66th BPSC Prelims 2020 Part 1 Question Paper with Answers and Solutions (Solved)

🏛️ Shri Krishna Singh – The First Chief Minister of Bihar

Dr. Shri Krishna Singh (also known as Shri Babu) was the first Chief Minister of Bihar. He became the head of the Bihar provincial government in 1937 under the Government of India Act, 1935. He again became the Premier of Bihar in 1946. After India’s independence on 15 August 1947, he continued as the first Chief Minister of independent Bihar. He served in this position until his death on 31 January 1961. He is remembered for his contribution to the Indian freedom movement and the development of modern Bihar.

📅 Important Political Timeline

👤 Important Facts about Shri Krishna Singh

• Popular name: Shri Babu.
• Birth: 21 October 1887, in the present-day Sheikhpura district of Bihar.
• Political association: Indian National Congress.
• Freedom movement: He actively participated in the Indian national movement and worked against British colonial rule.
• Important colleague: Dr. Anugrah Narayan Sinha was his close political colleague and served as Deputy Chief Minister and Finance Minister of Bihar.
• Land reforms: His government took important steps towards the abolition of the zamindari system in Bihar.
• Administrative contribution: His tenure is associated with the development of education, irrigation, industry and public institutions in Bihar.

📊 Important Facts about the Other Options

• Satya Pal Malik: He served as the Governor of Bihar from 2017 to 2018. He was not the first Chief Minister of Bihar.
• Nitish Kumar: He first became Chief Minister of Bihar in March 2000 and has served multiple terms.
• Rabri Devi: She became the first woman Chief Minister of Bihar in 1997.

🧠 Additional Exam-Oriented Facts

• First Chief Minister of Bihar: Shri Krishna Singh.
• First Deputy Chief Minister of Bihar: Dr. Anugrah Narayan Sinha.
• First woman Chief Minister of Bihar: Rabri Devi.
• First Governor of Bihar after independence: Jairamdas Daulatram.
• Separate Bihar province: Bihar became a separate province on 22 March 1912 after its separation from the Bengal Presidency.
• Bihar Diwas: 22 March is celebrated every year as Bihar Diwas.

Quick Revision: First Chief Minister → Shri Krishna Singh; popular name → Shri Babu; first Deputy Chief Minister → Anugrah Narayan Sinha; first woman Chief Minister → Rabri Devi; Bihar Diwas → 22 March.

✔️ Final Answer: (A) Shri Krishna Singh / श्रीकृष्ण सिंह

🇮🇳 First Indian National Congress Session in Bihar

The first session of the Indian National Congress held in Bihar took place at Bankipore (Patna) in December 1912. It was the 27th session of the Indian National Congress and was presided over by Raghunath Narasinha Mudholkar. Bankipore was an important locality of Patna during the colonial period. This session is significant in the history of Bihar’s participation in the Indian national movement. It should not be confused with the first session of the Indian National Congress in India, which was held in Bombay in 1885.

📅 Important Facts about the Bankipore Session, 1912

🏛️ Indian National Congress: Historical Background

• Foundation: The Indian National Congress was founded in 1885.
• First session: It was held in Bombay (now Mumbai) from 28 to 31 December 1885.
• First President: Womesh Chandra Bonnerjee (W.C. Bonnerjee).
• Founder associated with its establishment: Allan Octavian Hume, a retired British civil servant, played a major organisational role in its formation.
• First woman President: Annie Besant, in 1917.
• First Indian woman President: Sarojini Naidu, in 1925.
• Important Bihar connection: The Bankipore session of 1912 marked an important stage in the Congress organisation’s activities in Bihar.

📌 Related Bihar Freedom Movement Facts

• Champaran Satyagraha (1917): Mahatma Gandhi led his first major satyagraha in India against the exploitation of indigo cultivators in Champaran, Bihar.
• Rajendra Prasad: He became an important leader of the freedom movement and later the first President of independent India.
• Dr. Anugrah Narayan Sinha: He was a prominent freedom fighter and political leader of Bihar.
• Quit India Movement (1942): Bihar witnessed significant participation, including student movements and underground resistance activities.
• Bihar’s separation: Bihar became a separate province from Bengal on 22 March 1912, the same year as the Bankipore Congress session.

🧠 Important Congress Sessions for Competitive Examinations

Quick Revision: First Congress session in Bihar → Bankipore, Patna (1912); 27th INC session → R.N. Mudholkar; first INC session in India → Bombay (1885); first President → W.C. Bonnerjee.

✔️ Final Answer: (A) Patna / पटना

✊ Jayaprakash Narayan – Lok Nayak

Jayaprakash Narayan (11 October 1902 – 8 October 1979) was popularly known as Lok Nayak, meaning “Leader of the People”. He was a prominent freedom fighter, socialist thinker and political leader. He played an important role in the Indian independence movement and later became one of the leading figures of the movement against corruption and authoritarianism during the 1970s. He is especially remembered for giving the call for Total Revolution (Sampoorna Kranti) in 1974.

📅 Important Events in the Life of Jayaprakash Narayan

🔥 What Was Total Revolution (Sampoorna Kranti)?

Total Revolution was a broad programme of social, political, economic, educational and moral transformation advocated by Jayaprakash Narayan. It was not limited to changing the government. He called for fundamental reforms in public life, democratic institutions and society. His movement began in Bihar in 1974 and later influenced opposition politics at the national level.

🧠 Important Organisations and Related Personalities

• Congress Socialist Party: Established in 1934 as a socialist group within the Indian National Congress. Jayaprakash Narayan was one of its leading organisers.
• Socialism: JP was influenced by socialist thought during his education in the United States.
• Sarvodaya Movement: He later associated himself with the movement inspired by Mahatma Gandhi and led by Vinoba Bhave.
• Bhoodan Movement: A movement initiated by Vinoba Bhave in 1951 to encourage voluntary land donations for landless people.
• Emergency: The National Emergency was proclaimed on 25 June 1975 under Article 352 of the Constitution.
• Bharat Ratna: Jayaprakash Narayan was posthumously awarded India’s highest civilian award in 1999.

📌 Distinguish These Famous Titles

Quick Revision: Jayaprakash Narayan → Lok Nayak; Total Revolution → 1974; Bihar movement → 1974; Emergency → 25 June 1975; Bharat Ratna → 1999 (posthumously).

✔️ Final Answer: (B) Lok Nayak / लोकनायक

📚 Mahatma Gandhi’s Education – Samaldas College

Mohandas Karamchand Gandhi enrolled at Samaldas College in Bhavnagar, Gujarat, in 1888 after completing his school education. He attended the college for a short period before travelling to England in September 1888 to study law. Gandhi was then around 18 years old. His brief period at Samaldas College is an important fact in his educational biography.

📅 Educational Journey of Mahatma Gandhi

⚖️ Gandhi’s Legal Education in England

Gandhi went to London in 1888 to study law and joined the Inner Temple, one of the four Inns of Court in London. He completed his legal education and was called to the Bar in 1891. He returned to India in 1891 and initially attempted to practise law in Bombay before later moving to South Africa in 1893.

🇿🇦 Important Events after His Education

• South Africa (1893–1914): Gandhi worked as a lawyer and developed his methods of non-violent resistance against racial discrimination.
• Satyagraha: He developed and used the method of resistance based on truth and non-violence.
• Return to India: He returned to India from South Africa in January 1915.
• Champaran Satyagraha (1917): He led a movement in Bihar in support of indigo cultivators.
• Kheda Satyagraha (1918): He supported peasants in Gujarat seeking relief from land revenue demands during crop failure.
• Non-Cooperation Movement (1920): He led a nationwide movement against British rule.
• Salt March (1930): He led the Dandi March against the British salt law.
• Quit India Movement (1942): He gave the call of “Do or Die” during the movement against British rule.

🧠 Important Facts for Competitive Examinations

• Full name: Mohandas Karamchand Gandhi.
• Birth: 2 October 1869, Porbandar, Gujarat.
• Father: Karamchand Gandhi.
• Mother: Putlibai.
• Wife: Kasturba Gandhi.
• Autobiography: The Story of My Experiments with Truth.
• National observance: 2 October is observed as Gandhi Jayanti in India and the International Day of Non-Violence worldwide.
• International observance: The United Nations declared 2 October as the International Day of Non-Violence in 2007.

Quick Revision: Gandhi’s college → Samaldas College, Bhavnagar; enrolled → 1888; law studies → Inner Temple, London; returned from South Africa → 1915; Champaran Satyagraha → 1917.

✔️ Final Answer: (A) Samaldas College, Bhavnagar / सामलदास कॉलेज, भावनगर

⚔️ Revolt of 1857 – Major Leaders and Centres

The Revolt of 1857 was a major uprising against British rule in India. Nana Saheb, Begum Hazrat Mahal and Maulavi Ahmadullah Shah were prominent active leaders of the revolt. Begum Zeenat Mahal was also associated with the Mughal royal court and the events surrounding Bahadur Shah Zafar during the uprising. Therefore, more than one of the listed persons is associated with the revolt, and the correct choice is (E) None of the above/More than one of the above. The revolt began among Indian soldiers at Meerut on 10 May 1857 and spread to several regions of northern and central India.

📍 Major Leaders Mentioned in the Options

👑 Detailed Facts about the Four Leaders

1. Nana Saheb – Kanpur

• His original name was Dhondu Pant.
• He was the adopted son of the last Peshwa, Baji Rao II.
• He became a leading figure of the revolt at Kanpur in 1857.
• He was associated with military leaders such as Tantia Tope.
• His grievance against the British was connected with the refusal to continue the pension of the former Peshwa.

2. Begum Hazrat Mahal – Lucknow

• She was one of the prominent women leaders of the Revolt of 1857.
• She led resistance against the British in Awadh after its annexation in 1856.
• She declared her son Birjis Qadr the ruler of Awadh during the revolt.
• She worked with other rebel leaders and helped organise resistance in and around Lucknow.
• After the revolt was suppressed, she eventually took refuge in Nepal, where she died in 1879.

3. Maulavi Ahmadullah Shah – Faizabad

• He was a prominent leader of the 1857 uprising in Awadh.
• He mobilised people and soldiers against British rule.
• He was associated with resistance in Faizabad, Lucknow and surrounding areas.
• He was known for his courage, leadership and ability to organise resistance.
• He was killed in 1858 in the course of the continuing conflict in the region.

4. Begum Zeenat Mahal – Delhi

• She was the wife of Mughal emperor Bahadur Shah Zafar.
• She was associated with the Mughal court during the Revolt of 1857.
• Bahadur Shah Zafar was proclaimed the symbolic emperor by the rebels in Delhi.
• After the British recaptured Delhi, the Mughal royal family faced imprisonment and exile.
• Begum Zeenat Mahal accompanied Bahadur Shah Zafar to Rangoon, where he died in 1862. She died in 1886.

📊 Other Important Leaders and Centres of the Revolt of 1857

📌 Important Facts about the Revolt of 1857

• Beginning: The revolt began at Meerut on 10 May 1857, and the rebels reached Delhi soon afterwards.
• Symbolic leader: Bahadur Shah Zafar, the last Mughal emperor, was proclaimed the symbolic leader of the revolt.
• Immediate cause: The controversy over the Enfield rifle cartridges, which were believed to be greased with cow and pig fat, became the immediate trigger.
• Political causes: The Doctrine of Lapse, annexation policies and the treatment of Indian rulers created widespread resentment.
• Economic causes: Heavy revenue demands, exploitation of peasants and the decline of traditional industries contributed to discontent.
• Military causes: Discrimination in pay, promotion and service conditions created dissatisfaction among Indian soldiers.
• Aftermath: The Government of India Act, 1858 transferred the administration of India from the East India Company to the British Crown.
• End of Company rule: The Governor-General thereafter also held the title of Viceroy; Lord Canning became the first Viceroy of India.
• Queen’s Proclamation: Queen Victoria’s Proclamation was issued on 1 November 1858, announcing the new framework of British Crown rule in India.

🧠 Special Bihar Connection: Kunwar Singh

Veer Kunwar Singh was one of the most important leaders of the Revolt of 1857 in Bihar. He belonged to Jagdishpur in the present-day Bhojpur district and was around 80 years old when he joined the revolt. He fought against British forces in Bihar and neighbouring regions. His brother Amar Singh also played an important role in continuing the resistance. Kunwar Singh is remembered as a major symbol of courage and resistance in Bihar’s history.

📚 Important Historical Distinctions

• Nana Saheb: A leading rebel figure at Kanpur; associated with the Peshwa family.
• Begum Hazrat Mahal: A leading woman figure of the revolt in Awadh; associated with Birjis Qadr.
• Maulavi Ahmadullah Shah: A prominent religious and military leader of the uprising in Awadh.
• Begum Zeenat Mahal: Wife of Bahadur Shah Zafar and a member of the Mughal royal household during the uprising.
• Kunwar Singh: The major leader of the revolt in Bihar, associated with Jagdishpur.

Quick Revision: Nana Saheb → Kanpur; Begum Hazrat Mahal → Lucknow; Maulavi Ahmadullah Shah → Faizabad/Awadh; Begum Zeenat Mahal → Delhi; Kunwar Singh → Bihar; Revolt began → Meerut, 10 May 1857; Company rule ended → 1858.

✔️ Final Answer: (E) None of the above/More than one of the above

🏛️ Government of India Act, 1935

Jawaharlal Nehru strongly criticised the Government of India Act, 1935, describing the proposed constitutional arrangement as a system with extensive restrictions and inadequate democratic power. The famous expression that Indians were given a car with all brakes and no engine is associated with his criticism of this Act. The analogy highlighted that the proposed constitutional system contained numerous safeguards and controlling powers for the British authorities but did not provide genuine responsible government to Indians.

📜 Background and Major Provisions of the Act

The Government of India Act, 1935 was one of the longest Acts passed by the British Parliament at that time. It was based on recommendations and discussions arising from the Simon Commission, the Round Table Conferences and the Joint Select Committee. It received Royal Assent on 2 August 1935.

📚 Comparison of Important Constitutional Acts

🧠 Further Exam-Oriented Facts

• Simon Commission: Appointed in 1927 and arrived in India in 1928; it had no Indian member.
• Round Table Conferences: Three conferences were held in London between 1930 and 1932 to discuss constitutional reforms in India.
• Provincial Elections: Elections under the Government of India Act, 1935 were held in 1937.
• Congress Ministries: The Indian National Congress formed ministries in several provinces following the 1937 elections.
• Federal Court: Established in 1937, it was a predecessor of the Supreme Court of India.
• Constitutional Influence: Several features of the Government of India Act, 1935 influenced the Constitution of independent India, including federal features, provincial/state administration and the office of Governor.
• Important distinction: Provincial autonomy came into operation, but the proposed All-India Federation never became operational.

Quick Revision: Government of India Act, 1935 → Provincial Autonomy → Proposed All-India Federation → Three Legislative Lists → Federal Court (1937) → Nehru’s criticism: car with all brakes and no engine.

✔️ Final Answer: (D) Act of 1935

🧂 Dandi March (Salt March), 1930

The Dandi March, also known as the Salt March or Salt Satyagraha, lasted for 24 days. Mahatma Gandhi started the march on 12 March 1930 from Sabarmati Ashram near Ahmedabad, Gujarat, and reached the coastal village of Dandi on 5 April 1930. On 6 April 1930, he broke the British salt law by making salt from seawater. The march covered approximately 385 km (about 240 miles).

🚶 Important Events of the Dandi March

⚖️ Why Was Salt Chosen as a Symbol of Protest?

• British Salt Laws: The colonial government imposed restrictions on the production and sale of salt and collected taxes on it.
• Common Necessity: Salt was essential for people of every social and economic class, making the issue relevant to the entire population.
• Economic Protest: Gandhi used the salt tax to highlight the economic exploitation of Indians under British rule.
• Non-violent Resistance: The march demonstrated the power of peaceful civil disobedience against an unjust colonial law.
• Mass Participation: The movement encouraged people across India to manufacture salt, boycott foreign goods and violate selected colonial laws peacefully.

📚 Connection with the Civil Disobedience Movement

The Dandi March marked the beginning of the Civil Disobedience Movement at the national level in 1930. Unlike the Non-Cooperation Movement, which mainly involved withdrawing cooperation from British institutions, Civil Disobedience also involved the deliberate and peaceful violation of unjust colonial laws.

🧠 Further Exam-Oriented Facts

• Leader: Mahatma Gandhi led the Dandi March.
• Starting Point: Sabarmati Ashram, Ahmedabad, Gujarat.
• Destination: Dandi, on the Arabian Sea coast in Gujarat.
• Starting Date: 12 March 1930.
• Arrival at Dandi: 5 April 1930; salt law broken on 6 April 1930.
• Initial Volunteers: Gandhi was accompanied by 78 selected volunteers at the beginning of the march.
• Distance: Approximately 385 km or 240 miles.
• Viceroy: Lord Irwin was the Viceroy of India at the time.
• Dharasana Satyagraha: After Gandhi’s arrest, a major non-violent protest was organised at Dharasana Salt Works in May 1930; Sarojini Naidu was among its prominent leaders.
• International Coverage: Reports by foreign journalists, including Webb Miller, helped bring the brutality of British repression to international attention.

Quick Revision: Dandi March → 12 March to 5 April 1930 → 24 days → 78 initial volunteers → approximately 385 km → Salt Law broken on 6 April 1930 → beginning of the Civil Disobedience Movement.

✔️ Final Answer: (C) 24 days

✍️ “Sarfaroshi Ki Tamanna” — Poet and Revolutionary Tradition

The original author of the famous patriotic poem “Sarfaroshi Ki Tamanna Ab Hamare Dil Mein Hai” was Bismil Azimabadi, whose real name was Syed Shah Muhammad Hasan. He was an Urdu poet from Patna, Bihar. The poem became widely associated with the revolutionary freedom movement because Ram Prasad Bismil popularised and recited it. Therefore, Ram Prasad Bismil is frequently associated with the poem, but he was not its original author. Since Bismil Azimabadi is not included among options (A)–(D), option (E) is correct.

📖 Important Distinction: Author and Populariser

🔥 Important Revolutionary Personalities

• Ram Prasad Bismil (1897–1927): A revolutionary, poet and member of the Hindustan Republican Association (HRA). He was one of the principal figures in the Kakori Train Action of 1925 and was executed on 19 December 1927.
• Bhagat Singh (1907–1931): A prominent revolutionary and socialist thinker. He was executed on 23 March 1931 along with Rajguru and Sukhdev.
• Chandra Shekhar Azad (1906–1931): A leading revolutionary who reorganised revolutionary activities and was associated with the HSRA. He died at Alfred Park, Allahabad, on 27 February 1931.
• Surya Sen (1894–1934): Popularly known as Masterda, he led the Chittagong Armoury Raid on 18 April 1930. He was executed on 12 January 1934.
• Bismil Azimabadi: An Urdu poet from Patna whose patriotic poem became a powerful symbol of revolutionary nationalism.

📚 Important Revolutionary Organisations and Events

🧠 Further Exam-Oriented Facts

• Poem: “Sarfaroshi Ki Tamanna” is a patriotic Urdu poem.
• Original Poet: Bismil Azimabadi, not Ram Prasad Bismil.
• Populariser: Ram Prasad Bismil helped make the poem famous among revolutionaries.
• Meaning: “Sarfaroshi” conveys the spirit of readiness to sacrifice one’s life for a cause; the poem expresses courage, patriotism and resistance against colonial rule.
• Place of Association: Bismil Azimabadi was associated with Patna, Bihar.
• Important Caution: The similar names Bismil Azimabadi and Ram Prasad Bismil are a common source of confusion in competitive examinations.
• Historical Context: The poem became closely connected with the revolutionary movement against British colonial rule, especially through its association with the Kakori revolutionaries and Bhagat Singh’s generation.

Quick Revision: “Sarfaroshi Ki Tamanna” → Original poet: Bismil Azimabadi → Popularised by: Ram Prasad Bismil → Urdu patriotic poem → Option (E), because the original poet is not listed.

✔️ Final Answer: (E) None of the above

🇮🇳 Swadeshi Movement and Partition of Bengal (1905)

The Swadeshi Movement was launched as a reaction to the Partition of Bengal, which was announced by Lord Curzon and came into effect on 16 October 1905. The British government officially justified the partition on administrative grounds, but Indian nationalists regarded it as a deliberate policy of divide and rule, intended to weaken the growing nationalist movement by dividing Bengal along communal and regional lines. The movement promoted the boycott of British goods and encouraged the use of Indian-made products.

📅 Background of the Partition of Bengal

• Viceroy: Lord Curzon was the Viceroy of India when Bengal was partitioned.
• Announcement: The partition was announced in July 1905.
• Implementation: It came into effect on 16 October 1905.
• Official Explanation: The British government claimed that Bengal was too large to administer efficiently.
• Nationalist Opposition: Indian nationalists argued that the real objective was to weaken Bengali nationalism and encourage communal division.
• New Provinces: The partition created Eastern Bengal and Assam, with Dacca as its capital, while the remaining western part continued as Bengal.

🔥 Main Features of the Swadeshi Movement

👥 Important Leaders of the Swadeshi Movement

• Surendranath Banerjee: Played an important role in organising public opposition to the partition of Bengal.
• Bipin Chandra Pal: A prominent nationalist leader who advocated Swadeshi, boycott and national education.
• Bal Gangadhar Tilak: Supported the Swadeshi movement and helped extend the spirit of boycott beyond Bengal.
• Aurobindo Ghosh: Advocated militant nationalism, Swadeshi and national education.
• Rabindranath Tagore: Promoted unity and harmony through cultural activities and encouraged people to resist the partition.
• Lala Lajpat Rai: Supported the Swadeshi cause and helped spread nationalist ideas in Punjab.

📚 Important Events and Their Dates

🔍 Difference Between Important National Movements

🧠 Further Exam-Oriented Facts

• Partition Annulled: The partition of Bengal was annulled in 1911 during the reign of King George V.
• Delhi Durbar: The annulment was announced at the Delhi Durbar of 1911.
• Capital Shift: The transfer of the capital from Calcutta to Delhi was also announced at the 1911 Delhi Durbar and implemented in 1912.
• National Education: The Bengal National College was established in 1906, with Aurobindo Ghosh as its first principal.
• National Council of Education: Established in Bengal in 1906 to promote national education.
• Raksha Bandhan: Rabindranath Tagore encouraged the observance of Raksha Bandhan as a symbol of unity and solidarity during the anti-partition movement.
• Important Slogan: “Vande Mataram” became a prominent slogan and song associated with the Swadeshi movement.

Quick Revision: Lord Curzon → Partition of Bengal (1905) → Swadeshi and Boycott Movement → Indian-made goods → National Education → Partition annulled in 1911.

✔️ Final Answer: (C) Swadeshi Movement

⚖️ Indian National Army (INA) Trials, 1945–46

Bhulabhai Desai, a prominent Indian lawyer and freedom movement leader, was one of the principal defence advocates in the famous INA trials held at the Red Fort in Delhi in 1945–46. He played a leading role in defending the three officers—Shah Nawaz Khan, Prem Kumar Sahgal and Gurbaksh Singh Dhillon—who were tried by a British military court. The trials became a major political event and generated widespread public sympathy for the INA soldiers across India.

🪖 What Was the Indian National Army?

The Indian National Army (INA), also known as the Azad Hind Fauj, was an armed force formed to fight British rule in India. Its initial organisation was associated with Captain Mohan Singh in 1942, with support from Indian prisoners of war captured by Japan during the Second World War. Subhas Chandra Bose took leadership of the INA in 1943, reorganised it and gave it a prominent role in the struggle for India’s independence.

⚖️ Important Details of the INA Trials

👨‍⚖️ Role of Bhulabhai Desai

• Legal Defence: Bhulabhai Desai led the defence of the three INA officers in the first major Red Fort trial.
• Legal Argument: He challenged the prosecution’s case and argued against treating the INA officers as ordinary traitors, presenting their actions in the context of India’s struggle for independence.
• National Importance: His courtroom arguments helped draw public attention to the political and legal significance of the INA trials.
• Other Defence Advocates: Jawaharlal Nehru, despite being a political leader, also appeared as a member of the defence team, along with other prominent lawyers.
• Historical Significance: The trials strengthened nationalist sentiment and contributed to the growing pressure on British rule in India.

📚 Important Facts About the INA and Subhas Chandra Bose

🇮🇳 Why Were the INA Trials Historically Important?

• National Unity: The three officers belonged to different religious communities—Shah Nawaz Khan was Muslim, Prem Kumar Sahgal was Hindu and Gurbaksh Singh Dhillon was Sikh. Their joint trial became a symbol of national unity.
• Public Protest: Students, workers and ordinary citizens organised demonstrations in support of the INA soldiers.
• Military Discontent: The trials contributed to the atmosphere of unrest in the armed forces, which was also reflected in the Royal Indian Navy revolt of February 1946.
• Royal Indian Navy Revolt: The naval uprising began in Bombay on 18 February 1946 and spread to several other centres.
• End of British Rule: The INA trials and the wider unrest formed part of the broader political and military circumstances that weakened British authority in India.

🧠 Further Exam-Oriented Facts

• INA Full Form: Indian National Army.
• Hindi Name: Azad Hind Fauj.
• Initial Organiser: Captain Mohan Singh.
• Prominent Leader: Subhas Chandra Bose.
• Provisional Government: Azad Hind Government, established on 21 October 1943.
• First Major Red Fort Trial: Began in November 1945.
• Defence Lawyer Asked in the Question: Bhulabhai Desai.
• Three Accused Officers: Shah Nawaz Khan, Prem Kumar Sahgal and Gurbaksh Singh Dhillon.
• Naval Revolt: Royal Indian Navy revolt began on 18 February 1946.
• Important Distinction: Bhulabhai Desai was the leading defence advocate in the first major INA trial; Jawaharlal Nehru and other lawyers were also associated with the defence team.

Quick Revision: INA Trials → Red Fort, Delhi → 1945–46 → Shah Nawaz Khan, Prem Kumar Sahgal and Gurbaksh Singh Dhillon → Principal defence advocate: Bhulabhai Desai.

✔️ Final Answer: (B) Bhulabhai Desai

🇮🇳 Madam Bhikaji Cama and the Indian National Flag

Madam Bhikaji Rustom Cama unfurled an early version of the Indian national flag at the International Socialist Congress held in Stuttgart, Germany, in August 1907. She was an important revolutionary, nationalist and advocate of India’s independence who raised the issue of Indian freedom before an international audience. This event made her one of the earliest prominent figures to display an Indian flag on an international platform.

🚩 Important Facts about the 1907 Flag

• Place: Stuttgart, Germany.
• Year: 1907.
• Event: International Socialist Congress.
• Person: Madam Bhikaji Cama.
• Purpose: To draw international attention to India’s struggle for independence.
• Design: The flag was different from the present Indian national flag. It had three horizontal bands of green, saffron and red, with symbols including lotuses and the words associated with Vande Mataram.

📊 Madam Bhikaji Cama: Important Information

🌍 Other Important Facts about the Indian National Flag

• Pingali Venkayya: He is widely associated with the design of the flag adopted by the Constituent Assembly in 1931 as the basis for the national flag.
• 22 July 1947: The Constituent Assembly adopted the present design of the Indian national flag.
• 15 August 1947: The national flag became the flag of independent India.
• Present design: It consists of three equal horizontal bands—saffron at the top, white in the middle and green at the bottom—with a navy-blue Ashoka Chakra of 24 spokes at the centre.
• Ratio: The width-to-length ratio of the national flag is 2:3.
• Flag Code of India: The Flag Code of India, 2002, regulates the display of the national flag; its provisions were amended in 2021 and 2022.

Quick Revision: Madam Bhikaji Cama → Stuttgart, Germany → 1907 → International Socialist Congress → early Indian tricolour flag.

✔️ Final Answer: (C) Stuttgart

📚 Important Personalities and Their Historical Associations

More than one pair is correct. Both (A) Vinoba Bhave—Second Individual Satyagrahi and (B) C. R. Das—Deshbandhu are correct. Therefore, option (E), which includes the possibility of more than one correct answer, is the appropriate answer.

1. Vinoba Bhave — Second Individual Satyagrahi

Acharya Vinoba Bhave was selected by Mahatma Gandhi as the first Individual Satyagrahi in the Individual Satyagraha launched in October 1940. Jawaharlal Nehru was the second Individual Satyagrahi. Therefore, the pair in option (A) is incorrect.

The Individual Satyagraha was launched to assert the right to freedom of speech and oppose India’s forced participation in the Second World War without the consent of its people. It was a limited, non-violent protest rather than a mass movement.

2. C. R. Das — Deshbandhu

Chittaranjan Das (C. R. Das) was popularly known as Deshbandhu, meaning “Friend of the Nation”. He was a prominent nationalist leader, lawyer and political figure. He founded the Swaraj Party in 1923 along with Motilal Nehru to enter legislative councils and oppose colonial policies from within.

3. William Wedderburn — Congress President

Sir William Wedderburn was a British civil servant sympathetic to Indian political aspirations and an important early supporter of the Indian National Congress. He served as Congress President in 1889 and 1910, not in 1907. The Congress session of 1907 was presided over by Rash Behari Ghosh at Surat.

4. Shyamji Krishna Varma — Founder of India House

Shyamji Krishna Varma founded India House in London in 1905, not in Paris. India House became an important centre for Indian students and revolutionary nationalists in Britain. It was associated with figures such as V. D. Savarkar and Madan Lal Dhingra.

📊 Important Personalities: Quick Comparison

🧠 Additional Exam-Oriented Facts

• Individual Satyagraha: Started by Mahatma Gandhi in October 1940 during the Second World War.
• First Satyagrahi: Vinoba Bhave, who offered Satyagraha at Paunar, Wardha, on 17 October 1940.
• Second Satyagrahi: Jawaharlal Nehru.
• Third Satyagrahi: Brahma Datt is generally identified as the third Individual Satyagrahi.
• Swaraj Party: Founded in January 1923 by C. R. Das and Motilal Nehru; it was also known as the Congress-Khilafat Swarajya Party.
• Surat Split: The Indian National Congress split in 1907 between Moderates and Extremists at Surat.
• India House: Established in London in 1905 by Shyamji Krishna Varma; it became a centre of revolutionary nationalist activity abroad.

Quick Revision: Vinoba Bhave → First Individual Satyagrahi; Jawaharlal Nehru → Second; C. R. Das → Deshbandhu; Wedderburn → Congress President in 1889 and 1910; Shyamji Krishna Varma → India House, London, 1905.

✔️ Final Answer: (E) More than one of the above — (A) and (B)

🇮🇳 Purna Swaraj Day — 26 January 1930

The Indian National Congress declared 26 January 1930 as Purna Swaraj Day (Complete Independence Day). This followed the historic resolution of complete independence adopted at the Lahore Session of the Indian National Congress in December 1929 under the presidency of Jawaharlal Nehru. On 26 January 1930, people across India observed the day by taking a pledge to struggle for complete independence from British rule.

📜 Lahore Session of the Indian National Congress, 1929

• Place: Lahore, now in Pakistan.
• Session: 44th session of the Indian National Congress.
• President: Jawaharlal Nehru.
• Time: December 1929.
• Major resolution: Purna Swaraj, or complete independence.
• Flag hoisting: The tricolour was hoisted on the banks of the Ravi River on 31 December 1929.
• First Purna Swaraj Day: 26 January 1930.

🗓️ Why Was 26 January Chosen as Republic Day?

When India became independent on 15 August 1947, the Constituent Assembly later decided to bring the Constitution into force on 26 January 1950. This date was selected to honour the historic declaration of Purna Swaraj observed on 26 January 1930. Thus, Republic Day commemorates the commitment to complete independence as well as the commencement of the Constitution.

📊 Important Dates Related to India’s Freedom Struggle

🧠 Additional Exam-Oriented Facts

• Dominion Status: The Nehru Report of 1928 recommended dominion status; the Lahore Congress later adopted complete independence as its goal.
• Jawaharlal Nehru: He presided over the Lahore Session of 1929 and became the first Prime Minister of independent India in 1947.
• Ravi River: The tricolour was hoisted near the banks of the Ravi River at Lahore on the night of 31 December 1929.
• Constitution Day: 26 November is observed as Constitution Day (Samvidhan Diwas) because the Constitution was adopted on 26 November 1949.
• Republic Day: 26 January is celebrated every year because the Constitution came into force on that date in 1950.
• Independence Day: 15 August commemorates the end of British colonial rule and India’s independence in 1947.

Quick Revision: Lahore Session → December 1929 → Jawaharlal Nehru → Purna Swaraj Resolution → 26 January 1930 → first Purna Swaraj Day → 26 January 1950 → Republic Day.

✔️ Final Answer: (A) 26-01-1930

🏛️ Establishment of Bihar — 22 March 1912

Bihar was established as a separate province on 22 March 1912, following the annulment of the 1905 Partition of Bengal and the reorganisation announced by the British Government. Bihar and Orissa were separated from the Bengal Presidency and constituted as the Province of Bihar and Orissa. Therefore, 1912 is the correct answer to the question.

However, the present-day state of Bihar took its separate administrative identity when Bihar was separated from Orissa on 1 April 1936. These two dates are important and should not be confused in examinations.

📜 Historical Background

• 1905: Lord Curzon partitioned Bengal, creating a new province of Eastern Bengal and Assam. Bihar remained associated with the Bengal administrative structure.
• 1911: At the Delhi Durbar, King George V announced the annulment of the Partition of Bengal and the transfer of the capital of British India from Calcutta to Delhi.
• 22 March 1912: Bihar and Orissa became a separate province from the Bengal Presidency.
• 1 April 1936: Bihar and Orissa were separated into two distinct provinces.
• 15 November 2000: Jharkhand was carved out of Bihar and became a separate state under the Bihar Reorganisation Act, 2000.

📊 Important Dates in Bihar’s Administrative History

🗺️ Important Facts about Bihar

• Capital: Patna.
• High Court: Patna High Court, established in 1916.
• First Chief Minister: Shri Krishna Sinha, who became Premier of Bihar in 1937 under the provincial autonomy arrangements.
• First Governor after independence: Jairamdas Daulatram.
• Major rivers: Ganga, Kosi, Gandak, Son, Bagmati and Punpun.
• Neighbouring states: Uttar Pradesh, Jharkhand and West Bengal; Nepal lies to the north.
• Historical significance: Ancient Bihar was associated with the Magadha, Maurya and Gupta empires and the rise of Buddhism and Jainism.

🧠 Important Exam Distinction

1912: Formation of the separate Bihar and Orissa Province. 1936: Separation of Bihar from Orissa. 2000: Separation of Jharkhand from Bihar. The question asks when Bihar was established, so the expected answer is 1912.

Quick Revision: Bihar established → 22 March 1912 → Bihar and Orissa Province; Bihar separated from Orissa → 1 April 1936; Jharkhand separated from Bihar → 15 November 2000; Bihar Diwas → 22 March.

✔️ Final Answer: (B) 1912

🌿 Tinkathia System and the Champaran Satyagraha

Under the Tinkathia System, indigo cultivators in Champaran, Bihar, were compelled by European planters to grow indigo on 3 kathas out of every 20 kathas of land. Thus, 3/20 (three-twentieths) of the land had to be reserved for indigo cultivation. This system placed a heavy burden on peasants and became one of the major causes of the Champaran Satyagraha of 1917.

📐 Meaning of Tinkathia

The word Tinkathia literally refers to three kathas. In the Champaran system, a tenant had to cultivate indigo on three kathas out of every twenty kathas of his holding. Since one bigha was commonly divided into 20 kathas in the local land-measurement system, this meant that 3/20 of a bigha was required for indigo cultivation.

Calculation:

Required land = 3 kathas out of 20 kathas

Fraction = 3/20 = 0.15 = 15%

⚖️ Why Was the Tinkathia System Oppressive?

• Forced cultivation: Peasants were compelled to grow indigo on a fixed portion of their land, often against their wishes.
• Low returns: Planters generally paid inadequate prices for the indigo produced by cultivators.
• Loss of food crops: Land used for indigo cultivation could not be used for growing food crops during that period.
• Exploitation: Peasants faced coercive practices, illegal dues and other forms of pressure from planters.
• Changing market conditions: The development of synthetic indigo reduced the commercial importance of natural indigo, but planters continued to impose unfair demands on peasants.

🇮🇳 Champaran Satyagraha, 1917: Important Facts

The Champaran Satyagraha was Mahatma Gandhi’s first major experiment with Satyagraha in India. It was organised against the exploitation of indigo cultivators under the Tinkathia System.

📅 Important Events of Champaran Satyagraha

• 1916: Raj Kumar Shukla met Gandhi at the Lucknow Session of the Indian National Congress and requested him to visit Champaran.
• April 1917: Gandhi reached Champaran to investigate the condition of indigo cultivators.
• Official inquiry: Gandhi was associated with the official inquiry committee appointed to examine the grievances of peasants.
• 1918: The Champaran Agrarian Act was passed, providing relief to peasants and bringing the Tinkathia system to an end.

🧠 Additional Exam-Oriented Facts

• First major Satyagraha in India: Champaran Satyagraha, 1917.
• First Individual Satyagraha: Vinoba Bhave, 1940. Do not confuse it with Champaran Satyagraha.
• Raj Kumar Shukla: He played a crucial role in bringing Gandhi to Champaran.
• Gandhi’s method: Non-violent resistance, investigation of peasant grievances and public mobilisation.
• Champaran and Bihar: The movement helped establish Gandhi as a major national leader and marked an important stage in the development of the Indian freedom struggle.
• Other early Gandhian movements: Ahmedabad Mill Strike (1918) and Kheda Satyagraha (1918).

Quick Revision: Tinkathia System → 3 kathas out of 20 → 3/20 = 15% → forced indigo cultivation → Champaran Satyagraha → 1917 → Mahatma Gandhi and Raj Kumar Shukla.

✔️ Final Answer: (C) 03/20

📐 Algebraic Identity: Difference of Two Squares

The given expression is:

\[ \frac{(598+479)^2-(598-479)^2}{598\times479} \]

We use the important algebraic identity:

\[ (a+b)^2-(a-b)^2=4ab \]

Step 1: Compare the given expression with the identity. We get:

\[ a=598,\qquad b=479 \]

Step 2: Apply the identity to the numerator:

\[ (598+479)^2-(598-479)^2 =4\times598\times479 \]

Step 3: Substitute this result into the original expression:

\[ =\frac{4\times598\times479}{598\times479} \]

Cancel the common factors 598 and 479:

\[ =\boxed{4} \]

🧠 Important Algebraic Identities for Competitive Exams

🎯 Quick Exam Tricks

• When the numerator contains \((a+b)^2-(a-b)^2\), immediately use \(4ab\).
• Do not calculate the two large squares separately. Applying the identity saves time and reduces calculation errors.
• If the denominator is \(ab\), the entire expression simplifies directly to 4.
• This identity is especially useful in SSC, Railway, BPSC, and other competitive examinations involving simplification.

Quick Revision: \((a+b)^2-(a-b)^2=4ab\). Therefore, when divided by \(ab\), the answer is always 4, provided \(a\) and \(b\) are non-zero.

✔️ Final Answer: (A) 4

📈 Population Growth: Compound Growth Method

The initial population of the town is 176400, and the annual growth rate is 5%. We have to calculate the population after two years.

Since the population increases every year, the growth is calculated on the population of the preceding year. Therefore, we use the compound growth formula:

\[ P_n=P\left(1+\frac{r}{100}\right)^n \]

Where:

• \(P_n\) = Population after \(n\) years.
• \(P\) = Initial population.
• \(r\) = Annual growth rate.
• \(n\) = Number of years.

Step 1: Substitute the given values:

\[ P=176400,\quad r=5,\quad n=2 \]

Step 2: Apply the compound growth formula:

\[ P_2=176400\left(1+\frac{5}{100}\right)^2 \]

\[ =176400\left(\frac{105}{100}\right)^2 \]

\[ =176400\times\frac{21}{20}\times\frac{21}{20} \]

Step 3: Calculate year by year:

Population after the first year:

\[ =176400\times\frac{105}{100} =185220 \]

Population after the second year:

\[ =185220\times\frac{105}{100} =194481 \]

Therefore:

\[ \boxed{P_2=194481} \]

📊 Year-wise Population Growth

🧠 Important Formulas for Population and Percentage

• Population growth: \(P_n=P(1+r/100)^n\).
• Population decrease: \(P_n=P(1-r/100)^n\).
• Growth for two years: \(P_2=P(1+r/100)^2\).
• Growth for three years: \(P_3=P(1+r/100)^3\).
• Percentage increase: \(\frac{\text{Increase}}{\text{Original value}}\times100\).
• Percentage decrease: \(\frac{\text{Decrease}}{\text{Original value}}\times100\).

🎯 Important Exam Concepts

1. Compound growth: In compound growth, each year’s percentage increase is calculated on the updated value, not on the original value.

2. Simple versus compound growth: Under simple growth, the increase is calculated on the original population every year. Under compound growth, the increase is calculated on the population at the beginning of each year.

3. Successive percentage changes: For two successive increases of \(a\%\) and \(b\%\), the equivalent percentage increase is:

\[ a+b+\frac{ab}{100} \]

For two successive increases of 5%:

\[ 5+5+\frac{5\times5}{100}=10.25\% \]

Thus, the total increase over two years is 10.25%, not 10%.

Quick Revision: Initial population = 176400; annual growth = 5%; period = 2 years; final population = 176400 × 1.05 × 1.05 = 194481.

✔️ Final Answer: (A) 194481

🔢 Number Series: Pattern Recognition

The given number series is:

\[ 4,\ 18,\ 48,\ 100,\ ?,\ 294,\ 448 \]

Observe that each term can be expressed as the product of a natural number and the square of its successor.

The general pattern is:

\[ \boxed{T_n=n(n+1)^2} \]

Step 1: Verify the pattern for the given terms:

\[ 1\times(1+1)^2=1\times4=4 \]

\[ 2\times(2+1)^2=2\times9=18 \]

\[ 3\times(3+1)^2=3\times16=48 \]

\[ 4\times(4+1)^2=4\times25=100 \]

Step 2: Calculate the missing fifth term:

\[ T_5=5\times(5+1)^2 \]

\[ =5\times6^2 \]

\[ =5\times36=\boxed{180} \]

Step 3: Verify the remaining terms:

\[ T_6=6\times7^2=6\times49=294 \]

\[ T_7=7\times8^2=7\times64=448 \]

📊 Complete Pattern Table

🧠 Additional Number-Series Concepts

• Natural numbers: \(1,2,3,4,5,\ldots\)
• Square numbers: \(1,4,9,16,25,36,49,64,\ldots\)
• Cube numbers: \(1,8,27,64,125,216,\ldots\)
• General term of this series: \(T_n=n(n+1)^2\).
• First difference: The difference between consecutive terms is \(14,30,52,80,114,154\).
• Second difference: The differences are \(16,22,28,34,40\), showing a constant third difference of 6.

🎯 Quick Exam Tricks

In number-series questions, check whether the terms can be formed using:

1. Natural numbers and their squares.
2. Natural numbers and their cubes.
3. Multiplication of consecutive numbers.
4. Addition or subtraction of successive differences.
5. Alternating patterns or a combination of two mathematical operations.

Here, the most direct pattern is \(n(n+1)^2\), which gives 180 at the fifth position.

Quick Revision: The series follows \(1\times2^2,\ 2\times3^2,\ 3\times4^2,\ldots\). Therefore, the missing term is \(5\times6^2=\mathbf{180}\).

✔️ Final Answer: (C) 180

🧮 Permutation and Combination: Combination Formula

The given condition is:

\[ {}^{2n}C_3:{}^nC_2=44:3 \]

We know that the formula for combinations is:

\[ {}^nC_r=\frac{n!}{r!(n-r)!} \]

Therefore:

\[ {}^{2n}C_3=\frac{2n(2n-1)(2n-2)}{3!} \]

And:

\[ {}^nC_2=\frac{n(n-1)}{2} \]

Step 1: Convert the given ratio into a fraction:

\[ \frac{{}^{2n}C_3}{{}^nC_2}=\frac{44}{3} \]

Step 2: Substitute the combination formulas:

\[ \frac{\dfrac{2n(2n-1)(2n-2)}{6}} {\dfrac{n(n-1)}{2}}=\frac{44}{3} \]

Step 3: Simplify, using \(2n-2=2(n-1)\):

\[ \frac{2n(2n-1)\times2(n-1)}{6} \times\frac{2}{n(n-1)} =\frac{44}{3} \]

Cancel the common factors \(n\) and \((n-1)\):

\[ \frac{4(2n-1)}{3}=\frac{44}{3} \]

Step 4: Multiply both sides by 3:

\[ 4(2n-1)=44 \]

\[ 2n-1=11 \]

\[ 2n=12 \]

\[ \boxed{n=6} \]

📚 Important Concepts: Permutation and Combination

1. Factorial: The factorial of a positive integer \(n\) is the product of all positive integers from 1 to \(n\).

\[ n!=n(n-1)(n-2)\cdots3\times2\times1 \]

For example:

\[ 5!=5\times4\times3\times2\times1=120 \]

2. Combination: Combination is the selection of objects in which the order of selection does not matter.

\[ {}^nC_r=\frac{n!}{r!(n-r)!} \]

3. Permutation: Permutation is the arrangement of objects in which the order matters.

\[ {}^nP_r=\frac{n!}{(n-r)!} \]

📊 Important Differences Between Permutation and Combination

🧠 Important Combination Properties

• Symmetry property: \({}^nC_r={}^nC_{n-r}\).
• Selection of zero objects: \({}^nC_0=1\).
• Selection of all objects: \({}^nC_n=1\).
• Selection of one object: \({}^nC_1=n\).
• Relation between permutation and combination: \({}^nP_r={}^nC_r\times r!\).
• Pascal’s identity: \({}^nC_r={}^{n-1}C_r+{}^{n-1}C_{r-1}\).

Quick Revision: Convert the ratio into a fraction, substitute the combination formulas, simplify the common factors, and solve the resulting linear equation. The value obtained is \(n=6\).

✔️ Final Answer: (B) 6

📊 Average: Combined Average Method

We are given that:

• The average of \(m\) numbers is \(n^2\).
• The average of \(n\) numbers is \(m^2\).
• We have to find the average of all \(m+n\) numbers.

Important formula:

The sum of a group of numbers is equal to the product of the number of observations and their average.

\[ \text{Sum}=\text{Number of observations}\times\text{Average} \]

Step 1: Calculate the sum of the first group of \(m\) numbers:

\[ \text{Sum}_1=m\times n^2=mn^2 \]

Step 2: Calculate the sum of the second group of \(n\) numbers:

\[ \text{Sum}_2=n\times m^2=nm^2 \]

Step 3: Calculate the total sum of all \(m+n\) numbers:

\[ \text{Total Sum}=mn^2+nm^2 \]

Taking \(mn\) common:

\[ =mn(n+m) \]

Step 4: Apply the combined average formula:

\[ \text{Combined Average} =\frac{\text{Total Sum}}{\text{Total Number of observations}} \]

\[ =\frac{mn(m+n)}{m+n} \]

Cancel the common factor \((m+n)\):

\[ \boxed{mn} \]

📊 Summary Table of the Given Information

🧠 Important Average Formulas

• Average: \(\text{Average}=\frac{\text{Sum of observations}}{\text{Number of observations}}\).
• Total sum: \(\text{Sum}=\text{Average}\times\text{Number of observations}\).
• Combined average: \(\frac{n_1a_1+n_2a_2}{n_1+n_2}\), where \(n_1,n_2\) are group sizes and \(a_1,a_2\) are their respective averages.
• New average after adding an observation: \(\frac{\text{Old sum}+\text{New observation}}{\text{Old number}+1}\).
• New average after removing an observation: \(\frac{\text{Old sum}-\text{Removed observation}}{\text{Old number}-1}\).

🎯 Additional Exam-Oriented Facts

1. Combined average: When two or more groups are combined, their averages cannot simply be added or averaged directly. Their respective group sizes must be considered.

2. Equal-sized groups: If two groups contain the same number of observations, their combined average is the arithmetic mean of their individual averages.

3. Unequal-sized groups: When group sizes differ, the combined average is a weighted average. The larger group has a greater influence on the combined average.

4. Effect of a new observation: If a new observation is greater than the existing average, the average increases. If it is smaller than the existing average, the average decreases.

5. Important distinction: Average is a measure of central tendency. It represents the total value divided equally among the observations.

Quick Revision: First group sum = \(mn^2\); second group sum = \(nm^2\); combined sum = \(mn(m+n)\); total observations = \(m+n\). Hence, combined average = \(mn\).

✔️ Final Answer: (C) mn

🏀 Set Theory and Venn Diagram

This question is based on Set Theory and the concept of overlapping groups. We have to calculate the number of students who play football only, meaning they play football but neither hockey nor basketball.

📊 Given Information

🧮 Step-by-Step Calculation

Step 1: The number of students who play both football and basketball, but not hockey, is:

12 − 8 = 4

Step 2: The number of students who play both hockey and football, but not basketball, is:

15 − 8 = 7

Step 3: The number of students who play all three games is 8.

Step 4: Therefore, the number of students who play football only is:

Football only = Total football players − (Football and basketball only) − (Football and hockey only) − (All three)

= 29 − 4 − 7 − 8

= 10

📌 Direct Formula

When the pairwise intersections include the students who play all three games, the formula for the number of students playing only football is:

F only = F − (F ∩ B) − (F ∩ H) + (F ∩ B ∩ H)

= 29 − 12 − 15 + 8 = 10

🧠 Important Exam-Oriented Facts

• Set: A well-defined collection of distinct objects is called a set.
• Union (A ∪ B): Represents the elements belonging to A or B or both.
• Intersection (A ∩ B): Represents the elements common to both sets.
• Only A: Represents elements belonging to set A but not to the other specified sets.
• Three-set inclusion-exclusion formula: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(C ∩ A) + n(A ∩ B ∩ C).
• Important caution: If a pairwise intersection is given, it normally includes the students belonging to all three groups unless the question explicitly says “only”.
• Venn diagram: A Venn diagram uses overlapping circles to represent sets and their relationships.

Quick Revision: Football only = Total football players − Football and basketball − Football and hockey + All three = 29 − 12 − 15 + 8 = 10.

✔️ Final Answer: (A) 10

👷 Time and Work

This question is based on the relationship between work, time and efficiency. When two people work together, their daily work rates are added. After Mohan leaves, Sohan completes the remaining work alone.

📊 Given Information

• Mohan completes the entire work in 25 days.
• Sohan completes the entire work in 20 days.
• Both work together for 5 days.
• After 5 days, Mohan leaves and Sohan completes the remaining work.

🧮 Step-by-Step Calculation

Step 1: Assume the total work.

Take the total work as the LCM of 25 and 20:

LCM (25, 20) = 100 units

Step 2: Calculate the daily work of each person.

Mohan’s one-day work:

100 ÷ 25 = 4 units

Sohan’s one-day work:

100 ÷ 20 = 5 units

Step 3: Calculate their combined daily work.

4 + 5 = 9 units per day

Step 4: Calculate the work completed in 5 days.

9 × 5 = 45 units

Step 5: Calculate the remaining work.

100 − 45 = 55 units

Step 6: Calculate the time taken by Sohan alone.

Sohan completes 5 units of work in one day. Therefore:

Required time = 55 ÷ 5 = 11 days

📋 Work Distribution Table

📌 Important Formulas

• One-day work: Total work ÷ Number of days required.
• Combined work rate: Add the individual one-day work rates when people work together.
• Work completed: Daily work × Number of working days.
• Remaining work: Total work − Completed work.
• Time required: Remaining work ÷ Daily work rate of the person working alone.

🧠 Further Exam-Oriented Facts

• Efficiency and time: For the same amount of work, efficiency is inversely proportional to the time taken.
• Efficiency ratio: Mohan’s efficiency : Sohan’s efficiency = 4 : 5.
• Work together: Their combined efficiency is 9 units per day.
• Alternative method: Combined one-day work = 1/25 + 1/20 = 9/100. In 5 days, they complete 45/100 of the work, leaving 55/100. Sohan’s time = (55/100) ÷ (1/20) = 11 days.
• LCM method: Taking total work as the LCM of the given completion times makes calculations easier by converting daily work into whole numbers.
• Important distinction: The 5 days are the period during which both work together. The 11 days are the additional time Sohan needs after Mohan leaves.

Quick Revision: Total work = 100 units; combined daily work = 9 units; work done in 5 days = 45 units; remaining work = 55 units; Sohan’s remaining time = 55 ÷ 5 = 11 days.

✔️ Final Answer: (B) 11 days

🕔 Clock and Angle

This question is based on the angular movement of the hour hand. A clock completes one full revolution of 360° in 12 hours. Therefore, the hour hand moves at a constant rate of 30° per hour or 0.5° per minute.

🧮 Step-by-Step Calculation

Step 1: Calculate the total elapsed time.

The clock starts at 12:00 noon and the required time is 5:10 PM.

Elapsed time = 5 hours 10 minutes

Converting the time into minutes:

= (5 × 60) + 10 = 310 minutes

Step 2: Calculate the movement of the hour hand.

The hour hand completes 360° in 12 hours.

Movement per hour = 360° ÷ 12 = 30°

Movement per minute:

= 30° ÷ 60 = 0.5°

Step 3: Calculate the total angular movement.

Angle = 310 × 0.5°

= 155°

📊 Important Clock Movement Facts

📌 Important Clock Formulas

• Hour hand movement: 30° × Number of hours.
• Hour hand movement per minute: 0.5°.
• Minute hand movement: 6° × Number of minutes.
• Angle between the hands: |30H − 5.5M|, where H is the hour and M is the minute. For the smaller angle, take the smaller of this value and 360° minus this value.
• Relative speed: The minute hand gains 5.5° per minute over the hour hand.
• Full revolution of the hour hand: 12 hours.
• Full revolution of the minute hand: 60 minutes.

🧠 Further Exam-Oriented Facts

• At 12:00: Both the hour and minute hands are at 12, so the angle between them is 0°.
• At 3:00: The angle between the hands is 90°.
• At 6:00: The angle between the hands is 180°.
• At 9:00: The angle between the hands is 90°.
• At 5:10: The hour hand is at 155° clockwise from 12, while the minute hand is at 60° clockwise from 12.
• Important distinction: This question asks for the total rotation of the hour hand from 12:00, not the angle between the hour hand and the minute hand at 5:10.

Quick Revision: Hour hand speed = 0.5° per minute; elapsed time = 310 minutes; angular movement = 310 × 0.5° = 155°.

✔️ Final Answer: (C) 155°

🔢 Perfect Squares and Natural Numbers

A perfect square is a number that can be expressed as the product of a natural number multiplied by itself. We need to identify the number among the given options that cannot be expressed in this form.

🧮 Step-by-Step Verification

Option (A): 26569

163 × 163 = 26569

Therefore, 26569 is a perfect square.

Option (B): 163642

A perfect square cannot have 2 as its last digit. The possible last digits of a perfect square in the decimal number system are only 0, 1, 4, 5, 6 and 9.

Since 163642 ends in 2, it cannot be the square of any natural number.

Option (C): 30976

176 × 176 = 30976

Therefore, 30976 is a perfect square.

Option (D): 28561

169 × 169 = 28561

Therefore, 28561 is a perfect square.

📊 Verification Table

📌 Important Properties of Perfect Squares

• Last-digit rule: A perfect square in the decimal system can end only in 0, 1, 4, 5, 6 or 9. It can never end in 2, 3, 7 or 8.
• Unit digit: If a number ends in 1, its square may end in 1 or 9; if it ends in 2 or 8, its square ends in 4; if it ends in 3 or 7, its square ends in 9; if it ends in 4 or 6, its square ends in 6; and if it ends in 5, its square ends in 5.
• Prime factorisation: In the prime factorisation of a perfect square, every prime factor must have an even exponent.
• Consecutive squares: The difference between the squares of consecutive natural numbers is given by (n + 1)² − n² = 2n + 1, which is always odd.
• Number of zeros: A perfect square has an even number of trailing zeros.
• Between consecutive squares: There is no perfect square strictly between n² and (n + 1)².
• Natural number: Under the common convention in school mathematics, natural numbers are 1, 2, 3, …; some mathematical conventions also include 0.

🧠 Additional Exam-Oriented Facts

Nearby square numbers for option (B):

404² = 163216

405² = 164025

Since:

163216 < 163642 < 164025

163642 lies strictly between the squares of 404 and 405. Therefore, it cannot be a perfect square.

Important examination shortcut: Before calculating square roots, check the unit digit of the given number. If its last digit is 2, 3, 7 or 8, it can immediately be rejected as a perfect square. This saves time in competitive examinations.

Quick Revision: Perfect-square last digits = 0, 1, 4, 5, 6, 9. The number 163642 ends in 2, so it is not a perfect square.

✔️ Final Answer: (B) 163642

📐 Solving a Pair of Linear Equations in Two Variables

We are given the following two simultaneous linear equations:

217x + 131y = 913   … (i)
131x + 217y = 827   … (ii)

We can solve these equations conveniently by using the elimination method. Since the coefficients of x and y are interchanged in the two equations, adding and subtracting them will simplify the calculation.

Step 1: Add both equations

Adding equations (i) and (ii):

(217x + 131x) + (131y + 217y) = 913 + 827

348x + 348y = 1740

Dividing both sides by 348:

\[ x+y=\frac{1740}{348} \]

x + y = 5   … (iii)

Step 2: Subtract the second equation from the first

Subtracting equation (ii) from equation (i):

(217x-131x)+(131y-217y)=913-827

86x-86y=86

Dividing both sides by 86:

x − y = 1   … (iv)

Step 3: Calculate the values of x and y

We now have two simplified equations:

x + y = 5   … (iii)
x − y = 1   … (iv)

Adding equations (iii) and (iv):

2x = 6

x = 3

Substituting x = 3 into equation (iii):

3 + y = 5

y = 2

✅ Step 4: Verification of the answer

To verify the result, substitute x = 3 and y = 2 into both original equations.

First equation:

217(3) + 131(2) = 913

651 + 262 = 913

913 = 913 ✓

Second equation:

131(3) + 217(2) = 827

393 + 434 = 827

827 = 827 ✓

Both original equations are satisfied. Therefore, the calculated values are correct.

📊 Important Concepts: Linear Equations in Two Variables

A pair of linear equations in two variables can be represented in the general form:

\[ a_1x+b_1y=c_1 \] \[ a_2x+b_2y=c_2 \]

The following table explains the possible conditions for the number of solutions:

🧠 Further Exam-Oriented Facts

• Elimination method: One variable is eliminated by adding or subtracting equations after making its coefficients equal or opposite.
• Substitution method: The value of one variable is expressed in terms of the other and substituted into the second equation.
• Cross-multiplication method: It can also be used to solve a pair of simultaneous linear equations.
• Unique solution: Two non-parallel straight lines intersect at exactly one point, giving one unique solution.
• Determinant condition: For a unique solution, \(a_1b_2-a_2b_1\neq0\).
• Useful identity: Adding and subtracting \(x+y=p\) and \(x-y=q\) gives \(x=\frac{p+q}{2}\) and \(y=\frac{p-q}{2}\).

⚡ Quick Revision

• Adding the given equations gives: x + y = 5.
• Subtracting the second equation from the first gives: x − y = 1.
• Adding the simplified equations gives: x = 3.
• Substitution gives: y = 2.

✔️ Final Answer: (B) 3 and 2

🌱 Ginger: An Underground Modified Stem

Ginger (Zingiber officinale) is an underground modified stem known as a rhizome. It is classified as a stem rather than a root because it possesses characteristic stem structures, particularly nodes and internodes. The nodes bear buds and scale leaves, while the internodes are the regions between two successive nodes.

A ginger rhizome grows horizontally beneath the soil and stores food. However, the most important botanical evidence that identifies it as a stem is the presence of nodes, internodes and buds. Ordinary roots do not possess these typical stem structures.

🔬 Why Is Ginger a Stem and Not a Root?

• Nodes: These are points on the stem from which leaves, buds or branches may arise. Ginger rhizomes have clearly identifiable nodes.
• Internodes: These are the portions of a stem between two successive nodes. They are present in ginger rhizomes.
• Buds: Buds present on the rhizome can develop into new aerial shoots under suitable conditions.
• Scale leaves: Small, reduced scale leaves are present at the nodes of the rhizome.
• Food storage: Ginger stores reserve food, mainly in the form of starch, in its underground rhizome.

📊 Difference Between Root and Stem

🌿 Examples of Modified Underground Stems

🧠 Important Exam-Oriented Facts

• Ginger: An underground stem modification called a rhizome.
• Turmeric: Also a rhizome, belonging to the ginger family (Zingiberaceae).
• Potato: A stem tuber; its eyes represent buds.
• Sweet potato: A modified storage root, not a stem tuber.
• Onion: A bulb consisting of a short stem and fleshy scale leaves.
• Garlic: A bulb made up of several cloves, each of which is a modified bud.
• Banana: Its underground rhizome is the true stem; the apparent aerial trunk is a pseudostem formed by leaf bases.
• Vegetative propagation: Ginger can reproduce vegetatively through pieces of rhizome containing viable buds.

Quick Revision: Ginger → Rhizome → Underground stem → Nodes + internodes + buds. Potato → Stem tuber; Sweet potato → Root tuber; Onion → Bulb.

✔️ Final Answer: (B) it has nodes and internodes.

🍯 Fructose: The Sweetest Common Natural Sugar

Fructose is generally regarded as the sweetest naturally occurring common sugar among the options given. It is a simple sugar, or monosaccharide, with the molecular formula C₆H₁₂O₆. It is commonly found in fruits, honey and some vegetables. Fructose is also known as fruit sugar.

When sweetness is compared under similar conditions and at comparable concentrations, fructose is sweeter than glucose, sucrose and maltose. However, perceived sweetness can vary with temperature, concentration and the food in which the sugar is present.

🧪 Important Types of Sugars

🔬 Chemical Composition and Classification

• Fructose: A six-carbon ketohexose monosaccharide. Its molecular formula is C₆H₁₂O₆.
• Glucose: A six-carbon aldohexose monosaccharide. It is a major fuel used by living cells.
• Maltose: A disaccharide made of two glucose molecules joined by an α(1→4) glycosidic bond.
• Sucrose: A disaccharide made of one glucose unit and one fructose unit linked by a glycosidic bond.

📊 Monosaccharides and Disaccharides

Monosaccharides are the simplest carbohydrates and cannot be hydrolysed into smaller carbohydrate units. Disaccharides are formed when two monosaccharide units combine through a glycosidic bond, generally with the removal of a water molecule.

🧠 Further Exam-Oriented Facts

• Fruit sugar: Fructose is commonly called fruit sugar because it occurs naturally in many fruits.
• Blood sugar: Glucose is commonly called blood sugar because it is the principal sugar circulating in human blood.
• Milk sugar: Lactose is the principal sugar present in milk; it consists of glucose and galactose.
• Malt sugar: Maltose is also known as malt sugar and is produced during the breakdown of starch.
• Table sugar: Sucrose is the common household sugar obtained commercially mainly from sugarcane and sugar beet.
• Reducing sugars: Glucose, fructose, maltose and lactose are reducing sugars; sucrose is a non-reducing sugar.
• Photosynthesis: Plants produce carbohydrates through photosynthesis, initially forming simple carbohydrate products that are used to build other organic substances.
• Energy: Glucose is a major energy substrate for cellular respiration, while fructose can also be metabolised by the body.

Quick Revision: Fructose → Fruit sugar → Monosaccharide → Sweetest among the given options. Glucose → Blood sugar; Lactose → Milk sugar; Maltose → Malt sugar; Sucrose → Table sugar.

✔️ Final Answer: (A) fructose.

🍎 Apple: A False Fruit or Accessory Fruit

Apple is not considered a true fruit in the strict botanical sense. It is classified as a false fruit or accessory fruit because a significant part of its fleshy edible portion develops from the thalamus (receptacle), in addition to the ovary. The true fruit develops from the ovary of a flower after fertilisation, whereas an accessory fruit involves other floral parts in forming the edible structure.

The central core of an apple, which contains the seeds, develops from the ovary. The surrounding fleshy edible part develops largely from the thalamus. Therefore, apple is botanically described as a pome, a type of accessory fruit.

🌸 True Fruit and False Fruit

• True fruit: A fruit that develops only from the ovary of a flower after fertilisation.
• False fruit: A fruit in which parts other than the ovary, such as the thalamus or receptacle, also contribute substantially to the edible structure.
• Accessory fruit: Another name commonly used for a false fruit because additional floral tissues participate in its development.
• Apple: A classic example of an accessory fruit because its fleshy edible part develops mainly from the thalamus.

📊 Botanical Classification of the Given Fruits

🔬 Important Types of Botanical Fruits

• Pome: A fleshy accessory fruit with a core; examples include apple and pear.
• Berry: A simple fleshy fruit generally developing from a single ovary; examples include grape, tomato and banana.
• Drupe: A fleshy fruit with a hard, stony inner layer called the endocarp; examples include mango, peach and plum.
• Aggregate fruit: Develops from several free ovaries of a single flower; examples include strawberry, raspberry and custard apple.
• Multiple fruit: Develops from the ovaries of many flowers in an inflorescence; examples include pineapple, jackfruit and mulberry.

🧠 Further Exam-Oriented Facts

• Strawberry: It is an accessory fruit. The fleshy edible part develops from the receptacle, while the small structures on its surface are individual achenes.
• Cashew apple: The fleshy cashew apple is an accessory structure formed mainly from the swollen pedicel; the kidney-shaped cashew nut is the true fruit.
• Pineapple: It is a multiple fruit formed by the fusion of fruits and associated tissues of an inflorescence.
• Jackfruit: It is also a multiple fruit, developing from a whole inflorescence.
• Mango: It is a drupe with a fleshy mesocarp and a hard endocarp surrounding the seed.
• Tomato: Botanically, it is a true fruit of the berry type, although it is commonly used as a vegetable in cooking.
• Seed formation: In flowering plants, the ovule generally develops into a seed after fertilisation, while the ovary develops into the fruit.

Quick Revision: Apple → False fruit (Pome); Grape → Berry; Date → True fruit; Plum → Drupe. A true fruit develops from the ovary, while an accessory fruit also involves other floral parts.

✔️ Final Answer: (A) Apple.

🌾 Legumes: An Important Source of Plant Protein

Legumes are plants belonging to the family Fabaceae (Leguminosae). Their seeds, commonly known as pulses when harvested dry for food, are highly nutritious because they are rich in protein. Important edible legumes include lentils, chickpeas, peas, beans, kidney beans and pigeon peas.

Legumes are particularly important in human nutrition because they provide plant-based protein, dietary fibre, complex carbohydrates, vitamins and minerals. They are an important component of diets in India and many other countries, especially where plant-based foods form a major part of daily meals.

🌱 Why Are Legumes Rich in Protein?

Legume seeds store substantial amounts of proteins as reserve food for the developing embryo. In addition, many leguminous plants form a symbiotic association with nitrogen-fixing bacteria called Rhizobium, which live in root nodules. These bacteria convert atmospheric nitrogen into forms that plants can use, supporting plant growth and protein synthesis.

It is important to distinguish between these two facts: nitrogen fixation helps the plant obtain usable nitrogen, while the stored proteins in the seeds make pulses a valuable source of dietary protein for humans.

📊 Important Nutritional Components of Legumes

🦠 Rhizobium and Biological Nitrogen Fixation

• Rhizobium: A genus of bacteria associated with the roots of many leguminous plants.
• Root nodules: Small swellings on roots that provide a suitable environment for nitrogen-fixing bacteria.
• Nitrogen fixation: The conversion of atmospheric nitrogen (N₂) into ammonia or related usable nitrogen compounds by nitrogen-fixing organisms.
• Leghemoglobin: A pink-coloured oxygen-binding protein found in active legume root nodules; it helps regulate oxygen conditions for nitrogen fixation.
• Agricultural importance: Legumes can improve soil nitrogen availability and are commonly included in crop rotations.

📚 Examples of Important Legumes

🧠 Further Exam-Oriented Facts

• Pulse: The dry edible seeds of certain leguminous crops are commonly called pulses.
• Soybean: It is a legume with a particularly high protein content and is also used for extracting edible oil.
• Groundnut: It belongs to the legume family but is especially valued for its oil-rich seeds.
• Pea family: Fabaceae is also known as Leguminosae and is an important family of flowering plants.
• Fruit type: The characteristic fruit of many members of Fabaceae is a legume or pod.
• Crop rotation: Growing legumes in rotation with cereals can help improve soil fertility through biological nitrogen fixation.
• Dietary quality: Many pulses are relatively low in fat and rich in fibre and protein, although their precise nutritional composition varies by species and processing method.
• Complementary proteins: Combining pulses with cereals, such as dal with rice or roti, can improve the overall balance of essential amino acids in a meal.

Quick Revision: Legumes → Fabaceae → Protein-rich seeds → Rhizobium in root nodules → Biological nitrogen fixation → Improved soil fertility.

✔️ Final Answer: (B) protein.

🌸 Clove: A Spice Obtained from Unopened Flower Buds

Clove is obtained from the dried, unopened flower buds of the clove tree, scientifically known as Syzygium aromaticum. The plant belongs to the family Myrtaceae. The flower buds are harvested before they open and then dried, during which they develop their characteristic brown colour and strong aroma.

The dried clove is a highly valued spice used in cooking, traditional preparations and perfumery. Its distinctive smell and flavour are mainly due to eugenol, an aromatic compound present in clove essential oil.

🌿 Botanical Identity of Clove

• Common name: Clove.
• Scientific name: Syzygium aromaticum.
• Family: Myrtaceae.
• Plant part used: Dried, unopened flower buds.
• Important chemical constituent: Eugenol.
• Plant type: An evergreen tropical tree.

🧪 Eugenol: The Major Aromatic Compound

Eugenol is the principal aromatic constituent of clove essential oil. It is responsible for much of the characteristic fragrance and warm, spicy flavour of cloves. Eugenol is also used in dental preparations because of its characteristic local soothing and antiseptic properties. Clove oil is used in certain dental products, but concentrated clove oil should not be used casually because it can cause irritation and toxicity if misused.

📊 Common Spices and the Plant Parts Used

🌍 Cultivation and Production

The clove tree is native to the Maluku Islands (Moluccas) of Indonesia, historically known as the Spice Islands. Today, cloves are cultivated in several tropical countries, including Indonesia, Madagascar, Tanzania, Sri Lanka and India. In India, clove cultivation is associated with parts of Kerala, Tamil Nadu and Karnataka.

🧠 Further Exam-Oriented Facts

• Clove family: Myrtaceae, the same botanical family that includes eucalyptus and guava.
• Clove oil: It is an essential oil obtained from clove buds and other parts of the plant; eugenol is its major characteristic constituent.
• Flower bud: The spice sold as a whole clove is harvested before the flower opens.
• Saffron: It is obtained from the dried stigmas of Crocus sativus, not from its petals or seeds.
• Cinnamon: It is obtained from the inner bark of certain Cinnamomum species.
• Black pepper: It is obtained from the dried fruits of Piper nigrum and contains piperine, which contributes to its pungency.
• Turmeric: Its rhizome contains curcuminoids, including curcumin, which gives turmeric its characteristic yellow colour.
• India and spices: India is an important producer and consumer of spices, with the Spices Board of India functioning under the Ministry of Commerce and Industry.

Quick Revision: Clove → Dried flower bud → Syzygium aromaticum → Myrtaceae → Eugenol. Cinnamon → Bark; Turmeric → Rhizome; Saffron → Stigma; Black pepper → Fruit.

✔️ Final Answer: (D) Flower bud.