DSSSB TGT (Maths) Official Paper (Held On: 12 Nov, 2025 Shift 1) (Previous Year Paper)

Given: Seven people, A, B, C, D, E, F and G, are sitting in a row facing north.

1) Only one person sits to the left of E. 

2) Only two people sit between E and G.

3) F sits to the immediate right of B.

4. D sits to the immediate left of C.

5. Only one person sits between G and B.

The remaining position will be occupied by the only person left i.e. A.

Thus, two people sit to the right of G.

Hence, "Option 1" is the correct answer.

The logic followed here is:

Thus, "Option 1" is the correct answer.

The logic followed here is:

Option 1) KO-NR

Option 2) MO-TP

Option 3) WA-ZD

Option 4) SW-VZ

Thus out of all 'MO-TP' is the odd one out.

Hence, the correct answer is "Option 2".

Decoding symbols:

Given: P × Q - R + S

P × Q → P is the father of Q.

Q - R → Q is the sister of R.

R + S → R is the brother of S.

Thus, R is P's son.

Hence, the correct answer is "Option 2".

The logic followed here is:

Option 1) TVS

Option 2) QSO

Option 3) KMI

Option 4) NPL

Thus out of all 'TVS' is the odd one out.

Hence, the correct answer is "Option 1".

The logic followed here is:

PNQO is related to USVT

And,

JHKI is related to OMPN

Similarly,

MKNL is related to

Thus, "Option 3" is the correct answer.

Given: 

Naitik starts driving from point A and drives 9 km towards north.

He then turns right and drives 2 km.

He then turns right and drives 17 km.

He then turns right and drives 8 km.

He finally turns right and drives 8 km and stops at point P.​

Thus, Naitik should drive 6 km in the east direction to return to point A.

Hence, the correct answer is "Option 2".

According to the question:

Thus, ‘honor’ is coded as 'up'.

Hence, the correct answer is "Option 4".

Decoding signs:

Given: 92 C 22 A 11 B 3 D 24 = ?

92 C 22 A 11 B 3 D 24 = ? ⇒ 92 + 22 ÷ 11 × 3 - 24 = ?

⇒ 92 + 22 ÷ 11 × 3 - 24 = ?

⇒ 92 + 2 × 3 - 24 = ?

⇒ 92 + 6 - 24 = ?

⇒ 98 - 24 = ?

⇒ 74 = ?

Hence, "Option 3" is the correct answer.

The logic followed here is:

16 – 36 – 51 – 71

16 + 20 → 36

36 + 15 → 51

51 + 20 → 71

And,

35 – 55 – 70 – 90

35 + 20 → 55

55 + 15 → 70

70 + 20 → 90

Similarly,

28 – 48 – 63 – 83

28 + 20 → 48

48 + 15 → 63

63 + 20 → 83

Hence, the correct answer is "Option 4".

Given series: (Left) 823 574 432 351 287 (Right)

According to the question.

Thus, according to the final arrangement, positions of five numbers remains unchanged.

Hence, "Option 3" is the correct answer.

Given: 63 - 18 × 2 + 12 ÷ 4 = ? 

According to the question, after ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged:

63 - 18 × 2 + 12 ÷ 4 = ? ⇒ 63 + 18 ÷ 2 - 12 × 4 = ?

⇒ 63 + 18 ÷ 2 - 12 × 4 = ?

⇒ 63 + 9 - 12 × 4 = ?

⇒ 63 + 9 - 48 = ?

⇒ 72 - 48 = ?

⇒ 24 = ?

Hence, "Option 1" is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some benches are chairs → Does not follow (As all benches are tables and some chairs are tables. So it is possibe but not definite.)

II. No stool is a table → Does not follow (As some chairs are tables and no chair is a stool. As no direct relation is given between tables and stool, therefore it is false.)

∴ Here, Neither conclusion I nor conclusion II follows.​

Hence, the correct answer is "Option 4".

According to the question:

Total students → 45

Krishna's position from the right end → 16^th

Liana is 10^th to Krishna's left, so Liana's position from the right end → 16^th + 10 = 26^th

Liana's position from the left end → Total students - Liana's position from the right end + 1

→ 45 - 26 + 1 = 20^th

Hence, "Option 4" is the correct answer.

The logic followed here is:

21 - 20.3 - 19.6 - 18.9

→ 21 - 0.7 = 20.3

→ 20.3 - 0.7 = 19.6

→ 19.6 - 0.7 = 18.9

And,

28 - 27.3 - 26.6 - 25.9

→ 28 - 0.7 = 27.3

→ 27.3 - 0.7 = 26.6

→ 26.6 - 0.7 = 25.9

Similarly,

36 - 35.3 - 34.6 - 33.9

→ 36 - 0.7 = 35.3

→ 35.3 - 0.7 = 34.6

→ 34.6 - 0.7 = 33.9

Hence, the correct answer is "Option 1".

The logic followed here is:

Hence, the correct answer is "Option 1".

Given: A, B, C, D, E, F, and G each delivered a lecture on a different day of the same week, starting from Monday and ending on Sunday.

1) Only two people delivered a lecture before C. 

2) Only two people delivered a lecture between C and D.

3) E delivered a lecture immediately after D.

4. Only two people delivered a lecture between E and B.

5. A delivered a lecture immediately before G.

The remaining position will be occupied by the only person left i.e. F.

Thus, F delivered a lecture on Friday.

Hence, "Option 1" is the correct answer.

The logic followed here is:

Thus, "Option 2" is the correct answer.

Given

Statement:

To enhance security, the company has implemented two-factor authentication (2FA) for all user accounts.

Given

Assumptions:

I. Current security measures were deemed inadequate. → Implicit

When a company introduces an additional security layer like 2FA, it implies that existing measure were not sufficient to ensure desired security.

II.Users may find it challenging to adopt two-factor authentication. → Not Implicit

The statement focuses on enhancing security, not on user difficulty. There is no indication that the company considered users challenges.

Therefore, Only assumption I is implicit.

Hence, "Option 1" is the correct answer.

Given: HAS CUT RAN DYE

According to the question:

Thus, according to the final arrangement, in only four words thus formed will have no vowel.

Hence, "Option 2" is the correct answer.

The correct answer is Uttar Pradesh.

Key Points

• The Junior Boys National Football Championship, officially known as the Dr. BC Roy Trophy, for the 2024-25 season (referenced for the upcoming cycle) commenced in July 2024.
• The Tier 2 matches of this prestigious national tournament were hosted in the state of Uttar Pradesh.
• Specific matches were organized in the Naraini region of the Banda district, providing a platform for young athletes from various states to compete at a national level.
• The championship is a key initiative by the All India Football Federation (AIFF) to promote grassroots football and identify talent for the Under-15 and Under-16 national teams.
• The tournament is structured into two tiers; while Uttar Pradesh hosted the Tier 2 event, the Tier 1 matches for the same season were held in Narayantpur, Chhattisgarh.

Additional Information

• Dr. BC Roy Trophy History:
• The trophy is named after Dr. Bidhan Chandra Roy, a Bharat Ratna awardee and the second Chief Minister of West Bengal.
• Established in 1962, it was originally an Under-19 tournament but has been restructured over the years by the AIFF to focus on younger age groups like the Junior (U-15/U-17) category.
• All India Football Federation (AIFF):
• Founded in 1937 and headquartered in New Delhi, it is the governing body for association football in India.
• The federation received FIFA affiliation in 1948 and is currently led by President Kalyan Chaubey.
• It manages several national competitions, including the Santosh Trophy (Senior Men), Senior Women's NFC, and various youth leagues.
• Tournament Structure and Eligibility:
• The Junior Boys National Football Championship follows a tiered format (Tier 1 and Tier 2) to ensure that teams of similar skill levels compete against each other, with provisions for promotion and relegation.
• For the 2024-25 cycle, players born on or after January 1, 2009, and not later than December 31, 2010, were eligible to participate.

Important Points

• Regional Development: Hosting matches in districts like Banda (Uttar Pradesh) and Narayantpur (Chhattisgarh) is part of AIFF's Vision 2047 to take football to every corner of the country and improve sports infrastructure in rural and semi-urban areas.
• Scouting and Talent Identification: These championships serve as the primary source for national scouts to pick players for the India U-17 National Team, which participates in AFC and SAFF youth championships.
• Strategic Impact: The state of Uttar Pradesh has been increasingly active in hosting national sporting events, leveraging its investments in sports facilities to become a hub for national-level competitions in India.

The correct answer is Restrictions imposed on tribal livelihoods by the Madras Forest Act of 1882.

Key Points

• The Rampa Rebellion, also known as the Manyam Rebellion, took place between August 1922 and May 1924 in the Godavari agency area of the Madras Presidency (present-day Andhra Pradesh).
• The rebellion was primarily triggered by the Madras Forest Act of 1882. This act severely restricted the tribal communities from accessing their traditional forest lands and collecting minor forest produce. Hence, the option regarding the Madras Forest Act of 1882 is correct.
• The colonial government sought to ban the traditional Podu (shifting cultivation) system practiced by the tribal people. This system was vital for their food security and survival, and its prohibition caused widespread agrarian distress and socio-economic hardship.
• The rebellion was led by Alluri Sitarama Raju, who mobilized the Koya and Konda Dora tribes against British colonial exploitation. He claimed to possess astrological knowledge and mystical powers, asserting that he could heal people and survive bullet shots.
• The rebels utilized guerilla warfare tactics to attack several police stations, such as Chintapalli, Krishna Devi Peta, and Rajavommangi, to seize firearms and ammunition.

Additional Information

• Alluri Sitarama Raju:
• He was born on 4 July 1897 (some records say 1898) in the West Godavari district. Despite not being a tribal himself, he identified with their cause and became their most prominent leader, earning the title Manyam Veerudu (Hero of the Jungles).
• Raju was deeply influenced by the Non-Cooperation Movement launched by Mahatma Gandhi. He encouraged tribal people to wear Khadi and give up the consumption of liquor.
• However, he differed with Gandhi on the principle of non-violence. Raju believed that India could only be liberated from British rule through the use of force and armed struggle.
• Role of the British Government:
• To suppress the rebellion, the British deployed the Assam Rifles and spent over 40 lakh rupees.
• The colonial administration used a policy of brute force, burning villages and torturing tribal families to extract information about the rebels' whereabouts.
• Tribal Labor Exploitation:
• Apart from forest restrictions, the British forced the tribals into vetti (unpaid compulsory labor) for the construction of roads and forest buildings, which acted as a major catalyst for the 1922 revolt.

Important Points

• End of the Rebellion: The revolt came to an end after a massive manhunt led by British officers. Alluri Sitarama Raju was eventually trapped and captured by the British in the forests of Chintapalli. He was tied to a tree and executed by a firing squad on 7 May 1924.
• Legacy: In 1986, the Indian Postal Department issued a postage stamp in honor of Alluri Sitarama Raju to commemorate his contribution to the freedom struggle. In 2022, the Government of India celebrated his 125^th birth anniversary and unveiled a 30-foot tall bronze statue in Bhimavaram.
• Comparison with other options: While excessive land revenue (Option A) was a cause for the Santhal Rebellion of 1855 and political representation (Option B) was a demand of the urban elite, the Rampa Rebellion was specifically a tribal response to forest laws.

The correct answer is Not used anywhere.

Key Points

• The word 'federal' does not appear anywhere in the Constitution of India. The framers of the Constitution avoided using this term to emphasize the unique nature of the Indian polity. Hence, statement A is correct.
• Article 1 of the Constitution describes India, that is Bharat, as a 'Union of States'. It does not use the term 'Federation'. Hence, statement B is incorrect.
• Dr. B.R. Ambedkar clarified that the term 'Union of States' was preferred over 'Federation of States' to indicate two things: first, that the Indian Federation is not the result of an agreement among the states like the American Federation, and second, that the states have no right to secede from the Union.
• Part I of the Constitution (Articles 1 to 4) titled 'The Union and its Territory' uses the word 'Union' throughout but deliberately excludes the word 'federal'. Hence, statement C is incorrect.
• The Preamble of the Constitution describes India as a Sovereign, Socialist, Secular, Democratic, Republic. It contains no mention of the word 'federal'. Hence, statement D is incorrect.

Additional Information

• Nature of Indian Federalism: Although the word is missing, the Indian Constitution establishes a federal system of government. It contains all the essential characteristics of a federation, such as two governments, division of powers, written Constitution, supremacy of the Constitution, rigidity of the Constitution, independent judiciary, and bicameralism.
• Quasi-Federal Description: Due to its strong centralizing tendencies, many constitutional experts have described India as 'quasi-federal'. K.C. Wheare famously coined this term, while Morris Jones called it 'bargaining federalism' and Granville Austin termed it 'cooperative federalism'.
• Unitary Features: The Indian Constitution possesses several non-federal features including a strong Centre, single Constitution, single citizenship, flexibility of the Constitution, integrated judiciary, and the appointment of State Governors by the President.
• Emergency Provisions: Under Articles 352, 356, and 360, the federal structure can be converted into a unitary one during emergencies without a formal amendment, a feature unique to India.

Important Points

• Basic Structure Doctrine: In the landmark S.R. Bommai v. Union of India (1994) case, the Supreme Court ruled that Federalism is a part of the 'basic structure' of the Constitution, meaning it cannot be destroyed by the Parliament.
• Seventh Schedule: The distribution of powers between the Union and the States is clearly defined in the Seventh Schedule through three lists: Union List (100 subjects), State List (61 subjects), and Concurrent List (52 subjects).
• Financial Federalism: Article 280 provides for a Finance Commission every five years to recommend the distribution of financial resources between the Central Government and the State Governments.
• Historical Context: The Government of India Act, 1935 served as the blueprint for the federal structure of the Indian Constitution, providing for an All-India Federation which never actually came into being under the British Raj.

The correct answer is Ganges.

Key Points

• The Ganges, also known as the Ganga, is revered as the most sacred river in Hinduism and is personified as the goddess Ganga. It is believed that bathing in the river causes the remission of sins and facilitates Moksha (liberation from the cycle of life and death).
• The river originates from the Gangotri Glacier at Gaumukh in the Uttarakhand Himalayas, at an elevation of approximately 3,892 meters. At its source, it is known as the Bhagirathi, which later joins the Alaknanda at Devprayag to form the Ganges.
• The Ganges flows through the nations of India and Bangladesh, covering a total distance of approximately 2,525 km (1,569 miles) before emptying into the Bay of Bengal through the Sunderbans delta.
• It is mentioned in the Rigveda, the earliest of the Hindu scriptures, and plays a central role in various Puranic legends, particularly the story of King Bhagiratha, who performed penance to bring the river down from heaven to purify the souls of his ancestors.
• The river is a lifeline to millions of Indians who live along its course and depend on it for their daily needs, agriculture, and industry. Due to its spiritual and national importance, it was declared the National River of India in November 2008. Hence, the correct answer is the Ganges.

Additional Information

• Yamuna River:
• The Yamuna is the largest tributary of the Ganges. It originates from the Yamunotri Glacier in the Mussoorie range of the lower Himalayas.
• It passes through Delhi, Haryana, and Uttar Pradesh before merging with the Ganges at the Triveni Sangam in Prayagraj. This confluence is the site of the Kumbh Mela, the world's largest religious gathering.
• In Hindu mythology, Yamuna is the daughter of Surya (the Sun God) and the sister of Yama (the God of Death).
• Godavari River:
• The Godavari is the second-longest river in India after the Ganges and is often referred to as Dakshin Ganga (Ganges of the South).
• It originates in Trimbakeshwar near Nashik in Maharashtra and flows eastward across the Deccan Plateau into the Bay of Bengal.
• It holds immense religious significance in South India, with major pilgrimage centers like Rajamahendravaram and Bhadrachalam located on its banks.
• Saraswati River:
• The Saraswati is a mythical or lost river mentioned frequently in ancient Vedic texts. It is considered part of the holy trinity along with the Ganges and Yamuna at Prayagraj, where it is believed to flow underground.
• In Hinduism, it is personified as Saraswati, the goddess of knowledge, music, art, speech, wisdom, and learning.

Important Points

• Environmental Conservation: The Government of India launched the Namami Gange Programme in June 2014. It is an Integrated Conservation Mission with a budget outlay of Rs. 20,000 Crore to accomplish the twin objectives of effective abatement of pollution and conservation of the National River Ganga.
• Biodiversity: The Ganges is home to over 140 fish species, 90 amphibian species, and the endangered Ganges River Dolphin (Platanista gangetica), which is the National Aquatic Animal of India.
• Religious Festivals: Major cities on its banks include Haridwar, Varanasi, Patna, and Kanpur. Varanasi is considered the holiest city in Hinduism and is located on the crescent-shaped left bank of the Ganges.

The correct answer is Stealth Frigate.

Key Points

• Tavasya is the lead ship of the Project 17B class of Advanced Stealth Frigates, which was officially launched/commissioned in the year 2025.
• The vessel was constructed at Mazagon Dock Shipbuilders Limited (MDL), located in Mumbai, India, under the ambitious Project 17B, which serves as a more advanced follow-on to the Nilgiri-class (Project 17A).
• It is designed with advanced stealth features, including a significantly reduced Radar Cross Section (RCS) and a refined hull form to minimize acoustic and infrared signatures, making it difficult for enemy sensors to detect.
• The ship is equipped with state-of-the-art indigenous technology, supporting the Atmanirbhar Bharat initiative, with nearly 75% of its components being sourced from within the country.
• Tavasya is integrated with high-end weaponry such as the BrahMos supersonic cruise missiles and Barak-8 (LRSAM) surface-to-air missiles for multi-dimensional warfare capabilities.

Additional Information

• Stealth Frigates (The Correct Option):
• These are medium-sized multi-role warships designed for maritime security, escort duties, and anti-submarine warfare.
• They feature Integrated Platform Management Systems (IPMS) and dual-gas turbines for high-speed operations, reaching speeds over 30 knots.
• The Project 17B frigates, like Tavasya, have a displacement of approximately 6,800 to 7,000 tonnes and a length of about 150 meters.
• Submarines (Option A):
• These are underwater vessels used primarily for stealthy surveillance and torpedo attacks.
• In India, recent developments include the Kalvari-class (Project 75) diesel-electric submarines, built with French collaboration, and the nuclear-powered Arihant-class.
• Key features include AIP (Air Independent Propulsion) systems that allow them to stay submerged for longer periods.
• Amphibious Carriers (Option C):
• Also known as Landing Platform Docks (LPD) or Amphibious Assault Ships, these are used to transport troops, tanks, and helicopters to hostile shores.
• The Indian Navy operates INS Jalashwa and is planning to acquire four new LPDs to bolster its expeditionary warfare capabilities.
• These ships act as floating command centers and are vital for Humanitarian Assistance and Disaster Relief (HADR) operations.
• Missile Corvettes (Option D):
• Corvettes are smaller, highly maneuverable warships, such as the Kamorta-class (Project 28), primarily used for coastal defense and Anti-Submarine Warfare (ASW).
• They typically have a displacement of 2,500 to 3,500 tonnes and are armed with short-range missiles and anti-submarine rockets.

Important Points

• Technological Advancements: Tavasya incorporates an Active Electronically Scanned Array (AESA) radar, specifically the MF-STAR, which provides 360-degree coverage for tracking multiple aerial and surface targets simultaneously.
• Naming Convention: The name Tavasya is derived from Sanskrit, meaning Strength or Power, following the Indian Navy's tradition of naming frigates after mountain ranges or powerful attributes.
• Strategic Role: The commissioning of such advanced frigates is part of the Maritime Capability Perspective Plan (MCPP) to transform the Indian Navy into a 175-ship fleet by the year 2035 to counter rising challenges in the Indian Ocean Region (IOR).
• Project 17B Progress: This project was sanctioned by the Ministry of Defence to maintain the construction momentum after the completion of Project 17A, ensuring that shipyards like MDL and GRSE remain active in high-tech shipbuilding.

The correct answer is Periodic Labour Force Survey.

Key Points

• The Periodic Labour Force Survey (PLFS) was launched by the National Statistical Office (NSO) in April 2017. It was designed to provide more frequent and timely data on the labor market in India.
• The survey is conducted under the aegis of the Ministry of Statistics and Programme Implementation (MoSPI). Its primary objective is to estimate the key employment and unemployment indicators such as the Worker Population Ratio (WPR), Labour Force Participation Rate (LFPR), and Unemployment Rate (UR).
• The PLFS generates two types of reports: a Quarterly Bulletin for urban areas (based on Current Weekly Status) and an Annual Report covering both rural and urban areas (based on both Usual Status and Current Weekly Status).
• Before the introduction of PLFS, the National Sample Survey Office (NSSO) used to conduct Employment-Unemployment Surveys (EUS) every five years. The PLFS replaced this old system to provide annual continuity. Hence, option C is correct.
• The other options, such as the India Brand Equity Foundation survey and RBI data survey, do not serve as the official national source for comprehensive employment and unemployment statistics produced by MoSPI. Hence, options A, B, and D are incorrect.

Additional Information

• National Statistical Office (NSO): It was formed through the merger of the National Sample Survey Office (NSSO) and the Central Statistics Office (CSO) by an order dated 23 May 2019. It acts as the nodal agency for planned development of the statistical system in India.
• Labour Force Participation Rate (LFPR): This is defined as the percentage of persons in the labour force (i.e., those who are either working or seeking/available for work) in the total population. It helps in understanding the human resources available in the economy.
• Worker Population Ratio (WPR): This refers to the percentage of employed persons in the total population. It is a critical indicator to measure the employment generation capacity of the country.
• Unemployment Rate (UR): This is calculated as the percentage of persons unemployed among the persons in the labour force. It excludes those who are not looking for work, such as students or homemakers.
• Methodology: The PLFS uses a rotational panel sampling design in urban areas to measure short-term changes in the labor market every three months. In rural areas, households are visited once to capture the annual status.

Important Points

• Reference Periods: The survey uses Usual Status (ps+ss) with a reference period of 365 days preceding the date of the survey, and Current Weekly Status (CWS) with a reference period of the last 7 days.
• Data Trends: According to the Annual Report 2022-23, the Unemployment Rate in India showed a declining trend compared to previous years, reaching approximately 3.2% for persons aged 15 years and above.
• Scope of Survey: The PLFS covers almost all the States and Union Territories of India. It collects data on various aspects including education level, industry of work (based on National Industrial Classification), and earnings of the workers.
• Policy Impact: The data generated by NSO through this survey is used by the Government of India, NITI Aayog, and various research institutions to formulate labor laws and social security schemes for unorganized workers.

The correct answer is A - II, B - III, C - IV, D - I.

Key Points

• Sikhism was founded by Guru Nanak Dev, who was born in 1469 in Talwandi (now Nankana Sahib, Pakistan). He was the first of the ten Sikh Gurus and emphasized the belief in one God (Ik Onkar) and the equality of all human beings. Hence, the mapping of A with II is correct.
• Buddhism originated in ancient India with Siddhartha Gautama, who later became the Gautama Buddha. Born in Lumbini (modern-day Nepal) around the 6^th century BCE, he sought an end to suffering and attained Enlightenment in Bodh Gaya. Hence, the mapping of B with III is correct.
• Islam was established by the Prophet Muhammad in the early 7^th century CE in Mecca, Saudi Arabia. He is considered the final messenger of God by Muslims, and the revelations he received are compiled in the Holy Quran. Hence, the mapping of C with IV is correct.
• Jainism is an ancient Indian religion that traces its spiritual lineage through 24 Tirthankaras. The first Tirthankara was Rishabhdev (also known as Adinatha), who is credited with establishing the foundations of Jain philosophy long before the 24^th Tirthankara, Lord Mahavira. Hence, the mapping of D with I is correct.

Additional Information

• Sikhism:
• The holy scripture of Sikhism is the Guru Granth Sahib, which is treated as the living Guru.
• The Khalsa Panth was established by the tenth Guru, Guru Gobind Singh, in 1699 at Anandpur Sahib.
• Major practices include Langar (community kitchen), Sewa (selfless service), and the Five Ks (Kesh, Kangha, Kara, Kachera, and Kirpan).
• Buddhism:
• The core teachings include the Four Noble Truths and the Eightfold Path to achieve Nirvana.
• The religion split into various sects like Theravada, Mahayana, and Vajrayana over centuries.
• Famous Buddhist sites include Sarnath (where Buddha gave his first sermon) and Kushinagar (where he attained Mahaparinirvana).
• Islam:
• Islam is based on Five Pillars: Shahada (Faith), Salah (Prayer), Zakat (Almsgiving), Sawm (Fasting during Ramadan), and Hajj (Pilgrimage to Mecca).
• The two primary denominations are Sunni and Shia, which emerged after the death of the Prophet in 632 CE.
• The Islamic calendar (Hijri) began in 622 CE, marking the migration (Hijrah) from Mecca to Medina.
• Jainism:
• The main principles of Jainism are Ahimsa (non-violence), Satya (truth), Asteya (non-stealing), Brahmacharya (chastity), and Aparigraha (non-attachment).
• It is divided into two major sects: Digambara (sky-clad) and Shvetambara (white-clad).
• The Agamas are the primary canonical texts of Jainism, containing the teachings of the Tirthankaras.

Important Points

• Geographical Origins: While Sikhism, Buddhism, and Jainism were founded in the Indian Subcontinent, Islam originated in the Arabian Peninsula.
• Chronological Order: Jainism is considered one of the oldest living religions, followed by Buddhism (approx. 563 BCE), Islam (approx. 610 CE), and Sikhism (1469 CE).
• Founders vs. Reformers: In Jainism, Lord Mahavira (the 24^th Tirthankara) is often mistaken as the founder, but he was a reformer and the last Tirthankara, while Rishabhdev is the traditional founder.
• The Concept of God: Islam is strictly Monotheistic; Sikhism is Monotheistic (One Formless God); Buddhism and Jainism are generally Transtheistic or Atheistic in their classical forms, focusing more on spiritual liberation than a creator deity.

The correct answer is Canada.

Key Points

• The Constitution of India has borrowed the concept of a federal system with a strong Centre from the Canadian Constitution. This ensures that while power is distributed, the Union Government remains superior to maintain the integrity of the nation.
• Under Article 1, India is described as a 'Union of States' rather than a 'Federation of States'. This terminology is inspired by the British North America Act of 1867 (the Canadian Constitution), signifying that states have no right to secede from the union.
• The vesting of residuary powers in the Centre is another significant feature adopted from Canada. According to Article 248, any matter not mentioned in the State List or Concurrent List falls under the jurisdiction of the Parliament.
• The process of the appointment of State Governors by the Central Government is a distinct Canadian feature incorporated into the Indian political system to ensure coordination between the Union and the States.
• The advisory jurisdiction of the Supreme Court, as mentioned under Article 143, where the President can seek the opinion of the court, is also a feature derived from the Canadian model.

Additional Information

• United States of America (USA):
• The Indian Constitution borrowed the Preamble, Fundamental Rights (Part III), and the concept of Judicial Review from the USA.
• The independence of the judiciary and the impeachment of the President are other vital provisions sourced from the American Constitution.
• The removal of Supreme Court and High Court judges and the post of Vice-President are also based on the US model.
• United Kingdom (UK):
• India adopted the Parliamentary form of government, the Rule of Law, and Single Citizenship from the British Constitution.
• Other features include Bicameralism (two houses of Parliament), the Cabinet System, and Legislative procedures.
• The system of Prerogative Writs (Habeas Corpus, Mandamus, etc.) used by courts was also influenced by the UK.
• Ireland (Irish Constitution):
• The Directive Principles of State Policy (DPSP), which provide guidelines for the government to ensure social and economic justice, were borrowed from Ireland.
• The method of election of the President and the nomination of members to the Rajya Sabha by the President are Irish influences.
• South Africa:
• The procedure for the amendment of the Constitution under Article 368 is taken from South Africa.
• The election of members of the Rajya Sabha on the basis of proportional representation is also a South African feature.

Important Points

• Government of India Act, 1935: This act served as the primary blueprint for the Constitution of India. Features like the Federal Scheme, Office of Governor, Judiciary, Public Service Commissions, and Emergency provisions were largely derived from this act.
• Germany (Weimar Constitution): The provision for the suspension of Fundamental Rights during an Emergency was influenced by the German model.
• Australia: The Concurrent List, the freedom of trade, commerce, and intercourse, and the joint sitting of the two Houses of Parliament were borrowed from the Australian Constitution.
• USSR (Now Russia): The Fundamental Duties (added by the 42^nd Amendment Act, 1976) and the ideals of justice (social, economic, and political) in the Preamble were inspired by the Soviet Constitution.
• France: The ideals of Liberty, Equality, and Fraternity in the Preamble, as well as the concept of a Republic, were taken from the French Constitution.

The correct answer is Simultaneous uplift of the Himalayas and rapid river erosion by fast flowing rivers.

Key Points

• The formation of deep gorges and V-shaped valleys in the Himalayas is primarily due to Antecedent Drainage. This means the rivers existed before the mountains were uplifted and maintained their course by cutting through the rising land.
• During the Himalayan orogeny, which began approximately 65 million years ago in the Tertiary period, the land rose due to the collision of the Indian Plate and the Eurasian Plate.
• As the mountains rose, the major rivers like the Indus, Brahmaputra, and Satluj performed vigorous vertical down-cutting or down-cutting erosion to maintain their original flow levels, leading to the creation of deep, narrow valleys known as Gorges. Hence, statement B is correct.
• Lateral erosion typically occurs in the middle and lower courses of a river, where the velocity decreases and the river starts meandering, leading to the widening of valleys rather than deepening them into gorges. Hence, statement A is incorrect.
• Deposition of sediments and subsidence are processes associated with the formation of alluvial plains (like the Indo-Gangetic Plain) and deltaic regions, which are constructive rather than erosional features. Hence, statement C is incorrect.
• The Himalayas are Fold Mountains and not volcanic in origin; therefore, volcanic activity does not play a role in the formation of these river valleys. Hence, statement D is incorrect.

Additional Information

• Himalayan River Characteristics: These rivers are Perennial in nature, receiving water from both Monsoon rainfall and the melting of Glaciers. They are currently in their Youthful Stage, characterized by high velocity and massive erosional power.
• Gorges: A Gorge is a narrow valley between hills or mountains, typically with steep rocky walls and a stream running through it. The Indus Gorge near Bunji in Gilgit-Baltistan is one of the deepest in the world, reaching a depth of about 5,180 meters.
• V-shaped Valleys: These are formed in the upper course of the river where the gradient is steep. The river uses its kinetic energy to erode the riverbed vertically. Over time, weathering and mass wasting wear down the valley sides, creating the distinct 'V' shape.
• Major Antecedent Rivers:
• The Indus: Originates near Mansarovar Lake in Tibet and cuts through the Karakoram and Ladakh ranges.
• The Brahmaputra: Known as the Tsangpo in Tibet, it creates a massive gorge near Namcha Barwa before entering Arunachal Pradesh, India.
• The Satluj: It cuts a deep gorge through the Zanskar range at Shipki La pass.

Important Points

• Geological Process: The rate of tectonic uplift in the Himalayas (estimated at 5-10 mm per year in some regions) was balanced by the rate of river incision, allowing these Trans-Himalayan rivers to carve paths through the highest mountain range on Earth.
• Comparison with Peninsular Rivers: Unlike Himalayan rivers, Peninsular rivers (like the Godavari and Krishna) are older and have reached a graded profile or mature stage, resulting in broad, shallow valleys with very little vertical erosion.
• Evolution: The presence of fluvial terraces in these valleys provides geological evidence of the periodic upliftment of the Himalayas and the subsequent adjustments made by the river systems over millions of years.

The correct answer is Yajurveda.

Key Points

• Yajurveda is primarily known as the Veda of Rituals or Prose Mantras. It serves as a practical guidebook for the Adhvaryu priest who executes the physical steps of a sacrifice (Yajna).
• The text contains ritual formulas and guidelines necessary for the performance of various sacrificial ceremonies, such as the Ashvamedha (horse sacrifice) and Rajasuya (consecration of a king). Hence, the statement regarding guidelines for sacrificial ceremonies is correct for Yajurveda.
• It is divided into two major versions: the Shukla Yajurveda (White Yajurveda), which contains only the mantras, and the Krishna Yajurveda (Black Yajurveda), which includes both mantras and explanatory prose.
• Composed approximately between 1200 BCE and 900 BCE, this Veda reflects the transition from the early Vedic period to a more complex ritualistic society located in the Kuru-Panchala region of Ancient India.
• While Rigveda focuses on the recitation of hymns to praise deities, Yajurveda focuses on the actual application of those hymns during the ceremonial fire sacrifices.

Additional Information

• Rigveda:
• It is the oldest of the four Vedas, dated roughly between 1500 BCE and 1200 BCE.
• It consists of 1,028 hymns (Suktas) organized into 10 books known as Mandalas.
• The primary function is the invocation of deities like Agni, Indra, and Varuna through chants recited by the Hotri priest. Hence, option D is incorrect for sacrificial execution guidelines.
• Samaveda:
• Known as the Veda of Melodies or Chants, it is the root of Indian classical music and dance.
• It contains 1,549 verses, most of which are derived from the Rigveda but set to musical notations.
• The hymns are sung by the Udgatri priest during Soma sacrifices. Hence, option A is incorrect for the execution of sacrificial steps.
• Atharvaveda:
• This Veda was included in the Vedic canon much later and deals with charms, spells, and magical incantations.
• It contains 730 hymns divided into 20 books, focusing on healing diseases, averting evil, and daily life rituals.
• It also provides early knowledge of medicine and herbs, overseen by the Brahma priest. Hence, option C is incorrect regarding the specific guidelines for Vedic sacrifices.

Important Points

• The Vedas are collectively called Shruti (that which is heard), as they were transmitted orally for centuries before being written down.
• The Yajurveda provides the earliest evidence of social stratification and the expansion of the Vedic culture toward the Ganges valley.
• The Shukla Yajurveda is associated with the Vajasaneyi Samhita, while the Krishna Yajurveda includes branches like Taittiriya and Maitrayani.
• Each Veda has four subdivisions: the Samhitas (mantras), the Brahmanas (ritual commentaries), the Aranyakas (forest books/rituals), and the Upanishads (philosophical texts).

The correct answer is To examine the financial accounts of the Government and the reports of the Comptroller and Auditor General.

Key Points

• The Public Accounts Committee (PAC) is a standing parliamentary committee that acts as a watchdog over the government's spending and financial integrity.
• Its primary function is to examine the Appropriation Accounts and the Finance Accounts of the Union Government, ensuring that the money granted by Parliament has been spent within the scope of the demand. Hence, statement B is correct.
• The committee scrutinizes the audit reports submitted by the Comptroller and Auditor General (CAG) of India, which cover appropriation accounts, finance accounts, and public undertakings.
• It ensures financial accountability of the executive to the legislature by verifying if the expenditure was legally available for the service or purpose and whether it conformed to the authority that governed it.
• The Public Accounts Committee does not have the power to examine policy in the broader sense or intervene in appointments to higher positions in public sector units. Hence, statement C and D are incorrect.
• The Speaker of the Legislative Assembly or Lok Sabha certifies a bill as a Money Bill, but the PAC does not certify that legislation is necessary. Hence, statement A is incorrect.

Additional Information

• Origin and History: The Public Accounts Committee was first established in 1921 under the provisions of the Government of India Act of 1919 (Montagu-Chelmsford Reforms) and has existed since then.
• Composition: The committee consists of 22 members. Out of these, 15 members are elected from the Lok Sabha and 7 members are elected from the Rajya Sabha. The members are elected every year from amongst its members according to the principle of proportional representation by means of the single transferable vote.
• Term of Office: The term of office of the members is one year. A Minister cannot be elected as a member of the committee to ensure its independent functioning.
• Chairman of PAC: The Chairman is appointed by the Speaker from amongst its members. Since 1967, a convention has developed where the Chairman is invariably selected from the Opposition party.
• Role of CAG: The Comptroller and Auditor General (CAG) is often described as the "friend, philosopher, and guide" of the Public Accounts Committee. The CAG assists the committee during its deliberations and helps in identifying technical financial irregularities.

Important Points

• Scope of Examination: The PAC examines the audit reports of the CAG on revenue receipts, expenditure by various ministries, and stores and stocks. It also looks into cases involving losses, nugatory expenditure, and financial impropriety.
• Limitations: The committee is not an executive body; it can only make recommendations. It cannot stop expenditure as it conducts a post-mortem examination (examining expenditure after it has been incurred). Furthermore, its recommendations are advisory and not binding on the Government.
• Other Financial Committees: Apart from the PAC, the Parliament has two other important financial committees: the Estimates Committee (consisting of 30 members, all from Lok Sabha) and the Committee on Public Undertakings (consisting of 22 members).

The correct answer is Both I and II.

Key Points

• The Dendritic drainage pattern is the most common form and resembles the branching pattern of a tree. It develops in regions where the underlying rock structure offers uniform resistance to erosion, and the tributaries join the main river at acute angles.
• This pattern is extensively found in the rivers of the Northern Plains of India, such as the Ganga, Indus, and Brahmaputra, where the flat terrain allows for such branching networks. Hence, statement I is correct.
• A Radial drainage pattern is characterized by rivers that originate from a central high point, such as a volcanic cone or a dome-shaped hill, and flow outward in different directions.
• The classic example of this in India is the Amarkantak Hills in Madhya Pradesh and Chhattisgarh, where rivers like the Narmada, Son, and Johilla originate from the same plateau and flow in different directions. Hence, statement II is correct.
• The drainage pattern of an area is a result of the geological time period, the nature and structure of rocks, topography, slope, and the amount of water flowing through the system.

Additional Information

• Trellis Drainage Pattern:
• In this pattern, the primary tributaries of rivers flow parallel to each other and secondary tributaries join them at right angles.
• It is typically found in areas where hard and soft rocks exist parallel to each other, such as in the folded mountains of the Himalayan foothills.
• Centripetal Drainage Pattern:
• In this system, rivers discharge their waters from all directions into a lake or a central depression.
• An example of this in India is the Loktak Lake in Manipur, where various streams converge into the lake basin.
• Rectangular Drainage Pattern:
• This pattern develops on strongly jointed rocky terrain where the river follows the paths of faults and cracks.
• The tributaries join the main stream at nearly right angles, creating a geometric, rectangular appearance across the landscape.
• Geological Features:
• The Peninsular drainage system is older than the Himalayan one, as evidenced by the broad, largely graded shallow valleys and the maturity of the rivers.
• The Western Ghats running close to the western coast act as the water divide between the major Peninsular rivers, discharging their water in the Bay of Bengal and as small rivulets joining the Arabian Sea.

Important Points

• Antecedent Drainage: This occurs when a river maintains its original course and pattern despite the upliftment of land across its path. The Indus, Sutlej, and Brahmaputra are prominent examples of antecedent rivers as they cut through the Himalayas via deep gorges.
• River Basin Data: The Ganga basin is the largest in India, covering about 25% of the country's total land area, while the Godavari is the largest Peninsular river system, often referred to as the Dakshin Ganga.
• West Flowing Rivers: Unlike most major rivers in India that flow eastwards, the Narmada and Tapi flow towards the west and drain into the Arabian Sea because they flow through rift valleys formed by faulting.
• Evolution of Drainage: Geologists believe that a mighty river called the Shivalik or Indo-Brahma once flowed along the longitudinal extent of the Himalayas from Assam to Punjab before being dismembered into the three main river systems we see today during the Pleistocene period.

The correct answer is Ministry of Finance.

Key Points

• The Ministry of Finance released the draft Climate Finance Taxonomy in May 2025 for public consultation, marking a significant step in India’s sustainable finance roadmap.
• The draft taxonomy was developed to provide a comprehensive classification system that defines which economic activities can be considered environmentally sustainable or "green."
• This initiative directly follows the announcement made by the Union Finance Minister Nirmala Sitharaman during the presentation of the Union Budget 2024-25, where the government committed to creating a framework for climate finance.
• The primary objective of the taxonomy is to facilitate the flow of climate finance into critical sectors, thereby assisting India in achieving its Nationally Determined Contributions (NDCs).
• By standardizing definitions, the Ministry of Finance aims to prevent greenwashing, where companies or funds make misleading claims about the environmental benefits of their operations or assets.

Additional Information

• Definition of Climate Finance: It refers to local, national, or transnational financing—drawn from public, private, and alternative sources of financing—that seeks to support mitigation and adaptation actions that will address climate change.
• Sovereign Green Bonds: The Government of India began issuing Sovereign Green Bonds in January 2023 to mobilize resources for green infrastructure; the new taxonomy provides a clearer framework for the allocation of these funds.
• India's Net Zero Goal: India has set a target to achieve Net Zero carbon emissions by the year 2070, as announced at COP26 in Glasgow.
• Business Responsibility and Sustainability Reporting (BRSR): The Securities and Exchange Board of India (SEBI) introduced BRSR to mandate ESG disclosures for the top 1,000 listed companies, which will now align with the draft taxonomy.
• Global Context: India’s move aligns with international practices such as the European Union (EU) Taxonomy, ensuring that Indian green assets are attractive to global institutional investors.

Important Points

• Eligible Sectors: The draft taxonomy covers key sectors including renewable energy, energy efficiency, clean transportation, water and waste management, and sustainable agriculture.
• Department of Economic Affairs (DEA): The DEA within the Ministry of Finance acts as the lead agency in coordinating with the Ministry of Environment, Forest and Climate Change (MoEFCC) to refine these guidelines.
• Panchamrit Strategy: The taxonomy supports the five-fold strategy (Panchamrit) which includes reaching 500 GW non-fossil energy capacity by 2030.
• Task Force on Sustainable Finance: A dedicated task force was established by the Ministry of Finance in 2021 to suggest the roadmap that led to the drafting of this National Taxonomy.

The correct answer is Tamarind.

Key Points

• Tartaric acid is a white, crystalline organic acid that occurs naturally in many fruits, most notably in Tamarind, Grapes, and Bananas.
• In Tamarind, it provides the characteristic sour and tangy taste that is widely utilized in South Asian and Southeast Asian culinary traditions.
• The chemical formula of Tartaric Acid is C4H6O6. It is classified as a diprotic acid, meaning it has the capacity to donate two hydrogen ions per molecule in an aqueous solution.
• Tamarind (Tamarindus indica) fruit pulp contains a significant concentration of this acid, which not only contributes to flavor but also serves as a natural preservative. Hence, option D is correct.
• Aside from food, Tartaric acid is used as an antioxidant and is known as E334 in the food additive industry.

Additional Information

• Tomato: The primary organic acid found in Tomatoes is Oxalic acid, though they also contain Citric and Malic acids. Oxalic acid is a dicarboxylic acid that is found in various vegetables and leafy greens like spinach. Hence, option A is incorrect.
• Vinegar: It consists mainly of Acetic acid (also known as ethanoic acid), which is produced through the fermentation of ethanol by acetic acid bacteria. Commercial Vinegar typically contains an acetic acid concentration of 4% to 8%. Hence, option B is incorrect.
• Lemon: Like many members of the citrus family, Lemons and Limes are rich sources of Citric acid. This acid makes up approximately 5% to 6% of the fruit's juice, giving it a pH level of around 2.2. Hence, option C is incorrect.
• Baking Applications: Tartaric acid is a key component of Baking powder, where it reacts with sodium bicarbonate (baking soda) to release carbon dioxide gas, allowing dough to rise.
• Industrial Uses: Beyond food, it is used in pharmaceuticals, textile printing, and tanning. It is also used in metal cleaning to remove oxides from surfaces of copper and brass.

Important Points

• Chirality and History: Tartaric acid played a vital role in the discovery of molecular chirality. In 1848, the famous scientist Louis Pasteur observed the symmetry of tartaric acid crystals, laying the foundation for modern stereochemistry.
• Cream of Tartar: This is the common name for potassium bitartrate, a salt derived from Tartaric acid. It is a byproduct of the winemaking process, often found as sediment in wine casks.
• Other Common Acids:
• Malic Acid: Found predominantly in Apples and Pears.
• Lactic Acid: Found in Curd, Yogurt, and sour milk products.
• Ascorbic Acid: Commonly known as Vitamin C, found in Amla and Guava.
• Geographic Facts: India is the world's largest producer of Tamarind, where it is a staple in states like Tamil Nadu, Andhra Pradesh, and Karnataka.

The correct answer is Pradhan Mantri Gram Sadak Yojana.

Key Points

• The Pradhan Mantri Gram Sadak Yojana (PMGSY) was launched on 25^th December 2000 by the then Prime Minister of India, Atal Bihari Vajpayee. It was formulated as a nationwide plan to provide good all-weather road connectivity to unconnected habitations in the rural areas of India.
• The primary objective of the scheme is to provide connectivity, by way of an all-weather road (with necessary culverts and cross-drainage structures, which is operable throughout the year), to the eligible unconnected habitations in the rural areas with a population of 500 persons and above in the plain areas.
• In respect of Hill States (North-East, Sikkim, Himachal Pradesh, Jammu & Kashmir, Uttarakhand), the Desert Areas (as identified in the Desert Development Programme), the Tribal (Schedule V) areas and Selected Backward Districts (as identified by the Ministry of Home Affairs and Planning Commission), the objective is to connect habitations with a population of 250 persons and above.
• The scheme is a Centrally Sponsored Scheme and was initially 100% funded by the Central Government. However, following the recommendations of the 14^th Finance Commission, the funding pattern was modified to a ratio of 60:40 between the Centre and States (and 90:10 for North Eastern and Himalayan States).
• The Ministry of Rural Development is the nodal ministry responsible for the implementation and monitoring of this scheme across the country.

Additional Information

• National Highway Development Project (NHDP):
• The NHDP was a project to manage, expand and develop the National Highways network of India. It was launched in 1998 by the Government of India.
• The project was managed by the National Highways Authority of India (NHAI) under the Ministry of Road Transport and Highways. It primarily focused on the Golden Quadrilateral, North-South and East-West Corridors. Hence, this option does not specifically target rural roads as mentioned in the question.
• Bharatmala Phase-1 Connectivity Programme:
• The Bharatmala Pariyojana is an umbrella program for the highways sector that focuses on optimizing efficiency of freight and passenger movement across the country.
• Phase-1 of the project was approved by the Cabinet in October 2017. It aims to bridge critical infrastructure gaps through effective interventions like development of Economic Corridors, Inter-corridors and feeder routes, National Corridor Efficiency Improvement, and Border and International connectivity roads.
• North East Special Infrastructure Development Scheme (NESIDS):
• NESIDS was approved by the Government of India in December 2017. It is a Central Sector Scheme with 100% central funding.
• The scheme was formulated to provide infrastructure in the North Eastern Region specifically relating to water supply, power, connectivity, and also projects in the social sector like education and health.

Important Points

• Phases of PMGSY:
• PMGSY-I: The original phase launched in 2000 focused on new connectivity for unconnected habitations.
• PMGSY-II: Launched in 2013, it aimed at upgradation of 50,000 km of the existing rural road network which improved the overall efficiency of the rural transportation system.
• PMGSY-III: Launched in 2019, it focuses on the consolidation of 1,25,000 km through Routes and Major Rural Links that connect habitations to Gramin Agricultural Markets (GrAMs), Higher Secondary Schools, and Hospitals.
• Impact: The Pradhan Mantri Gram Sadak Yojana has been instrumental in increasing rural income, enhancing agricultural productivity, and providing better access to social services like healthcare and education by reducing transportation costs and travel time.

The correct answer is Tamil Nadu.

Key Points

• In January 2025, archaeologists and history enthusiasts discovered the ruins of an ancient Shiva temple dating back approximately 800 years.
• The site is located in Melakkal village within the Madurai district of Tamil Nadu, situated near the banks of the Vaigai River.
• Archaeological analysis confirms that the temple belongs to the Late Pandya period, which flourished between 1216 AD and 1345 AD.
• The excavation revealed several significant artifacts, including a granite Shiva Lingam, a Nandi (sacred bull) sculpture, and carved stone pillars featuring traditional motifs. Hence, the discovery in Tamil Nadu is correct.
• This discovery provides valuable insights into the religious and cultural life of the Pandyan Empire during the 13^th century.

Additional Information

• The Pandya Dynasty:
• The Pandyas were one of the three legendary Tamil dynasties, with their capital located in Madurai.
• The Late Pandya era began under Maravarman Sundara Pandyan I in 1216 AD, marking a period of territorial expansion and architectural brilliance.
• Architectural Features:
• Temples from this period are known for their Gopurams (monumental entrance towers) and detailed Vimanas.
• The use of hard granite was a hallmark of their construction, ensuring the survival of structures for centuries.
• Geographical Context:
• Tamil Nadu is a major hub for Dravidian architecture. The Vaigai River valley is particularly rich in archaeological sites, such as the famous Keeladi excavation site located nearby.
• While Andhra Pradesh, Karnataka, and Kerala have significant Shaivite traditions, this specific 800-year-old Pandya-era discovery is exclusive to the Madurai region.

Important Points

• Historical Timeline: The Late Pandya power reached its zenith under Jatavarman Sundara Pandyan I, who is often cited as one of the greatest conquerors of South India in the 13^th century.
• Religious Significance: The presence of a Shiva Lingam and Nandi indicates that the site was a dedicated Saivite place of worship, reflecting the dominant religious influence in Tamil Nadu during the medieval period.
• Preservation: Such discoveries are typically documented by the State Department of Archaeology of Tamil Nadu to protect them from encroachment and degradation.
• Numerical Facts: The temple dates back 8 centuries, aligning with the Pandyan resurgence after the decline of the Chola Empire around the year 1215.

The correct answer is Chandala.

Key Points

• The Matanga Jataka is one of the most significant Pali texts that provides a profound critique of the caste system in Ancient India. In this story, the Bodhisattva (the Buddha in a previous life) is born as a Chandala named Matanga. Hence, the statement regarding the Bodhisattva being a Chandala is correct.
• The narrative describes Matanga living outside the city of Varanasi, as Chandalas were considered "untouchable" and were forced to reside on the margins of society.
• A central conflict in the text arises when Matanga encounters Ditthamangalika, the daughter of a wealthy merchant. Upon seeing him, she washes her eyes in disgust, believing that the mere sight of a Chandala is inauspicious.
• The story illustrates how Matanga eventually gains spiritual wisdom and supernatural powers through his asceticism, thereby proving that birth does not determine a person's worth or spiritual potential.
• The Matanga Jataka is frequently cited by historians and sociologists to understand the social dynamics and the Varna system during the 6^th century BCE and later periods in India.

Additional Information

• Definition of Jataka Tales: The Jataka tales are a voluminous body of literature native to India concerning the previous births of Gautama Buddha in both human and animal form. There are approximately 547 such stories preserved in the Pali Canon.
• Social Status of Chandalas: In Ancient India, particularly in texts like the Manusmriti (dated between 200 BCE to 200 CE), Chandalas were placed at the bottom of the social hierarchy. Their primary functions included handling corpses and executing criminals. They were often required to use discarded utensils and wear clothes taken from the dead.
• The Role of Bodhisattva: In Theravada Buddhism, a Bodhisattva is someone on the path to Enlightenment. These stories emphasize Perfections (Paramitas) like generosity, patience, and wisdom.
• Linguistic Context: The Pali language was the lingua franca of early Buddhism in North India. It was used to make Buddhist teachings accessible to the common people, contrasting with the Sanskrit used by Brahmins for Vedic rituals.
• Comparison with Brahminism: While Brahminical texts emphasized purity and pollution based on birth, Buddhist literature like the Matanga Jataka argued that virtue (Dhamma) and conduct are the true markers of a superior individual.

Important Points

• Literary Significance: The Matanga Jataka (Jataka No. 497) specifically challenges the hegemony of the Brahmins. It portrays the Bodhisattva as a person who, despite his low social origin, achieves Great Renown and even commands respect from the gods.
• Historical Evidence: These texts serve as primary sources for historians to reconstruct the lives of marginalized communities in Ancient India. The location of the story in Varanasi (Kashi) is significant, as it was a major hub for both Brahminical orthodoxy and Shramanic heterodoxy.
• Moral Outcome: In the story, the son of Matanga, named Mandavya, initially displays caste pride but is eventually humbled and taught the importance of alms-giving without prejudice. This highlights the educational function of the Jatakas in promoting social equality.
• Global Influence: Jataka stories migrated across Asia, influencing the folklore and art of Sri Lanka, Myanmar, Thailand, and China. The Matanga story remains a powerful symbol of social justice within the Buddhist tradition.

The correct answer is Monohybrid crosses.

Key Points

• A Monohybrid cross is a genetic cross between two individuals that involves a single pair of contrasting characters. In Mendel's experiments, this was demonstrated by crossing a pure tall pea plant with a pure dwarf pea plant. Hence, Option D is correct.
• Gregor Mendel, often called the Father of Genetics, conducted his landmark research on inheritance using the garden pea plant, Pisum sativum, between the years 1856 and 1863.
• In the F1 generation (First Filial), Mendel observed that all the offspring exhibited only one of the parental traits (e.g., all were Tall). This led to the Law of Dominance, stating that the dominant allele masks the expression of the recessive allele.
• In the F2 generation, obtained by self-pollinating the F1 plants, both traits reappeared in a specific phenotypic ratio of 3:1 (3 Tall : 1 Dwarf) and a genotypic ratio of 1:2:1 (1 homozygous tall : 2 heterozygous tall : 1 homozygous dwarf).
• Test crosses involve crossing an organism with an unknown genotype with a homozygous recessive individual to determine the unknown's genetic identity. Hence, statement A is incorrect in this context.
• Dihybrid crosses involve the study of two pairs of contrasting traits simultaneously, such as seed shape and seed color. Hence, statement B is incorrect.
• Hybrid crosses is a general term for any cross between genetically different individuals, but it lacks the specific definition required for a cross of a single contrasting trait. Hence, statement C is incorrect.

Additional Information

• Mendel's Laws of Inheritance:
• Law of Dominance: In a heterozygous pair, the allele that expresses itself physically is dominant, while the other remains recessive.
• Law of Segregation: During gamete formation, the two alleles for a trait separate so that each gamete receives only one allele. This is also known as the Law of Purity of Gametes.
• Law of Independent Assortment: Emerged from dihybrid crosses, stating that the inheritance of one pair of characters is independent of the inheritance of another pair.
• Seven Contrasting Traits: Mendel identified 7 pairs of contrasting characters in Pisum sativum:
• Stem Height: Tall vs. Dwarf.
• Seed Shape: Round vs. Wrinkled.
• Seed Color: Yellow vs. Green.
• Flower Color: Violet vs. White.
• Flower Position: Axial vs. Terminal.
• Pod Shape: Inflated vs. Constricted.
• Pod Color: Green vs. Yellow.
• Dihybrid Cross Ratio: In the F2 generation of a dihybrid cross, the phenotypic ratio is consistently 9:3:3:1.
• Scientific Selection: Mendel chose the pea plant because it has a short life cycle, produces large numbers of seeds, and possesses easily distinguishable contrasting features.

Important Points

• Genotype vs. Phenotype: The Genotype is the genetic constitution of an organism (e.g., TT, Tt), while the Phenotype is the observable physical characteristic (e.g., Tall).
• Homozygous vs. Heterozygous: An individual with two identical alleles (TT or tt) is homozygous, whereas one with two different alleles (Tt) is heterozygous.
• Punnett Square: A graphical tool developed by Reginald C. Punnett in the early 20^th century to predict the probability of genotypes and phenotypes in offspring.
• Back Cross: A cross between an F1 hybrid and one of its parents. A test cross is a specific type of back cross.

The correct answer is decrease in average cost.

Key Points

• Economies of scale refers to the cost advantages that a business obtains due to its scale of operation, typically measured by the amount of output produced.
• As the quantity of output increases, the average cost per unit decreases. This occurs primarily because fixed costs, such as machinery, rent, and administrative salaries, are spread over a larger number of units. Hence, the statement regarding the decrease in average cost is correct.
• In microeconomics, this relationship is visualized through the Long-Run Average Cost (LRAC) curve, which generally slopes downward during the phase of economies of scale.
• A decrease in total cost while increasing output is generally impossible in a standard production environment, as variable costs (like raw materials and labor) will still increase with each additional unit produced. Hence, statement C is incorrect.
• While marginal cost (the cost of producing one more unit) might decrease initially, the fundamental definition of economies of scale focuses on the average cost over the long run. Hence, statement D is not the most accurate definition.
• Total cost always increases as more units are produced because even if the cost per unit drops, the sum of all costs for a larger volume will be higher than for a smaller volume. Hence, statement B is incorrect.

Additional Information

• Internal Economies of Scale: These are firm-specific advantages arising from within the organization.
• Technical Economies: Large firms can afford specialized capital equipment and advanced technology, such as automated assembly lines, which improve productivity.
• Managerial Economies: As a firm grows, it can hire specialist managers for finance, human resources, and marketing, leading to better decision-making and operational efficiency.
• Financial Economies: Larger companies often have better credit ratings and can access loans at lower interest rates compared to smaller firms, reducing their cost of borrowing.
• Marketing Economies: The cost of advertising and distribution can be spread over a massive sales volume, reducing the unit cost of promotion.
• External Economies of Scale: These occur outside the individual firm but within the entire industry or region.
• Infrastructure: When an industry clusters in a specific location, the government may invest in better transportation, telecommunications, and power grids, benefiting all local firms.
• Skilled Labor Pool: The presence of many firms in one geographic area encourages the development of a specialized workforce and training institutes.

Important Points

• Diseconomies of Scale: If a firm expands beyond its optimal size, it may experience diseconomies of scale, where the average cost per unit begins to increase. This is often caused by communication breakdowns, bureaucratic inefficiency, and loss of employee motivation in massive organizations.
• Minimum Efficient Scale (MES): This is the lowest point on the LRAC curve where a firm can produce its output at the minimum average cost. It represents the point where economies of scale have been fully exploited.
• Returns to Scale: This concept describes the proportionate change in output relative to a proportionate change in all inputs (land, labor, capital). Increasing returns to scale is the underlying physical phenomenon that leads to economies of scale in monetary terms.
• Real-world Examples: Global entities like Amazon and Walmart utilize massive logistics networks and bulk-buying power to achieve significant cost savings, allowing them to offer lower prices than smaller competitors.
• History: The concept was popularized by Adam Smith in his 1776 book, "The Wealth of Nations," through his famous example of the pin factory and the division of labor.

The correct answer is Shah Jahan.

Key Points

• The Peacock Throne, also known as Takht-i-Taus, was commissioned by the 5^th Mughal Emperor, Shah Jahan, in the early 17^th century. He ascended the throne in 1628 and his reign is often called the Golden Age of Mughal Architecture. Hence, the statement regarding Shah Jahan being the commissioner is correct.
• The construction of this magnificent throne began in 1628 and was completed in 1635. The project was supervised by the chief goldsmith of the Mughal court, Bebadal Khan.
• It was originally placed in the Diwan-i-Khas (Hall of Private Audience) within the Red Fort at Delhi, which served as the capital of the empire after Shah Jahan moved it from Agra.
• The throne was famous for being encrusted with massive amounts of gold, silver, and precious gemstones, including the legendary Koh-i-Noor diamond. It was estimated to cost around 10 million rupees at that time, which was double the cost of the Taj Mahal.
• The name Peacock Throne is derived from the two gem-studded peacocks positioned behind the throne, with their tails fanned out and inlaid with sapphires, rubies, emeralds, and pearls.

Additional Information

• Invasion and Looting: In 1739, the Persian ruler Nadir Shah invaded India and defeated the Mughal forces at the Battle of Karnal. During the sack of Delhi, he looted the Peacock Throne along with other treasures like the Koh-i-Noor and the Darya-i-Noor diamonds.
• Structure and Features: The throne was supported by 12 emerald-colored columns and featured a canopy encrusted with diamonds and rubies. A poem by the court poet Qudsi, praising the Emperor, was inscribed on it in emerald letters.
• Other Emperors mentioned:
• Akbar: The 3^rd Mughal Emperor (ruled 1556–1605), known for the Ibadat Khana, the city of Fatehpur Sikri, and the Buland Darwaza.
• Aurangzeb: The 6^th Mughal Emperor (ruled 1658–1707), known for his military conquests and the construction of the Badshahi Mosque in Lahore and the Bibi Ka Maqbara in Aurangabad.
• Humayun: The 2^nd Mughal Emperor (ruled 1530–1540 and 1555–1556), who built the city of Din Panah in Delhi; his tomb is a UNESCO World Heritage Site.
• Current Status: After the death of Nadir Shah in 1747, the original throne was reportedly dismantled, and its precious stones were scattered. Several subsequent thrones in Persia (Iran) were inspired by its design, but the original Shah Jahan version no longer exists.

Important Points

• The Koh-i-Noor diamond, which was part of the throne, eventually passed through various hands before becoming part of the British Crown Jewels in 1849 following the Treaty of Lahore.
• The Peacock Throne served as a powerful symbol of Mughal sovereignty and divine right, reflecting the absolute authority and immense wealth of the Mughal Empire during its peak.
• Architectural contributions of Shah Jahan include the Taj Mahal (Agra), Jama Masjid (Delhi), Moti Masjid (Agra), and the Shalimar Gardens (Lahore).

Shortcut Trick

Simplify first term: (5/6) × (18/25) = (1 × 3) / (1 × 5) = 3/5

Simplify bracket: (8/5 − 4) = (8 − 20) / 5 = −12/5

Combine results: 3/5 + (−12/5) = −9/5

∴ The correct answer is −9/5.

Alternate Method

Given: (5/6) × (18/25) + (8/5 − 4)

Formula: BODMAS Rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction)

⇒ (5/6) × (18/25) + ((8 − (4 × 5)) / 5)

⇒ ((5 × 18) / (6 × 25)) + ((8 − 20) / 5)

⇒ (90 / 150) + (−12 / 5)

⇒ 3/5 − 12/5

⇒ (3 − 12) / 5

⇒ −9/5

∴ The correct answer is −9/5.

Additional Information

BODMAS Rule

It defines the order of operations: Brackets (), Orders (powers/roots), Division (÷), Multiplication (×), Addition (+), and Subtraction (−).

Multiplying Fractions

Multiply the numerators together and the denominators together: (a/b) × (c/d) = (a × c) / (b × d).

Fraction Subtraction

To subtract a whole number from a fraction, find a common denominator: (a/b) − c = (a − (b × c)) / b.

Shortcut Trick

New speed percent = 100% − 53% = 47%

New Speed = 47% of 79

New Speed = 0.47 × 79 = 37.13 km/h

∴ The correct answer is 37.13 km/h.

Alternate Method

Given:

Initial Speed = 79 km/h

Reduction Percentage = 53%

Formula Used:

New Speed = Initial Speed − (Reduction% × Initial Speed)

New Speed = Initial Speed × (100 − Reduction%)/100

Initial Speed: 79 km/h (100%) New: 47% Reduction: 53% New Speed = 47% of 79 = 37.13 km/h

Calculations:

⇒ Reduction value = 53% of 79

⇒ Reduction value = (53 ÷ 100) × 79

⇒ Reduction value = 0.53 × 79 = 41.87 km/h

⇒ New Speed = 79 − 41.87

⇒ New Speed = 37.13 km/h

∴ The correct answer is 37.13 km/h.

Additional Information

Percentage Decrease Formula

When a value is decreased by x%, the multiplier is (100 − x)/100. New Value = Original Value × (1 − x/100).

Unit Conversion

To convert speed from km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Successive Percentage Change

If a speed changes by a% and then by b%, the net effective change is [a + b + (ab/100)]%.

Shortcut Trick

If three equal distances are covered at speeds s₁, s₂, and s₃, then Average Speed = 3s₁s₂s₃ / (s₁s₂ + s₂s₃ + s₃s₁).

Average Speed = (3 × 41 × 17 × 18) / (41 × 17 + 17 × 18 + 18 × 41)

⇒ Average Speed = 37638 / (697 + 306 + 738) = 37638 / 1741

⇒ Average Speed ≈ 21.618 km/hr

∴ The correct answer is 21.6 km/hr.

Alternate Method

Given: s₁ = 41 km/hr, s₂ = 17 km/hr, s₃ = 18 km/hr. Let each one-third distance be D km.

Formula: Average Speed = Total Distance ÷ Total Time

  D km D km D km 41 km/hr 17 km/hr 18 km/hr Total Journey = 3D

⇒ Total Time = Time₁ + Time₂ + Time₃

⇒ Total Time = (D/41) + (D/17) + (D/18)

⇒ Total Time = D × [(17 × 18 + 41 × 18 + 41 × 17) / (41 × 17 × 18)]

⇒ Total Time = D × [1741 / 12546]

⇒ Average Speed = 3D ÷ (D × 1741 / 12546)

⇒ Average Speed = (3 × 12546) / 1741 = 37638 / 1741

⇒ Average Speed ≈ 21.618 km/hr ≈ 21.6 km/hr

∴ The correct answer is 21.6 km/hr.

Additional Information

Average Speed for Two Equal Distances

If two equal distances are covered at speeds a and b, Average Speed = 2ab / (a + b).

Average Speed for Equal Time Intervals

If a person travels at speed s₁ for time T and s₂ for the same time T, Average Speed = (s₁ + s₂) / 2.

Relative Speed

In the same direction, relative speed = s₁ − s₂. In opposite directions, relative speed = s₁ + s₂.

Shortcut Trick

LCM(14, 21) = 42 units (Total Work). Efficiency: X = 3, Y = 2.

In 2 days (1 cycle), work done = 3 + 2 = 5 units.

In 8 cycles (16 days), work done = 8 × 5 = 40 units. X worked 8 full days.

Remaining 2 units done by X on Day 17. Time taken = 2 ÷ 3 = 2/3 day.

Total time for X = 8 + 2/3 = 26/3 days.

Total amount for X = (26/3) × ₹45 = ₹390.

∴ The correct answer is ₹390.

Alternate Method

Given:

Time taken by X = 14 days

Time taken by Y = 21 days

Wage rate = ₹45 per day

Formula Used:

Total Work = LCM of individual times

Efficiency = Total Work ÷ Time

Earnings = Time worked × Daily wage

⇒ Total work = 42 units.

⇒ Efficiency of X = 3 units/day; Efficiency of Y = 2 units/day.

⇒ Work in first 2 days (X on day 1, Y on day 2) = 3 + 2 = 5 units.

⇒ Work in 8 such cycles (16 days) = 8 × 5 = 40 units.

⇒ Remaining work = 42 − 40 = 2 units.

⇒ X takes the 17^th day to finish remaining 2 units. Time taken = 2 ÷ 3 = 2/3 day.

⇒ Total days X worked = 8 days (from 8 cycles) + 2/3 day = 26/3 days.

⇒ Total amount X gets = (26/3) × 45 = 26 × 15 = ₹390.

∴ The correct answer is ₹390.

Additional Information

Work and Wages Rule

Wages are generally distributed in the ratio of the work done by each person. If a daily rate is fixed, then Wage = Time × Daily Rate.

Alternate Day Work

In alternate work, calculate the combined work for one full cycle. Divide the total work by the cycle work to find completed cycles and remaining units.

LCM Method

Assuming total work as the LCM of individual days simplifies the calculation of efficiencies into integers, making the steps easier to follow.

Shortcut Trick

Property: If every observation in a data set is multiplied by a constant 'k', then the average is also multiplied by 'k'.

Initial average = 58

Constant factor (doubled) → k = 2

New average = Old average × k = 58 × 2 = 116

∴ The correct answer is 116.

Alternate Method

Given:

Number of students (n) = 13

Initial average = 58

Old Avg: 58 × 2 (Doubled) New Avg: 116 Scaling Property of Averages

Formula Used:

Average = (Sum of all observations) ÷ (Number of observations)

Calculations:

⇒ Total initial marks = Average × Number of students

⇒ Total initial marks = 58 × 13 = 754

⇒ If marks of each student are doubled, the new total marks will also be doubled.

⇒ New total marks = 754 × 2 = 1508

⇒ New average = New total marks ÷ Number of students

⇒ New average = 1508 ÷ 13

⇒ New average = 116

∴ The correct answer is 116.

Additional Information

Linear Property of Averages

If a constant 'k' is added to or subtracted from every value in a set, the new average becomes (Old Average + k) or (Old Average − k).

Multiplication and Division Rule

If every value is multiplied or divided by a non-zero constant 'k', the new average is (Old Average × k) or (Old Average ÷ k).

Combined Average Formula

For two groups with averages A₁, A₂ and sizes n₁, n₂, the combined average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Shortcut Trick

Total percentage for Computer and Hindi = 33% + 13% = 46%

Required value = 46% of 8000

⇒ 46 × 80 = 3680

∴ The correct answer is 3680 students.

Alternate Method

Given:

Total number of students = 8000

Percentage of students in Hindi = 13%

Percentage of students in Computer = 33%

Formula Used:

Value = (Percentage ÷ 100) × Total Value

Calculations:

⇒ Number of students in Hindi = (13 ÷ 100) × 8000 = 1040

⇒ Number of students in Computer = (33 ÷ 100) × 8000 = 2640

⇒ Total number of students in Computer and Hindi = 1040 + 2640

⇒ Total students = 3680

∴ The correct answer is 3680 students.

Additional Information

Central Angle Calculation

To find the angle of a sector in a pie chart: Central Angle = (Component Value ÷ Total Value) × 360° or (Percentage ÷ 100) × 360°.

Percentage to Absolute Value

Individual value can be found by: (Percentage of sector × Total aggregate) ÷ 100.

Sum of Percentages

The sum of all percentage components in a complete pie chart is always equal to 100%.

Shortcut Trick

In a parallelogram, the sum of squares of the diagonals equals the sum of squares of all sides: d₁² + d₂² = 2(a² + b²).

Substitute values: 8² + 14² = 2(9² + b²) → 64 + 196 = 2(81 + b²).

260 = 162 + 2b² → 2b² = 98 → b² = 49 → b = 7 cm.

Perimeter = 2(a + b) = 2(9 + 7) = 32 cm.

∴ The correct answer is 32 cm.

Alternate Method

Given: Side a = 9 cm, Diagonal d₁ = 8 cm, Diagonal d₂ = 14 cm

Formula Used: 2(a² + b²) = d₁² + d₂² (Parallelogram Law)

a = 9 cm b = ? d1 = 14 cm d2 = 8 cm A B C D

⇒ 2(9² + b²) = 8² + 14²

⇒ 2(81 + b²) = 64 + 196

⇒ 2(81 + b²) = 260

⇒ 81 + b² = 130

⇒ b² = 130 − 81

⇒ b² = 49 ⇒ b = √49 = 7 cm

⇒ Perimeter = 2 × (Side a + Side b)

⇒ Perimeter = 2 × (9 + 7) = 2 × 16 = 32 cm

∴ The correct answer is 32 cm.

Additional Information

Area of Parallelogram

The area can be calculated as Area = Base × Height or using diagonals and the angle θ between them: Area = 1/2 × d₁ × d₂ × sin(θ).

Apollonius Theorem in Parallelograms

The property used here is a form of Apollonius theorem where the diagonals of a parallelogram bisect each other, forming triangles where sides and medians are related.

Diagonal Intersection

The diagonals of a parallelogram always bisect each other, meaning they divide each other into two equal parts at the point of intersection.

Shortcut Trick

For semi-annual compounding, rate becomes half and time periods double.

Effective Rate (r) = 18% ÷ 2 = 9% per 6 months. Time (n) = 1 year × 2 = 2 periods.

Effective % for 2 periods = 9 + 9 + (9 × 9) ÷ 100 = 18.81%.

Amount = 118.81% of ₹90,000 ⇒ 1.1881 × 90,000 = ₹1,06,929.

∴ The correct answer is ₹1,06,929.

Alternate Method

Given: Principal (P) = ₹90,000, Annual Rate (R) = 18%, Time (T) = 1 year.

Formula Used: Amount (A) = P(1 + r/100)ⁿ, where r is rate per period and n is number of periods.

 0 Months 6 Months 12 Months   Rate = 9% Rate = 9% Principal = ₹90,000 Amount = ?

⇒ Semi-annual Rate (r) = 18% ÷ 2 = 9%

⇒ Number of periods (n) = 1 × 2 = 2

⇒ A = 90000 × (1 + 9/100)²

⇒ A = 90000 × (109/100) × (109/100)

⇒ A = 9 × 109 × 109

⇒ A = 9 × 11881

⇒ A = 106929

∴ The correct answer is ₹1,06,929.

Additional Information

Effective Rate of Interest

The actual annual rate earned after compounding. Effective Rate = (1 + r/100)ⁿ − 1, where r is the rate per compounding period.

Compounding Frequency

If compounded quarterly, rate = R/4 and time = 4T. If compounded monthly, rate = R/12 and time = 12T.

Difference between CI and SI

For 2 periods, the difference is CI − SI = P(r/100)², where r is the rate per period.

Shortcut Trick

Working backwards from Meenu: Biru's Total Cost = 1518 ÷ 1.38 = ₹1100.

Arvind's Selling Price = Biru's Purchase Price = 1100 − 113 = ₹987.

Arvind's Cost Price (x) = 987 ÷ 0.7 (at 30% loss) = ₹1410.

∴ The correct answer is ₹1410.

Alternate Method

Given:

Arvind's CP = ₹x

Loss % (Arvind to Biru) = 30%

Shipping cost by Biru = ₹113

Profit % (Biru to Meenu) = 38%

Meenu's CP = ₹1518

Formula Used:

SP = CP × (100 ± Gain or Loss%)/100

Arvind ₹x −30% Biru + ₹113 Shipping +38% Meenu ₹1518 Working Backwards: 1518 → 1100 → 987 → 1410

Let Arvind's CP be x.

⇒ Biru's buying price = x × (100 − 30)/100 = 0.7x

⇒ Biru's total investment = 0.7x + 113

⇒ Biru's SP (Meenu's CP) = (0.7x + 113) × (100 + 38)/100 = 1518

⇒ (0.7x + 113) × 1.38 = 1518

⇒ 0.7x + 113 = 1518 ÷ 1.38

⇒ 0.7x + 113 = 1100

⇒ 0.7x = 1100 − 113

⇒ 0.7x = 987

⇒ x = 987 ÷ 0.7 = 1410

∴ The correct answer is ₹1410.

Additional Information

Successive Transaction Rule

When an item is sold through a chain, the final price is calculated as: Final SP = Initial CP × (1 ± r₁/100) × (1 ± r₂/100)... Any overhead costs like shipping are added to the CP of that specific stage before calculating the next SP.

Overhead Expenses

Expenses such as repairs, transportation, or shipping are always added to the purchase price to calculate the Total Cost Price (Effective CP) before determining profit or loss percentage.

Effective Percentage Change

For two successive percentage changes a and b, the net change is given by [a + b + (ab/100)]%.

Note:

This applies only when there are no flat additions like shipping costs in between.

Shortcut Trick

Successive percentage formula: Net Change = a + b + (a × b) ÷ 100

Here, Markup (a) = +43% and Discount (b) = −10%.

Net Profit (x%) = 43 − 10 + [43 × (−10)] ÷ 100

x = 33 − 4.3 = 28.7

∴ The correct answer is 28.7%.

Alternate Method

Given:

Markup percentage = 43%

Discount percentage = 10%

Formula Used:

Marked Price (MP) = Cost Price (CP) × [1 + (Markup% ÷ 100)]

Selling Price (SP) = MP × [1 − (Discount% ÷ 100)]

Profit % (x) = [(SP − CP) ÷ CP] × 100

CP MP SP Markup +43% Discount −10% Profit = x%

Calculations:

⇒ Let Cost Price (CP) = 100 units

⇒ Marked Price (MP) = 100 + 43% of 100 = 100 + 43 = 143 units

⇒ Discount = 10% of MP = 0.10 × 143 = 14.3 units

⇒ Selling Price (SP) = MP − Discount = 143 − 14.3 = 128.7 units

⇒ Profit = SP − CP = 128.7 − 100 = 28.7 units

⇒ Profit % (x) = (28.7 ÷ 100) × 100 = 28.7%

∴ The correct answer is 28.7%.

Additional Information

CP, MP, and SP Relation

The ratio between Marked Price and Cost Price is given by: MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

Effective Discount

If two successive discounts d₁% and d₂% are offered, the single equivalent discount is d₁ + d₂ − (d₁ × d₂) ÷ 100.

Markup Percentage

Markup percentage is always calculated on the Cost Price: Markup% = [(MP − CP) ÷ CP] × 100.

Shortcut Trick

Total capacity of tank = LCM(6, 3, 2) = 6 units.

Efficiency of A = 6 ÷ 6 = 1; Efficiency of B = 6 ÷ 3 = 2; Efficiency of C = 6 ÷ 2 = 3.

Combined efficiency of A + B + C = 1 + 2 + 3 = 6 units/hour.

Time taken = Total capacity ÷ Combined efficiency = 6 ÷ 6 = 1 hour.

∴ The correct answer is 1 hour.

Alternate Method

Given:

Time taken by Pipe A = 6 hours

Time taken by Pipe B = 3 hours

Time taken by Pipe C = 2 hours

Formula Used:

Time taken = Total Work ÷ Combined Efficiency

⇒ Total Capacity (Work) = LCM of (6, 3, 2) = 6 units

⇒ Efficiency of A = 6 ÷ 6 = 1 unit/hr

⇒ Efficiency of B = 6 ÷ 3 = 2 units/hr

⇒ Efficiency of C = 6 ÷ 2 = 3 units/hr

⇒ Total Efficiency of (A + B + C) = 1 + 2 + 3 = 6 units/hr

⇒ Time taken to fill the tank = 6 ÷ 6 = 1 hour

∴ The correct answer is 1 hour.

Additional Information

Inlet and Outlet Pipes

Inlet pipes fill the tank (positive work), while outlet pipes empty it (negative work). Net efficiency = Efficiency of Inlets − Efficiency of Outlets.

Fractional Formula

If pipes fill a tank in x, y, and z hours, the time taken together is 1 ÷ (1/x + 1/y + 1/z) hours.

Efficiency and Time

Efficiency is inversely proportional to the time taken to complete the work. Ratio of times t₁:t₂ implies ratio of efficiencies e₁:e₂ = t₂:t₁.

Shortcut Trick

Simplify by dividing each term in the numerator by the denominator (3 × 3 × 3 = 27).

(0.3 × 0.3 × 0.3) ÷ 27 = 0.027 ÷ 27 = 0.001

(0.03 × 0.03 × 0.03) ÷ 27 = 0.000027 ÷ 27 = 0.000001

Subtracting the results: 0.001 − 0.000001 = 0.000999

∴ The correct answer is 0.000999.

Alternate Method

Given: ((0.3 × 0.3 × 0.3) − (0.03 × 0.03 × 0.03)) ÷ (3 × 3 × 3)

Formula Used: Simplification using power rules: (a × 10⁻ⁿ)³ = a³ × 10⁻³ⁿ

⇒ Numerator = (3 × 10⁻¹)³ − (3 × 10⁻²)³

⇒ Numerator = 27 × 10⁻³ − 27 × 10⁻⁶

⇒ Expression = (27 × 10⁻³ − 27 × 10⁻⁶) ÷ 27

⇒ Expression = 10⁻³ − 10⁻⁶

⇒ Expression = 0.001 − 0.000001

⇒ Expression = 0.000999

∴ The correct answer is 0.000999.

Additional Information

Decimal Multiplication Rule

When multiplying decimals, multiply the numbers as whole numbers and then place the decimal point so that the result has as many decimal places as the sum of the decimal places in the factors.

Laws of Exponents

The rule (a/b)ⁿ = aⁿ/bⁿ is useful for distributing a divisor across terms involving the same power.

BODMAS Rule

Always perform operations in the order: Brackets, Orders (powers/roots), Division and Multiplication (left to right), and Addition and Subtraction (left to right).

Shortcut Trick

Effective Interest Rate % = Rate × Time

Interest % = 16% × 8.5 = 136%

Simple Interest = 136% of ₹400

Simple Interest = 1.36 × 400 = 544

∴ The correct answer is ₹544.

Alternate Method

Given: Principal (P) = ₹400, Rate (R) = 16% p.a., Time (T) = 8.5 years

Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100

Principal (P) ₹400 Rate: 16% p.a. Time: 8.5 Years Simple Interest ₹544 Interest = (400 × 16 × 8.5) / 100

⇒ SI = (400 × 16 × 8.5) ÷ 100

⇒ SI = 4 × 16 × 8.5

⇒ SI = 64 × 8.5

⇒ SI = 512 + 32

⇒ SI = 544

∴ The correct answer is ₹544.

Additional Information

Amount Formula

Total Amount (A) = Principal (P) + Simple Interest (SI). In this case, A = 400 + 544 = ₹944.

Rate and Time Calculation

Rate R = (SI × 100) ÷ (P × T) and Time T = (SI × 100) ÷ (P × R).

Characteristic of Simple Interest

Simple Interest remains constant for every year if the principal and rate are unchanged.

Shortcut Trick

Mean Proportional (y) between two numbers a and b is given by y = √(a × b).

Here, a = 64 and b = 9.

⇒ y = √(64 × 9)

⇒ y = 8 × 3 = 24.

∴ The correct answer is 24.

Alternate Method

Given: 64 : y :: y : 9

Formula Used: Product of extremes = Product of means (for a : b :: c : d, a × d = b × c)

64 : y :: y : 9 Product of Extremes (64 × 9) Product of Means (y × y)

⇒ 64 / y = y / 9

⇒ y² = 64 × 9

⇒ y² = 576

⇒ y = √576

⇒ y = 24

∴ The correct answer is 24.

Additional Information

Mean Proportional

If three quantities a, b, and c are in continued proportion such that a : b :: b : c, then b is called the mean proportional between a and c, where b = √(ac).

Third Proportional

In the continued proportion a : b :: b : c, c is known as the third proportional to a and b, calculated as c = b² / a.

Fourth Proportional

If four quantities a, b, c, and d are in proportion (a : b :: c : d), then d is the fourth proportional, calculated as d = (b × c) / a.

Shortcut Trick

Curved Surface Area (CSA) depends on product of Radius (r) and Height (h).

Net % change in CSA = x + y + (xy/100) = 25 − 25 − (25 × 25)/100 = −6.25%.

New radius (r') = 7 × 0.75 = 5.25 cm; New height (h') = 20 × 1.25 = 25 cm.

New Total Surface Area (TSA) = 2 × (22/7) × 5.25 × (5.25 + 25) = 33 × 30.25.

TSA = 998.25 cm².

∴ The correct answer is 6.25% and 998.25 cm².

Alternate Method

Given:

Original radius (r) = 7 cm, Original height (h) = 20 cm, π = 22/7.

Formula Used:

Curved Surface Area (CSA) = 2πrh

Total Surface Area (TSA) = 2πr(r + h)

  Original (r=7, h=20) r → −25% h → +25%      New (r=5.25, h=25) TSA = 2πr'(r'+h') = 998.25 cm<sup>2</sup>

Calculations:

⇒ Original CSA = 2 × (22/7) × 7 × 20 = 880 cm²

⇒ New Radius (r') = 7 − (25% of 7) = 7 − 1.75 = 5.25 cm

⇒ New Height (h') = 20 + (25% of 20) = 20 + 5 = 25 cm

⇒ New CSA = 2 × (22/7) × 5.25 × 25 = 44 × 0.75 × 25 = 825 cm²

⇒ % Decrease in CSA = [(880 − 825) ÷ 880] × 100 = (55 ÷ 880) × 100 = 6.25%

⇒ New TSA = 2 × (22/7) × 5.25 × (5.25 + 25)

⇒ New TSA = 44 × 0.75 × 30.25 = 33 × 30.25 = 998.25 cm²

∴ The correct answer is 6.25% and 998.25 cm².

Additional Information

Volume of a Cylinder

The volume of a solid cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

Successive Percentage Change

For a product of two variables (A × B), if A changes by x% and B changes by y%, the net percentage change is given by [x + y + (xy/100)]%.

Cylinder Surface Area Properties

Total Surface Area (TSA) is the sum of the Curved Surface Area (2πrh) and the area of the two circular bases (2πr²).

Shortcut Trick

Profit Ratio = (Investment × Time) Ratio

2 : 1 = (138,000 × 12) : (B × 8)

B = (138,000 × 12 × 1) ÷ (8 × 2)

B = 138,000 × (3/4) = 103,500

∴ The correct answer is ₹1,03,500.

Alternate Method

Given: A's Capital (C_A) = ₹138,000 | A's Time (T_A) = 12 months | B's Time (T_B) = 12 − 4 = 8 months | Profit Ratio (P_A : P_B) = 2 : 1

Formula: P_A ÷ P_B = (C_A × T_A) ÷ (C_B × T_B)

Partner A ₹138,000 (12 Months) : Partner B ₹X (8 Months) Profit Ratio A : B = 2 : 1

⇒ 2 ÷ 1 = (138,000 × 12) ÷ (C_B × 8)

⇒ 2 = 1,656,000 ÷ (8 × C_B)

⇒ 2 × 8 × C_B = 1,656,000

⇒ 16 × C_B = 1,656,000

⇒ C_B = 1,656,000 ÷ 16

⇒ C_B = 103,500

∴ The correct answer is ₹1,03,500.

Additional Information

Profit Sharing Formula

The basic ratio of profits is P₁ : P₂ = (C₁ × T₁) : (C₂ × T₂), where C is capital and T is time.

Time Period Calculation

If profits and capitals are known, the ratio of time is T₁ : T₂ = (P₁ ÷ C₁) : (P₂ ÷ C₂).

Compound Partnership

In cases where partners change investments mid-way, effective capital is calculated as Σ(Capital × Duration) for each partner.

Shortcut Trick

1% of marks = 624 ÷ 24 = 26 marks.

Difference in marks = 624 − 598 = 26 marks.

Difference in percentage = 26 ÷ 26 = 1%.

Sudha percentage = 24% − 1% = 23%.

∴ The correct answer is 23%.

Alternate Method

Given:

Kalpana marks = 624

Kalpana percentage = 24%

Sudha marks = 598

Formula Used: Total Marks = (Marks Obtained ÷ Percentage) × 100

Kalpana: 624 (24%) Sudha: 598 (?%) 0% Total: 2600 (100%)

Calculations:

⇒ Total Marks = (624 ÷ 24) × 100

⇒ Total Marks = 26 × 100 = 2600

⇒ Sudha percentage = (Marks Obtained ÷ Total Marks) × 100

⇒ Sudha percentage = (598 ÷ 2600) × 100

⇒ Sudha percentage = 598 ÷ 26 = 23%

∴ The correct answer is 23%.

Additional Information

Basic Percentage Formula

Percentage = (Part value ÷ Total value) × 100. It represents the relative value out of a base of 100.

Percentage Increase or Decrease

Percentage Change = [(Difference ≬ Initial Value) ÷ Initial Value] × 100.

Marks to Percentage Conversion

When base is constant, Mark Ratio = Percentage Ratio. Marks₁ ÷ %₁ = Marks₂ ÷ %₂.

Shortcut Trick

Let the total sum of scores be 100%.

First student score = 60%. Then second student score = 100% − 60% = 40%.

Difference in percentage = 60% − 40% = 20%.

Given, 20% of the total sum = 14.

Total sum (100%) = 14 × (100 ÷ 20) = 14 × 5 = 70.

∴ The correct answer is 70.

Alternate Method

Given: Difference = 14, Marks₁ = 60% of (Marks₁ + Marks₂)

Formula: Total Sum = 100%; Difference = (Percentage₁ − Percentage₂) × Total Sum

Student A (60%) Student B (40%) 60% 40% Diff: 20% = 14 Marks Total Sum (100%) = ?

⇒ Let total sum of scores = S

⇒ Score of first student = 0.6S

⇒ Score of second student = S − 0.6S = 0.4S

⇒ Difference = 0.6S − 0.4S = 14

⇒ 0.2S = 14

⇒ S = 14 ÷ 0.2

⇒ S = 70

∴ The correct answer is 70.

Additional Information

Percentage and Sum

If two parts constitute a whole, and one part is x%, the other part must be (100 − x)%.

Ratio Method

Percentages can be converted to ratios: 60% : 40% = 3 : 2. If the difference (3 − 2) is 1 unit, the sum is 5 units.

Base Value Calculation

To find the total value when a percentage part is known, use the formula: Total = (Given Value ÷ Percentage Part) × 100.

Shortcut Trick

Cash discount is calculated on the price remaining after the trade discount.

Let the price after the 40% trade discount be 100%.

Final Selling Price = 100% − 15% (Cash Discount) = 85%.

Given 85% = ₹1,530 ⇒ 1% = 1530 ÷ 85 = ₹18.

Cash Discount = 15% = 18 × 15 = ₹270.

∴ The correct answer is ₹270.

Alternate Method

Given: Trade Discount = 40%, Cash Discount = 15%, Final Amount Paid (SP) = ₹1,530.

Formula: Price after Trade Discount = SP ÷ (1 − Cash Discount%).

 Total Marked Price (100%) TD (40%) CD (15% of Rem.) Final SP = ₹1,530 (85% of Rem.) Cash Discount = ₹1,800 − ₹1,530 = ₹270

⇒ Let P be the price after the 40% trade discount.

⇒ Final amount paid = P − (15% of P) = 0.85P

⇒ 1530 = 0.85 × P

⇒ P = 1530 ÷ 0.85

⇒ P = 1800

⇒ Cash Discount = P − Final Amount Paid

⇒ Cash Discount = 1800 − 1530 = ₹270

∴ The correct answer is ₹270.

Additional Information

Successive Discount Formula

When two discounts d₁% and d₂% are given, the single equivalent discount = d₁ + d₂ − (d₁ × d₂) / 100.

Trade Discount vs Cash Discount

Trade discount is allowed on the list price of goods, while cash discount is allowed on the amount payable after the trade discount for prompt payment.

Effective Discount Rate

In this problem, the net discount = 40 + 15 − (40 × 15)/100 = 55 − 6 = 49%. Thus, the customer pays 51% of the Marked Price.

Shortcut Trick

Average of ratio parts (3 : 5 : 7) = (3 + 5 + 7) ÷ 3 = 5 units.

Average price given = ₹5,235.

Equating: 5 units = 5,235 → 1 unit = 1,047.

Most expensive item = 7 units = 7 × 1,047 = ₹7,329.

∴ The correct answer is ₹7,329.

Alternate Method

Given:

Average price = ₹5,235

Ratio of prices = 3 : 5 : 7

Number of items = 3

Formula Used:

Total Sum = Average × Number of items

Individual Share = (Individual Ratio ÷ Total Ratio Sum) × Total Sum

3x 5x 7x (Max)  Total Ratio Parts = 3 + 5 + 7 = 15 Total Value = ₹15,705

Calculations:

⇒ Total price of items = 5235 × 3 = ₹15,705

⇒ Let the prices be 3x, 5x, and 7x

⇒ 3x + 5x + 7x = 15705

⇒ 15x = 15705

⇒ x = 15705 ÷ 15 = 1047

⇒ Most expensive item (7x) = 7 × 1047 = ₹7,329

∴ The correct answer is ₹7,329.

Additional Information

Average Concept

Average = (Sum of all observations) ÷ (Total number of observations). To find the total, multiply the average by the count.

Ratio Distribution

If a total value V is divided in the ratio a : b : c, then the share of 'c' is calculated as [c ÷ (a + b + c)] × V.

Arithmetic Progression Average

For numbers in an Arithmetic Progression with an odd number of terms (like 3 : 5 : 7 where the common difference is 2), the average is always the middle term (5 units).

The correct answer is: Option 1 i.e. rewarding.

Key Points

• The word "rewarding" means something that provides satisfaction, a sense of fulfillment, or is worthwhile. (फायदेमंद / संतोषजनक)
• Example: Teaching children can be challenging, but it is a very rewarding career.
• In the context of the sentence, "rewarding" fits well as it highlights the positive and fulfilling aspects of parenthood despite its challenges. (फायदेमंद अनुभव)
• Example: Parenthood is a journey that is both demanding and rewarding.

Therefore, the correct answer is: Option 1 i.e. rewarding.

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Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Exhausting (थकाऊ): Something that makes you feel extremely tired or drained of energy.
• Example: Working long hours every day can be very exhausting.
• Worthless (बेकार): Something that has no value, use, or importance.
• Example: The broken clock is completely worthless now.
• Difficult (कठिन): Something that is hard to do, deal with, or understand.
• Example: Solving this math problem is very difficult without proper guidance.

The correct answer is: Option 3 i.e. Nomophobia.

Key Points

• Nomophobia refers to the fear or anxiety of being without a mobile phone or being unable to use it. (मोबाइल फोन के बिना होने या उसका उपयोग न कर पाने का डर)
• Example: Many people experience nomophobia and feel uneasy when they forget their phone at home.
• This term is derived from "no mobile phone phobia." It is a modern-day condition linked to the dependency on smartphones for communication and daily activities.

Therefore, the correct answer is: Option 3 i.e. Nomophobia.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Xenophobia (विदेशियों का डर): Fear or hatred of strangers or foreigners.
• Example: His xenophobia made it difficult for him to accept people from different cultures.
• Agoraphobia (खुली जगहों का डर): Fear of open or crowded spaces, often linked to anxiety disorders.
• Example: She avoided going to markets because of her agoraphobia.
• Aquaphobia (पानी का डर): Fear of water or drowning.
• Example: His aquaphobia prevented him from learning how to swim.

The correct answer is: 2 i.e. Two heads are better than one.

Key Points

• The proverb "Two heads are better than one" means that working together with someone else often leads to better ideas, solutions, or outcomes than working alone. (दो लोग मिलकर काम करें तो बेहतर परिणाम मिल सकते हैं।)
• Example: When John and Mary collaborated on the project, they realized that two heads were indeed better than one.
• This proverb emphasizes the power of teamwork and collaboration. (यह कहावत टीमवर्क और सहयोग की शक्ति पर जोर देती है।)

Therefore, the correct answer is: 2 i.e. Two heads are better than one.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Birds of the same feather flock together (एक जैसे लोग साथ रहते हैं): This means people with similar interests or characteristics tend to associate with one another.
• Example: The students who enjoy reading often sit together during lunch, proving that birds of the same feather flock together.
• Robbing Peter to save Paul (एक को बचाने के लिए दूसरे को नुकसान पहुंचाना): This means taking from one person or area to pay or satisfy another, often resulting in no real solution.
• Example: Taking money from the marketing budget to cover production costs is like robbing Peter to save Paul.
• Absence makes the heart grow fonder (दूरी से प्यार बढ़ता है): This means being apart from someone or something often makes you appreciate them more.
• Example: After spending months apart, they realized that absence makes the heart grow fonder.

The correct answer is 'pensive'.

 

Key Points

• The word "pensive" is used to describe a person who is deep in thought, often in a serious or reflective way.
• The sentence refers to an expression that reveals deep concern, which aligns with the meaning of "pensive."
• Options 2 (placid), 3 (cheerful), and 4 (apathetic) do not convey the appropriate emotional tone described in the sentence.

Therefore, the correct answer is Option 1.

 

Complete Sentence: "The pensive expression on his face revealed his deep concern about the upcoming exam."

 

Additional Information

• Option 2: "placid" is incorrect because "placid" means calm and peaceful, which does not align with the concern described.
• Option 3: "cheerful" is incorrect because "cheerful" conveys a happy and optimistic emotion, which is not appropriate here.
• Option 4: "apathetic" is incorrect because "apathetic" describes a lack of interest or concern, which is the opposite of the intended meaning.

The correct answer is: Option 2 i.e. Novel.

Key Points

• The word "trite" means something that is overused, lacking originality, or stale. (पुराना, घिसा-पिटा)
• Example: The phrase "time heals all wounds" has become trite due to its overuse in everyday conversations.
• "Novel" refers to something new, original, or fresh, often implying creativity or innovation. (नया, मौलिक)
• Example: Her novel approach to solving the problem impressed everyone in the room.
• Hence, the word "novel" is the most appropriate antonym for the word "trite."

Therefore, the correct answer is: Option 2 i.e. Novel.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Hackneyed (घिसा-पिटा): Something that is unoriginal or overused, similar to "trite."
• Example: The movie was filled with hackneyed plotlines that failed to excite the audience.
• Banal (साधारण, नीरस): Lacking in originality and being obvious or boring, similar to "trite."
• Example: His banal jokes failed to make anyone laugh.
• Cliché (रूढ़िवादी वाक्यांश): A phrase or idea that has been overused to the point of losing its original meaning or effect, similar to "trite."
• Example: Saying "love conquers all" is such a cliché in romantic movies.

The correct answer is '4' i.e. 'the'.

 

Key Points

• The word "flute" is a singular, countable noun that refers to a specific musical instrument.
• In English, when referring to musical instruments in general, we use the definite article "the" before the name of the instrument.
• For example: "He plays the guitar" or "She plays the piano."

Therefore, the correct answer is Option 4.

 

Complete Sentence: "He plays the flute beautifully."

 

Additional Information

• Option 1: "No article required" is incorrect because the word "flute" requires a definite article in this context.
• Option 2: "an" is incorrect because "an" is used before words starting with vowel sounds, and "flute" does not start with a vowel sound.
• Option 3: "a" is incorrect because "a" is used with singular, countable nouns when referring to something non-specific, but here we are referring to a specific instrument.

The correct answer is: 1) Empathy.

Key Points

• The word "Empathy" refers to the ability to understand and share the feelings or experiences of another person. (सहानुभूति)
• Example: Her empathy for the victims of the disaster was evident as she organized relief efforts to help them.
• Empathy involves putting yourself in someone else's shoes and feeling what they are feeling, making it a key aspect of human connection and compassion.
• Hindi Meaning: सहानुभूति

Therefore, the correct answer is: Empathy.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Benevolence (परोपकार): The quality of being kind and generous; a desire to do good for others.
• Example: The benevolence of the donors helped the charity raise enough funds to support the orphanage.
• Compassion (दया): A deep awareness of the suffering of others along with a wish to relieve it.
• Example: His compassion for stray animals led him to open a shelter for them.
• Versatility (बहु-आयामी प्रतिभा): The ability to adapt or be adapted to many different functions or activities.
• Example: Her versatility as an actor allows her to play a wide range of roles.

The correct answer is Option 2.

Key Points

• The paragraph discusses the evolution of marriage videography in India, starting from its niche beginnings to its widespread adoption.
• Sentence B is the first sentence as it introduces the initial trend of recording weddings among the wealthy in Delhi:
• "The wedding film of Rajesh Khanna and Dimple Kapadia set a trend among the wealthy in Delhi to record weddings with 16 mm or Super 8 cameras."
• Sentence A follows as it explains why this trend had limited commercial potential:
• "However, this development showed little commercial potential, as film stock and camera equipment were available in limited supply and few could afford access to projection facilities."
• Sentence D comes next as it elaborates on the challenges faced during that time:
• "Moreover, developing and processing took time and labs did not prioritise home movies."
• Sentence C is the final sentence as it concludes by describing the widespread adoption of marriage videography with the advent of analogue video technology:
• "It is only with the advent of analogue video technology in the 1980s that marriage videography spread widely amongst the middle classes."
• The correct sequence is BADC.

Coherent paragraph after rearrangement:

"The wedding film of Rajesh Khanna and Dimple Kapadia set a trend among the wealthy in Delhi to record weddings with 16 mm or Super 8 cameras. However, this development showed little commercial potential, as film stock and camera equipment were available in limited supply and few could afford access to projection facilities. Moreover, developing and processing took time and labs did not prioritise home movies. It is only with the advent of analogue video technology in the 1980s that marriage videography spread widely amongst the middle classes."