Author name: Prasanna

Students who are searching for NCERT MCQ Questions for Class 12 Business Studies Chapter 8 Controlling with Answers Pdf free download are compiled here to get good practice on all fundamentals. Know your preparation level on MCQ Questions for Class 12 Business Studies with Answers. You can also verify your answers from our provided Controlling Class 12 MCQs Questions with Answers. So, ace up your preparation with MCQ on Controlling Class 12 Objective Questions.

Controlling Class 12 MCQs Questions with Answers

Question 1.
Which of the following is not applicable to responsibility accounting
(a) Accounting centre
(b) Cost centre
(c) Profit centre
(d) Investment centre

Answer

Answer: (a) Accounting centre

---

Question 2.
Management control is done by the __________________
(a) Managers at Top Level
(b) Managers at Middle Level
(c) Managers at Lower Level
(d) All of the above

Answer

Answer: (d) All of the above

---

Question 3.
What will be the corrective action for defective machinery?
(a) Sell at the book value
(b) Sell at a loss
(c) Sell at a profit
(d) Repair or Replace the machine

Answer

Answer: (d) Repair or Replace the machine

---

Question 4.
Which of the following is not a technique of controlling?
(a) Break-even analysis
(b) Budget
(c) Managerial Audit
(d) Cash Flow Statement

Answer

Answer: (d) Cash Flow Statement

---

Question 5.
Technological up-gradation is the best corrective action in case of _________
(a) Defective machinery
(b) Defective material
(c) Obsolete Machinery
(d) None of the above

Answer

Answer: (c) Obsolete Machinery

---

Question 6.
What will be the corrective action for defective material?
(a) Change in Quantity
(b) Change in Price
(c) Change in Quality Specifications for the material used
(d) None of the above

Answer

Answer: (c) Change in Quality Specifications for the material used

---

Question 7.
An efficient control system helps to
(a) Judges accuracy of standards
(b) Accomplishes organisational objectives
(c) Boosts employee morale
(d) All of the above

Answer

Answer: (d) All of the above

---

Question 8.
Controlling is __________ aspect of management.
(a) Physical
(b) Practical
(c) Mental
(d) Theoretical

Answer

Answer: (b) Practical

---

Question 9.
What is the last step in the controlling process?
(a) Setting Performance Standards
(b) Taking corrective action
(c) Comparing actual performance with standards
(d) Measurement of actual performance

Answer

Answer: (b) Taking corrective action

---

Question 10.
Why actual performance is compared with standards?
(a) To take corrective action
(b) To improve the quality of material
(c) To change the machinery
(d) None of the above

Answer

Answer: (a) To take corrective action

---

Question 11.
Controlling is _______________
(a) Economical
(b) Costly
(c) Free
(d) Very Cheap

Answer

Answer: (b) Costly

---

Question 12.
Which of the following is a limitation of controlling?
(a) Controlling improves employee motivation
(b) Controlling is goal-oriented
(c) Controlling is expensive
(d) Controlling ensures order and discipline

Answer

Answer: (c) Controlling is expensive

---

Question 13.
The main focus of controlling is on ________________
(a) Competition
(b) External Forces
(c) Results
(d) Business Environment

Answer

Answer: (c) Results

---

Question 14.
Management audit is a technique to keep a check on the performance of
(a) Company
(b) Management of the company
(c) Shareholders
(d) Customers

Answer

Answer: (b) Management of the company

---

Question 15.
When actual performance is better than the standard performance it is called _____
(a) Negative Deviation
(b) Poor Deviation
(c) Positive Deviation
(d) None of the above

Answer

Answer: (c) Positive Deviation

---

Question 16.
Controlling is necessary for ____________
(a) Medium Level Enterprise
(b) Small Scale Enterprise
(c) Large Scale Enterprise
(d) All of the above

Answer

Answer: (d) All of the above

---

Question 17.
There is one popular saying that Planning is looking _________ while controlling is looking ________
(a) Back, Ahead
(b) Ahead, Back
(c) Future, Present
(d) None of the above

Answer

Answer: (b) Ahead, Back

---

Question 18.
Budgetary control requires the preparation of
(a) Budgets
(b) Network diagram
(c) Responsibility Centres
(d) Training schedule

Answer

Answer: (a) Budgets

---

Question 19.
Which of the following is not correct?
(a) Controlling is goal-oriented
(b) Controlling is a pervasive function
(c) Controlling can prevent deviation
(d) Controlling ensures order and discipline

Answer

Answer: (c) Controlling can prevent deviation

---

Question 20.
What is the first step in the controlling process?
(a) Comparing actual performance with standards
(b) Analysing deviations
(c) Setting performance standards
(d) Measurement of actual performance

Answer

Answer: (c) Setting performance standards

---

Question 21.
What are the techniques of measurement of performance?
(a) Performance reports
(b) Sample Checking
(c) Personal Observation
(d) All of the above

Answer

Answer: (d) All of the above

---

Question 22.
Which of the following is a technique of controlling?
(a) Managerial Audit
(b) Break-even analysis
(c) Budget
(d) All of the above

Answer

Answer: (d) All of the above

---

Question 23.
The controlling function of an organisation is
(a) Forward as well as backward looking
(b) Backward looking
(c) Forward-looking
(d) None of the above

Answer

Answer: (a) Forward as well as backward-looking

---

Use the above-provided NCERT MCQ Questions for Class 12 Business Studies Chapter 8 Controlling with Answers Pdf free download and get a good grip on the fundamentals. Need any support from our end during the preparation of CBSE Class 12 Business Studies Controlling MCQs Multiple Choice Questions with Answers then leave your comments below. We’ll revert back to you soon.

Students are advised to practice the NCERT MCQ Questions for Class 11 Biology Chapter 5 Morphology of Flowering Plants with Answers Pdf free download is available here. MCQ Questions for Class 11 Biology with Answers are prepared as per the Latest Exam Pattern. Students can solve these Morphology of Flowering Plants Class 11 MCQs Questions with Answers and assess their preparation level.

Morphology of Flowering Plants Class 11 MCQs Questions with Answers

Solving the Morphology of Flowering Plants Multiple Choice Questions of Class 11 Biology Chapter 5 MCQ can be of extreme help as you will be aware of all the concepts. These MCQ Questions on Morphology of Flowering Plants Class 11 with answers pave for a quick revision of the Chapter thereby helping you to enhance subject knowledge. Have a glance at the MCQ of Chapter 5 Biology Class 11 and cross-check your answers during preparation.

I. Select the correct answer from the following questions:

Question 1.
Which one of the following is not a characteristic of root?
(a) Absence of buds
(b) Presence of chlorophyll
(c) Presence of root cap
(d) Presence of Unicellular hair

Answer

Answer: (b) Presence of chlorophyll

---

Question 2.
Roots that grow from any part of the plant body other than the radicle are called
(a) Tap roots
(b) Adventitious roots
(c) Modified roots
(d) Aerial roots

Answer

Answer: (b) Adventitious roots.

---

Question 3.
The place on stem or branch form where one or more leaves arise is called
(a) Apex
(b) Bud
(c) Internode
(d) Node

Answer

Answer: (d) Node

---

Question 4.
Which one of the following underground, fleshy structure is a stem?
(a) Carrot
(b) Potato
(c) Turnip
(d) Sweet Potato

Answer

Answer: (b) Potato

---

Question 5.
Phyllode is a modification of
(a) Root
(b) Flower
(c) Petiole
(d) Bud

Answer

Answer: (c) Petiole

---

Question 6.
Potato tubers are formed at the tips of
(a) Primary roots
(b) Adventitious roots
(c) Petiole
(d) Stolons

Answer

Answer: (d) Stolons

---

Question 7.
Mesocarp and endocarp is the edible part of the fruit of
(a) Apple
(b) Mango
(c) Banana
(d) Litchi

Answer

Answer: (c) Banana

---

Question 8.
Drupe is recognised by
(a) Stomy mesocarp
(b) Fleshy seed coat
(c) Thin seed coat
(d) Stony endocarp

Answer

Answer: (d) Stony endocarp

---

Question 9.
What do you eat in coconut?
(a) Mesocarp
(b) Fruit wall
(c) Entire seed
(d) Embryo

Answer

Answer: (c) Entire seed

---

Question 10.
The positions of shoot apex in monocot embryo is
(a) Lateral
(b) Basal
(c) Sub-terminal
(d) Terminal

Answer

Answer: (a) Lateral

---

Question 11.
In which one of the following plants the oil is stored in endosperm
(a) Coconut
(b) Ground nut
(c) Seasame
(d) Soyabean

Answer

Answer: (a) Coconut

---

Question 12.
In maize, the flower are
(a) Bisexual
(b) Unisexual but on the same plant
(c) Absent
(d) Unisexual but on different plants

Answer

Answer: (b) Unisexual but on the same plant

---

Question 13.
Epipetalous is condition of
(a) Aestivation of petal
(b) Placentation
(c) Stamens
(d) Position of ovary

Answer

Answer: (c) Stamens

---

Question 14.
A characteristic of angiosperm is
(a) Flower
(b) Root
(c) Seed
(d) All of these

Answer

Answer: (d) All of these

---

Question 15.
An aspect of flower shown in floral formula but not in floral diagram is
(a) Aestivation
(b) Floral symmestry
(c) Position of ovary
(d) Cohesion of floral parts

Answer

Answer: (c) Position of ovary

---

Question 16.
In grass and banyan tree these are roots arising from parts of the plant other than the radicle, these are called
(a) Adventitious roots
(b) Fibrous root system
(c) Tap root system
(d) Tertiary root system

Answer

Answer: (a) Adventitious roots

---

Question 17.
In some leguminous plants the leaf base may become swollen, which is called the
(a) Pulvinus
(b) Lamina
(c) Petiole
(d) Leaf base

Answer

Answer: (a) Pulvinus

---

Question 18.
The arrangement of flowers on the floral axis is termed as
(a) Inflorescence
(b) racemose
(c) cymose
(d) thalamus

Answer

Answer: (a) Inflorescence.

---

Question 19.
When the floral appendages are in multiple of 3,4 or 5 respec¬tively, a flower may be
(a) Trimerous
(b) Teramerous
(c) Pentamerous
(d) All of these types

Answer

Answer: (d) All of these types

---

Question 20.
A sterile stamen is called
(a) Staminode
(b) Stigma
(c) Apocarpous
(d) Syncarpous

Answer

Answer: (a) Staminode

---

II. Fill in the blanks

Question 1.
Solanaceae is a large family, commonly called as the ‘…………’

Answer

Answer: Potato family

---

Question 2.
Fabaceae family was earlier called ……………, a sub family of family …………….

Answer

Answer: Papilonoideae, Leguminosae

---

Question 3.
The following floral formula represents the …………… (Family: Brassicaceae)

Answer

Answer: mustard plant

---

Question 4.
In the floral formula, ‘K’ for …………. ‘P’ for ………….. ‘A’ for ……………

Answer

Answer: calyx, perianth, androecium

---

Question 5.
The outer covering of endosperm separates the embryo by a layer called …………..

Answer

Answer: aleurone layer

---

Question 6.
The embryo consists of one large and shield shaped cotyledon known as …………. and a short axis with a …………… and a radicle

Answer

Answer: scutellum, Plumule

---

Question 7.
Above the hilum, is a small pore called the …………..

Answer

Answer: Micropyle

---

Question 8.
If a fruit is formed without fertilisation of the ovary, it ……………

Answer

Answer: Parthenocarpic fruit.

---

Question 9.
The calyx is the outer most whorl of the flower and members are called ……………

Answer

Answer: Sepals

---

Question 10.
If gynoecium is situated in the centre and other parts of the flower are located on the rim of the thalamus almost at the same level, it is called ……………

Answer

Answer: Perigynous

---

Question 11.
Flowers with bracts, reduced, leaf found in flower are called …………. and those without bracts, ……………

Answer

Answer: bracteate, ebracteate.

---

Question 12.
In symmetry, the flower may be ……………. or ……………

Answer

Answer: actinomorphic (regular), zymomorphic (bilateral)

---

Question 13.
A flower having only stamens or carpel is ………….

Answer

Answer: unisexual

---

Question 14.
………….. is the pattern of arrangement of leaves on the stem or branch.

Answer

Answer: Phvllotaxy

---

Question 15.
When the incisions of the lamina reach up to the midrib breaking it into a number of leaflets, the leaf is called ………….

Answer

Answer: compound

---

III. Mark the statements True (T) or False (F):

Question 1.
The study of external features of plants is known as external morpholgy and that of internal features as anatomy.

Answer

Answer: True

---

Question 2.
The knowledge of external morpholgy of flowering plants is not essential for the study of all branches of botany.

Answer

Answer: False

---

Question 3.
The root is covered at the apex by a thimble-like structure called the not cap

Answer

Answer: True

---

Question 4.
A few millimetre above the root cap is the region of meristematic activity.

Answer

Answer: True

---

Question 5.
Tap roots of carrot, turnip and adventitious roots of sweet potato, get swollen and store food.

Answer

Answer: True

---

Question 6.
The main function of the stem is spreading out branches bearing leaves, flowers and fruits. It conducts water, minerals and photosynthates.

Answer

Answer: True

---

Question 7.
Underground stems of potato, ginger, turmeric, zaminkand modify to store food in them.

Answer

Answer: True

---

Question 8.
A typical leaf consists of three main parts: Leaf base, petiole and lamina.

Answer

Answer: True

---

Question 9.
In some leguminous plants the leafbase may become swollen, which is called the pulvinus.

Answer

Answer: True

---

Question 10.
The lamina or the leaf blade is the green expanded part of the leaf with veins and veinlets.

Answer

Answer: True

---

Question 11.
Veins provide rigidity to the leaf blade and act as channels of transport for water, minerals and food materials.

Answer

Answer: True

---

Question 12.
Leaves are often modified to perform functions other than photosynthesis. They are converted into tendrils for climbing as in peas, or into spines for defence as in cacti.

Answer

Answer: True

---

Question 13.
Calyx and corolla are accessory organs, while androecium and gynoecium are reproductive organs.

Answer

Answer: True

---

Question 14.
When a flower has both androecium and gynoecium, it is termed as bisexual.

Answer

Answer: True

---

Question 15.
A flower is asymmetric or irregular, if it cannot be divided into similar halves by any vertical plane passing through the centre as in canna.

Answer

Answer: True

---

IV. Match the items of Column I

Answer

Answer:
(a) → 4
(b) → 15
(c) →13
(d) → 14
(e) → 1
(f) → 3
(g) → 2
(h) → 5
(i) → 6
(j) → 7
(k) → 8
(l) → 9
(m) → 10
(n) → 11
(o) → 12

---

Hope the information shared regarding the NCERT MCQ Questions for Class 11 Biology Chapter 5 Morphology of Flowering Plants with Answers Pdf free download is true and genuine as far as our knowledge is concerned. If you feel any information regarding CBSE Class 11 Biology Morphology of Flowering Plants MCQs Multiple Choice Questions with Answers is missing do reach us and we will look into it and add it accordingly.

Students who are searching for NCERT MCQ Questions for Class 12 Business Studies Chapter 9 Financial Management with Answers Pdf free download are compiled here to get good practice on all fundamentals. Know your preparation level on MCQ Questions for Class 12 Business Studies with Answers. You can also verify your answers from our provided Financial Management Class 12 MCQs Questions with Answers. So, ace up your preparation with MCQ on Financial Management Class 12 Objective Questions.

Financial Management Class 12 MCQs Questions with Answers

Question 1.
Higher debt-equity ratio results in:
(a) a Higher degree of financial risk
(b) a Higher degree of operating risk
(c) Higher EPS
(d) Lower financial risk

Answer

Answer: (a) a Higher degree of financial risk

---

Question 2.
Cost of advertising and printing prospectus is called__________
(a) Floatation cost
(b) Debt cost
(c) Equity cost
(d) Dividend cost

Answer

Answer: (a) Floatation cost

---

Question 3.
The primary goal of the financial management is ____________
(a) To maximize the return
(b) To minimize the risk
(c) To maximize the wealth of owners
(d) To maximize profit

Answer

Answer: (c) To maximize the wealth of owners

---

Question 4.
Which of the following affects the Dividend Decision of a company?
(a) Taxation Policy
(b) Cash Flow Position
(c) Earnings
(d) All of the above

Answer

Answer: (d) All of the above

---

Question 5.
Which of the following affects capital budgeting decision?
(a) Investment Criteria and interest rate
(b) Rate of Return
(c) Cash Flow of the Project
(d) All of the above

Answer

Answer: (d) All of the above

---

Question 6.
Higher working capital usually results in:
(a) Higher equity, lower risk, and lower profits
(b) Lower current ratio, higher risk, and profits
(c) Lower equity, lower risk, and higher profits
(d) Higher current ratio, higher risk, and higher profits

Answer

Answer: (d) Higher current ratio, higher risk, and higher profits

---

Question 7.
Which of the following is not concerned with the Long term investment decision
(a) Management of fixed capital
(b) Inventory management
(c) Research and Development Programme
(d) Opening a new branch

Answer

Answer: (b) Inventory management

---

Question 8.
Favourable financial leverage is a situation where _____
(a) ROI is higher than the rate of interest on debt
(b) ROI is Equal to the Rate of interest on debt
(c) ROI is lower than the rate of interest on debt
(d) None of the above

Answer

Answer: (a) ROI is higher than the rate of interest on debt

---

Question 9.
Other things remaining the same, an increase in the tax rate on corporate profits will:
(a) Make the debt relatively cheaper
(b) Make the debt relatively the dearer
(c) Have no impact on the cost of debt
(d) None of the above

Answer

Answer: (a) Make the debt relatively cheaper

---

Question 10.
Higher dividend per share is associated with:
(a) High earnings, high cash flows, stable earnings, and high growth opportunities
(b) High earnings, high cash flows, stable earnings, and lower growth opportunities
(c) High earnings, low cash flows, stable earnings, and lower growth opportunities
(d) High earning, high cash flows, unstable earnings, and higher growth opportunities

Answer

Answer: (b) High earnings, high cash flows, stable earnings, and lower growth opportunities

---

Question 11.
The main objective of financial planning is to ensure that_________
(a) Enough funds are available at the right time
(b) Dividend is paid to shareholders at the right time
(c) Purchase of raw material
(d) Purchase of fixed assets

Answer

Answer: (a) Enough funds are available at the right time

---

Question 12.
Financial planning arrives at:
(a) Doing only what is possible with the funds that the firms have at its disposal
(b) Entering that the firm always have significantly more funds than required so that there is no paucity of funds
(c) Minimising the external borrowing by resorting to equity issues
(d) Ensuring that the firm faces neither a shortage nor a glut of unusable funds

Answer

Answer: (d) Ensuring that the firm faces neither a shortage nor a glut of unusable funds

---

Question 13.
Which of the following is not a financial Decision?
(a) Financing Decision
(b) Investment Decision
(c) Staffing Decision
(d) Dividend Decision

Answer

Answer: (c) Staffing Decision

---

Question 14.
The cheapest source of finance is:
(a) Preference share
(b) Retained earning
(c) Equity share capital
(d) Debenture

Answer

Answer: (b) Retained earning

---

Question 15.
Financial leverage is called favourable if:
(a) Return on Investment is lower than the cost of debt
(b) If the degree of existing financial leverage is low
(c) Debt is easily available
(d) ROI is higher than the cost of debt

Answer

Answer: (d) ROI is higher than the cost of debt

---

Question 16.
Short-term Investment Decision is also known as ____
(a) Working capital
(b) Dividend Decision
(c) Capital Budgeting
(d) None of the above

Answer

Answer: (a) Working capital

---

Question 17.
Which of the following affects the Dividend Decision of a company?
(a) Earnings
(b) Cash Flow Position
(c) Taxation Policy
(d) All of the above

Answer

Answer: (d) All of the above

---

Question 18.
Short term investment decisions affect the ___________
(a) Purchase of fixed assets
(b) Long term profitability
(c) Day to Day working of the business
(d) Large amount of funds for future

Answer

Answer: (c) Day to Day working of the business

---

Question 19.
Financial Management is mainly concerned with ______________
(a) All aspects of acquiring and utilizing financial resources for firms activities
(b) Arrangement of funds
(c) Efficient Management of every business
(d) Profit maximization

Answer

Answer: (a) All aspects of acquiring and utilizing financial resources for firms activities

---

Question 20.
A fixed asset should be financed through:
(a) A long-term liability
(b) A short-term liability
(c) A mix of long and short-term liabilities
(d) None of the above

Answer

Answer: (a) A long-term liability

---

Question 21.
Long term investment decision is also known as _____________
(a) Capital Budgeting
(b) Working Capital
(c) Dividend Decision
(d) None of the above

Answer

Answer: (a) Capital Budgeting

---

Question 22.
Current assets of a business firm should be financed through:
(a) Current liability only
(b) Long-term liability only
(c) Both of the above
(d) None of the above

Answer

Answer: (c) Both of the above

---

Question 23.
Companies with a higher growth pattern are likely to:
(a) Dividends are not affected by growth considerations
(b) Pay higher dividends
(c) Pay lower dividends
(d) None of the above

Answer

Answer: (c) Pay lower dividends

---

Use the above-provided NCERT MCQ Questions for Class 12 Business Studies Chapter 9 Financial Management with Answers Pdf free download and get a good grip on the fundamentals. Need any support from our end during the preparation of CBSE Class 12 Business Studies Financial Management MCQs Multiple Choice Questions with Answers then leave your comments below. We’ll revert back to you soon.

Students who are searching for NCERT MCQ Questions for Class 12 Business Studies Chapter 10 Financial Markets with Answers Pdf free download are compiled here to get good practice on all fundamentals. Know your preparation level on MCQ Questions for Class 12 Business Studies with Answers. You can also verify your answers from our provided Financial Markets Class 12 MCQs Questions with Answers. So, ace up your preparation with MCQ on Financial Markets Class 12 Objective Questions.

Financial Markets Class 12 MCQs Questions with Answers

Question 1.
Treasury bills are also known as _____________
(a) Fixed interest Bonds
(b) Low-Interest Bonds
(c) Flat Rate Bonds
(d) Zero-Coupon Bonds

Answer

Answer: (d) Zero-Coupon Bonds

---

Question 2.
Which of the following is a method of floatation?
(a) Offer for sale
(b) Private Placement
(c) Offer through the prospectus
(d) All of the above

Answer

Answer: (d) All of the above

---

Question 3.
Primary and secondary markets:
(a) Control each other
(b) Complement each other
(c) Compete with each other
(d) Function independently

Answer

Answer: (b) Complement each other

---

Question 4.
The total number of Stock Exchanges in India is:
(a) 22
(b) 21
(c) 23
(d) 20

Answer

Answer: (b) 21

---

Question 5.
Money market deals in ________
(a) Long term Securities
(b) Medium-term securities
(c) Short term Securities
(d) None of the above

Answer

Answer: (c) Short term Securities

---

Question 6.
A Treasury Bill is basically:
(a) An instrument to borrow short-term funds
(b) An instrument to borrow long-term funds
(c) An instrument of capital market
(d) None of the above

Answer

Answer: (a) An instrument to borrow short-term funds

---

Question 7.
What is meant by Demat Account?
(a) Development Market Account
(b) Depository Participant Account
(c) Dematerialisation of Securities
(d) Demand Depository Account

Answer

Answer: (c) Dematerialisation of Securities

---

Question 8.
To be listed on OTCEI, the minimum capital requirement for a company is:
(a) Rs. 10 crores
(b) Rs. 3 crores
(c) Rs. 25 crores
(d) Rs. 5 crores

Answer

Answer: (b) Rs. 3 crores

---

Question 9.
Clearing and settlement operations of NSE are carried out by:
(a) NSDL
(b) SBI
(c) NSCCL
(d) CDSL

Answer

Answer: (c) NSCCL

---

Question 10.
Instruments traded in capital market are__________
(a) Bonds
(b) Equity Shares and Preference Shares
(c) Debentures
(d) All of the above

Answer

Answer: (d) All of the above

---

Question 11.
OTCEI was started on the lines of:
(a) NSE
(b) NYSE
(c) NASDAQ
(d) NASAQ

Answer

Answer: (c) NASDAQ

---

Question 12.
_________ is not a participant in money market
(a) SEBI
(b) NBFCs
(c) RBI
(d) Mutual Funds

Answer

Answer: (a) SEBI

---

Question 13.
When a trade bill is accepted by a commercial bank, it is known as a _____
(a) Certificate of deposit
(b) Commercial Bill
(c) Call money
(d) None of the above

Answer

Answer: (b) Commercial Bill

---

Question 14.
What type of instruments are traded in a Money Market?
(a) Treasury bills
(b) Commercial bills
(c) Call money
(d) All of the above

Answer

Answer: (d) All of the above

---

Question 15.
Capital market deals in ___________
(a) Medium and long term securities
(b) Very short term securities
(c) Short term securities
(d) None of the above

Answer

Answer: (a) Medium and long term securities

---

Question 16.
What is the meaning of the right issue?
(a) Company sells the securities to some selected institutions
(b) Company offers new shares to its existing shareholders
(c) Securities are not issued to existing shareholders at all
(d) None of the above

Answer

Answer: (b) Company offers new shares to its existing shareholders

---

Question 17.
_______ Market instruments enjoy a higher degree of liquidity
(a) Both money and capital market
(b) Money market
(c) Capital market
(d) None of the above

Answer

Answer: (b) Money market

---

Question 18.
At present only two depositories are registered with SEBI _____
(a) NSDL and HDFC
(b) NSDL and CDSL
(c) NSDL and ABSL
(d) NEFT and TDS

Answer

Answer: (b) NSDL and CDSL

---

Question 19.
Which of the following is not a part of the capital market?
(a) Banks
(b) Financial Institutions
(c) Stock Exchanges
(d) RBI

Answer

Answer: (d) RBI

---

Question 20.
Securities Exchange Board of India (SEBI) was established in ________
(a) 1992
(b) 1956
(c) 2001
(d) 1984

Answer

Answer: (a) 1992

---

Question 21.
A Treasury bill is an instrument of _____________
(a) Long term debt
(b) Short term debt
(c) Interest
(d) Dividend

Answer

Answer: (b) Short term debt

---

Question 22.
The settlement cycle in NSE is:
(a) T + 2
(b) T + 5
(c) T + 3
(d) T + 1

Answer

Answer: (a) T + 2

---

Question 23.
Only institutional investors can participate in __________
(a) Loan Market
(b) Money Market
(c) Foreign Market
(d) Capital Market

Answer

Answer: (b) Money Market

---

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Students can access the NCERT MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 11 Maths with Answers during preparation and score maximum marks in the exam. Students can download the Complex Numbers and Quadratic Equations Class 11 MCQs Questions with Answers from here and test their problem-solving skills. Clear all the fundamentals and prepare thoroughly for the exam taking help from Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Objective Questions.

Complex Numbers and Quadratic Equations Class 11 MCQs Questions with Answers

Students are advised to solve the Complex Numbers and Quadratic Equations Multiple Choice Questions of Class 11 Maths to know different concepts. Practicing the MCQ Questions on Complex Numbers and Quadratic Equations Class 11 with answers will boost your confidence thereby helping you score well in the exam.

Explore numerous MCQ Questions of Complex Numbers and Quadratic Equations Class 11 with answers provided with detailed solutions by looking below.

Question 1.
Let z₁ and z₂ be two roots of the equation z² + az + b = 0, z being complex. Further assume that the origin, z₁ and z₂ form an equilateral triangle. Then
(a) a² = b
(b) a² = 2b
(c) a² = 3b
(d) a² = 4b

Answer

Answer: (c) a² = 3b
Given, z₁ and z₁ be two roots of the equation z²+ az + b = 0
Now, z₁ + z₂ = -a and z₁ × z₂ = b
Since z₁ and z₂ and z₃ from an equilateral triangle.
⇒ z₁² + z₂² + z₃² = z₁ × z₂ + z₂ × z₃ + z₁ × z₃
⇒ z₁² + z₂² = z₁ × z₂ {since z₃ = 0}
⇒ (z₁ + z₂)² – 2z₁ × z₂ = z₁ × z₂
⇒ (z₁ + z₂)² = 2z₁ × z₂ + z₁ × z₂
⇒ (z₁ + z₂)² = 3z₁ × z₂
⇒ (-a)² = 3b
⇒ a² = 3b

---

Question 2.
The value of iⁱ is
(a) 0
(b) e^-π
(c) 2e^-π/2
(d) e^-π/2

Answer

Answer: (d) e^-π/2
Let A = iⁱ
⇒ log A = i log i
⇒ log A = i log(0 + i)
⇒ log A = i [log 1 + i tan^-1 ∞]
⇒ log A = i [0 + i π/2]
⇒ log A = -π/2
⇒ A = e^-π/2

---

Question 3.
The value of √(-25) + 3√(-4) + 2√(-9) is
(a) 13 i
(b) -13 i
(c) 17 i
(d) -17 i

Answer

Answer: (c) 17 i
Given, √(-25) + 3√(-4) + 2√(-9)
= √{(-1) × (25)} + 3√{(-1) × 4} + 2√{(-1) × 9}
= √(-1) × √(25) + 3{√(-1) × √4} + 2{√(-1) × √9}
= 5i + 3 × 2i + 2 × 3i {since √(-1) = i}
= 5i + 6i + 6i
= 17 i
So, √(-25) + 3√(-4) + 2√(-9) = 17 i

---

Question 4.
If the cube roots of unity are 1, ω and ω², then the value of (1 + ω / ω²)³ is
(a) 1
(b) -1
(c) ω
(d) ω²

Answer

Answer: (b) -1
Given, the cube roots of unity are 1, ω and ω²
So, 1 + ω + ω² = 0
and ω³ = 1
Now, {(1 + ω)/ ω²}³ = {-ω²/ ω²}³ = {-1}³ = -1

---

Question 5.
If {(1 + i)/(1 – i)}ⁿ = 1 then the least value of n is
(a) 1
(b) 2
(c) 3
(d) 4

Answer

Answer: (d) 4
Given, {(1 + i)/(1 – i)}ⁿ = 1
⇒ [{(1 + i) × (1 + i)}/{(1 – i) × (1 + i)}]ⁿ = 1
⇒ [{(1 + i)²}/{(1 – i²)}]ⁿ = 1
⇒ [(1 + i² + 2i)/{1 – (-1)}]ⁿ = 1
⇒ [(1 – 1 + 2i)/{1 + 1}]ⁿ = 1
⇒ [2i/2]ⁿ = 1
⇒ iⁿ = 1
Now, iⁿ is 1 when n = 4
So, the least value of n is 4

---

Question 6.
The value of [i¹⁹ + (1/i)²⁵]² is
(a) -1
(b) -2
(c) -3
(d) -4

Answer

Answer: (d) -4
Given, [i¹⁹ + (1/i)²⁵]²
= [i¹⁹ + 1/i²⁵]²
= [i¹⁶ × i³ + 1/(i²⁴ × i)]²
= [1 × i³ + 1/(1 × i)]² {since i⁴ = 1}
= [i³ + 1/i]²
= [i² × i + 1/i]²
= [(-1) × i + 1/i]² {since i² = -1}
= [-i + 1/i]²
= [-i + i⁴ /i]²
= [-i + i³]²
= [-i + i² × i]²
= [-i + (-1) × i]²
= [-i – i]²
= [-2i]²
= 4i²
= 4 × (-1)
= -4
So, [i¹⁹ + (1/i)²⁵]² = -4

---

Question 7.
If z and w be two complex numbers such that |z| ≤ 1, |w| ≤ 1 and |z + iw| = |z – iw| = 2, then z equals {w is congugate of w}
(a) 1 or i
(b) i or – i
(c) 1 or – 1
(d) i or – 1

Answer

Answer: (c) 1 or – 1
Given |z + iw| = |z – iw| = 2 {w is congugate of w}
⇒ |z – (-iw)| = |z – (iw)| = 2
⇒ |z – (-iw)| = |z – (-iw)|
So, z lies on the perpendicular bisector of the line joining -iw and -iw.
Since, -iw is the mirror in the x-axis, the locus of z is the x-axis.
Let z = x + iy and y = 0
⇒ |z| < 1 and x² + 0² < 0
⇒ -1 ≤ x ≤ 1
So, z may take value 1 or -1

---

Question 8.
The value of {-√(-1)}⁴ⁿ⁺³, n ∈ N is
(a) i
(b) -i
(c) 1
(d) -1

Answer

Answer: (a) i
Given, {-√(-1)}⁴ⁿ⁺³
= {-i}⁴ⁿ⁺³ {since √(-1) = i}
= {-i}⁴ⁿ × {-i}³
= {(-i)⁴}ⁿ × (-i³) {since i⁴ = 1}
= 1ⁿ ×(-i × i²)
= -i × (-1) {since i² = -1}
= i

---

Question 9.
Find real θ such that (3 + 2i × sin θ)/(1 – 2i × sin θ) is real
(a) π
(b) nπ
(c) nπ/2
(d) 2nπ

Answer

Answer: (b) nπ
Given,
(3 + 2i × sin θ)/(1 – 2i × sin θ) = {(3 + 2i × sin θ)×(1 – 2i × sin θ)}/(1 – 4i² × sin² θ)
(3 + 2i × sin θ)/(1 – 2i × sin θ) = {(3 – 4sin² θ) + 8i × sin θ}/(1 + 4sin² θ) …………. 1
Now, equation 1 is real if sin θ = 0
⇒ sin θ = sin nπ
⇒ θ = nπ

---

Question 10.
If i = √(-1) then 4 + 5(-1/2 + i√3/2)³³⁴ + 3(-1/2 + i√3/2)³⁶⁵ is equals to
(a) 1 – i√3
(b) -1 + i√3
(c) i√3
(d) -i√3

Answer

Answer: (c) i√3
Given, 4 + 5(-1/2 + i√3/2)³³⁴ + 3(-1/2 + i√3/2)³⁶⁵
= 4 + 5w³³⁴ + 3w³⁶⁵ {since w = -1/2 + i√3/2}
= 4 + 5w + 3w² {since w³ = 1}
= 4 + 5(-1/2 + i√3/2) + 3(-1/2 – i√3/2) {since w² = (-1/2 – i√3/2)}
= i√3

---

Question 11.
The real part of the complex number √9 + √(-16) is
(a) 3
(b) -3
(c) 4
(d) -4

Answer

Answer: (a) 3
Given, √9 + √(-16) = √9 + √(16) × √(-1)
= 3 + 4i {since i = √(-1)}
So, the real part of the complex number is 3

---

Question 12.
The modulus of 5 + 4i is
(a) 41
(b) -41
(c) √41
(d) -√41

Answer

Answer: (c) √41
Let Z = 5 + 4i
Now modulus of Z is calculated as
|Z| = √(5² + 4²)
⇒ |Z| = √(25 + 16)
⇒ |Z| = √41
So, the modulus of 5 + 4i is √41

---

Question 13.
The modulus of 1 + i√3 is
(a) 1
(b) 2
(c) 3
(d) None of these

Answer

Answer: (b) 2
Let Z = 1 + i√3
Now modulus of Z is calculated as
|Z| = √{1² + (√3)²}
⇒ |Z| = √(1 + 3)
⇒ |Z| = √4
⇒ |Z| = 2
So, the modulus of 1 + i√3 is 2

---

Question 14.
The value of {-√(-1)}⁴ⁿ⁺³, n ∈ N is
(a) i
(b) -i
(c) 1
(d) -1

Answer

Answer: (a) i
Given, {-√(-1)}⁴ⁿ⁺³
= {-i}⁴ⁿ⁺³ {since √(-1) = i}
= {-i}⁴ⁿ × {-i}³
= {(-i)⁴}ⁿ ×(-i³) {since i⁴ = 1}
= 1ⁿ × (-i × i²)
= -i × (-1) {since i² = -1}
= i

---

Question 15.
If ω is cube root of unity (ω ≠ 1) , then the least value of n where n is a positive integer such that (1 + ω²)ⁿ = (1 + ω⁴)ⁿ is
(a) 2
(b) 3
(c) 5
(d) 6

Answer

Answer: (b) 3
Given ω is an imaginary cube root of unity.
So 1 + ω + ω² = 0 and ω³ = 1
Now, (1 + ω²)ⁿ = (1 + ω⁴)ⁿ
⇒ (-1)ⁿ ×(ω)ⁿ = (1 + ω × ω³)ⁿ
⇒ (-1)ⁿ × (ω)ⁿ = (1 + ω)ⁿ
⇒ (-1)ⁿ × (ω)ⁿ = (-ω²)ⁿ
⇒ (-1)ⁿ × (ω)ⁿ = (-1)ⁿ × ω²ⁿ
⇒ ωⁿ = ω²ⁿ
Since ω³ = 1, So the least value of n is 3

---

Question 16.
The value of i⁹ + i¹⁰ + i¹¹ + i¹² is
(a) i
(b) 2i
(c) 0
(d) 1

Answer

Answer: (c) 0
Given, i⁹ + i¹⁰ + i¹¹ + i¹²
= i9 (1 + i + i2 + i3 )
= i9 (1 + i – 1 – i ) {since i2 = (-1) and i4 = 1}
= i9 × 0
= 0

---

Question 17.
If a = cos α + i sin α and b = cos β + i sin β , then the value of 1/2(ab + 1/ ab) is
(a) sin (α + β)
(b) cos (α + β)
(c) sin (α – β)
(d) cos (α – β)

Answer

Answer: (b) cos (α + β)
Given a = cos α + i sin α and b = cos β + i sin β
Now, 1/a = 1/(cos α + i sin α)
⇒ 1/a = {1 × (cos α – i sin α)/{(cos α + i sin α) × (cos α + i sin α)}
⇒ 1/a = (cos α – i sin α)/(cos² α + i sin² α)
⇒ 1/a = (cos α – i sin α)
Again, 1/b = 1/(cos β + i sin β)
⇒ 1/b = {1 × (cos β – i sin β)/{(cos β + i sin β) × (cos β + i sin β)}
⇒ 1/b = (cos β – i sin β)/(cos² β + i sin² β)
⇒ 1/b = (cos β – i sin β)
Now, ab = (cos α + i sin α) × (cos β + i sin β)
⇒ ab = cos α × cos β + i cos α × sin β + i sin α × cos β – sin α × sin β
Again, 1/ab = (cos α – i sin α) × (cos β – i sin β)
⇒ 1/ab = cos α × cos β – i cos α × sin β – i sin α × cos β – sin α × sin β
Now, ab + 1/ab = cos α × cos β + i cos α × sin β + i sin α × cos β – sin α × sin β + cos α × cos β – i cos α × sin β – i sin α × cos β – sin α × sin β
⇒ ab + 1/ab = 2(cos α × cos β – sin α × sin β)
⇒ 1/2(ab + 1/ ab) = 2(cos α × cos β – sin α × sin β)/2
⇒ 1/2(ab + 1/ ab) = cos α × cos β – sin α × sin β
⇒ 1/2(ab + 1/ ab) = cos(α + β)

---

Question 18.
The polar form of -1 + i is
(a) √2(cos π/2 + i × sin π/2)
(b) √2(cos π/4 + i × sin π/4)
(c) √2(cos 3π/2 + i × sin 3π/2)
(d) √2(cos 3π/4 + i × sin 3π/4)

Answer

Answer: (d) √2(cos 3π/4 + i × sin 3π/4)
The polar form of a com plex number = r(cos θ + i × sin θ)
Given, complex number = -1 + i
Let x + iy = -1 + i
Now, x = -1, y = 1
Now, r = √{(-1)² + 1²} = √(1 + 1) = √2
and tan θ = y/x
⇒ tan θ = 1/(-1)
⇒ tan θ = -1
⇒ θ = 3π/4
Now, polar form is √2(cos 3π/4 + i × sin 3π/4)

---

Question 19.
For all complex numbers z₁, z₂ satisfying |z₁| = 12 and |z₂ – 3 – 4i| = 5, the minimum value of |z₁ – z₂| is
(a) 0
(b) 2
(c) 7
(d) 17

Answer

Answer: (b) 2
Given For all complex numbers z₁, z₂ satisfying |z₁| = 12 and |z₂ – 3 – 4i| = 5
Now, mod(z₁) = 12 represents a circle centred at 0 and radius 12
mod(z₂ – 3 – 4i) = 5 represents a circle centred at (3, 4) and radius 5
This circle passes through the origin. Distance of diametrically opposite end is 10
So, the minimum value (z₁ – z₂) = 2

---

Question 20.
The value of (1 – i)² is
(a) i
(b) -i
(c) 2i
(d) -2i

Answer

Answer: (d) -2i
Given, (1 – i)² = 1 + i² – 2i
= 1 + (-1) – 2i
= 1 – 1 – 2i
= -2i

---

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Linear Inequalities Class 11 MCQs Questions with Answers

Students are advised to solve the Linear Inequalities Multiple Choice Questions of Class 11 Maths to know different concepts. Practicing the MCQ Questions on Linear Inequalities Class 11 with answers will boost your confidence thereby helping you score well in the exam.

Explore numerous MCQ Questions of Linear Inequalities Class 11 with answers provided with detailed solutions by looking below.

Question 1.
If -2 < 2x – 1 < 2 then the value of x lies in the interval
(a) (1/2, 3/2)
(b) (-1/2, 3/2)
(c) (3/2, 1/2)
(d) (3/2, -1/2)

Answer

Answer: (b) (-1/2, 3/2)
Given, -2 < 2x – 1 < 2
⇒ -2 + 1 < 2x < 2 + 1
⇒ -1 < 2x < 3
⇒ -1/2 < x < 3/2
⇒ x ∈ (-1/2, 3/2)

---

Question 2.
If x² < -4 then the value of x is
(a) (-2, 2)
(b) (2, ∞)
(c) (-2, ∞)
(d) No solution

Answer

Answer: (d) No solution
Given, x² < -4
⇒ x² + 4 < 0
Which is not possible.
So, there is no solution.

---

Question 3.
If |x| < -5 then the value of x lies in the interval
(a) (-∞, -5)
(b) (∞, 5)
(c) (-5, ∞)
(d) No Solution

Answer

Answer: (d) No Solution
Given, |x| < -5
Now, LHS ≥ 0 and RHS < 0
Since LHS is non-negative and RHS is negative
So, |x| < -5 does not posses any solution

---

Question 4.
The graph of the inequations x ≤ 0 , y ≤ 0, and 2x + y + 6 ≥ 0 is
(a) exterior of a triangle
(b) a triangular region in the 3rd quadrant
(c) in the 1st quadrant
(d) none of these

Answer

Answer: (b) a triangular region in the 3rd quadrant
Given inequalities x ≥ 0 , y ≥ 0 , 2x + y + 6 ≥ 0
Now take x = 0, y = 0 and 2x + y + 6 = 0
when x = 0, y = -6
when y = 0, x = -3
So, the points are A(0, 0), B(0, -6) and C(-3, 0)

So, the graph of the inequations x ≤ 0 , y ≤ 0 , and 2x + y + 6 ≥ 0 is a triangular region in the 3rd quadrant.

---

Question 5.
The graph of the inequalities x ≥ 0, y ≥ 0, 2x + y + 6 ≤ 0 is
(a) a square
(b) a triangle
(c) { }
(d) none of these

Answer

Answer: (c) { }
Given inequalities x ≥ 0, y ≥ 0, 2x + y + 6 ≤ 0
Now take x = 0, y = 0 and 2x + y + 6 = 0
when x = 0, y = -6
when y = 0, x = -3
So, the points are A(0, 0), B(0, -6) and C(-3, 0)

Since region is outside from the line 2x + y + 6 = 0
So, it does not represent any figure.

---

Question 6.
Solve: 2x + 1 > 3
(a) [-1, ∞]
(b) (1, ∞)
(c) (∞, ∞)
(d) (∞, 1)

Answer

Answer: (b) (1, ∞)
Given, 2x + 1 > 3
⇒ 2x > 3 – 1
⇒ 2x > 2
⇒ x > 1
⇒ x ∈ (1, ∞)

---

Question 7.
The solution of the inequality 3(x – 2)/5 ≥ 5(2 – x)/3 is
(a) x ∈ (2, ∞)
(b) x ∈ [-2, ∞)
(c) x ∈ [∞, 2)
(d) x ∈ [2, ∞)

Answer

Answer: (d) x ∈ [2, ∞)
Given, 3(x – 2)/5 ≥ 5(2 – x)/3
⇒ 3(x – 2) × 3 ≥ 5(2 – x) × 5
⇒ 9(x – 2) ≥ 25(2 – x)
⇒ 9x – 18 ≥ 50 – 25x
⇒ 9x – 18 + 25x ≥ 50
⇒ 34x – 18 ≥ 50
⇒ 34x ≥ 50 + 18
⇒ 34x ≥ 68
⇒ x ≥ 68/34
⇒ x ≥ 2
⇒ x ∈ [2, ∞)

---

Question 8.
Solve: 1 ≤ |x – 1| ≤ 3
(a) [-2, 0]
(b) [2, 4]
(c) [-2, 0] ∪ [2, 4]
(d) None of these

Answer

Answer: (c) [-2, 0] ∪ [2, 4]
Given, 1 ≤ |x – 1| ≤ 3
⇒ -3 ≤ (x – 1) ≤ -1 or 1 ≤ (x – 1) ≤ 3
i.e. the distance covered is between 1 unit to 3 units
⇒ -2 ≤ x ≤ 0 or 2 ≤ x ≤ 4
Hence, the solution set of the given inequality is
x ∈ [-2, 0] ∪ [2, 4]

---

Question 9.
Solve: -1/(|x| – 2) ≥ 1 where x ∈ R, x ≠ ±2
(a) (-2, -1)
(b) (-2, 2)
(c) (-2, -1) ∪ (1, 2)
(d) None of these

Answer

Answer: (c) (-2, -1) ∪ (1, 2)
Given, -1/(|x| – 2) ≥ 1
⇒ -1/(|x| – 2) – 1 ≥ 0
⇒ {-1 – (|x| – 2)}/(|x| – 2) ≥ 0
⇒ {1 – |x|}/(|x| – 2) ≥ 0
⇒ -(|x| – 1)/(|x| – 2) ≥ 0

Using number line rule:
1 ≤ |x| < 2
⇒ x ∈ (-2, -1) ∪ (1, 2)

---

Question 10.
If x² < 4 then the value of x is
(a) (0, 2)
(b) (-2, 2)
(c) (-2, 0)
(d) None of these

Answer

Answer: (b) (-2, 2)
Given, x² < 4
⇒ x² – 4 < 0
⇒ (x – 2) × (x + 2) < 0
⇒ -2 < x < 2
⇒ x ∈ (-2, 2)

---

Question 11.
Solve: 2x + 1 > 3
(a) [1, 1)
(b) (1, ∞)
(c) (∞, ∞)
(d) (∞, 1)

Answer

Answer: (b) (1, ∞)
Given, 2x + 1 > 3
⇒ 2x > 3 – 1
⇒ 2x > 2
⇒ x > 1
⇒ x ∈ (1, ∞)

---

Question 12.
If a is an irrational number which is divisible by b then the number b
(a) must be rational
(b) must be irrational
(c) may be rational or irrational
(d) None of these

Answer

Answer: (b) must be irrational
If a is an irrational number which is divisible by b then the number b must be irrational.
Ex: Let the two irrational numbers are √2 and √3
Now, √2/√3 = √(2/3)

---

Question 13.
Sum of two rational numbers is ______ number.
(a) rational
(b) irrational
(c) Integer
(d) Both 1, 2 and 3

Answer

Answer: (a) rational
The sum of two rational numbers is a rational number.
Ex: Let two rational numbers are 1/2 and 1/3
Now, 1/2 + 1/3 = 5/6 which is a rational number.

---

Question 14.
If |x| = -5 then the value of x lies in the interval
(a) (-5, ∞)
(b) (5, ∞)
(c) (∞, -5)
(d) No solution

Answer

Answer: (d) No solution
Given, |x| = -5
Since |x| is always positive or zero
So, it can not be negative
Hence, given inequality has no solution.

---

Question 15.
The value of x for which |x + 1| + √(x – 1) = 0
(a) 0
(b) 1
(c) -1
(d) No value of x

Answer

Answer: (d) No value of x
Given, |x + 1| + √(x – 1) = 0, where each term is non-negative.
So, |x + 1| = 0 and √(x – 1) = 0 should be zero simultaneously.
i.e. x = -1 and x = 1, which is not possible.
So, there is no value of x for which each term is zero simultaneously.

---

Question 16.
If x² < -4 then the value of x is
(a) (-2, 2)
(b) (2, ∞)
(c) (-2, ∞)
(d) No solution

Answer

Answer: (d) No solution
Given, x² < -4
⇒ x² + 4 < 0
Which is not possible.
So, there is no solution.

---

Question 17.
The solution of |2/(x – 4)| > 1 where x ≠ 4 is
(a) (2, 6)
(b) (2, 4) ∪ (4, 6)
(c) (2, 4) ∪ (4, ∞)
(d) (-∞, 4) ∪ (4, 6)

Answer

Answer: (b) (2, 4) ∪ (4, 6)
Given, |2/(x – 4)| > 1
⇒ 2/|x – 4| > 1
⇒ 2 > |x – 4|
⇒ |x – 4| < 2
⇒ -2 < x – 4 < 2
⇒ -2 + 4 < x < 2 + 4
⇒ 2 < x < 6
⇒ x ∈ (2, 6), where x ≠ 4
⇒ x ∈ (2, 4) ∪ (4, 6)

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Question 18.
The solution of the function f(x) = |x| > 0 is
(a) R
(b) R – {0}
(c) R – {1}
(d) R – {-1}

Answer

Answer: (b) R – {0}
Given, f(x) = |x| > 0
We know that modulus is non negative quantity.
So, x ∈ R except that x = 0
⇒ x ∈ R – {0}
This is the required solution

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Question 19.
Solve: |x – 1| ≤ 5, |x| ≥ 2
(a) [2, 6]
(b) [-4, -2]
(c) [-4, -2] ∪ [2, 6]
(d) None of these

Answer

Answer: (c) [-4, -2] ∪ [2, 6]
Given, |x – 1| ≤ 5, |x| ≥ 2
⇒ -(5 ≤ (x – 1) ≤ 5), (x ≤ -2 or x ≥ 2)
⇒ -(4 ≤ x ≤ 6), (x ≤ -2 or x ≥ 2)
Now, required solution is
x ∈ [-4, -2] ∪ [2, 6]

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Question 20.
The solution of the 15 < 3(x – 2)/5 < 0 is
(a) 27 < x < 2
(b) 27 < x < -2
(c) -27 < x < 2
(d) -27 < x < -2

Answer

Answer: (a) 27 < x < 2
Given inequality is:
15 < 3(x – 2)/5 < 0
⇒ 15 × 5 < 3(x – 2) < 0 × 5
⇒ 75 < 3(x – 2) < 0
⇒ 75/3 < x – 2 < 0
⇒ 25 < x – 2 < 0
⇒ 25 + 2 < x < 0 + 2
⇒ 27 < x < 2

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