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Correct option is (C) 1600

Volume = \(lbh\)

\(=20\times10\times8\) \(=1600\,cm^3\)

Correct option is  C) 1600

Correct option is (B) lbh

Volume of cuboid is \(V=lbh\)

Correct option is  B) lbh

(i) 2 * 3 = 3 x 2² - 3 = 12 - 3 = 9

Given ; a*b = 3a² - b

b*a = 3b² - a ≠ a*b

Hence not commutative.

(ii) f of (x) = f (f(x)) = f (x² -3x +2)

=(x² -3x + 2)² - 3 (x² - 3x + 2)

= x⁴ + 9x² + 4 - 6x³ + 4x² - 12x - 3x² + 9x - 6 +2

= x⁴ - 6x³ + 10x² - 3x

f of (1) = 1 - 6 + 10 - 3 = 2

(i) (a) Let x , x , ∈ R 

ƒ(x₁) = ƒ(x₂) ⇒ 5x₁ + 2 

= 5x₂ + 2 

⇒ 5x₂ = 5x₂ ⇒ x₁ = x₂ 

Therefore s one-one.

(b) Yes. 

Let y e range of ƒ 

⇒ ƒ(x) = y ⇒ 5x + 2 = y

⇒ x = \(\frac{y-2}{5}\) ∈ R

Therefore corresponding to every y ∈ R there existsa real number \(\frac{y-2}{5}\) Therefore f is onto. 

Hence bijective, so invertible.

(ii) (a) Yes. 

a * b = HCF (a,b) = HCF (b,a) = b * a 

Hence commutative.

(b) Yes. 

a * (b * c) = a* HF(b,c) = HCF(a,b,c) 

(a*b) * c =HCF(a,b) * c HCF(a,b,c) 

a * (b * c) = (a * b) * c

 Hence associative.

Correct option is (C) 980

Volume of water tank = \(lbh\)

\(=1.4\times1\times0.7\,m^3\)

\(=0.98\,m^3\)

= 0.98 \(\times\) 1000 litres  \((\because1m^3\) = 1000 litres)

= 980 litres

Correct option is  C) 980

a) ii) one-one and not onto

b) LCM of 2 and 3 is 6 ∉ A, therefore not a binary operation.

R = {(1,1)(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1)}

f(x₁) = f(x₂) ⇒ \(\frac{x_1}{x_1+2}\) =\(\frac{x_2}{x_2 + 2}\)

⇒ x₁(x₂+ 2) = x₂ (x₁ + 2)

⇒ x₁x₂ + 2x₁ = x₂x₁ + 2x₂

⇒2x₁ = 2x₂ ⇒ x₁ = x₂

Hence one-one

(iii) a*e = a⇒ \(\frac{ae}{6}\) = a ⇒ e=6

e*a = a⇒ \(\frac{ea}{6}\) = a ⇒ e = 6

identity element = 6

a*b = e ⇒ 9*b = 6 ⇒ \(\frac{9b}{6}\) = 6 ⇒ b = \(\frac{36}{9}\) = 4

b*a = e ⇒ b*9  = 6 ⇒ \(\frac{b9}{6}\) = 6 ⇒ b = \(\frac{36}{9}\) = 4

Inverse element = b = 4

Let x₁, x₂ ∈ R f (x.) = f (x₁)

f(x₁) = f(x₂) ⇒ |x₁| = |x₂|

⇒ x₁ = x₂

|-2| = |+2| = 2

hence f is not one-one.

Range of functions is only non negative real numbers

Range of f = {0, ∞) ≠ R

∴ f is not onto.

x₁, x₂ ∈ A, f (x₁) = f (x₂) 

⇒ x₁ = x₂ 

∴ hence one-one

f(1) = 4, f(2) = 5, f(3) ≠ R, hence f is one-one.

a) (a,a) ∈ R,  ∀a ∈ A

b) f(x₁) = f(x₂) ⇒ \(\frac{x_1}{x_1 +2}\) = \(\frac{x_2}{x_2 + 1}\)

⇒ x₁x₂ + 2x₁ = x₁x₂ + 2x₂

⇒ x₁ = x₂ Hence one - one

Let the original dimensions be Length – l units

Breadth – b units 

Height – h units 

Then T.S.A = 2 (lb + bh + lh) 

If the dimensions are doubled then 

Length = 2l 

Breadth = 2b 

Height = 2h 

T.S.A. = 2 (2l. 2b + 2b . 2h + 2l . 2h) 

= 2 (4lb + 4bh + 4lh) 

= 4 × [2 (lb + bh + lh] 

= 4 × original T.S.A. 

i.e., T.S.A. increases by 4 times.

f (x) = 1 ∀ x ∈ [0, ∞ ) 

hence f is not one-one Range of f = {-1,0, 1} hence f is not onto.

Correct option is (A) T.S.A. of the box will become 4 times of original area.

Let \(l,b\;and\;h\) are parameters of original box.

\(\therefore\) \(2l,2b\;and\;2h\) are parameters of new box.

\(\therefore\) Total surface area of new box \(=2\,(2l\times2b+2b\times2h+2h\times2l)\)

\(=8\,(lb+bh+hl)\)

\(=4\times2\,(lb+bh+hl)\)

\(=4\times\) Total surface area of original box

Thus, if each dimension is doubled of a box then total surface area of box will become 4 times of original area.

A) T.S.A. of the box will become 4 times of original area.

Correct option is (B)1/3 πr²h

Volume of a cone \(=\frac{1}{3}\pi r^2h\)

Correct option is  B) 1/3πr²h

Given,

Depth of tubewell = 280 m

Diameter of tubewell = 3 m

So radius = \(\cfrac32\) m

Volume of tubewell = πr²h 

= \(\cfrac{22}7\times\cfrac94\times\)280

= 1980 m³

Curved surface area of tubewell = 2πrh

= 2\(\times\cfrac{22}7\times\cfrac{3}2\times\)280

= 2640 m²

∴ cost of sinking at rate Rs 3.60/m³ = 3.60 × 1980 = Rs. 7128.

∴ cost of cementing at rate Rs. 2.50/m² = 2.50 × 2640 = Rs. 6600.

Given A = [(1,-1),(-1,1)]

Then, A² = [(1,-1),(-1,1)][(1,-1),(-1,1)]

= [(1 + 1,-1 + (-1)),(-1 + (-1),1 + 1)] 

= [(2,-2),(-2,2)]

So, A³ = A².A = [(2,-2,-2,2)][(1,-1,-1,1)]

= [(2 + 2,-2 - 2),(-2 - 2,2 + 2)] 

= [(4,-4),(-4,4)]

b) Tenancy system

Correct Answer is: a) Keri

d) Hunting and gathering society

c) Division of labour

Correct Answer is: b) Maciver

1. Stone

2. Plough

3. Division of labour

4. Communication

5. Industrial

The process of engaging in animal husbandry of cattle like sheep, goat, cow and buffalo for general sustenance is called pastoral society.

Correct Answer is: a) Community

1. Small in size 

2. Influence of primary and family relationships. 

3. Simple economic life. 

4. Neighbourhood. 

• Simple economic life : As there is limited source of income which is low, rural people lead a life of simple and non luxury. Their dependence of agriculture and tradition is the main reason for their low demands.

1. Society is community of communities. 

2. Society is web of social relationship. 

3. Similarity and Resemblance 

4. Co-operation and Division of labour. 

5. Social control 

6. Society is dynamic

1. Zamindari system : 

• Zamindar is a Persian word. 
• Zamindar indicated the head of a region. 
• Any person who has the hereditary rights to have a share in farmer’s crops was officially called as Zamindar. 

2. Ryotwari system : 

• When the British government move to tax farmers. Zamindars started harassing them more. 
• In order to save farmers the court of directors introduced it in 1817. 
• Farmer was head of the land.

1. Universal :- 

• Society was there before the birth of an individual and remains even after his death. 

2. Protection and Nourishment :- 

• Co-operation, Division of labour, social control, institutions and similarities society takes care of the needs of human beings. 

3. Personality formation :- 

• Society provides proper channels to showcase one’s talents. It regulates the natural human weakness. 

4. Reinforces life :- 

• It is a complex one forming an individuals uniqueness thoughts and emotions.

1. Human beings and society are the two faces of the same coin. 

2. Human being can’t live alone, and prefer to live in social groups.

Correct Answer is: (d) Bhagirathi

The main feature of this ecosystem is that here vegetation and organisms can survive in a mixture of fresh and salt water. This delta region is expanding towards the ocean continuosly.

The lower Ganga plain is spread across Kishanganj (Purnea-Bihar) up till entire West Bengal (excluding upper hilly areas) and Bangladesh.

1. The process of engaging in animal husbandry of cattle like sheep, goat, cow and buffalo for general sustenance is called pastoral society. 

2. Cattle herding was the main occupation. 

3. The society was under the leadership of single leader.

1. Industry based economy :- 

• It will have capitalists, labour class and business class. 

2. Professional works :- 

• They need specific training and skills. 

3. Transport and communication P :- 

• This network is used for transporting raw materials and finished goods also. 

4. Increase in migration :-

• This is turn affected the traditional occupations and institutions.

1. It is the influence of information technology on socio-economical life. 

2. The information itself has become a commodity. 

3. To solve society’s problems and challenges. 

4. Helps to attain education commerce and business

1. At the agricultural society stage human beings left nomadic life and settled in a place engaging in agriculture. 

2. This society is a village based society. 

3. Majority of the people engage in agriculture related works. 

4. Producing food primarily through agriculture is another important feature. 

5. India is called as a land of village and agriculture. 

6. Jajmani system, Zamindari system, Ryothwari system, Mahalwari system. Tenancy system are close linked with agriculture

Industrialization gave rise to another type of society, the industrial society. Utilizing scientific production ways and searching for energy sources is called Industrial society.

1. Majority of the people engage in agricultural works. 

2. Producing food primarily through agriculture is another important feature. 

3. With the invention of plough during 3000BC the agricultural revolution stated. 

4. In rural area 59% of men and 75% of women are engaged in Agriculture.

1. As the information society is needed for all it has assumed more importance. 

2. People take help from information technologies to solve their problems and challenges. 

3. Helps to attain education, commerce and business 

4. Socio-economic life 

5. Information itself has become a commodity. 

6. Computers have become the information storage hubs.

1. It was a simple and ancient society. It is very small size. 

2. The human beings were engaged in fishing hunting animals etc. 

3. There was no desire of accumulation of wealth. 

4. Hunting was done using stone tools. 

5. Sharing the sources is the important trait

Correct Answer is: (d) Gangotri

(c) streams originates from the glaciers of Uttarakhand

1. Hunting and gathering society 

2. Pastrol society

3. Agricultural society 

4. Urban society 

5. Industrial society 

6. Information society

(c) Royal Bengal Tiger

The number of species of living organisms and plants available in a natural region is called bio – diversity.

The situation of Sunderbans: In the eastern part of India, a delta region has been formed by the Ganges river. The Ganges as well as its tributaries have extended their contribution in its. Due to the very mild slope of the Ganges and its tributaries, a deposition of alluvial soil is seen merges before the river enters into, the ocean. The expanse of this delta part is approximately 60000 square km. There are many forests found in this seaward swampy area, which have an abundance of a tree named Sundari. On this basis, this Delta region has been named as Sunderbans.

Bio – diversity in the Sunderbans: Due to swampy and humid conditions in the Sunderbans Delta part, various types of fauna and plant species are found. This is one of the leading areas of the world in terms of bio-diversity. Here, mangrove and tidal vegetation is found. Here the flora and fauna can survive in the mixture of fresh and salt water. The world-famous Royal Bengal Tiger is found in this area. Apart from these, many types of carnivorous and herbivorous creatures are also found in the Sunderbans.

(c) Three-tier system of governance – The village panchayat

Secondary type relations are significant in urban community.

Over 55% of the tribal population in India is found in the central region of the country.

Correct option is (c) Manipulation.

Correct option is (d) Coercion.