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Edge of the big solid cube = 14 cm

Volume of the big solid cube = 14 x 14 x 14 cm³ = 2744 cm³ 

Edge of the small cube = 2 cm

Volume of one small cube = 2 x 2 x 2 cm3 = 8 cm³ 

Number of smaller cubes obtained = Volume of big cube/Volume of one small cube = 2744/8 = 343

Given, (2n + 4) / (5n + 5) = { 2a1 + (n-1) d1 } / { 2a2 + (n-1) d2 }

Putting n = 1, we get a2 = 5/3 a1 .....(1)

Putting n = 2 and n = 3, we get,

d1 = 2/5 d2 .....(2)

3/5 d2 = a1 ......(3)

So, we have the relations b/w a1, a2, d1 and d2. Hence, the ratio comes as 5/12

Volume of each cube = edge x edge x edge

= 3 x 3 x 3 cm²

= 27 cm³

Number of cubes in the surface structure = 15

Volume of the structure = 27 x 15 cm³

405 cm³

Let the side length of square ABCD is a.

The length of diagonal of square is \(\sqrt{a^2+a^2}\) = \(\sqrt 2 a\). 

Let A₁ and A₂ are areas of equilateral triangles described on one side of square and one diagonal of that square, respectively.

And we also know that area of equilateral triangle whose side length is a is \(\frac{\sqrt 3}{4}\)a² 

∴ A₁ = \(\frac{\sqrt 3}{4}\) a². 

And A₂ = \(\frac{\sqrt 3}{4}\) (\(\sqrt 2 a\))² 

= \(\frac{\sqrt 3}{4}\) × 2a² 

= \(\frac{2\sqrt 3}{4}\) a² 

∴\(\frac{A_1}{A_2}\) = \(\frac{1}{2}\) 

⇒ A₁ = \(\frac{1}{2}\)A₂. 

Hence Proved.

Calculation: 

(2,3), (3,5), (5,7), (7,11), 

In above series all are consecutive prime numbers,

⇒ Next digit also will prime number 

⇒ Next number is series is (11, 13)

∴ Required answer is (11, 13)

(a) Isomers have same molecular formula but different arrangement of atoms.

CH₃CH₂ - O - CH₃ and CH₃ - CH₂ - CH₂ - OH are the pair of isomers. 

They have same molecular formula but different arrangement of atoms.

(b) They show metamerism isomerism because they have different groups present on either side of a oxygen atom and have same molecular formula

Given:

Income ratio of P and Q = 5 : 6

Individual savings of P and Q = ₹ 200

Expenditure ratio = 3 : 4

Formula used:

Profit = Investment × Time period

Calculation:

Let income of P be 5x

Let income of Q be 6x

(5x – 200)/(6x – 200) = 3/4

⇒ 20x – 800 = 18x – 600

⇒ 20x – 18x = 800 – 600

⇒ 2x = 200

⇒ x = 100

Income of P = 100 × 5 = 500

Income of Q = 100 × 6 = 600

∴ The income of Q is 600.

Total weight of girls and boys = Mean x no. of students

 = 23 x 50 = 1150

Weight of boys = Mean of boys x no. of boys

 = 30 x 20 = 600

Weight of girls = Mean of girls x no. of girls

Total weight - Weight of boys = Mean of girls x 30

1150 - 600 = Mean of girls x 30

550 = Mean of girls x 30

\(\therefore\) Mean of girls ≡ 550/30 ≡ 18

Mean of the girls weight ≡ 18

Given:

The ratio of income of A and B = 8 : 9

Increment in A’s income = 1700

The decrement in B’s income = 100

New ratio of income of A and B = 9 : 8

Formula used:

Income = Expenditure + Saving

Calculation:

Let the income of A and B is Rs. 8x and 9x respectively.

Then, (17x + 1700)/(9x – 100) = 17/8

⇒ 136x + 13600 = 153x – 1700

⇒ 136x – 153x = 13600 + 1700

⇒ 17x = 15300

⇒ x = 900

A’s income = 8 × 900

⇒ 7200

B’s income = 9 × 900

⇒ 8100

∴ The income of A and B is Rs. 7200 and Rs. 8100 respectively.

(i) If with fall in the price of X, demand for good Y rises, they are complementary goods. For example: Car and petrol. When price of car decreases, demand for petrol increases.

(ii) If with fall in the price of X, demand for y falls, they are substitute goods, For example: Tea and Coffee. When price of tea falls, demand for coffee falls.

(i) Change in price of given commodity 

(ii) Change in price of input 

The correct answer is 1966.

• In 1947, Gurgaon became a part of independent India and fell under the Indian state of Punjab.
• In 1966, the city came under the administration of Haryana with the creation of the new state. 
• Gurgaon district, officially known as Gurugram district, is one of the 22 districts of Haryana in northern India. 
• On its north, it is bounded by the district of Jhajjar and the Union Territory of Delhi.
• Faridabad district lies to its east.
• On its south, lie the districts of Palwal and Nuh. To its west lies Rewari district.

• Chief Minister of Haryana - Manohar Lal Khattar (July 2021)
• Governor of Haryana - Bandaru Dattatreya
• The largest district of Haryana - Sirsa
• The smallest district of Haryana - Faridabad
• Dances of Haryana - Ghumar, Phag, Loor, Khoria, Daph, Gugga, etc. 

(d) Exploitation

(d) Development banks – SBI

(d) Stranger to the contract

The State Bank of India came into being in 1995.

(d) Construction industries are involved in the successive stages for manufacturing sugar and paper, etc.

Correct option is: (C) An owner and an agent

Correct option: B) Wholesaler

(b) Multinational company

The compensation given for breach of contract is Damage.

An Indent is a document prepared by the importer and sent to the exporter to buy the goods.

An Indent is a document prepared by the importer and sent to the exporter to buy the goods.

(b) Forwarding agent

Correct option: a) Federal Trade Commission

Central warehousing corporation

• Quit India Movement, 1942, 
• Farmers shall not pay land tax. 
• Princely state shall recognize the sovereignty of the people.
• The soldiers shall disobey the order to shoot the Indians. 
• Government officials shall disclose their loyalty to Indian National Congress without quitting their positions.
• If possible, students shall boycott education till attaining freedom.

Anusheelan Samithi – Bareender Kumar Ghose:

The brother of Aravinda Ghosh formed Anusheelan Samithi in Bengal in 1902. To stop British rule through violence was the goal.

Abhinava Bharat: The secret agency formed by Savarkar in 1904. They helped Indians from foreign countries.

Yuganthar Party: Formed as a result of the news paper ‘ Yugaathar’ published by Bhupendra Dutta and his friends. Hemachandra Das was the leader.

Gaddar Party of rebellion: Formed in 1913. Mostly Hindus and Muslims Lala Harddayal gave leadership. The meaning of word Gaddar is rebellion. The main aim was to free India from Britain.

Hindustan Republic Association: Socialist activist Sughdev, Bhagat Singh, Chandrasekhar Azad formed in 1928.

Swaraj party, Motilal Nehru, C R Dascon tested to the legislative assemblies and made legi slative assemblies platforms for raising the voice.

Hindustan Socialist Republican Association Bhagat Singh, Chandrasekhar Azad, Raj Guru and Sukh Dev were at the helm of this organisation. They planned to overthrew the colonial government through military action and establish a federal republic of Indian states. To show protest against the attempt to pass laws curtailing civil rights, threw bombs at the central legislative assembly.

Forward Bloc was formed by Subhash Chandra Bose. He took the leadership of I N A formed by Rash Bihari Bose. He formed a provincial government of India in Singapore with an aim of forcing the British to quit India. With the Support of the Japanese army, the Indian National Army marched to the north eastern border of India and hoisted the Indian flag in Imphal.

• Gandhiji’s principle was Ahimsa. 
• Others adopted violence.

• Reduce 50% of land tax and lease charge.
• Write off debts. 
• Cancel feudal taxes. 
• Ensure minimum wage for agricultural workers. 
• Recognize peasant unions.

• The All India Kisan Samiti Conference held in Bombay prepared Kisan Manifesto. 
• Reduce 50% of land tax and lease charge. 
• Write off debts. 
• Cancel feudal taxes. 
• Ensure minimum wage for agricultural workers. 
• Recognise peasant unions.

“If the Battle of Plassey laid the foundation for the British rule, the Jallianwala Bagh shook the foundation.”

All India Kisan Samithi conference held in Bombay prepared the Farmer’s Manifesto.

• Reduce 50%of land tax and lease charge.
• Write off debts. 
• Cancel feudal taxes. 
• Ensure minimum wage for agricultural workers.
• Recognize peasant unions.

Many such movements and persons who had difference of opinion towards the Gandhian approach to the struggle for independence also played crucial roles in attaining freedom for our country. Their objective was also nothing but India’s freedom from colonial cinches.

C.R. Das and Motilal Nehru, who opposed Gandhian idea of boycott movement, formed the Swaraj Party in 1923. They argued for making legislative assemblies as platforms for raising our voices instead of boycotting them and they contested elections.

Gradually, the opposition to Gandhian method of struggle intensified. Revolutionaries from Punjab, Rajasthan, Uttar Pradesh and Bihar gathered in Delhi and Formed the Hindustan Socialist Republican Association in 1928.

• To intensify Hindu – Muslim unity 
• To spread anti – British feeling to the nook and corner of the nation.

Jallianwala Bagh massacre had a vital role in Indian National Movement. The massacre intensified the protests at the national level. Those who believed in British too turned against them. The executive council under the membership of Sir. C. Sankaran Nair resigned.

• Satyagraha was his policy.
• Ahimsa was the principle he adopted against enemies.
• Foreign textiles were put down and Indian goods were promoted.
• He violated salt law as a part of civil disobedience movement.

a. Bengal. 

b. Telengana Struggle. 

c. Bombay.

The struggle was against the British decision to collect tax from the people who were in misery due to drought and famine. As a result of this Government agreed to reduce tax.

Due to drought and crop failure farmers in Kheda were living in utter misery. The rulers decided to collect tax from these poor villagers starting sathyagraha Gandhiji protested against the decision.

He advised people not to pay tax. Consequently, the authorities were forced to reduce tax rates. His early struggles based on Satyagraha and Ahimsa made Gandhiji a popular leader.

Correct option is (iii) Champaran Satyagraha, 1917

Gandhiji believed that the Hindu-Muslim unity could be restored through Khilafat Movement. The people joined in the struggle of independence through Khilafat Movement as a part of National Movement the active participation of Muslims in the freedom struggle could be ensured.

• Maulana Mohammad Ali 
• Maulana Shoukath Ali

• To spread anti. 
• British feeling to the nook and comer of India.
• To intensify Hindu. 
• Muslim unity.

The rulers decided to collect tax from the farmers of Kheda who were living in utter misery due to drought and crop failure. Gandhiji used the weapons of Satyagraha and non payment of tax in this agitation. The authorities agreed to reduce tax rates.

Correct option is (ii) Sir Sydney Rowlatt 

Civil Disobedience Movement: 

The Lahore Congress Session of 1929 decided to start a civil disobedience movement under the leadership of Gandhiji. This was the second mass movement launched by Gandhiji against the British.

With the civil disobedience movement, Gandhiji meant to disobey all anti-popular and antidemocratic laws made by the British government. As part of the movement, Gandhiji proposed the following.

• To lift salt tax. 
• To declare 50% tax relaxation for farmers. 
• To increase the tax on imported foreign clothes. 
• To release political prisoners. 
• To cut short military budget and high salary of top officials. 
• To dissolve the secret surveillance wing formed to watch Indians. 
• To start coastal shipping service. 
• To implement prohibition of liquor.

Gandhiji gave top priority to reducing salt tax due to a variety of reasons. He selected salt as a powerful tool against the British because:

• Salt tax constituted two fifth portion of the income collected by the British through taxes. 
• Salt tax was a heavy burden for the poor people. 
• There was three fold hike on salt price. 
• The British government banned small scale indegenous salt production. 
• The demand for lifting salt tax was a slogan suitable to inspire all segments of the society.

Gandhiji began the civil disobedience with Salt Satyagraha. The Salt Satyagraha began with the famous Dandi March by Gandhiji on 30 March, 1930. Gandhiji along with 78 followers marched from Sabarmali Ashram to Dandi, a coastal village in Gujarat. He broke the salt law by making salt. Inspired by the call of Gandhiji, people in various parts of the country started to produce salt on their own, violating the British regulations.

Payyannur in Kerala, Vedaranyam in Tamil Nadu, Bombay in Maharashtra, Naokhali in Bengal and North West Frontier Province were some of the centres of this protest. As part of the protest, volunteers made salt and distributed it to the people, hoisted national flag and chanted anti- British slogans. Gandhiji was arrested and the movement was suppressed callously.