SSC GD Constable 2026 Official Paper (Held On 07 May, 2026 Shift 3) (Previous Year Paper)

Logic followed here is,

4096 ÷ 2 = 2048

2048 ÷ 4 = 512

512 ÷ 2 = 256

256 ÷ 4 = 64

64 ÷ 2 = 32

32 ÷ 4 = 8

8 ÷ 2 = 4

Hence, the correct answer is “Option 2”.

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Pattern followed here is,

Hence, the correct answer is “Option 2”.

For 'PS' related to 'SX':

For 'XT' related to 'AY':

Applying the same logic to find the cluster related to 'DK':

Thus, AF is related to DK.

Hence, the correct answer is 'Option 4'.

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VA : BZ →

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LI : RR →

Similarly,

GY : ? →

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Hence, the correct answer is “Option 2”.

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Pattern followed here is,

Hence, the correct answer is “Option 3”.

For the set '(TK, PE, LY)':

For the set '(KF, GZ, CT)':

Applying the same logic to the alternatives:

Checking '(RV, NP, JJ)':

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Hence, the correct answer is "Option 1".

Given: December 25 of a leap year is Sunday.

First, we determine the day of the week on which February 1 of the next year falls:

Remaining days in December = 31 − 25 = 6 days

Days in January of the next year = 31 days

Total days from December 25 to the end of January = 6 + 31 = 37 days

To find the day on January 31, we calculate the number of odd days:

37 ÷ 7 = 5 weeks and 2 odd days

Day on January 31 = Sunday + 2 days = Tuesday

Therefore, February 1 of the next year is a Wednesday.

Since the next year is a non-leap year, February has 28 days.

In a 28-day month, every day occurs exactly 4 times:

Number of Wednesdays = 4 (falling on the 1st, 8th, 15th, and 22nd)

Number of Sundays = 4 (falling on the 5th, 12th, 19th, and 26th)

Total number of Wednesdays and Sundays = 4 + 4 = 8

Hence, the correct answer is “Option 1”.

We need to calculate the number of days from 5 September 2015 to 5 February 2016:

Days remaining in September 2015 = 30 − 5 = 25 days

Days in October 2015 = 31 days

Days in November 2015 = 30 days

Days in December 2015 = 31 days

Days in January 2016 = 31 days

Days in February 2016 = 5 days (up to the target date)

Total number of days = 25 + 31 + 30 + 31 + 31 + 5 = 153 days

To find the odd days, divide the total days by 7:

153 ÷ 7 = 21 weeks and 6 odd days (remainder)

Given that 5 September 2015 was Saturday.

The day on 5 February 2016 = Saturday + 6 odd days

Counting 6 days forward from Saturday: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday.

Hence, the day on 5 February 2016 was Friday.

Alternate Method

We can find the odd days for each month individually to simplify the addition:

September: 25 days ⇒ 25 ÷ 7 = 4 odd days

October: 31 days ⇒ 31 ÷ 7 = 3 odd days

November: 30 days ⇒ 30 ÷ 7 = 2 odd days

December: 31 days ⇒ 31 ÷ 7 = 3 odd days

January: 31 days ⇒ 31 ÷ 7 = 3 odd days

February: 5 days ⇒ 5 odd days

Total sum of odd days = 4 + 3 + 2 + 3 + 3 + 5 = 20 days

Final odd days = 20 ÷ 7 = 2 weeks and 6 odd days

The day was Saturday + 6 days = Friday.

Therefore, the correct answer is Friday.

5 persons C, D, F, G and H are sitting in a row facing north (not necessarily in the same order).

1. Only C and F are to the left of D.
2. Only H is to the right of G.
3. F is at one of the extreme ends of the row.

Only one person sitting between D and H.

Hence, the correct answer is “Option 1”.

Given that there are 6 girls P, Q, R, S, T and U with different heights.

From the clues, we can deduce the following relationships:

1. R is taller than only four girls.

→ This means only one girl is taller than R, so R is the 2nd tallest.

→ _ > R > _ > _ > _ > _

2. U is taller than both S and P.

→ U > S and U > P.

3. S and P both are taller than both Q and T.

→ S > Q, S > T, P > Q, P > T.

4. Since R is the 2nd tallest, the only girl taller than R must be U.

→ The possible order from tallest to shortest is:

→ U > R > S > P > Q > T

5. T is the shortest and its height is 140 cm.

Therefore, R must be taller than S, P, Q and T but shorter than U.

Among the given options, the possible height of R is 168 cm.

Thus, the possible height order can be:

U > 168 (R) > S > P > Q > 140 (T)

Hence, the correct answer is "Option 1".

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 3”.

Pattern followed here is,

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Similarly,

Hence, the correct answer is “Option 4”.

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KO825 : HK425

HF916 : EB516

Similarly,

? : CT428

Hence, the correct answer is “Option 3”.

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GKN11 : CGJ121

LMF13 : HIB169

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Similarly,

OSR15 : ?

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Hence, the correct answer is “Option 4”.

The logic followed here is:

Logic: Second Number = First Number + 229

For the pair 13 : 242

⇒ 13 + 229 = 242.

Similarly, for the pair 138 : 367

138 : 367

Applying the same logic to the pair

608 : ?

⇒ 608 + 229 = 837.

Hence, the correct answer is 'Option 2'.

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For TILE is coded as UKKA →

For NUMB is coded as OWLX →

Similarly,

let's find the code for NOTE:

Hence, the correct answer is “Option 4”.

The time interval from 7 AM to 7 PM on the same day is:

Total duration = 12 hours

Converting the total duration into minutes:

Total minutes = 12 × 60 = 720 minutes

Given that the clock gains 2 seconds every 3 minutes:

Gain in 3 minutes = 2 seconds

Gain in 1 minute = 2/3 seconds

Total gain in 720 minutes = (2/3) × 720

Total gain = 2 × 240 = 480 seconds

Now, convert the total gain from seconds to minutes:

Total gain in minutes = 480 ÷ 60 = 8 minutes

Since the clock is gaining time, the time it shows at 7 PM will be the actual time plus the gain:

Time shown = 7:00 PM + 8 minutes = 7:08:00 PM

Hence, the time the clock will show is 7:08:00.

Hence, the correct answer is “Option 3”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

The ratio of the present ages of two persons = 7 : 12

The sum of their present ages = 57

Let the present ages of the two persons be 7x and 12x.

According to the question:

7x + 12x = 57

19x = 57

x = 57 ÷ 19

x = 3

 

Ages 6 years ago from now:

Age of the first person = 21 − 6 = 15 years

Age of the second person = 36 − 6 = 30 years

Ratio of their ages 6 years ago:

Required Ratio = 15 : 30

Ratio = 1 : 2

Hence, the correct answer is “Option 2”.

The correct answer is The act of storytelling.

Key Points

• The word Kathak is etymologically derived from the Sanskrit word Katha, which literally means story. Therefore, a Kathakar is a person who tells a story through the medium of dance.
• This classical dance form originated in Northern India, primarily in the states of Uttar Pradesh and Rajasthan, where it was performed by nomadic bards known as Kathakars.
• Historically, these storytellers traveled from village to village and performed in temple courtyards, using music, song, and rhythmic movements to narrate episodes from Indian epics like the Ramayana and Mahabharata.
• Kathak is formally recognized as one of the eight major classical dance forms of India by the Sangeet Natak Akademi, distinguished by its unique blend of Hindu and Muslim cultural influences.
• The performance involves a transition from a slow invocation to high-speed footwork and pirouettes, all while maintaining the core objective of conveying a narrative or Bhaav (emotion).

 Additional Information

• Evolution and Gharanas:
• The dance style evolved significantly during the Bhakti Movement, incorporating the legends of Radha and Krishna, which added a layer of divine romance to the storytelling.
• During the Mughal era, Kathak moved from temples to royal courts, where it developed into a more sophisticated and technical form focusing on Tatkar (footwork) and Chakkars (spins).
• There are three main Gharanas or schools of Kathak: the Lucknow Gharana (emphasizing grace and expression), the Jaipur Gharana (emphasizing rhythmic speed and power), and the Banaras Gharana (emphasizing spiritual depth).
• Musical accompaniment typically includes instruments such as the Tabla, Pakhawaj, Harmonium, and Sarangi, which provide the rhythmic and melodic framework for the storyteller.

The correct answer is Mahabharata.

Key Points

• The Mahabharata is one of the two major Sanskrit epics of ancient India, and it explicitly describes the spiritual significance of Uttarayana through the narrative of Bhishma Pitamaha.
• Bhishma, the patriarch of the Kuru dynasty, possessed the rare boon of Iccha Mrityu (death at will), granted by his father, King Shantanu.
• After being mortally wounded during the Kurukshetra War by Arjuna, Bhishma chose to lie on a bed of arrows (Sharashayya) rather than giving up his life immediately.
• He intentionally delayed his departure from the mortal world for 58 days to wait for the onset of Uttarayana, the period when the sun begins its northward journey.
• According to the epic, dying during this auspicious period allows the soul to travel through the Devayana (the path of gods), leading directly to Salvation or Moksha and liberation from the cycle of rebirth.

 Additional Information

• Uttarayana and its Significance:
• It is the six-month period between the Winter Solstice and the Summer Solstice, characterized by the sun moving into the northern hemisphere.
• The festival of Makar Sankranti traditionally marks the beginning of this period in the Hindu solar calendar.
• In the Bhagavad Gita, which is a section of the Mahabharata, Lord Krishna confirms that those who depart the world during the light of the day and the six months of the northern sun attain the Supreme Abode.
• Other Epics and Texts:
• Ramayana: An epic chronicling the life of Lord Rama, but the theological focus on waiting for Uttarayana for salvation is specific to the legend of Bhishma in the Mahabharata.
• Vedas: The oldest scriptures of Hinduism containing hymns and rituals; while they discuss cosmic order (Rta), the specific narrative of Bhishma's death is found in the Itihasa (History) category.
• Bhagavata Purana: Focuses on Bhakti (devotion) and the incarnations of Vishnu, particularly Krishna, but is distinct from the primary historical account of the Kuru war.

The correct answer is 7.6 × 10⁶ s.

Key Points

• The orbital period is defined as the time a celestial object takes to complete one full revolution around another object; in this context, it refers to a planet orbiting the Sun.
• To determine the period in seconds, we must convert 88 Earth days using standard units of time: 1 day consists of 24 hours, 1 hour contains 60 minutes, and 1 minute contains 60 seconds.
• The total number of seconds in a single solar day is calculated by the product: 24 × 60 × 60 = 86,400 seconds.
• By multiplying the given orbital duration of 88 days by the number of seconds per day, we find: 88 × 86,400 = 7,603,200 seconds.
• In scientific notation, this value is expressed as 7.6032 × 10⁶ s. Rounding to two significant figures as per the provided options results in 7.6 × 10⁶ s.

 Additional Information

• Mercury and Orbital Mechanics
• Mercury is the planet characterized by an orbital period of approximately 88 Earth days (specifically 87.97 days), making it the fastest planet in our Solar System.
• Because it is the closest planet to the Sun, it must maintain a high orbital velocity (averaging 47.36 km/s) to counteract the Sun's massive gravitational pull.
• Kepler's Third Law
• The relationship between a planet's distance from the Sun and its period is governed by Kepler's Law of Periods, which states that the square of the orbital period (T) is proportional to the cube of the semi-major axis (a) of its orbit (T² ∝ a³).
• This law implies that planets further from the Sun, such as Jupiter or Neptune, have significantly longer orbital periods compared to terrestrial planets like Earth or Mercury.

The correct answer is Jupiter.

Key Points

• Jupiter is the largest planet in our Solar System and is primarily classified as a gas giant due to its composition of hydrogen and helium.
• It is widely known as the stormy planet because its atmosphere is in a constant state of turbulence, featuring high-velocity zonal winds and massive vortices.
• The most famous feature of Jupiter is the Great Red Spot, an enormous anticyclonic storm that is larger than Earth and has been raging for at least 350 years.
• Because Jupiter lacks a solid rocky surface, there is no friction to slow down these atmospheric disturbances, allowing storms to persist for decades or even centuries.
• The planet also exhibits White Ovals and Brown Barges, which are smaller but equally intense storm systems within its distinct cloud bands.

 Additional Information

• Mercury:
• It is the closest planet to the Sun and the smallest in the solar system.
• Mercury has a very thin exosphere instead of a traditional atmosphere, meaning it cannot generate weather or storms.
• Mars:
• Often called the Red Planet due to the prevalence of iron oxide on its surface.
• While it experiences massive dust storms that can occasionally cover the entire planet, its thin atmosphere lacks the complex gaseous dynamics found on Jupiter.
• Venus:
• Known as Earths twin, it has an extremely dense atmosphere of carbon dioxide and clouds of sulfuric acid.
• It is the hottest planet in the solar system due to a runaway greenhouse effect, rather than being defined primarily by storm activity.

The correct answer is Brazil.

Key Points

• The 2nd BRIC Summit was held on April 15, 2010, in the capital city of Brasília, Brazil.
• The summit was attended by the leaders of the four founding nations: President Luiz Inácio Lula da Silva of Brazil, President Dmitry Medvedev of Russia, Prime Minister Manmohan Singh of India, and President Hu Jintao of China.
• The primary focus of this summit was the recovery from the 2008 global financial crisis and the necessity of reforming international financial institutions like the International Monetary Fund (IMF) and the World Bank to provide more voting power to emerging economies.
• A significant outcome of the 2010 meeting was the discussion regarding the expansion of the group, which eventually led to South Africa being invited to join the bloc by the end of that year.
• The leaders signed several agreements regarding technical cooperation and cooperation between their respective development banks to facilitate trade and investment.

 Additional Information

• Chronology of Early Summits:
• 1st BRIC Summit: Held in Yekaterinburg, Russia, on June 16, 2009. It was the first formal meeting of the group.
• 3rd BRICS Summit: Held in Sanya, China, in 2011. This was the first summit where South Africa participated as a full member, changing the acronym to BRICS.
• 4th BRICS Summit: Hosted by India in New Delhi on March 29, 2012.
• BRICS Concept and Expansion:
• The acronym BRIC was originally coined by Jim O'Neill of Goldman Sachs in 2001 to highlight the economic potential of these four nations.
• In August 2023, during the 15th BRICS Summit in South Africa, the group announced a major expansion, inviting countries including Egypt, Ethiopia, Iran, and the United Arab Emirates to join starting January 1, 2024.

The correct answer is Naya Bharat.

Key Points

• The 79th Independence Day of India, to be celebrated on August 15, 2025, marks a significant milestone in the country's journey toward its centenary of freedom in 2047.
• The theme Naya Bharat (New India) reflects the government's commitment to building a nation that is self-reliant, technologically advanced, and inclusive of all social strata.
• The celebrations held at the historic Red Fort (Lal Qila) in New Delhi traditionally feature the unfurling of the National Flag by the Prime Minister, followed by a speech outlining the national roadmap.
• The theme emphasizes the vision of Amrit Kaal, focusing on the Panch Pran (Five Vows) which include the goal of a developed India, removing any trace of colonial mindset, taking pride in roots, unity, and sense of duty among citizens.
• Naya Bharat serves as an umbrella concept for various flagship schemes like Digital India, Make in India, and PM Gati Shakti, aiming to position India as a global powerhouse in the 21st century.

 Additional Information

• Viksit Bharat @ 2047:
• This is the overarching vision to transform India into a Developed Nation by its 100th year of independence.
• Key pillars include economic growth, social progress, environmental sustainability, and good governance.
• The Red Fort's Historical Role:
• Built by Mughal Emperor Shah Jahan, it has been the site for Independence Day addresses since Jawaharlal Nehru first hoisted the flag here in 1947.
• It is a UNESCO World Heritage Site representing the architectural fusion of Persian, Timurid, and Indian styles.
• Atmanirbhar Bharat:
• A core component of the Naya Bharat theme, focusing on making India a global manufacturing hub and reducing import dependency.
• It highlights advancements in sectors like Defense, Space, and Semiconductors.

The correct answer is Evaporation from oceans.

Key Points

• Water vapor is the gaseous state of water and serves as the primary greenhouse gas, responsible for maintaining the Earth's temperature through the Hydrological Cycle.
• The Oceans are the largest reservoirs of liquid water on the planet, covering approximately 71 percent of the Earth's total surface area.
• Due to the massive surface area and the absorption of Solar Radiation, approximately 85 percent to 90 percent of all atmospheric water vapor originates from the evaporation of seawater.
• Evaporation occurs when thermal energy increases the kinetic energy of water molecules, allowing them to overcome surface tension and escape into the air as a gas.
• The rate of this process is governed by Surface Temperature, Wind Speed, and the Vapor Pressure Gradient between the ocean surface and the lower atmosphere.

 Additional Information

• Transpiration:
• This is the biological process where plants release water vapor through Stomata. When combined with land evaporation (Evapotranspiration), it accounts for the remaining 10 percent of atmospheric moisture.
• Combustion:
• The chemical reaction of Hydrocarbons with oxygen produces Carbon Dioxide and water vapor. While significant in urban microclimates, it is a negligible contributor to global water vapor levels.
• Photosynthesis:
• This is the process by which green plants use Sunlight to convert water and carbon dioxide into Glucose. It acts as a consumer of water rather than a primary source of atmospheric vapor.
• Industrial Smoke:
• Emissions from factories often contain Steam and particulate matter. However, these Anthropogenic sources are localized and do not compare to the scale of natural oceanic evaporation.

The correct answer is Narinder Singh Kapany.

Key Points

• Narinder Singh Kapany was an Indian-American physicist who is widely recognized globally as the father of fiber optics for his pioneering research in the 1950s.
• In 1953, while working at Imperial College London, he successfully demonstrated that light can be transmitted through a bundle of glass fibers, overcoming the traditional challenge of light leaking out of the sides.
• He achieved this by using a cladding material with a lower refractive index, which enabled Total Internal Reflection, the fundamental principle behind all modern optical communication.
• The term fiber optics was first coined by Kapany in a seminal article for Scientific American in 1960, establishing the nomenclature for the entire industry.
• His work paved the way for a revolution in telecommunications, high-speed broadband internet, and medical applications like endoscopy and laser-assisted surgery.
• In recognition of his monumental contributions to science and engineering, the Government of India posthumously awarded him the Padma Vibhushan, the country's second-highest civilian honor, in 2021.

 Additional Information

• Jay Chaudhry:
• An Indian-American billionaire entrepreneur and the CEO of Zscaler, a leading company in cloud security and zero-trust architecture.
• Vivek Sehgal:
• The chairman and co-founder of Motherson Group, a major global player in the automotive component manufacturing industry.
• Fiber Optic Cables:
• These cables transmit data as pulses of light through strands of glass or plastic, offering significantly higher bandwidth and lower attenuation compared to traditional copper wires.
• This technology is the backbone of the World Wide Web and long-distance digital data transmission.

The correct answer is Luni.

Key Points

• The Luni River is the only major river system in the Thar Desert (Great Indian Desert) and serves as the primary source of water for the arid regions of western Rajasthan.
• It originates in the Pushkar Valley of the Aravalli Range, near Ajmer, at an elevation of approximately 550 meters, where it is initially known as the Sagarmati.
• The river flows for a total length of about 495 kilometers, passing through several districts including Nagaur, Pali, Jodhpur, Barmer, and Jalore before entering Gujarat.
• A distinctive hydrological feature of the Luni is its salinity; the water remains fresh until it reaches Balotra in the Barmer district, but becomes saline thereafter due to high salt accumulation in the desert soil.
• It is an endorheic river, meaning it does not reach the sea; instead, its course terminates in the marshy Rann of Kutch.
• Its major tributaries include the Jojari, Sukri, Guhiya, Bandi, and Jawai rivers, most of which originate from the western slopes of the Aravallis.

 Additional Information

• Chambal River:
• Originates from the Janapav Hills in the Vindhya Range (Madhya Pradesh).
• It is a perennial river that flows through south-eastern Rajasthan and is famous for its badland topography and ravines.
• Banas River:
• Known as Vana Ki Asha (Hope of the Forest), it originates from the Khamnor Hills in the Rajsamand district.
• It is a seasonal river that flows entirely within Rajasthan before joining the Chambal as a tributary.
• Sabarmati River:
• Originates in the Udaipur district from the Aravalli Range.
• While it begins in Rajasthan, the majority of its course and catchment area lie in Gujarat, eventually draining into the Gulf of Khambhat.

The correct answer is Manipur.

Key Points

• Loktak Lake is situated in the Bishnupur district of Manipur and is recognized as the largest freshwater lake in North-East India.
• The lake is globally renowned for its unique phumdis, which are floating islands composed of a heterogeneous mass of vegetation, soil, and organic matter in various stages of decomposition.
• It serves as a primary source for hydropower generation, irrigation, and drinking water supply in the region, while also supporting the livelihoods of local fishermen.
• The Keibul Lamjao National Park, located in the southeastern part of the lake, is the world’s only floating national park and is an integral part of the Loktak ecosystem.
• This ecosystem provides the sole natural habitat for the critically endangered Sangai (Rucervus eldii eldii), also known as the dancing deer, which is the state animal of Manipur.

 Additional Information

• Conservation Status:
• Loktak Lake was designated as a wetland of international importance under the Ramsar Convention on March 23, 1990.
• In 1993, it was listed under the Montreux Record due to ecological changes resulting from human activities and the construction of the Ithai Barrage.
• Other Regional Lakes:
• Tripura: Home to Rudrasagar Lake, a Ramsar site featuring the famous Neermahal water palace.
• Assam: Contains Deepor Beel, a permanent freshwater lake in the Kamrup district and a significant bird sanctuary.
• Nagaland: Known for Shilloi Lake, a natural foot-shaped lake located in the Phek district.

The correct answer is Zakat.

Key Points

• Zakat is defined as a mandatory religious tax and represents one of the Five Pillars of Islam, making it a compulsory duty for all eligible Muslims to support the needy.
• During the Delhi Sultanate (1206–1526), the administrative and fiscal systems were largely governed by the Shariat (Islamic Law), which identified Zakat as a specific tax on property and wealth.
• It was typically levied at a fixed rate of 2.5% (or one-fortieth) on specific assets including gold, silver, livestock, and merchandise that had been in the owner's possession for at least one lunar year.
• The revenue generated from Zakat was strictly utilized for charitable purposes, such as providing for the poor, widows, orphans, and religious institutions, rather than for general state expenditures or military funding.
• It was distinct from other taxes like Kharaj (land tax) and Jizya because it was a purely religious obligation performed only by the Muslim subjects of the Sultanate.

 Additional Information

• Mamluk:
• Refers to the Slave Dynasty (1206–1290), the first ruling house of the Delhi Sultanate founded by Qutub-ud-din Aibak.
• The term Mamluk is an Arabic word for 'owned', signifying slave-soldiers of Turkish origin who rose to political power.
• Ur:
• This was a type of village assembly found specifically in the Chola Empire of South India, consisting of tax-paying residents.
• It operated alongside the Sabha, which was the assembly of Brahmin landholders in Brahmadeya villages.
• Jizya and Khums:
• Jizya was a protection tax levied on non-Muslim subjects (Dhimmis) in exchange for state protection and military exemption.
• Khums referred to the state's share of war booty, which was traditionally one-fifth of the total spoils captured during military campaigns.

The correct answer is January.

Key Points

• Union Home Minister and Minister of Cooperation Amit Shah officially unveiled the National Cooperation Policy 2025 on January 1, 2025, during a ceremony held at Bharat Mandapam, New Delhi.
• The policy is designed to realize the vision of Sahakar-se-Samriddhi (Prosperity through Cooperation) by creating a more vibrant, transparent, and professional cooperative movement across the country.
• The draft of this policy was prepared by a 47-member National Level Committee headed by former Union Minister Suresh Prabhu, which incorporated suggestions from various stakeholders, state governments, and national cooperative federations.
• The policy focuses on 10 major themes, including strengthening the legal and institutional framework, enhancing financial sustainability, and promoting the use of modern technology and digitalization in cooperatives.
• It aims to increase the contribution of cooperatives to the national GDP and create a level playing field for them compared to other economic sectors.

 Additional Information

• Ministry of Cooperation:
• Established by the Government of India in July 2021 to provide a separate administrative, legal, and policy framework for the cooperative sector.
• It works to streamline processes for Ease of Doing Business for cooperatives and to enable the development of Multi-State Cooperative Societies (MSCS).
• Primary Agricultural Credit Societies (PACS):
• A major component of the new policy is the strengthening of approximately 63,000 functional PACS by converting them into Common Service Centres (CSCs).
• The computerization of PACS is a key project aimed at improving transparency and efficiency at the village level.
• Constitutional Framework:
• The 97th Constitutional Amendment Act, 2011 added Part IXB to the Constitution, providing constitutional status and protection to cooperative societies.
• Promotion of cooperatives is also a Directive Principle of State Policy under Article 43B.

The correct answer is Gujarat.

Key Points

• The PM-JANMAN (Pradhan Mantri Janjati Adivasi Nyaya Maha Abhiyan) was launched on November 15, 2023, to coincide with Janjatiya Gaurav Divas, aiming to provide comprehensive development for 75 Particularly Vulnerable Tribal Groups (PVTGs).
• For the ranking period of July 2025, Gujarat secured the first rank among all states by achieving the highest percentage of saturation in individual entitlement schemes, specifically in the issuance of Aadhaar cards, caste certificates, and Jan Dhan bank accounts for the PVTG population.
• The state demonstrated exceptional administrative efficiency by conducting intensive Information, Education, and Communication (IEC) campaigns and saturation camps across districts such as Narmada, Tapi, and Dahod.
• Gujarat led the national tally in the implementation of the 11 critical interventions, particularly in ensuring 100 percent registration for Ayushman Bharat cards and PM-Kisan benefits among its five identified PVTG communities: Sidi, Padhar, Kathodi, Kotwalia, and Kolgha.
• The Ministry of Tribal Affairs recognized the state's progress in utilizing GIS mapping for tribal habitations, which facilitated the rapid approval of pucca houses under PM-Awas Yojana (Gramin) and the extension of off-grid solar power to remote areas.

 Additional Information

• PM-JANMAN Scheme Framework:
• The scheme has a total financial outlay of 24,104 crore, with a central share of 15,336 crore and a state share of 8,768 crore.
• It focuses on 11 key interventions coordinated by 9 Central Ministries, including the Ministry of Health and Family Welfare, Ministry of Power, and Ministry of Rural Development.
• The mission aims to bridge gaps in safe housing, clean drinking water, sanitation, and telecommunication connectivity for approximately 28 lakh PVTG individuals living in 22,000 habitations across 18 states and one UT.
• Infrastructural targets include the construction of 8,000 km of all-weather roads and the setting up of 2,500 Anganwadi centres and Multipurpose Centres (MPCs).

The correct answer is IIT Kanpur.

Key Points

• The Sabal 20 is a sophisticated Electric Unmanned Helicopter designed specifically for heavy-lift logistics and reconnaissance in challenging terrains.
• This cutting-edge technology was developed by EndureAir Systems, a deep-tech startup incubated at the Indian Institute of Technology (IIT) Kanpur.
• The Indian Army officially inducted the Sabal 20 in November 2024 to enhance its logistics capabilities in high-altitude sectors such as Ladakh and Sikkim.
• It features a Vertical Take-Off and Landing (VTOL) capability, which allows it to operate effectively in restricted spaces without the need for a runway.
• The helicopter is designed to carry payloads of up to 20 kilograms and can operate at altitudes exceeding 15,000 feet, providing a critical advantage in mountainous warfare.

 Additional Information

• EndureAir Systems:
• Founded by researchers and alumni from the Aerospace Engineering department of IIT Kanpur under the mentorship of Professor Abhishek.
• The startup focuses on providing indigenous unmanned aerial solutions for both defense and civilian applications, aligning with the Atmanirbhar Bharat initiative.
• Operational Features:
• The electric propulsion system ensures a significantly lower acoustic signature compared to traditional combustion engines, making it ideal for covert operations.
• It is equipped with advanced autonomous navigation systems, allowing it to perform last-mile delivery of medicines and essential supplies to remote forward posts.
• Strategic Significance:
• Reduces the reliance on animal transport or large manned helicopters (like the Cheetah or Dhruv) for small-scale logistics, thereby saving operational costs and reducing risk to human pilots.
• Supports the Indian Army in maintaining a constant supply chain in low-oxygen and high-wind environments where traditional drones often fail.

The correct answer is Council of Scientific and Industrial Research.

Key Points

• The Council of Scientific and Industrial Research (CSIR), specifically through the Indian Institute of Chemical Technology (IICT) based in Hyderabad, announced the successful development of a fully indigenous technology for Paracetamol production in January 2025.
• The project focused on synthesizing the Active Pharmaceutical Ingredient (API) using locally sourced raw materials, effectively reducing the heavy reliance on imported Key Starting Materials (KSMs) like Para-Aminophenol.
• This development is a critical milestone under the Atmanirbhar Bharat initiative, which seeks to secure India s medical supply chain and achieve self-sufficiency in essential drug manufacturing.
• The newly developed process is designed to be environmentally sustainable and cost-competitive, allowing domestic manufacturers to produce high-quality analgesics and antipyretics for both local consumption and global export.

 Additional Information

• Council of Scientific and Industrial Research (CSIR):
• Established in September 1942, it is India s premier public sector Research and Development organization.
• It operates under the Ministry of Science and Technology and is presided over by the Prime Minister of India.
• With a network of 37 national laboratories, it plays a pivotal role in fields such as genomics, oceanography, and pharmaceutical chemistry.
• Active Pharmaceutical Ingredients (APIs):
• An API is the primary chemical component in a drug responsible for the therapeutic effect.
• To boost domestic production, the Indian government introduced the Production Linked Incentive (PLI) Scheme for Bulk Drugs and promoted the establishment of Bulk Drug Parks.
• Reducing import dependency (specifically from China) for APIs is a strategic priority to prevent medicine shortages.

The correct answer is 2020.

Key Points

• The 2020 Summer Olympics, officially known as the Games of the XXXII Olympiad, were hosted by Tokyo, Japan, marking the city second time hosting the summer event.
• Although scheduled to begin in July 2020, the games were officially postponed by the International Olympic Committee (IOC) to 2021 due to the global COVID-19 pandemic.
• The event eventually took place from July 23 to August 8, 2021, but retained the official branding of Tokyo 2020 for marketing and record-keeping purposes.
• Tokyo was awarded the games during the 125th IOC Session held in Buenos Aires, Argentina, on September 7, 2013, after defeating finalist bids from Istanbul and Madrid.
• With this hosting, Tokyo became the first city in Asia to host the Summer Olympic Games twice, with the previous instance occurring in 1964.
• The Japan National Stadium served as the primary venue for the opening and closing ceremonies, as well as athletics competitions.

 Additional Information

• Evolution of the Tokyo Games:
• Historical Legacy: The 1964 Summer Olympics were a landmark event for Japan, showcasing its technological resurgence with the debut of the Shinkansen bullet train and the first global satellite broadcast.
• New Sporting Additions: The 2020 program introduced several new sports to appeal to younger audiences, including skateboarding, surfing, sport climbing, and karate.
• Sustainability Initiatives: The organizers launched the Tokyo 2020 Medal Project, where approximately 5,000 medals were manufactured using 100 percent recycled metal extracted from small electronic devices like mobile phones.
• Mascots and Motto: The official mascots were Miraitowa and Someity, and the games were conducted under the motto United by Emotion, highlighting global unity during challenging times.

The correct answer is Only II.

Key Points

• The 4×100 metres relay is a standard track and field sprint event where four runners each complete a distance of 100 metres in succession. This event is a primary discipline in the Summer Olympic Games and World Athletics Championships, requiring athletes to pass a baton within a 30-metre exchange zone. Hence, statement I is correct.
• The 4×600 metres is not a recognized or standard international relay event in competitive athletics. Standard middle-distance relays sanctioned by World Athletics (formerly IAAF) include the 4×400 metres, 4×800 metres, and 4×1500 metres, but the 600m distance is not utilized for major championship relay formats. Hence, statement II is incorrect.

 Additional Information

• Relay Race Mechanics:
• Baton Passing: In short relays like the 4×100m, runners typically use a non-visual exchange (blind handoff) to maintain top speed, while longer relays may use a visual exchange.
• Legs: A relay team consists of a lead-off leg, two middle runners, and an anchor leg (usually the fastest runner).
• Exchange Zone: For the 4×100m, the current World Athletics rules define a single 30-metre zone where the baton must be handed over; failing to do so results in disqualification.
• Standard Track Events:
• 4×400 metres: Often the finale of track meets, involving one full lap per runner.
• Mixed 4×400 metres Relay: A modern event featuring two men and two women, which made its Olympic debut at the Tokyo 2020 Games.
• Medley Relays: These involve legs of different distances (e.g., 1200m, 400m, 800m, 1600m in the Distance Medley Relay).

The correct answer is Direction of current.

Key Points

• Fleming's Left-Hand Rule is a simple visualization tool used to find the direction of the mechanical force (motion) experienced by a current-carrying conductor when it is placed in an external magnetic field.
• To apply the rule, the thumb, forefinger (first finger), and middle finger (second finger) of the left hand are held mutually perpendicular (at 90 degrees) to one another.
• The Forefinger (First finger) represents the direction of the Magnetic Field (B), typically pointing from the North pole to the South pole.
• The Middle Finger (Second finger) represents the direction of the Electric Current (I) flowing through the conductor.
• The Thumb represents the direction of the Thrust or Force (F) acting on the conductor, which dictates its direction of motion.
• This rule is essentially a mnemonic for the Lorentz Force equation, where the force vector is the cross-product of the current and magnetic field vectors.

 Additional Information

• Direction of magnetic field
• In the left-hand rule, this is indicated by the index finger.
• In SI units, the strength of this field is measured in Tesla (T).
• Force acting on the conductor
• This is represented by the thumb.
• The magnitude of this force is given by the formula F = B × I × L × sin(θ), where L is the length of the wire and θ is the angle between the current and the field.
• Measure of resistance
• Resistance is a property of a material to oppose the flow of current, defined by Ohm's Law (R = V / I).
• It is not determined or represented by Fleming's rules, which deal with electromagnetism and motion rather than circuit properties.
• Electric Motors
• Fleming's Left-Hand Rule is the fundamental principle used to understand the operation of DC Motors, where electrical energy is converted into mechanical torque.

The correct answer is Ramamatya.

Key Points

• The treatise Swaramelakalanidhi was composed by the scholar-musician Ramamatya in approximately 1550 AD.
• Ramamatya served as a prominent minister and court musician under Aliya Rama Raya, the de facto ruler of the Vijayanagara Empire.
• This work is historically significant as it marks the formal beginning of the Carnatic music system, acting as a bridge between the ancient traditions and modern practices.
• In Swaramelakalanidhi, the author introduced the Mela system of classification, identifying 20 Melas (parent scales) to organize various Ragas of that era.
• The text provides a detailed study of Veena construction and tuning, categorizing them into types like Shuddha Mela Veena and Madhya Mela Veena.

 Additional Information

• Matanga:
• Author of the influential text Brihaddeshi, dated between the 6th and 8th centuries.
• He was the first to technically define the term Raga and introduced the Desi (regional) music tradition.
• Sharngadeva:
• Composed the Sangeeta Ratnakara in the 13th century during the Yadava dynasty in Devagiri.
• His work is known as Saptadhyayi (consisting of seven chapters) and is a foundational text for both Hindustani and Carnatic music.
• Haripala:
• A Chalukyan king credited with writing Sangeeta Sudhakara in the 12th or 14th century.
• He is recognized for being one of the earliest theorists to explicitly differentiate between Hindustani and Carnatic musical styles.

The correct answer is 70.

Key Points

• Magnetite is the most superior and finest iron ore found in the Earth's crust, distinguished by its high metallic iron concentration, which can reach up to 70%.
• Chemically, it is a ferrimagnetic mineral represented by the formula Fe₃O₄, making it the most magnetic of all the naturally occurring minerals on Earth.
• Due to these excellent magnetic qualities, Magnetite is of immense value in the electrical industry, where it is utilized in the production of specialized components and high-efficiency motors.
• The ore typically appears black or brownish-black with a metallic luster and is primarily found in igneous and metamorphic rocks, as well as in banded iron formations (BIFs).
• In India, high-grade Magnetite deposits are concentrated in the Kudremukh mines of Karnataka, which are known to be one of the largest deposits of this type in the world.

 Additional Information

• Hematite (Fe₂O₃):
• It is often referred to as 'red ore' and contains a slightly lower iron content ranging from 50% to 60%.
• Despite having a lower iron percentage than magnetite, it is the most important industrial iron ore in terms of the total quantity used in iron and steel manufacturing.
• Limonite and Siderite:
• Limonite is a secondary iron ore with a content of 40% to 60%, often appearing yellowish in color.
• Siderite is an iron carbonate (FeCO₃) containing less than 40% iron, making it less economically desirable for extraction.
• Geographic Distribution:
• The major iron ore belts in India include the Odisha-Jharkhand belt, the Durg-Bastar-Chandrapur belt, and the Bellary-Chitradurga-Chikkamagaluru-Tumakuru belt.
• While Hematite is predominantly found in Odisha and Chhattisgarh, Magnetite is largely exported from the Mangaluru port.

Shortcut Trick

Apply the BODMAS rule by solving the bracket and division first.

Expression: 81 + 24 − 38 + 17 + 22 − 16

Combine positive terms: 81 + 24 + 17 + 22 = 144

Combine negative terms: 38 + 16 = 54

Final result: 144 − 54 = 90

∴ The correct answer is 90.

Alternate Method

Given: 81 + (24 × 1) − 38 + 17 + 44 ÷ 2 − 16

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

⇒ 81 + 24 − 38 + 17 + 44 ÷ 2 − 16 (Solving bracket 24 × 1 = 24)

⇒ 81 + 24 − 38 + 17 + 22 − 16 (Solving division 44 ÷ 2 = 22)

⇒ 105 − 38 + 17 + 22 − 16 (Addition from left: 81 + 24 = 105)

⇒ 67 + 17 + 22 − 16 (Subtraction: 105 − 38 = 67)

⇒ 84 + 22 − 16 (Addition: 67 + 17 = 84)

⇒ 106 − 16 (Addition: 84 + 22 = 106)

⇒ 90

∴ The correct answer is 90.

Additional Information

BODMAS Rule

It is an acronym to help remember the order of mathematical operations: Brackets (), Orders (exponents/roots), Division (÷), Multiplication (×), Addition (+), and Subtraction (−).

Left-to-Right Rule

When operators like addition and subtraction (or multiplication and division) appear in the same step, solve the expression from left to right.

Grouping for Speed

In expressions involving only addition and subtraction, grouping all positive terms and negative terms separately before the final subtraction can reduce errors and save time.

Shortcut Trick

The Product of two numbers = HCF × LCM = 24 × 360 = 8640.

Check options for Difference = 48 and Product = 8640.

Option (1): 144 − 96 = 48; 144 × 96 = 13824 (Incorrect).

Option (4): 120 − 72 = 48; 120 × 72 = 8640 (Correct).

∴ The correct answer is 120 and 72.

Alternate Method

Given:

HCF = 24

LCM = 360

Difference (x − y) = 48

Formula Used:

Product of numbers (x × y) = HCF × LCM

(x + y)² = (x − y)² + 4xy

Calculations:

⇒ x × y = 24 × 360 = 8640

⇒ (x + y)² = (48)² + 4 × (8640)

⇒ (x + y)² = 2304 + 34560 = 36864

⇒ x + y = √36864 = 192

⇒ Adding (x + y = 192) and (x − y = 48):

⇒ 2x = 192 + 48 = 240 → x = 120

⇒ Subtracting (x − y = 48) from (x + y = 192):

⇒ 2y = 192 − 48 = 144 → y = 72

∴ The correct answer is 120 and 72.

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 of LCM

The HCF of any set of numbers is always a factor of their LCM. If the HCF does not divide the LCM, such numbers cannot exist.

Co-prime Factors

Two numbers can be represented as (HCF × a) and (HCF × b), where 'a' and 'b' are co-prime integers (meaning HCF(a, b) = 1).

Shortcut Trick

Combine the internal terms within the bracket first: 11.85 − (5.45 + 4.60) = 11.85 − 10.05 = 1.80.

Final calculation: 12.1 − 1.80 = 10.3.

∴ The correct answer is 10.3.

Alternate Method

Given Expression: 12.1 − (11.85 − 5.45 − 4.60)

Using the BODMAS rule, we must simplify the terms inside the parentheses first from left to right:

⇒ 12.1 − (6.40 − 4.60)

⇒ 12.1 − 1.80

⇒ 10.3

∴ The correct answer is 10.3.

Additional Information

BODMAS Rule

This rule specifies the priority of operations: Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

Decimal Subtraction

When subtracting decimals, always align the decimal points and append zeros (e.g., 12.1 as 12.10) to ensure the numbers have the same number of decimal places.

Shortcut Trick

The given expression follows the algebraic identity: a³ − 3a²b + 3ab² − b³ = (a − b)³.

Here, let a = 5.1 and b = 0.1.

Substituting the values: (5.1 − 0.1)³ = (5.0)³.

Calculation: 5 × 5 × 5 = 125.

∴ The correct answer is 125.

Alternate Method

Given: (5.1)² × 5.1 − 3 × 0.1 × (5.1)² + 3 × 5.1 × (0.1)² − (0.1)³

Formula Used: (a − b)³ = a³ − 3a²b + 3ab² − b³

⇒ Let a = 5.1 and b = 0.1.

⇒ a² × a − 3 × b × a² + 3 × a × b² − b³

⇒ a³ − 3a²b + 3ab² − b³

⇒ (a − b)³

⇒ (5.1 − 0.1)³

⇒ (5.0)³

⇒ 5 × 5 × 5 = 125

∴ The correct answer is 125.

Additional Information

Cube of Sum Identity

(a + b)³ = a³ + 3a²b + 3ab² + b³, which can also be written as a³ + b³ + 3ab(a + b).

Sum and Difference of Cubes

a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²).

Conditional Identity

If a + b + c = 0, then a³ + b³ + c³ = 3abc.

Shortcut Trick

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

Here, a = √6 and b = √2.

⇒ Result = 2((√6)² + (√2)²)

⇒ Result = 2(6 + 2) = 2 × 8 = 16.

∴ The correct answer is 16.

Alternate Method

Given: (√6 + √2)² + (√6 − √2)²

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

⇒ [(√6)² + (√2)² + 2(√6 × √2)] + [(√6)² + (√2)² − 2(√6 × √2)]

⇒ (6 + 2 + 2√12) + (6 + 2 − 2√12)

⇒ (8 + 2√12) + (8 − 2√12)

⇒ 8 + 8 + 2√12 − 2√12

⇒ 16

∴ The correct answer is 16.

Additional Information

Standard Algebraic Identities

The identity (a + b)² + (a − b)² = 2(a² + b²) is derived by adding the expansions of square of sum and square of difference.

Difference of Identities

Subtracting the two squares gives (a + b)² − (a − b)² = 4ab, which is often used in simplification problems involving roots.

Surds and Squares

For any positive number x, (√x)² = x. This property allows for quick elimination of square root signs in algebraic expressions.

Shortcut Trick

For an odd number of consecutive terms, the Average is always the middle number.

Middle number = Total Sum ÷ Count of numbers = 54 ÷ 3 = 18

Since the numbers are consecutive even, they are 18 − 2, 18, and 18 + 2.

The numbers are 16, 18, and 20.

The largest among them is 20.

∴ The correct answer is 20.

Alternate Method

Given: Sum of 3 consecutive even numbers = 54

Let the three consecutive even numbers be x, x + 2, and x + 4.

⇒ Sum = x + (x + 2) + (x + 4) = 54

⇒ 3x + 6 = 54

⇒ 3x = 54 − 6

⇒ 3x = 48

⇒ x = 48 ÷ 3

⇒ x = 16

⇒ Largest number = x + 4 = 16 + 4

⇒ Largest number = 20

∴ The correct answer is 20.

Additional Information

Consecutive Even/Odd Numbers

Whether consecutive numbers are even or odd, the common difference between them is always 2.

Middle Term Property

In an Arithmetic Progression (AP) with an odd number of terms, the Average is always the middle term (Median).

Sum of AP Series

The sum of an AP is given by S_n = n/2 × (first term + last term) or S_n = n × Average.

Shortcut Trick

The given expression 9³ + 7³ + 3 × 9 × 7 × 16 is in the form of the algebraic identity a³ + b³ + 3ab(a + b) = (a + b)³.

Here, a = 9, b = 7, and (a + b) = 16.

Substituting these values: (9 + 7)³ = 16³.

Evaluating the cube: 16 × 16 × 16 = 4096.

∴ The correct answer is 4096.

Alternate Method

Given:

Expression: 9³ + 7³ + 3 × 9 × 7 × 16

Formula Used:

The algebraic identity for the cube of a sum is: (a + b)³ = a³ + b³ + 3ab(a + b)

Calculations:

⇒ Let a = 9 and b = 7.

⇒ Then a + b = 9 + 7 = 16.

⇒ The expression becomes: 9³ + 7³ + 3 × 9 × 7 × (9 + 7).

⇒ According to the identity, this is equal to (9 + 7)³.

⇒ (16)³ = 16 × 16 × 16

⇒ 256 × 16 = 4096.

∴ The correct answer is 4096.

Additional Information

Cube of a Difference Identity

The expansion for the cube of a difference is (a − b)³ = a³ − b³ − 3ab(a − b).

Sum and Difference of Cubes

Factorization formulas are a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²).

Binomial Square Identities

Standard squares: (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Shortcut Trick

Observe that x and y are reciprocals of each other, hence xy = 1.

For expressions of the form (a+√b)/(a−√b) + (a−√b)/(a+√b), the sum x + y = 2(a² + b) / (a² − b).

Substitute a = 2 and b = 6: x + y = 2(2² + 6) / (2² − 6) = 2(10) / (−2) = −10.

Apply the identity x² + y² = (x + y)² − 2xy.

Calculation: (−10)² − 2(1) = 100 − 2 = 98.

∴ The correct answer is 98.

Alternate Method

Given: x = (2 + √6) / (2 − √6) and y = (2 − √6) / (2 + √6)

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

Rationalizing x by multiplying with the conjugate (2 + √6):

⇒ x = [(2 + √6) × (2 + √6)] / [(2 − √6) × (2 + √6)]

⇒ x = (4 + 6 + 4√6) / (4 − 6) = (10 + 4√6) / −2

⇒ x = −5 − 2√6

Similarly, rationalizing y by multiplying with the conjugate (2 − √6):

⇒ y = −5 + 2√6

Now, calculate the sum and product:

⇒ x + y = (−5 − 2√6) + (−5 + 2√6) = −10

⇒ xy = (−5 − 2√6) × (−5 + 2√6) = (−5)² − (2√6)² = 25 − 24 = 1

Using the identity for x² + y²:

⇒ x² + y² = (x + y)² − 2xy

⇒ x² + y² = (−10)² − 2(1) = 100 − 2

⇒ x² + y² = 98

∴ The correct answer is 98.

Additional Information

Rationalization of Surds

To rationalize a denominator of the form (a − √b), multiply both the numerator and denominator by the conjugate (a + √b).

Algebraic Identity for Sum of Squares

The expression a² + b² can be derived using the formula (a + b)² − 2ab or (a − b)² + 2ab.

Reciprocal Relations

If x = 1/y, then xy = 1. In such cases, xⁿ + yⁿ is always an integer if (x+y) is an integer.

Shortcut Trick

For a Rectangle, the length, breadth, and diagonal form a right-angled triangle.

Recognize the standard Pythagorean Triplet: (5, 12, 13).

Given: Length = 12 cm and Diagonal (hypotenuse) = 13 cm.

Therefore, the remaining side (Breadth) must be 5 cm.

∴ The correct answer is 5 cm.

Alternate Method

Given:

Length (l) = 12 cm

Diagonal (d) = 13 cm

Formula Used:

In a Rectangle, Diagonal² = Length² + Breadth² (by Pythagoras Theorem)

Calculations:

⇒ 13² = 12² + b²

⇒ 169 = 144 + b²

⇒ b² = 169 − 144

⇒ b² = 25

⇒ b = √25

⇒ b = 5 cm

∴ The correct answer is 5 cm.

Additional Information

Area of Rectangle

The total space occupied by the rectangle is given by Area = Length × Breadth.

Perimeter of Rectangle

The total boundary length is given by Perimeter = 2 × (Length + Breadth).

Common Pythagorean Triplets

Frequently used sets of integers satisfying a² + b² = c² include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

Shortcut Trick

Solve the bracket first using known squares: 25² = 625 and 15² = 225.

Sum of squares = 625 + 225 = 850.

Subtracting 450 from the sum: 850 − 450 = 400.

Multiply the result by 40: 40 × 400 = 16000.

∴ The correct answer is 16000.

Alternate Method

Given expression: 40 × (25² + 15² − 450)

Apply the BODMAS rule by solving terms inside the parentheses first:

⇒ 40 × (625 + 225 − 450)

⇒ 40 × (850 − 450)

⇒ 40 × 400

⇒ 16000

∴ The correct answer is 16000.

Additional Information

BODMAS Rule

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

Squares ending in 5

To find the square of a number ending in 5 (like n5), multiply n by (n+1) and suffix 25. For example, 25² = (2 × 3) and suffix 25 = 625.

Multiplication with Zeros

When multiplying numbers with trailing zeros, multiply the non-zero digits and then append the total count of zeros to the result (e.g., 40 × 400: 4 × 4 = 16, append three zeros = 16000).

Shortcut Trick

The difference between the sums of two groups with a common element is always equal to the difference in their averages multiplied by the number of terms.

Since m is common, the difference between the averages of (l, m) and (m, n) is simply half the difference between l and n.

Difference between l and n = 17 × 2 = 34.

∴ The correct answer is 34.

Alternate Method

Given:

Average of l and m = (l + m) / 2

Average of m and n = (m + n) / 2

Difference between averages = 17

Calculations:

⇒ ((l + m) / 2) − ((m + n) / 2) = 17

⇒ (l + m − m − n) / 2 = 17

⇒ (l − n) / 2 = 17

⇒ l − n = 17 × 2

⇒ l − n = 34

∴ The correct answer is 34.

Additional Information

Average Property

The Sum of observations is always equal to the Average × Number of observations.

Overlap Method

When subtracting two averages of the same size, any common term between the sets is cancelled out during the subtraction of their sums.

Linear Transformation

If each term in a set is increased or decreased by a constant k, the average of the set also changes by k.

Shortcut Trick

If Passed students = 30%, then Failed students = 100% − 30% = 70%.

Given that 70% represents 42,000 students.

Applying the Unitary Method: 1% = 42,000 ÷ 70 = 600.

Number of Passed students (30%) = 30 × 600 = 18,000.

∴ The correct answer is 18000.

Alternate Method

Given:

Total appeared students = 100%

Pass Percentage = 30%

Number of Failed Students = 42,000

Calculations:

⇒ Failed Percentage = 100% − 30% = 70%

⇒ Let the Total students be x.

⇒ 70% of x = 42,000

⇒ (70 ÷ 100) × x = 42,000

⇒ x = (42,000 × 100) ÷ 70

⇒ x = 600 × 100 = 60,000

⇒ Passed students = 30% of Total students

⇒ Passed students = 0.30 × 60,000

⇒ Passed students = 18,000

∴ The correct answer is 18000.

Additional Information

Percentage Base Calculation

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

Complementary Percentages

In any binary outcome (pass/fail, win/loss), the sum of percentages must always equal 100%.

Percentage to Fraction Conversion

Converting percentages to fractions (e.g., 70% = 7/10) can often simplify complex division and multiplication steps.

Shortcut Trick

If the Cost Price (CP) and Selling Price (SP) are both increased or decreased by the same percentage, the ratio between them remains unchanged.

Since the ratio SP : CP remains constant, the Profit Percentage will also remain the same as the initial value.

Initial profit = 30%.

New profit = 30%.

∴ The correct answer is 30%.

Alternate Method

Given: Initial profit = 30%, CP and SP increase = 40%.

Formula Used: Profit Percentage = [(Selling Price − Cost Price) ÷ Cost Price] × 100

⇒ Let the initial Cost Price (CP) = 100

⇒ Since profit is 30%, initial Selling Price (SP) = 100 + 30% of 100 = 130

⇒ New CP = 100 + (40 ÷ 100) × 100 = 140

⇒ New SP = 130 + (40 ÷ 100) × 130 = 130 + 52 = 182

⇒ New Profit = New SP − New CP = 182 − 140 = 42

⇒ New Profit Percentage = (42 ÷ 140) × 100

⇒ New Profit Percentage = (3 ÷ 10) × 100 = 30%

∴ The correct answer is 30%.

Additional Information

Invariant Profit Percentage

If both CP and SP are multiplied by the same factor k, the profit percentage remains constant because (k × SP − k × CP) ÷ (k × CP) = (SP − CP) ÷ CP.

Profit and Loss Formulas

Profit % = (Profit ÷ CP) × 100 | Loss % = (Loss ÷ CP) × 100. Profit or loss is always calculated on the Cost Price unless specified otherwise.

Selling Price Calculation

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

Shortcut Trick

Let total fruits be 100 units.

Sold = 60 units, Remaining = 40 units.

Spoilt = 30% of 40 = 12 units.

Given: 12 units = 48 fruits ⇒ 1 unit = 4 fruits.

Fruits sold = 60 units × 4 = 240.

∴ The correct answer is 240.

Alternate Method

Given:

Percentage sold = 60%

Spoilage rate = 30% of remaining fruits

Total spoilt = 48 fruits

Calculations:

⇒ Let Initial Fruits = x

⇒ Fruits remaining after selling 60% = x − 0.60x = 0.40x

⇒ Spoilt fruits = 30% of 0.40x = 0.30 × 0.40x = 0.12x

⇒ According to the question: 0.12x = 48

⇒ x = 48 ÷ 0.12 = 4800 ÷ 12 = 400

⇒ Number of fruits sold = 60% of 400 = 0.60 × 400 = 240

∴ The correct answer is 240.

Additional Information

Successive Percentage Application

When a percentage is calculated on a leftover amount, it is a form of successive deduction. Net Percentage = (Remaining%) × (Subsequent%).

Unitary Method in Percentages

Assuming the base value as 100 units simplifies multi-step percentage problems by converting them into basic arithmetic ratios.

Shortcut Trick

Profit on Selling Price (SP) = 25% = 1/4.

This implies if SP = 4 units, then Profit = 1 unit.

Cost Price (CP) = SP − Profit = 4 − 1 = 3 units.

Profit percentage on CP = (Profit ÷ CP) × 100 = (1 ÷ 3) × 100 = 33.33%.

∴ The correct answer is 33.33 percent.

Alternate Method

Given:

Profit earned on Selling Price = 25%

Formula Used:

Profit = Selling Price (SP) − Cost Price (CP)

Profit % on CP = (Profit ÷ CP) × 100

Calculations:

⇒ Let the Selling Price (SP) be ₹100.

⇒ Profit = 25% of ₹100 = ₹25.

⇒ Cost Price (CP) = SP − Profit = 100 − 25 = ₹75.

⇒ Profit % on CP = (25 ÷ 75) × 100

⇒ Profit % on CP = (1 ÷ 3) × 100

⇒ Profit % on CP = 33.333...

∴ The correct answer is 33.33 percent.

Additional Information

Relationship between Profit on SP and CP

If a person earns x% profit on SP, the actual profit percentage (on CP) is always higher and is given by [x ÷ (100 − x)] × 100.

Relationship between Loss on SP and CP

If a person incurs x% loss on SP, the actual loss percentage (on CP) is always lower and is given by [x ÷ (100 + x)] × 100.

Markup Percentage

Markup % is the percentage by which the Marked Price is higher than the Cost Price. Formula: Markup % = [(MP − CP) ÷ CP] × 100.

Shortcut Trick

Remaining food for 900 men lasts for (60 − 6) = 54 days.

After 300 men left, remaining men = 900 − 300 = 600.

Ratio of men = 900 : 600 = 3 : 2 ⇒ Ratio of days = 2 : 3 (inverse).

2 units = 54 days ⇒ 1 unit = 27 days.

3 units = 3 × 27 = 81 days.

∴ The correct answer is 81 days.

Alternate Method

Given: Initial men = 900, Total food duration = 60 days, Days passed = 6, Men who left = 300.

Formula Used: M₁ × D₁ = M₂ × D₂ (where work/food is constant).

⇒ Remaining days for 900 men = 60 − 6 = 54 days

⇒ Total remaining food units = 900 × 54

⇒ Remaining men in group = 900 − 300 = 600

⇒ Let the remaining food last for x days for 600 men.

⇒ 600 × x = 900 × 54

⇒ x = (900 × 54) ÷ 600

⇒ x = (3 × 54) ÷ 2

⇒ x = 3 × 27 = 81

∴ The correct answer is 81 days.

Additional Information

Chain Rule Formula

The general formula for work and men is (M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂, where M is men, D is days, H is hours, and W is work.

Inverse Variation

The number of days is inversely proportional to the number of men (D ∝ 1/M). If manpower decreases, the food duration increases proportionally.

Man-Days Concept

Total Food Stock is often measured in Man-Days. Total Work = Strength × Duration.

Shortcut Trick

Efficiency Ratio of A : B = 1 : 2 (since A takes twice as long as B).

Total Work = Efficiency of A × Time of A = 1 × 60 = 60 units.

Efficiency of C = Efficiency of (A + B) = 1 + 2 = 3 units/day.

Total Efficiency (A + B + C) = 1 + 2 + 3 = 6 units/day.

Required Time = Total Work ÷ Total Efficiency = 60 ÷ 6 = 10 days.

∴ The correct answer is 10 days.

Alternate Method

Given:

Time taken by A = 60 days

Time taken by B = 60 ÷ 2 = 30 days (since A takes twice as long)

Formula Used:

Efficiency = Total Work ÷ Time

Time taken by C = Time taken by (A + B) together

Calculations:

⇒ 1 day work of (A + B) = 1/60 + 1/30 = (1 + 2)/60 = 3/60 = 1/20

⇒ Time taken by (A + B) = 20 days

⇒ Time taken by C = 20 days

⇒ Combined efficiency of A, B, and C = 1 + 2 + 3 = 6 units/day

⇒ Total days taken by A, B, and C together = 60 ÷ 6 = 10 days

∴ The correct answer is 10 days.

Additional Information

Relationship between Time and Efficiency

Efficiency is inversely proportional to the time taken. If the ratio of time taken by A and B is x : y, then the ratio of their efficiencies is y : x.

Combined Work Formula

If A can do a work in 'x' days and B can do it in 'y' days, then together they can finish it in (x × y) ÷ (x + y) days.

Work and Wages

Wages are always distributed in the ratio of the work done by each person, which is equivalent to the ratio of their efficiencies if they work for the same duration.

Shortcut Trick

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

Shortcut: 270 × (5/18) = 15 × 5 = 75.

∴ The correct answer is 75 m/s.

Alternate Method

Given:

Speed of the car = 270 km/hr

Formula Used:

Speed (m/s) = Speed (km/hr) × (5 ÷ 18)

Calculations:

⇒ Speed in m/s = 270 × (5 ÷ 18)

⇒ Speed in m/s = (270 ÷ 18) × 5

⇒ Speed in m/s = 15 × 5

⇒ Speed in m/s = 75 m/s

∴ The correct answer is 75 m/s.

Additional Information

Unit Conversion Factor

1 km/hr = 1000 m ÷ 3600 s = 5/18 m/s. To convert m/s to km/hr, multiply by 18/5.

Speed, Distance and Time

Speed = Distance ÷ Time. If distance is in meters and time is in seconds, speed will be in m/s.

Average Speed

Average Speed = Total Distance ÷ Total Time. This is useful when the object moves with different speeds over different intervals.

Shortcut Trick

Since the speed is constant, the distance covered is directly proportional to the time taken.

Distance 1 (Length of Train) corresponds to the time to cross a man = 5 sec.

Distance 2 (Length of Train + Platform) corresponds to the time to cross the platform = 12 sec.

The required ratio of lengths is equal to the ratio of the respective times taken.

Required Ratio = 5 : 12.

∴ The correct answer is 5 : 12.

Alternate Method

Given:

Time to cross a standing man = 5 sec

Time to cross a platform of length 'y' = 12 sec

Formula Used:

Distance = Speed × Time

Calculations:

⇒ Let the length of the train be L and its speed be S.

⇒ When crossing a man, Distance = L. ∴ L = S × 5

⇒ When crossing a platform of length y, Distance = L + y. ∴ L + y = S × 12

⇒ We need to find the ratio of length of train (L) to the total length (L + y).

⇒ Ratio = L : (L + y)

⇒ Ratio = (S × 5) : (S × 12)

⇒ Ratio = 5 : 12

∴ The correct answer is 5 : 12.

Additional Information

Point Object vs Extended Object

When a train crosses a point object (man, pole, tree), distance = length of train. When it crosses an extended object (platform, bridge, tunnel), distance = length of train + length of object.

Speed Conversion

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

Relative Speed

For two objects moving in the same direction, relative speed = S₁ − S₂. For opposite directions, relative speed = S₁ + S₂.

Shortcut Trick

Assume Marked Price (X) = 100 units.

Purchased Price (Y) = 80% of 100 = 80 units (after 20% discount).

Selling Price (Z) = 120% of 80 = 96 units (20% more than Y).

Ratio of Z : X = 96 : 100 = 24 : 25.

∴ The correct answer is 24 : 25.

Alternate Method

Given:

Marked Price = Rs. X

Discount = 20%

Purchased Price = Rs. Y

Selling Price = Rs. Z (where Z is 20% more than Y)

Calculations:

⇒ Y = X − 20% of X

⇒ Y = 0.8X

⇒ Z = Y + 20% of Y

⇒ Z = 1.2Y

⇒ Substitute Y = 0.8X in the equation for Z:

⇒ Z = 1.2 × (0.8X)

⇒ Z = 0.96X

⇒ Z/X = 0.96

⇒ Z/X = 96/100

⇒ Z/X = 24/25

∴ The correct answer is 24 : 25.

Additional Information

Successive Percentage Change

When a value is changed by a% and then by b%, the net effective change is given by the formula: [a + b + (a × b)/100]%.

Relationship between MP, CP, and SP

Marked Price (MP) × (100 − Discount%)/100 = Selling Price (SP). Also, Cost Price (CP) × (100 + Profit%)/100 = Selling Price (SP).

Fraction to Ratio Conversion

To find a ratio from a decimal like 0.96, write it as a fraction (96/100) and simplify it to its lowest terms by dividing by the Greatest Common Divisor (GCD).

The correct answer is 'the beau monde'.

 

Key Points

• The phrase 'the beau monde' is borrowed from French, literally meaning 'the beautiful world'.
• In an English context, it refers specifically to fashionable society or the world of high society, wealth, and celebrity.
• The sentence indicates that Rabina was more focused on her professional craft (acting) than on the social status or the glamorous lifestyle associated with the elite.

Therefore, the correct answer is 'Option 2'.

Complete Sentence: Rabina had no interest in the beau monde, but she wanted to focus on acting.

Additional Information

• Anima mundi: A Latin phrase meaning 'the soul of the world', referring to an intrinsic connection between all living things on the planet.
• Spiritus mundi: A Latin phrase meaning 'the spirit of the world', often used to describe a collective unconscious or a universal storehouse of images.
• Le monde: A French term meaning 'the world'. Using it with 'the' (the le monde) is grammatically incorrect in English as 'le' already serves as the definite article.

The correct answer is: Enemy.

Key Points

• The word 'foe' refers to an individual or group that is hostile or opposed to another; it signifies an adversary or an opponent. (शत्रु)
• Example: The two kingdoms were long-standing foes, having fought many battles over the contested territory.
• 'Enemy' refers to a person who is actively opposed or hostile to someone or something. It is a direct synonym for 'foe' as both terms describe a person who feels enmity toward another. (दुश्मन)
• Example: He was a fierce competitor on the field, but he never treated his opponent as an enemy.
• Hence, we can infer that the synonym of 'foe' is 'enemy'.

Therefore, the correct answer is: Enemy.

Additional Information

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

• Ally (सहयोगी / मित्र): A person, group, or nation that is associated with another for some common cause or purpose.
• Example: The two companies decided to become allies to dominate the emerging market.
• Friend (दोस्त / मित्र): A person whom one knows and with whom one has a bond of mutual affection.
• Example: She has been my closest friend since we were in primary school.
• Guest (अतिथि / मेहमान): A person who is invited to visit someone's home or attend a particular social occasion.
• Example: We are preparing a special meal for our guests arriving this evening.

The correct answer is discrimination.

Key Points

• The word discrmination as used in the sentence is misspelled. The correct spelling is discrimination, which includes the letter i after the consonant c.
• The term is derived from the Latin word discriminatio, which refers to the act of distinguishing or perceiving differences. In a modern legal context, it specifically refers to the prejudicial treatment of different categories of people.
• The word consists of five syllables: dis-crim-i-na-tion. The common spelling error occurs by omitting the middle vowel i, leading to the incorrect form discrmination.
• In the context of the Indian Constitution, protection against discrimination is a fundamental right under Article 15, which prohibits the State from discriminating against any citizen on grounds only of religion, race, caste, sex, or place of birth.
• The sentence highlights a judicial directive aimed at ensuring social justice and egalitarianism by preventing biased practices in the allocation of public goods.

 Additional Information

• equitable:
• This term refers to being fair and impartial. It is often distinguished from equality; while equality means giving everyone the same thing, equity involves distributing resources based on the specific needs of individuals to reach an equal outcome.
• In legal terminology, equitable remedies are actions a court prescribes to resolve a dispute when monetary damages are insufficient.
• resources:
• Refers to the assets, supplies, or capital used by an individual or organization to function effectively.
• These are often classified into tangible resources (land, machinery) and intangible resources (knowledge, brand reputation).
• marginalised:
• This describes groups or individuals who are pushed to the fringes of society, often experiencing social exclusion and limited access to political or economic power.
• The spelling with an s is the standard British English variant used in India, while the American English variant is spelled with a z (marginalized).

The correct answer is: Ambeince.

Key Points

• The word 'Ambeince' is misspelt in the given options; it is an incorrect spelling of 'Ambience'. (अशुद्ध वर्तनी)
• Example: His essay contained several spelling errors, including writing Ambeince instead of the correct term.
• 'Ambience' refers to the character and atmosphere of a place or the mood that it creates. (माहौल / वातावरण)
• Example: The restaurant had a very pleasant ambience with soft lighting and comfortable seating.
• Hence, we can infer that the misspelt word is 'Ambeince'.

Therefore, the correct answer is: Ambeince.

Additional Information

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

• Consequence (परिणाम): A result or effect, typically one that is unwelcome or unpleasant.
• Example: The loss of habitat is a direct consequence of deforestation.
• Convergence (अभिसरण): The process or state of converging; coming together from different directions.
• Example: The convergence of these two major roads often causes heavy traffic.
• Excellence (उत्कृष्टता): The quality of being outstanding or extremely good.
• Example: The university is world-renowned for its academic excellence.

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

Key Points

• The word 'express' refers to the act of communicating a thought, feeling, or idea through words, gestures, or images. (व्यक्त करना)
• Example: He found it difficult to express his true feelings to his parents.
• 'Suppress' means to forcibly put an end to something or to prevent the development or expression of a feeling, impulse, or idea. It is the direct opposite of express. (दबाना/रोकना)
• Example: She tried hard to suppress her anger during the meeting.
• Hence, we can infer that the opposite of 'express' is 'suppress'.

Therefore, the correct answer is- suppress.

Additional Information

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

• Convey (सूचित करना/पहुंचाना): To transport or carry to a place; or to make an idea or feeling known or understandable to someone.
• Example: It is hard to convey the complexity of the situation in just a few words.
• Announce (घोषणा करना): To make a formal public statement about a fact, occurrence, or intention.
• Example: The government will announce the new policy next week.
• Declare (स्पष्ट रूप से कहना): To say something in a solemn and emphatic manner.
• Example: The country decided to declare independence after years of struggle.

The correct answer is 'lord'.

 

Key Points

• The word 'lord' refers to a person who has authority, control, or power over others; in a historical context, it refers to a feudal superior.
• Historically, a knight was a soldier of high social rank who provided military service to a lord in exchange for land or protection, making the act of pledging loyalty contextually appropriate.
• The other options do not fit the context of the sentence: 'lured' is a verb meaning to tempt, and 'load' refers to a heavy weight or burden.

Therefore, the correct answer is 'Option 1'.

Complete Sentence: The knight pledged his loyalty to the lord.

Additional Information

• Lured: To tempt a person or animal to do something or to go somewhere, especially by offering some form of reward.
• Load: A heavy or bulky thing that is being carried or is about to be carried.
• Knight: A man who served his sovereign or lord as a mounted soldier in armor during the Middle Ages.

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

Key Points

• The phrase 'A newly coined word or expression' refers to a term or usage that has been recently created or invented, often to describe new concepts or technologies. (नया गढ़ा गया शब्द या अभिव्यक्ति)
• Example: In the digital age, we frequently encounter a newly coined word or expression that describes a new type of software or social trend.
• 'Neologism' is the specific term for a relatively recent or isolated word, phrase, or usage that is in the process of entering common use but has not yet been fully accepted into mainstream language. (नया शब्द / नवशब्द)
• Example: Many literary critics enjoy analyzing the neologisms created by authors like Lewis Carroll or George Orwell.
• Hence, we can infer that the one-word substitution for 'a newly coined word or expression' is 'neologism'.

Therefore, the correct answer is- Neologism.

Additional Information

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

• Neoplasm (अर्बुद / रसौली): A new and abnormal growth of tissue in some part of the body, especially as a characteristic of cancer.
• Example: The medical tests revealed a small, benign neoplasm that required monitoring but not immediate surgery.
• Neoteny (चिरयौवन / अपरिपक्वता प्रतिधारण): The retention of juvenile or larval traits in the adult stage of an animal.
• Example: The Axolotl is a classic example of neoteny because it retains its external gills and aquatic lifestyle throughout its entire life.
• Maxim (सूक्ति / कहावत): A short, pithy statement expressing a general truth or a fundamental principle of conduct.
• Example: He lived his life by the maxim that one should treat others as they wish to be treated themselves.

The correct answer is 'over'.

 

Key Points

• The phrase brood over is a common phrasal verb which means to think deeply or worry about something for a long time, especially something that is unhappy, anxious, or distressing.
• In this context, the speaker is expressing their dislike for dwelling on past events which negatively impacts their present life.
• The other prepositions provided do not form the correct idiomatic expression with the verb brooding.

Therefore, the correct answer is Option 1.

 

Complete Sentence: 'I don't like brooding over my past events and killing my present.'

 

Additional Information

• Option 2: 'for' is incorrect because brood is not paired with this preposition to indicate the subject of thought.
• Option 3: 'regarding' is a preposition meaning 'about' or 'concerning', but it is not used as a phrasal verb component with brooding.
• Option 4: 'related' is primarily an adjective or a past participle and does not function as a preposition to connect the verb to the object in this structure.

The correct answer is The worm is caught by the early bird.

Key Points

• To transform a sentence from Active Voice to Passive Voice, the Object of the active sentence (the worm) must be shifted to the Subject position.
• The original sentence is in the Simple Present Tense, following the structure: Subject + Verb (s/es) + Object.
• The passive voice construction for the Simple Present Tense requires the structure: New Subject + is/am/are + Past Participle (V3) + by + New Object.
• The Main Verb 'catches' must be converted into its Third Form (V3), which is 'caught'.
• Since the new subject 'the worm' is a Singular Noun, the Auxiliary Verb 'is' is used to maintain subject-verb agreement.
• The Agent (the early bird) is introduced at the end of the sentence following the Preposition 'by'.

 Additional Information

• Voice Transformation Rules:
• Interchange of Positions: The Subject and Object are swapped; the person or thing acted upon becomes the focus of the sentence.
• Verb Conjugation: The Passive Voice always utilizes the Past Participle form of the verb, regardless of the original tense.
• Tense Consistency:
• Present Continuous: changes to is/am/are + being + V3.
• Present Perfect: changes to has/have + been + V3.
• Simple Past: changes to was/were + V3.
• Transitivity: Only Transitive Verbs (verbs that require an object) can be converted into Passive Voice. Intransitive verbs like 'sleep' or 'go' cannot undergo this transformation because they lack a direct object to become the new subject.

The correct answer is Researchers have made several important archaeological discoveries in the desert region.

Key Points

• The provided sentence is in the Passive Voice and follows the Present Perfect Tense structure: Object + have/has + been + V3 (past participle) + by + Subject (Agent).
• In the passive sentence, Several important archaeological discoveries is the grammatical subject (receiver), and researchers is the agent (doer) introduced by the preposition by.
• To convert the sentence into the Active Voice, the agent researchers must be moved to the subject position at the beginning of the sentence.
• The Present Perfect Tense in active voice requires the formula: Subject + has/have + V3 (past participle) + Object. Since Researchers is a plural noun, the auxiliary verb have is used.
• The main verb made is the past participle (V3) form of 'make', which remains unchanged in the perfect tense active construction.
• The phrase Several important archaeological discoveries shifts from the subject position to the direct object position, while the prepositional phrase in the desert region remains at the end as an adverbial of place.

 Additional Information

• Understanding Tense Mismatches in Incorrect Options:
• Simple Present Tense: Option 1 uses the verb make, which denotes a habitual action or a general truth, failing to reflect the completed nature of the Present Perfect.
• Past Continuous Tense: Option 2 uses were making, which describes an ongoing action that was happening at a specific point in the past, which is a significant change in grammatical aspect.
• Past Perfect Tense: Option 4 uses had made, which indicates an action completed before another past action. This shift from Present Perfect to Past Perfect is incorrect in voice conversion unless the reporting verb is in the past (as in indirect speech).

The correct answer is 'of'.

 

Key Points

• The preposition 'of' is used after the verb 'admit' to form the phrasal verb 'admit of'.
• The phrase 'admit of' means to permit, allow for, or to leave room for a certain possibility or action.
• In the given sentence, it indicates that the matter is so critical that it does not allow or permit any delay.
• Options 1, 3, and 4 do not form the correct idiomatic expression required in this context.

Therefore, the correct answer is Option 2.

 

Complete Sentence: 'Being a matter of utmost importance, it admits of no delay.'

 

Additional Information

• Admit (verb): Generally means to allow someone to enter a place or to agree that something is true.
• Admit to (phrasal verb): Used when confessing to a crime, mistake, or a specific action (e.g., He admitted to stealing the watch).
• Admit of (phrasal verb): Used primarily with abstract nouns like doubt, delay, or excuse (e.g., The rules admit of no exceptions).

The correct answer is Option 4.

Key Points

• The paragraph describes a majestic scene of Frederick (the Emperor) leading his army. The goal is to arrange the sentences to maintain the narrative flow between the leader and his knights.
• S1 is the fixed starting sentence: It introduces Frederick riding his war steed.
• Sentence C follows S1: It expands the scene by mentioning who was "behind him," introducing the thousand knights.
• """"A thousand knights, clad in glittering suits of mail, were behind him.""""
• Sentence B follows C: It returns focus to Frederick’s action as he leads the group, describing his flashing sword.
• """"His gleaming sword flashed like lightning as he waved it above his head.""""
• Sentence A follows B: It uses the pronoun 'They' to refer back to the knights introduced in sentence C, describing their prestige.
• """"They were the flower of Germany, the bravest and best of the heroes of the Rhineland.""""
• Sentence D is the final jumbled sentence: It provides a vivid visual description of the emperor's beard (""like the tail of a flaming red comet"").
• """"The emperor's long beard streamed in the wind like the tail of a flaming red comet.""""
• S2 is the fixed closing sentence: It connects stylistically to Sentence D; while D describes a visual (comet), S2 describes an auditory detail (""voice like rolling thunder"") as he turns to his followers.
• The correct sequence is CBAD.

Coherent paragraph after rearrangement:

""""Then Frederick rode up and down upon his prancing war steed. A thousand knights, clad in glittering suits of mail, were behind him. His gleaming sword flashed like lightning as he waved it above his head. They were the flower of Germany, the bravest and best of the heroes of the Rhineland. The emperor's long beard streamed in the wind like the tail of a flaming red comet. His voice was like rolling thunder as he turned in his saddle and called to his eager followers.""""

The correct answer is Option 4.

Key Points

• The paragraph begins with S1, which introduces the two main types of buildings owned by King Louis: palaces and castles.
• Sentence D is the second sentence because it elaborates on the first part of S1 (the palaces), describing them as places of joy and gaiety.
• Sentence A follows next as it provides a contrast by describing the second part of S1 (the castles), mentioning the gloomy prisons they contained.
• Sentence C is the fourth sentence as it narrows the focus from general prisons to a specific example: a prison castle on the island of Sainte Marguerite.
• Sentence B follows Sentence C by providing a physical description of this specific island prison, noting it was built near the shore of the sea.
• Finally, S2 (the fixed last sentence) completes the narrative by describing the sensory experience of the prisoners trapped in that sea-side location.
• The logically coherent sequence is DACB.

Coherent paragraph after rearrangement:

Now this grand King Louis had many fine palaces and strong castles. In his palaces was everything that could make life joyous and gay. In some of his castles there were gloomy prisons where men whom he did not like were shut up. One of these prison castles was on a small island called Sainte Marguerite. A dark and lonely place it was, built close by the shore of the sea. The prisoners gazing out of the narrow windows saw only the water and the sky, and the only sound they heard was that of the waves lapping on the cold stones.

The correct answer is I can't help but feel sorry for her.

Key Points

• The underlined part 'can't help feel' is a variation of an idiomatic expression that typically requires either a gerund or a specific conjunction to be considered grammatically standard in formal written English.
• The expression 'cannot help' is an idiom meaning to be unable to refrain from or avoid a particular action, emotion, or impulse.
• When using this idiom with a bare infinitive (the base form of a verb like 'feel'), the conjunction 'but' must be placed between 'help' and the verb. This creates the standard construction 'cannot help but [verb]'.
• In this structure, 'but' functions as a restrictive preposition meaning 'except'. Therefore, the phrase 'can't help but feel' literally implies that the speaker is unable to do anything except feel sorry for the individual.
• While the original phrasing 'can't help feel' is occasionally used in informal speech, it is technically incomplete. Option 1 provides the necessary grammatical bridge required for standard English usage.

 Additional Information

• Linguistic Structures of the Idiom:
• Gerund Construction: One of the most common standard forms is 'cannot help + [verb]-ing'. For example, 'I cannot help feeling sympathy.' This is widely used in both British English and American English.
• Double Negative Function: The construction 'cannot help but' is technically a double negative that functions as an affirmative. It is often preferred in literary and formal contexts to emphasize a lack of choice.
• Grammatical Avoidance:
• Solecisms: It is important to avoid mixing these two rules. Phrases such as 'cannot help but feeling' (mixing 'but' with a gerund) or 'cannot help from' are considered grammatical errors.
• Semantic Nuance: The use of 'cannot help' suggests a psychological or emotional compulsion, distinguishing the statement from a simple declaration of feeling (e.g., Option 2), and highlighting the speaker's involuntary empathetic response.

The correct answer is Option 1.

 

Key Points

• The primary grammatical error in the sentence is the usage of the phrase 'on the' to precede 'evening'.
• In standard English, parts of the day like morning, afternoon, or evening typically take the preposition 'in' (e.g., 'in the evening').
• When referring to a specific evening previously mentioned or implied in a narrative, the demonstrative adjective 'that' is used (e.g., 'that evening'), and the preposition 'on' is dropped.
• The construction 'on the evening' is only correct if followed by a specific date or event, such as 'on the evening of the ceremony'.
• Thus, the error is located in Part 1 of the sentence.

Therefore, the correct answer is 1.

 

Correct Sentence: 'However, that evening, he returned with one foot limping because his heel was wounded.'

 

Additional Information

• (2): 'evening, he returned with' – This segment is correct; the comma properly separates the introductory temporal phrase from the main subject and verb.
• (3): 'one foot limping because' – This part is grammatically sound, using a present participle 'limping' to describe the state of the foot and the conjunction 'because' to introduce the reason.
• (4): 'his heel was wounded.' – This is a grammatically correct clause in the passive voice, completing the explanation.