 and balance sheet as on that using Tally.
Solution

12th Accountancy Guide Computerised Accounting System-Tally Additional Important Questions and Answers

III Short Answer Questions

Question 1.
What do you mean by a Computerised Accounting system?
Answer:
Computerized accounting system refers to the system of maintaining accounts using f computers. It involves the processing of accounting transactions through the use of a computer in order to maintain and produce accounting records and reports. Computerized accounting system takes accounting transactions as input that are processed through accounting software to generate various reports.

Question 2.
What are the applications of the Computerised Accounting system?
Answer:
The application of CAS are as follows:
(1) Maintaining accounting records: In CAS, accounting records can be maintained easily and efficiently for the low time period. It does not require a large amount of physical space. It facilitates fast and accurate retrieval of data and information.

(2) Inventory management: CAS facilitates efficient management of inventory. Fast-moving, slow-moving, and obsolete inventory can be identified. Updated information about the availability of inventory, level of inventory, etc., can be obtained instantly.

(3) Payroll preparation: Payroll involves the calculation of the amount due to an employee, pay of an employee may be calculated based on hours/days worked or units produced. CAS records the attendance of employees, computes the amount of salary, makes deductions such as provident fund, income ta, etc.

(4) Report generation: CAS helps to generate various routine and special purpose reports.

(5) Data import/export: Accounting data and information can be imported from or exported to other users within the organization as well as outside the organization.

(6) Taxation: CAS helps to compute various taxes and to deduct these and deposit the same to the Government account.

Question 3.
What are the steps involved in designing accounting reports?
Answer:
Following are the steps involved in designing accounting reports:

1. Define the objective of generating the report.
2. Specify the structure of the report
3. Creating database queries to interact with the database to retrieve, modify, add, or delete data from the records.
4. Write notes on the following
   • Contra Voucher
   • Purchase Voucher
   • Journal Voucher

(a) Contra Voucher:
A transaction involving both cash account and bank account is recorded using contra voucher. The transaction may be for deposit of cash into bank account or withdrawal of cash from bank account To record Contra:
Gateway of Tally > Transactions > Accounting Voucher > F4:Contra

(b) Purchase Voucher:
Purchase voucher are used for recording both cash and credit purchases of goods. To record Purchases:
Gateway of Tally > Transactions > Accounting Vouchers > F9:Purchase

(c) Journal Voucher:
Journal voucher are used for recording transactions involving other than cash, bank, purchases and sales such as depreciation, provision for bad bebts.
To record Journal:
Gateway of Tally > Transactions > Accounting vouchers > F7:Journal

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 8 Differentials and Partial Derivatives Ex 8.8 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 8 Differentials and Partial Derivatives Ex 8.8

Choose the most suitable answer from the given four alternatives:

Question 1.
A circular template has a radius of 10 cm. The measurement of the radius has an approximate error of 0.02 an. Then the percentage error in the calculating the area of this template is
(a) 0.2 %
(b) 0.4 %
(c) 0.04 %
(d) 0.08 %
Solution:
(b) 0.4 %
Hint:
Radius of a circular plate = 10 cm
error in radius dr = 0.02
A = πr²
dA = 2πrdr

Question 2.
The percentage error of the fifth root of 31 is approximately how many times the percentage error in 31?
(a) \(\frac{1}{31}\)
(b) \(\frac{1}{5}\)
(c) 5
(d) 31
Solution:
(b) \(\frac{1}{5}\)
Hint:
(i.e.) the percentage error in the nth root of a number is approximately \(\frac{1}{n}\) times the percentage error in the number.

Question 3.
If u (x, y) = e^{x2 + y2} then \(\frac{\partial u}{\partial x}\) is equal to
(a) e^{x2 + y2}
(b) 2xu
(c) x²u
(d) y²u
Solution:
(b) 2xu
Hint:
u = e^{x2 + y2}
\(\frac{\partial u}{\partial x}\) = e^{x2 + y2} (2x) = 2xu

Question 4.
If v (x, y) = log (e^x + e^y), then \(\frac{\partial v}{\partial x}\) + \(\frac{\partial u}{\partial y}\) is equal to
(a) (e^x + e^y)
(b) \(\frac{1}{e^x+e^y}\)
(c) 2
(d) 1
Solution:
(d) 1
Hint:
v = log (e^x + e^y)

= 1

Question 5.
If w (x, y) = x^y, x > 0, then \(\frac{\partial w}{\partial x}\) is equal to
(a) x^y log x
(b) y log x
(c) y x^y-1
(d) x log y
Solution:
(c) y x^y-1
Hint:
w(x, y) = x^y
\(\frac{\partial w}{\partial x}\) = y x^y-1

Question 6.
If f (x, y) = e^xy, then \(\frac{\partial^2 f}{\partial x \partial y}\) is equal to
(a) xy e^xy
(b) (1 + xy)e^xy
(c) (1 + y) e^xy
(d) (1 + x)e^xy
Solution:
(b) (1 + xy)e^xy
Hint:
f(x, y) = e^xy
\(\frac{\partial f}{\partial y}\) = x e^xy (x) = xe^xy
\(\frac{\partial^2 f}{\partial x \partial y}\) = x e^xy (y) + e^xy = e^xy(1 + xy)

Question 7.
If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is
(a) 0.4 cu.cm
(b) 0.45 cu.cm
(c) 2 cu.cm
(d) 4.8 cu.cm
Solution:
(d) 4.8 cu.cm
Hint:
Side of the cube = 4 cm
Volume V = x³
dV = 3x²dx
= 3 × 16 × 0.1
= 4.8 cu. cm

Question 8.
The change in the surface area S = 6x² of a cube when the edge length varies from x₀ to x₀ + dx is
(a) 12 x₀ + dx
(b) 12 x₀ dx
(c) 6 x₀ dx
(d) 6 x₀ + dx
Solution:
(b) 12 x₀ dx
Hint:
Surface Area S = 6x²
dS = 12 × dx
dS = 12 x₀ dx

Question 9.
The approximate change in volume V of a cube of side x meters caused by increasing the side by 1% is
(a) 0.3 x m³
(b) 0.03 x m³
(c) 0.03 x² m³
(d) 0.03 x³ m³
Solution:
(c) 0.03 x² m³
Hint:
Volume of the cube V = x³
dV = 3x² dx
= 3x² × 0.01
= 0.03 x² m³

Question 10.
If g (x, y) = 3x² – 5y + 2y², x(t) = e^t and y(t) = cos t then \(\frac{dg}{dt}\) is equal to
(a) 6 e^2t + 5 sin t – 4 cos t sin t
(b) 6 e^2t – 5 sin t – 4 cos t sin t
(c) 3 e^2tt + 5 sin t + 4 cos t sin t
(d) 3 e^2t – 5 sint + 4 cos t sin t
Solution:
(a) 6 e^2t + 5 sin t – 4 cos t sin t
Hint:
x = e^t, y = cos t

= 6 x e^t + (-5 + 4y) – sin t
= 6 e^t e^t + 5 sin t – 4 cos t sin t
= 6e^2t + 5 sin t – 4 cos t sin t

Question 11.
If f(x) = \(\frac{x}{x+1}\), then its differential is given by
(a) –\(\frac{x}{(x+1)^2}\) dx
(b) \(\frac{x}{(x+1)^2}\) dx
(c) \(\frac{x}{x+1}\) dx
(d) –\(\frac{x}{x+1}\) dx
Solution:
(b) \(\frac{x}{(x+1)^2}\) dx
Hint:

Question 12.
If u (x, y) = x² + 3xy + y – 2019, then \(\frac{\partial u}{\partial x}\)| _{(4, -5)} is equal to
(a) -4
(b) -3
(c) -7
(d) 13
Solution:
(c) -7
Hint:
u (x, y) = x² + 3xy + y – 2019
\(\frac{\partial u}{\partial x}\) = 2x + 3y
\(\frac{\partial u}{\partial x}\)| _{(4, -5)} = 8 – 15 = -7

Question 13.
Linear approximation for g(x) = cos x at x = \(\frac{π}{2}\) is
(a) x + \(\frac{π}{2}\)
(b) -x + \(\frac{π}{2}\)
(c) x – \(\frac{π}{2}\)
(d) -x – \(\frac{π}{2}\)
Solution:
(b) -x + \(\frac{π}{2}\)
Hint:
linear approximation

Question 14.
If w (x, y, z) = x² (y – z) + y² ( z – x)+ z²(x – y) then \(\frac{\partial w}{\partial x}\) + \(\frac{\partial w}{\partial y}\) + \(\frac{\partial w}{\partial z}\) is
(a) xy + yz + zx
(b) x (y + z)
(c) y (z + x)
(d) 0
Solution:
(d) 0
Hint:
w (x, y, z) = x² (y – z) + y² ( z – x)+ z²(x – y)

= 2xy – 2xz – y² + z² + x² + 2yz – 2yx – z² – x² + y² + 2zx – 2zy
= 0

Question 15.
If f (x, y, z) = xy + yz + zx, then f_x – f_z is equal to
(a) z – x
(b) y – z
(c) x – z
(d) y – x
Solution:
(a) z – x
Hint:
f (x, y, z) = xy + yz + zx
\(\frac{\partial f}{\partial x}\) = y + z
\(\frac{\partial f}{\partial z}\) = y + x
f_x – f_z = y + z – y – x = z – x

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Accountancy Guide Pdf Chapter 1 Accounts from Incomplete Records Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Accountancy Solutions Chapter 1 Accounts from Incomplete Records

12th Accountancy Guide Accounts from Incomplete Records Text Book Back Questions and Answers

I Multiple Choice Questions

Choose the correct answer

Question 1.
Incomplete records are generally maintained by
(a) A company
(b) Government
(c) Small sized sole trader business
(d) Multinational enterprises
Answer:
(c) Small sized sole trader business

Question 2.
Statement of affairs is a
(a) Statement of income and expenditure
(b) Statement of assets and liabilities
(c) Summary of cash transactions
(d) Summary of credit transactions
Answer:
(b) Statement of assets and liabilities

Question 3.
Opening statement of affairs is usually prepared to find out the
(a) Capital in the beginning of the year
(b) Capital at the end of the year
(c) Bills payable accepted during the year
(d) Loss occurred during the year
Answer:
(a) Capital in the beginning of the year

Question 4.
The excess of assets over liabilities is
(a) Loss
(b) Cash
(c) Capital
(d) Profit
Answer:
(c) Capital

Question 5.
Which of the following items relating to bills payable is transferred to the total creditors account?
(a) Loss
(b) Cash
(c) Capital
(d) Profit
Answer:
(c) Capital

Question 6.
The amount of credit sales can be computed from
(a) Total debtors account
(b) Total creditors account
(c) Bills receivable account
(d) Bills payable account
Answer:
(a) Total debtors account

Question 7.
Which one of the following statements is not true in relation to incomplete records?
(a) It is an unscientific method of recording transactions
(b) Records are maintained only for cash and personal accounts
(c) It is suitable for all types of organisations
(d) Tax authorities do not accept
Answer:
(c) It is suitable for all types of organisations

Question 8.
What is the amount of capital of the proprietor, if his assets Rs. 85,000 and Liabilities Rs 21,000.
(a) ₹ 85,000
(b) ₹ 1,06,000
(c) ₹ 21,000
(d) ₹ 64,000
Answer:
(d) ₹ 64,000
Hint:
Assets = Capital – Liabilities
85,000 = Capital – 21,000
Capital = 85,000 – 21,000
Capital = 64,000

Question 9.
When capital, in the beginning, is ₹ 10,000, drawings during the year is ₹ 6,000 profit made during the year is ₹ 2,000 and the additional capital introduced is ₹ 3,000, find out the amount of capital at the end.
(a) ₹ 9,000
(b) ₹ 11,000
(c) ₹ 21,000
(d) ₹ 3,000
Answer:
(a) ₹ 9,000
Hint:

Question 10.
Opening balance of debtors: ₹ 30,000, cash received: ₹ 1,00,000, credit sales: ₹ 90,000; closing balance of debtors is
(a) ₹ 30,000
(b) ₹ 1,30,000
(c) ₹ 40,000
(d) ₹ 20,000
Answer:
(d) ₹ 20,000
Hint:

II. Very Short Answer Questions

Question 1.
What is meant by incomplete records?
Answer:

1. When accounting records are not strictly maintained according to the double-entry system, these records are called incomplete accounting records.
2. Generally, cash accounts and the personal accounts of customers and creditors are maintained fully and other accounts are maintained based on necessity.

Question 2.
State the accounts generally maintained by the small-sized sole trader when a double-entry accounting system is not followed.
Answer:
Cash account and the personal accounts of customers and creditors are maintained fully and other accounts are maintained based on necessity.

Question 3.
What is a statement of affairs?
Answer:
A statement of affairs is a statement showing the balances of assets and liabilities on a particular date. The balance of assets is shown on the right side and the balance of liabilities on the left side. This statement resembles a balance sheet. The difference between the total of assets and the total of liabilities is taken as capital.
Capital = Assets – Liabilities.

III Short Answer Questions

Question 1.
What are the features of incomplete records?
Answer:
1. Nature:

• It is an unscientific and unsystematic way of recording transactions.
• Accounting principles and accounting standards are not followed properly.

2. Types of accounts maintained – In general only cash and personal accounts are maintained fully. Real accounts and nominal accounts are not maintained properly. Some transactions are correctly omitted.

3. Lack of uniformity – There is no uniformity in recording the transactions among different organizations. Different organizations record their transactions according to their needs and conveniences.

4. Financial statements may not represent true and fair view – Due to the incomplete information and inaccurate records of accounts, the profit or loss calculated from these records cannot be relied upon. It may not represent true profitability. Assets and liabilities may not represent a true and fair view of financial position.

5. Suitability – Only the business concerns which have no legal obligation to maintain books of accounts under the double-entry system may maintain incomplete records. Hence, it may be maintained by small-sized sole traders and partnership firms.

6. Mixing up of personal and business transactions – Generally, personal transactions of the owners are mixed up with the business transactions. For example, the purchase of goods for their own use may be mixed up along with business purchases.

Question 2.
What are the limitations of incomplete records?
Answer:

• Lack of proper maintenance of records: It is an unscientific and unsystematic way of maintaining records. Real and Nominal accounts are not maintained properly.
• Difficulty in preparing trial balance: As accounts are not maintained for all items, the accounting records are incomplete. Hence, it is difficult to prepare a trial balance to check the arithmetical accuracy of the accounts.
• Difficulty in ascertaining true profitability of the business: Profit is found out based on available information and estimates. hence, it is difficult to ascertain true profit as the trading and profit and loss account cannot be prepared with accuracy.

Question 3.
State the differences between double-entry system and incomplete records.
Answer:

Question 4.
State the procedure for calculating profit or loss through the statement of affairs.
Answer:
The difference between the closing capital and the opening capital is taken as profit or loss of the business. Due adjustments are to be made for any withdrawal of capital from the business and for the additional capital introduced in the business.
Adjusting closing capital = Closing capital + Drawings – Opening capital.
Closing capital + Drawings – Additional capital – Opening capital = Proft/Loss.

Question 5.
Differentiate between the statement of affairs and the balance sheet.
Answer:

Question 6.
How is the amount of credit sale ascertained from incomplete records?
Answer:
For ascertaining the amount of credit sales, the total debtor’s account should be prepared. The specimen of the total dr’s A/c is given below.

IV Exercise

Question 1.
From the following particulars ascertain profit or loss:

Solution:
Statement of profit or loss for the year ended 31.03.2019

Answer:
Profit: ₹ 3,00,000

Question 2.
From the following particulars ascertain profit or loss :

Solution:
Statement of profit or loss for the year ended 31.12.2018

Answer:
Loss: ₹ 30,000

Question 3.
From the following details, calculate the missing figure.

Solution:
Calculation \ of opening capital

Answer:
Opening capital: ₹ 90,000

Question 4.
From the following details, calculate the capital as on 31st December 2018.

Calculation of closing capital

Answer:
Closing Capital: ₹ 1,45,000

Question 5.
From the following details, calculate the missing figure:

Solution:
Calculation of drawings

Answer:
Drawings: ₹ 5,000

Question 6.
Following are the balance in th books of thomas as on 31st March 2019.

Prepare a statement of affairs as on 31st March 2019 and calculate capitals as at that date.
Solution:
Statement of affairs as on 31.3.2019

Answer :
Capital: ₹ 2,80,000

Question 7.
On 1st April 2018 Subha started her business with a capital of ₹ 1,20,000. She did not maintain a proper book of accounts. Following particulars are available from her books as on 31.03.2019.

During the year she withdraw ₹ 30,000 for her personal use. She introduced further capital of ₹ 40,000 during the year. Calculate her profile or loss.
Solution:
Statement of affairs as on 31.03.2019

Statement of profit or Loss for year ending 31st March 2019

Answer:
Closing Capital: ₹ 2,80,000; Profit: ₹ 2,90,000

Question 8.
Raju does not keep proper books of accounts. The following details are taken from his records.

During the year he introduced further capital of ₹ 50,000 and withdraw ₹ 2,500 per month from the business for his personal use. Prepare a statement of profit or loss with the above information.
Solution:
Statement of affairs as on 1.1.2018

Answer:
Opening Capital: ₹ 2,50,000; Closing capital: ₹ 3,00,000; Profit: ₹ 30,000

Question 9.
Ananth does not keep his books under the double-entry system. Find the profit or loss made by him for the year ending 31st March 2019.

Ananth had withdrawn ₹ 60,000 for his personal use. He had introduced ₹ 17,000 as capital for expansion of his business. Create a provision of 5% on debtors. Plant and machinery is to be depreciated at 10%.
Solution:
Statement of Affairs As on 31.3.2018

Answer:
Opening Capital: ₹ 1,93,000; Closing capital: ₹ 1,57,000; Profit: ₹ 7,000

Question 10.
Find out credit sales from the following information.

Solution:

Question 11.
From the following details find out total sales made during the year.

Solution:

Total sales = Credit Sales + Cash Sales
= 5,40,000 + 4,60,000
Total Sales = Rs. 10,00,000
Answer :
Credit sales : ₹ 5,40,000; Total Sales : ₹ 10,00,000

Question 12.
From the following particulars, prepare bills receivable amount and compute the bills received from the debtors.

Solution:

Answer:
B/R received: ₹ 4,80,000;

Question 13.
From the following particulars, calculate total sales.

Prepare a statement of affairs as on 31st March 2019 and calculate capitals as at that date.
Solution:

Total sales = Credit Sales + Cash Sales
= 9,85,000 + 3,15,000
Total Sales = Rs. 13,00,000
Answer:
B/R received : ₹ 2,05,000; Credit sales: ₹ 9,85,000; Total sales: ₹ 13,00,000

Question 14.
From the following details, calculate credit puchases

Solution:

Answer:
Credit sales : ₹ 2,80,000

Question 15.
From the following particulars calculate total purchases.

Solution:

Total Purchase = Cr Purchase + Cash Purchase
= 1,55,000 + 2,25,000
Total Purchase = Rs. 3,80,000
Answer:
B/P accepted: ₹ 25,000; Credit purchases: ₹ 1,55,000; Total Purchases: ₹ 3,80,000

Question 16.
From the following details you are required to calculate credit sales and credit purchases by preparing total debtors account, total creditors account, bills receivable account and bills payable account.

Solution:

Answers:
B/R received: ₹ 42,000; Credit sales : ₹ 6,59,000; B/P accepted : ₹ 40,000; Credit Purchases: ₹ 4,00,000

Question 17.
From the following details of Rakesh, prepare Trading and Profit and Loss account for the year ended 31st March, 2019 and a Balance Sheet as on that date.

Other details

Solution:

Answer:
Credit Sales: ₹ 13,85,000; Credit purchases: ₹ 11,85,000; Gross profit: ₹ 1,60,000; Net profit: ₹ 50,000, Balance Sheet Total: 8,90,000

Question 18.
Mary does not keep her books under double entry system. From the following details prepare trading and profit and loss account for the year ending 31st March, 2019 and a balance sheet as on that date.

Solution:

Question 19.
Arun carries on hardware business and does not keep his books on double entry basis The following particulars have been extracted from his books.

Other information for the year ending 31.12.2018 showed the following:

Total sales during the year were ₹ 7,70,000. Purchases returns during the year were 30,000 and sales returns were ₹ 25,000. Depreciate land and building by 5%. Provide ₹ 1,500 for doubtful debts. Prepare trading and profit and loss account for the year ending 31st December, 2018 and a balance sheet as on that date.
Solution:

Answer:
Opening capital: ₹ 3,80,000; Credit purchases: ₹ 6,25,000; Gross profit: ₹ 1,35,000; Net profit:: ₹ 86,000, Balance Sheet Total: ₹ 5,01,000

Question 20.
Selvam does not keep ; books under double entry system. From the following information prepare trading and Profit and loss A/c and Balance Sheet as on 31-12-2018

Adjustments: Write off depreciation of 10% on machinery Create a reserve of 1% on debtors for doubtful debts.
Solution:

Answer:
Opening capital: ₹ 1,50,000; Gross Profit: ₹ 1,11,000; Net profit:: ₹ 69,000, Balance Sheet Total: ₹ 2,46,000

12th Accountancy Guide Accounts from Incomplete Records Additional Important Questions and Answers

I. Choose the best answer

Question 1.
Companies must maintain accounting records under double entry system as per
(a) Sec. 128 (1) of Indian Companies Act, 1956
(b) Sec. 128 (1) of Indian Companies Act, 2000
(c) Sec. 128 (1) of Indian Companies Act, 2013
Answer:
(b) Sec. 128 (1) of Indian Companies Act, 2000

Question 2.
Single entry system is an ………………….system of bookkeeping.
(a) incomplete
(b) inefficient
(c) adequate
Answer:
(a) incomplete

Question 3.
Single entry system maintains only ……………. and cash accounts
(a) Real
(b) Personal
(c) Nominal
Answer:
(b) Personal

Question 4.
Single entry system does maintain ………………… and ………………… accounts
(a) Assets & liabilities
(b) Debtors, Creditors
(c) Read, Nominal
Answer:
(c) Read, Nominal

Question 5.
Single entry system is not based on …………….. as pect concept
(a) Double Entry
(b) Dual
(c) Single
Answer:
(b) Dual

Question 6.
Incomplete records are those records which are not kept under……………………….
(a) Single Entry
(b) Double Entry
(c) None of the above
Answer:
(b) Double Entry

Question 7.
Credit purchases can be ascertained as a balancing figure in the ……………………
(a) Total Creditors A/c
(b) Debtors A/c
(c) Capital A/c
Answer:
(a) Total Creditors A/c

Question 8.
To know total purchases and total sales under single entry system, one has to depend on
(a) Trading A/c
(b) Copies of invoice and Vouchers
(c) Profit 8c Loss A/c
Answer:
(b) Copies of invoice and Vouchers

Question 9.
Under single entry system, the arithmetical accuracy of………………. cannot be checked.
(a) Trial Balance
(b) Trading A/c
(c) Balance Sheet
Answer:
(a) Trial Balance

Question 10.
If the adjusted closing capital is more than the opening capital, it is …………………
(a) Loss
(b) Profit
(c) Asset
Answer:
(b) Profit

Question 11.
If the adjusted closing capital is less than the opening capital, it is…………….
(a) Loss
(b) Profit
(c) Asset
Answer:
(a) Loss

Question 12.
Statement of Affairs resembles a…………………
(a) Balance Sheet
(b) Trading A/c
(c) Profit A/c Loss A/c
Answer:
(a) Balance Sheet

Question 13.
Profit under ……………… Entry system is only an estimate
(a) Double
(b) Single
(c) Income
Answer:
(b) Single

Question 14.
The total assets of a proprietor is Rs. 5,00,000. His liabilities are Rs.3,50,000 His capital in the business is
(a) Rs. 1,50,000
(b) Rs. 8,50,000
(c) Rs. 3,50,000
Hint:
Assets = Capital – Liabilities
5,00,000 = ? – 3,50,000
Capital = 5,00,000 – 3,50,000
= 1,50,000
Answer:
(a) Rs. 1,50,000

Question 15.
Statement of affairs method is also called
(a) Conversion method
(b) Net worth method
(c) Adjusted closing capital method
Answer:
(b) Net worth method

II Short Answer Questions

Question 16.
Define single Entry System
Answer:
According to Kohler, Single Entry System is a system of book keeping in which as a rule only records of cash and personal accounts are maintained. It is always incomplete double entry varying with circumstances.

Question 17.
What is conversion method?
Answer:
If it is desired to calculated profit by preparing trading and profit & loss Account under single entry system then it is called conversion method.

Question 18.
State the steps to be followed to prepare final accounts from incomplete records
Answer:
Following are the steps to be followed to prepare final accounts from incomplete records.
1. Opening statement of affairs is to be prepared, to ascertain the opening capital.

2. Missing figures must be found out with the available data.
This can be done by preparing memorandum accounts or by making necessary adjustments to the existing figures. For example,

• It may become necessary to prepare a cash book to find out the missing items such as cash purchases, cash sales, etc.
• By preparing total debtors account and total creditors account, credit sales and credit purchases can be ascertained respectively.
• Bills receivable account and bills payable account are to be prepared to find out the balances of bills receivable received and bills payable accepted respectively.

3. The final step is to prepare trading and profit and loss account and balance sheet.

III Exercises

Question 1.
Find out profit or loss from the following information

Solution:

Question 2.
Calculate the missing information from the following.

Solution:
Calculation of Closing Capital

Answer:
Capital at the end Rs. 16,000

Note:

Step1: Add Profit of Rs. 4,800 with opening capital Rs. 9,600 = Adjusted closing capital Rs. 14,400
Step2: Add Additional capital of Rs. 4,000 with Adjusted closing capital Rs. 14,400 = Rs. 18,400
Step3: Deduct drawing Rs.2,400 from the total amount arrived (Step 2) Rs. 18,400 = Clsoing Capital Rs. 16,000.

Question 3.
Mr. Suresh Strated business with Rs. 2,00,000 on 1st April 2003. His books are kept under single entry. On 31st March, 2004 his position was as under:

Ascertain the profit or loss made by Mr.Suresh for the year ended 31st March 2004.
Solution:
Statement of affairs of Mr. Suresh as on 31.03.2004

Question 4.
Prakash keeps his books by ‘Single Entry System His position on 01.04.2003 and
3 1.03.2004 was as follows.

He introduced an additional capital of Rs. 8,000 during the financial year. He withdraw Rs.= 14,000 for domestic purpose. Find out the profit for the year ended 3 1.03.2004.
Solution:
i) Calculation of opening capital:

Question 5.
Mrs. Vanitha keeps her books on singly entry basis. Find out the profit or loss made for the period ending 31. 03. 2004.

Mrs. Vanitha had withdrawn Rs. 10,000 for her personal use and had intrdocued fresh capital of Rs.4,000. A provision of 5% on debtors is necessary. Write off depreciation of plant at 10% and furniture at 15%.
Solution:

Question 6.
Ram and Laxman are equal partners in a business in which the books are kept by single entry. On 01.04.2004 their position was as under:

Solution:
Calculation of closing capital:

Question 7.
Find out total purchases and total sales from the following details by making necessary accounts:

Solution:

Total Purchases = Cash Purchases + Credit Purchases
= Rs. 12,000 + Rs. 24,500
= Rs. 36,500

Total Sales = Cash Sales + Credit Sales
= Rs. 24,000 + Rs. 2,96,000
= Rs. 3,20,000

Question 8.
Mr. James commenced business on 1.04.2004 with a Capital of Rs. 75,000. he immediately bought furniture for Rs. 12,000. During the year, he borrowed Rs. 15,000 from his wife as loan. He has withdrawn Rs. 21,600 for his family expenses. From the following particulars you are required to prepare Trading and Profit & Loss A/c and Balance Sheet as on 31.03.2005.

Provide 10% depreciationon furnitures
Solution:

Question 9.
Mrs. Malathy maintained her account books on single entry system. On 01.04.2003 her Capital was Rs. 2,50,000.
Additional Information:

Prepare trading and profit & loss account for the year ended 31.03.2004 and balance sheet
as on that date.
Solution:

Question 10.
From the following details, prepare Trading and Profit & Loss account for the period ended 31.03.2004 and a Balance sheet on that date.

Additional Information:

Solution:

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 8 Differentials and Partial Derivatives Ex 8.7 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 8 Differentials and Partial Derivatives Ex 8.7

Question 1.
If each of the following cases, determine whether the following function is homogeneous or not. If it is so, find the degree.
(i) f(x, y) = x²y + 6x³ + 7
(ii) h(x, y) = \(\frac { 6x^2y^3-πy^5+9x^4y }{ 2020x^2+2019y^2 }\)
(iii) g(x, y, z) = \(\frac { \sqrt{3x^2+5y^2+z^2} }{ 4x+7y }\)
(iv) U(x, y, z) = xy + sin(\(\frac { y^2-2z^2 }{ xy }\))
Solution:
(i) f(x, y) = x²y + 6x³ + 7
f(λx, λy) = λ³x²y + 6λ³x³ + 7
There is no common λ in this equation.
∴ It is not homogeneous

Thus f is homogeneous with degree 3.

Thus g is homogeneous with degree 0.

There is no common λ
∴ It is not homogeneous.

Question 2.
Prove that f(x, y) = x³ – 2x²y + 3xy² + y³ is homogeneous. What is the degree? Verify Euler’s Theorem for f.
Solution:
f(x, y) = x³ – 2x²y + 3xy² + y³
f(λx, λy) = λ³x³ -2λ²x²λy + 3λxλ²y² + λ³y³
= λ³ (x³ – 2x²y + 3xy² + y³)
f is a homogeneous function of degree 3
By Euler’s Theorem,

x \(\frac{\partial f}{\partial x}\) + y \(\frac{\partial f}{\partial y}\) = 3x³ – 4x²y + 3xy² – 2x²y + 6xy² + 3y³
= 3x³ – 6x²y + 9xy² + 3y³
= 3(x³ – 2x²y + 3xy² + y³)
x \(\frac{\partial f}{\partial x}\) + y \(\frac{\partial f}{\partial y}\) = 3 f
We verified the Euler’s Theorem.

Question 3.
Prove that g (x, y) = x log(y/x) is homogeneous What is the degree? Verify Eulers Theorem for g.
Solution:
g (x, y) = x log(y/x)
g (tx, ty) = tx log(\(\frac { ty }{ tx }\))
g is a homogeneous function of degree 1.
∴ By Euler’s Theorem,

Hence verified

Question 4.
If u(x, y) = \(\frac { x^2+y^2 }{ \sqrt{x+y} }\), prove that
x \(\frac{\partial u}{\partial x}\) + y\(\frac{\partial u}{\partial y}\) = \(\frac{3}{2}\)u.
Solution:

Question 5.
If v (x, y) = log(\(\frac{x^2+y^2}{x+y}\)) Prove that
x \(\frac{\partial v}{\partial x}\) + y\(\frac{\partial u}{\partial y}\) = 1.
Solution:

Hence Proved

Question 6.
If w(x, y, z) = log (\(\frac{5x^3y^4+7y^2xz^4-75y^3z^4}{x^2+y^2}\)), find x \(\frac{\partial w}{\partial x}\) + y\(\frac{\partial w}{\partial y}\) + z\(\frac{\partial w}{\partial z}\).
Solution:

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 8 Differentials and Partial Derivatives Ex 8.6 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 8 Differentials and Partial Derivatives Ex 8.6

Question 1.
If u (x, y) = x²y + 3xy⁴, x = e^t and y = sin t, find \(\frac { du }{ dt }\) and evaluate if at t = 0
Solution:
u (x, y) = x²y + 3xy⁴, x = e^t, y = sin t

∴ \(\frac { du }{ dt }\) = (2xy + 3y⁴) e^t + (x² + 12xy³) cos t
= (2e^t sin t + 3 sin⁴t) e^t + (e^2t + 12 e^t sin³t) cos t
\(\frac { du }{ dt }\) = e^t(2 e^t sin t + 3 sin⁴t + e^t cos t + 12 sin³t cos t)
at t = 0
\(\frac { du }{ dt }\) = e⁰(2 e⁰ sin 0 + 3 sin⁴ 0 + e⁰ cos 0 + 12 sin³0 cos 0)
= 1(0 + 0 + 1 + 0) (cos (0) = 1, sin(0) = 0, e⁰ = 1)
\(\frac { du }{ dt }\) = 1

Question 2.
Let u (x, y, z) = xy²z³ x = sin t, y = cos t, z = 1 + e^2t, Find \(\frac { du }{ dt }\).
Solution:
u (x, y, z) = xy²z³ x = sin t, y = cos t, z = 1 + e^2t

= y²z³ cos t – 2xyz³ sin t + 6 xy²z² e^2t
= cos²t (1 + e^2t)³ cost – 2 (sin t) cost (1 + e^2t)³ sin t + 6 (sin t) cos²t) (1 + e^2t)² e^2t
= (1 + e^2t)² [cos³t (1 + e^2t) – sin t sin2t (1 + e^2t) + 6 e^2t sin t cos²t]

Question 3.
If w (x, y, z) = x² + y² + z², x = e^t, y = e^t sin t and z = e^t cos t, find \(\frac { dw }{ dt }\)
Solution:
w (x, y, z) = x² + y² + z², x = e^t, y = e^t sin t and z = e^t cos t

\(\frac { dw }{ dt }\) = 2x e^t + 2y (e^t sin t + e^t cos t) + 2z (e^t cos t – e^t sin t)
= 2 e^2t + 2 (e^t sin t) (e^t sin t + e^t cos t) + 2 (e^t cos t) (e^t cos t – e^t sin t)
= 2 e^2t [1 + sin²t + sin t cos t + cos²t – sin t cos t]
= 2 e^2t (1 + sin²t + cos²t)
[∵ sin²t + cos²t = 1]
= 2 e²t (1 + 1) = 4 e^2t
\(\frac { dw }{ dt }\) = 4 e^2t

Question 4
Let U(x, y, z) = xyz, x = e^-t, y = e^-t cos t, z – sin t, t ∈ R, find \(\frac { dU }{ dt }\)
Solution:
U(x, y, z) = xyz, x = e^-t, y = e^-t cos t

\(\frac { dU }{ dt }\) = -(e^-t cos t sin t) e^-t + e^-t sin t [ e^-t (cos t – sin t )] + e^-2t cos t (cos t)
= -e^-2t cos t sin t – e^-2t sin t cos t – e^-2t sin²t + e^-2t cos²t
= -e^-2t (2 sin t cos t + sin²t – cos²t)
= -e^-2t [sin 2t – (cos²t – sin²t)]
= -e^-2t (sin 2t + cos 2t)

Question 5.
Let w(x, y) = 6x³ – 3xy + 2y², x = e^s, y = cos s, s ∈ R. Find \(\frac { dw }{ ds }\) and evaluate at s = 0.
Solution:
w(x, y) = 6x³ – 3xy + 2y²

Question 6.
Let z(x, y) = x tan^-1(xy), x = t², y = s e^t, s, t ∈ R. Find \(\frac{\partial z}{\partial s}\) and \(\frac{\partial z}{\partial t}\) at s = t = 1
Solution:

Question 7.
Let U (x, y) = e^x sin y where x = st², y = s²t, s, t ∈ R. Find \(\frac{\partial U}{\partial s}\), \(\frac{\partial U}{\partial t}\) and evaluate then s = t = 1. dt
Solution:
U (x, y) = e^x sin y, x = st², y = s²t

= e^st2 sin (s²t) t² + e^st2 cos(s²t) 2st
= e^st2 [t² sin (s²t) + 2st cos (s²t)]
= t e^x [t sin(s²t) + 2s cos (s²t)]
\(\frac{\partial U}{\partial t}\) = e^x sin y 2st + e^x cos y (s²)
= e^st2 sin(s²t) 2st + e^st2 cos(s²t) s²
= s e^st2 [2t sin (s²t) + s cos(s²t)]
At s = t = 1
\(\frac{\partial U}{\partial s}\) = e[sin(1) + 2 cos (1)]
= e[sin(1) + 2 cos (1)]
\(\frac{\partial U}{\partial t}\) = e[2 sin(1) + cos (1)]

Question 8.
Let z (x, y) = x³ – 3x²y³ where x = se^t, y = se^-t, s, t ∈ R. Find \(\frac{\partial z}{\partial s}\) and \(\frac{\partial z}{\partial t}\)
Solution:
z (x, y) = x³ – 3x²y³

(3x² – 6xy³) e^t – 9 (xy)² e^-t
[3 (s e^t)² – 6 (s e^t) (se^-t)³]e^t
-9 (s e^t s e^-t)² × e^-t
= (3 s² e^2t – 6 s⁴ e^-2t) e^t – 9 s⁴ e^-t
= 3s² [(e^2t – 2s² e^-2t) e^t -3 e^-t s²]
\(\frac{\partial z}{\partial s}\) = 3s² e^t (e^2t -2s² e^-2t – 3 e^-2t s²)
\(\frac{\partial z}{\partial t}\) = \(\frac{\partial z}{\partial x}\) \(\frac{\partial x}{\partial t}\) + \(\frac{\partial z}{\partial y}\) \(\frac{\partial y}{\partial t}\)
= (3x² – 6xy³) (s e^t)+ (-9x²y²) (- s e^-t)
= [3 (s e^t)² – 6 (s e^t) (s e^-t)³] s e^t + 9(se^t s e^-t)² s e^-t
= (3 s² e^2t – 6 s⁴ e^-2t) s e^t + 9 s⁵ e^-t
= 3 s³ e^3t – 6 s⁵ e^-t + 9 s⁵ e^-t
= 3 s³ e^3t + 3 s⁵ e^-t
\(\frac{\partial y}{\partial t}\) = 3 s³ (e^3t + s² e^-t)

Question 9.
W(x, y, z) = xy + yz + zx, x = u – v, y = uv, z = u + v, u, v ∈ R. Find \(\frac{\partial W}{\partial u}\), \(\frac{\partial W}{\partial v}\) evaluate then at (\(\frac{1}{2}\), 1)
Solution:

= (y + z) × 1 + (x + z) × v + (y + x) × 1
= uv + u + v + (u – v + u + v) v+ (uv + u – v)
= uv + u + v + uv + uv + uv + u – v
= 4 uv + 2u
\(\frac{\partial w}{\partial u}\) (\(\frac{1}{2}\), 1) = 4 × \(\frac{1}{2}\) × 1 + 2 × \(\frac{1}{2}\) = 2 + 1 = 3
\(\frac{\partial w}{\partial v}\) = \(\frac{\partial W}{\partial x}\) \(\frac{\partial x}{\partial v}\) + \(\frac{\partial W}{\partial y}\) \(\frac{\partial y}{\partial v}\) + \(\frac{\partial W}{\partial z}\) \(\frac{\partial z}{\partial v}\)
= (y + z) (-1) + (x + z) u + (y + x) × 1
= -y – z + xu + zu + y + x
= -u – v + (u – v) u + (u + v) u + u – v
= -u – v + u² – vu + u² + vu + u – v
= 2u² – 2v
\(\frac{\partial W}{\partial v}\) (\(\frac{1}{2}\), 1) = 2 × \(\frac{1}{4}\) – 2 × 1
= \(\frac{1}{2}\) – 2 = –\(\frac{3}{2}\)

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Bio Zoology Guide Pdf Chapter 10 Organisms and Population Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Bio Zoology Solutions Chapter 10 Organisms and Population

12th Bio Zoology Guide Organisms and Population Text Book Back Questions and Answers

Question 1.
All populations in a given physical area are defined as
(a) Biome
(b) Ecosystem
(c) Territory
(d) Biotic factors
Answer:
(a) Biome

Question 2.
Organisms which can survive a wide range of temperature are called
(a) Ectotherms
(b) Eurytherms
(c) Endotherms
(d) Stenotherms
Answer:
(b) Eurytherms

Question 3.
The interaction in nature, where one gets benefit on the expense of other is …………………
(a) Predation
(b) Mutualism
(c) Amensalism
(d) Commensalism
Answer:
(d) Commensalism

Question 4.
Predation and parasitism are which type of interactions?
(a) (+,+)
(b) (+, O)
(c) (-, -)
(d) (+, -)
Answer:
(d) (+, -)

Question 5.
Competition between species leads to
(a) Extinction
(b) Mutation
(c) Amensalism
(d) Symbiosis
Answer:
(a) Extinction

Question 6.
Which of the following is an r-species?
(a) Human
(b) Insects
(c) Rhinoceros
(d) Whale
Answer:
(b) Insects

Question 7.
Match the following and choose the correct combination from the options given below.

Dispersal
(a) A – 4, B – 5, C – 2, D – 3, E – 1
(b) A – 3, B – 1, C – 4, D – 2, E – 5
(c) A – 2, B -3, C – l,D – 5, E – 4
(d) A – 5, B – 4, C – 2, D – 3, E – 1
Answer:
(a) A- 4, B – 5, C – 2, D -3, E – 1

Question 8.
The figure given below is a diagrammatic representation of response of organisms to abiotic factors. What do A, B and C represent respectively.

Answer:
(a) Conformer, Regulator, Partial Regulator

Question 9.
The relationship between sucker fish and shark is ………………..
(a) Competition
(b) Commensalism
(c) Predation
(d) Parasitism
Answer:
(b) Commensalism

Question 10.
What type of human population is represented by the following age pyramid?
(a) Vanishing (a) Vanishing population
(b) Stable population
(c) Declining population
(d) Expanding population
Answer:
(b) Stable population

Question 11.
Which of the following is correct for r-selected species?
(a) large number of progeny with small size
(b) large number of progeny with large size
(c) small number of progeny with small size
(d) small number of progeny with large size
Answer:
(a) large number of progeny with small size

Question 12.
Animals that can move from fresh water to sea called as ………………..
(a) Stenothermal
(b) Eurythermal
(c) Catadromous
(d) Anadromous
Answer:
(c) Catadromous

Question 13.
Some organisms are able to maintain homeostasis by physical means …………………
(a) Conform
(b) Regulate
(c) Migrate
(d) Suspend
Answer:
(b) Regulate

Question 14.
What is a Habitat?
Answer:
A habitat can be considered as the ‘address’ of the organism. Organisms in a habitat interact with each other and can be part of trophic levels to form food chains and food webs.

Question 15.
Define ecological niche.
Answer:
Niche of an organism can be defined as the total position and function of an individual in its environment.

Question 16.
What is Acclimatisation?
Answer:
Animals are known to modify their response to environmental changes (stress) in reasonably short time spans. This is known as Acclimatization. This is observed when people who have moved from the plains to higher altitudes show enhanced RBC count within a few days of settling in their new habitat. This helps them cope with lower atmospheric oxygen and higher oxygen demand.

Question 17.
What is Pedogenesis?
Answer:
Pedogenesis is the process of formation of soil (embryonic soil) from the rock materials by weathering.

Question 18.
What is Zero Stress?
Answer:
Stress refers to any environmental factor causing a change in the biological system which is potentially injurious.

Question 19.
What is soil permeability?
Answer:
The characteristic of soil that determines the movement of water through pore spaces is known as soil permeability. Soil permeability is directly dependent on the pore size. Water holding capacity of the soil is inversely dependent on soil porosity.

Question 20.
Differentiate between Eurytherms and Stenotherms.
Answer:

Question 21.
Explain hibernation and aestivation with examples.
Answer:
In certain conditions, if the organisms is unable to migrate, it may avoid the stress by becoming inactive. This is seen commonly in bears going into hibernation during winter. Some snails and fish go into aestivation to avoid summer related problems like heat and desiccation.

Question 22.
Give the diagnostic characters features of a Biome.
Answer:

• Location, Geographical position (Latitude and Longitude)
• Climate and physiochemical environment
• Predominant plant and animal life
• Boundaries between biomes are not always sharply defined. Transition or transient zones are seen.

Question 23.
Classify the aquatic biomes of Earth.
Answer:

• Freshwater (Lakes, ponds and rivers)
• Brackish water (Estuaries / Wetlands)
• Marine (Coral reefs, pelagic zones and abyssal zones)

Question 24.
What are the ways by which organisms respond to abiotic factors?
Answer:
The ways by which organism respond to abiotic stress are Regulate, Conform, Migrate and Suspends, etc.

Question 25.
Classify the adaptive traits found in organisms.
Answer:
The adaptive traits may be structural adaptation, behavioural adaptation and physiological adaptation.

Question 26.
Differentiate Natality and Mortality?
Answer:

Question 27.
Differentiate J and S shaped curve.
Answer:

Question 28.
Give an account of population regulation.
Answer:
The inherent tendency of all animal populations is to increase in number. But it does not increase indefinitely. Once the carrying capacity of the environment is reached, population numbers remain static or fluctuate depending on environmental conditions. This is regulated by many factors which are

• Density independent – Extrinsic factors
• Density dependent – Intrinsic factors
  Extrinsic factors include availability of space, shelter, weather and food, etc. Intrinsic factors include competition, predation, emigration, immigration and diseases.

Question 29.
What is ecological density, crude density and population density?
Answer:

Question 30.
Give an account of the properties of soil.
Answer:

• Texture of soil – The texture of soil is determined by the size of the soil particles. The types of soil include sand, silt and clay on the basis of their size differences.
• Porosity – The space present between soil particles in a given volume of soil are called pore spaces. The percentage of soil volume occupied by pore space or by the interstitial spaces is cal Ted porosity of the soil.
• Permeability of soil – The characteristic of soil that determines the movement of water through pore spaces is known as soil permeability. Soil permeability is directly dependent on the pore size. Water holding capacity of the soil is inversely dependent on soil porosity.
• Soil Temperature – Soil gets its heat energy from solar radiation, decomposing organic matter, and heat from the interior of Earth. Soil temperature effects the germination of seeds, growth of roots and biological activity of soil-inhabiting micro-and macroorganisms.
• Soil water – In soil, water is not only important as a solvent and transporting agent, but also maintains soil texture, arrangement and compactness of soil particles, making soil habitable for plants and animals.

Question 31.
Differentiate between Tundra and Taiga Biomes.
Answer:

Question 32.
List the adaptations seen in terrestrial animals.
Answer:

• Earthworms, land Planarians secrete a mucus coating to maintain a moist situation for burrowing, coiling and respiration, etc.
• Arthropods have an external covering over the respiratory surfaces and well – developed tracheal systems.
• In vertebrate skin, there are many cellular layers besides the well-protected respiratory surfaces that help in preventing loss of water.
• Some animals obtain their water requirement from food as partial replacement of water lost through excretion.
• Birds make nests and breed before the rainy season as there is availability of abundant food. But during drought birds rarely reproduce.
• Camels are able to regulate water effectively for evaporative cooling through the-skin and respiratory system and excrete highly concentrated urine, and can also withstand
  dehydration up to 25% of their body weight.

Question 33.
Describe Population Age Distribution.
Answer:
The proportion of the age groups (pre-reproductive, reproductive and post reproductive) in a population is its age distribution attribute. This determines the reproductive status of the population at the given time and is an indicator of the future population size. Usually a rapidly growing population will have larger proportion of young individuals. A stable population will have an even distribution of various age classes. A declining population tends to have a larger proportion of older individuals.

Question 34.
Describe Growth Models/Curves.
Answer:

Populations show characteristic growth patterns or forms. These patterns can be plotted and termed as J-shaped growth form and S-shaped growth form (Sigmoid form). Their growth is represented by S shaped growth curve.
J shaped growth form: When a population increases rapidly in an exponential fashion and then stops abruptly due to environmental resistance or due to sudden appearance of a limiting factor, they are said to exhibit J-shaped growth form. Many insects show explosive increase in number during the rainy season followed by their disappearance at the end of the season. S-Shaped growth form (sigmoid growth) Some populations, as in a population of small mammals, increase slowly at first then more rapidly and gradually slow down as environmental resistance increases whereby equilibrium is reached and maintained. Their growth is represented by S shaped growth curve.

12th Bio Zoology Guide Organisms and Population Additional Important Questions and Answers

12th Bio Zoology Guide Organisms and Population One Mark Questions and Answers

Question 1.
The study dealing with animal behaviour is called as
(a) Euthenics
(b) Ethology
(c) Ecology
(d) Pedogenesis
Answer:
(b) Ethology

Question 2 .
Identify the proper sequence in increasing order of population
(a) Species → Population → Community → biome
(b) Population → Community → Species → biome
(c) Biome → Species → Community → Population ‘
(d) Community → Population → Biome → Species
Answer:
(a) Species → Population → Community → biome

Question 3.
Functional status of an organism in its community is ………………….
(a) Biome
(b) Niche
(c) Species
(d) Population
Answer:
(A) Niche

Question 4.
Pick out the eurythermal organism
(a) Fish
(b) Frog
(c) Tiger
(d) Lizards
Answer:
(c) Tiger

Question 5.
Locomotary speed of an organism changes due to light. This phenomenon is referred as ……………….
(a) Photonasty
(b) Photokinesis
(c) Phototropism
(d) Phototaxis
Answer:
(b) Photokinesis

Question 6.
Identify the incorrect statement
(a) Water is a universal solvent
(b) Water has less surface tension
(c) Water is heavier than air
(d) When freezes water contracts
Answer:
(b) Water has less surface tension

Question 7.
The soil zone is known as …………………..
(a) Pedosphere
(b) Atmosphere
(c) Hydrosphere
(d) Stratosphere
Answer:
(a) Pedosphere

Question 8.
Assertion (A): Snake is a stenotherm.
Reason (R): Organism can tolerate narrow temperature fluctuations.
(a) Both A and R are correct R explain A
(b) A is correct R is incorrect
(c) R does not explain A
(d) Both A and R are incorrect
Answer:
(a) Both A and R are correct R explain A

Question 9.
Assertion (A): Diapause is carried out to overcome abiotic stress.
Reason (R): Animals become inactive during winter.
(a) Both A and R are correct R explain A
(b) A is correct R is incorrect
(c) R does not explain A
(d) Both A and R are incorrect
Answer:
(b) A is correct R is incorrect

Question 10.
Assertion (A): Movement of organism from one place to another and back is called migration.
Reason (R): Eel is an example for aradromous migration.
(a) Both A and R are correct R explain A ‘
(b) A is correct R is incorrect
(c) R does not explain A
(d) Both A and R are incorrect
Answer:
(a) Both A and R are correct R explain A

Question 11.
Which is not a feature of Tundra?
(a) Large population oscillation
(b) Short season of growth and reproduction
(c) Low biotic diversity
(d) Extremely hot climate
Answer:
(d) Extremely hot climate

Question 12.
Pick out the correct statement regarding K-selected species
(a) Produce many offsprings
(b) Only few reach adulthood
(c) Unstable environment
(d) Long life expectancy
Answer:
(d) Long life expectancy

Question 13.
Maximum reproductive capacity of an organism under favourable condition is referred as ………………..
(a) Carrying capacity
(b) Biotic potential
(c) Natality
(d) Fecundity
Answer:
(b) Biotic potential

Question 14.
During breeding season, Salmon migrates from sea to fresh water. This is an example for……………
Answer:
Anadromous migration.

Question 15.
Exponential growth shows ……………. growth patterns.
Answer:
J-shaped

Question 16.
Interaction between Ascaris in human gut is an example for……………..
Answer:
Parasitisim

Question 17.
If both the species of an interaction is benefitted then it is said to be………………….
Answer:
Mutualism

Question 18.
Match the following

(a) a – ii, b – i, c – iv, d – iii
(b) a – iii, b – ii, c – i, d – iv
(c) a – iv, b – iii, c – ii, d – i
(d) a – i, b -iv, c – iii, d – ii
Answer:
(a) a – ii, b – i, c – iv, d – iii

Question 19.
As altitude increases ……………….
(a) O₂ density increases
(b) Precipitation decreases
(c) Temperature increases
(d) Snowing decreases
Answer:
(b) Precipitation decreases

12th Bio Zoology Guide Organisms and Population Two Marks Questions and Answers

Question 1.
What is ecosphere?
Answer:
The largest and most nearly self-sufficient biological system is often designated as the Ecosphere, which includes all the living organisms of the Earth, interacting with the physical ~ environment to regulate their distribution, abundance, production and evolution.

Question 2.
List out the adaptation of fish to survive in aquatic environment.
Answer:
Fishes possess fins for locomotion, streamlined body (aerodynamic) sensory lateral line system, gills for respiratory purpose and air sacs for floatation.

Question 3.
Define niche.
Answer:
Niche of an organism can be defined as the total position and function of an individual in its environment.

Question 4.
Name few abiotic factors that influence organisms in an environment.
Answer:
Temperature, light, water, soil, humidity and altitude, etc.

Question 5.
State Allen’s rule and Bergmann’s rule.
Answer:
Allen’s rule: Warm blooded animals living in cold climates have shorter limbs, ears and other appendages than the same species in warm climates.
Bergmann’s rule: Birds and mammals have larger body size in cold regions than warmer regions.

Question 6.
What does Jordon’s rule state?
Answer:
In some aquatic environments, an inverse relationship between water temperature and fish meristic characters is observed – lower the temperature, more the vertebrae.

Question 7.
State Van’t Hoff’s rule.
Answer:
Van’t Hoff’s rule states that with the increase of every 10°C, the rate of metabolic activity is doubled or the reaction rate is halved with the decrease of 10°C.

Question 8.
What is Q₁₀ value? How it is calculated?
Answer:
The effect of temperature on the rate of reaction is expressed in terms of temperature coefficient or Q₁₀ value. The Q₁₀ values are estimated taking the ratio between the rate of reaction at X°C and rate of reaction at (X-10°C).

Question 9.
Differentiate between Eurytherms and Stenotherm
Answer:

Question 10.
Snakes are stenotherms. Why?
Answer:
Snakes are stenotherms since they can tolerae only a narrow range of temperature fluctuation.

Question 11.
Define phototaxis.
Answer:
The movement of organism in response to light, either towards the source of light as in Moths (positive phototaxis) or away from light (Earthworm (negative phototaxis).

Question 12.
What is photokinesis?
Answer:
A change in the speed of locomotion (or frequency of turning) in a motile organism or cell which is made in response to a change in light intensity is called photokinesis. It involves undirected random movement in response to light.

Question 13.
What is pedosphere and soil profile?
Answer:
Pedosphere: The outer soil zone of the Earth.
Soil profile: Soil is formed by many horizontal layers called soil profile.

Question 14.
Point out the major functions of soil.
Soil has four major functions

• medium for plant grbwth .
• means for water storage and purification
• modifier of Earth’s atmosphere
• habitat for many organisms, which in turn modify the soil

Question 15.
Define humidity and mention its types.
Answer:
Moisture in the form of invisible vapor in the atmosphere is called humidity, which is generally expressed in terms of absolute humidity, relative humidity or specific humidity.

Question 16.
What is a Biome?
Answer:
Biomes are large regions of Earth that have similar or common vegetation and climatic conditions. They play a crucial role in sustaining life on Earth. They are defined by their soil,climate, flora and fauna. Biomes have distinct biological communities that have been formed in response to a shared physio-chemical climate.

Question 17.
Enumerate the characters of a Biome.

• Location, Geographical position (Latitude and Longitude)
• Climate and physiochemical environment
• Predominant plant and animal life ‘
• Boundaries between biomes are not always sharply defined. Transition or transient zones are seen.

Question 18.
Which is the largest biome on Earth? Classify it.
Answer:
Aquatic biome is the largest biome occupying 71% of biosphere.
The aquatic biomes on Earth are:
a) Fresh water biome (Lakes and Ponds)
b) Brackish water biome (Estuaries / Wetlands)
c) Marine biome (Coral reefs and abyssal zones)

Question 19.
Define alpine zone.
The alpine zone between timber line and snow zone includes in the descending order, a sub¬snow zone immediately below the snow zone, a meadow zone in the centre and a shrub zone which gradually merges into the timber zone.

Question 20.
What is a forest? Name the major forest biomes.
Answer:
Forest is a broad term used to describe areas where there are a large number of trees. The major forest biomes are the Tropical forests and the Temperate forest.

Question 21.
What are the types of tropical forest?
Answer:
(a) Evergreen rain forest
(b) Seasonal rain forest
(c) Semi evergreen forest
(d) Dry deciduous forest

Question 22.
How the cold deserts are characterized? Give an example.
Answer:
Cold deserts are characterized by cold winters with snowfall and high overall rainfall throughout the winter and occasionally over the summer.
E.g.: Ladakh region in India.

Question 23.
Fishes are said to be conformers Justify.
Answer:
In fishes, the osmotic concentration of the body fluids changes with that of surrounding water osmotic concentration. Hence they are called conformers.

Question 24.
When and why do snails go into aestivation?
Answer:
Snails undergo aestivation during summer to avoid heat and overcome dessication.

Question 25.
How do animals like fishes and bears avoid unfavourable climatic conditions?
Answer:
Fishes undergo aestivation to avoid summer related problems.
Bears undergo hibernation to avoid winter related problems.

Question 26.
What are cryptic animals? How cryptic adaptation helps them?
Answer:
Cryptic animals are those which camouflage perfectly with their environment and are almost impossible to detect. Certain reptiles and insects such as chameleons and stick insects show this type of adaptation, which helps in prey capture or to evade from predators.

Question 27.
Explain any two behavioural adaptations?
Answer:
The two most characteristic forms of behavioral adaptations are migration and courtship. Migration allows the animals to find better resources or evade threat. Courtship is a set of bhavioral patterns to find a mate to reproduce.

Question 28.
Define population.
Answer:
Population is defined as any group of organisms of the same species which can interbreed among themselves, and occupy a particular space and function as part of a biotic community.

Question 29.
What are the attributes of population?
Population density, Natality, Mortality, Age distribution, dispersion . (immigration and emigration)

Question 30.
Camels are well adapted to xeric conditions, how?
Answer:
Camels are able to regulate water effectively for evaporative cooling through the skin and respiratory system and excrete highly concentrated urine, and can also withstand dehydration up to 25% of their body weight.

Question 31.
How natality and mortality can be calculated?
Answer:

Question 32.
Define biotic potential.
Answer:
It is the maximum reproductive capacity of an organism under optimum environmental conditions.

Question 33.
Which type of species interaction is noticed between a) Cat and Rat (b) Crocodile and birds
Answer:
(a) Amensalism
(b) Mutualism

Question 34.
Define Commensalism.
Answer:
Commensalism is species interaction in which one species (the commensal) is benefitted whereas the host is neither benefitted nor affected.
Eg: Sucker fish on Shark.

12th Bio Zoology Guide Organisms and Population Three Marks Questions and Answers

Question 35.
Define the terms (a) guilds (b) ecological equivalents
Answer:
Groups of species with comparable role and niche dimensions within a community are termed ‘guilds’. Species that occupy the same niche in different geographical regions, are termed ‘ecological equivalents’.

Question 36.
Define temperature. How it impacts the life of an organism?
Answer:
Temperature or degree of hotness and coldness is an essential and variable factor in any environment. It influences all forms of life by affecting many vital activities of organisms like metabolism, behaviour, reproduction, development and even death in the Biosphere.

Question 37.
Light is essential for life. Why?
Answer:
Light influences growth, pigmentation, migration and reproduction. The intensity and frequency of light influences metabolic activity, induce gene mutations (UV, X-rays). Light is essential for vision. This is proved by the poorly developed or absence of eyes in cave dwelling organisms. Diapause is also influenced by light in animals. Gonads of birds become more active with increasing light in summer. Light influences the locomotion and movement of lower animals.

Question 38.
What is Acclimatization? Explain with example.
Answer:
Animals are known to modify their response to environmental changes (stress) in reasonably short time spans. This is known as Acclimatization. This is observed when people who have moved from the plains to higher altitudes show enhanced RBC count within a few days of settling in their new habitat. This helps them cope with lower atmospheric oxygen and higher oxygen demand.

Question 39.
Enlist the characteristics of Tundra.
Answer:

• Extremely cold climate
• Low biotic diversity
• Simple vegetation structure
• Limitation of drainage
• Short season of growth and reproduction
• Energy and nutrients in the form of dead organic material
• Large population oscillations

Question 40.
Name the major biomes of the Earth.
Answer:
Tundra biome, Taiga biome, Grassland biome, Alpine biome, Forest biome and Desert biome.

Question 41.
Why do organisms migrate? Give example.
Answer:
Organisms tend to move away temporarily from a stressful habitat to a new, hospitable area and return when the stressful period is over. Birds migrate from Siberia to Vedanthangal in Tamilnadu to escape from the severe winter periods.

Question 42.
Define (a) Diapause (b) Ethology
Answer:
Diapause: Some lower animals suspend a certain phase of their life cycle, which is referred to as diapause.
Ethology: The study of animal behaviour, under natural conditions.

Question 43.
Comment on the J-shaped growth form.
Answer:
When a population increases rapidly in an exponential fashion and then stops abruptly due to environmental resistance or due to sudden appearance of a limiting factor, they are said to exhibit J-shaped growth form. Many insects show explosive increase in number during the rainy season followed by their disappearance at the end of the season.

Question 44.
Explain sigmoid growth.
Answer:
Some populations, as in a population of small mammals, increase slowly at first then more rapidly and gradually slow down as environmental resistance increases whereby equilibrium is reached and maintained. Their growth is represented by S shaped growth curve.

12th Bio Zoology Guide Organisms and Population Five Marks Questions and Answers

Question 45.
Enumerate the properties of water.
Answer:

• Water is one of the main agents in Pedogenesis (soil formation).
• It is the medium for several different ecosystems.
• It is present as moisture in the atmosphere and the outer layers of the lithosphere and is uneven in distribution on the Earth.
• Water is heavier than air and imparts greater buoyancy to the aquatic medium. This enables organism to float at variable levels.
• Water has high heat capacity and latent heat, due to which it can withhold large amounts of heat. Thus, oceans and lakes tend to maintain a relatively constant temperature, and the biosphere is relatively thermostable.
• Water is physically unique because it is less dense as a solid (ice) than as a liquid.
• When water freezes (0°C), it contracts. The maximum density of liquid water occurs at 4°C. Below that, it expands markedly. This enables ice to float on the top of water bodies. Hence, only the surface of water bodies will freeze, while below the surface, water will be in liquid form, sustaining life.

Question 46.
Give an account of grass land biome.
Answer:

• Grasslands occur in temperate and in the tropical regions.
• They have hot summers, cold winters, and irregular rainfall.
• Often they are characterized by high winds.
• The low irregular rainfall is the factor which makes the difference between a temperate deciduous forest and a temperate grassland.
• Herbivores like antelope, bison, wild horse, jack rabbit, ground squirrel and prairie dogs are abundant.
• Predators include coyotes, foxes, hawks and snakes.
• In India, fauna of grasslands includes Elephant, Gaur, Rhino and Antelope.
• Flora of grasslands include purple needle grass, wild oats, foxtail, ryegrass and buffalo grass.

Question 47.
Write in detail about Temperate forest and its types.
Answer:

1. These forests occur in eastern North America, northeastern Asia and western and central Europe.
2. Have well-defined seasons with a distinct winter. Moderate climate and a growing season of 140-200 days during 4-6 frost-free months distinguish temperate forests.
3. Annual temperature varies from -30° C to 30° C.
4. Precipitation (750-1500 mm) is distributed evenly throughout the year.
5. Soil is fertile, enriched with decaying litter.
6. Canopy is moderately dense and allows light to penetrate, resulting in well-developed and richly diversified understorey vegetation and stratification of animals.
7. Flora is characterized by 3-4 tree species per km2. Trees have broad leaves that are lost annually such as oak, hickory, beech, hemlock, maple, basswood, cottonwood, elm, willow, and spring-flowering herbs.
8. Fauna consists of squirrels, rabbits, skunks, birds, deer, mountain lion, bobcat, timber wolf, ~ fox, and black bear. Based on seasonal distribution of rainfall, the types of temperate forests are:

• Moist conifer and evergreen broad-leaved forests: wet winters and dry summers.
• Dry conifer forests: dominate higher elevation zones; low precipitation.
• Mediterranean forests: precipitation is concentrated in winter (<1000 mm /year).
• Temperate coniferous forests: mild winters, high annual precipitation (> 2000 mm /year).
• Temperate broad-leaved rainforests: mild, frost-free winters, high precipitation (> 1500 mm/year), evenly distributed throughout the year.

Question 48.
Point out the adaptive traits of aquatic animals.
Answer:

• The pectoral fins and dorsal fins act as stabilizers or balancers and the caudal fin helps in changing the direction as a rudder.
• Arrangement of body muscles in the form of bundles (myotomes) help in locomotion.
• Stream lined structure helps in the swift movement of the animals in water.
• Respiration by gills making use of gases dissolved in water.
• Presence of air-bladders filled with air for buoyancy.
• Presence of lateral-line system. They function as rheoreceptors which is helpful in echolocating objects in water.
• Integuments rich in mucous glands are protected by scales.
• Maintain water and ionic balance in its body with excretory structures.

Question 49.
Differentiate between r-selected species and k-selected species.
Answer:

Question 50
Describe in detail on population interaction.
Answer:
Organisms belonging to different populations interact for food, shelter, mating or for other

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 8 Differentials and Partial Derivatives Ex 8.5 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 8 Differentials and Partial Derivatives Ex 8.5

Question 1.
If w(x, y) = x³ – 3xy + 2y², x, y ∈ R, find the linear approximation for w at (1, -1) linear approximation for w at (1, -1)
Solution:
w(x, y) = x³ – 3xy + 2y², x, y ∈ R, (1, -1)

∴ L(x, y, z) = 6 + 6(x – 1) -7(y + 1)
L (x, y, z) = 6x – 7y – 7

Question 2.
Let z (x, y) = x² y + 3xy⁴, x, y ∈ R. Find the linear approximation for z at (2, -1).
Solution:

L (x, y, z) = 2 – (x – 2) – 20 (y + 1)
= 2 – x + 2 – 20y – 20
= -x – 20y – 16
= -(x + 20y + 16)

Question 3.
If v (x, y) = x² – xy + \(\frac { 1 }{ 4 }\)y² + 7, x, y ∈ R find the differential dv.
Solution:
First let us find v_x, v_y
Now, v_x = \(\frac{\partial v}{\partial x}\) = 2x – y
v_y = \(\frac{\partial v}{\partial y}\) = -x + \(\frac { 1 }{ 2 }\) y
The differential is
dv = v_x dx + v_y dy
dv = (2x – y) dx + (\(\frac { 1 }{ 2 }\) y – x) dy

Question 4.
Let W (x, y, z) = x² – xy + 3sinz, x, y, z ∈ R. Find the linear approximation at (2, -1, 0).
Solution:
W (x, y, z) = x² – xy + 3sinz, x, y, z ∈ R

L (x, y, z) = 6 + 5 (x – 2)- 2 (y + 1) + 3 (z)
= 6 + 5x – 10 – 2y – 2 + 3z
= 5x – 2y + 3z – 6

Question 5.
Let V (x, y, z) = xy + yz + zx, x, y, z ∈ R. Find the differential dV.
Solution:
V(x, y, z) = xy + yz + zx
V_x = y + z
V_y = x + z
V_z = y + x
The differential is dV = (y + z) dx + (x + z) dy + (y + x) dz

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 8 Differentials and Partial Derivatives Ex 8.3 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 8 Differentials and Partial Derivatives Ex 8.3

Question 1.
Evaluate \(\lim _{(x, y) \rightarrow(1,2)}\) g(x, y), if the limit exists where g(x, y) = \(\frac { 3x^2-xy }{ x^2+y^2+3 }\)
Solution:
\(\lim _{(x, y) \rightarrow(1,2)}\) g(x, y) = \(\lim _{(x, y) \rightarrow(1,2)}\) \(\frac { 3x^2-xy }{ x^2+y^2+3 }\)
= \(\frac { 3(1)-1×2 }{ 1+4+3 }\)
= \(\frac { 1 }{ 8 }\)

Question 2.
Evaluate \(\lim _{(x, y) \rightarrow(0,0)}\) cos(\(\frac { x^3+y^2 }{ x+y+2 }\)), if the limit exists.
Solution:
\(\lim _{(x, y) \rightarrow(0,0)}\) cos(\(\frac { x^3+y^2 }{ x+y+2 }\))
= cos (\(\frac { 0+0 }{ 0+0+2 }\))
= cos 0
= \(\lim _{(x, y) \rightarrow(0,0)}\) cos(\(\frac { x^3+y^2 }{ x+y+2 }\)) = 1

Question 3.
Let f(x, y) \(\frac { y^2-xy }{ √x-√y }\) for (x, y) ≠ (0, 0) show that \(\lim _{(x, y) \rightarrow(0,0)}\) f(x, y) = 0
Solution:
f(x, y) = \(\frac { y^2-xy }{ √x-√y }\)

Question 4.
Evaluate \(\lim _{(x, y) \rightarrow(0,0)}\) cos(\(\frac { e^xsin y }{ y }\)), if the limit exists.
Solution:

Question 5.
Let g(x, y) = \(\frac { x^2y }{ x^4+y^2 }\) for (x, y) ≠ (0, 0) and f(0, 0) = 0
(i) Show that \(\lim _{(x, y) \rightarrow(0,0)}\) g(x, y) = 0 along every line y = mx, m ∈ R
(ii) Show that \(\lim _{(x, y) \rightarrow(0,0)}\) g(x, y) = \(\frac { k }{ 1+k^2 }\) along every parabola y = kx², k ∈ R\{0}
Solution:
(i) Let g(x, y) = \(\frac { x^2y }{ x^4+y^2 }\) for (x, y) ≠ (0, 0) and f(0, 0) = 0
Let y = mx

= 0
Hence proved

(ii) for parabola y = kx²

Hence proved

Question 6.
Show that f (x, y) = \(\frac { x^2-y^2 }{ y^+1 }\) is continuous at every (x, y) ∈ R²
Solution:
Let (a, b) ∈ R² be an arbitrary point.
We shall investigate the continuity of f at (a,b).
That is, we shall check if all the three conditions for continuity hold for f at (a, b)
To check first condition, note that
f(a, b) = \(\frac { a^2-b^2 }{ b^2+1 }\) is defined
Next we want t0 find lf \(\lim _{(x, y) \rightarrow(a,b)}\) f(x, y) exist or not
so we calculate \(\lim _{(x, y) \rightarrow(a,b)}\) x² – y² = a² – b² and
\(\lim _{(x, y) \rightarrow(a,b)}\) y² + 1 = b² + 1
By the properties of limit we see that
\(\lim _{(x, y) \rightarrow(a,b)}\) f(x, y) = \(\frac { x^2-y^2 }{ y^2+1 }\) = \(\frac { a^2-b^2 }{ b^2+1 }\) = f(a, b) = L exists
Now, we note that \(\lim _{(x, y) \rightarrow(a,b)}\) f(x, y) = L = f(a, b).
Hence f satisfies all the there conditions for continuity of f at (a, b).
Since (a, b) is an arbitrary point in R², we conclude that f is continuous at every point of R².

Question 7.
Let g (x, y) = \(\frac { e^ysinx }{ x }\) for x ≠ 0 and g(0, 0) = 1 shoe that g is continuous at (0, 0)
Solution:
g(x, y) = \(\frac { e^ysinx }{ x }\)
To check first condition,note that
\(\lim _{(x, y) \rightarrow(0,0)}\) g(x, y) = \(\lim _{(x, y) \rightarrow(0,0)}\) \(\frac { e^ysinx }{ x }\) = 1 is defined
Next \(\lim _{(x, y) \rightarrow(0,0)}\) g(x, y) = \(\frac { e^ysinx }{ x }\) = 1 = L Exist
Now we note \(\lim _{(x, y) \rightarrow(0,0)}\) g(x, y) = L = g(0, 0)
Hence g satisfies all the three conditions for; continuity of g at (0, 0).
We conclude that g is continuous at (0, 0).

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 8 Differentials and Partial Derivatives Ex 8.4 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 8 Differentials and Partial Derivatives Ex 8.4

Question 1.
Find the partial dervatives of the following functions at indicated points.
(i) f(x, y) = 3x² – 2xy + y² + 5x + 2, (2, -5)
(ii) g(x, y) = 3x² + y² + 5x + 2, (2, -5)
(iii) h(x, y, z) = x sin (xy) + z² x, (2, π/4, 1)
(iv) G(x, y) = e^{x + 3y} log (x² + y²), (-1, 1)
Solution:
(i) f(x, y) = 3x² – 2xy + y² + 5x + 2, (2, -5)

(ii) g(x, y) = 3x² + y² + 5x + 2, (2, -5)

(iii) h(x, y, z) = x sin (xy) + z² x, (2, π/4, 1)

(iv) G(x, y) = e^{x + 3y} log (x² + y²), (-1, 1)

Question 2.
For each of the following functions find the f_x, and f_y and show that f_xy = f_yx
(i) f(x, y) = \(\frac { 3x }{ y+sinx }\)
(ii) f(x, y) = tan^-1(x/y)
(iii) f(x, y) = cos (x² – 3xy)
Solution:
(i) f(x, y) = \(\frac { 3x }{ y+sinx }\)

(ii) f(x, y) = tan^-1(x/y)

(iii) f(x, y) = cos (x² – 3xy)
\(\frac{\partial f}{\partial x}\) = -sin (x² – 3xy) × (2x – 3y)
\(\frac{\partial^2 f}{\partial y \partial x}\) = – sin (x² – 3xy) x – 3 + (2x – 3y) × [-cos (x² – 3xy)] × – 3x
= 3 sin (x² – 3xy) + 3x (2x – 3y) cos (x² – 3xy)
\(\frac{\partial f}{\partial x}\) = – sin (x² – 3xy) × -3x
= 3x sin (x² – 3xy)
\(\frac{\partial^2 f}{\partial x \partial y}\) = 3sin (x² – 3xy) + 3x cos (x² – 3xy) (2x – 3y)
∴ \(\frac{\partial^2 f}{\partial y \partial x}\) = \(\frac{\partial^2 f}{\partial x \partial y}\)

Question 3.
If U (x, y, z) = \(\frac { x^2+y^2 }{ xy }\) + 3z²y, find \(\frac{\partial U}{\partial x}\), \(\frac{\partial U}{\partial y}\) and \(\frac{\partial U}{\partial z}\)
Solution:

Question 4.
If U(x, y, z) = log (x³ + y³ + z³) find
\(\frac{\partial U}{\partial x}\) + \(\frac{\partial U}{\partial y}\) + \(\frac{\partial U}{\partial z}\)
Solution:

Question 5.
For each of the following functions find the g_xy, g_xx, g_yy and g_yx
(i) g(x, y) = x e^y + 3x²y
(ii) g(x, y) = log (5x + 3y)
(iii) g(x, y) = x² + 3xy – 7y + cos(5x)
Solution:
(i) g(x, y) = x e^y + 3x²y

(ii) g(x, y) = log (5x + 3y)

(iii) g(x, y) = x² + 3xy – 7y + cos(5x)
g_x = 2x+ 3y – sin 5x × 5
g_x = 2x+ 3y – 5 sin 5x
g_xx = 2 – 25 cos 5x
g_yx = 3
g_y = 3x – 7
g_yy = 0
g_xy = 3

Question 6.
Let w(x, y, z) = \(\frac { 1 }{ \sqrt{x^2+y^2+z^2} }\) = 1, (x, y, z) ≠ (0, 0, 0), show that \(\frac{\partial^ w}{\partial x^2}\) + \(\frac{\partial^2 w}{\partial y^2}\) + \(\frac{\partial^2 w}{\partial z^2}\) = 0
Solution:

Question 7.
If V (x, y) = e^x ( x cosy – y siny), then Prove that \(\frac{\partial^2 V}{\partial x^2}\) + \(\frac{\partial^2 V}{\partial y^2}\) = 0
Solution:

Question 8.
If w (x, y) = xy + sin (xy), then Prove that \(\frac{\partial^2 w}{\partial y \partial x}\) = \(\frac{\partial^2 w}{\partial x \partial y}\)
Solution:
Now, w (x, y) = xy + sin (xy)

Question 9.
If v(x, y, z) = x³ + y³ + z³ +3xyz, Show that \(\frac{\partial^2 v}{\partial y \partial z}\) = \(\frac{\partial^2 v}{\partial z \partial y}\)
Solution:
v (x, y, z) = x³ + y³ + z³ + 3xyz

Question 10.
A from produces two types of calculates each week, x number of type A and y number of type B. The weekly revenue and cost functions = (in rupees) are
R (x, y) = 80x + 90y + 0.04xy – 0.05x² – 0.05y² and C (x, y) = 8x + 6y + 2000 respectively.
(i) Find the Profit function P(x, y).
(ii) Find \(\frac{\partial P}{\partial x}\) (1200, 1800) and \(\frac{\partial P}{\partial y}\) (1200, 1800) and interpret these results.
Solution:
(i) Profit = Revenue – Cost
= (80x + 90y + 0.04 xy – 0.05 x² – 0.05y²) – (8x + 6y + 2000)
= 80x + 90y + 0.04 xy – 0.05 x² – 0.05y² – 8x – 6y – 2000
P(x, y) = 72x + 84y + 0.04 xy – 0.05 x² – 0.05y² – 2000

(ii) \(\frac{\partial P}{\partial x}\) = 72 + 0.04y – 0.1 x
\(\frac{\partial P}{\partial x}\) (1200, 1800) = 72 + 0.04 × 1800 – 0.1 × 1200
= 72 + 72 – 120
= 144 – 120
= 24
\(\frac{\partial P}{\partial y}\) = 84 + 0.04x – 0.1 y
\(\frac{\partial P}{\partial y}\) (1200, 1800) = 84 + 0.04 × 1200 – 0.1 × 1800
= 84 + 48 – 180
= 132 – 180
= -48