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The square of 0.7 is 0.49.

= 0.7²

= 0.7 × 0.7

= 0.49

The digit at the ones place of 57² is 9.

We know that, 3 or 7 at the units place ends in 9.

= 57²

= 57 × 57

= 3249

(i) (8, 15, 17)

L.H.S = 82 + 152

= 289

R.H.S = 172

= 289

L.H.S = R.H.S

∴ The given triplet is a Pythagorean.

(ii) (18, 80, 82)

L.H.S = 18² + 80²

= 6724

R.H.S = 82²

= 6724

L.H.S = R.H.S

∴ The given triplet is a Pythagorean

(iii) (14, 48, 51)

L.H.S = 14² + 48²

= 2500

R.H.S = 51²

= 2601

L.H.S ≠ R.H.S

∴ The given triplet is not a Pythagorean.

(iv) (10, 24, 26)

L.H.S = 10² + 24²

= 676

R.H.S = 26²

= 676

L.H.S = R.H.S

∴ The given triplet is a Pythagorean.

False

A perfect square can never have 8 as its unit’s digit.

False.

Three natural numbers a, b, c are said to form a Pythagorean triplet if a² + b² = c².

Then,

Pythagorean triplet as, 7² = 6² + 5²

6 is not an odd number.

True.

We know that, natural numbers between a and b = b –a – 1

= 101² – 100² – 1

= (101 + 100) (101 – 100) – 1

= 201 – 1

= 200

Given, one of the number in the Pythagorean triplet i.e. 4.

Then,

2m = 4

m = 4/2

m = 2

So,

= m² + 1

= 2² + 1

= 4 + 1

= 5

And,

= m² – 1

= 2² – 1

= 4 – 1

= 3

∴The Pythagorean triplet is 3, 4 and 5.

False.

It is not a perfect square.

1000 is a perfect cube, i.e. 10 × 10 × 10 = 1000

The sum of first six odd natural numbers is 36.

The first six odd numbers are 1, 3, 5, 7, 9, and 11

Then,

Sum of first six odd numbers = 1 + 3 + 5 + 7 + 9 + 11

= 36

Given, one of the number in the Pythagorean triplet i.e. 5.

= m² + 1 = 5

= m² = 4

= m = 2

Then,

2m = 2 × 2

m = 4

So,

And,

= m² – 1

= 2² – 1

= 4 – 1

= 3

∴The Pythagorean triplet is 3, 4 and 5.

Similarly,

The other Pythagorean triplet is 5, 12 and 13.

We know that, 

According to the Pythagorean triplet, 

For a natural number m, 

(2m, m² – 1, m² + 1) is a Pythagorean triplet. 

Hence, 

Considering the Pythagorean triplet, 

Let m = 4 

2m = 8 

m² – 1 = 15 

m²+ 1 = 17 

Thus, 

(8, 15, 17) is the Pythagorean triplet. 

Hence, 

Option (D) is the correct option.

True.

The sum of odd numbers = ∑(2n – 1)

= (2 × n × (n + 1))/2 –n

= n² + n – n

= n²

False.

For every natural number m > 1, 2m, m²–1 and m² + 1 form a Pythagorean triplet.

(d) √m

n² = m

Then,

n = √m

If γ = 0. the two variables x and y are independent, i.e., Non correlated.

The cause and effect relationship between the two correlated variables is called causation.

The absence of causation between two variables even though they vary together is called spurious correlation.

• It is independent of units of measurement 
• It is independent of origin and the scale.

b_xy and b_yx are called regression co-efficients.

(A) Polar region

Answer is (A) Iceland

There will be no sunlight during the winter in the polar region. At this time, the light of stars 

falls on the ice, reflects, and fills the region with bright colourful lights.

These are known as ‘Aurora Borialisis’. During winter they get light with these Aurora borialisis, oil and fat lamps. In what ways are the resources available in their surroundings used for making houses?

1. They use skins of animals and wood for tents. 

2. They use logs and whale ribs in building round houses. 

3. They form ice blocks (like bricks) and build domed houses.

Thus they use available resources in the surroundings.

 The correct answer is True.

Answer is (C) 1850

Mukluks are Boots of the Eskimos.

The lives of people in Tundra have changed for better or worst both because of their interaction with the outside world. 

The pattern of relations between the Eskimos and outsiders has been described as “boom and bust”. Waves of outsiders have brought brief periods of wealth, education, and employment. This was followed by periods of poverty and disorganisation. Peak periods have been those of whaling (1859 to 1910), the modern fur trade (1925 to about 1950), the building of military and defence bases (the mid-1950s), the building of urban centres (mid- 1960s), and oil exploration and development (the 1970s).

Each wave of activity has drawn the Eskimos into contact with different social and economic forces. The once isolated northlands have been opened up by air travel, highways, powerful modern ships, and satellite communications. These changes have produced great strains on the Eskimo way of life.

The boundary of the polar region is known as the ‘Arctic Circle’.

They celebrate some major ceremonies, performed at birth and death or when hunting was very poor or very successful.

(D) All correct

(D) Greenland

The people of the earlier times wore raw skins of animals. They are too heavy. They use the horns of animals, harpoons, sharp edged instruments to hunt. 

In the modern times they wore designed caps, dresses which are light in weight. Guns occupied the place of traditional weapons.

The northern part of the continents within the polar region is known as the Tundra.

There are no seasons or seasonal differences in tundras. They have likely temperatures and seasons. They face nominal summers. So they cannot cultivate crops here. They have no tasty foods and different kinds of foods. During winters the whole region becomes dark, deserted and desolate. 

So they did not live here throughout the year.

‘Igloo’ means Shelter

Answer is (B) Winter

Answer is (B) Shamans

Answer is (B) 25 – 45

Answer is (A) Shelter

Answer is (B) 1100

Mirage is an optical illusion created by total internal reflection of light Under normal circumstances the density of air is uniform on tar roads and hence light travels in straight line. The air layer in contact with earth gets heated up and becomes rare when compared to the upper strata of atmosphere.

Light coming from the distant objects is total internally reflected. This creates an illusion of reflection in water. The inverted image caused due to the hot air volume below is responsible for this. This phenomenon is rare in case of positions above the level of the observer.

'Igloo’ means house in the language of Eskimos.

This picture shows north polar region. The circles on this show latitudes and lines show longitudes. The place where the longitudes meet is called N pole. The southern tip of Greenland and about that is shown out of the globe. I think this is not correct. The earth is swollen at the equator and flat at the poles.

A) 1 – c, 2 – e, 3 – a, 4 – d, 5 – b

Tundra Vegetation: The Tundra region gets very little sunlight, it has a unique type of vegetation known as the ‘Tundra Vegetation’.

(a) maize cultivation

Any curved piece of transparent medium is called a lens. 

The two types of lens are 

1. convex lens 

2. concave lens.

The most commonly accepted meaning of ‘Eskimo’ is “snowshoe-netter”. There are two main groups referred to as 

Eskimos : 

Inuit and Yupik. Inuit in their language means ‘the people’ or ‘the real people’. The Eskimos are descendants of Siberia, now a part of the Russia in northern Asia.

Eskimos lead a group life. They lead a nomadic life. They share all their activities, food and shelters, and their joys, sorrows everything. They have such unity which we cannot see in the so-called civilized societies. Really we should praise it.

Kayaks: Kayaks are small canoe-like boats made of animal skins stretched over a wooden frame.

The type of lens used by watch repairers is convex lens.