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(i) 6, 9, 15 and 20 

L.C.M of given 4 numbers is 180 

180 = 2² × 3² × 5 

To make it a perfect square, we have to multiply the number with 5 

Therefore, 

180 × 5 = 2² × 3² × 5² 

900 is the least square number divisible by 6, 9, 15 and 20 

3600 is the least square number divisible by 8, 12, 15 and 20 

(ii) 8, 2, 15 and 20 

L.C.M of given 4 numbers is 360 

360 = 2² × 3² ×2 × 5 

To make it a perfect square, we have to multiply the number with 2 × 5 = 10 

Therefore, 

360 × 10 = 2² × 3² × 5² × 2²

Let ‘a’ be the side of square field 

Therefore,

a² = 5184 m² 

a = \(\sqrt{5184}\) m 

a = 2 × 2 ×2 × 9 

= 72 m 

Perimeter of square = 4a 

= 288 m 

Perimeter of rectangle = 2 (l + b) 

= 288 m 

2 (2b + b) = 288 

b = 48 and l = 96 

Area of rectangle = 96 × 48 m² = 4608 m²

 = 4608 m²

(c) 0.99

\(\frac34+\frac5{36}+\frac7{144}+........+\frac{17}{5184}+\frac{19}{8100} \)

= \(\frac{3}{1^2.2^2}\) + \(\frac{5}{2^2.3^2}\) + \(\frac{7}{4^2.3^2}\) + ........ + \(\frac{17}{8^2.9^2}\) + \(\frac{19}{9^2.10^2}\)

= \(\big(1-\frac1{2^2}\big) + \big(\frac1{2^2}-\frac1{3^2}\big) + \big(\frac1{3^2}-\frac1{4^2}\big) + ...... +\big(\frac{1}{8^2}-\frac1{9^2}\big) + \big(\frac{1}{9^2}-\frac1{10^2}\big)\)

= 1 - \(\frac1{10^2}\) = 1 - \(\frac1{100} = \frac{99}{100}\) = 0.99.

(i) 3.02 × 10⁻⁶ = 0.00000302

(ii) 4.5 × 10⁴ = 45000

(iii) 3 × 10⁻⁸ = 0.00000003

(iv) 1.0001 × 10⁹ = 1000100000

(v) 5.8 × 10¹² = 5800000000000

(vi) 3.61492 × 10⁶ = 3614920

(i) 9801

Since, unit digit of 9801 is 1

\(\therefore\) Unit digit of square root = 1 or 9

Since the number is odd, square root is also odd

(ii) 99856

Since, unit digit of 99856 = 6

\(\therefore\) Unit digit of square root = 4 or 6

Since the number is even, square root is also even

(iii) 998001

Since,unit digit of 998001 = 10

 \(\therefore\) Unit digit of square root = 10 or 9

Since the number is odd, square root is also odd

(iv) 657666025

Since, unit digit of 657666025 = 5

\(\therefore\) Unit digit of square root = 5

Since the number is odd, square root is also odd

We can solve the given question as:

= \(\sqrt{2{\frac{1}{4}}}\)

= \(\sqrt{\frac{9}{4}}\)

= \(\frac{\sqrt{9}}{\sqrt{4}}\)

= \(\frac{\sqrt{3\times3}}{\sqrt{2\times2}}\)

= \(\frac{3}{2}\)

= \(1\frac{1}{2}\)

Hence,

Option (B) is the correct option

(i) 9801 

Unit digit = 1 

Unit digit of square root = 1 or 9 

As number is odd, square root is also odd 

(ii) 99856 

Unit digit = 6 

Unit digit of square root = 4 or 6 

As number is even, square root is also even 

(iii) 998001 

Unit digit = 1 

Unit digit of square root = 1 or 9 

As number is odd, square root is also odd 

(iv) 657666025 

Unit digit = 5 

Unit digit of square root = 5 

As number is odd, square root is also odd

Answer : (a) 1 : 2 

Let a and d be the first term and common difference respectively of the A.P.

S₁₀ = \(\frac{10}{2}\) [2a + 9d]

S₅ = \(\frac{5}{2}\)[2a + 4d]

Given, S₁₀ = 4S₅ 

⇒ 5(2a + 9d) = 4 × \(\frac{5}{2}\) [2a + 4d] 

⇒ 10a + 45d = 20a + 40d 

⇒ 5d = 10a 

⇒ \(\frac{a}{d}\)= \(\frac{5}{10}\) = \(\frac{1}{2}\)

⇒ a : d = 1 : 2

It is given that AB || CD and CD || EF

∴ AB || CD || EF (Lines parallel to the same line are parallel to each other) It can be observed that

x = z (Alternate interior angles) … (1)

It is given that y: z = 3: 7

Let the common ratio between y and z be a.

∴ y = 3a and z = 7a

Also, x + y = 180º (Co-interior angles on the same side of the transversal)

z + y = 180º [Using equation (1)]

7a + 3a = 180º

10a = 180º

a = 18º

∴ x = 7a = 7 × 18º = 126º

It can be observed that,

50º + x = 180º (Linear pair)

x = 130º … (1)

Also, y = 130º (Vertically opposite angles)

As x and y are alternate interior angles for lines AB and CD and also measures of these angles are equal to each other, therefore, line AB || CD.

According to the question,

For real value of

28 – x ≠0

⇒ x≠ 28

Therefore, the domain of f = R–{28}

Given: f(x) = 1-|x-2|

To find: the range of function

Explanation: So, the range of a function consists of all the second elements of all the ordered pairs, i.e., f(x), so we have to find the values of f(x) to get the required range

Given,

f(x) = 1-|x-2|

Now for real value of f,

|x-2|≥ 0

Adding negative sign, we get

Or -|x-2|≤ 0

Adding 1 we get

⇒ 1-|x-2|≤ 1

Or f(x)≤1

⇒ f(x)∈ (-∞, 1]

Hence the range of f = (-∞, 1]

Given: f(x) = |x-3|

To find: the range of function

Explanation: So, the range of a function consists of all the second elements of all the ordered pairs, i.e., f(x), so we have to find the values of f(x) to get the required range

Given,

f(x) = |x-3|

We know |x| are defined for all real values.

And |x-3| will always be greater than or equal to 0.

i.e., f(x)≥0

Hence the range of f = [0, ∞)

(i) According to the question,

h = {(4, 6), (3, 9), (– 11, 6), (3, 11)}

Therefore, element 3 has two images, namely, 9 and 11.

A relation is said to be function if every element of one set has one and only one image in other set.

Hence, h is not a function.

(ii) According to the question,

f = {(x, x) | x is a real number}

This means the relation f has elements which are real number.

Therefore, for every x ∈ R there will be unique image.

A relation is said to be function if every element of one set has one and only one image in other set.

Hence, f is a function.

(iii) According to the question,

g = n, (1/n) |n is a positive integer

Therefore, the element n is a positive integer and the corresponding 1/n will be a unique and distinct number.

Therefore, every element in the domain has unique image.

A relation is said to be function if every element of one set has one and only one image in other set.

Hence, g is a function.

(iv) According to the question,

s = {(n, n²) | n is a positive integer}

Therefore, element n is a positive integer and the corresponding n² will be a unique and distinct number, as square of any positive integer is unique.

Therefore, every element in the domain has unique image.

A relation is said to be function if every element of one set has one and only one image in other set.

Hence, s is a function.

(v) According to the question,

t = {(x, 3) | x is a real number.

Therefore, the domain element x is a real number.

Also, range has one number i.e., 3 in it.

Therefore, for every element in the domain has the image 3, it is a constant function.

A relation is said to be function if every element of one set has one and only one image in other set.

Hence, t is a function.

Given: f (x) = 1 + 3 cos2x

To find: the range of function

Explanation: So, the range of a function consists of all the second elements of all the ordered pairs, i.e., f(x), so we have to find the values of f(x) to get the required range

Given,

f (x) = 1 + 3 cos2x

We know the value of cos 2x lies between -1, 1, so

-1≤ cos 2x≤ 1

Multiplying by 3, we get

-3≤ 3cos 2x≤ 3

Adding with 1, we get

-2≤ 1 + 3cos 2x≤ 4

Or, -2≤ f(x)≤ 4

Hence f(x)∈ [-2, 4]

Hence the range of f = [-2, 4]

Given: f (x) = 1/√x−5 .

To find: the domain and range of function

Explanation: So, the domain of a function consists of all the first elements of all the ordered pairs, i.e., x, so we have to find the values of x to get the required domain

Given,

f (x) = 1/√x−5 .

Now for real value of

x-5≠0 and x-5>0

⇒ x≠5 and x>5

Hence the domain of f = (5, ∞)

And the range of a function consists of all the second elements of all the ordered pairs, i.e., f(x), so we have to find the values of f(x) to get the required range

Now we know for this function

x-5>0

taking square root on both sides, we get

√x−5 > 0

Or

1/√x−5 > 0

Or

f(x)>0

⇒ f(x)∈(0, ∞)

Hence the range of f = (0, ∞)

(i) {(1, 2), (2, 3), (3, 4), (2, 1)}

It is not a function because element 2 corresponds to two elements 3 and 1.

(ii) {(a, 0), (b, 0), (c, 1), (d, 1)}

It is a function because under this each element corresponds to one and only one element.

(iii) {(1, a), (2, b), (1, b), (2, a)}

It is not a function because element 1 corresponds to two elements a and b.

(iv) {(a, a), (b, b), (c, c)}

It is a function because first element of ordered pair set is not same.

(v) {a, b}

It is a function because a corresponds to b

(vi) {(4, 1), (4, 2), (4, 3), (4, 4)}

It is not a function because first element of ordered pair set is same.

(vii) {(1, 4), (2, 4), (3, 4), (4, 4)}

It is a function because first element of ordered pair set is unequal.

(viii) {(x, y) : x, y ∈ R, y² = x}

Here y² = x ⇒ y = ±√x and if x = 4 then y = ±2

Hence, element of y is related with 2 and -2 so, it is not a function.

(ix) {(x, y) : x, y ∈ R, x² = y}

It is a function because for y = x², each real value of x there is a unique image in R for each element of R

(x) {(x, y) : x, y ∈ R, x = y³}

It is a function because y = x^1/3, ∀ x ∈ R unique image is the set B.

(xi) {(x, y) : x, y ∈ R, y = x³}

It is also a function because for y = x³ ∀ x ∈ R unique image is in set B.

Given: Given: f(x) = √x and g (x) = x two functions defined in the domain R ⁺ ∪{0},

To find: (f-g)(x)

Explanation: this can be obtained by subtracting functions f(x) from g(x), i.e.,

⇒ (f-g)(x) = f(x)-g(x)

Substituting the corresponding equation, we get

⇒ (f-g)(x) = √x-x

Given: f(x) = √x and g (x) = x two functions defined in the domain R ⁺ ∪{0},

To find: (fg)(x)

Explanation: this can be obtained by multiplying functions f(x) and g(x), i.e.,

⇒ (fg)(x) = f(x) g(x)

Substituting the corresponding equation, we get

⇒ (fg)(x) = (√x)(x)

⇒ (fg)(x) = x√x

Given: f(x) = √x and g (x) = x two functions defined in the domain R ⁺ ∪{0},

To find: (f + g)(x)

Explanation: this can be obtained by adding functions f(x) and g(x), i.e.,

⇒ (f + g)(x) = f(x) + g(x)

Substituting the corresponding equation, we get

⇒ (f + g)(x) = √x + x

(A) -34x⁵y⁴z³

(D) -2(7x + 12y)

(3x – 11y) – (17x + 13y) 

= 3x – 11y – 17x – 13y

= (– 14x) – 24y 

= (– 2) × 7x – 2 × 12y 

= – 2(7x + 12y)

यदि (x + 2), बहुपद (x + 1)⁷ + (2x + k)³ का एक गुणनखण्ड है तो

x + 2 = 0 या x = 0 – 2 = -2 रखने पर

शेषफल = 0

(-2 + 1)⁷ + (2 × -2 + k)³ = 0

(-1)⁷ + (-4 + k)³ = 0

-1 + (-4 + k)³ = 0

(-4 + k)³ = 1

(-4 + k)³ = (1)³

-4 + k = 1

k = 1 + 4 = 5

यदि (x + 5) से 4x³ + 16x² – x + 5 को पूर्णतया विभाजित किया जाए तो

x + 5 = 0 या x = 0 – 5 = -5 रखने पर

शेषफल = 4(-5)³ + 16(-5)² – (-5) + 5

= 4(-125) + 16(25) + 5 + 5

= -500 + 400 + 10 = -90

(x – 1), बहुपद x¹⁰ – 1 का गुणनखण्ड होगा। यदि x – 1 = 0 या x = 1 रखने पर

x¹⁰ – 1 का शेषफल = (1)¹⁰ – 1 = 1 – 1 = 0

∴ (x – 1), x¹⁰ – 1 का गुणनखण्ड है।

x¹¹ – 1 का शेषफल = (1)¹¹ – 1 = 1 – 1 = 0

∴ (x – 1), x¹¹ – 1 का गुणनखण्ड है।

बहुपद x² + x – 12 के गुणनखण्ड (x – 3) तथा (x + 4) होंगे।

यदि x – 3 = 0 या x = 3 रखने पर शेषफल = (3)² + 3 – 12 = 9 + 3 – 12 = 0

यदि x + 4 = 0 या x = -4 रखने पर शेषफल = (-4)² – 4 – 12 = 16 – 16 = 0

∴ (x – 3) व (x + 4) बहुपद x² + x – 12 के गुणनखण्ड हैं।

2x⁴ – 6x³ + 3x² + 3x – 2 को x² – 3x + 2 से भाग करने पर

∵ x² – 3x + 2 = (x – 2)(x -1) यदि x – 2 = 0 या x = 2 रखने पर

शेषफल = 2(2)⁴ – 6(2)³ + 3(2)² + 3(2) – 2

= 32 – 48 + 12 + 6 – 2

= 50 – 50 = 0

∴ (x – 2) से पूर्णतया विभाजित है।

यदि x – 1 = 0 या x = 1 रखने पर

शेषफल = 2(1)⁴ – 6(1)³ + 3(1)² + 3(1) – 2

= 2 – 6 + 3 + 3 – 2

= 8 – 8 = 0

∴ (x – 1) से पूर्णतया विभाजित है।

यदि (x – 1), x⁴ – 3x³ + bx² + 8x – 4 का एक गुणनखण्ड है तो x – 1 = 0 या x = 1 रखने पर

शेषफल = 0

(1)⁴ – 3(1)³ + b(1)² + 8(1) – 4 = 0

1 – 3 + b + 8 – 4 = 0

b + 2 = 0

b = 0 – 2 ⇒ b = -2

x³ – 6x² + 11x – 6 में x = 1 रखने पर

शेषफल = (1)³ – 6(1)² + 11(1) – 6 = 1 – 6 + 11 – 6 = 0

अतः (x – 1) इसका एक गुणनखण्ड है।

इसी प्रकार (x – 2) व (x – 3) भी इसके गुणनखण्ड हैं।

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Factors affecting elasticity of demand are as follows:

(i) Availability of Close Substitutes: A commodity will have elastic demand if there are good substitutes available. For example Pepsi, Coca-Cola, Frooti. A commodity having no substitutes, For example, salt will have inelastic demand.

(ii) Postponement of Use: Usually the demand for such commodities whose use can be postponed for some time is elastic. For example ; the demand for DVD player is elastic because its use can be postponed for some time, if its price goes up, but the demand for wheat and rice is inelastic because their use cannot be postponed when price goes up.

Price elasticity of demand is a measure of degree of the responsiveness of the demand for a good to change in its price.

Factor affecting:

(i) Nature of goods.

(ii) Number of substitutes.

(iii) Proportion of income spent on a good.

(iv) Any other relevant factor.

Price elasticity of demand is a measure of degree of the responsiveness of the demand for a good to change in its price.

Factors effecting Elasticity of Demand:

The elasticity of demand is affected by the following factors:

(i) Nature of Commodity: Goods maybe necessaries, luxuries and comforts. Demand for necessaries (like salt) is highly inelastic; demand for luxuries (like ACs) is highly elastic; and demand for comforts (like air coolers) is moderately elastic.

(ii) Availability of Substitutes: Commodities which have substitutes, elastic demand, like tea and coffee. Commodities having no substitutes like liquor and cigarettes, etc. have inelastic demand.

(iii) Alternative Uses of a Commodity: If a commodity is used for different purpose, it has elastic demand. Example: electricity and coal.

(iv) Price Level: Higher the level of price, higher is the elasticity of demand for a commodity.

(v) Time Period: Elasticity of demand is high over a long period (compared to a short period), because during a short period of time, consumption habits tend to be stable.

(a) D 

(b) E 

(c) D

Pre conglomerate:

1. Because it involve firms with nothing in common or conducted between unrelated companies.

2. They are not the competitors.

3. Buyers and sellers so not show much relationship or no evident relationship.

Absolute error is calculated by subtracting true value from observed value. 

Absolute error = Observed value – Time value

i. Absolute deviation : 

An absolute deviation is the modulus of the difference between an observed value and the arithmetic mean for the set of several measurements made in the same way. It is a measure of absolute error in the repeated observation. 

It is expressed as follows : 

Absolute deviation = |Observed value – Mean|

ii. Mean absolute deviation : 

Arithmetic mean of all the absolute deviations is called the mean absolute deviation in the measurements

iii. Relative deviation : 

The ratio of mean absolute deviation to its arithmetic mean is called relative deviation.

It is expressed as follows :

Relative deviation = \(\frac{Mean\,absolute\,deviation}{Mean}\) x 100%

1. Relative error is the ratio of an absolute error to the true value.

2. Relative error is generally a more useful quantity than absolute error.

3. Relative error is expressed as a percentage and can be calculated as follows :

Relative error = \(\frac{Absolute\,error}{True\,value}\) x 100%

• Uncertainty in measured value leads to uncertainty in calculated result.
• Uncertainty in a value is indicated by mentioning the number of significant figures in that value. e.g. Consider, the column reading 10.2 ± 0.1 mL recorded on a burette having the least count of 0.1 mL. Here, it is said that the last digit ‘2’ in the reading is uncertain, its uncertainty is ±0.1 mL. On the other hand, the figure ‘10’ is certain.
• The significant figures in a measurement or result are the number of digits known with certainty plus one uncertain digit.
• In a scientific experiment, a result is obtained by doing calculation in which values of a number of quantities measured with equipment of different least counts are used.

The word “co-operative” means “an organisation wherein the stakeholders work with one another”. Thus, a co-operative society is a voluntary association of individuals who work together to protect or promote their common interests. 

Features of a co-operative society: 

i. Separate legal entity: The registration of a co-operative society is compulsory under the Co-operative Societies Act 1912. Once the registration is complete, the company is granted the status of a separate legal entity. This implies that it can hold properties in its name and enter into contracts. Also, the company can sue others and can be sued by others. 

ii. Management and control: In a co-operative society, the management and control lie in the hands of a managing committee formed by its members. 

iii. Democratic Management: A co-operative society is a democratic form of organisation, as it is managed and controlled by a managing committee formed by its members following the principle of “one member, one vote”. 

iv. Equal voting rights: A co-operative society grants equal voting rights to all its members. This implies that each member in the society has an equal voting right, irrespective of the amount of capital contributed by him/her in the society. 

v. Limited liability: In a co-operative society, the liability of all members is limited to amount of capital invested by them in the business. In other words, the personal property of the members cannot be used for paying off the liabilities of the business. 

vi. Service motive: The primary objective of a co-operative organisation is to provide services to its members, while its secondary objective is to earn profit. Thus, it works in the interest of its members and provides goods and services to them.

A joint Hindu family firm is owned and managed by the members of a Hindu undivided family. Membership in this business is by birth; that is, as soon as a child is born in the family, he/she becomes the member of the family business. This type of organisation is governed by the Hindu Succession Act 1956. 

Merits of a joint Hindu family business: 

i. Easy formation: The formation of a joint Hindu family business requires the existence of ancestral property and at least two family members. It is governed by the Hindu Succession Act 1956 and does not require any agreement for its formation. 

ii. Continuity: The continuity of a joint Hindu family business remains unaffected by the death of the Karta. This is because, in case of the death of the existing Karta, the next eldest member of the family takes over his responsibilities. Thus, the business continues to operate even after the death of the existing Karta. 

iii. Limited liability: In a joint Hindu family business, the liability of all members is limited to the amount of capital invested by them in the business. In other words, the personal property of the members cannot be used to meet the liabilities of the business. However, the liability of the Karta is unlimited. 

Demerits of a joint Hindu family business: 

i. Limited capital: The amount of capital available with a joint Hindu family firm is limited to the amount of inherited wealth. The limited availability of funds, in turn, restricts the scope of expansion of the business. 

ii. Limited managerial skills: The management of the family business lies in the hands of the Karta, who may not be professionally skilled to handle all the business operations. Thus, the efficiency in the management of the business solely depends on the managerial skills of the Karta. 

iii. Unlimited liability of Karta: The liability of the Karta is unlimited in a joint Hindu family firm. In other words, if the business assets are insufficient to meet the business debts, then the personal property of the Karta can be utilised for the purpose.

A joint Hindu family firm is owned and managed by the members of a Hindu undivided family. Membership in this business is by birth; this means that as soon as a child is born in the family, he/she becomes the member of the family business. This type of organisation is governed by the Hindu Succession Act 1956. 

The following characteristics distinguish a joint Hindu family business from other forms of organisations: 

i. Easy formation: The formation of a joint Hindu family business requires the existence of ancestral property and at least two family members. It is governed by the Hindu Succession Act 1956 and does not require any agreement for its formation. 

ii. Liability: In a joint Hindu family business, the liability of all members except the Karta is limited to their amount of share in the family property. However, the liability of the Karta is unlimited. 

iii. Control: The Karta is solely responsible for all the management and decision making in the family business. In other words, he has complete control over the business. Other members have a share in the decision making; however, the final decision is taken by the Karta only. 

iv. Continuity: The continuity of a joint Hindu family business remains unaffected by the death of the Karta. This is because, in case of the death of the existing Karta, the next eldest member of the family takes over his responsibilities. Thus, the business continues to operate even after the death of the existing Karta. 

v. Status of minors: In a joint Hindu family, membership in the family business is by birth. This means that as soon as a boy is born in a Joint Hindu family, he is automatically entitled to a share in the family business. In such cases, a minor has equal ownership rights over the inherited property. However, his liability is limited to the extent of his share in the joint property. 

vi. Quick decision making: In a joint Hindu family business, the Karta takes all important decisions; he need not consult other members of the family. Thus, it results in quick decision making.

• Molality is the number of moles of solute present in 1 kg of solvent. Therefore, molality is mass dependent.
• Mass remains unaffected with temperature.

Hence,

Molality is not affected by temperature.

Portfolio manager.

Given : 

Molarity of the solution = 3 M, 

Density of the solution = 1.25 g mL 

To find : 

Molality of the solution 

Formula :

Molality = \(\frac{Number\,of\,moles\,of\,solute}{Mass\,of\,solvent\,in\,kilograms}\) 

Calculation : 

Molarity = 3 mol L^-1

∴ Mass of NaCl in 1 L solution 

= 3 × 58.5 

= 175.5 g

Mass of 1 L solution = 1000 × 1.25 

= 1250 g

(∵ Density = 1.25 g mL^-1)

Mass of water in solution = 1250 – 175.5 

= 1074.5 g 

= 1.0745 kg

Molality = \(\frac{Number\,of\,moles\,of\,solute}{Mass\,of\,solvent\,in\,kilograms}\)  

= \(\frac{3\,mol}{1.0745\,kg}\) 

= 2.790 m (by using log table)

∴ Molality of the NaCl solution = 2.790 m

[Calculation using log table : \(\frac{3}{1.0745}\) 

= Antilog₁₀[log₁₀(3) – log₁₀(1.0745)]

= Antilog₁₀[0.4771 – 0.0315]

= Antilog₁₀[0.4456] = 2.790]

In scientific notations, numbers are expressed in the form of N × 10ⁿ, where ‘n’ is an exponent with positive or negative values and N can have a value between 1 to 10.

e.g. i. The number, 

602,200,000,000,000,000,000,000 is expressed as 6.022 × 10²³.

ii. The mass of a H atom,

0.00000000000000000000000166 g is expressed as 1.66 × 10^-24g.

iii. The number 123.546 is written as 1.23546 × 10².

iv. The number 0.00015 is written as 1.5 × 10^-4

The two merits of partnership are: 

1. A partnership enjoys flexibility in operations. The operations of a partnership can be easily adjusted or changed according to changing business conditions. 

2. A partnership is not subject to strict Government control. Therefore, it enjoys greater freedom in administration.

Jointly and severally

When a magnet is placed in a magnetic field it aligns itself along the field lines with the North Pole in the direction of the magnetic field.

On the surface of earth a magnetic field exists due to the contents of the earth making it behave like a magnet. Because of this a magnetic needle is used to find the direction on the surface of the earth.

B. inner core 

The outer core is the layer surrounding the inner core. It is a liquid layer. It is also made up of iron and nickel.