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(i) In hard water soaps get precipitated as calcium and magnesium soap which being insoluble in water stick to the clothes as gummy mass. 

(ii) This is because aspartame is unstable at cooking temperature.

Poulaine-French shoe with exaggerated lengths

Panier-lighter supporting frame stitched to an underskirt.

a. Social status- choice of colour, clothes and fabric consumption.

b. Rank-evoke obedience, allegiance, loyalty etc.

c. Profession- judge’s wig, uniform of army personnel

d. Marital status- yoruk turkis, Indian culture and western culture

e. Individual status- shaman, warrior’s costume.

India- vermillion applied in the parting of the hair and mangalsutra necklace. Western- wedding band on the ring finger.

To conceal the soldier’s presence thus making him inconspicuous as a target.

Animal skin- for warmth

Bones- assembly of pieces threaded by long manes.

Human beings are essentially the same everywhere. Their virtues, strange habits and weaknesses know no boundaries. So, it is not difficult to win over others if you are confident and skilful. The first important skill is communication skill. Then comes the ability to analyse and utilise the opportunities available. All these skills can help you impress others and achieve praiseworthy goals.
Therefore, it is appropriate to say that nothing is difficult in this world. This is the message conveyed by ‘Best Seller’.

Buchanan on Rajmahal hills 

(i) Productive 

i. Land should be cleared of woods 

ii. Plantations of Asan and Palas, for Tessar (Tassar silk worms) and Lac, should occupy the place of woods 

iii. For the expansion and extension of cultivable area

iv. The land which was not fit for cultivation might rear plamira and mahua

(ii) Buchanan and local inhabitants 

i. Locals wanted to be in their land 

ii. They wanted to carry on their subsistence cultivation but British wanted extensive cultivation. 

iii. Locals were close and sentimental to their trees whereas British wanted to clear the lands for cultivation.

(iii) Feelings of locals 

i. Suspicious towards Buchanan 

ii. Felt discriminated iii Felt critical for each other P

(i) System of Varnas 

i. The highest caste was the Brahmanaand as the Brahman was only another name for the force called nature, and the head was the highest part of the body, the Brahmana are the choice part of the whole genus. Therefore the Hindus considered them as the very best of mankind. 

ii. The next caste was the Kshatriya, who was created, as they say, from the shoulders and hands of Brahman. Their degree was not much below that of the Brahmana. 

iii. After them follow the Vaishya, who were created from the thigh of Brahman iv. Shudra, who were created from his feet ... Between the latter two classes there is no very great distance.

(ii) As social pollution

i. Based on exploitation 

ii. Created out of the Brahman/ nature 

iii Differential treatment

(iii) He considered the caste system contrary to the law of nature as god has created everyone equal and this system was not prevalent in the western society. He considered it as social pollution.

(i) Mother’s advice king conquered the earthi. 

i.The wise man in control of his senses that guards his kingdom. 

ii. By avoiding greed and anger

(ii) Views on feud war 

i. She wanted to makepeace. 

ii. There is no victory at the end. 

iii. She told a person could happily enjoy the earth along with the wise and heroic Pandavas 

iv. There is no good in a war, no law (dharma) and profit).

(iii)Gandhari’s appeal to her son

i. She appealed to make peace with Pandavas 

ii. Told him to avoid war 

iii. War would not bring good to man 

iv. There is no victory at the end 

v. To be friendly with the Pandavas 

vi. There would be no good in a war and set his mind off from the war

Factors responsible for Partition of India 

i. Separate electorates given by the British to Muslims in 1909 and expanded in 1919. (Govt. of India Act-1909 and 1919) 

ii. Sectarian slogans used on the basis of religion in the 1920s. 

iii. Tabligh and Shuddhi movements -Music before Mosque, cow protection movement etc. 

iv. Communal tensions and riots deepened the differences between the two communities. 

v. Outcome of 1937 elections. 

vi. Muslim league demanded a joint government in UP and was rejected by INC. 

vii. Jinnah’s insistence that the league should be recognized as the sole spokesman of the Muslims and other developments. 

viii. Demand for communal vote in the executive council by Jinnah. 

ix. Pakistan resolution by Muslim league in 1940 

x. Congress ministries also contributed to the widening of rift. The party rejected the Muslim league proposal for coalition govt. 

xi. Provincial elections of 1946. 

xii. Cabinet Mission Plan. 

xiii. Direct Action Day. 

xiv. Partition of India and Communal riots 

xv. Any other relevant point

Non cooperation movement 

i. Protest against Rowlatt act, Jallianwala Bagh massacre, Khilafat movement for Swaraj and against the Govt. of India Act 1919 

iii. Knitted apopular movement throughHindu Muslims participated together against the colonial power. 

iv. Swadeshi and boycott movement became popular 

v. People defied laws 

vi. Tribal people violated forest laws. 

vii. Traders, farmers, workers joined in the movement 

viii. Non-cooperation with the colonial power ix. He became people’s leader byentailed renunciation and self discipline 

x. Gandhiji emerged as undisputed leader 

xi. Shaken the foundation of British power. 

xii. It was a training for self-rule

Importance and limitations of Ain-i- Akbari 

A. Importance

i. The Ain gives detailed accounts of the organization of the court, administration and army, the sources of revenue and the physical layout of the provinces and the literary, cultural and religious traditions of the people. 

ii. Along with a description of the various departments of Akbar’s government and elaborate descriptions of the various provinces (subas) of the empire 

iii. TheAin gives us intricate quantitative information of those provinces. 

iv. The Ain is therefore a mine of information for us about the Mughal Empire during Akbar’s reign. 

v. The Ain is made up of five books (daftars), of which the first three books describe the administration. 

vi. The first book, called manzil-abadi, concerns the imperial Household and its maintenance. 

vii. The second book, sipah-abadi, covers the military and civil administration and the establishment of servants. 

viii. The third book, mulk-abadi, is the one which deals with the fiscal side

B. limitations of Ain-i- Akbari

i. Numerouserrors in totaling have been detected. These areascribed to simple slips of arithmetic or of transcription by Abu’l Fazl’s assistants. 

ii. Ain is the somewhatskewed nature of the quantitative data. 

iii. Data werenot collected uniformly from all provinces. 

iv. For many subas detailed information was compiled about the caste composition of the zamindars such information is not available forBengal and Orissa. 

v. Vital parameters such as prices and wagesfrom these areas are not as well documented except Agra. 

vi. It has limited relevance for the rest ofthe country

First letter can be posted in 6 letter boxes in 6 ways. Similarly second letter can be posted in 6 letter boxes in 6 ways and so on.
Hence all the 4 letters can be posted in = 4 x 4 x 4 x 4 = 256

The direction ratios of line parallel to AB is 1, –2 and 4.

The following steps have to be followed to animate the given scenario:

• Select frame 1 from the timeline and drag the image of fish from library on stage on the right hand side.
• Select frame 25 from the timeline and Select Insert Keyframe
• Change the position and size of the bird as shown on left side
• Select any frame between 1 and 25
• Select Create motion tween.
• Click on Insert and select guide layer
• Take pencil tool and draw the path of fish as shown 
• Click on previous layer and align the fish with the path at both ends
• Run the movie

The stacking order of objects determines how they appear when they overlap.

(i) In a single layer, Flash stacks objects in the order in which they are created, placing the most recently created object at the top of the stack.

(ii) Multiple Layers also affect the stacking order. Everything on Layer 2 appears in front of everything on Layer 1, and so on.

Total marbles from 1 to 6 marked in a box = 6

(i) The probability of drawing a marble with number 2.

⇒ P (drawing one marble) = 1/6

(ii) The probability of drawing a marble with number 5.

⇒ P (drawing one marble) = 1/6

A coin has two possible outcomes Head and Tail.

Probability of getting Head or Tail is equal.

P (Starting game) =1/2

When sodium metal is heated in free supply of air, it reacts vigorously with oxygen to form sodium peroxide.

2Na + O₂ → Na₂O₂

Because of low bond dissociation enthalpy F – F bond and high hydration enthalpy of f – ions.

When sodium peroxide dissolves in water, it gives sodium hydroxide and hydrogen peroxide.

Na₂O₂ + 2H₂O → 2NaOH + H₂O₂

(1) 2FeSO₄ + H₂SO₄ + Cl₂  → Fe₂(SO₄) ₃ + 2HCl

(2) P₄ + 20HNO₃ → 4H₃PO₄ + 20NO₂ + 4H₂O

Graphite cleaves easily between the layers so it is very soft and slippery. As a result, it is used as a dry lubricant in machines at high temperature.

(i) NH₃ and (iv) C₂H₅O^– act as nucleophiles. 

(i) CH₃ – CH = CH₂

IUPAC name = Propene

(ii) CH₃ – CO – CH₃

IUPAC name = Propan-2-one

The stability of +1 oxidation state progressively increases for the heavier element of group 13 due to inert pair effect in which on moving down the group, due to poor shielding effect of intervening d and f orbitals, the increased effective nuclear charge holds ns electrons tightly and thereby, restricting their participation in bonding and only p-orbital electron may be involved in bonding.

Due to non-availability of d-orbitals, boron is unable to expand its octet. So, the maximum covalence of boron cannot exceed 4. Hence, boron is unable to form [BF₆]^-3.

The collection of all subsets of a set A is called the power set of A.

No of ways of choosing 4 cards = ⁵²C₄ = 270725 

(1) No. of ways of choosing 4 cards of same suit 

= 13C₄ + 13C₄ + 13C₄ + 13C₄ = 2860 

(2) No. of ways of choosing cards of different suits 

= 13C₁ x 13C_{1 x} 13C₁ x 13C₁ = 28561 

(3) No. of ways of choosing 4 face cards 

= ¹²C₄ = 495 

(4) No. of ways of choosing 2 red and 2 black cards 

= ²⁶C₂ x ²⁶C₂ = 105625

500=5³x2²

Since prime factors of 500 are 2 and 5 only.

500/231 has terminating decimal.

Let the ten’s digit be x and unit’s digit = y

Number = 10x + y
10x + y = 4(x + y)  ⇒  6x = 3y  ⇒  2x = y

Again 10x + y = 3xy

10x + 2x = 3x (2x) ⇒ 12x = 6x² ⇒ x = 2 (rejecting x = 0)

2x = y ⇒ y = 4

The required number is 24

The value of x = ±4

It is given that  P(A) = \(\frac12\)​, P(B) = \(\frac7{12}\) and \(P( A'\cup B')\) = \(\frac14\)​. 

⇒ \(P( A'\cup B')= \frac14\) 

⇒​ \(P((A\cap B)')= \frac14\)      \([A'\cup B' = (A\cap B)']\)

⇒ \(1-P(A\cap B)= \frac14\)

⇒ \(P(A\cap B)= \frac34\)  ......(1)

However, P(A) ⋅ P(B) = \(\frac 12.\frac7{12} = \frac7{24}\) .....(2)

Here, \(\frac34 \ne \frac7{24}\)

∴ P(A ∩ B) \(\ne\) P(A) ⋅ P(B)

Therefore, A and B are not independent events.

Given integral

\(\int \frac{2x}{(x^2 + 1)(x^2 + 2)}dx\)

\(=\int \frac{dy}{(y + 1) (y + 2)^2}\)  [By substituting x² = y]

\(= \int \frac{dy}{y +1}- \int \frac{dy }{y +2} - \int \frac{dy}{(y +2)^2}\)   (Using partial fractions)

\(= log(y +1) - log(y +2)+ \frac 1{y+2} + C\)

\(= log(x^2 + 1) - log(x^2 + 2) + \frac1{x^2 + 2} + C\)

Let common difference be ݀

⇒ 14/2 [2(10) + (݊ − 1)݀] = 1050

⇒ d = 10

a₂₀ = a + 19d

= 10 + 19 (10) = 200 

No, the capacity to hold a charge for the spherical conductor is C= 4πɛ_or. It depends on the radius and not on whether hollow or solid.

When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the center of the obstacle shadow because of the constructive interference of diffracted rays of light by the tiny circular obstacles.

 Due to higher number of unpaired electrons. 

Absence of unpaired d- electron in Sc³⁺ whereas in Ti³⁺ there is one unpaired electron or Ti³⁺shows d-d transition.

(a) Drops of liquid assume spherical shape on falling due to surface tension. Liquid tends to have a minimum surface area because of surface tension, so, the small drops of liquid are spherical. 

(b) Viscosity of a liquid decreases with rise in temperature because force required to maintain the flow decreases due to increase in velocity.

l = 10 cm

b = 10 cm

h = 10cm

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

= \(\frac13\times\frac{22}7\times2.1\times2.1\times6\)

= 22 x 0.1 x 2.1 x 6

= 27.72 cm³

Volume of wood carved out to make 5 conical cavities = 5 x volume of one cone

= (5 x 27.72) cm³

= 138.6 cm³

(2) Volume of wood = volume of cuboid - volume of 5 conical cavities

= (10 x 10 x 8) - 138.6

= 800 - 138.6 

= 661.4 cm³

Yes, the given statement is correct. In a two sector economy, the firms produce goods and services and make factors payments to the households. The factor income earned by the households will be used to buy the goods and services which would be equal to income of firms. The aggregate consumption expenditure by the households in the economy is equal to the aggregate expenditure on goods and services produced by the firms in the economy (Income of the producers). 

Depreciation on capital asset  = cost of the capital asset - Scrap Value/Estimated life of the capital asset

Depreciation = 1000 - 0/20

Depreciation = Rs. 50 cores

Reallocation of resources - Government through its budgetary policies tries to reallocate resources to ensure fulfillment of various socio-economic objectives. The government may influence the allocation of resources through:

(a) Taxation policy - Heavy taxes may be imposed on harmful products to discourage their production and subsidies may be provided on the production of socially useful products to encourage their production. 

(b) Government may directly undertake production of certain goods and services in the areas where private sector may not be willing to participate in production activities. 

The given statement is correct. Real Gross Domestic Product (GDP) is a better indicator of economic growth than Nominal Gross Domestic Product (GDP) as it is not affected by changes in general price level.

Numerical Example:

In the above example the difference between Real GDP (∑P₀Q₁) and Nominal GDP (∑P₁Q₁) is 5,500-3,000 = ₹2,500. This is only the monetary difference as the quantity sold in the market remains unchanged and the variation in the value of GDP is merely due to the change in the prices in the economy. 

In Arrhenius equation show examines rate constant variation with temperature and activation energy.

(i) Because of large number of unpaired electrons in their atoms, the transition metals have strong interatomic interactions and hence stronger bonding between atoms, resulting in higher enthalpies of atomization.

(ii) In the same group of d-block elements, the 4d and 5d transition elements are larger in size than than those of 3d elements. Hence, the valence electrons are less tightly held and form metal–metal bond more frequently.

(iii) Mn³⁺(d 4 ) is less stable than Mn²⁺ (d 5 , half filled) while Fe³⁺ (d 5 , half filled) is more stable than Fe²⁺ (d 4 ). That is why Mn²⁺ is more resistance than Fe²⁺ towards oxidation.