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NCERT | CLASS 11 Recording of Transactions – I | IMPORTANT QUESTIONS

Question 1 : What is the purpose of posting J.F numbers that are entered in the journal at the time entries are posted to the accounts?

ANSWER:

J.F. number is the number that is entered in the ledger at the time of posting entries into their respective accounts. It helps in determining whether all transactions are properly posted in their accounts. It is recorded at the time of posting and not at the time of recording the transactions.

The purpose of entering the J.F. number in the ledger is because of the below-given benefits.

J.F. number helps in locating the entries of accounts in the journal book. In other words, J.F number helps to locate the position of the related journal entry and subsidiary book in the journal book.
J.F. number in accounts ensures that recording in the books of original entry has been posted or not.

Question 2 : Describe how debits and credits are used to analyse transactions.

ANSWER:

Debit originated from the Italian word debito, which in turn is derived from the Latin word debeo, which means ‘owed to proprietor’ and credit comes from the Italian word credito, which is derived from the Latin word credo, which means belief, i.e., ‘owed by proprietor’.

According to the dual aspect concept, all the business transactions that are recorded in the books of accounts, have two aspects- debit and credit. The dual aspect can be better understood with the help of an example; bought goods worth Rs 500 on cash. This transaction affects two accounts with the same amount simultaneously. As goods are brought in exchange of cash, so the cash balances in the business reduce by Rs 500, i.e. why the cash account is credited. Simultaneously, the amount of goods increases by Rs 500, so the purchases account will be debited. Debit and credit depend on the nature of accounts involved; such as assets, expenses, income, liabilities, and capital. There are five types of Accounts.

Assets– These include all properties or legal rights owned by a firm for its operations, such as cash in hand, plant and machinery, bank, land, building, etc. All assets have debit balance. If assets increase, they are debited and if assets decrease, they are credited.

For example, furniture purchased and payment made by cheque. The journal entry is:

Furniture A/c	Dr.
To Bank A/c

Here, furniture and bank balance, both are assets to the firm. As furniture is purchased, so furniture account will increase and will be debited. On the other hand, payment of furniture is being made by cheque that reduces the bank balance of the business, so bank account will be credited.

Expense− It is made to run business smoothly and to carry day to day business activites.

All expenses have a debit balance. If an expense is incurred, it must be debited.

For example, rent paid. The journal entry is:

Rent A/c	Dr.
To Cash A/c

Here, rent is an expense. All expenses have a debit balance. Hence, rent is debited. On the other hand, as rent is paid in cash that reduces the cash balances, so the cash account is credited.

Liability− Liability is an obligation of business. Increase in liability is credited and decrease in liability is debited.

For example, a loan taken from the bank. The journal entry is:

Bank A/c	Dr.
To Bank Loan A/c

Here, a loan from the bank is a liability to the firm. As all liabilities have a credit balance, so loan from the bank has been credited because it increases the liabilities.

Income− Income means profit earned during an accounting period from any source. Income also means excess of revenue over its cost during an accounting period. Income has credit balance because it increases the balance of capital.

For example, rent received from the tenant. The journal entry is:

Cash A/c	Dr.
To Rent A/c

Here, rent is an income; hence, the rent account has been credited and cash has been debited, as rent received increases the cash balances.

Capital− Capital is the amount invested by the proprietor in the business. Capital has credit balance. Increase in capital is credited and decrease in capital is debited

For example, additional capital is introduced by the owner. The journal entry is:

Cash A/c	Dr.
To Capital A/c

As additional capital is introduced, so the amount of capital will increase, i.e. why, the capital account is credited. On the other hand, as capital is introduced in form of cash, so the cash balances decrease, i.e. why, the cash account is debited.

Question 3 : Differentiate between source documents and vouchers.

ANSWER :

Basis of Difference	Source Documents	Vouchers
Meaning	It refers to the documents in writing, containing the details of events or transactions.	When a source document is considered as evidence of an event or transaction, then it is called a voucher.
Purpose	It is used for preparing accounting vouchers.	It is used for analyzing transactions.
Recording	It acts as a basis for preparing an accounting voucher that helps in the recording.	It acts as a basis for recording transactions.
Preparation	It is prepared at the time when an event or a transaction occurs.	It can be prepared either when an event or a transaction occurs, or later on.
Legality/Validity	It can be used as evidence in a court of law.	It can be used for assessing the authentication of transactions.
Prepared By	It is prepared by the persons who are directly involved in the transactions, or who are authorized to prepare or approve these documents.	It is prepared by authorized persons or by accountants.
Examples	Cash memo, invoice, and pay-in-slip, etc.	Cash memo, invoice, pay-in-slip (if used as evidence), debit note, credit note, cash vouchers, transfer vouchers, etc.

Question 4:

Prepare accounting equation on the basis of the following:

(a) Harsha started the business with cash of Rs 2,00,000

(b) Purchased goods from Naman for cash Rs 40,000

(c) Sold goods to Bhanu costing Rs 10,000/- Rs 12,000

(d) Bought furniture on credit Rs 7,000

ANSWER :

S.No.

Explanation

Assets

Liabilities

Capital

Cash

Stock

Debtors

Furniture

Creditors

(a)

Increase in cash

2,00,000

Increase in capital

2,00,000

NIL

2,00,000

(b)

Increase in stock

40,000

Decrease in cash

(40,000)

1,60,000

40,000

NIL

2,00,000

(c)

Increase in debtors

12,000

Decrease in stock

(10,000)

Profit

2,000

1,60,000

30,000

12,000

NIL

2,02,000

(d)

Increase in furniture

7,000

Increase in creditors

7,000

1,60,000

30,000

12,000

7,000

2,02,000

Question 5 :

Show the accounting equation on the basis of the following transaction:

(a)	Udit started business with:	Rs
	(I) Cash	5,00,000
	(ii) Goods	1,00,000
(b)	Purchased building for cash	2,00,000
(c)	Purchased goods from Himani	50,000
(d)	Sold goods to Ashu (Cost Rs 25,000)	36,000
(e)	Paid insurance premium	3,000
(f)	Rent outstanding	5,000
(g)	Depreciation on building	8,000
(h)	Cash withdrawn for personal use	20,000
(i)	Rent received in advance	5,000
(j)	Cash paid to Himani on account	20,000
(k)	Cash received from Ashu	30,000

ANSWER :

S.No.	Explanation	Assets	=	Liabilities	+	Capital
Cash	+	Stock	+	Building	+	Debtors		Creditors	+	Outstanding Expenses	+	Unaccrued Income
(a)	Increase in cash	5,00,000
	Increase in stock			1,00,000
	Increase in capital															6,00,000
		5,00,000	+	1,00,000					=	NIL					+	6,00,000
(b)	Increase in building					2,00,000
	Decrease in cash	(2,00,000)							=
		3,00,000	+	1,00,000	+	2,00,000			=	NIL					+	6,00,000
(c)	Increase in stock			50,000
	Increase in creditors								=	50,000
		3,00,000	+	1,50,000	+	2,00,000			=	50,000					+	6,00,000
(d)	Increase in debtors							36,000
	Decrease in stock			(25,000)
	Increase in the capital (Profit)															11,000
		3,00,000	+	1,25,000	+	2,00,000	+	36,000	=	50,000					+	6,11,000
(e)	Decrease in cash	(3,000)
	Decrease in the capital (Expense)															(3,000)
		2,97,000	+	1,25,000	+	2,00,000	+	36,000	=	50,000	+				+	6,08,000
(f)	Decrease in the capital (Expense)											5,000
	Increase in liabilities															(5,000)
		2,97,000	+	1,25,000	+	2,00,000	+	36,000	=	50,000	+	5,000			+	6,03,000
(g)	Decrease in building					(8,000)
	Decrease in capital															(8,000)
		2,97,000	+	1,25,000	+	1,92,000	+	36,000	=	50,000	+	5,000			+	5,95,000
(h)	Decrease in cash	(20,000)
	Decrease in capital															(20,000)
		2,97,000	+	1,25,000	+	1,92,000	+	36,000	=	50,000	+	5,000			+	5,75,000
(i)	Increase in cash	5,000
	Increase in liability													5,000
		2,82,000	+	1,25,000	+	1,92,000	+	36,000	=	50,000	+	5,000	+	5,000	+	5,75,000
(j)	Decrease in creditors									(20,000)
	Decrease in cash	(20,000)
		2,62,000	+	1,25,000	+	1,92,000	+	36,000	=	30,000	+	5,000	+	5,000	+	5,75,000
(k)	Increase in cash	30,000
	Decrease in debtors							(30,000)
		2,92,000	+	1,25,000	+	1,92,000	+	6,000	=	30,000	+	5,000	+	5,000	+	5,75,000

Question 6: Describe the events recorded in accounting systems and the importance of
source documents in those systems?

ANSWER :

It is beyond human capabilities to memorize each financial transaction and that is why source documents have their own importance in the accounting system. They are
considered as evidence of transactions and can be presented in a court of law.
Transactions supported by evidence can be verified. Source documents also ensure
that transactions recorded in the books are free from personal biases.
A few events that are supported by the source document are given below.
1. Sale of goods worth Rs 200 on credit, supported by sales invoice/bill
2. Purchase of goods worth Rs 500 on credit, supported by purchase invoice/bill
3. Cash sales worth Rs 1,000, supported by cash memo
4. Cash purchase of goods worth Rs 400, supported by cash memo

5. Goods worth Rs 100 returned by the customer, supported by credit note
6. Return of goods purchased on credit worth Rs 200, supported by debit note
7. Payment worth Rs 1,200 through the bank, supported by cheques
8. Deposits into bank worth Rs 500, supported by pay-in slips.
Out of the above events, only those events that can be expressed in monetary terms,
are recorded in the books of accounts. However, the non-monetary events
are not recorded in accounts; for example, the promotion of the manager cannot be recorded
but an increment in salary can be recorded at the time when salary is paid or due.
Source document in accounting is important because of the below-given reasons.
1. It provides evidence that the transaction has actually occurred.
2. It provides information about the date, amount and parties involved, and other details of a particular transaction.
3. It acts as evidence in a court of law.
4. It helps in verifying the transaction during the auditing process.

Question 7 :

Journalise the following transactions is the journal of M/s. Goel Brothers and post them to the ledger.

2017		Rs
Jan. 01	Started business with cash	1,65,000
Jan. 02	Opened bank account in PNB	80,000
Jan. 04	Goods purchased from Tara	22,000
Jan.05	Goods purchased for cash	30,000
Jan.08	Goods sold to Naman	12,000
Jan.10	Cash paid to Tara	22,000
Jan.15	Cash received from Naman	11,700
	Discount allowed	300
Jan. 16	Paid wages	200
Jan. 18	Furniture purchased for office use	5,000
Jan. 20	Withdrawn from the bank for personal use	4,000
Jan. 22	Issued cheque for rent	3,000
Jan. 23	Goods issued for household purpose	2,000
Jan. 24	Drawn cash from the bank for office use	6,000
Jan. 26	Commission received	1,000
Jan. 27	Bank charges	200
Jan. 28	Cheque is given for insurance premium	3,000
Jan. 29	Paid salary	7,000
Jan. 30	Cash sales	10,000

ANSWER:

Books of M/s Goel Brothers
Journal
Date		Particulars	L.F.	Debit Amount Rs	Credit Amount Rs
2017
Jan.01	Cash A/c	Dr.	1,65,000
		To Capital A/c			1,65,000
	(Started business with cash)

Jan.02	Bank A/c	Dr.	80,000
		To Cash A/c			80,000
	(Bank account opened with PNB)

Jan.04	Purchases A/c	Dr.	22,000
		To Tara			22,000
	(Goods purchased from Tara)

Jan.05	Purchases A/c	Dr.	30,000
		To Cash A/c			30,000
	(Goods purchased for cash)

Jan.08	Naman	Dr.	12,000
		To Sales A/c			12,000
	(Sale of goods to Naman)

Jan.10	Tara	Dr.	22,000
		To Cash A/c			22,000
	(Cash paid to Tara)

Jan.15	Cash A/c	Dr.	11,700
	Discount Allowed A/c	Dr.	300
		To Naman			12,000
	(Cash received from Naman and discount allowed)

Jan.16	Wages A/c	Dr.	200
		To Cash A/c			200
	(Wages paid)

Jan.18	Furniture A/c	Dr.	5,000
		To Cash A/c			5,000
	(Furniture purchased for cash)

Jan.20	Drawings A/c	Dr.	4,000
		To Bank A/c			4,000
	(Cash drawn from bank for personal use)

Jan.22	Rent A/c	Dr.	3,000
		To Bank A/c			3,000
	(Rent paid through cheque)

Jan.23	Drawings A/c	Dr.	2,000
		To Purchases A/c			2,000
	(Goods drawn for household purpose)

Jan.24	Cash A/c	Dr.	6,000
		To Bank A/c			6,000
	(Cash drawn from the bank)

Jan.26	Cash A/c	Dr.	1,000
		To Commission A/c			1,000
	(Commission received)

Jan.27	Bank Charges A/c	Dr.	200
		To Bank A/c			200
	(Bank charged charges)

Jan.28	Insurance A/c	Dr.	3,000
		To Bank A/c			3,000
	(Insurance paid through cheque)

Jan.29	Salaries A/c	Dr.	7,000
		To Cash A/c			7,000
	(Salary paid)

Jan.30	Cash A/c	Dr.	10,000
		To Sales A/c			10,000
	(Cash received for the sale of goods)
		Total		3,84,400	3,84,400

Ledger

Cash Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	AmountRs
2017				2017
Jan.01	Capital		1,65,000	Jan.02	Bank		80,000
Jan.15	Naman		11,700	Jan.05	Purchases		30,000
Jan.24	Bank		6,000	Jan.10	Tara		22,000
Jan.26	Commission		1,000	Jan.16	Wages		200
Jan.30	Sales		10,000	Jan.18	Furniture		5,000
				Jan.29	Salaries		7,000
				Jan.31	Balance c/d		49,500

			1,93,700				1,93,700

Capital Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
				Jan.01	Cash		1,65,000
Jan.31	Balance c/d		1,65,000
			1,65,000				1,65,000

Bank Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.02	Cash		80,000	Jan.20	Drawings		4,000
				Jan.22	Rent		3,000
				Jan.24	Cash		6,000
				Jan.27	Bank charges		200
				Jan.28	Insurance		3,000
				Jan.31	Balance c/d		63,800
			80,000				80,000

Tara’s Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.10	Cash		22,000	Jan.04	Purchases		22,000

			22,000				22,000

Purchases Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.04	Tara		22,000	Jan.23	Drawings		2,000
Jan.05	Cash		30,000	Jan.31	Balance c/d		50,000

			52,000				52,000

Sales Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
				Jan.08	Naman		12,000
Jan.31	Balanced c/d		22,000	Jan.30	Cash		10,000

			22,000				22,000

Naman’s Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.08	Sales		12,000	Jan.15	Cash		11,700
				Jan.15	Discount Allowed		300
			12,000				12,000

Discount Allowed Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.15	Naman		300
				Jan.31	Balance c/d		300
			300				300

Wages Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.16	Cash		200
				Jan.31	Balance c/d		200
			200				200

Furniture Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.18	Cash		5,000
				Jan.31	Balance c/d		5,000
			5,000				5,000

Drawings Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.20	Bank		4,000
Jan.23	Purchases		2,000	Jan.31	Balance c/d		6,000

			6,000				6,000

Rent Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.22	Bank		3,000
				Jan.31	Balance c/d		3,000
			3,000				3,000

Commission Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
				Jan.26	Cash		1,000
Jan.31	Balance c/d		1,000
			1,000				1,000

Bank Charges Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.27	Bank		200
				Jan.31	Balance c/d		200
			200				200

Insurance Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	AmountRs
2017				2017
Jan.28	Bank		3,000
				Jan.31	Balance c/d		3,000
			3,000				3,000

Salaries Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.29	Cash		7,000
				Jan.31	Balance c/d		7,000
			7,000				7,000

Question 8:

Journalize the following transaction in the books of Sanjana and post them into the ledger:

January 2017		Rs
1	Cash in hand	6,000
2	Cash at bank	55,000
3	Stock of goods	40,000
4	Due to Rohan	6,000
5	Due from Tarun	10,000
6	Sold goods to Karuna	15,000
7	Cash sales	10,000
8	Goods sold to Heena	5,000
9	Purchased goods from Rupali	30,000
10	Goods returned from Karuna	2,000
11	Cash received from Karuna	13,000
12	Cheque given to Rohan	6,000
13	Cash received from Heena	3,000
14	Cheque received from Tarun	10,000
15	Cheque received from to Heena	2,000
16	Cash given to Rupali	18,000
17	Paid cartage	1,000
18	Paid salary	8,000
19	Cash sale	7,000
20	Cheque given to Rupali	12,000
21	Sanjana took goods for Personal use	4,000
22	Paid General expense	500

ANSWER:

Books of Sanjana
Journal Entries
S.No.		Particulars	L.F.	Debit Amount Rs	Credit Amount Rs
2017
Jan.01	Cash A/c	Dr.	6,000
	Bank A/c	Dr.	55,000
	Stock A/c	Dr.	40,000
	Tarun	Dr.	10,000
		To Rohan			6,000
		To Capital A/c			1,05,000
	(Balance brought from the last month)

Jan.03	Karuna	Dr.	15,000
		To Sales A/c			15,000
	(Goods sold to Karuna)

Jan.04	Cash A/c	Dr.	10,000
		To Sales A/c			10,000
	(Goods sold for cash)

Jan.06	Heena	Dr.	5,000
		To Sales A/c			5,000
	(Goods sold to Henna)

Jan.08	Purchases A/c	Dr.	30,000
		To Rupali			30,000
	(Goods purchased from Rupali)

Jan.10	Sales Return A/c	Dr.	2,000
		To Karuna			2,000
	(Goods returned by Karuna)

Jan.14	Cash A/c	Dr.	13,000
		To Karuna			13,000
	(Cash received from Karuna)

Jan.15	Rohan	Dr.	6,000
		To Bank A/c			6,000
	(Cheque issued to Rohan)

Jan.16	Cash A/c	Dr.	3,000
		To Heena			3,000
	(Cash received from Heena)

Jan.20	Bank A/c	Dr.	10,000
		To Tarun			10,000
	(Cheque received from Tarun)

Jan.22	Bank A/c	Dr.	2,000
		To Heena			2,000
	(Cheque received from Heena)

Jan.25	Rupali	Dr.	18,000
		To Cash A/c			18,000
	(Payment made to Rupali)

Jan.26	Cartage A/c	Dr.	1,000
		To Cash A/c			1,000
	(Cartage paid)

Jan.27	Salaries A/c	Dr.	8,000
		To Cash A/c			8,000
	(Salaries paid)

Jan.28	Cash A/c	Dr.	7,000
		To Sales A/c			7,000
	(Goods sold for cash)

Jan.29	Rupali	Dr.	12,000
		To Bank A/c			12,000
	(Cheque issued to Rupali)

Jan.30	Drawings A/c	Dr.	4,000
		To Purchases A/c			4,000
	(Goods drawn for personal use)

Jan.31	General Expenses A/c	Dr.	500
		To Cash A/c			500

	Total		2,57,500	2,57,500

Ledger

Cash Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.01	Balance b/d		6,000	Jan.25	Rupali		18,000
Jan.04	Sales		10,000	Jan.26	Cartage		1,000
Jan.14	Karuna		13,000	Jan.27	Salaries		8,000
Jan.16	Heena		3,000	Jan.31	General Expenses		500
Jan.28	Sales		7,000	Jan.31	Balance c/d		11,500
			39,000				39,000

Capital Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	AmountRs
2017				2017
				Jan.01	Balance b/d		1,05,000
Jan.31	Balance c/d		1,05,000
			1,05,000				1,05,000

Bank Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.01	Balance b/d		55,000	Jan.15	Rohan		6,000
Jan.20	Tarun		10,000	Jan.29	Rupali		12,000
Jan.22	Heena		2,000	Jan.31	Balance c/d		49,000

			67,000				67,000

Stock Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.01	Balance b/d		40,000
				Jan.31	Balance c/d		40,000
			40,000				40,000

Rohan’s Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.15	Bank		6,000	Jan.01	Balance b/d		6,000

			6,000				6,000

Tarun’s Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.01	Balance b/d		10,000	Jan.20	Bank		10,000

			10,000				10,000

Sales Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
				Jan.03	Karuna		15,000
				Jan.04	Cash		10,000
				Jan.06	Heena		5,000
Jan.31	Balance c/d		37,000	Jan.28	Cash		7,000
			37,000				37,000

Karuna’s Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.03	Sales		15,000	Jan.10	Sales Return		2,000
				Jan.14	Cash		13,000
			15,000				15,000

Heena’s Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.06	Sales		5,000	Jan.16	Cash		3,000
				Jan.22	Bank		2,000
			5,000				5,000

Purchases Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.08	Rupali		30,000	Jan.30	Drawings		4,000
				Jan.31	Balance c/d		26,000
			30,000				30,000

Rupali’s Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.25	Cash		18,000	Jan.08	Purchases		30,000
Jan.29	Bank		12,000
			30,000				30,000

Sales Return Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.10	Karuna		2,000
				Jan.31	Balance c/d		2,000
			2,000				2,000

Cartage Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.26	Cash		1,000
				Jan.31	Balance c/d		1,000
			1,000				1,000

Salaries Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.27	Cash		8,000
				Jan.31	Balance c/d		8,000
			8,000				8,000

Drawings Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.30	Purchases		4,000
				Jan.31	Balance c/d		4,000
			4,000				4,000

General Expenses Account
Dr.							Cr.
Date	Particulars	J.F.	Amount Rs	Date	Particulars	J.F.	Amount Rs
2017				2017
Jan.31	Cash		500
				Jan.31	Balance c/d		500
			500				500

Question 9: What entry (debit or credit) would you make to

increase revenue,
decrease in expense
record drawings,
record the fresh capital introduced by the owner.

ANSWER :

The following entry will be made in the above case
1. Increase Revenue-Revenue account have always credit balance so credit entry will be made to record increase in revenue.
2. Decrease in Expense- Expense account always have a debit balance so credit entry will be made to record decrease in expenses.
3. Record Drawings- Drawings is a reduction of capital balance so debit entry will be made in capital account to record drawings.
4. Record the fresh Capital Introduced by the Owner- Capital account always have a credit balance so credit entry will be made to record increase in capital.

Question 10: Describe the events recorded in accounting systems and the importance of
source documents in those systems?

Answer: It is beyond human capabilities to memorize each financial transaction and that is why source documents have their own importance in the accounting system. They are
considered as evidence of transactions and can be presented in the court of law.
Transactions supported by evidence can be verified. Source documents also ensure
that transactions recorded in the books are free from personal biases.
A few events that are supported by the source document are given below.
1. Sale of goods worth Rs 200 on credit, supported by sales invoice/bill
2. Purchase of goods worth Rs 500 on credit, supported by purchase invoice/bill
3. Cash sales worth Rs 1,000, supported by cash memo
4. Cash purchase of goods worth Rs 400, supported by cash memo

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NCERT | CLASS 11 Theory Base of Accounting | IMPORTANT QUESTIONS

Question 1: What is matching concept? Why should a business concern follow this concept? Discuss?

ANSWER:

Matching Concept states that all expenses incurred during the year, whether paid or not and all revenues earned during the year, whether received or not, should be taken into account while determining the profit of that year. In other words, expenses incurred in a period should be set off against revenues earned in the same accounting period for ascertaining profit or loss. For example, insurance premium paid for a year is Rs1200 on July 01 and if accounts are closed on March 31, every year, then the insurance premium of the current year will be ascertained for nine months (i.e. from July to March) and will be calculated as,

Rs 1200 − Rs 900 = Rs 300

Thus, according to the matching concept, the expense of Rs 900 will be taken into account and not Rs 1200 for determining profit, as the benefit of only Rs 900 is availed in the current accounting period.

The business entities follow this concept mainly to ascertain the true profit or loss during an accounting period. It is possible that in the same accounting period, the business may either pay or receive payments that may or may not belong to the same accounting period. This leads to either overcasting or undercasting of the profit or loss, which may not reveal the true efficiency of the business and its activities in the concerned accounting period. Similarly, there may be various expenditures like purchase of machinery, buildings, etc. These expenditures are capital in nature and their benefits can be availed over a period of time. In such cases, only the depreciation of such assets is treated as an expense and should be taken into account for calculating profit or loss of the concerned year. Thus, it is very necessary for any business entity to follow the matching concept.

Question 2: What is the money measurement concept? Which one factor can make it difficult to compare the monetary values of one year with the monetary values of another year?

Answer:

Money Measurement Concept states that only those transactions and events are recorded in accounting that is capable of being expressed in terms of money. An event even though may be very important for business, will not be recorded in the books of accounts unless its effect can be measured in terms of money. For Example, a business has 5 machines then this thing cannot be added up unless expressed in terms of money. In order to record this item, we must have to express it in monetary terms say Rs. 1,00,000. Thus, the money measurement concept enables consistency in maintaining accounting records.
But on the other hand, the adherence to the money measurement concept makes it difficult to compare the monetary values of one period with that of another. It is because of the fact that the money measurement concept ignores the changes in the purchasing power of the money, i.e. only the nominal value of money is concerned with and not the real value. What Rs 1 could buy 10 years back cannot buy today; hence, the nominal value of money makes comparison difficult. In fact, the real value of money would be a more appropriate measure as it considers the price level (inflation), which depicts the changes in profits, expenses, incomes, assets, and liabilities of the business.

Question 3: International Financial Reporting Standards (IFRS):-

Answer:

Globalization has unified different economies of the world. Enterprises are carrying on business worldwide. As accounting is the language of business, different enterprises around the world should not be speaking different languages in their financial statements. It will be very difficult to understand and compare these statements.
International Financial Reporting Standards (IFRS) are issued by the International Accounting Standard Board (IASB). IASB replaced International Accounting. Standard Committee (LASC) in 2001.LASC was formed in 1973 to develop accounting standards that have global acceptance and make different accounting statements of different countries similar and comparable.
Assumptions in IFRS:-
The underlying assumptions in IFRS are as follows:

Measuring Unit Assumption:- Current purchasing power is the measuring unit which means that assets in the balance sheet are shown at current or fair value and not at historical cost.
Constant Purchasing Power Assumption:- It means that the value of capital is to be adjusted for inflation at the end of the financial year.
Accrual Assumption:- Transactions are recorded as and when they occur and the date of settlement is irrelevant.
Going Concern Assumption:- It is assumed that the life of the business is infinite.

Question 4 : What is the money measurement concept? Which one factor can make it difficult to compare the monetary values of one year with the monetary values of another year?

ANSWER:

Money Measurement Concept states that only those events that can be expressed in monetary terms are recorded in the books of accounts. For example, 12 television sets of Rs10,000 each are purchased and this event is recorded in the books with a total amount of Rs 1,20,000. Money acts a common denomination for all the transactions and helps in expressing different measurement units into a common unit, for example rupees. Thus, money measurement concept enables consistency in maintaining accounting records. But on the other hand, the adherence to the money measurement concept makes it difficult to compare the monetary values of one period with that of another. It is because of the fact that the money measurement concept ignores the changes in the purchasing power of the money, i.e. only the nominal value of money is concerned with and not the real value. What Rs 1 could buy 10 years back cannot buy today; hence, the nominal value of money makes comparison difficult. In fact, the real value of money would be a more appropriate measure as it considers the price level (inflation), which depicts the changes in profits, expenses, incomes, assets and liabilities of the business.

Question 5 : When should revenue be recognised? Are there exceptions to the general rule?

Answer

Revenue is recognised only when it is realised i.e., when a legal right to receive it arises. Thus credit sales are treated as revenue on the day sales are made and not when cash is received from the buyers. Similarly, rent for the month of March even if received in April month will be treated as revenue of the financial year ending 31st March.
There are two exceptions to this rule:
→ In case of sales on installment basis, only the amount collected in installments is treated as revenue.
→ In case of long-term construction contracts, proportionate amount of revenue, based on part of the contracted completed by the end of the financial year is treated as realised.

Question 6 : ‘Only financial transactions are recorded in accounting’. Explain the statement.

Answer :

According to this principle, only those transactions and events are recorded in accounting which are capable of being expressed in terms of money are recorded in the books of accounts, such as the sale of goods or payment of expenses or receipt of income, etc.
An event may be important for the business (such as dispute among the owners or managers, the appointment of a manager, etc.), but it will not be recorded in the books of accounts simply because it can not be converted or recorded in terms of money. For instance, strike by workers may adversely affect the business but it cannot be recorded in the books of accounts unless its effect can be measured in terms of money with a fair degree of accuracy.
Another aspect of this principle is that the transactions that can be expressed in terms of money have to be converted in terms of money before being recorded.It should be remembered that money is the only measurement which enables various things of diverse nature to be added up together and dealt with. The money measurement assumption is not free from limitations. Due to the changes in price, the value of money does not remain the same over a period of time. The value of rupee today on account of rising in price is much less than what it was, say ten years back. As the change in the value of money is not reflected in the book of accounts, the accounting data does not reflect the true and fair view of the affairs of an enterprise. As, such, to make accounting records relevant, simple, understandable and homogeneous, they are expressed in a common unit of measurement,i.e., money.

Question 7 : What are the advantages of Book‐Keeping ?

Answer :

1. To the Management of a Business
(a) In evaluating various alternative proposals so as to take maximum benefit from the best alternative.

(b) In deciding matters such as elimination of an unprofitable activity, department or product, replacement of fixed assets, expansion of business etc.

(d) Comparing various year’s account to know the progress or deterioration of the business and take actions to improve the business.

(e) Accounting information helps in providing evidence in a court of law in case of legal action taken by others.

(f) Accounting information helps in assessing the income tax, sales tax and property tax of the business.

(g) Accounting information constitutes one of the basis for borrowing loans from external source.

(h) It helps to detect errors and frauds that have taken place in the business.

2. To the Investors:
(a) Types of property owned by the business.

(b) Sources and amount of earnings made or losses incurred by the business.

(d) Whether rate of earnings is high or low.

3. To the Employees:
It provides information to employees so as to claim fair wages, bonus, and other welfare facilities.

4. To the Government:
(a) Accounting information helps Government to extend subsidies and incentives and other exemptions to certain types of business.

(b) The industrial progress can be known by the Government of the country. It can formulate industrial policies for further growth and development of industries.

(d) It helps in amending various laws or enacting laws governing the functioning of business enterprises.

(e) It helps the Government in deciding price control, wage fixation, excise duties, sales tax etc.

5. To the Consumers:
Customers are not overcharged as selling price is fixed on the total expenses incurred by adding a reasonable rate of profit.

6. To the Prospective Investors:
It helps the prospective investors in choosing the right type of investment depending upon the profit earning capacity of the business enterprises and the profit earned during past few years.

7. To the Creditors and Suppliers:
Creditors can decide the solvency position of the business through the accounting information. Similarly, suppliers can also decide whether goods can be sold in future on credit basis.

Question 8 : Discuss the concept-based on the premise ‘do not anticipate profits but provide for all losses’.

Answer :

According to the Conservatism Principle, profits should not be anticipated; however, all losses should be accounted (irrespective whether they occurred or not). It states that profits should not be recorded until they get recognised; however, all possible losses even though they may happen rarely, should be provided. For example, stock is valued at cost or market price, whichever is lower. If the market price is lower than the cost price, loss should be accounted; whereas, if the former is more than the latter, then this profit should not be recorded until unless the stock is sold. There are numerous provisions that are maintained based on the conservatism principle like, provision for discount to debtors, provision for doubtful bad debts, etc. This principle is based on the common sense and depicts pessimism. This also helps the business to deal uncertainty and unforeseen conditions.

Question 9 : Why is it important to adopt a consistent basis for the preparation of financial statements? Explain.

Answer :

It is important to adopt a consistent basis for the preparation of financial statements because it helps in comparability of financial statements. For Example: if a firm choose straight line method for showing depreciation but in the next accounting period switched over to written down method then the results of this year cannot be compared to that of the previous years. However, it does not mean that firm cannot changes its accounting policies. A better method, if available which will lead to better presentation and better understanding of the financial results, the firm may adopt but it must be stated clearly by way of footnotes to enable the users of the financial statements to be aware of the changes.

Question 10 : What is Book-Keeping?

Answer :

Book‐Keeping is a systematic manner of recording transactions related to business in the books of accounts. In Book‐Keeping, transactions are recorded in the order of the dates. An Accountant is a person who records the transactions in the books of the business and is expected to show the financial results of a business for every financial year. A financial year in India is followed from 1st April to 31st March.

According to J. R. Batliboi :

“Book‐Keeping is an art of recording business dealings in a set of books.”

According to R.N Carter:

“Book‐Keeping is an art of recording in the books of accounts, all those business transactions that result in transfer of money’s worth”

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NCERT MCQ CLASS-9 CHAPTER-10 | CIRCLES | EDUGROWN

NCERT MCQ ON CIRCLES

1. In the figure, if O is the centre of a circle, then the measure of ∠ACB is:

(i) 80°(ii) 100°(iii) 40°(iv) 60°

Answer- (iii) 40°

2. The angle subtended by the diameter of a semicircle is:

(i) 45°(ii) 180°(iii) 90°(iv) 60°

Answer- (iii) 90°

3. In the figure, if O is the Centre of the circle, then the measure of x is:

(i) 40°(ii) 80°(iii) 50°(iv) 110°

Answer- (iii) 50°

4. In the figure, if O is the centre of the circle, then what is the measure of ∠ADC?

(i) 45°(ii) 60°(iii) 90°(iv) 110°

Answer- (i) 45°

5. In the figure, O is the centre of the circle. What is the measure of ∠AOC?

(i) 120°(ii) 136°(iii) 128°(iv) 158°

Answer- (iv) 158°

6. In the figure, O is the centre of the circle and PR = QR. What is the measure of ∠PQR?

(i) 60°(ii) 110°(iii) 75°(iv) 45°

Answer- (iv) 45°

7. In the figure, O is the centre of the circle. What is the measure of ∠ACB?

(i) 45°(ii) 60°(iii) 70°(iv) 90°

Answer- (ii) 60°

8. In the figure, O is the centre of the circle. What is the value of x?

(i) 125°(ii) 105°(iii) 95°(iv) 85°

Answer- (ii) 105°

9. In the figure, O is the centre of the circle. If ∠ADC = 140°, then what is the value of x?

(i) 45°(ii) 55°(iii) 60°(iv) 45°

Answer- (iv) 45°

10. If ∠A and ∠C are in the ratio 3 : 2, then we have: ∠A = ? and ∠B = ?

(i) 108°, 75°(ii) 120°, 60°(iii) 105°, 75°(iv) 125°, 55°

Answer- (i) 108°, 75°

11.If there are two separate circles drawn apart from each other, then the maximum number of common points they have:
(i) 0
(ii) 1
(iii) 2
(iv) 3

Answer: (i) 0

12.D is diameter of a circle and AB is a chord. If AD = 50 cm, AB = 48 cm, then the distance of AB from the centre of the circle is
(i) 6 cm
(ii) 8 cm
(iii) 5 cm
(iv) 7 cm

Answer: (iv) 7 cm

13.In a circle with center O and a chord BC, points D and E lie on the same side of BC. Then, if ∠BDC=80°, then ∠BEC =
(i) 80°
(ii) 20°
(iii) 160°
(iv) 40°

Answer: (i) 80°

14.The center of the circle lies in______ of the circle.
(i) Interior
(ii) Exterior
(iii) Circumference
(iv) None of the above

Answer: (i) Interior

15.If chords AB and CD of congruent circles subtend equal angles at their centers, then:
(i) AB = CD
(ii) AB > CD
(iii) AB < AD
(iv) None of the above

Answer: (i) AB = CD

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NCERT MCQ CLASS-9 CHAPTER-9 | AREAS OF PARALLELOGRAM AND TRIANGLES | EDUGROWN

NCERT MCQ ON PARALLELOGRAM AND TRIANGLES

Question 1.
What is the area of a parallelogram?
(a) 12 × Base × Altitude
(b) Base × Altitude
(c) 14 × Base × Median
(d) Base × Base

Answer: (b) Base × Altitude

Question 2.
AE is a median to side BC of triangle ABC. If area(ΔABC) = 24 cm, then area(ΔABE) =
(a) 8 cm
(b) 12 cm
(c) 16 cm
(d) 18 cm

Answer: (b) 12 cm

Question 3.
In the figure, ∠PQR = 90°, PS = RS, QP = 12 cm and QS = 6.5 cm. The area of ΔPQR is
MCQ Questions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles with Answers 1
(a) 30 cm²
(b) 20 cm²
(c) 39 cm²
(d) 60 cm²

Answer: (a) 30 cm²

Question 4.
BCD is quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD
ABCD is quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD
(a) is a rectangles
(b) is a parallelogram
(c) is a rhombus
(d) need not be any of (a), (b) or (c).

Answer: (d) need not be any of (a), (b) or (c).

Question 5.
In ΔPQR, if D and E are points on PQ and PR respectively such that DE || QR, then ar (PQE) is equal to
MCQ Questions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles with Answers 2
(a) ar (PRD)
(b) ar (DQM)
(c) ar (PED)
(d) ar (DQR)

Answer: (a) ar (PRD)

Question 6.
If Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Then,
(a) ar (AOD) = ar (BOC)
(b) ar (AOD) > ar (BOC)
(c) ar (AOD) < ar (BOC)
(d) None of the above

Answer: (a) ar (AOD) = ar (BOC)

Question 7.
For two figures to be on the same base and between the same parallels, one of the lines must be.

(a) Making an acute angle to the common base
(b) The line containing the common base
(c) Perpendicular to the common base
(d) Making an obtuse angle to the common base

Answer: (b) The line containing the common base

Question 8.
Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is:

(a) 1 : 3
(b) 1 : 2
(c) 2 : 1
(d) 1 : 1

Answer: (d) 1 : 1

Question 9.
If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of parallelogram is
(a) 1 : 3
(b) 1 : 2
(c) 3 : 1
(d) 1 : 4

Answer: (b) 1 : 2

Question 10 .
The median of a triangle divides it into two
(a) isosceles triangle
(b) congruent triangles
(c) right angled triangle
(d) triangles of equal areas

Answer: (d) triangles of equal areas

Question 11.
PQRS is a parallelogram and A and B are any points on PQ and QR. If ar(PQRS) = 48 cm², then ar(ΔPBS) + ar(ΔASR) is equal to
MCQ Questions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles with Answers 1
(a) 96 cm²
(b) 36 cm²
(c) 48 cm²
(d) 24 cm²

Answer: (c) 48 cm²

Question 12.
A, B, C and D are the mid-points of sides of parallelogram PQRS. If ar(PQRS) = 36 cm², then ar(ABCD) is
MCQ Questions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles with Answers 2
(a) 24 cm²
(b) 18 cm²
(c) 30 cm²
(d) 36 cm²

Answer: (b) 18 cm²

Question 13.
ABCD is a trapezium in which AB || DC. If ar(ΔABD) = 24 cm² and AB = 8 cm, then height of ΔABC is
MCQ Questions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles with Answers 3
(a) 3 cm
(b) 6 cm
(c) 8 cm
(d) 4 cm

Answer: (d) 4 cm

Question 14.
PQRS is a parallelogram. If X and Y are the mid-points of PQ and SR and diagonal SQ is joined, then ar(XQRY) : ar(ΔQSR) is

MCQ Questions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles with Answers 4
(a) 1 : 2
(b) 1 : 4
(c) 1 : 1
(d) 2 : 1

Answer: (c) 1 : 1

Question 15 .
In quadrilateral PQRS, M is the mid-point of PR. If ar(SMQR) = 18 cm², then ar(PQMS) is

MCQ Questions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles with Answers 5
(a) 24 cm²
(b) 12 cm²
(c) 18 cm²
(d) 36 cm²

Answer: (c) 18 cm²

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NCERT | CLASS 11 ACCOUNTANCY | IMPORTANT QUESTIONS

Question 1: Distinguish between debtors and creditors; Profit and Gain.

ANSWER: The difference between Debtors and Creditors is given below.

Basis of difference	Debtors	Creditors
Meaning	Persons or organizations that are liable to pay money to a firm are called debtors.	Persons or organizations to whom the firm is liable to pay money are called creditors.
Nature	They have a debit balance to the firm.	They have a credit balance to the firm.
Payment	Payments are received from them.	Payments are made to them.
Shown	They are shown as assets in the Balance sheet under Current Assets.	They are shown as liabilities in the Balance Sheet under Current Liabilities.

The difference between Profit and Gain is given below.

Gain− Gain is incidental to the business. They arise from irregular activities or non-recurring transactions; for example, profit on sale of fixed assets, appreciation in value of asset, profit on sale of investment, etc.
Profit− This refers to the excess of revenue over the expense. It is normally categorised into gross profit or net profit. Net profit is added to the capital of the owner, which increases the owner’s capital. For example, goods sold above its cost

Question 2: What is accounting? Define its objectives.

ANSWER:

Accounting is a process of identifying the events of financial nature, recording them in the journal, classifying in their respective accounts and summarising them in profit and loss account and balance sheet and communicating results to users of such information, viz. owner, government, creditor, investors, etc.

According to the American Institute of Certified Accountants, 1941, “Accounting is the art of recording, classifying and summarizing in a significant manner and in terms of money, transactions, and events that are, in part at least, of financial character and interpreting the results thereof.”

In 1970, the American Institute of Certified Public Accountants changed the definition and stated, “The function of accounting is to provide quantitative information, primarily financial in nature, about economic entities, that is intended to be useful in making economic decisions.”

Objectives of Accounting:

Recording business transactions systematically− It is necessary to maintain systematic records of every business transaction, as it is beyond human capacities to remember such large number of transactions. Skipping the record of any one of the transactions may lead to erroneous and faulty results.
Determining profit earned or loss incurred− In order to determine the net result at the end of an accounting period, we need to calculate profit or loss. For this purpose trading and profit and loss account are prepared. It gives information regarding how much of goods have been purchased and sold, expenses incurred and amount earned during a year.
Ascertaining financial position of the firm− Ascertaining profit earned or loss incurred is not enough; proprietor also interested in knowing the financial position of his/her firm, i.e. the value of the assets, amount of liabilities owed, net increase or decrease in his/her capital. This purpose is served by preparing the balance sheet that facilitates in ascertaining the true financial position of the business.
Assisting management− Systematic accounting helps the management in effective decision making, efficient control on cash management policies, preparing budget and forecasting, etc.
Assessing the progress of the business− Accounting helps in assessing the progress of business from year to year, as accounting facilitates the comparison both inter-firm as well as intra-firm.
Detecting and preventing frauds and errors− It is necessary to detect and prevent fraud and errors, mismanagement and wastage of the finance. Systematic recording helps in the easy detection and rectification of frauds, errors and inefficiencies, if any.
Communicating accounting information to various users− The important step in the accounting process is to communicate financial and accounting information to various users including both internal and external users like owners, management, government, labour, tax authorities, etc. This assists the users to understand and interpret the accounting data in a meaningful and appropriate manner without any ambiguity.

Question 3: What do you mean by an asset and what are different types of assets?

ANSWER:

Any valuable thing that has monetary value, which is owned by a business, is its asset. In other words, assets are the monetary values of the properties or the legal rights that are owned by the business organizations.

Fixed Assets− These are those assets that are held for the long term and increase the profit earning capacity and productive capacity of the business. These assets are not meant for sale, for example, land, building machinery, etc.

Current Assets− Assets that can be easily converted into cash or cash equivalents are termed as current assets. These are required to run day-to-day business activities; for example, cash, debtors, stock, etc.

Tangible Assets− Assets that have a physical existence, i.e., which can be seen and touched, are tangible assets; for example, car, furniture, building, etc.

Intangible Assets− Assets that cannot be seen or touched, i.e. those assets that do not have a physical existence, are intangible assets; for example, goodwill, patents, trademark, etc.

Liquid Assets− Assets that are kept either in cash or cash equivalents are regarded as liquid assets. These can be converted into cash in a very short period of time; for example, cash, bank, bills receivable, etc.

Fictitious Assets− These are the heavy revenue expenditures, the benefit of whose can be derived in more than one year. They represent loss or expense that is written off over a period of time, for example, if advertisement expenditure is Rs 1,00,000 for 5 years, then each year Rs 2,00,000 will be written off.

Question 4: Describe the role of accounting in the modern world.

Answer:

The role of accounting has been changing over the period of time. In the modern world, the role of accounting is not only limited to record financial transactions but also to provide a basic framework for various decision making, providing relevant information to various users, and assists in both short-run and long-run planning. The role of accounting in the modern world are given below.

→ Assisting management- Management uses accounting information for short-term and long-term planning of business activities, to predict the future conditions, prepare budgets, and various control measures.

→ Comparative study- In the modern world, accounting information helps us to know the performance of the business by comparing the current year’s profit with that of the previous years and also with other firms in the same industry.

→ Substitute of memory- In the modern world, every business incurs a large number of transactions and it is beyond human capability to memorize each and every transaction. Hence, it is very necessary to record transactions in the books of accounts.

→ Information to end-user- Accounting plays an important role in recording, summarising, and providing relevant and reliable information to its users, in form of financial data that helps in decision making.

Question 5: Explain the qualitative characteristics of accounting information.

Answer:

The qualitative characteristics of accounting information are:

→ Reliability: Accounting information must be reliable so that business owners can be reasonably assured that accounting information presents an accurate picture of the company. All accounting information is verifiable and can be verified from the source document (voucher), via cash memos, bills, etc. Hence, the available information should be free from any errors and unbiased.

→ Relevance: It means that essential and appropriate information should be easily and timely available and any irrelevant information should be avoided. The users of accounting information need relevant information for decision making, planning, and predicting future conditions.

→ Understandability: Accounting information should be presented in such a way that every user is able to interpret the information without any difficulty in a meaningful and appropriate manner.

→ Comparability: It allows business owners to compare accounting information of a current year with that of the previous years. Comparability enables intra-firm and inter-firm comparisons. This assists in assessing the outcomes of various policies and programs adopted in different time horizons by the same or different businesses. Further, it helps to ascertain the growth and progress of the business over time and in comparison to other businesses.

Question 6: Accounting information refers to financial statements. The information provided by these statements can be categorized into various types. Briefly describe them.

Answer:

Types of Accounting Information Accounting information refers to the information provided in financial statements of the business, generated through the process of book keeping and summarising. By using the accounting information, the users are in a position to take the correct decision. The financial statements so generated are the income statement i.e., profit and loss account and the position statement i.e., balance sheet and a Cash Flow Statement. The information made available by these statements can be categorised into the following categories:
1. Information Related to Profit or Loss during the year: Information about the profit earned or loss incurred by the business during an accounting period is made available through the income statement of the business i.e., the profit and loss account. Trading account provides information about gross profit or gross loss whereas the profit and loss account provides information about the net profit or net loss during the year. It also gives details of all the expenses and incomes during the year.
2. Information Related to Financial Position of the business : Information about the financial position of the enterprise is determined through its position statement i.e., the balance sheet.
  It provides information about the assets and liabilities of a business on a particular date. The difference between the two is represented by capital i.e., amount due to owners. In the case of not-for-profit organisation, difference between assets and liabilities is termed as general fund.
3. Information about Cash Flow during the year : Cash flow statement is a statement that shows inflow and outflow of cash during a specific period. It helps in making various decisions such as payment of liabilities, payment of dividend and expansion of business, etc., as all these are based on availability of cash. It gives a clear picture of the liquidity of the business.

Question 7:

Giving examples, explain each of the following accounting terms:

Fixed assets
Revenue
Expenses
Short-term liability
Capital

ANSWER:

Fixed assets− These are held for long term and increase the profit earning capacity of the business, over various accounting periods. These assets are not meant for sale; for example, land, building, machinery, etc.
Revenue− It refers to the amount received from day to day activities of business, viz. amount received from sales of goods and services to customers; rent received, commission received, dividend, royalty, interest received, etc. are items of revenue that are added to the capital.
Capital− It refers to the amount invested by the owner of a firm. It may be in form of cash or asset. It is an obligation of the business towards the owner of the firm, since business is treated separate or distinct from the owner.

Capital = Assets − Liabilities.

Expenses− Expenses are those costs that are incurred to maintain the profitability of business, likerent, wages, depreciation, interest, salaries, etc. These help in the production, business operations and generating revenues.
Short term liabilities− Those liabilities that are incurred with an intention to be paid or are payable within a year; for example, bank overdraft creditors, bills payable, outstanding wages, short-term loans, etc.

Question 8: Describe the informational needs of external users.

Answer:

The various external users and their needs are:

• Investors and potential investors: information on the risks and return on investment;

• Unions and employee groups: information on the stability, profitability, and distribution of wealth within the business;

• Lenders and financial institutions: information on the creditworthiness of the company and its ability to repay loans and pay interest;

• Suppliers and creditors-information on whether amounts owed will be repaid when due, and on the continued existence of the business;

• Customers-information on the continued existence of the business and thus the probability of a continued supply of products, parts, and after-sales service;

• Government and other regulators- information on the allocation of resources and the compliance to regulations;

• Social responsibility groups, such as environmental groups-information on the impact on the environment and its protection;

• Competitors: information on the relative strengths and weaknesses of their competition and for comparative and benchmarking purposes.

Question 9: Distinguish between financial accounting, cost accounting, and management accounting.

Answer:

Basis	Financial Accounting	Cost Accounting	Management Accounting
Meaning	Financial accounting is a specialized branch of accounting that keeps track of a company’s financial transactions. Using standardized guidelines, the transactions are recorded, summarized, and presented in a financial report or financial statements such as an income statement or a balance sheet.	Cost accounting is an accounting method that aims to capture a company’s costs of production by assessing the input costs of each step of production as well as fixed costs, such as the depreciation of capital equipment. Cost accounting will first measure and record these costs individually, then compare input results to output or actual results to aid company management in measuring financial performance.	Management accounting also called managerial accounting or cost accounting is the process of analyzing business costs and operations to prepare an internal financial report, records, and account to aid managers’ decision-making process in achieving business goals. In other words, it is the act of making sense of financial and costing data and translating that data into useful information for management and officers within an organization.
Objects	Record transaction and determine financial position & profit or loss	Ascertainment, allocation, accumulation, and accounting for the cost	To assist the management in decision making & policy formulation
Nature	Concerned with historical data	concerned with both past and present recorded( historical in nature)	Deals with a projection of data for the future( futuristic in nature)
Principle followed	Governed by GAAP	certain principles followed for recording cost	No set principles are followed in it
Data Used	Qualitative aspects are not recorded	Only quantitative aspects are recorded	Uses both qualitative and quantitative concepts

Question 10: What are the functions or steps of the accounting process?

Answer:

Following attributes or major steps that can be drawn from the definition of Accounting:

① Identifying and Measurement
② Recording
③ Classifying
④ Summarizing
⑤ Analysis, Interpretation, and Communication

(1) Identifying financial transactions and events

Accounting records only those transactions and events which are of financial nature. So, first of all, such transactions and events are identified.

The first step in accounting is to determine what to record, i.e., to identify the financial events which are to be recorded in the books of accounts. It involves observing all business activities and selecting those events or transactions which can be considered as financial transactions.

(2) Measuring the transactions

Accounting measures the transactions and events in terms of money which are considered as a common unit.

In Accounting, we record only those transactions which can be measured in terms of money or which are of financial nature. If a transaction or event cannot be measured in monetary terms, it is not considered for recording in financial accounts.

There are few events directly or indirectly make an effect on the working of a business firm but cannot be recorded in the books of accounts because they cannot be measured in terms of money.
For example, the appointment of a new managing director, signing of contracts, strikes, death of an employee etc is not shown in the books of accounts.

(3) Recording of transactions

Accounting involves recording the financial transactions of inappropriate books of accounts such as journals or Subsidiary Books.

A transaction will be recorded in the books of accounts only if it is considered an economic event and can be measured in terms of money. Once the economic events are identified and measured in financial terms, these are recorded in books of account in monetary terms and in chronological order. The recording should be done in a systematic manner so that the information can be made available when required.

(4) Classifying the transactions

Transactions recorded in the books of original entry – Journal or Subsidiary books are classified and grouped according to nature and posted in separate accounts known as ‘Ledger Accounts’.

Once the financial transactions are recorded in journal or subsidiary books, all the financial transactions are classified by grouping the transactions of one nature at one place in a separate account. This is known as the preparation of Ledger.

(5) Summarising the transactions

It involves presenting the classified data in a manner and in the form of statements, which are understandable by the users.

It includes Trial balance, Trading Account, Profit and Loss Account, and Balance Sheet.

It is concerned with the presentation of data and it begins with a balance of ledger accounts and the preparation of trial balance with the help of such balances. A trial balance is required to prepare the financial statements i.e. Trading Account, Profit & Loss Account, and Balance Sheet.

(6) Analysing and interpreting financial data

Results of the business are analyzed and interpreted so that users of financial statements can make a meaningful and sound judgment.

The main purpose of accounting is to communicate the financial information to the users who analyze them as per their individual requirements.

(7) Communicating the financial data or reports to the users

Communicating the financial data to the users on time is the final step of Accounting so that they can make appropriate decisions. Providing financial information to its users is a regular process.

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Class 11th Chapter – 5 Complex Numbers and Quadratic Equations | NCERT Maths Solution | NCERT Solution | Edugrown

In This Post we are providing Chapter -5 Complex Numbers and Quadratic Equations NCERT Solutions for Class 11 Maths which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These Class 11 Complex Numbers and Quadratic Equations solutions can be really helpful in the preparation of Board exams and will provide you with in depth detail of the chapter.

We have solved every question stepwise so you don’t have to face difficulty in understanding the solutions. It will also give you concepts that are important for overall development of students. Class 11 Maths Complex Numbers and Quadratic Equations NCERT Written Solutions will be useful in higher classes as well because variety of questions related to these concepts can be asked so you must study and understand them properly.

Class 11th Chapter 5 Complex Numbers and Quadratic Equations| NCERT MATHS SOLUTION |

Chapter 5 Complex Numbers and Quadratic Equations EX 5.1 NCERT Solutions

Express each of the complex number given in the Exercises 1 to 10 in the form a + ib.
Ex 5.1 Class 11 Maths Question 1.
$\left( 5i \right) \left( -\frac { 3 }{ 5 } i \right)$
Solution.
$\left( 5i \right) \left( -\frac { 3 }{ 5 } i \right)$
= -3i² = -3(-1) [∵ i² = -1]
= 3 = 3 + 0i

Ex 5.1 Class 11 Maths Question 2.
i⁹+ i¹⁹
Solution.
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 1

Ex 5.1 Class 11 Maths Question 3.
i^-39
Solution.
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 2

Ex 5.1 Class 11 Maths Question 4.
3(7 + i7) + i(7 + i7)
Solution.
3(7 + i7) + i(7 + i7) = 21 + 21i + 7i + 7i²
= 21 + (21 + 7)i + (-1)7 = 21 – 7 + 28i
= 14 + 28i.

Ex 5.1 Class 11 Maths Question 5.
(1 – i) – (- 1 +i6)
Solution.
(1 – i) – (-1 + i6) = 1 – i + 1 – 6i
= (1 +1) – i(1 + 6)
= 2 – 7i

Ex 5.1 Class 11 Maths Question 6.
$\left( \frac { 1 }{ 5 } +i\frac { 2 }{ 5 } \right) -\left( 4+i\frac { 5 }{ 2 } \right)$
Solution.
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 3

Ex 5.1 Class 11 Maths Question 7.
$\left[ \left( \frac { 1 }{ 3 } +i\frac { 7 }{ 3 } \right) +\left( 4+i\frac { 1 }{ 3 } \right) \right] -\left( -\frac { 4 }{ 3 } +i \right)$
Solution.
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 4

Ex 5.1 Class 11 Maths Question 8.
(1 -i)⁴
Solution.
(1 -i)⁴ = [(1 – i)²]² = [1 – 2i + i²]²
= [1 – 2i + (-1)]²
= (-2i)² = 4i² = 4(-1) = – 4
= – 4 + 0i

Ex 5.1 Class 11 Maths Question 9.
${ \left( \frac { 1 }{ 3 } +3i \right) }^{ 3 }$
Solution.
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 5

Ex 5.1 Class 11 Maths Question 10.
${ \left( -2-\frac { 1 }{ 3 } i \right) }^{ 3 }$
Solution.
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 6

Find the multiplicative inverse of each of the complex numbers given in the Exercises 11 to 13.
Ex 5.1 Class 11 Maths Question 11.
4 – 3i
Solution.
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 7

Ex 5.1 Class 11 Maths Question 12.
$\sqrt { 5 } +3i$
Solution.
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 8

Ex 5.1 Class 11 Maths Question 13.
-i
Solution.
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 9

Ex 5.1 Class 11 Maths Question 14.
Express the following expression in the form of a + ib:
$\frac { \left( 3+i\sqrt { 5 } \right) \left( 3-i\sqrt { 5 } \right) }{ \left( \sqrt { 3 } +\sqrt { 2 } i \right) -\left( \sqrt { 3 } -i\sqrt { 2 } \right) }$
Solution.
We have, $\frac { \left( 3+i\sqrt { 5 } \right) \left( 3-i\sqrt { 5 } \right) }{ \left( \sqrt { 3 } +\sqrt { 2 } i \right) -\left( \sqrt { 3 } -i\sqrt { 2 } \right) }$
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 10

We hope the NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1, drop a comment below and we will get back to you at the earliest.

Chapter 5 Complex Numbers and Quadratic Equations EX 5.2 NCERT Solutions

Find the modulus and the arguments of each of the complex numbers in Exercises 1 to 2.
Ex 5.2 Class 11 Maths Question 1.
$z=-1-i\sqrt { 3 }$
Solution.
We have, $z=-1-i\sqrt { 3 }$
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 1

Ex 5.2 Class 11 Maths Question 2.
$z=-\sqrt { 3 } +i$
Solution.
We have, $z=-\sqrt { 3 } +i$
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 2

Convert each of the complex numbers given in Exercises 3 to 8 in the polar form:
Ex 5.2 Class 11 Maths Question 3.
1 – i
Solution.
We have, z = 1 – i
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 3

Ex 5.2 Class 11 Maths Question 4.
-1 + i
Solution.
We have, z = -1 + i
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 4

Ex 5.2 Class 11 Maths Question 5.
-1 – i
Solution.
We have, z = -1 – i
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 5

Ex 5.2 Class 11 Maths Question 6.
-3
Solution.
We have, z = -3, i.e., z = -3 + 0i
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 6

Ex 5.2 Class 11 Maths Question 7.
$\sqrt { 3 } +i$
Solution.
We have, $z=\sqrt { 3 } +i$
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 7

Ex 5.2 Class 11 Maths Question 8.
i
Solution.
We have, z = i, i.e., z = 0 + 1.i
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 8

We hope the NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2, drop a comment below and we will get back to you at the earliest.

Chapter 5 Complex Numbers and Quadratic Equations EX 5.3 NCERT Solutions

Solve each of the following equations:
Ex 5.3 Class 11 Maths Question 1.
x² + 3 = 0
Solution.
We have, x² + 3 = 0 ⇒ x² = -3
⇒ $x=\pm \sqrt { -3 }$ ⇒ x = $\pm \sqrt { 3 } i$

Ex 5.3 Class 11 Maths Question 2.
2x² + x + 1 = 0
Solution.
We have, 2x² + x + 1 = 0
Comparing the given equation with the general form ax² + bx + c = 0, we get
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 1

Ex 5.3 Class 11 Maths Question 3.
x² + 3x + 9 = 0
Solution.
We have, x² + 3x + 9 = 0
Comparing the given equation with the general form ax² + bx + c = 0,we get a = 1, b = 3, c = 9
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 2

Ex 5.3 Class 11 Maths Question 4.
-x² + x – 2 = 0
Solution.
We have, -x² + x – 2 = 0
Comparing the given equation with the general form ax² + bx + c = 0,we get
a = 1, b = 1, c = -2
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 3

Ex 5.3 Class 11 Maths Question 5.
x² + 3x + 5 = 0
Solution.
We have, x² + 3x + 5 = 0
Comparing the given equation with the general form ax² + bx + c = 0, we get a = 1, b = 3, c = 5.
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 4

Ex 5.3 Class 11 Maths Question 6.
x² – x + 2 = 0
Solution.
We have, x² – x + 2 = 0
Comparing the given equation with the general form ax² + bx + c = 0, we get a = 1, b = -1, c = 2.
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 5

Ex 5.3 Class 11 Maths Question 7.
$\sqrt { 2 } { x }^{ 2 }+x+\sqrt { 2 } =0$
Solution.
We have, $\sqrt { 2 } { x }^{ 2 }+x+\sqrt { 2 } =0$
Comparing the given equation with the general form ax² + bx + c = 0, we get
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 6

Ex 5.3 Class 11 Maths Question 8.
$\sqrt { 3 } { x }^{ 2 }+\sqrt { 2 } x+3\sqrt { 3 } =0$
Solution.
We have, $\sqrt { 3 } { x }^{ 2 }+\sqrt { 2 } x+3\sqrt { 3 } =0$
Comparing the given equation with the general form ax² + bx + c = 0, we get
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 7

Ex 5.3 Class 11 Maths Question 9.
${ x }^{ 2 }+x+\frac { 1 }{ \sqrt { 2 } } =0$
Solution.
We have, ${ x }^{ 2 }+x+\frac { 1 }{ \sqrt { 2 } } =0$
Comparing the given equation with the general form ax² + bx + c = 0, we get
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 8

Ex 5.3 Class 11 Maths Question 10.
${ x }^{ 2 }+\frac { x }{ \sqrt { 2 } } +1=0$
Solution.
We have, ${ x }^{ 2 }+\frac { x }{ \sqrt { 2 } } +1=0$
Comparing the given equation with the general form ax² + bx + c = 0, we get
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 9

We hope the NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3, drop a comment below and we will get back to you at the earliest.

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Class 11th Chapter -4 Principle of Mathematical Induction | NCERT Maths Solution | NCERT Solution | Edugrown

In This Post we are providing Chapter – 4 Principle of Mathemarical Induction NCERT Solutions for Class 11 Maths which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These Class 11 Principle of Mathemarical Induction solutions can be really helpful in the preparation of Board exams and will provide you with in depth detail of the chapter.

We have solved every question stepwise so you don’t have to face difficulty in understanding the solutions. It will also give you concepts that are important for overall development of students. Class 11 Maths Principle of Mathemarical Induction NCERT Written Solutions will be useful in higher classes as well because variety of questions related to these concepts can be asked so you must study and understand them properly.

Class 11th Chapter 4 Principle of Mathemarical Induction| NCERT MATHS SOLUTION |

Chapter 4 Principle of Mathemarical Induction EX 4.1 NCERT Solutions

Prove the following by using the principle of mathematical induction for aline n ∈ N :
Ex 4.1 Class 11 Maths Question 1.
$1+{ 3 }^{ 2 }+{ 3 }^{ 3 }+cdot cdot cdot cdot cdot cdot cdot cdot +{ 3 }^{ n }=frac { left( { 3 }^{ n }-1 right) }{ 2 }$
Solution.
Let the given statement be P(n) i.e.,
P(n) : $1+{ 3 }^{ 2 }+{ 3 }^{ 3 }+cdot cdot cdot cdot cdot cdot cdot cdot +{ 3 }^{ n }=frac { left( { 3 }^{ n }-1 right) }{ 2 }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 1

Ex 4.1 Class 11 Maths Question 2.
${ 1 }^{ 3 }+{ 2 }^{ 3 }+{ 3 }^{ 3 }+cdot cdot cdot cdot cdot cdot cdot cdot +{ n }^{ 3 }={ left( frac { nleft( n+1 right) }{ 2 } right) }^{ 2 }$
Solution.
Let the given statement be P(n) i.e.,
P(n) : ${ 1 }^{ 3 }+{ 2 }^{ 3 }+{ 3 }^{ 3 }+cdot cdot cdot cdot cdot cdot cdot cdot +{ n }^{ 3 }={ left( frac { nleft( n+1 right) }{ 2 } right) }^{ 2 }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 3

Ex 4.1 Class 11 Maths Question 3.
$1+frac { 1 }{ left( 1+2 right) } +frac { 1 }{ left( 1+2+3 right) } +cdot cdot cdot cdot cdot cdot cdot cdot +frac { 1 }{ left( 1+2+3+cdot cdot cdot cdot cdot cdot cdot cdot +n right) } =frac { 2 }{ left( n+1 right) }$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $1+frac { 1 }{ left( 1+2 right) } +frac { 1 }{ left( 1+2+3 right) } +cdot cdot cdot cdot cdot cdot cdot cdot +frac { 1 }{ left( 1+2+3+.cdot cdot cdot cdot cdot cdot cdot cdot +n right) } =frac { 2 }{ left( n+1 right) }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 5

Ex 4.1 Class 11 Maths Question 4.
$1.2.3+2.3.4+cdot cdot cdot cdot cdot cdot cdot cdot +nleft( n+1 right) left( n+2 right) =frac { nleft( n+1 right) left( n+2 right) left( n+3 right) }{ 4 }$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $1.2.3+2.3.4+cdot cdot cdot cdot cdot cdot cdot cdot +nleft( n+1 right) left( n+2 right) =frac { nleft( n+1 right) left( n+2 right) left( n+3 right) }{ 4 }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 7

Ex 4.1 Class 11 Maths Question 5.
$1.3+{ 2.3 }^{ 2 }+{ 3.3 }^{ 3 }+cdot cdot cdot cdot cdot cdot cdot cdot +{ n.3 }^{ n }=frac { left( 2n-1 right) { 3 }^{ n+1 }+3 }{ 4 }$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $1.3+{ 2.3 }^{ 2 }+{ 3.3 }^{ 3 }+cdot cdot cdot cdot cdot cdot cdot cdot +{ n.3 }^{ n }=frac { left( 2n-1 right) { 3 }^{ n+1 }+3 }{ 4 }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 9

Ex 4.1 Class 11 Maths Question 6.
$1.2+2.3+3.4+cdot cdot cdot cdot cdot cdot cdot cdot +n.left( n+1 right) =left[ frac { nleft( n+1 right) left( n+2 right) }{ 3 } right]$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $1.2+2.3+3.4+cdot cdot cdot cdot cdot cdot cdot cdot +n.left( n+1 right) =left[ frac { nleft( n+1 right) left( n+2 right) }{ 3 } right]$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 11

Ex 4.1 Class 11 Maths Question 7.
$1.3+3.5+5.7+cdot cdot cdot cdot cdot cdot cdot cdot +left( 2n-1 right) left( 2n+1 right) =frac { nleft( { 4n }^{ 2 }+6n-1 right) }{ 3 }$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $1.3+3.5+5.7+cdot cdot cdot cdot cdot cdot cdot cdot +left( 2n-1 right) left( 2n+1 right) =frac { nleft( { 4n }^{ 2 }+6n-1 right) }{ 3 }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 13

Ex 4.1 Class 11 Maths Question 8.
$1.2+2.{ 2 }^{ 2 }+3.{ 2 }^{ 3 }+cdot cdot cdot cdot cdot cdot cdot cdot +n.{ 2 }^{ n }=left( n-1 right) { 2 }^{ n+1 }+2$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $1.2+2.{ 2 }^{ 2 }+3.{ 2 }^{ 3 }+cdot cdot cdot cdot cdot cdot cdot cdot +n.{ 2 }^{ n }=left( n-1 right) { 2 }^{ n+1 }+2$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 16

Ex 4.1 Class 11 Maths Question 9
$frac { 1 }{ 2 } +frac { 1 }{ 4 } +frac { 1 }{ 8 } +cdot cdot cdot cdot cdot cdot cdot cdot +frac { 1 }{ { 2 }^{ n } } =1-frac { 1 }{ { 2 }^{ n } }$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $frac { 1 }{ 2 } +frac { 1 }{ 4 } +frac { 1 }{ 8 } +cdot cdot cdot cdot cdot cdot cdot cdot +frac { 1 }{ { 2 }^{ n } } =1-frac { 1 }{ { 2 }^{ n } }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 17

Ex 4.1 Class 11 Maths Question 10.
$frac { 1 }{ 2.5 } +frac { 1 }{ 5.8 } +frac { 1 }{ 8.11 } +cdot cdot cdot cdot cdot cdot cdot cdot +frac { 1 }{ left( 3n-1 right) left( 3n+2 right) } =frac { n }{ left( 6n+4 right) }$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $frac { 1 }{ 2.5 } +frac { 1 }{ 5.8 } +frac { 1 }{ 8.11 } +cdot cdot cdot cdot cdot cdot cdot cdot +frac { 1 }{ left( 3n-1 right) left( 3n+2 right) } =frac { n }{ left( 6n+4 right) }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 19

Ex 4.1 Class 11 Maths Question 11.
$frac { 1 }{ 1.2.3 } +frac { 1 }{ 2.3.4 } +frac { 1 }{ 3.4.5 } +cdot cdot cdot cdot cdot cdot cdot cdot +frac { 1 }{ nleft( n+1 right) left( n+2 right) } =frac { nleft( n+3 right) }{ 4left( n+1 right) left( n+2 right) }$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $frac { 1 }{ 1.2.3 } +frac { 1 }{ 2.3.4 } +frac { 1 }{ 3.4.5 } +cdot cdot cdot cdot cdot cdot cdot cdot +frac { 1 }{ nleft( n+1 right) left( n+2 right) } =frac { nleft( n+3 right) }{ 4left( n+1 right) left( n+2 right) }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 21

Ex 4.1 Class 11 Maths Question 12.
$a+ar+{ ar }^{ 2 }+cdot cdot cdot cdot cdot cdot cdot cdot +{ ar }^{ n-1 }=frac { aleft( { r }^{ n }-1 right) }{ r-1 }$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $a+ar+{ ar }^{ 2 }+cdot cdot cdot cdot cdot cdot cdot cdot +{ ar }^{ n-1 }=frac { aleft( { r }^{ n }-1 right) }{ r-1 }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 24

Ex 4.1 Class 11 Maths Question 13.
$left( 1+frac { 3 }{ 1 } right) left( 1+frac { 5 }{ 4 } right) left( 1+frac { 7 }{ 9 } right) cdot cdot cdot cdot cdot cdot cdot cdot left( 1+frac { left( 2n+1 right) }{ { n }^{ 2 } } right) ={ left( n+1 right) }^{ 2 }$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $left( 1+frac { 3 }{ 1 } right) left( 1+frac { 5 }{ 4 } right) left( 1+frac { 7 }{ 9 } right) cdot cdot cdot cdot cdot cdot cdot cdot left( 1+frac { left( 2n+1 right) }{ { n }^{ 2 } } right) ={ left( n+1 right) }^{ 2 }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 26

Ex 4.1 Class 11 Maths Question 14.
$left( 1+frac { 1 }{ 1 } right) left( 1+frac { 1 }{ 2 } right) left( 1+frac { 1 }{ 3 } right) cdot cdot cdot cdot cdot cdot cdot cdot left( 1+frac { 1 }{ n } right) =left( n+1 right)$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $left( 1+frac { 1 }{ 1 } right) left( 1+frac { 1 }{ 2 } right) left( 1+frac { 1 }{ 3 } right) cdot cdot cdot cdot cdot cdot cdot cdot left( 1+frac { 1 }{ n } right) =left( n+1 right)$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 28

Ex 4.1 Class 11 Maths Question 15.
${ 1 }^{ 2 }+{ 3 }^{ 2 }+{ 5 }^{ 2 }+cdot cdot cdot cdot cdot cdot cdot cdot +{ left( 2n-1 right) }^{ 2 }=frac { nleft( 2n-1 right) left( 2n+1 right) }{ 3 }$
Solution.
Let the given statement be P(n), i.e.,
P(n) : ${ 1 }^{ 2 }+{ 3 }^{ 2 }+{ 5 }^{ 2 }+cdot cdot cdot cdot cdot cdot cdot cdot +{ left( 2n-1 right) }^{ 2 }=frac { nleft( 2n-1 right) left( 2n+1 right) }{ 3 }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 30

Ex 4.1 Class 11 Maths Question 16.
$frac { 1 }{ 1.4 } +frac { 1 }{ 4.7 } +frac { 1 }{ 7.10 } +cdot cdot cdot cdot cdot cdot cdot cdot +frac { 1 }{ left( 3n-2 right) left( 3n+1 right) } =frac { n }{ left( 3n+1 right) }$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $frac { 1 }{ 1.4 } +frac { 1 }{ 4.7 } +frac { 1 }{ 7.10 } +cdot cdot cdot cdot cdot cdot cdot cdot +frac { 1 }{ left( 3n-2 right) left( 3n+1 right) } =frac { n }{ left( 3n+1 right) }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 32

Ex 4.1 Class 11 Maths Question 17.
$frac { 1 }{ 3.5 } +frac { 1 }{ 5.7 } +frac { 1 }{ 7.9 } +cdot cdot cdot cdot cdot cdot cdot cdot +frac { 1 }{ left( 2n+1 right) left( 2n+3 right) } =frac { n }{ 3left( 2n+3 right) }$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $frac { 1 }{ 3.5 } +frac { 1 }{ 5.7 } +frac { 1 }{ 7.9 } +cdot cdot cdot cdot cdot cdot cdot cdot +frac { 1 }{ left( 2n+1 right) left( 2n+3 right) } =frac { n }{ 3left( 2n+3 right) }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 34

Ex 4.1 Class 11 Maths Question 18.
$1+2+3+cdot cdot cdot cdot cdot cdot cdot cdot +n<frac { 1 }{ 8 } { left( 2n+1 right) }^{ 2 }$
Solution.
Let the given statement be P(n), i.e.,
P(n) : $1+2+3+cdot cdot cdot cdot cdot cdot cdot cdot +n<frac { 1 }{ 8 } { left( 2n+1 right) }^{ 2 }$
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 36

Ex 4.1 Class 11 Maths Question 19.
n(n+1 )(n + 5) is a multiple of 3.
Solution.
Let the given statement be P(n), i.e.,
P(n): n(n + l)(n + 5) is a multiple of 3.
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 38

Ex 4.1 Class 11 Maths Question 20.
${ 10 }^{ 2n-1 }+1$ is divisible by 11.
Solution.
Let the given statement be P(n), i.e.,
P(n): ${ 10 }^{ 2n-1 }+1$ is divisible by 11
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 40

Ex 4.1 Class 11 Maths Question 21.
${ x }^{ 2n }-{ y }^{ 2n }$ is divisible by x + y.
Solution.
Let the given statement be P(n), i.e.,
P(n): ${ x }^{ 2n }-{ y }^{ 2n }$ is divisible by x + y.
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 41

Ex 4.1 Class 11 Maths Question 22.
${ 3 }^{ 2n+2 }-8n-9$ is divisible by 8.
Solution.
Let the given statement be P(n), i.e.,
P(n): ${ 3 }^{ 2n+2 }-8n-9$ is divisible by 8.
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 42

Ex 4.1 Class 11 Maths Question 23.
${ 41 }^{ n }-{ 14 }^{ n }$ is a multiple of 27.
Solution.
Let the given statement be P(n), i.e.,
P(n): ${ 41 }^{ n }-{ 14 }^{ n }$ is a multiple of 27.
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 43

Ex 4.1 Class 11 Maths Question 24.
$left( 2n+7 right) <{ left( n+3 right) }^{ 2 }$
Solution.
Let the given statement be P(n), i.e.,
P(n): $left( 2n+7 right) <{ left( n+3 right) }^{ 2 }$
First we prove that the statement is true for n = 1.
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction 44

We hope the NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction, drop a comment below and we will get back to you at the earliest.

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Class 11th Chapter -3 Trigonometric Functions | NCERT Maths Solution | NCERT Solution | Edugrown

In This Post we are providing Chapter -3 Trigonometric Fuctions NCERT Solutions for Class 11 Maths which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These Class 11 Trigonometric Fuctions solutions can be really helpful in the preparation of Board exams and will provide you with in depth detail of the chapter.

We have solved every question stepwise so you don’t have to face difficulty in understanding the solutions. It will also give you concepts that are important for overall development of students. Class 11 Maths Trigonometric Fuctions NCERT Written Solutions will be useful in higher classes as well because variety of questions related to these concepts can be asked so you must study and understand them properly.

Class 11th Chapter 3 Trigonometric Fuctions | NCERT MATHS SOLUTION |

Chapter 3 Trigonometric Fuctions EX 3.1 NCERT Solutions

Ex 3.1 Class 11 Maths Question 1.
Find the radian measures corresponding to the following degree measures:
(i) 25°
(ii) -47°30′
(iii) 240°
(iv) 520°
Solution.
We have, 180° = π Radians
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 1
Ex 3.1 Class 11 Maths Question 2.
Find the degree measures corresponding to the following radian measures $\left( Use\quad \pi =\frac { 22 }{ 7 } \right)$
(i) $\frac { 11 }{ 16 }$
(ii) -4
(iii) $\frac { 5\pi }{ 3 }$
(iv) $\frac { 7\pi }{ 6 }$
Solution.
We have π Radians = 180°
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 2

Ex 3.1 Class 11 Maths Question 3.
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second ?
Solution.
Number of revolutions made by wheel in one minute = 360
As we know that, 1 Revolution = 27 π Radians
∴ 360 Revolutions = 720 π Radians
∴ In 1 minute wheel can make = 720 π Radians
⇒ In 60 seconds wheel can make = 720 π Radians
⇒ In 1 second wheel can make
$\frac { 720\pi }{ 3 } Radians=12\pi \quad Radians$

Ex 3.1 Class 11 Maths Question 4.
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm $\left( Use\quad \pi =\frac { 22 }{ 7 } \right)$
Solution.
Let O be the centre and AB be the arc length of the circle.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 3

Ex 3.1 Class 11 Maths Question 5.
In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of Xhe chord.
Solution.
Let AB be the minor arc of the chord.
AB = 20 cm, OA = OB = 20 cm
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 4

Ex 3.1 Class 11 Maths Question 6.
If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their, radii.
Solution.
Let r₁ r₂ and θ₁, θ₂ be the radii and angles subtended at the centre of two circles respectively.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 5

Ex 3.1 Class 11 Maths Question 7.
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
(i) 10 cm
(ii) 15 cm
(iii) 21 cm
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 6

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Chapter 3 Trigonometric Fuctions EX 3.2 NCERT Solutions

Find the values of other five trigonometric functions in Exercises 1 to 5.
Ex 3.2 Class 11 Maths Question 1.
$\cos { x } =\frac { -1 }{ 2 }$ , x lies in third quadrant.
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 1

Ex 3.2 Class 11 Maths Question 2.
$\sin { x } =\frac { 3 }{ 5 }$ , x lies in second quadrant.
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 2

Ex 3.2 Class 11 Maths Question 3.
$\cot { x= } \frac { 3 }{ 4 }$ , xlies in third quadrant.
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 3

Ex 3.2 Class 11 Maths Question 4.
$\sec { x } =\frac { 13 }{ 5 }$ , x lies in fourth quadrant.
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 4

Ex 3.2 Class 11 Maths Question 5.
$\tan { x } =-\frac { 5 }{ 12 }$ , x lies in second quadrant.
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 4

Find the values of the trigonometric functions in Exercises 6 to 10.
Ex 3.2 Class 11 Maths Question 6.
sin 765°
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 5

Ex 3.2 Class 11 Maths Question 7.
cosec (-1410°)
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 6

Ex 3.2 Class 11 Maths Question 8.
$tan\quad \frac { 19\pi }{ 3 }$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 7

Ex 3.2 Class 11 Maths Question 9.
$sin\left( -\frac { 11\pi }{ 3 } \right)$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 8

Ex 3.2 Class 11 Maths Question 10.
$cot\left( -\frac { 15\pi }{ 4 } \right)$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 9

We hope the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2, drop a comment below and we will get back to you at the earliest.

Chapter 3 Trigonometric Fuctions EX 3.3 NCERT Solutions

Ex 3.3 Class 11 Maths Question 1.
Prove that: ${ sin }^{ 2 }\frac { \pi }{ 6 } +{ cos }^{ 2 }\frac { \pi }{ 3 } -{ tan }^{ 2 }\frac { \pi }{ 4 } =-\frac { 1 }{ 2 }$
Solution.
L.H.S. = ${ sin }^{ 2 }\frac { \pi }{ 6 } +{ cos }^{ 2 }\frac { \pi }{ 3 } -{ tan }^{ 2 }\frac { \pi }{ 4 } =-\frac { 1 }{ 2 }$
$=\left[ { \left( \frac { 1 }{ 2 } \right) }^{ 2 }+{ \left( \frac { 1 }{ 2 } \right) }^{ 2 }-{ \left( 1 \right) }^{ 2 } \right] =\frac { 1 }{ 4 } +\frac { 1 }{ 4 } -1=\frac { -1 }{ 2 } =\quad R.H.S.$

Ex 3.3 Class 11 Maths Question 2.
$2{ sin }^{ 2 }\frac { \pi }{ 6 } +{ cosec }^{ 2 }\frac { 7\pi }{ 6 } { cos }^{ 2 }\frac { \pi }{ 3 } =\frac { 3 }{ 2 }$
Solution.
L.H.S. = $2{ sin }^{ 2 }\frac { \pi }{ 6 } +{ cosec }^{ 2 }\frac { 7\pi }{ 6 } { cos }^{ 2 }\frac { \pi }{ 3 }$
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 1

Ex 3.3 Class 11 Maths Question 3.
${ cot }^{ 2 }\frac { \pi }{ 6 } +cosec\frac { 5\pi }{ 6 } +3{ tan }^{ 2 }\frac { \pi }{ 6 } =6$
Solution.
L.H.S. = ${ cot }^{ 2 }\frac { \pi }{ 6 } +cosec\frac { 5\pi }{ 6 } +3{ tan }^{ 2 }\frac { \pi }{ 6 }$
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 2

Ex 3.3 Class 11 Maths Question 4.
$2{ sin }^{ 2 }\frac { 3\pi }{ 4 } +2{ cos }^{ 2 }\frac { \pi }{ 4 } +2{ sec }^{ 2 }\frac { \pi }{ 3 } =10$
Solution.
L.H.S. = $2{ sin }^{ 2 }\frac { 3\pi }{ 4 } +2{ cos }^{ 2 }\frac { \pi }{ 4 } +2{ sec }^{ 2 }\frac { \pi }{ 3 }$
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 3

Ex 3.3 Class 11 Maths Question 5.
Find the value of:
(i) sin 75°
(ii) tan 15°
Solution.
(i) sin (75°) = sin (30° + 45°)
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 4

(ii) tan 15° = tan (45° – 30°)
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 5

Prove the following:
Ex 3.3 Class 11 Maths Question 6.
$cos\left( \frac { \pi }{ 4 } -x \right) cos\left( \frac { \pi }{ 4 } -y \right) -sin\left( \frac { \pi }{ 4 } -x \right) sin\left( \frac { \pi }{ 4 } -y \right)$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 6

Ex 3.3 Class 11 Maths Question 7.
$\frac { tan\left( \frac { \pi }{ 4 } +x \right) }{ tan\left( \frac { \pi }{ 4 } -x \right) } ={ \left( \frac { 1+tan\quad x }{ 1-tan\quad x } \right) }^{ 2 }$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 7

Ex 3.3 Class 11 Maths Question 8.
$\frac { cos\left( \pi +x \right) cos\left( -x \right) }{ sin\left( \pi -x \right) cos\left( \frac { \pi }{ 2 } +x \right) } ={ cot }^{ 2 }x$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 8

Ex 3.3 Class 11 Maths Question 9.
$cos\left( \frac { 3\pi }{ 2 } +x \right) cos\left( 2\pi +x \right) \left[ cot\left( \frac { 3\pi }{ 2 } -x \right) +cot\left( 2\pi +x \right) \right] =1$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 9

Ex 3.3 Class 11 Maths Question 10.
sin(n +1 )x sin(n + 2)x + cos(n +1 )x cos(n + 2)x = cosx
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 10

Ex 3.3 Class 11 Maths Question 11.
$cos\left( \frac { 3\pi }{ 4 } +x \right) -cos\left( \frac { 3\pi }{ 4 } -x \right) =-\sqrt { 2 } sinx$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 11

Ex 3.3 Class 11 Maths Question 12.
sin²6x – sin²4x= sin²x sin10x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 12

Ex 3.3 Class 11 Maths Question 13.
cos²2x – cos²6x = sin 4x sin 8x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 13

Ex 3.3 Class 11 Maths Question 14.
sin2x + 2 sin 4x + sin 6x = 4 cos² x sin 4x
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 14

Ex 3.3 Class 11 Maths Question 15.
cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 15

Ex 3.3 Class 11 Maths Question 16.
$\frac { cos9x-cos5x }{ sin17x-sin3x } =-\frac { sin2x }{ cos10x }$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 16

Ex 3.3 Class 11 Maths Question 17.
$\frac { sin5x+sin3x }{ cos5x+cos3x } =tan4x$
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 17

Ex 3.3 Class 11 Maths Question 18.
$\frac { sinx-siny }{ cosx+cosy } =tan\left( \frac { x-y }{ 2 } \right)$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 18

Ex 3.3 Class 11 Maths Question 19.
$\frac { sinx+sin3x }{ cosx+cos3x } =tan2x$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 19

Ex 3.3 Class 11 Maths Question 20.
$\frac { sinx-sin3x }{ { sin }^{ 2 }x-{ cos }^{ 2 }x } =2sinx$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 20

Ex 3.3 Class 11 Maths Question 21.
$\frac { cos4x+cos3x+cos2x }{ sin4x+sin3x+sin2x } =cot3x$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 21

Ex 3.3 Class 11 Maths Question 22.
cot x cot 2x – cot 2x cot 3x – cot3x cotx = 1
Solution.
We know that 3x = 2x + x.
Therefore,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 22

Ex 3.3 Class 11 Maths Question 23.
$tan4x=\frac { 4tanx\left( 1-{ tan }^{ 2 }x \right) }{ 1-6{ tan }^{ 2 }x+{ tan }^{ 4 }x }$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 23

Ex 3.3 Class 11 Maths Question 24.
cos 4x = 1 – 8 sin²x cos²x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 24

Ex 3.3 Class 11 Maths Question 25.
cos 6x = 32 cos6 x – 48 cos⁴x + 18 cos² x -1
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 25

We hope the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3, drop a comment below and we will get back to you at the earliest.

Chapter 3 Trigonometric Fuctions EX 3.4 NCERT Solutions

Find the principal and general solutions of the following equations:
Ex 3.4 Class 11 Maths Question 1.
$tanx=\sqrt { 3 }$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 1

Ex 3.4 Class 11 Maths Question 2.
sec x = 2
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 2

Ex 3.4 Class 11 Maths Question 3.
$cotx=-\sqrt { 3 }$
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 3

Ex 3.4 Class 11 Maths Question 4.
cosec x = -2
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 5

Find the general solution for each of the following equations:
Ex 3.4 Class 11 Maths Question 5.
cos 4x = cos 2x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 6

Ex 3.4 Class 11 Maths Question 6.
cos 3x + cos x – cos 2x=0
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 7

Ex 3.4 Class 11 Maths Question 7.
sin 2 x + cos x = 0
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 8

Ex 3.4 Class 11 Maths Question 8.
sec²2x = 1 – tan 2x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 9

Ex 3.4 Class 11 Maths Question 9.
sin x + sin 3x + sin 5x = 0
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 10

We hope the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4, drop a comment below and we will get back to you at the earliest.

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Class 11th Chapter -2 Relations and Functions | NCERT Maths Solution | NCERT Solution | Edugrown

In This Post we are providing Chapter 2 Relations and functions NCERT Solutions for Class 11 Maths which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These Class 11 Relations and functions solutions can be really helpful in the preparation of Board exams and will provide you with in depth detail of the chapter.

We have solved every question stepwise so you don’t have to face difficulty in understanding the solutions. It will also give you concepts that are important for overall development of students. Class 11 Maths Relations and functions NCERT Written Solutions will be useful in higher classes as well because variety of questions related to these concepts can be asked so you must study and understand them properly.

Class 11th Chapter 1 Relations and Functions | NCERT MATHS SOLUTION |

Chapter 1 - Relations and functions EX 2.1 NCERT Solutions

Ex 2.1 Class 11 Maths Question 1.
If $\left( \frac { x }{ 3 } +1,y-\frac { 2 }{ 3 } \right) =\left( \frac { 5 }{ 3 } ,\frac { 1 }{ 3 } \right)$ , find the values of x and y.
Solution.
Since the ordered pairs are equal. So, the corresponding elements are equal
∴ $\frac { x }{ 3 } +1=\frac { 5 }{ 3 }$ and $y-\frac { 2 }{ 3 } =\frac { 1 }{ 3 }$
⇒ $\frac { x }{ 3 } =\frac { 5 }{ 3 } -1$ and $y=\frac { 1 }{ 3 } +\frac { 2 }{ 3 }$ ⇒ x = 2 and y = 1.

Ex 2.1 Class 11 Maths Question 2.
If the set A has 3 elements and the set B {3, 4, 5}, then find the number of elements in (A x B).
Solution.
According to question, n(A) = 3 and n(B) = 3.
∴ n(A x B) = n(A) x n(B) = 3 x 3 = 9
∴ There are total 9 elements in (A x B).

Ex 2.1 Class 11 Maths Question 3.
If G = {7, 8} and H = {5, 4, 2}, find G x H and H x G.
Solution.
We have G = {7, 8} and H = {5, 4, 2} Then, by the definition of the cartesian product, we have
G x H = {(7, 5), (7, 4), (7, 2), (8, 5), (8, 4), (8, 2)}
H x G = {(5, 7), (5, 8), (4, 7), (4, 8), (2, 7), (2, 8)}.

Ex 2.1 Class 11 Maths Question 4.
State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.
(i) If P = {m, n} and Q = {n, m}, then P x Q = {(m, n), (n, m)}.
(ii) If A and B are non-empty sets, then Ax B is a non-empty set of ordered pairs (x, y) such
that x ∈ A and y ∈ B.
(iii) If A = {1, 2}, B = {3, 4}, then A x (B ∩φ) = φ
Solution.
(i) False, if P = {m, n} and Q = {n, m}
Then P x Q = {(m, n), (m, m), (n, n), (n, m)}.
(ii) True, by the definition of cartesian product.
(iii) True, We have A = {1, 2} and B = {3, 4}
Now, B ∩ φ = φ ∴ A x (B ∩ φ) = A x φ = φ.

Ex 2.1 Class 11 Maths Question 5.
If A = {-1, 1},find A x A x A.
Solution.
A = {-1, 1}
Then, A x A = {-1, 1} x {-1, 1} = {(-1, -1), (-1,1),(1,-1), (1,1)}
A x A x A = ((-1,-1),(-1,1),(1,-1),(1,1)} x {-1,1}
= {(-1, -1, -1), (-1, -1, 1), (-1, 1, -1), (-1, 1,1), (1, -1, -1), (1, -1,1), (1,1,-1), (1,1,1)}

Ex 2.1 Class 11 Maths Question 6.
If A x B = {(a, x), (a, y), (b, x), (b, y)}. Find A and B.
Solution.
Given, A x B = {(a, x), (a, y), (b, x), (b, y)}
If {p, q) ∈ A x B, then p ∈ A and q ∈ B
∴ A = {a, b} and B = {x, y}.

Ex 2.1 Class 11 Maths Question 7.
Let A = {1, 2}, B = (1, 2, 3, 4), C = {5, 6} and D = {5, 6, 7, 8}. Verify that
(i) A x (B ∩ C = (A x B) ∩ (AxC)
(ii) A x C is a subset of B x D.
Solution.
Given, A = {1, 2}, B ={1, 2, 3, 4}, C = {5, 6}, D = (5, 6, 7, 8}
NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Ex 2.1 1

Ex 2.1 Class 11 Maths Question 8.
Let A = {1, 2} and B = {3, 4}. Write 4 x B. How many subsets will 4 x B have? List them.
Solution.
Given, A = {1, 2} and B = {3, 4}
Then, A x B = {(1, 3), (1,4), (2, 3), (2, 4)}
i. e., A x B has 4 elements. So, it has 2⁴ i.e. 16 subsets.
The subsets of A x B are as follows :
φ, {(1, 3)1, ((1, 4)), {(2, 3)|, {(2, 4)}, {(1, 3), (1,4)}, {(1,3), (2,3)},{(1,3), (2,4)), ((1,4), (2,3)},
{(1, 4), (2, 4)},{(2, 3), (2, 4)},{(1, 3), (1, 4), (2, 3)}, {(1, 3), (1, 4), (2, 4)}, {(1, 4), (2, 3), (2,4)},{(1, 3), (2, 3), (2, 4)}, {(1, 3), (1, 4), (2, 3), (2,4)}.

Ex 2.1 Class 11 Maths Question 9.
Let A and B be two sets such that n (A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A x B, find A and B, where x, y and z are distinct elements.
Solution.
Given, n(A) = 3 and n(B) = 2
Now (x, 1) ∈ A x B ⇒ x ∈ A and 1 ∈ B,
(y, 2) ∈ A x B ⇒ y ∈ A and 2 ∈ B
(z, 1) ∈ A x B ⇒z ∈ A and 1 ∈ B
∴ x, y, z ∈ A and 1, 2 ∈ B
Hence, A = {x, y, z} and B = {1, 2}.

Ex 2.1 Class 11 Maths Question 10.
The Cartesian product 4×4 has 9 elements among which are found (-1, 0) and (0, 1). Find the set 4 and the remaining elements of 4 x 4.
Solution.
Since, we have n(A x A) = 9
⇒ n(A) x n(A) = 9 [ ∵ n (A x B) = n(A) x n(B)]
⇒ (n(A))² = 9 ⇒ n(A) = 3
Also, given (-1, 0) ∈ A x A ⇒ -1, 0 ∈ A ,
and (0,1) ∈ A x A ⇒ 0, 1 ∈ A
∴ -1, 0,1 ∈ A
Hence, A = {-1, 0, 1} (∵ n(A) = 3)
and the remaining elements of A x A are (-1, -1), (-1,1), (0, -1), (0,0), (1, -1), (1,0), (1,1).

We hope the NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Ex 2.1 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Ex 2.1, drop a comment below and we will get back to you at the earliest.

Chapter 1 - Relations and functions EX 2.2 NCERT Solutions

Ex 2.2 Class 11 Maths Question 1.
Let 4 = {1,2,3, ,14}. Define a relation R from A to A by R = {(x,y): 3x – y = 0, where x, y ∈ 4}.
Write down its domain, codomain and range.
Solution.
We have A = (1, 2, 3,……..,14)
Given relation R = {(x, y) : 3x – y = 0, where x, y ∈ A}
= {(x, y): y = 3x, where x, y ∈ A)
= {(x, 3x), where x, 3x ∈ A}
= {(1, 3), (2, 6), (3, 9), (4,12)}
[∵ 1 ≤ 3x ≤ 14, ∴ $\frac { 1 }{ 3 } \le x\le \frac { 14 }{ 3 }$ ⇒ x = 1, 2, 3, 4 ]
Domain of R = {1, 2, 3, 4}
Codomain of R = {1, 2,……, 14}
Range of R = {3, 6, 9, 12}.

Ex 2.2 Class 11 Maths Question 2.
Define a relation R on the set N of natural numbers by R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ∈ N}. Depict this relationship using roster form. Write down the domain and the range.
Solution.
Given relation R = {(x, y): y = x + 5, x < 4 and x, y ∈ N)
= {(x, y): y = x + 5, x ∈ (1, 2, 3) & y ∈ N}
= {(x, x + 5): x = 1, 2, 3}
Thus, R = {(1, 6), (2, 7), (3, 8)}.
Domain of R = {1, 2, 3}, Range of R = {6, 7, 8}.

Ex 2.2 Class 11 Maths Question 3.
A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ 4, y ∈B}. Write R in roster form.
Solution.
We have, A = {1, 2, 3, 5} and B = {4, 6, 9} R = {(x, y): difference between x and y is odd;
x ∈ A, y ∈B}
= {(x, y): y – x = odd; x ∈ A, y ∈ B}
Hence R = {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)}.

Ex 2.2 Class 11 Maths Question 4.
The figure shows a relationship between the sets P and Q. Write this relation
(i) in set-builder form
(ii) roster form.
What is its domain and range?
NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Ex 2.2 1
Solution.
(i) Its set builder form is
R = {(x, y): x – y = 2; x ∈ P, y ∈ Q}
i.e., R = {(x, y): y = x – 2 for x = 5, 6, 7)}

(ii) Roster form is R = {(5, 3), (6, 4), (7, 5)}
Domain of R = {5, 6, 7} = P,
Range of R = {3, 4, 5} = Q.

Ex 2.2 Class 11 Maths Question 5.
Let A = {1,2,3,4,6}. Let R be the relation on A defined by {(a, b): a, b ∈ A, b is exactly divisible by a}.
(i) Write R in roster form
(ii) Find the domain of R
(iii) Find the range of R?.
Solution.
Given A = {1, 2, 3, 4, 6}
Given relation is R = {(a, b):a,b ∈ A, b is exactly divisible by a}
(i) Roster form of R = {(1,1), (1,2), (1,3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6) (4, 4), (6, 6)}.
(ii) Domain of R = {1, 2, 3, 4, 6} = A.
(iii) Range of R = {1, 2, 3, 4, 6} = A.

Ex 2.2 Class 11 Maths Question 6.
Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.
Solution.
Given relation is R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5)}
= {(0, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5,10)}
∴Domain of R = {0,1, 2, 3, 4, 5} and
Range of R = {5, 6, 7, 8, 9, 10}.

Ex 2.2 Class 11 Maths Question 7.
Write the relation R = {(x, x³): x is a prime number less than 10} in roster form.
Solution.
Given relation is R = {(x, x³): x is a prime number less than 10)
= {(x, x³): x ∈ {2, 3, 5, 7}}
= {(2, 23), (3, 33), (5, 53), (7, 73)}
= {(2, 8), (3, 27), (5, 125), (7, 343)}.

Ex 2.2 Class 11 Maths Question 8.
Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.
Solution.
Given A = {x, y, z} and B = {1, 2}
∴ n(A) = 3 & n(B) = 2
Since n(A x B) = n(A) x n(B)
∴ n(A x B) = 3 x 2 = 6
Number of relations from A to B is equal to the number of subsets of A x B.
Since A x B contains 6 elements.
⇒ Number of subsets of A x B = 2⁶ = 64
So, there are 64 relations from A to B.

Ex 2.2 Class 11 Maths Question 9.
Let R be the relation on Z defined by R = {{a, b): a, b ∈ Z, a – b is an integer}. Find the domain and range of R.
Solution.
Given relation is R = {(a, b): a, b ∈ Z, a – b is an integer}
If a, b ∈ Z, then a- b ∈ Z ⇒ Every ordered pair of integers is contained in R.
R = {(a, b) :a,b ∈ Z}
So, Range of R = Domain of R = Z.

We hope the NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Ex 2.2 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Ex 2.2, drop a comment below and we will get back to you at the earliest.

Chapter 1 - Relations and functions EX 2.3 NCERT Solutions

Ex 2.3 Class 11 Maths Question 1.
Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.
(i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
(ii) {{2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
(iii) {(1, 3), (1, 5), (2, 5)}.
Solution.
(i) We have a relation R = {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} Since 2, 5, 8, 11, 14, 17 are the elements of domain of R having their unique images.
∴ The given relation is a function.
Hence domain = {2, 5, 8, 11, 14, 17) and Range = {1}.

(ii) We have a relation
R = {(2,1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
Since 2, 4, 6, 8, 10, 12, 14 are the elements of domain of R having their unique images.
∴ The given relation is a function.
Hence domain = {2, 4, 6, 8, 10, 12, 14} and Range = {1, 2, 3, 4, 5, 6, 7}.

(iii) We have a relation R = {(1, 3), (1, 5), (2, 5)}
Since the distinct ordered pairs (1, 3) and (1, 5) have same first element i.e., 1 does not have a unique image under R.
∴ It is not a function.

Ex 2.3 Class 11 Maths Question 2.
Find the domain and range of the following real functions:
(i) f(x) = $-\left| x \right|$
(ii) f(x) = $\sqrt { 9-{ x }^{ 2 } }$
Solution.
NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Ex 2.3 1

Ex 2.3 Class 11 Maths Question 3.
A function f is defined by f (x) = 2x – 5. Write down the values of
(i) f (0)
(ii) f (7)
(iii) f (-3)
Solution.
We are given f (x) = 2x – 5
(i) f (0) = 2(0) – 5 = 0- 5 = -5
(ii) f (7) = 2(7) – 5 = 14- 5 = 9
(iii) f (-3) = 2(-3) – 5 = -6 – 5 = -11.

Ex 2.3 Class 11 Maths Question 4.
The function T which maps temperature in degree Celsius into temperature in degree by
$t(C)=\frac { 9C }{ 5 } +32$
Find
(i) t (0)
(ii) t (28)
(iii) t (-10)
(iv) The value of C, when t (C = 212
Solution.
NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Ex 2.3 2
Ex 2.3 Class 11 Maths Question 5.
Find the range of each of the following functions.
(i) f(x) = 2 – 3x, x ∈ R, x>0.
(ii) f(x)=x²+ 2, x is a real number.
(iii) f (x) = x, x is a real number.
Solution.
(i) Given f (x) = 2 – 3x, x ∈ R, x > 0
∵ x > 0 ⇒ -3x < 0 ⇒ 2 – 3x < 2 + 0 ⇒ f (x) < 2
∴ The range of f (x) is (-2).

(ii) Given f (x) = x² + 2, x is a real number
We know x²≥ 0 ⇒ x² + 2 ≥ 0 + 2
⇒ x² + 2 > 2 ∴ f (x) ≥ 2
∴ The range of f (x) is [2, ∞).

(iii) Given f (x) = x, x is a real number.
Let y =f (x) = x ⇒ y = x
∴ Range of f (x) = Domain of f (x)
∴ Range of f (x) is R.

We hope the NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Ex 2.3 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Ex 2.3, drop a comment below and we will get back to you at the earliest.

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NCERT MCQ CLASS 9 CHAPTER – 8 | QUADRILATERALS | EDUGROWN

NCERT MCQ ON QUADRILATERALS

Question 1.

Three angles of a quadrilateral are 75°, 90°and 75°, the fourth angle is
(a) 90°
(b) 95°
(c) 105°
(d) 120°

Answer: (d) 120°

Question 2.

A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is
(a) 55°
(b) 50°
(c) 40°
(d) 25°

Answer: (b) 50°

Question 3.

ABCD is a rhombus such that ∠ACB = 40°, then ∠ADB is
(a) 40°
(b) 45°
(c) 50°
(d) 60°

Answer: (c) 50°

Question 4.

If angles A, B, C and D of a quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4, then ABCD is a
(a) rhombus
(b) parallelogram
(c) trapezium
(d) kite.

Answer: (c) trapezium

Question 5.

The diagonals AC and BD of a || gm ABCD intersect each other at the point O. If ∠DAC = 32° and ∠AOB = 70°, then ∠DBC is equal to
(a) 24°
(b) 86°
(c) 38°
(d) 32°

Answer: (c) 38°

Question 6.

ABCD is a rhombus such that ∠ABC = 40°, then ∠ADC is equal to
(a) 40°
(b) 45°
(c) 50°
(d) 20°

Answer: (a) 40°

Question 7.

In the following figure, ABCD and AEFG are two parallelograms. If ∠C = 60°, then ∠GFE is
MCQ Questions for Class 9 Maths Chapter 8 Quadrilaterals with Answers
(a) 30°
(b) 60°
(c) 90°
(d) 120°

Answer: (b) 60°

Question 8.

The bisectors of any two adjacent angles of a || gm intersect at
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: (d) 90°

Question 9.

If one angle of a parallelogram is 24° less than twice the smallest angle, then the measure of the largest angle of a parallelogram is
(a) 176°
(b) 68°
(c) 112°
(d) 102°

Answer: (c) 112°

Question 10.

If the diagonal of a rhombus are 18 cm and 24 cm respectively, then its side is equal to
(a) 16 cm
(b) 15 cm
(c) 20 cm
(d) 17 cm

Answer: (b) 15 cm

Question 11.

In the given figure, ABCD is a parallelogram. Find the value of x.
MCQ Questions for Class 9 Maths Chapter 8 Quadrilaterals with Answers
(a) 25°
(b) 60°
(c) 75°
(d) 45°

Answer: (d) 45°

Question 12 .

1. The quadrilateral whose all its sides are equal and angles are equal to 90 degrees, it is called:
a. Rectangle
b. Square
c. Kite
d. Parallelogram

Answer: (b) square

Question 13.

The sum of all the angles of a quadrilateral is equal to:
a. 180°
b. 270°
c. 360°
d. 90°

Answer: (c) 360°

Question 14.

A trapezium has:
a. One pair of opposite sides parallel
b. Two pair of opposite sides parallel to each other
c. All its sides are equal
d. All angles are equal

Answer: (a) One pair of opposite sides parallel

Question 15.

A rhombus can be a:
a. Parallelogram
b. Trapezium
c. Kite
d. Square

Answer: (d) Square

NCERT | CLASS 11 Recording of Transactions – I | IMPORTANT QUESTIONS

Question 1 : What is the purpose of posting J.F numbers that are entered in the journal at the time entries are posted to the accounts?

ANSWER:

Question 2 : Describe how debits and credits are used to analyse transactions.

ANSWER:

Question 3 : Differentiate between source documents and vouchers.

ANSWER :

Question 4:

Question 7 :

ANSWER:

Question 8:

ANSWER:

NCERT | CLASS 11 Theory Base of Accounting | IMPORTANT QUESTIONS

Question 1: What is matching concept? Why should a business concern follow this concept? Discuss?

ANSWER:

Question 4 : What is the money measurement concept? Which one factor can make it difficult to compare the monetary values of one year with the monetary values of another year?

ANSWER:

NCERT MCQ CLASS-9 CHAPTER-10 | CIRCLES | EDUGROWN

NCERT MCQ CLASS-9 CHAPTER-9 | AREAS OF PARALLELOGRAM AND TRIANGLES | EDUGROWN

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NCERT | CLASS 11 ACCOUNTANCY | IMPORTANT QUESTIONS

Question 2: What is accounting? Define its objectives.

ANSWER:

Question 3: What do you mean by an asset and what are different types of assets?

ANSWER:

Question 7:

ANSWER:

Class 11th Chapter – 5 Complex Numbers and Quadratic Equations | NCERT Maths Solution | NCERT Solution | Edugrown

Class 11th Chapter 5 Complex Numbers and Quadratic Equations| NCERT MATHS SOLUTION |

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Class 11th Chapter 1 Relations and Functions | NCERT MATHS SOLUTION |

NCERT MCQ CLASS 9 CHAPTER – 8 | QUADRILATERALS | EDUGROWN

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Question 1 : What is the purpose of posting J.F numbers that are entered in the journal at the time entries are posted to the accounts?

ANSWER:

Question 2 : Describe how debits and credits are used to analyse transactions.

ANSWER:

Question 3 : Differentiate between source documents and vouchers.

ANSWER :

Question 4:

Question 7 :

ANSWER:

Question 8:

ANSWER:

Question 1: What is matching concept? Why should a business concern follow this concept? Discuss?

ANSWER:

Question 4 : What is the money measurement concept? Which one factor can make it difficult to compare the monetary values of one year with the monetary values of another year?

ANSWER:

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Question 2: What is accounting? Define its objectives.

ANSWER:

Question 3: What do you mean by an asset and what are different types of assets?

ANSWER:

Question 7:

ANSWER:

Class 11th Chapter 5 Complex Numbers and Quadratic Equations| NCERT MATHS SOLUTION |

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Class 11th Chapter 3 Trigonometric Fuctions | NCERT MATHS SOLUTION |

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