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A pendulum swings through an angle of 30^0 and describes an arc 8.8 cm in length.

Length of the pendulum = Radius of sector of the circle

Arc length = 8.8

θ/360 (2πr) = 8.8

30/360 x 2 x 22/7 x r = 8.8

r = 16.8

Therefore, the length of the pendulum is 16.8 cm.

We know that diameter = 2 \(\times\) radius

= d = 2r

As we know that circumference of a circle = 2πr = π \(\times\)2r 

= π\(\times\)d

Diameter of circle = 42 cm

Radius = 42/2 = 21 cm

Central angle = 60°

We know that,

Length of the arc = θ/360 (2πr)

= 60/360 x 2 x 22/7 x 21

= 22

Length of the arc is 22 cm

Answer : (c) 384 π cm²

Total area cleaned at each sweep of the blades 

= 2 × Area of sector cleaned by the sweep of one blade

= 2 × \(\big[\) \(\frac{120}{360}\times \pi \times (24)^2 \big]\) \(\big[\because radius\,of\,sector\,=\,length\,of\,blade\big]\)

 = 384 π cm².

The correct option is:

(C) 1210 cm²

We know that diameter = 2 × radius i.e. d = 2r ⇒ r = \(\frac{d}{2}\)

Also Area of a circle = πr²  = π (\(\frac{d}{2}\))² 

= \(\frac{\pi d^2}{4}\)

Given, square circumscribes a circle of radius a cm.

Side of the square = 2 x radius of circle = 2a cm

Now, perimeter of the square = (4 x 2a) = 8a cm

Perimeter of the square is 8a cm.

Given length of rectangular wire = 18.7 cm

Breadth of rectangular wire = 14.3 cm

According to the question length of wire = circumference of the circle

= 2 (l + b) = 2 × (18.7 + 14.3)

= 2 (33)

= 66 cm

Let the wire bent in the form of circle of radius r cm then we have

Circumference = 66 cm

2 π r = 66

2 × (22/7) × r = 66

44/7 r = 66

r = (66 × 7)/44

r = 462/44

= 10.5 cm

D. 50 cm

Area of first circle = πr² = π(24)² = 576π m²

Area of second circle = πr² = π(7)² = 49π m²

Now, we are given that,

Area of the circle = Area of first circle + Area of second circle

∴ πR² = 576π +49π

(where, R is the radius of the new circle)

⇒ πR² = 625π

⇒ R² = 625

⇒ R = 25

∴ Radius of the circle = 25cm

Thus, diameter of the circle = 2R = 50 cm.

False

Explanation:

It is not true because in case of major segment, area is always greater than the area of its corresponding sector. It is true only in the case of minor segment.

Thus, we can conclude that it is not true to say that area of a segment of a circle is less than the area of its corresponding sector.

Side of a square = 10 cm

Diameter of the inscribed circle = 10 cm

Radius of the inscribed circle = 5 cm

Diameter of the circumscribed circle = Diagonal of the square

Radius circumscribed circle = 5√2 cm

(i) the area of the inscribed circle

= 22/7 x 5 x 5 = 78.57 cm²

(ii) the area of the circumscribed circle

= 22/7 x 5√2 x 5√2 = 157.14 cm²

Answer : (d) 2.2 cm

Area of a sector = \(\frac{\theta}{360^0}\) × \(\pi r^2\)

⇒ \(\frac{36}{360}\) × \(\frac{22}{7}\) × r² = 3.85

⇒ r² = \(\frac{3.85 \times 10\times 7}{22}\) = 12.25

⇒ r = 3.5 cm.

∴ Length of arc =   \(\frac{\theta}{360^0}\) × \(\pi r^2\)

=   \(\frac{36}{360}\) × 2 × \(\frac{22}{7}\) × 3.5 

= 2.2 cm

In one revolution of the wheel, the car travels a distance equal to the circumference of the wheel.

Given diameter of the wheel of a car = 98 cm

Circumference of the wheel of the car = π d

= 227 x 98

= 308 cm

The distance travelled by the car in one revolution = 308 cm

Total distance travelled by the car = 6160 m = 616000 cm

Therefore number of revolution = total distance travelled by the car/ distance travelled by the car in one hour

Number of revolution = 616000/308 = 2000

D. 9π cm²

Let a be the side of square = 6 cm

∴ Diameter of a circle = Side of square = 6 cm

∴ Radius of the circle = Diameter/2 = 3 cm

∴ Area of the circle = πr² = π(3)² = 9π cm²

Angle described by minute hand in one minute = \(\frac{360^0}{60^0}\) = 6^º 

Statement is not true. It is true only for a minor segment. In the case of a major segment, area of the triangle will have to be added to the corresponding area of the sector.

Given side of equilateral triangle = 6.6 cm

Length of the wire = the perimeter of equilateral triangle

Perimeter of equilateral triangle = 3 × side

= 3 × 6.6 = 19.8 cm

Therefore circumference = 19.8 cm

C = 2 π r

19.8 = 2 × (22/7) × r

19.8 = 44/7 r

r = (19.8 × 7)/44

r = 138.6/44

= 3.15 cm

Diameter = 2r

Therefore diameter of ring = 2 × 3.15 = 6.3 cm

(B) Area of the circle > Area of the square

Explanation:

According to the question,

Circumference of a circle = Perimeter of square

Let r be the radius of the circle and a be the side of square.

∴ From the given condition, we have 2π r = 4a

(22/7)r = 2a

⇒ 11r = 7a

⇒ a = (11/7)a

⇒ r = (7/11)a …………..(i)

Now, area of circle = A₁ = πr² and area of square = A₂ = a²

From equation (i ), we have

A₁ = π × (7/11)²

= (22/7) × (49/121)a²

= (14/11)a² and A₂ = a²

∴ A₁ = (14/11) A₂

⇒ A₁ > A₂

Hence, Area of the circle > Area of the square.

∴ Option B is correct.

Grameen Bank of Bangladesh was founded by Professor Muhammad Yunus, and he was also the recipient of the 2006 Nobel Prize for Peace.

Correct option is (d) Corporate-level planning

Correct option is (a) building up new attitudes,

The gas which is expelled during expiration is carbon-di¬oxide. It is produced as a result of oxidation of glucose in the tissues. (Cellular respiration)

Correct option is (c) Ohio State studies

Correct option is (c) Domestic demand.

Correct option is (c) Risk

Correct option is (a) Lower order

Which of the following does not ensure effective ethical practices in a business enterprise?

Correct option is (b) Abraham Maslow.

Ethics governs the Behaviour.

Correct Answer is: (d) All of them

Correct option is (c) Changing their inputs and/or outcomes

(d) Correct decision making

Code of ethics documents the generally accepted principles of ethical conduct. They are statements of values and principles which define the purpose of an organisation. It gives a clear picture of the standards that employees should follow. It guides them in decision making. 

The code of business ethics can include the following:

1. To offer goods at fair prices. 

2. To supply goods of good quality and not to deal in spurious and sub standard products. 

3. To listen to consumer’s complaints and to reduce them. 

4. Not to raise the price of its products unjustifiably. 

5. Not to resort hoarding and lack marketing. 

6. Not to resort to price cutting with the sole aim of killing competition. 

7. Not to issue advertisement containing false information or exaggerated claims. 

8. To pay fair wages to its employees and not to exploit them. 

9. To provide congenial work atmosphere. 

10. To design production process in such a way as to reduce environmental pollution.

11. To keep proper books of accounts and records. 

12. To pay taxes regularly. 

13. To complaint with various business loss and never to flout Government regulations.

Correct option is (d) Manufacturing environment friendly products.

Correct option is (c) Co-alition

(c) Ethically upright behaviour

Correct option is (c) lower order

All business units have realized that ethics is vitally important for the existence and progress of the business as well as the society. Ethics and profits go together in the long run. It enhances the quality of life, standard of living and business.

(b) Competitive

(i) Black Soil

(ii) Red Soil

Correct option is (a) a new competitive product

Correct option is (d) South Asia Free Trade Agreement

(a) Clayey Soil

(b) Sandy Soil

(i) Deltaic Alluvial Soil

(ii) Alluvial Soil

1. Broadly utilitarian arguments 

• Biodiversity plays a major role in maintaining and sustaining supply of goods and services from various species as well as ecological systems.

• The different ecological services provided are: 

a. Amazon forest is estimated to contribute 20 per cent of the total oxygen in the atmosphere on earth. 

b. Ecosystem provides pollinators like bees, bumble bees, birds and bats which pollinate plants to form fruits and seeds. 

c. Aesthetic pleasures like bird watching, spring flowers in full bloom, walking through the thick forest, waking up to a bulbul’s song, etc. are some other benefits of the ecosystem.

2. Ethical reasons 

• There are thousands of plants, animals and microbes on this earth which are not useless. Every one has some intrinsic value even if it is not of any economic value to us. 

• It is, therefore, our moral duty to ensure well-being of all the living creatures for the utilisation of future generations.

Correct option is (c) Frederick Herzberg

Correct option is (c) Strategic Business Unit

Asia : Independent Directors are a requirement for listed companies in all Asian economies, where most require at least l/3rd of the Board to be independent.

USA : The Council of Institutional Investors (CII), Corporate Governance Policies state that at least 2/3rd of the directors should be independent.

Europe : European commission urges member states to have sufficient number of independent npn-executive or supervisory directors on Board.

G20 / OECD : The latest principles encourage the prominent role of independent Board members.

Japan : In early. 2014, Japanese Prime Minister announced the goal of increasing the percentage of women in executive positions at Japanese companies to 30% by 2020.

UK : UK businesses had voluntary targets first set in 2011 i.e. to have 25% women on FTSE 100 (The Financial Times Stock Exchange) Boards by 2015.

Canada : At the Federal level, two bills are currently being tabled which will impose a 40% quota for female Board members of public companies and other regulated entities such as banks and insurance companies.

Brazil : A bill pending in the Brazilian Senate would impose a 40% female quota on the Boards of state owned enterprises by 2022.

France : French parliament adopted a bill that requires public companies making at least 50 million Euros in turnover and employing more than 500 workers to have 40% female Board representation by 2017.

(a) Loamy Soil

(b) Laterite Soil

Correct option is (b) Expectancy theory