SSC GD Constable 2026 Official Paper (Held On 07 May, 2026 Shift 2) (Previous Year Paper)

Logic followed here is,

-555 (wrong term is -557) - 7 = -562

-562 - 7 = -569

-569 - 7 = -576

-576 - 7 = -583

-583 - 7 = -590

-590 - 7 = -597

-597 - 7 = -604

Hence, the correct answer is “Option 3”.

Logic followed here is,

−199 − 3 = −202

−202 − 5 = −207

−207 − 7 = −214

−214 − 9 = −223

−223 − 11 = −234

−234 − 13 = −247

−247 − 15 = −262

Hence, the correct answer is “Option 1”.

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Pattern followed here is,

Hence, the correct answer is “Option 1”.

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Pattern followed here is,

Hence, the correct answer is “Option 1”.

For the set '(YS, BW, FB)':

For the set '(QW, TA, XF)':

Applying the same logic to option (2) '(CA, FE, JJ)':

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Hence, the correct answer is 'Option 2'.

The logic followed here is,

-708 + 70 = -638

-638 + 70 = -568

-568 + 70 = -498

-498 + 70 = -428

-428 + 70 = -358

-358 + 70 = -288

-288 + 70 = -218

Hence, the correct answer is “Option 4”.

5 boys A, B, C, D and E are sitting in a row facing north (not necessarily in the same order).

1. C is in the middle of the row.
2. D and E are to the right of C.
3. A and B are to the left of C.
4. B and D are not at any ends of the row. 
   

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E is sitting at the right end of the row.

Hence, the correct answer is “Option 3”.

7 girls P, Q, R, S, T, U and V are sitting around a circular table facing towards the centre (not necessarily in the same order).

1. S is next to both P and V.
2. V is second to the left of U.
3. T is second to the right of U.
4. R is not the immediate neighbour of V. 

Considering towards left of S, two girls are sitting between S and R.

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 2”.

AE80 : DZ40

TK60 : JS20

Similarly,

LP70 : ?

Hence, the correct answer is 'Option 4'.

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IK13 : OS168 →

JH15 : PP224 → 

DC11 : ? → 

Hence, the correct answer is 'Option 3'.

The logic followed here is:

Logic: Second Number = First Number + 50

For the first pair 3641 : 3691

⇒ 3641 + 50 = 3691

For the second pair 1717 : 1767

⇒ 1717 + 50 = 1767

Applying the same logic to the third pair

? : 5946

⇒ ? + 50 = 5946

⇒ ? = 5946 − 50 = 5896

Hence, the correct answer is 'Option 4'.

The logic followed here is:

Logic: Second Number = First Number + 474

For the first pair 798 : 1272

⇒ 798 + 474 = 1272.

Applying the same logic to the second pair

578 : 1052

⇒ 578 + 474 = 1052.

Applying the same logic to find the missing number

? : 889

⇒ 889 − 474 = 415.

Hence, the correct answer is 'Option 3'.

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NAME is coded as OFLZ →

GOAT is coded as HTZO →

Similarly,

let us find the code for VOID:

Hence, the correct answer is “Option 2”.

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MUST is coded as 35 →

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Sum of reverse positional values = 14 + 6 + 8 + 7 = 35

PAUZE is coded as 66 →

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Sum of reverse positional values = 11 + 26 + 6 + 1 + 22 = 66

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Similarly,

let's find the code for SOAP:

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Sum of reverse positional values = 8 + 12 + 26 + 11 = 57

Hence, the correct answer is “Option 2”.

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Pattern followed here is,

Hence, the correct answer is “Option 1”.

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Pattern followed here is,

Hence, the correct answer is “Option 1”.

Concept:

The hands of a clock are opposite to each other when the angle between them is 1800.

The relative speed of the minute hand with respect to the hour hand is 5.50 per minute.

The hour hand covers 3600 in 12 hours, so in 1 hour it covers 300.

Calculation:

At 4 AM, the minute hand is at 12 and the hour hand is at 4.

Angle between the hands at 4:00 = 4 × 300 = 1200.

To be opposite (1800), the minute hand must cover the initial 1200 gap and then gain an additional 1800.

Total relative angular distance to be covered = 1200 + 1800 = 3000.

Time taken = Distance ÷ Relative Speed

Time = 300 ÷ 5.5 = 600 ÷ 11

Time ≈ 54.54 minutes.

The approximate time is 4:54.54 AM, which rounds to 4:55 AM.

Hence, the correct answer is “Option 1”.

Alternate Method

The angle between the hour hand and minute hand is given by the formula: θ = |30H − 5.5M|

Here, θ = 1800 (opposite hands) and H = 4.

180 = |30 × 4 − 5.5M|

180 = |120 − 5.5M|

Since the minute hand has passed the hour hand to be opposite, we use:

180 = 5.5M − 120

180 + 120 = 5.5M

300 = 5.5M

M = 300 ÷ 5.5 = 600 ÷ 11 ≈ 54.54

The time is approximately 4:55 AM.

Hence, the correct answer is 4:55.

The time elapsed from 3 AM to 9 AM on the same day is 6 hours.

To calculate the gain, first convert the total elapsed time into minutes:

6 hours = 6 × 60 = 360 minutes

The clock is given to gain 1 second for every 2 minutes.

Total gain in 360 minutes = (360 / 2) × 1 second = 180 seconds

Now, convert the total gain from seconds into minutes:

180 seconds = 180 / 60 = 3 minutes

The time shown by the clock at 9 AM will be the actual time plus the total gain:

Time shown = 9:00 AM + 3 minutes = 9:03 AM

Hence, the correct answer is “Option 3”.

The correct answer is 25 years.

Key Points

• The Lok Sabha, or the House of the People, is the Lower House of India’s bicameral Parliament.
• As per Article 84 (b) of the Constitution of India, a person must be a citizen of India and not less than 25 years of age to be eligible to contest elections for the Lok Sabha.
• This age requirement also applies to the Legislative Assembly (Vidhan Sabha) of various states across the country.
• The members of the Lok Sabha are elected through Direct Elections based on Universal Adult Suffrage for a normal term of five years.
• Apart from the age criteria, a candidate must be registered as an elector for any parliamentary constituency and must not hold any office of profit under the Government of India or the Government of any State.

 Additional Information

• Constitutional Age Requirements for Other Offices:
• 30 years: This is the minimum age required to become a member of the Rajya Sabha (Council of States) and the State Legislative Council (Vidhan Parishad) as per Article 84 and Article 173 respectively.
• 35 years: This age limit is mandatory for the posts of the President of India (Article 58), the Vice-President of India (Article 66), and the Governor of a State (Article 157).
• 21 years: Following the 73rd and 74th Constitutional Amendment Acts, the minimum age to contest elections for Panchayats and Municipalities is set at 21 years.
• 18 years: This is the minimum age for Voting in India. The 61st Constitutional Amendment Act, 1988 reduced the voting age from 21 years to 18 years by amending Article 326.

The correct answer is Puducherry.

Key Points

• Puducherry is a Union Territory that operates with a unique administrative structure including its own Legislative Assembly and Council of Ministers.
• The creation of a legislature for Puducherry was made possible by the 14th Constitutional Amendment Act, 1962, which added Article 239A to the Constitution of India.
• The Puducherry Legislative Assembly comprises 33 members, out of which 30 are directly elected by the people and 3 are nominated by the Central Government.
• While the President of India governs the territory through a Lieutenant Governor, the Chief Minister and the Council of Ministers handle the executive functions for subjects in the State List and Concurrent List, excluding certain reserved matters.
• This setup allows the territory to have a representative form of government, distinguishing it from most other Union Territories that are governed directly by the Union Government.

 Additional Information

• Union Territories with Legislatures:
• Delhi: Established as the National Capital Territory (NCT) with an assembly via the 69th Constitutional Amendment Act, 1991 (Article 239AA).
• Jammu and Kashmir: Created as a UT with a legislative assembly under the Jammu and Kashmir Reorganisation Act, 2019.
• Union Territories without Legislatures:
• Chandigarh: Serves as the joint capital of Punjab and Haryana; it is managed by an Administrator.
• Andaman and Nicobar Islands: An archipelago in the Bay of Bengal governed by a Lieutenant Governor without a local assembly.
• Lakshadweep: India's smallest UT, located in the Arabian Sea, administered through an Administrator appointed by the President.
• Ladakh: Separated from J&K in 2019, it functions as a UT without a legislative body.

The correct answer is President.

Key Points

• The Vice President of India holds a constitutional office for a term of five years from the date on which they enter upon their office.
• According to Article 67(a) of the Constitution of India, the Vice President may, by writing under their hand addressed to the President, resign their office.
• The resignation is a voluntary act and becomes effective as soon as it is accepted by the President of India.
• This provision ensures a formal constitutional protocol where the second-highest constitutional authority reports their departure to the highest authority of the Republic of India.

 Additional Information

• Vice President's Constitutional Role:
• The Vice President serves as the Ex-officio Chairman of the Rajya Sabha (Council of States) as per Article 64.
• Under Article 65, the Vice President acts as the President during casual vacancies or the absence of the President.
• The election of the Vice President is conducted by an Electoral College consisting of members of both Houses of Parliament.
• Other Resignation Hierarchies:
• The President submits their resignation letter to the Vice President, creating a reciprocal constitutional arrangement.
• The Speaker of Lok Sabha resigns by writing to the Deputy Speaker of the Lok Sabha.
• The Chief Justice of India and other Supreme Court Judges address their resignation to the President.
• The Prime Minister and other Union Ministers submit their resignations directly to the President.

The correct answer is Rasidi Ticket.

Key Points

• Amrita Pritam (1919−2005) was a legendary figure in Punjabi literature and was the first woman to be awarded the Sahitya Akademi Award.
• Her autobiography is titled Rasidi Ticket (translated as The Revenue Stamp), which was first published in 1976.
• The title of the book originated from a comment by the famous writer Khushwant Singh, who suggested that her life story was so brief it could be written on the back of a revenue stamp.
• The book is an intensely personal and honest account of her life, detailing her experiences during the Partition, her literary struggles, and her relationships with the poet Sahir Ludhianvi and the artist Imroz.

 Additional Information

• Pinjar (The Skeleton):
• This is a world-renowned novel written by Amrita Pritam in 1950.
• It deals with the traumatic events of the Partition of India and focuses on the plight of women, represented through the character Puro.
• Sunehade (Messages):
• This is a celebrated poetry collection published in 1955.
• It won her the Sahitya Akademi Award in 1956, making her the first female recipient of this prestigious Indian literary honor.
• Main Tenu Phir Milangi (I Will Meet You Again):
• This is one of her most famous and poignant poems, written as a tribute to her life partner, Imroz.
• It is widely regarded as a masterpiece of modern Punjabi poetry, expressing the theme of eternal love.
• Other Awards:
• In 1981, she received the Jnanpith Award, India's highest literary award, for her collection Kagaz Te Kanvas.
• She was also honored with the Padma Shri in 1969 and the Padma Vibhushan in 2004.

The correct answer is Central Pollution Control Board.

Key Points

• The Central Pollution Control Board (CPCB) is a statutory organization established in September 1974 under the Water (Prevention and Control of Pollution) Act, 1974.
• It was later entrusted with powers and functions under the Air (Prevention and Control of Pollution) Act, 1981, making it the apex body for monitoring environmental quality in India.
• The National Air Quality Index (AQI) was launched by the Ministry of Environment, Forest and Climate Change in 2014 to disseminate real-time information about air quality in an easily understandable format for the general public.
• CPCB operates the Continuous Ambient Air Quality Monitoring System (CAAQMS), which provides live data on pollutant concentrations across various cities.
• The AQI calculates a single value based on eight major pollutants: Particulate Matter (PM10 and PM2.5), Nitrogen Dioxide (NO2), Sulphur Dioxide (SO2), Carbon Monoxide (CO), Ozone (O3), Ammonia (NH3), and Lead (Pb).
• Air quality is classified into six categories: Good, Satisfactory, Moderately Polluted, Poor, Very Poor, and Severe.

 Additional Information

• National Institution for Transforming India (NITI Aayog):
• Formed on January 1, 2015, it replaced the Planning Commission.
• It serves as the premier policy think tank of the Government of India, promoting cooperative federalism.
• Council of Scientific and Industrial Research (CSIR):
• Established in 1942, it is one of the largest research and development (R&D) organizations in India.
• While it conducts research on environmental engineering through its lab NEERI, it is not the primary agency for regulatory real-time monitoring.
• Sameer App:
• An official mobile application developed by the CPCB that provides hourly updates of the National Air Quality Index and allows citizens to lodge complaints related to air pollution.

The correct answer is Alert citizens about upcoming high pollution days.

Key Points

• The Air Quality Early Warning System (AQEWS) is an integrated system designed to provide advance information about anticipated air quality deterioration, specifically in the Delhi-NCR region.
• Developed by the Indian Institute of Tropical Meteorology (IITM), Pune, the system uses complex mathematical models to predict pollution levels up to 72 hours to 10 days in advance.
• The primary objective is to facilitate proactive decision-making by authorities and allow citizens to take preventive health measures during periods of extreme pollution.
• It utilizes real-time data from satellite observations, including Aerosol Optical Depth (AOD) and active fire counts, to estimate the contribution of stubble burning to local air quality.

 Additional Information

• The system is a crucial component of the Graded Response Action Plan (GRAP), which dictates specific emergency measures like banning construction or vehicle entry based on Air Quality Index (AQI) forecasts.
• Pollutants Tracked: The system focuses heavily on PM2.5, PM10, and Nitrogen Oxides (NOx), which are the primary drivers of respiratory ailments.
• Regulatory Framework: It works in coordination with the Central Pollution Control Board (CPCB) and the Commission for Air Quality Management (CAQM).
• Technological Scope: Unlike industrial air filtration which uses Electrostatic Precipitators, this is an informatics tool for monitoring and prediction rather than a mechanical cleaning device.
• Alternative Monitoring: Concepts like soil contamination or water pollution fall under different regulatory systems, such as the National Water Quality Monitoring Programme, and are not the focus of AQEWS.

The correct answer is 2013.

Key Points

• The Indian Badminton League (IBL), which served as the precursor to the current Premier Badminton League (PBL), successfully held its inaugural edition in 2013.
• The tournament was organized by the Badminton Association of India (BAI) and took place from August 14 to August 31, 2013, featuring top-tier domestic and international talent.
• A total of six city-based franchises participated in the first edition, including Hyderabad Hotshots, Awadhe Warriors, Pune Pistons, Mumbai Masters, Banga Beats, and Krrish Delhi Smashers.
• The championship match of the 2013 season was played at the Sardar Patel Stadium in Mumbai, where the Hyderabad Hotshots defeated the Awadhe Warriors with a final score of 3-1.
• The league was led by prominent icon players, such as Saina Nehwal for the Hyderabad franchise and Lee Chong Wei for the Mumbai franchise, which significantly enhanced the commercial appeal of badminton in India.

 Additional Information

• Premier Badminton League (PBL):
• After a hiatus following the 2013 season, the league was rebranded as the Premier Badminton League for its second edition, which commenced in January 2016.
• The PBL has since become one of the most-watched badminton leagues globally, attracting elite players like P.V. Sindhu, Carolina Marin, and Viktor Axelsen.
• The league follows a unique points system and match format designed to make the sport more fast-paced and television-friendly for a global audience.
• Badminton Association of India (BAI):
• The BAI is the official governing body for the sport in India, responsible for hosting national championships and managing the Indian Badminton League ecosystem.
• Headquartered in New Delhi, the association plays a pivotal role in the development of grassroots talent and the selection of athletes for the Olympic Games and BWF World Tour.

The correct answer is Olfactory receptors.

Key Points

• Olfactory receptors are specialized sensory neurons located within the olfactory epithelium, a small patch of tissue at the top of the nasal cavity.
• These receptors are responsible for the sense of olfaction (smell) by detecting airborne odorant molecules that enter the nose during inhalation.
• When an odorant binds to a specific receptor, it initiates a biochemical cascade that generates an electrical signal or nerve impulse.
• This signal is transmitted through the Olfactory nerve (Cranial Nerve I) directly to the olfactory bulb in the brain, which then processes the information to identify the scent.
• Humans possess approximately 10 million to 20 million olfactory receptor cells, enabling the detection of a vast array of distinct chemical compounds.

 Additional Information

• Gustatory receptors:
• These are the sensory receptors responsible for the sense of taste.
• They are primarily clustered in taste buds located on the papillae of the tongue, soft palate, and epiglottis.
• They detect five basic modalities: sweet, sour, salty, bitter, and umami.
• Auditory receptors:
• These receptors, known as hair cells, are responsible for the sense of hearing.
• They are located within the Organ of Corti inside the cochlea of the inner ear.
• They convert mechanical sound vibrations into electrical signals sent to the brain via the vestibulocochlear nerve.
• Visual receptors:
• These are photoreceptors located in the retina of the eye.
• Rods are sensitive to low light levels and provide peripheral and night vision.
• Cones are responsible for color vision and high-spatial acuity in bright light.

The correct answer is Statecraft and administration.

Key Points

• The Arthashastra is an ancient Indian Sanskrit treatise on statecraft, economic policy, and military strategy, traditionally attributed to Kautilya (also known as Chanakya or Vishnugupta), who was the prime minister and mentor of Chandragupta Maurya.
• The text is a comprehensive manual for a ruler, focusing on how to manage a kingdom efficiently, maintain law and order, and expand the state's influence through both diplomatic and military means.
• It introduces the Saptanga Theory, which describes the state as an organic entity composed of seven elements: Swami (the King), Amatya (Ministers), Janapada (Territory and Population), Durga (Fort), Kosha (Treasury), Danda (Army), and Mitra (Ally).
• The treatise details the Mandala Theory of foreign policy, illustrating a complex system of inter-state relations based on the principle that a neighbor is a natural enemy and a neighbor's neighbor is a natural friend.
• It provides exhaustive guidance on taxation, agriculture, trade, espionage, and the legal system, emphasizing that the welfare of the people is the primary responsibility of the sovereign.

 Additional Information

• The Arthashastra is structured into 15 Adhikaranas (books), 150 chapters, and 180 topics, making it one of the most organized political texts of antiquity.
• Poetry and literature: While ancient India produced vast literary works like the Mahabharata and Ramayana, the Arthashastra is strictly a pragmatic and secular document.
• Religious rituals: These are primarily the domain of the Vedas, Brahmanas, and Upanishads; Kautilya focuses on Artha (material prosperity) rather than Dharma (religious duty) in a purely ritualistic sense.
• Astronomy: Scientific treatises like the Aryabhatiya or Surya Siddhanta deal with celestial movements, whereas the Arthashastra limits its scope to geopolitical and socio-economic governance.

The correct answer is Self-sufficiency in steel and heavy industry.

Key Points

• The establishment of the Bhilai, Rourkela, and Durgapur steel plants was a strategic move during the Second Five-Year Plan (1956–1961) to lay the foundation for industrialization in India.
• The primary objective was to achieve self-sufficiency in the production of iron and steel, which are the basic requirements for manufacturing machinery, building infrastructure, and expanding the railway network.
• This industrial strategy was guided by the Mahalanobis Model, which advocated for heavy investment in capital goods industries to ensure long-term economic independence and reduce the need for foreign imports.
• These plants were located in the resource-rich regions of eastern and central India to utilize local iron ore and coal deposits effectively, fostering regional economic growth.
• By focusing on heavy industry, the government aimed to create a multiplier effect that would generate demand and provide raw materials for various other sectors of the economy.

 Additional Information

• Specific Plant Collaborations:
• Bhilai Steel Plant: Set up in Chhattisgarh with the technical and financial assistance of the USSR (Soviet Union) in 1955.
• Rourkela Steel Plant: Established in Odisha in 1959 with the collaboration of German firms (Krupp and Demag). It was the first to use the LD process of steelmaking in India.
• Durgapur Steel Plant: Developed in West Bengal with the help of a British consortium of companies, becoming operational in the early 1960s.
• Industrial Policy Context:
• The Industrial Policy Resolution of 1956 categorized industries into three schedules, giving the State exclusive responsibility for the growth of the steel sector.
• Hindustan Steel Limited (HSL) was initially formed to manage these plants before they were brought under the Steel Authority of India Limited (SAIL) in 1973.
• The Second Five-Year Plan is often called the Industrial and Transport Plan due to its massive shift away from the agricultural focus of the First Plan (1951–1956).

The correct answer is Both were designed for military service in exchange for revenue rights.

Key Points

• The Iqta system was a centralized administrative and land revenue system introduced by the Delhi Sultanate, reaching its systematic form under Sultan Iltutmish in the 13th century.
• Under this mechanism, the Sultan assigned the right to collect land revenue from specific territories, known as Iqtas, to military officers and nobles called Iqtadars or Muqtis.
• The primary function of an Iqtadar was to maintain a standing army of a specified size, which was to be presented for the Sultan’s service during wars or emergencies.
• Similarly, Feudalism in Medieval Europe was a social and political hierarchy where the Crown granted land, known as fiefs, to vassals or lords.
• The vassals were obligated to provide military service and political counsel to their superior in exchange for the right to govern and extract economic benefits from the granted land.
• Therefore, the fundamental resemblance between the two systems is their reliance on decentralized land revenue to sustain a military force without the need for a massive central cash treasury.

 Additional Information

• Hereditary nature and differences:
• Initially, the Iqta system was strictly non-hereditary and Iqtadars were frequently transferred to prevent them from developing local roots or challenging the Sultan’s authority.
• In contrast, European Feudalism was inherently hereditary, with land and titles passing from father to son, leading to more permanent local power structures.
• However, during the reign of Firoz Shah Tughlaq, the Iqta system was made hereditary, which increased the resemblance to the European model but eventually weakened the central authority of the Sultanate.
• Administrative Roles:
• The Muqti or Iqtadar was responsible for law and order within their territory and was required to send the surplus revenue (fawazil) to the central treasury after meeting military and personal expenses.
• The Feudal system in Europe was more comprehensive, involving a complex web of manorialism where peasants (serfs) were legally tied to the land owned by the lord.

The correct answer is Indian Councils Act, 1909.

Key Points

• The Indian Councils Act, 1909, commonly known as the Morley-Minto Reforms, introduced the elective principle for the first time, marking a significant step in the representation of Indians in the legislative process.
• It substantially increased the size of the Central Legislative Council (then the Imperial Legislative Council) from 16 to 60 members, allowing for a wider range of Indian voices.
• The act provided for the first time the association of Indians with the Executive Council of the Viceroy; Satyendra Prasad Sinha became the first Indian to join as a Law Member.
• It expanded the deliberative functions of the legislative councils, empowering members to move resolutions on the budget and ask supplementary questions for the first time.
• A controversial yet major feature was the introduction of separate electorates for Muslims, establishing the system of communal representation where Muslim members were elected only by Muslim voters.

 Additional Information

• Indian Councils Act, 1861:
• It made a beginning of representative institutions by associating Indians with the law-making process through the nomination of non-official members.
• In 1862, Lord Canning nominated the Raja of Benares, the Maharaja of Patiala, and Sir Dinkar Rao to the council.
• Indian Councils Act, 1892:
• It introduced the principle of representation through an indirect elective process called recommendations by local bodies.
• It increased the number of additional members and allowed them to discuss the budget, though they could not vote on it.
• Government of India Act, 1919:
• Also known as the Montagu-Chelmsford Reforms, it introduced bicameralism at the center, creating the Central Legislative Assembly and the Council of State.
• It introduced direct elections in the country for the first time and established dyarchy (dual government) in the provinces.

The correct answer is August.

Key Points

• The Nasha Mukt Bharat Abhiyaan (NMBA), or the Drug-Free India Campaign, was officially launched by the Government of India on August 15, 2020.
• The initiative is spearheaded by the Ministry of Social Justice and Empowerment and serves as a flagship program to combat substance abuse through mass community mobilization.
• Since the launch date is fixed to the Independence Day of 2020, every milestone anniversary is celebrated annually in the month of August.
• The year 2025 marks the completion of five full years of the campaign, making August 2025 the month of its 5th anniversary celebration.
• The campaign was initially implemented in 272 most vulnerable districts identified by the Narcotics Control Bureau and the ministry based on the Comprehensive National Survey on Extent and Pattern of Substance Use in India.

 Additional Information

• Key Objectives and Achievements:
• The NMBA focuses on demand reduction and raising awareness among youth, educational institutions, and the general community.
• By 2024, the campaign had already reached over 11 crore people, including a massive involvement of 3.5 crore students and 8,000 master volunteers.
• It utilizes State-level and District-level Nasha Mukt Bharat Committees for localized implementation and monitoring.
• Strategic Pillars:
• Supply Reduction: Handled by the Narcotics Control Bureau (NCB) to prevent the flow of illicit drugs.
• Demand Reduction: Focused on counseling, rehabilitation, and community awareness activities led by the Ministry of Social Justice.
• Harm Reduction: Providing specialized healthcare and treatment facilities to those suffering from addiction.
• Global Alignment:
• The mission aligns with United Nations Sustainable Development Goal 3.5, which aims to strengthen the prevention and treatment of substance abuse globally.

The correct answer is Lord Shiva.

Key Points

• The Kanwar Yatra is a major annual pilgrimage in Northern India, particularly across the state of Uttarakhand, dedicated to the worship of Lord Shiva.
• The participants of this pilgrimage are known as Kanwariyas, who travel to sacred river banks like Haridwar, Gaumukh, and Gangotri to fetch holy water from the River Ganga.
• The yatra predominantly takes place during the auspicious Hindu month of Shravan (July–August), which is traditionally dedicated to Lord Shiva.
• Devotees carry the holy water in pitchers called Kanwars, which are balanced on bamboo poles, and often walk hundreds of kilometers barefoot to reach their destinations.
• The pilgrimage concludes with the Jalabhishek (ritual offering of water) to Shivalingas at local temples or major shrines like Baidyanath Dham on the day of Maha Shivratri or Sawan Shivratri.

 Additional Information

• Deities and Traditions:
• Goddess Lakshmi: She is the deity of wealth, fortune, and prosperity. Her primary worship occurs during the festival of Diwali and Sharad Purnima.
• Lord Ganesha: Recognized as the remover of obstacles and the god of new beginnings. His most significant festival is Ganesh Chaturthi, widely celebrated in Maharashtra and surrounding regions.
• Goddess Durga: Representing Shakti or divine feminine energy, she is the protector of the universe. Her worship is central to the ten-day festival of Navratri and Durga Puja.
• Uttarakhand Culture: Often referred to as Devbhoomi (Land of the Gods), it is home to the Chota Char Dham circuit, which includes sites dedicated to Vishnu, Shiva, and the river goddesses Ganga and Yamuna.

Concept:

The discovery of new plant species is a critical aspect of biodiversity research in India. New species are identified through morphological and molecular analysis by organizations like the Botanical Survey of India (BSI) or academic researchers. The naming of a species often reflects its geographic origin, a notable person, or its national significance.

Given

• Name of the new species: Portulaca Bharat
• Genus: Portulaca (a group of succulent flowering plants)
• Month of Discovery: June 2025

Calculation

1. The genus Portulaca belongs to the family Portulacaceae, which are typically found in arid and semi-arid regions due to their succulent nature and ability to withstand high temperatures.
2. The Aravalli hills are one of the oldest fold mountain ranges in the world, stretching through the states of Gujarat, Rajasthan, Haryana, and the Union Territory of Delhi.
3. This region provides a unique micro-habitat for xerophytic (dry-climate) plants. Researchers identifying the species Portulaca Bharat in this region highlight the ecological richness of the Aravalli Range, which acts as a natural barrier against the expansion of the Thar Desert.
4. While other species of this genus, like Portulaca laljii, have been found in the Eastern Ghats, the specific discovery of Portulaca Bharat is localized to the Aravalli hills according to the recent biological findings of 2025.

Final Answer: ✅ Aravalli hills

The correct answer is They get detached and drop out.

Key Points

• Ultrasonic cleaning utilizes high-frequency sound waves, typically ranging from 20 kHz to 400 kHz, to remove contaminants from various objects.
• When these waves are transmitted through a cleaning liquid, they create alternating high-pressure and low-pressure cycles, leading to a phenomenon called acoustic cavitation.
• During the low-pressure cycle, millions of microscopic bubbles or voids form in the liquid; these bubbles grow until they reach an unstable size.
• In the high-pressure cycle, these bubbles implode violently, releasing a significant amount of energy in the form of localized shock waves.
• This rapid implosion creates an intense scrubbing action that acts on the surface of the submerged object, reaching into deep crevices, holes, and cracks.
• The mechanical force generated by these shock waves effectively breaks the adhesion between the object and the contaminants, such as dust, grease, and dirt, causing them to be physically dislodged.
• Once the bond is broken, these particles are detached from the surface and eventually drop out or remain suspended in the cleaning solution.

 Additional Information

• Cavitation Intensity:
• Higher frequencies (e.g., 80 kHz to 120 kHz) produce smaller, gentler bubbles, ideal for delicate items like electronics or optical lenses.
• Lower frequencies (e.g., 25 kHz to 40 kHz) produce larger, more powerful bubbles suited for heavy-duty cleaning of engine parts or industrial machinery.
• Contaminant Behavior:
• Particles do not evaporate or burn because the process is mechanical and occurs at temperatures far below the boiling or combustion points of the dirt.
• While a chemical solvent in the solution may help some grease to dissolve, the defining feature of ultrasonic technology is the physical detachment of insoluble particles.
• Applications:
• It is the preferred method for cleaning surgical instruments, jewelry, and watch movements where manual cleaning might cause damage or fail to reach hidden areas.

The correct answer is Only I.

Key Points

• According to the Census 2011, the Jain community is identified as the most urbanized religious group in India. Data reveals that approximately 79.7% of the total Jain population resides in urban areas, which is significantly higher than any other religious community. Their concentration is primarily driven by their historical and traditional involvement in trade, commerce, finance, and mercantile activities that are predominantly centered in cities such as Mumbai, Ahmedabad, and Delhi. Hence, statement I is correct.
• The Christian population in India displays a more balanced distribution between rural and urban sectors but remains a majority rural group. According to the 2011 Census, about 40% of Christians live in urban areas, while roughly 60% reside in rural regions. This is especially true in states with high Christian populations like Kerala and the North-Eastern states (such as Nagaland and Meghalaya), where agrarian and tribal lifestyles are more common. Hence, statement II is incorrect.

 Additional Information

• The Census 2011 highlights distinct urbanization trends across major religious groups in India:
• Hindus: As the largest religious group, they have an urbanization rate of approximately 32.7%, with the vast majority remaining in rural villages.
• Muslims: They are the second most urbanized major group, with about 44% of their population living in urban centers, often engaged in small-scale manufacturing and artisanal trades.
• Sikhs: This community has one of the lowest urbanization rates at about 28.1%, largely due to their deep connection to agricultural land in Punjab and Haryana.
• Buddhists: Roughly 43% of the Buddhist population is urbanized, with a major concentration in urban clusters within Maharashtra.

The correct answer is devaluation.

Key Points

• Devaluation refers to the deliberate downward adjustment of the value of a country's currency relative to another currency, a group of currencies, or a standard like gold. This policy tool is exclusively used within a Fixed Exchange Rate System.
• In this context, increasing the exchange rate means that more units of the domestic currency are required to purchase one unit of a foreign currency (e.g., shifting from 70 to 80 units of domestic currency per USD). This action directly makes the domestic currency cheaper or less valuable in the international market.
• The primary objective of devaluation is often to correct a Balance of Payments (BoP) deficit. By making domestic goods cheaper for foreign buyers, it encourages Exports, while making foreign goods more expensive for domestic consumers, thereby discouraging Imports.
• A significant historical instance occurred in India in July 1991, when the Reserve Bank of India devalued the Rupee by approximately 18-19 percent in two steps to address a severe economic crisis and low foreign exchange reserves.

 Additional Information

• Revaluation:
• This is the opposite of devaluation within a fixed exchange rate system. It involves an official upward adjustment of the currency value by the government or Central Bank, making the domestic currency stronger and foreign goods cheaper.
• Depreciation and Appreciation:
• Depreciation refers to a decrease in a currency's value caused by market forces (demand and supply) rather than government mandate. This occurs in a Flexible (Floating) Exchange Rate System.
• Appreciation refers to an increase in the currency's value due to market demand in a floating system.
• Managed Floating System:
• This is a hybrid system where the exchange rate is primarily determined by the market, but the Central Bank intervenes occasionally to stabilize or influence the rate, often referred to as a dirty float.

The correct answer is International Solar Alliance.

Key Points

• The Towards 1000 strategy is a flagship initiative launched by the International Solar Alliance (ISA) during the COP26 climate summit held in Glasgow in 2021.
• This strategic framework aims to mobilize USD 1 trillion (1,000 billion) in solar energy investments by the year 2030 to accelerate the global transition to clean energy.
• The initiative is centered around four pillars: providing energy access to 1,000 million people, facilitating the installation of 1,000 GW of solar energy capacity, and achieving the mitigation of 1,000 million tonnes of carbon dioxide (CO2) emissions annually.
• It focuses on scaling up solar technologies in Least Developed Countries (LDCs) and Small Island Developing States (SIDS) to ensure equitable energy distribution and climate resilience.
• The strategy also emphasizes the development of the One Sun One World One Grid (OSOWOG) project to interconnect solar energy networks across different continents.

 Additional Information

• International Solar Alliance (ISA):
• It was launched jointly by the Prime Minister of India and the President of France on 30 November 2015 at the COP21 in Paris.
• The alliance is headquartered in Gurugram, India, making it the first international intergovernmental organization to have its headquarters in India.
• The ISA serves as an action-oriented platform for the increased deployment of solar energy technologies to enhance energy security and drive sustainable development.
• World Trade Organisation (WTO):
• Established in 1995, this body deals with the global rules of trade between nations and is headquartered in Geneva, Switzerland.
• International Court of Justice (ICJ):
• Known as the World Court, it is the principal judicial organ of the United Nations and is located at the Peace Palace in The Hague, Netherlands.
• SAARC:
• The South Asian Association for Regional Cooperation was established in 1985 to promote economic and regional integration in South Asia, with its secretariat in Kathmandu, Nepal.

The correct answer is India.

Key Points

• India secured the bronze medal in the men's hockey competition at the Paris Olympics 2024 by defeating Spain with a scoreline of 2-1.
• The high-stakes bronze medal match was contested at the Yves-du-Manoir Stadium on August 8, 2024.
• Indian captain Harmanpreet Singh was the star performer, scoring both goals for the team via penalty corners in the 30th and 33rd minutes of the game.
• This victory marked India's second consecutive Olympic bronze medal in hockey, following their success at the Tokyo 2020 Olympics.
• This win represents India's 13th overall Olympic medal in field hockey, maintaining its record as the most successful nation in the history of the sport at the Summer Games.
• The match also marked the final international appearance of legendary goalkeeper P.R. Sreejesh, often celebrated as the 'Great Wall of India', who retired after the tournament.

 Additional Information

• Netherlands:
• Claimed the gold medal in the men's event after defeating Germany in a penalty shootout.
• This victory ended their 24-year wait for an Olympic gold in men's hockey.
• Germany:
• Finished the tournament with the silver medal after a closely contested final match.
• Individual and Team Statistics:
• Harmanpreet Singh finished as the top goal-scorer of the Paris 2024 hockey tournament with a total of 10 goals.
• The Paris 2024 edition featured 12 teams in the men's category, divided into two pools of six teams each.
• This was the first time in 52 years (since the 1972 Munich Games) that India won medals in back-to-back Olympic Games.

Shortcut Trick

Solve the expression using the BODMAS rule priority.

First, evaluate the bracket: (33 + 26) = 59.

Next, perform multiplication: 52 × 2 = 104.

Then, group addition and subtraction: (89 + 96 + 104) − (47 + 59).

Final calculation: 289 − 106 = 183.

∴ The correct answer is 183.

Alternate Method

Given:

89 − 47 + 96 − (33 + 26) + 52 × 2

Formula Used:

The BODMAS rule determines the order of operations: Brackets, Of, Division, Multiplication, Addition, and Subtraction.

Calculations:

⇒ 89 − 47 + 96 − 59 + 52 × 2 (Solving bracket)

⇒ 89 − 47 + 96 − 59 + 104 (Solving multiplication)

⇒ 42 + 96 − 59 + 104 (Performing subtraction)

⇒ 138 − 59 + 104 (Performing addition)

⇒ 79 + 104 (Performing subtraction)

⇒ 183

∴ The correct answer is 183.

Additional Information

BODMAS Rule

It stands for Brackets (), Orders (powers/roots), Division (÷), Multiplication (×), Addition (+), and Subtraction (−). Operations must be performed in this specific sequence.

Unit Digit Check

For quick verification, use unit digits: 9 − 7 + 6 − (3 + 6) + (2 × 2) → 9 − 7 + 6 − 9 + 4 = 3. The final answer must end in 3.

Grouping Method

To avoid errors, group all positive terms and negative terms separately before the final subtraction: (Sum of Positives) − (Sum of Negatives).

Shortcut Trick

Solve using BODMAS rule: Bracket → Division → Multiplication → Addition → Subtraction.

Step 1: 87 + 22 − 6 + 29 − 13 + 18

Step 2: Group positive and negative terms: (87 + 22 + 29 + 18) − (6 + 13)

Step 3: 156 − 19 = 137

∴ The correct answer is 137.

Alternate Method

Given: 87 + 22 − (36 ÷ 6) + 29 × 1 − 13 + 18

Formula Used: BODMAS Rule

⇒ 87 + 22 − 6 + 29 × 1 − 13 + 18 (Solving Bracket and Division)

⇒ 87 + 22 − 6 + 29 − 13 + 18 (Solving Multiplication)

⇒ 109 − 6 + 29 − 13 + 18 (Solving Addition from left)

⇒ 103 + 29 − 13 + 18

⇒ 132 − 13 + 18

⇒ 119 + 18

⇒ 137

∴ The correct answer is 137.

Additional Information

BODMAS / VBODMAS Rule

It defines the order of operations: Vinculum (bar), Brackets, Of (orders/powers), Division, Multiplication, Addition, and Subtraction.

Left-to-Right Precedence

Addition and subtraction have the same priority level; they are typically solved from left to right to avoid confusion, though grouping positives and negatives is also a valid shortcut.

Multiplication by 1

Any number multiplied by 1 remains unchanged (Identity property of multiplication), which simplifies 29 × 1 to 29.

Shortcut Trick

To find the maximum number of students, calculate the HCF (Highest Common Factor) of 84 and 108.

The difference between 108 and 84 is 24. Factors of 24 are 24, 12, 8, 6, 4, 3, 2, 1.

Check the largest factor of the difference that divides both numbers: 12 × 7 = 84 and 12 × 9 = 108.

So, the maximum students = 12.

Items per student: 84 ÷ 12 = 7 chocolates and 108 ÷ 12 = 9 candies.

∴ The correct answer is 12 students; 7 chocolates and 9 candies.

Alternate Method

Given: Total chocolates = 84 and total candies = 108.

For equal distribution among the maximum number of students, we need the HCF of (84, 108).

⇒ Prime factorization of 84 = 2² × 3 × 7

⇒ Prime factorization of 108 = 2² × 3³

⇒ HCF = 2² × 3 = 4 × 3 = 12

⇒ Number of chocolates for each student = 84 ÷ 12 = 7

⇒ Number of candies for each student = 108 ÷ 12 = 9

∴ The correct answer is 12 students; 7 chocolates and 9 candies.

Additional Information

HCF (Highest Common Factor)

HCF is the largest number that divides two or more numbers without leaving a remainder. It is used for problems involving maximum grouping or equal distribution.

Relationship between HCF and LCM

For any two numbers a and b, the product of the numbers is equal to the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b).

HCF by Difference Method

The HCF of two numbers is always a factor of their difference. This is a quick way to narrow down potential HCF values in competitive exams.

Shortcut Trick

Use the algebraic identity: (a − b)² + 4ab = (a + b)²

Here, let a = 12.35 and b = 7.65.

Substituting the values: (12.35 + 7.65)²

⇒ (20)² = 400

∴ The correct answer is 400.

Alternate Method

Given:

The mathematical expression to solve is: (12.35 − 7.65)² + 4 × 12.35 × 7.65

Formula Used:

The standard algebraic expansion formulas are:

1. (a − b)² = a² + b² − 2ab

2. (a + b)² = a² + b² + 2ab

Adding 4ab to the first equation gives: (a − b)² + 4ab = a² + b² − 2ab + 4ab = a² + b² + 2ab = (a + b)²

Calculations:

⇒ Let a = 12.35 and b = 7.65.

⇒ The given expression is in the form: (a − b)² + 4ab

⇒ According to the identity, (a − b)² + 4ab = (a + b)²

⇒ Expression = (12.35 + 7.65)²

⇒ Expression = (20.00)²

⇒ Expression = 400

∴ The correct answer is 400.

Additional Information

Standard Algebraic Identities

Familiarity with identities like (a+b)² − (a−b)² = 4ab and (a+b)² + (a−b)² = 2(a²+b²) helps in solving complex simplification problems quickly.

Sum and Difference Properties

When the sum (a+b) or difference (a−b) results in a base number (like 10, 20, 100), always look for expansion patterns to avoid direct multiplication of decimals.

Shortcut Trick

Apply the standard algebraic identity: (a + b)² + (a − b)² = 2(a² + b²).

Here, let a = √3 and b = √2.

Result = 2 × [(√3)² + (√2)²]

Result = 2 × (3 + 2) = 2 × 5 = 10.

∴ The correct answer is 10.

Alternate Method

Given:

(√3 + √2)² + (√3 − √2)²

Formula Used:

(a + b)² = a² + b² + 2ab

(a − b)² = a² + b² − 2ab

Calculations:

⇒ [(√3)² + (√2)² + 2 × √3 × √2] + [(√3)² + (√2)² − 2 × √3 × √2]

⇒ [3 + 2 + 2√6] + [3 + 2 − 2√6]

⇒ 5 + 2√6 + 5 − 2√6

⇒ 5 + 5 + 2√6 − 2√6

⇒ 10

∴ The correct answer is 10.

Additional Information

Square of Difference Identity

The difference between the squares of sum and difference is given by (a + b)² − (a − b)² = 4ab.

Difference of Squares

The product of sum and difference of two terms is (a + b)(a − b) = a² − b².

Square of a Binomial

A basic expansion formula: (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Shortcut Trick

Recognize the algebraic identity a² − b² = (a + b)(a − b).

Here, a = 6.203 and b = 5.797.

Sum (a + b) = 12 and Difference (a − b) = 0.406.

The expression becomes (12 × 0.406) ÷ 0.812.

Since 0.812 = 2 × 0.406, the result is 12 ÷ 2 = 6.

∴ The correct answer is 6.

Alternate Method

Given:

Expression: ((6.203)² − (5.797)²) ÷ 0.812

Formula Used:

Algebraic identity: a² − b² = (a + b)(a − b)

Calculations:

⇒ [(6.203 + 5.797) × (6.203 − 5.797)] ÷ 0.812

⇒ [12.000 × 0.406] ÷ 0.812

⇒ 4.872 ÷ 0.812

⇒ 4872 ÷ 812

⇒ 6

∴ The correct answer is 6.

Additional Information

Difference of Squares

The identity a² − b² = (a + b)(a − b) is used to simplify the subtraction of two squared terms.

Square of a Sum

(a + b)² = a² + 2ab + b² is used for calculating the square of the sum of two numbers.

Square of a Difference

(a − b)² = a² − 2ab + b² is used for calculating the square of the difference between two numbers.

Shortcut Trick

Use the standard Pythagorean Triplet (3, 4, 5).

Multiply the triplet by 3: (3 × 3, 4 × 3, 5 × 3) = (9, 12, 15).

Given Length = 9 cm and Diagonal = 15 cm, the Width must be 12 cm.

Area = Length × Width = 9 × 12 = 108 cm².

∴ The correct answer is 108 cm².

Alternate Method

Given:

Length (l) = 9 cm

Diagonal (d) = 15 cm

Formula Used:

Diagonal² = Length² + Width²

Area = Length × Width

Calculations:

⇒ 15² = 9² + Width²

⇒ 225 = 81 + Width²

⇒ Width² = 225 − 81

⇒ Width² = 144

⇒ Width = √144 = 12 cm

⇒ Area of Rectangle = Length × Width

⇒ Area = 9 cm × 12 cm = 108 cm²

∴ The correct answer is 108 cm².

Additional Information

Pythagorean Triplet

A set of three integers satisfying a² + b² = c². Common examples are (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Perimeter of Rectangle

The distance around the outside of the rectangle, calculated as P = 2 × (length + width).

Properties of Rectangle

Opposite sides are equal and parallel, all four angles are 90°, and diagonals are equal and bisect each other.

Shortcut Trick

Use the algebraic identity: (a − b)² + 4ab = (a + b)²

Here, let a = 412 and b = 388.

⇒ (412 + 388)² = (800)²

⇒ 640000

∴ The correct answer is 640000.

Alternate Method

Given: (412 − 388)² + 4 × 412 × 388

Formula Used: Expansion of (a − b)² and (a + b)²

⇒ (412 − 388) = 24

⇒ (24)² + 4 × 412 × 388

⇒ 576 + 639424

⇒ 640000

∴ The correct answer is 640000.

Additional Information

Square of Sum

The identity for the square of a sum is (a + b)² = a² + 2ab + b².

Square of Difference

The identity for the square of a difference is (a − b)² = a² − 2ab + b².

Relationship Identity

Combining the two provides the useful relation: (a + b)² − (a − b)² = 4ab.

Shortcut Trick

Let the Ratio of Length to Breadth be 3 : 1.

Perimeter ratio = 2 × (3 + 1) = 8 units = 48 cm.

1 unit = 6 cm ⇒ Breadth = 6 cm and Length = 18 cm.

Diagonal = √(18² + 6²) = 6 × √(3² + 1²) = 6√10 cm.

∴ The correct answer is 6√10 cm.

Alternate Method

Given: Perimeter of Rectangle = 48 cm, Length (L) = 3 × Breadth (B).

Formula Used: Perimeter = 2(L + B) | Diagonal (d) = √(L² + B²)

⇒ 2(L + B) = 48

⇒ L + B = 24

⇒ Substitute L = 3B: 3B + B = 24

⇒ 4B = 24 ⇒ B = 6 cm

⇒ L = 3 × 6 = 18 cm

⇒ Diagonal (d) = √(18² + 6²)

⇒ d = √(324 + 36) = √360

⇒ d = √(36 × 10) = 6√10 cm

∴ The correct answer is 6√10 cm.

Additional Information

Area of a Rectangle

The total space occupied by a Rectangle is calculated as Area = Length × Breadth.

Pythagoras Theorem

For a Right-angled Triangle formed by the Diagonal, L² + B² = d².

Circumcircle of a Rectangle

The Radius of the circle passing through all four vertices of a Rectangle is half of its Diagonal (R = d/2).

Shortcut Trick

Ratio of Average of first 4 and last 4 numbers = 2 : 1.

Since the count of numbers is the same (4 each), the Sum ratio is also 2 : 1.

Total units for sum = 2 + 1 = 3 units.

Total Sum of 8 numbers = 8 × 57 = 456.

Sum of last 4 numbers (1 unit) = 456 ÷ 3 = 152.

∴ The correct answer is 152.

Alternate Method

Given: Average of 8 numbers = 57. Average of first 4 is double the average of the last 4.

Formula Used: Sum = Average × Number of observations.

⇒ Total Sum of all 8 numbers = 8 × 57 = 456.

⇒ Let the average of the last 4 numbers = x.

⇒ Average of the first 4 numbers = 2x.

⇒ Sum of first 4 numbers = 4 × 2x = 8x.

⇒ Sum of last 4 numbers = 4 × x = 4x.

⇒ Total sum = 8x + 4x = 12x.

⇒ 12x = 456.

⇒ x = 456 ÷ 12 = 38.

⇒ Sum of the last 4 numbers = 4x = 4 × 38 = 152.

∴ The correct answer is 152.

Additional Information

Weighted Average

When two groups are combined, the total average is calculated as A = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).

Sum of Observations

The total sum is always the product of the Arithmetic Mean and the total number of items: Sum = Average × Count.

Equal Groups Property

If the number of items in two groups is equal, the Combined Average is simply the average of their individual averages: (a₁ + a₂) ÷ 2.

Shortcut Trick

For any set of numbers in an Arithmetic Progression (like consecutive natural numbers), the Average is always equal to the Arithmetic Mean of the first and last terms.

Average (A) = (Smallest + Largest) ÷ 2

By cross-multiplying:

Sum of Smallest and Largest = 2 × Average = 2A

∴ The correct answer is 2A.

Alternate Method

Given: Total numbers (n) = 17, Average of these consecutive numbers = A.

Formula Used: Average of an Arithmetic Progression (AP) = (a + l) ÷ 2, where 'a' is the first term and 'l' is the last term.

⇒ Let the 17 consecutive natural numbers be n₁, n₂, n₃, ..., n₁₇.

⇒ These numbers form an Arithmetic Progression with a common difference (d) = 1.

⇒ For any AP, the Sum of all terms = (n ÷ 2) × (First term + Last term).

⇒ Also, Average = Sum ÷ n.

⇒ Average (A) = [(n ÷ 2) × (n₁ + n₁₇)] ÷ n

⇒ A = (n₁ + n₁₇) ÷ 2

⇒ n₁ + n₁₇ = 2 × A = 2A

∴ The correct answer is 2A.

Additional Information

Middle Term Property

In an Arithmetic Progression with an odd number of terms (n), the Average is always the exact middle term, which is the ((n+1)/2)^th term.

Sum of First 'n' Natural Numbers

The sum of the first 'n' natural numbers is calculated using the formula: S_n = n(n + 1) ÷ 2.

Average of Even and Odd Numbers

The average of the first 'n' consecutive even numbers is (n + 1), while the average of the first 'n' consecutive odd numbers is simply n.

Shortcut Trick

To find the maximum number of boys, calculate the HCF of 210 and 294.

HCF(210, 294): 294 − 210 = 84. Factors of 84 are 42, 21, etc. Since 42 divides both, HCF = 42.

Number of chips per boy = Total chips ÷ HCF = 210 ÷ 42 = 5.

∴ The correct answer is 5 chips.

Alternate Method

Given: Total chips = 210, Total toffees = 294.

Formula Used: Maximum group size = HCF (Highest Common Factor); Items per person = Total items ÷ Group size.

⇒ Prime factorization of 210 = 2 × 3 × 5 × 7

⇒ Prime factorization of 294 = 2 × 3 × 7 × 7

⇒ HCF (Maximum number of boys) = 2 × 3 × 7 = 42

⇒ Chips received by each boy = Total chips ÷ Total boys

⇒ Chips per boy = 210 ÷ 42 = 5

∴ The correct answer is 5 chips.

Additional Information

Highest Common Factor (HCF)

HCF is the greatest number that divides two or more numbers without leaving a remainder. It is used to find the maximum possible size for equal distribution.

Least Common Multiple (LCM)

LCM is the smallest positive integer that is divisible by each of the given numbers. Relationship: Product of two numbers = HCF × LCM.

HCF by Difference Method

The HCF of two numbers is also a factor of their difference. This is a quick way to narrow down the HCF in exams.

Shortcut Trick

Let the total number be 100%.

Given that 30% of the number + 70 = 100%.

Subtracting percentages: 100% − 30% = 70%.

This implies that 70% of the number is equal to 70.

Calculating the full value: 100% = (70 / 70) × 100 = 100.

∴ The correct answer is 100.

Alternate Method

Given:

Percentage added = 30%

Constant value added = 70

Formula Used:

Number = [Value / (100% − Percentage)] × 100

Let the number be x.

⇒ (30 / 100) × x + 70 = x

⇒ 0.3x + 70 = x

⇒ 70 = x − 0.3x

⇒ 70 = 0.7x

⇒ x = 70 / 0.7

⇒ x = 100

∴ The correct answer is 100.

Additional Information

Percentage to Fraction

To convert a percentage to a fraction, divide the number by 100. Example: 30% = 30/100 = 3/10.

Percentage Change

The percentage change is calculated as [(Final Value − Initial Value) / Initial Value] × 100.

Base Value Rule

In most word problems, the 'number' or 'original quantity' is always treated as the 100% base for calculations.

Shortcut Trick

Profit of 30% implies that the Selling Price (SP) is 130% of the Cost Price (CP).

Ratio method: 30% = 3/10 ⇒ CP = 10 units, Profit = 3 units, SP = 13 units.

13 units = ₹7540

1 unit = 7540 ÷ 13 = 580

CP = 10 units = 580 × 10 = ₹5800

∴ The correct answer is ₹5800.

Alternate Method

Given:

Selling Price (SP) = ₹7540

Profit Percentage = 30%

Formula Used:

Cost Price (CP) = [Selling Price × 100] ÷ [100 + Profit %]

Calculations:

⇒ CP = [7540 × 100] ÷ [100 + 30]

⇒ CP = 754000 ÷ 130

⇒ CP = 75400 ÷ 13

⇒ CP = ₹5800

∴ The correct answer is ₹5800.

Additional Information

Basic Profit and Loss Formulas

Profit = SP − CP and Profit % = (Profit ÷ CP) × 100.

Selling Price Calculation

SP = CP × (100 + Profit %)/100 (if profit) or SP = CP × (100 − Loss %)/100 (if loss).

Marked Price and Discount

SP = Marked Price (MP) − Discount. Discount % is always calculated on the MP.

Shortcut Trick

The difference between Selling Price (SP) and Cost Price (CP) is the Profit.

Given Profit = 30% of CP = ₹120.

⇒ 30% → 120

⇒ 1% → 4

Selling Price = 100% (CP) + 30% (Profit) = 130%.

⇒ 130 × 4 = ₹520.

∴ The correct answer is ₹520.

Alternate Method

Given: Difference between CP and SP (Profit) = ₹120, Profit Percentage = 30%.

Formula Used: Profit = SP − CP; Profit % = (Profit ÷ CP) × 100; SP = CP + Profit.

⇒ Let the Cost Price (CP) be ₹x.

⇒ Profit = 30% of x = 120

⇒ (30 ÷ 100) × x = 120

⇒ x = (120 × 100) ÷ 30

⇒ x = 4 × 100 = ₹400

⇒ Selling Price (SP) = CP + Profit

⇒ SP = 400 + 120

⇒ SP = ₹520

∴ The correct answer is ₹520.

Additional Information

Profit and Loss Fundamentals

Profit occurs when SP > CP and Loss occurs when CP > SP. Profit/Loss is always calculated on the Cost Price unless specified otherwise.

Basic Formulas

Profit % = (Profit ÷ CP) × 100 | Loss % = (Loss ÷ CP) × 100.

Finding CP from SP

CP = [100 ÷ (100 + Profit %)] × SP (for profit) or CP = [100 ÷ (100 − Loss %)] × SP (for loss).

Shortcut Trick

Let the first number be 20 units.

The sum of the two numbers = 45/20 × 20 = 45 units.

The second number = Sum − First number = 45 − 20 = 25 units.

Required percentage = (Second number / First number) × 100

Required percentage = (25 / 20) × 100 = 125%.

∴ The correct answer is 125 percent.

Alternate Method

Given:

Let the first number be 'x' and the second number be 'y'.

The sum of the two numbers (x + y) = (45 / 20) × x

Formula Used:

Percentage = (Value / Base) × 100

Calculations:

⇒ x + y = (45 / 20)x

⇒ y = (45 / 20)x − x

⇒ y = (45x − 20x) / 20

⇒ y = 25x / 20

⇒ y / x = 25 / 20

⇒ Required Percentage = (y / x) × 100

⇒ Required Percentage = (25 / 20) × 100

⇒ Required Percentage = 1.25 × 100 = 125%

∴ The correct answer is 125 percent.

Additional Information

Percentage Representation

A fraction a/b can be converted to a percentage by multiplying it by 100. Percentage = (a/b) × 100%.

Ratio and Proportion

If the sum and one part are known in terms of units, the other part is the difference between the total sum and the known part.

Percentage of Base

To find what percent 'y' is of 'x', 'x' always acts as the denominator (base) in the calculation.

Shortcut Trick

Time taken is directly proportional to the volume of the tank to be emptied.

1/4 part → 8 min

Multiply both sides by 2 to get 1/2 part:

(1/4 × 2) part → 8 × 2 min

1/2 part → 16 min

∴ The correct answer is 16 min.

Alternate Method

Given:

Time to empty 1/4 part = 8 min

Formula Used:

Total Time = Time taken / Fraction of work done

Calculations:

⇒ Time to empty the full tank (1 part) = 8 × 4

⇒ Full tank time = 32 min

⇒ Time to empty 1/2 part of the tank = 32 × (1/2)

⇒ Time = 16 min

∴ The correct answer is 16 min.

Additional Information

Unitary Method for Fractions

If 1/n part of a task is completed in 't' time, then the full task (1 unit) is completed in (n × t) time.

Pipes and Cisterns Efficiency

Efficiency of an emptying pipe is considered negative when working together with an inlet pipe in total work calculations.

Time and Work Relation

Work Done = Rate of Work × Time. For a constant rate, Work and Time are in direct proportion.

Shortcut Trick

Given P + R = 5Q. Adding Q to both sides: P + Q + R = 6Q.

This means the Total Efficiency of P, Q, and R combined is 6 times the efficiency of Q alone.

Since Time is inversely proportional to Efficiency, Q will take 6 times as much time as the group.

Time taken by Q = 6 × 10 = 60 days.

∴ The correct answer is 60 days.

Alternate Method

Given: P, Q and R together complete work in 10 days.

Ratio of efficiencies: (Q + R) / P = 8 / 1 (Total units = 9) and (P + R) / Q = 5 / 1 (Total units = 6).

⇒ To equalize the total efficiency, take LCM(9, 6) = 18.

⇒ New Ratio 1 (multiply by 2): (Q + R) : P = 16 : 2.

⇒ New Ratio 2 (multiply by 3): (P + R) : Q = 15 : 3.

⇒ Thus, efficiency of P = 2, Q = 3, and Total = 18.

⇒ Total Work = Total Efficiency × Total Days = 18 × 10 = 180 units.

⇒ Time taken by Q alone = Total Work ÷ Efficiency of Q = 180 ÷ 3 = 60 days.

∴ The correct answer is 60 days.

Additional Information

Efficiency and Time Relationship

Efficiency (E) is inversely proportional to Time (T) for a constant amount of work: E₁ × T₁ = E₂ × T₂.

Combined Efficiency

When multiple people work together, their individual Efficiencies are added to find the Total Efficiency of the group.

Work-Wages Principle

Wages are generally distributed in the direct ratio of the Work Done or the ratio of Efficiencies (if time spent is same).

Shortcut Trick

When two trains cross in opposite direction, their Relative Speed is the sum of their individual speeds.

Relative Speed = (Length of Train A + Length of Train B) ÷ Time

Total Speed = (400 + 800) ÷ 80 = 1200 ÷ 80 = 15 m/s

∴ The correct answer is 15 m/s.

Alternate Method

Given:

Length of Train A (L_A) = 400 m

Length of Train B (L_B) = 800 m

Time taken to cross (t) = 80 sec

Formula Used:

Relative Speed (Opposite Direction) = (L_A + L_B) ÷ t

Calculations:

⇒ Total Distance to be covered = 400 + 800 = 1200 m

⇒ Relative Speed = 1200 ÷ 80

⇒ Relative Speed = 15 m/s

∴ The correct answer is 15 m/s.

Additional Information

Relative Speed in Same Direction

If two trains of speeds S_A and S_B run in the same direction, the relative speed is |S_A − S_B|.

Unit Conversion

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

Crossing a Stationary Point Object

When a train crosses a pole or a man, the distance covered is equal to the length of the train itself.

Shortcut Trick

Relative Speed = Distance ÷ Time = 400 ÷ 8 = 50 m/s.

Ratio of Train speed to Man speed = 4 : 1.

In opposite direction, relative units = 4 + 1 = 5 units.

5 units = 50 m/s ⇒ 1 unit = 10 m/s.

Speed of train = 4 units = 40 m/s = 40 × (18/5) = 144 km/hr.

∴ The correct answer is 144 km/hr.

Alternate Method

Given:

Length of Train (L) = 400 m

Time taken (t) = 8 seconds

Speed of train (V_t) = 4 × Speed of man (V_m)

Formula used:

Relative Speed = Total Distance ÷ Time

In opposite direction, Relative Speed = V₁ + V₂

Calculations:

⇒ Relative Speed = 400 ÷ 8

⇒ V_t + V_m = 50 m/s

⇒ Since V_t = 4V_m, substituting the value:

⇒ 4V_m + V_m = 50

⇒ 5V_m = 50 ⇒ V_m = 10 m/s

⇒ Speed of train (V_t) = 4 × 10 = 40 m/s

⇒ Converting to km/hr: 40 × (18 ÷ 5)

⇒ 8 × 18 = 144 km/hr

∴ The correct answer is 144 km/hr.

Additional Information

Relative Speed in Trains

When two objects move in opposite directions, Relative Speed = S₁ + S₂. When they move in the same direction, Relative Speed = |S₁ − S₂|.

Speed Unit Conversion

To convert m/s to km/hr, multiply by 18/5. To convert km/hr to m/s, multiply by 5/18.

Crossing a Point Object

When a train crosses a man, pole, or tree, the distance covered is equal to the length of the train itself.

The correct answer is Option(3) i.e. Something is very clear, obvious, and easy to understand.

Key Points

• The idiom 'Be as plain as day' refers to something that is very easy to see, perceive, or understand; it is completely obvious and requires no proof. (स्पष्ट होना)
• Example: The reason for his resignation was as plain as day to everyone who worked with him.
• 'Something is very clear, obvious, and easy to understand' defines the state of a fact or situation being manifest and unmistakable. (कुछ बहुत स्पष्ट, प्रत्यक्ष और समझने में आसान होना)
• Example: The instructions were as plain as day, yet he still managed to make a mistake.
• Hence, we can infer that the correct meaning of the idiom is 'something is very clear, obvious, and easy to understand'.

Therefore, the correct answer is- Something is very clear, obvious, and easy to understand.

Additional Information

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

• Very different from the other (एक दूसरे से बहुत अलग): Used to describe two things that have no similarities.
• Example: Although they are twins, their personalities are very different from each other.
• In very good spirits (बहुत प्रसन्न या उत्साहित): Feeling happy, lively, and optimistic.
• Example: The team was in very good spirits after winning the championship.
• Very happy in thought (विचारों में बहुत खुश): Being in a state of mental joy or pleasant contemplation.
• Example: She sat by the window, very happy in thought while remembering her childhood.

The correct answer is Option (1) i.e. 'To try to entice one with the promise of a reward'.

Key Points

• The idiom 'Dangle a carrot in front of someone' means to tempt or entice someone by promising a reward in exchange for their cooperation or hard work. (किसी को लालच देकर लुभाना)
• Example: The boss decided to dangle a carrot in front of his employees by promising a huge bonus if they met the year-end targets.
• 'To try to entice one with the promise of a reward' is the direct meaning of the idiom, where the 'carrot' represents the incentive being offered. (किसी को इनाम के वादे से लुभाने की कोशिश करना)
• Example: The tech giant dangled a carrot of stock options in front of the lead developer to prevent him from joining a rival firm.
• Hence, we can infer that the meaning of the idiom is to entice someone with a reward.

Therefore, the correct answer is- To try to entice one with the promise of a reward.

Additional Information

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

• To be very compatible and congenial together (एक दूसरे के साथ बहुत अनुकूल और मिलनसार होना): Refers to people who get along very well.
• Example: The two musicians found they were very compatible and started a band together.
• An incentivization method in which a reward and a punishment are simultaneously offered (प्रोत्साहन और दंड की नीति): This is specifically known as the 'carrot and stick' approach.
• Example: The government used a carrot and stick approach to enforce the new tax laws.
• A person with red orange hair (लाल नारंगी बालों वाला व्यक्ति): A literal description often associated with the word 'ginger' or 'carrot-top'.
• Example: Since he was a person with red orange hair, his friends nicknamed him Rusty.

The correct answer is: Heinous.

Key Points

• The word 'Heinous' refers to an action, typically a crime, that is utterly wicked, odious, or deeply offensive to the senses. (जघन्य)
• Example: The court condemned the heinous nature of the assault on the innocent civilians.
• 'Heinous' is correctly spelled and represents something that is hateful or shocking in its level of evil. (जघन्य)
• Example: It is hard to imagine anyone committing such a heinous act of betrayal.
• Hence, we can identify that the correctly spelled word among the given options is 'Heinous'.

Therefore, the correct answer is: Heinous.

Additional Information

Here are the correct spellings and meanings of the other options:

• Hapless (अभागा): This is the correct spelling of 'Happless' and refers to a person who is persistently unfortunate or unlucky.
• Example: The hapless driver found himself stuck in traffic for five hours.
• Hysteria (उन्माद): This is the correct spelling of 'Hystiria' and refers to uncontrollable or exaggerated emotion, often in a large group.
• Example: The arrival of the movie star caused a state of hysteria among the fans.
• Hubris (अति-अभिमान): This is the correct spelling of 'Hubries' and refers to excessive pride or dangerous self-confidence.
• Example: The general's hubris led him to underestimate the strength of the enemy.

The correct answer is: Rash.

Key Points

• The word 'reckless' refers to a person or their actions characterized by a lack of care about the danger or the consequences of their behavior. (लापरवाह)
• Example: The driver was arrested for reckless driving after he sped through a red light.
• 'Rash' means acting or done without careful consideration of the possible consequences; it is often used for impulsive or hasty actions. (उतावला/अविवेकी)
• Example: You should think carefully before making any rash decisions about your career.
• Hence, we can infer that the most appropriate synonym of 'reckless' is 'rash'.

Therefore, the correct answer is: Rash.

Additional Information

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

• Careful (सावधान): Taking care or paying attention to avoid mistakes, damage, or danger.
• Example: Please be careful with those glass vases as they are very fragile.
• Thoughtful (विचारशील): Showing consideration for the needs of other people or showing careful thought.
• Example: It was very thoughtful of him to bring flowers for his host.
• Wise (बुद्धिमान): Having or showing experience, knowledge, and good judgment.
• Example: It is wise to plan for the future rather than spending all your money now.

The correct answer is: Profesional.

Key Points

• The word 'Profesional' is the misspelt word among the given options because it is missing the second 's' required for the correct spelling. (गलत वर्तनी)
• Example: The application was rejected because the candidate made a spelling error by writing 'Profesional' instead of the correct term.
• 'Professional' is the correct spelling, which refers to a person who is competent, skilled, or engaged in a specific activity as a main paid occupation. (पेशेवर)
• Example: It is important to maintain a professional attitude while dealing with clients in the office.
• Hence, we can infer that the misspelt word is 'Profesional'.

Therefore, the correct answer is- Profesional.

Additional Information

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

• Essential (आवश्यक): Something that is absolutely necessary or extremely important for a particular task or for survival.
• Example: A healthy diet and regular exercise are essential for maintaining good health.
• Industrial (औद्योगिक): Relating to or characterized by industry, factories, or manufacturing on a large scale.
• Example: The industrial revolution brought significant changes to the economy and society.
• Sensational (सनसनीखेज): Causing or intended to cause great public interest, excitement, or shock.
• Example: The sensational news about the discovery of a new planet spread rapidly across the globe.

The correct answer is Option (3) i.e. ordinary.

Key Points

• The word extraordinary refers to something that is very unusual, remarkable, or beyond what is regular or customary. (असाधारण)
• Example: The athlete demonstrated extraordinary endurance during the marathon.
• ordinary refers to something that is common, normal, or having no special or distinctive features. (साधारण)
• Example: It was just an ordinary day at school until the surprise assembly was announced.
• Hence, we can infer that the opposite of extraordinary is ordinary.

Therefore, the correct answer is- ordinary

Additional Information

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

• Remarkable (उल्लेखनीय): Worthy of attention; striking or unusual.
• Example: The young artist showed remarkable talent in her first exhibition.
• Exceptional (असाधारण/विशिष्ट): Unusually good or outstanding; not typical.
• Example: He is an exceptional student who excels in both academics and sports.
• Unusual (असामान्य): Not habitually or commonly occurring or done.
• Example: It is unusual to see such heavy rain in this desert region.

The correct answer is Option (1) i.e. Decathlon.

Key Points

• The phrase 'an athletic event comprising ten different events' refers to a multi-stage competition in track and field where athletes compete in ten distinct disciplines. (दस विभिन्न आयोजनों वाली एक एथलेटिक प्रतियोगिता)
• Example: The decathlon is considered an athletic event comprising ten different events that tests the ultimate versatility of an athlete.
• 'Decathlon' is a combined event in athletics consisting of ten track and field events, usually held over two days, with the winner determined by the highest total points. (दशप्रतियोगिता)
• Example: He spent years training to compete in the Olympic decathlon, mastering ten separate events from sprinting to shot put.
• Hence, we can infer that 'decathlon' is the most suitable one-word substitution for the given phrase.

Therefore, the correct answer is- Decathlon

Additional Information

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

• Pentathlon (पंचप्रतियोगिता): An athletic event comprising five different events, such as the modern pentathlon which includes fencing, swimming, horse riding, shooting, and running.
• Example: The modern pentathlon is a challenging contest that requires a diverse range of athletic skills across five disciplines.
• Tetratlon (चतुष्प्रतियोगिता): An athletic event comprising four different events, often used in youth competitions as a precursor to the pentathlon.
• Example: The junior games included a tetratlon where young athletes competed in four specific track events.
• Heptathlon (सप्तप्रतियोगिता): An athletic event comprising seven different events, which is the standard multi-event contest for women in outdoor athletics.
• Example: She won the gold medal in the heptathlon by performing consistently well across all seven track and field events.

The correct answer is Will all the orders have been shipped by us by the end of the day?.

Key Points

• The original sentence is an interrogative sentence in the Future Perfect Tense. The active voice structure is: Will + Subject (we) + have + V3 (shipped) + Object (all the orders)?
• To convert a Future Perfect sentence into Passive Voice, the construction follows this rule: Will + Object (new subject) + have been + V3 (Past Participle) + by + Agent?
• In the transformation, the object all the orders takes the position of the subject, and the subject we is converted into its objective case us acting as the agent.
• The phrase have been shipped is the correct passive form for the perfect aspect, ensuring that the completion of the action in the future is properly conveyed.
• The time-related phrase by the end of the day remains unchanged at the end of the sentence to maintain the original meaning and context.

 Additional Information

• Analysis of incorrect options:
• Future Indefinite Passive: Option 1 uses be shipped, which is the structure for Simple Future Passive, failing to reflect the perfective aspect (have + V3).
• Grammatical Incompatibility: Option 2 incorrectly uses had been. The modal verb will must be followed by the base form have, never the past form had.
• Incomplete Verb Phrase: Option 4 is missing the essential auxiliary verbs have been, rendering the sentence grammatically fragmented.
• The Future Perfect Tense is utilized to describe an event that is expected or planned to happen before a particular time in the future, typically indicated by the preposition by.

The correct answer is The tower will have been completed by the builders by next summer.

Key Points

• The given sentence 'By next summer, the builders will have completed the tower' is in the Active Voice and follows the Future Perfect Tense structure.
• The active structure for this tense is: Subject + will have + Past Participle (V3) + Object. In this sentence, the builders is the subject, will have completed is the verb, and the tower is the object.
• To convert a Future Perfect sentence into Passive Voice, the structure used is: New Subject (Object of active) + will have been + Past Participle (V3) + by + New Object (Subject of active).
• Following this rule, the tower moves to the subject position, the auxiliary verb becomes will have been, and the main verb completed remains in its V3 form.
• The phrase by next summer is an Adverbial of Time indicating a deadline in the future, which remains unchanged in position or tense during the conversion.

 Additional Information

• Future Perfect Tense (Passive):
• It emphasizes the completion of an action before a specific point in the future rather than the doer of the action.
• The inclusion of been is mandatory to distinguish the passive form from the active future perfect.
• Distinguishing other Tenses:
• Simple Future Passive: Uses will be + V3 (e.g., 'The tower will be completed'). This lacks the 'completion by a deadline' nuance.
• Present Perfect Passive: Uses has/have been + V3 (e.g., 'The tower has been completed'). This refers to an action already finished in the past with current relevance.
• Simple Past Passive: Uses was/were + V3 (e.g., 'The tower was completed'). This indicates the action occurred at a specific time in the past.

The correct answer is forest passing with trees.

Key Points

• The sentence involves identifying a grammatical or semantic error within its segments. Part (1) I want to spend is grammatically accurate as it uses the standard Subject + Verb + to-infinitive pattern. Hence, statement 1 is correct.
• Part (2) some time in the correctly applies the quantifier some before the uncountable noun time and initiates a prepositional phrase to indicate location. Hence, statement 2 is correct.
• Part (3) forest passing with trees is the erroneous segment. The use of the preposition with after the participle passing is semantically incorrect in this context. Trees are stationary biological entities; therefore, one cannot pass with them. The intended meaning suggests movement through the forest or being surrounded by trees. The correct prepositional usage for traversing a wooded area is passing through. Hence, statement 3 is incorrect.
• Part (4) and enjoying the natural beauty maintains grammatical consistency by using the present participle form (enjoying) to describe an action occurring while spending time in the forest. Hence, statement 4 is correct.

 Additional Information

• Prepositions of Movement and Place:
• Through: Specifically used when moving within a three-dimensional space or an area filled with objects, such as a forest, a crowd, or a tunnel.
• Among: Used when one is in the middle of or surrounded by multiple distinct entities, such as among the trees.
• Participle Phrases:
• The words passing and enjoying function as participles that modify how the subject intends to spend time.
• Proper parallelism requires that multiple activities linked by a conjunction (like and) share the same grammatical structure to ensure sentence flow and clarity.

The correct answer is 'for'.

 

Key Points

• The noun genius, when used to describe a natural ability, talent, or exceptional aptitude, is idiomatically followed by the preposition for.
• The phrase genius for indicates that someone has a special talent for a particular activity or subject.
• In the given sentence, Alexander is described as having an exceptional talent for tactical warfare.

Therefore, the correct answer is Option 1.

 

Complete Sentence: 'Alexander had a genius for tactical warfare.'

 

Additional Information

• Option 2: in is occasionally used to denote a field of study (e.g., a genius in mathematics), but for is the standard preposition for specific skills or actions.
• Option 3: of is used to show possession or origin (e.g., the genius of Mozart) rather than the talent someone possesses for a task.
• Option 4: to is grammatically incorrect in this context.

The correct answer is conducive to bringing stability to.

Key Points

• The adjective conducive means making a certain situation or outcome likely or possible. In English grammar, it is a fixed collocation that this word is always followed by the preposition to. Therefore, phrases like 'conducive in' or 'conducive of' are idiomatic errors.
• When the word to acts as a preposition (as it does following the adjective 'conducive'), any subsequent verb must be in the gerund form (verb + ing). This explains why bringing is required instead of the base form 'bring'.
• The phrase bring stability to is the standard idiomatic construction used to indicate the recipient or the system affected by the stabilization. The preposition to correctly identifies the financial system as the entity receiving the benefit of the measures.
• The original sentence is incorrect because it uses the preposition 'in' after 'conducive', fails to use the gerund form of the verb, and uses the wrong preposition before 'the financial system'.

 Additional Information

• Prepositional Idioms:
• Certain adjectives require specific prepositions to be grammatically correct. Examples include detrimental to, beneficial to, and immune to.
• Conducive to is frequently used in formal reports and academic writing to describe factors that contribute to a desired environment or result, such as economic growth or peace.
• Gerund vs. Infinitive:
• Learners often mistake the prepositional to for the infinitive marker to. In phrases like 'look forward to', 'object to', or 'conducive to', the word to is a preposition and must be followed by a noun or gerund.
• Example: 'The environment is conducive to learning' (Noun) or 'The environment is conducive to studying' (Gerund).

The correct answer is Option 4.

Key Points

• The paragraph describes a chronological sequence of events during a hospital stay following a surgery. S1 and S2 are fixed in their positions.
• Sentence A follows S1 as it provides the first chronological update after the appendix surgery:
• 'After two days they gave me food, but I couldn't keep it down.'
• Sentence D follows A because it introduces a subsequent medical complication that arose after the narrator was unable to process food:
• 'And then a fever arrived.'
• Sentence B follows D as it explains the medical response to the symptoms described in A and D (vomiting and fever):
• 'No one could isolate any bacteria or figure out what had gone wrong.'
• Sentence C follows B to provide an emphatic closure to the diagnostic mystery mentioned in the previous sentence:
• 'No one ever did.'
• The paragraph concludes with S2, which details the ongoing treatment with IV fluids and antibiotics to manage the unknown condition.
• The correct sequence is ADBC.

Coherent paragraph after rearrangement:

'I had gone into the hospital to have my appendix out. After two days they gave me food, but I couldn't keep it down. And then a fever arrived. No one could isolate any bacteria or figure out what had gone wrong. No one ever did. I took fluids through one IV, and antibiotics came through another.'

The correct answer is Option 2.

Key Points

• The paragraph follows a chronological and thematic contrast between a memory of the past and the reality of the present.
• S1 is the fixed starting sentence, which introduces the theme of the father's resilience to heat:
• 'When had the heat ever bothered her father before?'
• Sentence C follows S1 because it shifts the narrative into a flashback, providing context to the question asked in S1:
• 'She remembered going out to the farthest field with water for him, before he had given up that part of the farm.'
• Sentence A is the third sentence as it continues the specific action within the memory (the act of him taking the water):
• 'And he would take the jug from her and lift it to his lips and it would seem to Helen... that the water flowed into her magnificent father and enlivened him...'
• Sentence B follows A by further describing the father's powerful physical state in that memory, completing the image of the 'magnificent father':
• 'And his chest would swell, his reddened arms eager with muscle emerging out from his rolled-up sleeves...'
• Sentence D is the fifth sentence because it acts as a bridge, identifying the previous sentences as a 'vision' and contrasting it with the present reality:
• 'The vision pleased and confused her, for what had it to do with the man now beside her?'
• S2 is the fixed closing sentence, providing the physical details of the 'man now beside her' that contrast sharply with the memory:
• 'She stared at him and saw that his nose was queerly white... and his hair was thinning and jagged...'
• The logical sequence is CABD.

Coherent paragraph after rearrangement:

'When had the heat ever bothered her father before? She remembered going out to the farthest field with water for him, before he had given up that part of the farm. And he would take the jug from her and lift it to his lips and it would seem to Helen, the sweet child Helen standing in the dusty corn, that the water flowed into her magnificent father and enlivened him as if it were secret blood of her own she had given him. And his chest would swell, his reddened arms eager with muscle emerging out from his rolled-up sleeves, and his eyes now wiped of sweat and exhaustion. The vision pleased and confused her, for what had it to do with the man now beside her? She stared at him and saw that his nose was queerly white and that there were many tiny red veins about it, hardly more than pen lines; and his hair was thinning and jagged, growing back stiffly from his forehead as if he had brushed it back impatiently with his hand once too often.'

The correct answer is Option 2.

 

Key Points

• The primary grammatical error in the sentence is the redundant use of the conjunction ‘so’ after the subordinating conjunction ‘Since’.
• In English grammar, words like Since, Because, and As introduce a reason (subordinate clause). When a sentence starts with these words, the result (main clause) should follow after a comma without another conjunction like ‘so’ or ‘therefore’.
• Using both ‘Since’ and ‘so’ in the same sentence is a common error known as double conjunction or redundancy.
• Removing the word ‘so’ makes the sentence grammatically sound: ‘Since the people... early, I had to take a bus home.’
• Therefore, Option 2 is the correct replacement.

Therefore, the correct answer is I had to take a bus home.

 

Correct Sentence: ‘Since the people who gave me a ride decided to leave the concert early, I had to take a bus home.’

 

Additional Information

• Option 1: ‘so I had taken a bus home’ – This retains the redundant ‘so’ and unnecessarily changes the tense to past perfect, which does not fit the context of the simple past sequence.
• Option 3: ‘so I had to get a bus home’ – This also retains the redundant ‘so’, making it grammatically incorrect regardless of the verb change from ‘take’ to ‘get’.
• Option 4: ‘No improvement required’ – This is incorrect because the original sentence contains a redundancy error.
• Similar rules apply to Although/Though; you should not use ‘but’ in the same sentence (e.g., ‘Although it was raining, but he went out’).

The correct answer is Option 1.

 

Key Points

• The passage emphasizes that although India has grown fast, it has the potential to develop even faster and more effectively.
• The core theme is the concept of inclusive growth, which is defined as growth that distributes economic gains across the entire population rather than a specific group.
• The author argues that growth should be viewed as an instrument for spreading prosperity to all segments of society, particularly the poorest segment.
• By advocating for both an increase in the pace of development and a broader distribution of its benefits, Option 1 most accurately captures the central idea.

Therefore, the correct answer is Demanding more rapid and widely shared economic growth.

 

Additional Information

• Option 2: This is incorrect because the passage explicitly mentions that high growth alone is not a sufficient condition for eradicating poverty.
• Option 3: While global standing is mentioned as a point of comparison, it is not the defining concept or goal discussed in the text.
• Option 4: While the government's role in redistribution is mentioned, the passage focuses more broadly on the nature of economic growth itself as a tool for inclusive progress.
• The passage suggests measuring success through the per capita income and growth rate of the bottom 20 per cent of the population.