SSC GD Constable 2026 Official Paper (Held On 09 May, 2026 Shift 1) (Previous Year Paper)

Logic followed here is,

1920 ÷ 2 = 960

960 ÷ 4 = 240

240 ÷ 2 = 120

120 ÷ 4 = 30

30 ÷ 2 = 15

15 ÷ 4 = 3.75

3.75 ÷ 2 = 1.875

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

For 'AI' related to 'GO':

For 'RG' related to 'XM':

Applying the same logic to 'FP':

Thus, FP is related to LV.

Hence, the correct answer is 'Option 1'.

Pattern followed here is,

Hence, the correct answer is “Option 2”.

For 'HO' related to 'CH':

For 'MZ' related to 'HS':

Applying the same logic to 'GS':

Thus, GS is related to BL.

Hence, the correct answer is 'Option 4'.

For the set '(TN, OI, IC)':

For the set '(GW, BR, VL)':

Applying the same logic to the clusters in '(UX, PS, JM)':

Thus, the letter clusters (UX, PS, JM) follow the same logic.

Hence, the correct answer is 'Option 2'.

The dates given are from 10 January 2020 to 25 September 2020 (inclusive).

January: 31 − 10 + 1 = 22 days (Since 10th January is included)

February: 29 days (2020 is a leap year)

March: 31 days

April: 30 days

May: 31 days

June: 30 days

July: 31 days

August: 31 days

September: 25 days (Up to 25th September inclusive)

Total number of days = 22 + 29 + 31 + 30 + 31 + 30 + 31 + 31 + 25

Total number of days = 260

There are 260 days from 10 January 2020 to 25 September 2020.

Hence, the correct answer is “Option 3”.

Let us check the pair 2011 and 2022:

Year 2011 is an ordinary year (not divisible by 4).

Year 2022 is an ordinary year (not divisible by 4).

Both are of the same type.

The odd days for each year are as follows:

• 2011 (Ordinary Year) = 1
• 2012 (Leap Year) = 2
• 2013 (Ordinary Year) = 1
• 2014 (Ordinary Year) = 1
• 2015 (Ordinary Year) = 1
• 2016 (Leap Year) = 2
• 2017 (Ordinary Year) = 1
• 2018 (Ordinary Year) = 1
• 2019 (Ordinary Year) = 1
• 2020 (Leap Year) = 2
• 2021 (Ordinary Year) = 1

Total odd days = 1 + 2 + 1 + 1 + 1 + 2 + 1 + 1 + 1 + 2 + 1 = 14

Since 14 ÷ 7 = 2 with a remainder of 0, the sum of odd days is a multiple of 7.

Therefore, the calendar of 2011 and 2022 will be identical.

Checking other options:

2017 and 2027: Total odd days = 12 (Not a multiple of 7).

2003 and 2007: Total odd days = 5 (Not a multiple of 7).

2014 and 2020: 2014 is an ordinary year while 2020 is a leap year (Different types).

Hence, the correct answer is “Option 1”.

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

1. E is third to the left of C.
2. D is to the right of A and to the left of B.
3. A is at an end of the row.

Three persons are sitting to the right of E.

Hence, the correct answer is “Option 4”.

7 boys A, B, C, P, Q, R and S are sitting around a circular table facing towards the centre (not necessarily in the same order).

1. S is fifth to the right of C.
2. S is second to the right of P.
3. Q is not the immediate neighbour of P or S.
4. B is fourth to the right of A. 

C is sitting third to the left of P.

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 4”.

AZ205 : CB112

CB200 : ED107

Similarly,

For, XM999: ?

Hence, the correct answer is 'Option 1'.

DI30 : HC75

KR40 : OL100

Similarly,

For ? : HL150

Hence, the correct answer is 'Option 3'.

The logic followed here is:

Logic: Second Number = (First Number − 2)³

For the first pair 11 : 729

⇒ (11 − 2)³

⇒ 9³ = 729.

For the second pair 15 : 2197

⇒ (15 − 2)³

⇒ 13³ = 2197.

Applying the same logic to the third pair

23 : ?

⇒ (23 − 2)³

⇒ 21³ = 9261.

Hence, the correct answer is 'Option 2'.

LORD is coded as OPSE →

WAST is coded as DBTU →

Similarly,

let us find the code for NORM:

Hence, the correct answer is “Option 4”.

The watch is slow by 12 minutes at 4 AM.

To show the correct time, the watch must gain 12 minutes.

Total time to gain in seconds = 12 × 60 = 720 seconds

The watch gains 48 seconds every hour.

Number of hours required to gain 720 seconds = 720 ÷ 48

Required time = 15 hours

Now, we add 15 hours to the starting time of 4 AM:

4 AM + 12 hours = 4 PM

4 PM + 3 hours = 7 PM

The watch will show the correct time at 7:00 PM.

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Hence, the correct answer is “Option 3”.

Given that the ratio of present ages of two persons is 2 : 5.

Let the present ages of the two persons be 2x and 5x respectively.

The sum of their present ages is given as 21.

2x + 5x = 21

7x = 21

x = 21 ÷ 7

x = 3

Present age of the first person = 2 × 3 = 6 years

Present age of the second person = 5 × 3 = 15 years

Age of the first person after 7 years = 6 + 7 = 13 years

Age of the second person after 7 years = 15 + 7 = 22 years

The required ratio of their ages after 7 years = 13 : 22

Hence, the correct answer is “Option 1”.

The correct answer is 2000.

Key Points

• The Sangeet Natak Akademi officially recognized Sattriya as a classical dance of India on November 15, 2000.
• This formal recognition increased the number of recognized Indian classical dance forms, placing Sattriya alongside established traditions like Bharatanatyam, Kathak, and Kathakali.
• The dance form originated in the 15th century in the Sattras (monasteries) of Assam as a part of the Neo-Vaishnavite movement.
• It was introduced by the great saint and polymath Mahapurush Sankaradeva and his disciple Madhavadeva to preach the Vaishnava faith through performing arts.
• Historically, the dance was performed exclusively by male monks, known as Bhokots, as a form of worship and ritualistic practice.

 Additional Information

• Sattriya Dance Characteristics:
• The performance is based on Ankiya Nat (one-act plays) and centers on mythological themes related to Lord Krishna and Lord Vishnu.
• The dance is accompanied by musical compositions called Borgeets and instruments like the Khol (drum), Bhortal (cymbals), and Flute.
• Costumes are distinctly Assamese, utilizing Pat Silk (mulberry silk) with traditional motifs like the Kingkhap.
• It follows the principles of the Natya Shastra, incorporating both Nritta (pure dance) and Abhinaya (expressive dance).
• Sangeet Natak Akademi:
• Established in 1953, it is India's national academy for music, dance, and drama, acting as an autonomous body under the Ministry of Culture.
• Its primary objective is the preservation and promotion of India's diverse performing arts heritage.
• The academy is headquartered at Rabindra Bhavan in New Delhi.

Therefore, the correct option is 3.

The correct answer is Ramayana.

Key Points

• Dashara, also known as Vijayadashami, is a major Hindu festival celebrated at the end of Navaratri every year.
• The Ramayana, traditionally attributed to the sage Valmiki, is the primary scripture that narrates the life and exploits of Lord Rama, the prince of Ayodhya.
• The festival commemorates the day Lord Rama killed the ten-headed demon king Ravana, who had kidnapped Sita, Rama's wife.
• The victory signifies the triumph of Dharma (righteousness) over Adharma (evil) and is celebrated on the 10th day of the Ashwin month in the Hindu calendar.
• In many parts of India, large effigies of Ravana, Kumbhakarna, and Meghnad are burned to symbolize the destruction of evil forces.

 Additional Information

• Mahabharata:
• An ancient Indian epic attributed to Sage Vyasa, centered on the struggle between two groups of cousins, the Kauravas and the Pandavas.
• It is the longest epic in the world and contains the Kurukshetra War, though some regional traditions also link the Pandavas returning from exile to the day of Dashara.
• Bhagavad Gita:
• A 700-verse Hindu scripture that is part of the Mahabharata, specifically the Bhishma Parva.
• It presents a dialogue between Lord Krishna and Arjuna regarding the nature of duty, soul, and Moksha.
• Vedas:
• The oldest layer of Sanskrit literature, consisting of the Rigveda, Samaveda, Yajurveda, and Atharvaveda.
• They are religious texts containing hymns, incantations, and rituals rather than narrative historical epics like the Ramayana.

The correct answer is Shashi Tharoor.

Key Points

• Shashi Tharoor, a senior Member of Parliament representing the Thiruvananthapuram constituency and a veteran leader of the Indian National Congress, was designated to lead a high-level diplomatic outreach concerning Operation Sindoor in 2025.
• The mission involved extensive engagement with political and diplomatic leadership in the United States and Panama to communicate India's strategic rationale and secure international understanding regarding the humanitarian aspects of the operation.
• His background as a former Under-Secretary-General of the United Nations and Minister of State for External Affairs provided the necessary global credibility to navigate complex geopolitical sensitivities during this period.
• The outreach in Panama was particularly critical due to the country's influence in maritime security and its role as a key gateway in the Western Hemisphere, which was vital for Garnering support among Global South nations.

 Additional Information

• Rahul Gandhi:
• He currently serves as the Leader of the Opposition in the Lok Sabha.
• While he conducts international interactions, his primary focus in 2025 remained on domestic policy and the Bharat Jodo ideological framework.
• P. Chidambaram:
• A former Union Finance Minister and Home Minister of India.
• His contributions are primarily centered on economic policy, constitutional law, and internal party strategy rather than active foreign diplomatic tours.
• Sonia Gandhi:
• She holds the position of Chairperson of the Congress Parliamentary Party (CPP).
• Her role is largely focused on high-level party governance and mentorship, rarely undertaking active diplomatic assignments abroad.

The correct answer is Eutrophication.

Key Points

• Eutrophication is an enrichment of water by nutrient salts, primarily nitrates and phosphates, which causes structural changes to the ecosystem.
• It is triggered by the excessive entry of nitrogen and phosphorus from sources such as agricultural runoff (fertilizers), detergents, and untreated sewage into lakes, rivers, and coastal waters.
• These nutrients act as a fertilizer for aquatic plants, leading to an overgrowth of algae and phytoplankton, a phenomenon commonly known as an algal bloom.
• The dense layer of algae blocks sunlight from reaching submerged plants, causing them to die and reducing photosynthesis in deeper water layers.
• When the algae die, microorganisms and aerobic bacteria decompose the organic matter, consuming vast amounts of dissolved oxygen (DO) in the process.
• This depletion of oxygen creates hypoxic conditions or dead zones, where fish and other aquatic organisms cannot survive, ultimately leading to a loss of biodiversity.

 Additional Information

• Global warming:
• Refers to the long-term rise in the average temperature of Earth's climate system due to the accumulation of greenhouse gases like carbon dioxide (CO₂) and methane (CH₄).
• Smog:
• A type of intense air pollution that is a mixture of smoke and fog; it often results from the reaction of sunlight with nitrogen oxides (NO_x) and volatile organic compounds (VOCs).
• Acid rain:
• Caused by chemical reactions involving sulfur dioxide (SO₂) and nitrogen oxides that rise into the atmosphere and mix with water and oxygen to form acidic pollutants.
• Biological Oxygen Demand (BOD):
• An important parameter in measuring water quality; it represents the amount of oxygen consumed by bacteria while decomposing organic matter under aerobic conditions. High BOD levels are typically associated with high levels of organic pollution and eutrophication.

The correct answer is Shwetha Menon.

Key Points

• Shwetha Menon was elected as the president of the Association of Malayalam Movie Artists (AMMA) in 2025, marking a milestone for female representation.
• This milestone represents a progressive shift towards empowering female leadership in the administrative bodies of the regional entertainment industry.
• Prior to her election as president, she served in key administrative capacities, including as the vice-president of the association, and has advocated for actor welfare.

 Additional Information

• Association of Malayalam Movie Artists (AMMA):
• Establishment: Formed in 1994, AMMA is a prominent organization based in Kochi, Kerala, representing actors in Malayalam cinema.
• Background: The association faced major restructurings following the historic Justice Hema Committee Report, leading to resignations and calls for transparent governance.
• Other Entities:
• Ansiba Hassan: A popular Malayalam actress, director, and television anchor known for her notable role in the movie Drishyam.
• Cuckoo Parameswaran: A veteran Malayalam actress who has been actively involved in various socio-cultural forums and actors' welfare initiatives.
• Lakshmipriya: A well-known Malayalam film and television actress recognized for her comedic and supporting roles.

The correct answer is Igneous and metamorphic rocks.

Key Points

• The Peninsular Plateau is one of the oldest and most stable landmasses of the Earth, having been formed from the breaking and drifting of the ancient Gondwana land.
• It is primarily composed of ancient crystalline igneous and metamorphic rocks, which date back to the Pre-Cambrian era, representing the stable Indian Shield.
• The plateau is characterized by broad and shallow valleys and rounded hills, with its foundation consisting of Archean gneisses and schists that have undergone extensive transformation over billions of years.
• The region is divided into two broad categories: the Central Highlands (north of the Narmada River) and the Deccan Plateau (south of the river), both of which share this fundamental geological composition.
• The rocks in this region, such as Granite and Gneiss, are highly durable and have been subjected to significant tectonic and denudational processes over geological time.

 Additional Information

• Igneous Rocks:
• These are formed by the cooling of molten magma or lava. In the plateau, Plutonic rocks like Granite are prevalent in the Bundelkhand and Nilgiri regions.
• Basalt, a volcanic igneous rock, is the primary component of the Deccan Trap, formed by fissure eruptions during the Cretaceous period.
• Metamorphic Rocks:
• Rocks such as Schist, Gneiss, and Quartzite are common here, having been transformed from sedimentary or igneous precursors under intense heat and pressure.
• Sedimentary Rocks:
• While not the primary composition, they are found in basins like the Vindhyan and Cuddapah systems, containing Sandstone, Shale, and Limestone.

The correct answer is Rudramadevi.

Key Points

• Rudramadevi (reigned 1262−1289 CE) was one of the most prominent rulers of the Kakatiya dynasty, which was centered in Orugallu (present-day Warangal, Telangana).
• She was the daughter of King Ganapatideva; as he had no male heirs, he formally designated her as his successor through the Putrika ceremony, treating her as a son.
• To establish authority in a patriarchal society and gain the support of her nobles, she assumed the male name Rudradeva Maharaja in her inscriptions and often appeared in public in male attire.
• She successfully defended her kingdom against the Yadavas of Devagiri and the Chola empire, proving her military prowess despite initial opposition to a female ruler.
• The famous Venetian traveler Marco Polo visited the Kakatiya kingdom during the later years of her reign and left detailed accounts praising her administrative skills and the prosperity of her domain.

 Additional Information

• Kittur Chennamma:
• She was the Queen of Kittur, a princely state in Karnataka.
• She is renowned for leading an armed rebellion against the British East India Company in 1824 in defiance of the Doctrine of Lapse.
• Chand Bibi:
• She served as the Regent of Bijapur and later as the Regent of Ahmednagar.
• She is celebrated for her valiant defense of the Ahmednagar Fort against the Mughal army led by Emperor Akbar's son, Prince Murad, in the late 16th century.
• Rani Durgawati:
• She was the ruling Queen of Gondwana from 1550 to 1564, belonging to the Chandel dynasty.
• She martyred herself in battle while fighting the Mughal forces commanded by Asaf Khan to protect the autonomy of her kingdom.

The correct answer is Jharkhand.

Key Points

• The Jharkhand state government, under the leadership of Chief Minister Hemant Soren, officially launched the Mukhyamantri Maiya Samman Yojana (JMMSY) in August 2024.
• The scheme is designed to provide direct financial assistance of 1,000 rupees per month to eligible women, totaling an annual benefit of 12,000 rupees.
• It specifically targets women in the age group of 21 to 50 years, aiming to cover approximately 48 lakh beneficiaries across the state.
• To facilitate the registration process, the state government organized special camps at the Panchayat and Ward levels between August 3 and August 10, 2024.
• The core objective of the initiative is to enhance women empowerment, promote financial independence, and improve the overall nutritional and health status of women from economically weaker sections.
• The funds are disbursed directly into the Aadhar-linked bank accounts of the beneficiaries through the Direct Benefit Transfer (DBT) system to ensure transparency.

 Additional Information

• Eligibility Criteria:
• Applicants must be permanent residents of Jharkhand.
• The beneficiary must possess a valid Ration Card, such as the Antyodaya Anna Yojana (AAY), Priority Household (PHH), or White Ration Card.
• Women whose family members are Income Tax payers or regular government employees are excluded from the scheme benefits.
• Implementation Details:
• The Department of Women, Child Development, and Social Security is the nodal agency responsible for the execution of the Mukhyamantri Maiya Samman Yojana.
• The scheme is considered a significant social security initiative in the state, aiming to bridge the gender gap in financial resource management at the household level.
• The government allocated substantial funds in the state budget to sustain the recurring monthly expenditure required for this welfare project.

The correct answer is Ministry of New and Renewable Energy.

Key Points

• The Ministry of New and Renewable Energy (MNRE) is the nodal agency for the implementation of the National Green Hydrogen Mission, which was formally approved in January 2023.
• The Green Hydrogen Certification Scheme of India (GHCI) was introduced to establish a standardized framework for defining and certifying Green Hydrogen based on its carbon footprint.
• According to the notified standards, hydrogen is certified as 'Green' if its well-to-gate emission (including water treatment, electrolysis, and purification) does not exceed 2 kg CO2 equivalent per kg of hydrogen.
• The Bureau of Energy Efficiency (BEE), which operates under the Ministry of Power, is tasked with the accreditation of agencies for monitoring and verifying the production processes, while the overall scheme is governed by MNRE.
• The scheme is a critical component in achieving India's Energy Independence by 2047 and meeting Net Zero targets by 2070, ensuring that domestic production aligns with global trade requirements.

 Additional Information

• National Green Hydrogen Mission:
• The mission has a financial outlay of 19,744 crore and aims for a production capacity of 5 Million Metric Tonnes (MMT) per annum by 2030.
• It intends to reduce fossil fuel imports by over 1 lakh crore and attract investments worth 8 lakh crore.
• Ministry of Petroleum & Natural Gas:
• Responsible for the exploration, production, and distribution of natural gas and petroleum; it oversees the transition from Grey Hydrogen (fossil fuel-based) to cleaner variants in refineries.
• Ministry of Power:
• Focuses on the National Grid and Energy Conservation; it facilitates the transmission of renewable energy required for green hydrogen production through initiatives like Green Energy Open Access.
• Ministry of Environment, Forest & Climate Change:
• Handles Climate Action and environmental clearances; it monitors India's Nationally Determined Contributions (NDCs) under international climate treaties.

The correct answer is Jitendra Singh.

Key Points

• Union Minister of State (Independent Charge) for Science and Technology, Dr. Jitendra Singh, officially launched Srijanam in February 2025.
• Srijanam is India's first indigenous and fully automated Bio Medical Waste Treatment Plant, developed to enhance the safety and efficiency of hospital waste management.
• The plant is designed to handle various categories of biomedical waste, utilizing advanced technologies to ensure that hazardous materials are neutralized without significant human intervention.
• This initiative is a critical component of the Atmanirbhar Bharat mission, showcasing India's growing capability in high-end medical engineering and environmental technology.
• The project emphasizes the Waste-to-Wealth mission, transforming hazardous refuse into safer byproducts while maintaining strict environmental standards.

 Additional Information

• Srijanam Technical Features:
• The facility employs IoT-integrated systems for real-time monitoring of waste processing parameters, ensuring compliance with the Bio-Medical Waste Management Rules.
• It utilizes high-efficiency microwave-based sterilization or plasma pyrolysis techniques (depending on the specific module) to achieve 99.99% microbial disinfection.
• The development was spearheaded by the Department of Biotechnology (DBT) in collaboration with private sector partners and research institutions like IIT Delhi.
• Regulatory and Strategic Context:
• The launch supports the National Health Policy and the Swachh Bharat Mission, focusing on the safe disposal of infectious waste generated by the expanding healthcare infrastructure.
• By reducing reliance on imported waste treatment machinery, Srijanam helps lower the operational costs for Indian hospitals and clinics.

The correct answer is 6000.

Key Points

• As of August 2025, the official NASA Exoplanet Archive confirmed that the number of discovered alien worlds outside our solar system has surpassed the 6,000 mark.
• This milestone follows the previous record of 5,000 confirmed exoplanets, which was officially reached in March 2022, indicating a consistent discovery rate of several hundred planets per year.
• The primary driver for these discoveries is the Transiting Exoplanet Survey Satellite (TESS) mission, which has identified thousands of TESS Objects of Interest (TOIs) that were later validated as confirmed planets.
• A significant portion of these confirmations results from the legacy data of the Kepler Space Telescope and the K2 mission, processed using advanced Machine Learning and Artificial Intelligence algorithms to distinguish real planets from stellar noise.
• Confirmation of an exoplanet typically requires detection by at least two different methods or multiple observations by independent telescopes to verify its orbital period and mass.

 Additional Information

• NASA Missions and Facilities:
• James Webb Space Telescope (JWST): Launched in late 2021, it focuses on the atmospheric characterization of these 6,000 worlds, searching for biosignatures like methane and water vapor.
• Nancy Grace Roman Space Telescope: Expected to launch by 2027, it will use Gravitational Microlensing to find thousands more planets in the Milky Way.
• Detection Methodologies:
• Transit Method: Measures the dimming of a star; responsible for over 75 percent of all confirmed exoplanets.
• Radial Velocity: Detects the gravitational tug a planet exerts on its host star, causing a detectable Doppler shift.
• Planet Classifications:
• Super-Earths: Planets larger than Earth but smaller than Neptune; they are the most common type of planet found in the current catalog.
• Goldilocks Zone: The region around a star where conditions are favorable for liquid water, a key focus for researchers studying the latest discoveries.

The correct answer is 2009.

Key Points

• Chandrayaan-1 was India's inaugural lunar exploration mission, launched by the Indian Space Research Organisation (ISRO) to study the lunar surface.
• The spacecraft was launched on October 22, 2008, from the Satish Dhawan Space Centre (SDSC) at Sriharikota, Andhra Pradesh.
• The probe was launched using the Polar Satellite Launch Vehicle (PSLV-C11) and carried eleven scientific instruments intended for chemical, mineralogical, and photo-geologic mapping of the Moon.
• Communication with the Chandrayaan-1 spacecraft was unexpectedly lost at 01:30 IST on August 29, 2009, after the probe had completed over 3,400 orbits around the Moon.
• Following the loss of radio signals, the mission was officially declared concluded by ISRO on August 30, 2009, after approximately 312 days in operation.

 Additional Information

• Scientific Milestones:
• The mission's most significant achievement was the definitive discovery of water molecules (H₂O) and hydroxyl (OH) on the lunar surface.
• This discovery was confirmed by the Moon Mineralogy Mapper (M3), an imaging spectrometer provided by NASA.
• The Moon Impact Probe (MIP), an Indian-built instrument, successfully separated from the orbiter and struck the lunar surface near the Shackleton Crater on November 14, 2008.
• Post-Mission Developments:
• In March 2017, NASA scientists successfully relocated the derelict Chandrayaan-1 spacecraft in a polar orbit approximately 200 kilometers above the lunar surface using ground-based radar.
• The mission paved the way for subsequent lunar explorations, including Chandrayaan-2 in 2019 and the successful soft landing of Chandrayaan-3 in August 2023.

The correct answer is Gauhati.

Key Points

• In February 2025, a state-of-the-art 5G Lab was inaugurated at Gauhati University in Assam, marking a significant milestone for the telecommunication infrastructure in Northeast India.
• The laboratory was developed by the Centre for Development of Telematics (C-DOT), which is the premier Research and Development (R&D) organization under the Department of Telecommunications (DoT), Ministry of Communications, Government of India.
• This initiative is part of a broader national strategy to establish 100 5G labs across various academic institutions to foster innovation and develop indigenous 5G use-cases.
• The primary objective of the lab is to provide students, researchers, and startups with a platform to test and develop high-speed communication solutions, specifically targeting regional challenges in sectors like healthcare, agriculture, and disaster management.
• By integrating this technology into the academic curriculum, the university aims to enhance skill development and prepare the workforce for the evolving 6G and Internet of Things (IoT) landscape.

 Additional Information

• Centre for Development of Telematics (C-DOT):
• Established in August 1984, C-DOT has been instrumental in the indigenous design and development of digital exchanges and rural communication systems.
• It currently focuses on advanced technologies such as Quantum Key Distribution (QKD), Artificial Intelligence (AI), and Indigenous 5G Core.
• Gauhati University:
• Located in Jalukbari, Guwahati, it was established in 1948 and is the oldest university in North East India.
• It serves as a critical academic hub, supporting over 300 affiliated colleges and driving technological literacy in the state of Assam.
• Digital Transformation in Northeast:
• The inauguration of such labs is a core component of the 'Digital North East Vision', aimed at bridging the digital divide and promoting Atmanirbhar Bharat in the telecom sector.
• The facility is expected to boost local entrepreneurship by providing end-to-end 5G testbeds for testing network software and hardware.

The correct answer is Russia.

Key Points

• The S-400 Triumf, previously known as the S-300 PMU-3, is a mobile, surface-to-air missile (SAM) system designed by the Almaz Central Design Bureau of Russia.
• It was developed in the 1990s as an upgrade to the S-300 family and officially entered service with the Russian Armed Forces in April 2007.
• The system is designed to provide high-altitude air defense against a variety of aerial threats, including strategic bombers, electronic warfare aircraft, cruise missiles, and ballistic missiles.
• It is capable of tracking up to 100 targets simultaneously and can engage up to 36 targets at a time using four different missile types with ranges between 40 km and 400 km.
• The S-400 is considered one of the most dangerous operationally deployed modern long-range SAM systems in the world, surpassing the capabilities of many Western counterparts.

 Additional Information

• Geopolitical Impact:
• India signed a 5.43 billion dollar deal with Russia in October 2018 to acquire five regiments of the S-400 system to bolster its air defense against regional threats.
• China was the first foreign buyer of the S-400, signing the agreement in 2014 and receiving its first deliveries in 2018.
• Turkey, despite being a NATO member, procured the system, which led to significant diplomatic tension and its subsequent expulsion from the USA-led F-35 fighter jet program.
• Competitor Technologies:
• The USA utilizes the Patriot (MIM-104) and the Terminal High Altitude Area Defense (THAAD) systems for similar long-range defense purposes.
• Germany contributes to European air defense through the IRIS-T SLM and the Medium Extended Air Defense System (MEADS) project.
• China has developed its own indigenous long-range systems like the HQ-9, which incorporates elements from both Russian and Western technology.

The correct answer is Shanghai.

Key Points

• The Shanghai Cooperation Organisation (SCO) is a permanent intergovernmental international organization that was formally established on June 15, 2001.
• The founding ceremony took place in Shanghai, China, where the leaders of China, Kazakhstan, Kyrgyzstan, Russia, Tajikistan, and Uzbekistan signed the Declaration of Shanghai Cooperation Organisation.
• The organization emerged from the Shanghai Five mechanism, which was originally created in 1996 to ensure regional security and resolve border disputes between China and the former Soviet republics.
• The SCO Charter was subsequently signed during the Saint Petersburg Summit in June 2002 and entered into full legal force in September 2003.

 Additional Information

• Organizational Structure and Membership:
• While established in Shanghai, the permanent Secretariat of the SCO is located in Beijing, China.
• The Regional Anti-Terrorist Structure (RATS), which focuses on combating the 'three evils' of terrorism, separatism, and extremism, is headquartered in Tashkent, Uzbekistan.
• India and Pakistan officially joined the organization as full members during the Astana Summit in June 2017.
• Recent expansions include Iran, which became a full member in 2023, and Belarus, which joined in July 2024.
• The official working languages used within the organization are Chinese and Russian.

The correct answer is London.

Key Points

• The 2012 Summer Olympic Games, officially known as the Games of the XXX Olympiad, were held in London, United Kingdom, from July 27 to August 12, 2012.
• With this edition, London became the first city in history to host the modern Olympic Games three times, having previously hosted them in 1908 and 1948.
• The majority of the events took place in the purpose-built Olympic Park in Stratford, East London, which included the Olympic Stadium, the Aquatics Centre, and the London Velopark.
• The games saw the participation of 204 National Olympic Committees and featured the debut of women's boxing, ensuring that women competed in every sport on the Olympic program for the first time.
• The official motto of the London 2012 games was 'Inspire a Generation', aimed at creating a lasting sporting legacy worldwide.
• Notable milestones included Michael Phelps becoming the most decorated Olympian of all time and Usain Bolt winning gold in the 100m, 200m, and 4×100m relay.

 Additional Information

• Paris:
• The city hosted the Summer Olympics in 1900 and 1924, and was the host for the 2024 Olympic Games. It was the runner-up in the bidding process for the 2012 edition.
• Sydney:
• This Australian city hosted the 2000 Summer Olympics, which were widely acclaimed for their organization and the significant role of volunteerism.
• Beijing:
• The capital of China hosted the 2008 Summer Olympics. By hosting the 2022 Winter Olympics, it became the first city to host both the Summer and Winter editions of the games.
• India's Achievement in 2012:
• India won a total of six medals in London, its best tally until the 2020 Tokyo Games. Medallists included Sushil Kumar (Silver), Vijay Kumar (Silver), Saina Nehwal (Bronze), Mary Kom (Bronze), Gagan Narang (Bronze), and Yogeshwar Dutt (Bronze).

The correct answer is 3000 m steeplechase.

Key Points

• The 3000 m steeplechase is a specialized obstacle race in athletics that is conducted exclusively on a 400-meter synthetic track inside a stadium.
• It is categorized as a track event because it requires permanent infrastructure, specifically a water jump pit that is typically built into the inner or outer curve of the track.
• During the race, athletes must clear a total of 28 fixed barriers and 7 water jumps; the height of the hurdles is 0.914 meters for men and 0.762 meters for women.
• Standardization of the track surface is crucial for the 3000 m steeplechase to ensure uniform safety and timing, distinguishing it from variable road surfaces used for outside events.

 Additional Information

• Marathon:
• This is a long-distance road race with an official distance of 42.195 kilometers (26.2 miles).
• It is held on public roads and urban streets, often starting and finishing in different locations, although many major championships finish inside a stadium for ceremonial purposes.
• Race Walking (20 km and 50 km):
• Both the 20 km walking and 50 km walking events are classified as road events by World Athletics.
• These competitions take place on road circuits, usually consisting of 1 km or 2 km loops on flat terrain outside the main stadium arena.
• The 50 km race walk was a long-standing Olympic event for men until it was removed after the Tokyo 2020 Olympics to maintain gender balance and modernize the athletic program.
• In these events, athletes must maintain visible contact with the ground at all times to avoid disqualification by judges stationed along the course.

The correct answer is 15A.

Key Points

• In domestic electrical installations, circuits are generally divided into two main categories based on the current-carrying capacity of the wires and the power consumption of the devices.
• A 15 Ampere (15A) circuit is specifically designed for high-power appliances such as geysers, air conditioners, electric ovens, and air coolers that consume significant electrical energy.
• The relationship between power, voltage, and current is given by the formula P = V × I. In India, the standard domestic supply voltage is 220V.
• For an appliance like a geyser with a power rating of 3000 Watts, the current drawn is calculated as I = 3000 / 220, which is approximately 13.63A. Therefore, a 15A socket is required to safely handle this load.
• Using a lower rating, such as the standard 5A circuit meant for bulbs and fans, for high-load appliances would lead to overheating of the wires and potential electrical fires.

 Additional Information

• Safety Devices in Household Circuits:
• Miniature Circuit Breaker (MCB): It is an electromechanical device that automatically switches off the circuit during overload or short-circuit conditions to prevent damage.
• Fuse: A safety component consisting of a wire with a low melting point. It melts and breaks the circuit if the current exceeds a specific threshold, protecting the home from surges.
• Earthing: For high-power appliances with metallic bodies, a third wire (Earth wire) is used. It provides a low-resistance path to the ground for leakage current, preventing electric shocks to users.
• Standard Wiring Color Codes (India):
• Live Wire: Traditionally Red, now frequently Brown in newer installations.
• Neutral Wire: Traditionally Black, now often Blue.
• Earth Wire: Typically Green or Yellow-Green.

The correct answer is Uttarakhand.

Key Points

• Hurkiya Baul is a traditional folk song and dance form native to the Kumaon region of Uttarakhand.
• The name is derived from the Hurka, a small percussion instrument similar to a Damaru, which is played by the lead singer while performing.
• This folk form is intrinsically linked to agricultural activities, specifically performed during the collective transplantation of paddy and maize in the terraced fields of the Himalayan foothills.
• The performance serves as a narrative medium where the lead singer, the Hurkiya, recites heroic ballads known as Gathas, which detail the valor of legendary kings and local folk heroes.
• It acts as a source of motivation and entertainment for the farmers, helping them synchronize their rhythmic physical labor with the musical beats of the drum.

 Additional Information

• Bihar
• Prominent folk songs include Sohar, which is sung to celebrate the birth of a child, and Bideshiya, which focuses on the pain of migration.
• The state is also known for Chaita and Kajari, which are seasonal songs related to the agricultural cycle.
• West Bengal
• Known for the Baul tradition, a group of mystic minstrels whose music is recognized as a UNESCO Masterpiece of the Oral and Intangible Heritage of Humanity.
• Other significant forms include Bhatiali (sung by boatmen) and Gombhira.
• Mizoram
• Features traditional songs like Chailam and Khuallam, which are often accompanied by the Cheraw (bamboo dance).
• These are typically performed during the Chapchar Kut festival, marking the completion of the Jhum operation.

The correct answer is Neither I nor II.

Key Points

• Cerium (Ce), with the atomic number 58, is the most abundant of the rare earth elements and belongs to the lanthanide series. It is widely used in catalytic converters for automobiles and as a polishing agent for glass. Since it is a rare earth element, it does not satisfy the 'NOT' condition of the question. Hence, statement I is incorrect.
• Europium (Eu) is a chemical element with the atomic number 63 and is recognized as the most reactive member of the lanthanide group. It plays a critical role in the electronics industry, particularly in the production of red and blue phosphors for television and computer screens. As it is fundamentally classified as a rare earth element, it fails the negative criteria. Hence, statement II is incorrect.
• The Rare Earth Elements (REEs) group includes 17 elements: the 15 lanthanides plus Scandium and Yttrium. Since both provided options, Cerium and Europium, are members of this specific group, neither can be excluded from the classification of rare earth elements. Hence, the selection 'Neither I nor II' is the correct answer.

 Additional Information

• Classification of Rare Earth Elements (REEs):
• The Lanthanide Series: These are the 15 metallic elements from Lanthanum (57) to Lutetium (71) in the Periodic Table.
• Scandium (21) and Yttrium (39): These are included because they tend to occur in the same ore deposits as lanthanides and exhibit similar chemical properties.
• Light Rare Earth Elements (LREEs): This subgroup includes elements from Lanthanum to Samarium, including Cerium and Praseodymium.
• Heavy Rare Earth Elements (HREEs): This subgroup includes elements from Europium to Lutetium, as well as Yttrium, which are typically less common and more valuable.
• Economic and Industrial Importance:
• Magnets: Elements like Neodymium and Dysprosium are essential for high-performance magnets in wind turbines and electric motors.
• Defense Technology: REEs are vital for guidance systems, lasers, and radar components due to their unique magnetic and luminescent properties.
• Clean Energy: They are indispensable for the transition to green energy, featuring heavily in rechargeable batteries and energy-efficient lighting.

Shortcut Trick

Solve using the BODMAS rule by processing Multiplication and Division first.

27 × 2 = 54 and 44 ÷ 2 = 22.

Group positive and negative values: (91 + 54 + 16 + 22) − (38 + 31).

183 − 69 = 114.

∴ The correct answer is 114.

Alternate Method

Given:

Expression = 91 − 38 + 27 × 2 + (16) + 44 ÷ 2 − 31

Method Used:

Apply the BODMAS rule (Brackets, Of, Division, Multiplication, Addition, Subtraction).

Calculations:

⇒ Expression = 91 − 38 + 54 + 16 + 22 − 31

⇒ Expression = 91 + 54 + 16 + 22 − 38 − 31

⇒ Expression = 183 − 69

⇒ Expression = 114

∴ The correct answer is 114.

Additional Information

BODMAS Rule

It defines the order of operations: Brackets (), Of (multiplication), Division (÷), Multiplication (×), Addition (+), and Subtraction (−).

Grouping Technique

In long addition/subtraction, group all positive terms together and all negative terms together to minimize errors.

Mental Math Tip

Convert complex divisions into simple fractions or multiples to speed up the Simplification process.

Shortcut Trick

The Product of two numbers = HCF × LCM.

Product = 6 × 36 = 216.

Given Sum = 30. We need factors of 216 that add up to 30.

Checking options: 12 + 18 = 30 and 12 × 18 = 216.

∴ The correct answer is 12 and 18.

Alternate Method

Let the two numbers be a and b.

Given: HCF = 6, LCM = 36, a + b = 30.

Using the property: a × b = HCF × LCM

⇒ a × b = 6 × 36 = 216

⇒ (a − b)² = (a + b)² − 4ab

⇒ (a − b)² = (30)² − 4(216)

⇒ (a − b)² = 900 − 864 = 36

⇒ a − b = √36 = 6

⇒ Adding (a + b = 30) and (a − b = 6): 2a = 36 ⇒ a = 18

⇒ Subtracting: 2b = 24 ⇒ b = 12

∴ The correct answer is 12 and 18.

Additional Information

Fundamental Property of HCF and LCM

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

HCF as a Factor

If the HCF of two numbers is h, the numbers can be represented as hx and hy, where x and y are co-prime integers (HCF of x and y is 1).

LCM in terms of HCF

Using the representation above, LCM = h × x × y. This is very useful in solving ratio-based HCF/LCM problems.

Shortcut Trick

Equalize decimal places in the numerator and denominator: √(0.1225 / 0.2500).

Simplify the fraction by removing the decimals: √(1225 / 2500).

Divide both values by 25: √(49 / 100).

Calculate the square root: 7 / 10 = 0.7.

∴ The correct answer is 0.7.

Alternate Method

Given: √(0.1225 / 0.25)

Formula: √(a / b) = √a / √b

⇒ √(0.1225 ÷ 0.25) ⇒ √(1225 × 10⁻⁴ ÷ (25 × 10⁻²)) ⇒ √((1225 ÷ 25) × 10⁻⁴⁺²) ⇒ √(49 × 10⁻²) ⇒ √0.49 ⇒ 0.7

∴ The correct answer is 0.7.

Additional Information

Square Root of Decimals

When finding the square root of a decimal, the number of digits after the decimal point in the result is exactly half of that in the original number (e.g., √0.0001 = 0.01).

Squares Ending in 25

Any number ending in 5, when squared, results in a number ending in 25. For example, (35)² = (3 × 4) followed by 25 = 1225.

Fraction Simplification

Always try to simplify radicands by finding common factors or converting decimals to powers of 10 before applying the square root operation.

Shortcut Trick

Identify the expression in the form [(a + b)² + (a − b)²] / (a² + b²).

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

The expression simplifies to 2(a² + b²) / (a² + b²) = 2.

Since the result is a constant, the specific values 4.2 and 3.8 do not change the final answer.

∴ The correct answer is 2.

Alternate Method

Given:

Expression = ((4.2 + 3.8)² + (4.2 − 3.8)²) / (4.2 × 4.2 + 3.8 × 3.8)

Formula Used:

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab + b²

Calculations:

⇒ Let a = 4.2 and b = 3.8.

⇒ Numerator = (4.2 + 3.8)² + (4.2 − 3.8)²

⇒ Numerator = (8.0)² + (0.4)²

⇒ Numerator = 64 + 0.16 = 64.16

⇒ Denominator = (4.2 × 4.2) + (3.8 × 3.8)

⇒ Denominator = 17.64 + 14.44 = 32.08

⇒ Final Value = 64.16 ÷ 32.08

⇒ Final Value = 2

∴ The correct answer is 2.

Additional Information

Difference of Squares of Sum and Difference

The identity (a + b)² − (a − b)² = 4ab is frequently used in simplification and algebra problems.

Standard Expansion Identities

(a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b² are the foundation for more complex quadratic reductions.

Sum of Squares

a² + b² can be expressed as [(a + b)² + (a − b)²] ÷ 2, which is the direct derivation for the given question.

Shortcut Trick

Solve for square roots first: √81 = 9, √9 = 3, and √36 = 6.

Evaluate x using BODMAS: 9 ÷ 3 + 6 = 3 + 6 = 9.

The required value is 2x = 2 × 9 = 18.

∴ The correct answer is 18.

Alternate Method

Given: x = √81 ÷ √9 + √36

Formula Used: Order of operations (BODMAS) where Division is performed before Addition.

⇒ x = 9 ÷ 3 + 6

⇒ x = 3 + 6

⇒ x = 9

To find the value of 2x:

⇒ 2x = 2 × 9

⇒ 2x = 18

∴ The correct answer is 18.

Additional Information

BODMAS Rule

This rule specifies the precedence of operations: Brackets, Orders (powers/roots), Division and Multiplication, followed by Addition and Subtraction.

Square Roots of Perfect Squares

Knowing perfect squares helps in quick simplification (e.g., 6² = 36, 9² = 81).

Linear Expressions

When a variable x is solved, any expression like nx is calculated by multiplying the constant n with the found value of x.

Shortcut Trick

Identify prime numbers between 40 and 50 directly.

The numbers are 41, 43, and 47.

Sum = 41 + 43 + 47 = 131.

∴ The correct answer is 131.

Alternate Method

Given: Range of numbers from 40 to 50.

Step 1: List all integers between 40 and 50.

⇒ Integers: 41, 42, 43, 44, 45, 46, 47, 48, 49.

Step 2: Test each number for primality (divisibility by 2, 3, 5, 7, etc.).

⇒ 41: Not divisible by 2, 3, 5, or 7. (Prime)

⇒ 42: Even number. (Composite)

⇒ 43: Not divisible by 2, 3, 5, or 7. (Prime)

⇒ 44: Even number. (Composite)

⇒ 45: Divisible by 5. (Composite)

⇒ 46: Even number. (Composite)

⇒ 47: Not divisible by 2, 3, 5, or 7. (Prime)

⇒ 48: Even number. (Composite)

⇒ 49: Divisible by 7 (7 × 7). (Composite)

Step 3: Calculate the sum of the identified primes.

⇒ Sum = 41 + 43 + 47

⇒ Sum = 131

∴ The correct answer is 131.

Additional Information

Prime Numbers

A prime number is a natural number greater than 1 that has exactly two distinct factors: 1 and itself. The smallest prime number is 2 (the only even prime).

Composite Numbers

A composite number has more than two factors. For example, 49 is composite because its factors are 1, 7, and 49.

Primes up to 100

There are 25 prime numbers between 1 and 100. Identifying them often involves checking divisibility by primes up to √n.

Shortcut Trick

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

Here, a = 1 and b = √5

⇒ (1 + √5)² − (1 − √5)² = 4 × 1 × √5 = 4√5

⇒ 4√5 − 14√5 = −10√5

∴ The correct answer is −10√5.

Alternate Method

Given: (1 + √5)² − (1 − √5)² − 14√5

Formula Used: (a ± b)² = a² + b² ± 2ab

⇒ [(1)² + (√5)² + 2 × 1 × √5] − [(1)² + (√5)² − 2 × 1 × √5] − 14√5

⇒ [1 + 5 + 2√5] − [1 + 5 − 2√5] − 14√5

⇒ (6 + 2√5) − (6 − 2√5) − 14√5

⇒ 6 + 2√5 − 6 + 2√5 − 14√5

⇒ 4√5 − 14√5

⇒ −10√5

∴ The correct answer is −10√5.

Additional Information

Algebraic Identities

The identity (a + b)² − (a − b)² = 4ab is used to quickly find the difference between the squares of conjugate sums.

Sum of Conjugate Squares

Another useful related identity is (a + b)² + (a − b)² = 2(a² + b²).

Square of a Binomial

The base expansion for any binomial is (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Shortcut Trick

To find the sum of n natural numbers from 1 to 35, use the direct formula: [n × (n + 1)] ÷ 2.

Here, n = 35.

Required Sum = (35 × 36) ÷ 2 = 35 × 18 = 630.

∴ The correct answer is 630.

Alternate Method

Given:

The series is an Arithmetic Progression (AP): 1, 2, 3, ..., 35.

Formula Used:

Sum of an AP, S_n = (n ÷ 2) × (a + l), where a is the first term, l is the last term, and n is the total number of terms.

Calculations:

⇒ First term (a) = 1

⇒ Last term (l) = 35

⇒ Total terms (n) = 35

⇒ S₃₅ = (35 ÷ 2) × (1 + 35)

⇒ S₃₅ = 17.5 × 36

⇒ S₃₅ = 630

∴ The correct answer is 630.

Additional Information

Sum of first n odd numbers

The sum of the first n odd natural numbers (1 + 3 + 5 + ... + (2n − 1)) is equal to n².

Sum of first n even numbers

The sum of the first n even natural numbers (2 + 4 + 6 + ... + 2n) is equal to n × (n + 1).

Sum of squares of first n natural numbers

The sum of squares (1² + 2² + ... + n²) is given by the formula [n × (n + 1) × (2n + 1)] ÷ 6.

Shortcut Trick

A number is divisible by 8 if its last three digits are divisible by 8.

The last three digits of 73P2 are 3P2.

Checking the options: 302 ÷ 8 = 37.75 (No), 312 ÷ 8 = 39 (Yes), 352 ÷ 8 = 44 (Yes), 392 ÷ 8 = 49 (Yes).

Only P = 0 does not satisfy the condition.

∴ The correct answer is 0.

Alternate Method

Given: The number is 73P2 and it is divisible by 8.

Formula Used: Divisibility rule of 8 → The last 3 digits of a number must be divisible by 8.

⇒ The last three digits are 3P2.

⇒ For P = 0, last three digits = 302. 302 ÷ 8 = 37.75 (Remainder = 6, not divisible).

⇒ For P = 1, last three digits = 312. 312 ÷ 8 = 39 (Remainder = 0, divisible).

⇒ For P = 5, last three digits = 352. 352 ÷ 8 = 44 (Remainder = 0, divisible).

⇒ For P = 9, last three digits = 392. 392 ÷ 8 = 49 (Remainder = 0, divisible).

⇒ Since 302 is the only value not divisible by 8, P cannot be 0.

∴ The correct answer is 0.

Additional Information

Divisibility Rule of 4

A number is divisible by 4 if its last two digits are divisible by 4.

Divisibility Rule of 16

A number is divisible by 16 if its last four digits are divisible by 16.

General 2ⁿ Rule

A number is divisible by 2ⁿ if its last n digits are divisible by 2ⁿ.

Shortcut Trick

Identify the Pythagorean triplet with a hypotenuse of 17: (8, 15, 17).

Check if these dimensions satisfy the Area condition: 15 × 8 = 120 cm² (Correct).

Calculate the Perimeter = 2 × (Length + Breadth).

⇒ 2 × (15 + 8) = 2 × 23 = 46 cm.

∴ The correct answer is 46 cm.

Alternate Method

Given: Area (L × W) = 120 cm², Diagonal (d) = 17 cm.

Formula Used: L² + W² = d² and (L + W)² = L² + W² + 2LW.

⇒ L² + W² = 17² = 289

⇒ 2 × (L × W) = 2 × 120 = 240

⇒ (L + W)² = (L² + W²) + 2LW

⇒ (L + W)² = 289 + 240 = 529

⇒ L + W = √529 = 23 cm

⇒ Perimeter = 2(L + W) = 2 × 23 = 46 cm.

∴ The correct answer is 46 cm.

Additional Information

Pythagorean Triplets

Sets of three positive integers a, b, and c such that a² + b² = c². Common triplets include (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Perimeter and Area Relationship

For a rectangle, the square of the sum of sides relates to the diagonal and area by the equation: (Sum of sides)² = Diagonal² + 2 × Area.

Rectangle Properties

A rectangle is a quadrilateral with four right angles. Its diagonals are equal in length and bisect each other.

Shortcut Trick

The difference between the averages of two pairs with a common element (m) is always half the difference between the distinct elements (l and n).

Shortcut formula: |l − n| = 2 × |Difference in averages|

⇒ |l − n| = 2 × 23

⇒ |l − n| = 46

∴ The correct answer is 46.

Alternate Method

Given:

Average of l and m = (l + m) ÷ 2

Average of m and n = (m + n) ÷ 2

Difference between these averages = 23

Calculations:

⇒ [(l + m) ÷ 2] − [(m + n) ÷ 2] = 23

⇒ (l + m − m − n) ÷ 2 = 23

⇒ (l − n) ÷ 2 = 23

⇒ l − n = 23 × 2

⇒ l − n = 46

∴ The correct answer is 46.

Additional Information

Average of Grouped Terms

The average of a set of n numbers is the sum of all numbers divided by n. Sum = Average × n.

Effect of Constant Difference

If the difference between the sums of two groups is d, and both groups have the same number of elements k, the difference between their averages is d ÷ k.

Arithmetic Progression Average

For any Arithmetic Progression (AP), the average is exactly equal to the middle term (if n is odd) or the mean of the two middle terms (if n is even).

Shortcut Trick

Profit % = 20% = 1/5 (where 5 is CP and 1 is Profit)

Selling Price (SP) = CP + Profit = 5 + 1 = 6 units

Given: 6 units = ₹2400 ⇒ 1 unit = ₹400

Cost Price (CP) = 5 units = 5 × ₹400 = ₹2000

∴ The correct answer is ₹2000.

Alternate Method

Given:

Selling Price (SP) of the article = ₹2400

Profit Percentage = 20%

Formula Used:

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

Calculations:

⇒ CP = [2400 × 100] ÷ [100 + 20]

⇒ CP = 240000 ÷ 120

⇒ CP = 2000

∴ The correct answer is ₹2000.

Additional Information

Profit and Loss Basics

Profit = SP − CP, when SP > CP. Loss = CP − SP, when CP > SP.

Loss Percentage Formula

Loss % = (Loss ÷ CP) × 100. If there is a loss, CP = [SP × 100] ÷ [100 − Loss %].

Marked Price and Discount

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

Shortcut Trick

Identify the ratio of B to A as 9X : 4X = 9 : 4.

Apply the fraction-to-percentage conversion: 9/4 × 100.

Since 1/4 is 25%, 9 × 25% = 225%.

∴ The correct answer is 225%.

Alternate Method

Given: A = 4X and B = 9X.

Formula Used: Percentage = (Value ÷ Base) × 100

⇒ Required Percentage = (B ÷ A) × 100

⇒ Percentage = (9X ÷ 4X) × 100

⇒ Percentage = (9 ÷ 4) × 100

⇒ Percentage = 2.25 × 100

⇒ Percentage = 225%

∴ The correct answer is 225%.

Additional Information

Base Identification

In the phrase 'B is what percent of A', the quantity following 'of' (which is A) is always the base (denominator).

Percentage vs. Percentage More

If B is 225% of A, then B is 125% more than A. Percentage More = ((B−A)/A) × 100.

Reciprocal Percentage

To find A as a percent of B: (4/9) × 100 ≈ 44.44%.

Shortcut Trick

Convert all units to cm: True Height = 470 cm and Estimated Height = 352 cm.

Error = 470 − 352 = 118 cm.

Error % = (Error / Original Value) × 100 = (118 / 470) × 100.

Approximation: 118 / 470 ≈ 1/4 = 25% (Exact calculation: 25.106...%).

∴ The correct answer is 25.11%.

Alternate Method

Given:

True Height = 4 m 70 cm = (4 × 100) + 70 = 470 cm

Estimated Height = 3 m 52 cm = (3 × 100) + 52 = 352 cm

Formula:

Error Percentage = (Absolute Error / True Value) × 100

Calculations:

⇒ Absolute Error = True Value − Estimated Value

⇒ Absolute Error = 470 − 352 = 118 cm

⇒ Error % = (118 / 470) × 100

⇒ Error % = 1180 / 47

⇒ Error % ≈ 25.10638...

⇒ Error % ≈ 25.11%

∴ The correct answer is 25.11%.

Additional Information

Absolute Error

It is the numerical difference between the measured value and the true value, expressed as |True Value − Measured Value|.

Relative Error

It is the ratio of the absolute error to the true value of the quantity being measured: Relative Error = Absolute Error / True Value.

Unit Conversion

Always ensure all measurements are in the same unit before calculation (1 meter = 100 cm).

Percentage Change

The formula for percentage increase or decrease is (Difference / Original Value) × 100.

Shortcut Trick

Ratio of Cost Price (CP) to Selling Price (SP) is the inverse of their percentage coefficients.

CP : SP = 30 : 40 = 3 : 4

Profit = 4 − 3 = 1 unit

Profit % = (1 / 3) × 100 = 33.33%

∴ The correct answer is 33.33%.

Alternate Method

Given:

40% of Cost Price (CP) = 30% of Selling Price (SP)

Formula Used:

Profit % = [(SP − CP) / CP] × 100

⇒ (40 / 100) × CP = (30 / 100) × SP

⇒ 40 × CP = 30 × SP

⇒ CP / SP = 30 / 40

⇒ CP / SP = 3 / 4

⇒ Let CP = 3 units and SP = 4 units.

⇒ Profit = SP − CP = 4 − 3 = 1 unit

⇒ Profit Percentage = (1 / 3) × 100

⇒ Profit % = 33.33%

∴ The correct answer is 33.33%.

Additional Information

Profit and Loss Base

Profit % and Loss % are always calculated on the Cost Price (CP) unless the question specifically mentions the Selling Price.

Relationship between CP and SP

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

Marked Price and Discount

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

Shortcut Trick

Remaining food is sufficient for 1000 men for 50 days (60 − 10).

New strength = 1000 − 500 = 500 men.

Apply M₁D₁ = M₂D₂ logic on the remaining food.

1000 × 50 = 500 × D₂ ⇒ D₂ = 100 days.

∴ The correct answer is 100 days.

Alternate Method

Given:

Initial men (M₁) = 1000

Initial days = 60

Time passed = 10 days

Men left = 500

Total initial food units = 1000 × 60 = 60,000 units

Food consumed in 10 days = 1000 × 10 = 10,000 units

⇒ Remaining food = 60,000 − 10,000 = 50,000 units

⇒ Remaining men = 1000 − 500 = 500 men

⇒ Number of days = Remaining food ÷ Remaining men

⇒ Days = 50,000 ÷ 500

⇒ Days = 100 days

∴ The correct answer is 100 days.

Additional Information

Chain Rule Formula

For work and time problems, the relation is M₁D₁H₁/W₁ = M₂D₂H₂/W₂, where M is men, D is days, H is hours, and W is work.

Inverse Proportion

When the amount of food (work) is constant, the number of men is inversely proportional to the number of days (M ∝ 1/D).

Food Provision Logic

Always calculate the remaining resource first and then divide by the new capacity to find the extended duration.

Shortcut Trick

Ratio of Efficiency (and Wages) of X : Y : Z = 1/10 : 1/15 : 1/30.

Multiply by LCM (30) ⇒ 3 : 2 : 1.

Given X share (3 units) = ₹8000.

Combined share of Y and Z = 2 + 1 = 3 units.

Since 3 units = ₹8000, then Y + Z share is also ₹8000.

∴ The correct answer is ₹8000.

Alternate Method

Given: Days taken by X = 10, Y = 15, Z = 30. Wage of X = ₹8000.

Formula Used: Efficiency = Total Work ÷ Time. Wages are distributed in the ratio of efficiency when time is constant.

⇒ Ratio of efficiency X : Y : Z = 3 : 2 : 1

⇒ Let efficiency (wage share) be 3k, 2k, and 1k.

⇒ 3k = ₹8000

⇒ Wage of Y and Z = 2k + 1k = 3k

⇒ Total wage of Y and Z = ₹8000

∴ The correct answer is ₹8000.

Additional Information

Wage Distribution Rule

When workers work for the same duration, wages are proportional to their efficiency. If time varies, Wage ∝ Efficiency × Time.

Inverse Relation of Time and Efficiency

Efficiency is inversely proportional to the time taken to complete the work (E = 1/T).

Combined Work Formula

If X and Y do work in 'a' and 'b' days, together they take (a × b) ÷ (a + b) days.

Shortcut Trick

When Distance is constant, Speed is inversely proportional to Time (S ∝ 1/T).

Ratio of Speeds of A and B = 14 : 38 = 7 : 19.

Ratio of Time taken (A : B) = Inverse of Speed Ratio = 19 : 7.

∴ The correct answer is 19 : 7.

Alternate Method

Given:

Speed of A (S_A) = 14 km/hr

Speed of B (S_B) = 38 km/hr

Formula Used:

Time = Distance ÷ Speed

Calculations:

Let the common distance be D km.

⇒ Time taken by A (T_A) = D ÷ 14

⇒ Time taken by B (T_B) = D ÷ 38

⇒ Required Ratio = T_A : T_B

⇒ Required Ratio = (D/14) : (D/38)

⇒ Required Ratio = 38 : 14

⇒ Required Ratio = (38 ÷ 2) : (14 ÷ 2) = 19 : 7

∴ The correct answer is 19 : 7.

Additional Information

Inverse Relationship of Speed and Time

For a fixed distance, if the speed ratio is x : y, then the time ratio will be y : x.

Average Speed Formula

When a person covers equal distances at speeds x and y, the average speed is given by [2 × x × y] ÷ [x + y].

Relative Speed

Relative speed is S₁ − S₂ for objects moving in the same direction and S₁ + S₂ for objects moving in opposite directions.

Shortcut Trick

Relative Speed when moving in opposite directions = Total Distance ÷ Time

Relative Speed = 500 ÷ 5 = 100 km/hr

Speed of H = Relative Speed − Speed of G

Speed of H = 100 − 60 = 40 km/hr

∴ The correct answer is 40 km/hr.

Alternate Method

Given:

Total distance between P and Q = 500 km

Meeting time = 5 hours

Speed of G = 60 km/hr

Formula Used:

Distance = Speed × Time

Calculations:

⇒ Distance covered by G in 5 hours = Speed × Time

⇒ Distance (G) = 60 × 5 = 300 km

⇒ Since they meet at S, the remaining distance is covered by H.

⇒ Distance covered by H = Total Distance − Distance (G)

⇒ Distance (H) = 500 − 300 = 200 km

⇒ Speed of H = Distance (H) ÷ Time

⇒ Speed of H = 200 ÷ 5 = 40 km/hr

∴ The correct answer is 40 km/hr.

Additional Information

Relative Speed in Opposite Direction

When two objects move towards each other, their relative speed is the sum of their individual speeds: V_rel = S₁ + S₂.

Relative Speed in Same Direction

When two objects move in the same direction, their relative speed is the difference between their individual speeds: V_rel = |S₁ − S₂|.

Meeting Point Logic

If two objects start at the same time and meet, the time taken by both to reach the meeting point is identical.

Shortcut Trick

Let the Marked Price (X) be 100 units.

Purchase Price (Y) = 100 − 40% = 60 units.

Selling Price (Z) = 60 + 30% of 60 = 60 + 18 = 78 units.

Required Ratio Z : X = 78 : 100 = 39 : 50.

∴ The correct answer is 39 : 50.

Alternate Method

Given:

Marked Price = X

Discount = 40% on X

Purchase Price (Y) = X − (40/100) × X = 0.6X

Selling Price (Z) = Y + 30% of Y = 1.3Y

Calculations:

⇒ Y = 0.6X

⇒ Z = 1.3 × (0.6X)

⇒ Z = 0.78X

⇒ Z / X = 0.78

⇒ Z / X = 78 / 100

⇒ Z / X = 39 / 50

⇒ Z : X = 39 : 50

∴ The correct answer is 39 : 50.

Additional Information

Marked Price and Discount

Selling Price = Marked Price × (100 − Discount%) ÷ 100. Discount is always calculated on the Marked Price.

Profit Percentage

Selling Price = Cost Price × (100 + Profit%) ÷ 100. Profit is generally calculated on the Cost Price (or Purchase Price).

Successive Percentage Change

When a value is changed by a% and then by b%, the net change is [a + b + (a × b)/100]%. For discounts, use negative values.

The correct answer is 'vented her spleen'.

Key Points

• The idiom 'vent one’s spleen' means to express or release one’s anger, resentment, or bitterness about something. (अपना गुस्सा या नाराजगी निकालना)
• In the given sentence, Suhani was reprimanded (scolded) by Raghubeer, and as a result, she took out that frustration on her son.
• The other options like 'rented her spleen', 'threw her liver', and 'fried her liver' are incorrect and do not exist as standard English idioms.

Therefore, the correct answer is 'Option 1'.

Complete Sentence: Suhani vented her spleen on her son after being reprimanded by Raghubeer.

Additional Information

• The origin of this idiom dates back to medieval medicine, where the spleen was believed to be the organ responsible for producing anger and malice (one of the four humors).
• Similar expressions include 'letting off steam' or 'giving vent to' one’s feelings.

The correct answer is: smile.

Key Points

• The word 'grin' refers to a broad smile, often one that shows the teeth, indicating high spirits, amusement, or satisfaction. (दाँत निकालकर मुस्कुराना)
• Example: He gave a sheepish grin when he was caught playing a prank.
• 'Smile' is a facial expression characterized by the upward curving of the corners of the mouth, typically used to express happiness, pleasure, or approval. (मुस्कान)
• Example: She had a kind smile that put everyone at ease.
• Hence, we can infer that the most appropriate synonym of 'grin' is 'smile'.

Therefore, the correct answer is: smile.

Additional Information

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

• Cry (रोना): To shed tears as an expression of distress, pain, or sorrow.
• Example: The child began to cry when he fell down in the park.
• Shout (चिल्लाना): To speak or call out suddenly and loudly, often to express strong emotion or to be heard at a distance.
• Example: He had to shout to get the attention of the lifeguard.
• Yawn (जम्हाई लेना): An involuntary act of opening the mouth wide and inhaling deeply, usually due to tiredness or boredom.
• Example: I couldn't help but yawn during the long and tedious meeting.

The correct answer is indigenous.

Key Points

• The word indigenous is the correct spelling of the term, which is frequently misspelled as 'indiginous' or 'indigenious' in competitive examinations.
• The word indigenous refers to species, ecosystems, or people originating or occurring naturally in a particular place or native to a specific region.
• The word fauna is spelled correctly in the sentence and refers to all of the animal life present in a particular region or time.
• The word flora is spelled correctly in the sentence and refers to all of the plant life present in a particular region or time.
• The word intervention is spelled correctly in the sentence and refers to the action of interposing, interfering, or intervening in order to alter an outcome.

 Additional Information

• A detailed breakdown of the related scientific and ecological terms includes:
• Fauna:
• Derived from the name of the Roman goddess of fertility and earth, Fauna, or the forest god Faunus.
• In ecology, it is paired with flora to describe the entire biodiversity of a specific habitat.
• Flora:
• Derived from the Roman goddess of flowers, Flora.
• It represents the plant kingdom and is essential for studying botany and ecological distribution.
• Intervention:
• Derived from the Latin word 'intervenire', meaning 'to come between'.
• In developmental and environmental projects, minimal intervention is a key principle to protect sensitive ecological zones.

The correct answer is: opulance.

Key Points

• The word 'opulance' is the misspelt word among the given options. The correct spelling is 'opulence', which refers to great wealth, luxuriousness, or lavishness. (वैभव )
• Example: The sheer opulence of the royal ballroom left all the guests speechless.
• 'Opulence' is a noun used to describe a state of having an abundance of wealth or expensive things. (प्रचुरता )
• Example: Despite his opulence, he chose to live in a modest apartment in the city.
• Hence, we can infer that 'opulance' is the incorrectly spelled word.

Therefore, the correct answer is: opulance.

Additional Information

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

• Brilliance (प्रतिभा / चमक): Exceptional talent, intelligence, or great brightness.
• Example: The brilliance of the young mathematician was recognized globally.
• Defiance (अवज्ञा): Open resistance or bold disobedience to authority.
• Example: The students staged a protest in defiance of the new school regulations.
• Tolerance (सहनशीलता): The ability or willingness to tolerate something, especially opinions or behavior that one does not necessarily agree with.
• Example: Religious tolerance is a fundamental value in a diverse society.

The correct answer is: Option (3) i.e. obscure.

Key Points

• The word explain refers to the act of making something clear or easy to understand by describing it in more detail or giving relevant facts. (समझाना/स्पष्ट करना)
• Example: The professor took a moment to explain the complex theory to the class.
• Obscure means to make something difficult to see, understand, or perceive; it is the act of hiding or concealing the meaning of something. (अस्पष्ट करना/धुंधला करना)
• Example: He used technical jargon to obscure the fact that he did not know the answer.
• Hence, we can infer that the opposite of explain is obscure.

Therefore, the correct answer is- obscure.

Additional Information

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

• Clarify (स्पष्ट करना): To make a statement or situation less confused and more comprehensible.
• Example: I would like to clarify my position on the new policy.
• Describe (वर्णन करना): To give a detailed account in words of someone or something.
• Example: Can you describe the appearance of the missing bag?
• Define (परिभाषित करना): To state or describe exactly the nature, scope, or meaning of something.
• Example: It is hard to define the exact moment when the trend started.

The correct answer is 'altar'.

Key Points

• The word 'altar' refers to a table or flat-topped block used as the focus for a religious ritual, especially in a church. (वेदी)
• In the given sentence, the action of kneeling and praying in a church makes 'altar' the contextually and grammatically correct noun.
• The other options, particularly 'alter', are homophones (words that sound the same but have different meanings and spellings).

​Therefore, the correct answer is 'Option 2'.

Complete Sentence: The couple knelt before the church altar to pray.

Additional Information

• Alter (बदलना): is a verb that means to change or modify something in character or composition.
• Alert (सतर्क): means being quick to notice any unusual and potentially dangerous or difficult circumstances; vigilant.
• Altar (वेदी): is a noun representing a sacred place or table in a house of worship.

The correct answer is Option(2) i.e. Calligraphy.

Key Points

• The phrase 'The art of beautiful handwriting' refers to the practice of producing decorative and artistic lettering by hand. (सुलेख)
• Example: She spent years mastering the art of beautiful handwriting to become a professional invitation designer.
• 'Calligraphy' is the specific term for the design and execution of lettering with a broad-tipped instrument, brush, or other writing tool. (सुलेख)
• Example: The certificates were written in elegant calligraphy to give them a formal and classic look.
• Hence, we can infer that the one-word substitution for the given phrase is 'Calligraphy'.

Therefore, the correct answer is- Calligraphy.

Additional Information

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

• Typography (मुद्रण कला): The style, arrangement, and appearance of printed letters on a page.
• Example: The typography in the new magazine is very clean and easy to read.
• Etymology (शब्द-व्युत्पत्ति): The study of the origin of words and how their meanings have changed over time.
• Example: A dictionary of etymology helps you understand the historical roots of various English words.
• Lithography (शिलामुद्रण): A printing process that uses a flat stone or metal plate on which the image areas are worked using a greasy substance.
• Example: Lithography was used to produce many of the famous posters seen in the late 19th century.

The correct answer is 'from'.

Key Points

• The verb dismissed means to officially remove someone from their employment or office.
• When indicating the position or job from which someone is removed, the preposition from is used.
• The expression dismissed from the job is a standard collocation in English.

Therefore, the correct answer is Option 1.

Complete Sentence: 'He was dismissed from the job because of his laziness.'

Additional Information

• Option 2: off is incorrect because it is not used with dismissed to describe job termination.
• Option 3: out is incorrect because although thrown out exists, dismissed out is ungrammatical in this context.
• Option 4: away is incorrect as it does not fit the intended meaning of losing a job.

The correct answer is The house had been sold by her years before the real estate boom..

Key Points

• The given sentence is in the Active Voice and uses the Past Perfect Tense. The structure of the sentence is: Subject (She) + had + V3 (sold) + Object (the house) + Adverbial Phrase (years before the real estate boom).
• To transform a sentence from Active Voice to Passive Voice in the Past Perfect Tense, the following structural formula is applied: New Subject (Object of Active) + had + been + V3 (Past Participle) + by + New Object (Subject of Active).
• The Object of the active sentence, the house, shifts to the Subject position in the passive sentence.
• The auxiliary verb had been must be used to maintain the Past Perfect aspect while indicating the Passive Voice.
• The main verb sold remains in its Past Participle (V3) form, which is standard for all passive constructions.
• The Subject of the active sentence, She, is converted into its Objective Case pronoun, which is her, and is preceded by the preposition by.
• The prepositional phrase years before the real estate boom remains unchanged as it provides the temporal context for the action.

 Additional Information

• Understanding the tense discrepancies in the incorrect options:
• Present Perfect Passive: Option 1 uses has been sold. This is the Present Perfect form, which indicates an action connected to the present, whereas the original sentence describes an action completed before another past event.
• Simple Past Passive: Option 2 uses was sold. While this is a past tense, it fails to capture the Past Perfect nuance (the past of the past) established by had sold.
• Structural Incompleteness: Option 4 uses had sold in a passive-looking structure but omits the word been. Without been, the sentence does not function as a passive construction and remains grammatically incorrect in this context.
• Pronoun Transformation: In English grammar, when the subject She (nominative) moves to the object position (after by), it must always change to her (accusative).

The correct answer is The school authorities organise the annual science exhibitions with great enthusiasm..

Key Points

• The provided sentence is in the Passive Voice and follows the structure of the Simple Present Tense: Object + is/am/are + V3 (Past Participle) + by + Agent.
• In the passive sentence, The annual science exhibitions acts as the object receiving the action, and the school authorities is the agent performing the action.
• To convert the sentence into the Active Voice, the agent the school authorities must be shifted to the Subject position at the beginning of the sentence.
• The verb phrase are organised (passive form) is converted to the Active Verb form organise. Since the new subject the school authorities is plural, the verb follows the Subject-Verb Agreement rule for the simple present tense without the suffix -s or -es.
• The original subject The annual science exhibitions is moved to the Object position, appearing immediately after the main verb.
• The prepositional phrase with great enthusiasm remains at the end as an Adverbial Modifier to retain the original context and manner of the action.

 Additional Information

• Active vs. Passive Voice Fundamentals:
• Active Voice: The subject of the sentence performs the action. Structure: Subject + Verb + Object. It is generally more direct and concise.
• Passive Voice: The subject of the sentence is the recipient of the action. Structure: Object + form of be + V3 + by + Agent. It is used when the actor is unknown or less important than the action itself.
• Tense Preservation in Voice Conversion:
• Simple Present: Active (V1/V1+s/es) changes to Passive (is/am/are + V3).
• Present Perfect: Active (has/have + V3) changes to Passive (has/have + been + V3). Option 2 uses a form of this tense, which is incorrect here.
• Past Perfect: Active (had + V3) changes to Passive (had + been + V3). Option 3 uses this tense, which changes the timeline of the original sentence.
• Simple Future: Active (will + V1) changes to Passive (will + be + V3). Option 4 incorrectly shifts the meaning to the future.

The correct answer is Option 2.

Key Points

• The primary error in the sentence lies in the use of the preposition on in part B.
• The verb move indicates a transition or change of location from one point to another, which typically requires the preposition to to indicate the destination.
• While on describes a static position atop something, to is used to show the direction of the movement.
• The correct phrase should be to the upper one instead of on the upper one.
• Thus, the error is located in part B of the sentence.

Therefore, the correct answer is B.

Correct Sentence: 'Let's move all the books kept on this shelf to the upper one and make space for the new books purchased from the market today.'

Additional Information

• Part A: 'Let's move all the books kept on this' – This part is grammatically correct as it correctly identifies the objects being acted upon.
• Part C: 'make space for the new books' – This part is correct; the phrase make space for is the standard idiomatic expression.
• Part D: 'purchased from the market today.' – This part is grammatically correct, using the past participle purchased to describe the books.

The correct answer is 'in'.

Key Points

• The word lacking in this sentence functions as an adjective (or a present participle used as an adjective) meaning deficient in or not having enough of something.
• Standard English grammar requires the preposition in to follow the adjective lacking when specifying the quality or attribute that is missing.
• Common idiomatic expressions include being lacking in confidence, lacking in resources, or lacking in courtesy.
• Options 1, 3, and 4 do not follow the standard idiomatic usage with the word lacking in this context.

Therefore, the correct answer is Option 2.

Complete Sentence: 'They are lacking in minimum courtesy.'

Additional Information

• Lack (Verb): When lack is used as a verb, it is transitive and takes no preposition. Example: 'They lack basic manners.'
• Lack (Noun): When lack is used as a noun, it is usually followed by the preposition of. Example: 'There is a lack of courtesy in their behavior.'
• Lacking (Adjective): When lacking is used as an adjective (following a form of the verb 'to be'), the preposition in is the correct choice. Example: 'He is lacking in experience.'

The correct answer is Option 3.

Key Points

• The paragraph begins by describing the origin of Hercule Poirot's career as a private detective following a specific case.
• Sentence D is the first sentence as it provides a direct consequence of the Styles Case mentioned in S1:
• 'His success brought him notoriety, and he decided to devote himself to the solving of problems in crime.'
• Sentence A follows as it introduces the narrator's personal background and explains how he came to reside with Poirot in London:
• 'Having been wounded on the Somme and invalidated out of the Army, I finally took up my quarters with him in London.'
• Sentence C is the third sentence because it builds on the narrator's proximity to Poirot, explaining that his firsthand knowledge led to the suggestion that he record the cases:
• 'Since I have a firsthand knowledge of most of his cases, it has been suggested to me that I select some of the most interesting and place them on record.'
• Sentence B is the fourth as the phrase 'In doing so' refers back to the act of recording cases mentioned in C, and it introduces a specific strange tangle:
• 'In doing so, I feel that I cannot do better than begin with that strange tangle which aroused such widespread public interest at the time.'
• The final fixed sentence S2 completes the thought by identifying the case as the affair at the Victory Ball.
• The correct sequence is DACB.

Coherent paragraph after rearrangement:

'Pure chance led my friend Hercule Poirot, formerly chief of the Belgian force, to be connected with the Styles Case. His success brought him notoriety, and he decided to devote himself to the solving of problems in crime. Having been wounded on the Somme and invalidated out of the Army, I finally took up my quarters with him in London. Since I have a firsthand knowledge of most of his cases, it has been suggested to me that I select some of the most interesting and place them on record. In doing so, I feel that I cannot do better than begin with that strange tangle which aroused such widespread public interest at the time. I refer to the affair at the Victory Ball.'

The correct answer is Option 1.

Key Points

• The paragraph describes the arduous and secretive journey of Richard through a foreign land back to his home in England.
• Sentence D follows S1 because it provides immediate detail about how Richard navigated the wild and rough country mentioned in the first sentence:
• 'Alone and quietly he made his way through woods and over mountains, not daring to tell who he was.'
• Sentence A follows D as it provides the justification for his secrecy and fear of being recognized:
• 'For in those rude times no stranger was safe in a foreign land and a shipwrecked king would have been a fine prize.'
• Sentence C follows A because the word 'So' indicates the consequence of the danger mentioned in A, describing his disguise:
• 'So, as a poor pilgrim returning from the Holy Land, he trudged onward, looking very ragged and forlorn and keeping out of the way of people as much as he could.'
• Sentence B follows C as it elaborates on the daily struggles of his journey as a pilgrim before concluding with the final fixed sentence S2:
• 'Now and then he found food and lodging at the hut of some poor woodsman, but often he had no shelter under which to rest at night.'
• The correct sequence is DACB.

Coherent paragraph after rearrangement:

'The country in which Richard found himself was wild and rough. Alone and quietly he made his way through woods and over mountains, not daring to tell who he was. For in those rude times no stranger was safe in a foreign land and a shipwrecked king would have been a fine prize. So, as a poor pilgrim returning from the Holy Land, he trudged onward, looking very ragged and forlorn and keeping out of the way of people as much as he could. Now and then he found food and lodging at the hut of some poor woodsman, but often he had no shelter under which to rest at night. He did not know how far it was to England, yet he kept going, toward the northwest, and every day he felt that he was a little nearer home.'

The correct answer is I am confused because.

Key Points

• The original sentence contains a redundant expression, also known as a pleonasm. The phrase the reason and the subordinating conjunction because both indicate causality. Using them together in a single clause is considered tautological in standard English.
• The word reason acts as a noun that points to a cause, while because introduces the cause itself. Grammatically, 'the reason' should be followed by a complement clause starting with that (e.g., 'The reason is that...'), not an adverbial clause starting with 'because'.
• Option 3, I am confused because, provides the most direct and concise way to convey the message. It eliminates the wordiness of the original sentence by removing the unnecessary subject phrase 'The reason why'.
• In Sentence Improvement tasks, the goal is to choose the option that is both grammatically accurate and stylistically superior. Simplifying the structure to Subject + Verb + Conjunction ensures clarity and follows the principle of economy in language.

 Additional Information

• Analysis of incorrect options:
• Why am I confused is because: This option incorrectly uses an interrogative word order ('Why am I') within a declarative sentence. Furthermore, it retains the redundancy between 'Why' and 'because'.
• The reason for my confusion is because: While it replaces 'why I am confused' with a noun phrase, it fails to correct the fundamental grammatical error of pairing 'reason' with 'because'. A correct alternative would have been 'The reason for my confusion is that'.
• Redundancy Rule: Common redundant phrases often tested include 'return back', 'reason why... because', 'repeat again', and 'sufficient enough'. Removing the repetitive element is a standard error detection strategy.
• Conjunction usage: Because is a subordinating conjunction that connects a dependent clause to an independent clause. When the purpose of the sentence is to state a fact directly, starting with the subject is preferred over complex nominalizations.