SSC CGL 2025 (Held On: 15 Sept, 2025 Shift 3) (Previous Year Paper)

Correct Option - 3

The logic followed here is:

Logic: Object : Device it is used in

Mercury : Thermometer → Mercury is used in thermometers.

Similarly,

Fuel : ? → Fuel is used in Engine.

Hence, the correct answer is "Option 3".

Correct Option - 4

The logic followed here is:

Logic: Concept : Core principle

Justice :: Equity → Equity is the principle/essence of Justice.

Similarly,

Governance : ? → Legitimacy is the principle/foundation of governance.

Hence, the correct answer is "Option 4".

Correct Option - 4

The position and positional values or English Alphabets are:

 

The logic followed here is:

Thus, HEK can replace the question mark (?) in the following series.

Hence, the correct answer is "Option 4".

The logic followed here is:

Clearly, ABC can replace the question mark (?) in the following series.

Hence, the correct answer is "Option 3".

Correct Option - 3

The position and positional values or English Alphabets are:

 

The logic followed here is:

Clearly, STU can replace the question mark (?) in the following series.

Hence, the correct answer is "Option 3".

The logic followed here is:

Thus, PSNF can replace the question mark (?) in the series.

Hence, the correct answer is "Option 1".

The logic followed here is:

Thus, BLVF can replace the question mark (?) in the series.

Hence, the correct answer is "Option 1".

The logic followed here is:

Thus, 128 will complete the series.

Hence, the correct answer is "Option 1".

Given: Each of the letters in the word FAMILY is arranged in alphabetical order. 

The position and positional values or English Alphabets are:

F is second from the left and L is third from the right in the new letter-cluster formed.

Thus, there are 5 letters between F and L.

Hence, the correct answer is "Option 4".

Thus, option 1 and 4 is exactly the same as the one given.

Hence, the correct answer is "Option 1".

Correct Option - 3

Clearly, option 1 and 4 are identical to the given address.

Hence, the correct answer is "Option 3".

The logic followed here is:

PAPER : QBUFS

Similarly,

STONE : TUTOF

Hence, the correct answer is "Option 3".

The logic followed here is:

HxL : 8×12

Similarly,

TxZ : ?

Hence, the correct answer is "Option 1".

Given: In a row of 60 students, Meena is 25th from the left and Rupa is 20th from the right

.

Total number of students = 60

 

Meena's position from  left = 25

 

Rupa's position from right = 20

 

Rupa’s position from left = (60 − 20) + 1 = 40 + 1 = 41

 

So, number of students between Meena and Rupa = (41 - 25) - 1

= 16 - 1 = 15

<br>

Thus, there are 15 students between Meena and Rupa.

 

Hence, the correct answer is "Option 4".

The logic followed here is:

EIGHTY : GIEYTH

Similarly,

OUTPUT : ?

Thus, OUTPUT is related to TUOTUP.

Hence, the correct answer is "Option 4".

The logic followed here is:

NATION : ANTINO 

Similarly,

HUNGRY : ?

Thus, HUNGRY is related to  UHNGYR.

Hence, the correct answer is "Option 4".

Given: M introduces R as the son of the only brother of her mother's husband.

Clearly, R is cousin of M.

Hence, the correct answer is "Option 1".

The logic followed here is:

Thus, 42 will come next in the series.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: Both letters and numbers move 2 steps forward.

1. M13 : O15 : Q17

2. N14 : P16 : R18 

3. L12 : N14 : P16 

4. O15 : Q17 : S21

Thus, "O15 : Q17 : S21" is the odd one out.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: Letters move 2 steps forward, numbers move 2 steps forward and third element is a symbol.

1. A2@ : C4# : E6$

2. B3% : D5^ : F7&

3. C4* : E6( : G8)

4. D5_ : G9@ : J13$

Thus, "D5_ : G9@ : J13$" is the odd one out.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: First number, Second number, Third number = Second number + (Second number - First number) × 2

Let's check each option:

1. 20, 30, 50 → 30 + (30 - 20) × 2 = 30 + 10 × 2 = 30 + 20 = 50
2. 15, 25, 40 → 25 + (25 - 15) × 2 = 25 + 10 × 2 = 25 + 20 = 45 ≠ 40
3. 18, 24, 36 → 24 + (24 - 18) × 2 = 24 + 6 × 2 = 24 + 12 = 36
4. 14, 28, 56 → 28 + (28 - 14) × 2 = 28 + 14 × 2 = 28 + 28 = 56

Hence, the correct answer is "Option 2".

Given: Introducing a boy, a woman says, 'He is the son of my only brother's wife.'

Clearly, the boy is Nephew of the Woman.

Hence, the correct answer is "Option 3".

Decoding the Symbols:

Given:  R # S & T 

It means: R is father of S, S is husband of T.

Clearly, R is R is the father-in-law of T.

Hence, the correct answer is "Option 3".

Given: Looking at a man, a woman said, ""His mother is the only daughter of my mother.""

Clearly, the man is Son of the Woman.

Hence, the correct answer is "Option 3".

Given equation: 5 + 6 × 2 - 2 = ?

After replacing the symbols by their meaning, we get:

⇒ 5 × 6 + 2 ÷ 2 = ?

⇒ 5 × 6 + 1 = ?

⇒ 30 + 1 = ?

⇒ 31 = ?

Hence, the correct answer is "Option 4".

The correct answer is Option 3.

Key Points

• Statement 1: A gold reliquary with figures in an arcade was found at Bimaran—This is correct. The Bimaran casket, discovered in Afghanistan, is a gold reliquary attributed to the Gandhara art style. It features intricate depictions of Buddha and other figures, showcasing Gandhara's fusion of Hellenistic and Buddhist art.
• Statement 2: Intricately carved ivory plaques were discovered at Begram—This is also correct. The Begram ivories, excavated from the ancient city of Begram in Afghanistan, are well-known examples of Gandhara art. These carvings reflect a blend of local and foreign artistic traditions, including Indian, Greco-Roman, and Central Asian influences.
• The Gandhara art style is renowned for its fusion of Indo-Greek, Roman, and Indian artistic elements, which is evident not only in stone sculptures but also in artifacts such as reliquaries, ivories, and coins.
• Both statements collectively highlight the diversity of Gandhara art beyond stone sculptures, emphasizing its influence on various forms of artistic expression.

Additional Information

• Gandhara Art:
• Gandhara art flourished during the Kushan Empire (1st–5th century CE) in the northwestern region of the Indian subcontinent, encompassing parts of modern-day Pakistan and Afghanistan.
• It is known for its depiction of Buddhist themes, particularly the life of the Buddha, using techniques and styles influenced by Greco-Roman art.
• The use of schist stone, stucco, and metal for sculptures was common, and the art often depicted intricate drapery, realistic facial expressions, and curly hair reminiscent of Hellenistic influences.
• Artifacts Found at Bimaran:
• The Bimaran casket, a notable gold reliquary, is a key example of Gandhara art. It is believed to have contained relics of the Buddha and features exquisite depictions of Buddhist figures in an arcade setting.
• This artifact demonstrates the influence of Hellenistic art on Buddhist iconography in the region.
• Artifacts Found at Begram:
• Begram, an ancient city on the Silk Road, yielded a treasure trove of artifacts, including intricately carved ivory plaques, glassware, and coins.
• The Begram ivories, in particular, showcase exceptional craftsmanship and provide insights into the cultural exchanges between India, Central Asia, and the Mediterranean during ancient times.

The correct answer is It is dedicated to honoring cattle used in agriculture.

Key Points

• Kanuma Festival is celebrated as part of the four-day harvest festival of Sankranti in Andhra Pradesh, specifically on the third day.
• This festival is primarily dedicated to honoring cattle, which are considered sacred and play a vital role in agricultural activities.
• The day is marked by rituals and ceremonies that involve worshipping cows, bulls, and other livestock, recognizing their contribution to farming and rural livelihoods.
• Cattle are adorned with flowers, painted horns, and other decorations as a form of respect and gratitude.
• Farmers express their appreciation for the animals that assist in plowing fields, transporting goods, and other agricultural tasks.
• Kanuma is a symbol of harmony between humans and animals in agrarian societies and reflects the deep cultural connection to agriculture.

Additional Information

• Sankranti and Kanuma
• Sankranti is a harvest festival celebrated across India with regional variations, including Pongal in Tamil Nadu, Lohri in Punjab, and Bihu in Assam.
• Kanuma is an integral part of Sankranti celebrations in Andhra Pradesh, emphasizing the agrarian lifestyle and the cultural importance of livestock.
• Kanuma serves as a reminder of the symbiotic relationship between humans and animals in traditional farming practices.

The correct answer is Narsingha.

Key Points

• Narsingha is a traditional wind instrument commonly used in the folk music of Himachal Pradesh.
• It is characterized by its ornate curved hornpipe design, often crafted from brass or copper.
• The instrument holds great ceremonial significance and is primarily used in rituals, festivals, and traditional celebrations.
• Narsingha produces a deep and resonant sound, making it ideal for musical accompaniment in open-air folk performances.
• Its name is derived from the Sanskrit term "Narasimha," symbolizing strength and auspiciousness in Indian culture.

Additional Information

• Traditional Wind Instruments in Himachal Pradesh
• Himachal Pradesh is known for its rich musical heritage, including instruments such as the Narsingha, Flute, and Shehnai.
• These instruments are integral to folk music performances and reflect the cultural vibrancy of the region.
• They are often used in religious ceremonies and festivals, symbolizing joy and celebration.

The correct answer is Option 3: 1 and 2 are correct.

Key Points

• Statement 1: Men and women compete in identical freestyle distances from 50m to 1500m in World Championship swimming events (50m pool). This includes events such as 50m, 100m, 200m, 400m, 800m, and 1500m freestyle.
• Statement 2: Individual Medley events are held only up to 400m for both men and women. The recognized distances include 200m and 400m Individual Medley events at the World Championships (50m pool).
• Both statements are factually correct, as the International Swimming Federation (FINA) defines the standard distances and event formats for World Championship swimming competitions.
• These events are held under standardized rules to maintain consistency in competition formats for all genders and categories.

Additional Information

• Freestyle Events:
• Freestyle swimming events are conducted at various distances, including 50m, 100m, 200m, 400m, 800m, and 1500m.
• Both male and female swimmers compete in these distances under identical formats in World Championship competitions conducted in a 50m pool.
• The 800m freestyle event for men and the 1500m freestyle event for women were added to the Olympic Games program in 2020, ensuring parity in event offerings.
• Individual Medley Events:
• Individual Medley (IM) consists of four strokes—Butterfly, Backstroke, Breaststroke, and Freestyle—performed in succession during a single race.
• At the World Championship level, IM events are limited to 200m and 400m distances for both men and women.
• No IM events longer than 400m are conducted in 50m pools as per FINA regulations.
• World Championship Swimming Format:
• The World Aquatics Championships are governed by FINA, the international federation responsible for overseeing swimming competitions.
• Events are conducted in 50m pools (long course) and include freestyle, backstroke, breaststroke, butterfly, and medley disciplines.
• All events are divided into heats, semi-finals, and finals, depending on the distance and format.

The correct answer is 1946.

Key Points

• The Amateur Athletics Federation of India (AAFI) was founded in 1946 as the governing body for athletics in India.
• AAFI is responsible for managing, promoting, and developing track and field athletics across the country.
• It is affiliated with the International Association of Athletics Federations (IAAF) and the Asian Athletics Association (AAA).
• The organization has played a crucial role in organizing national championships, selecting athletes for international events, and nurturing talent in various disciplines of athletics.
• In 2001, the AAFI was renamed the Athletics Federation of India (AFI) to align with global nomenclature trends.

Additional Information

• Olympics & Athletics 
• Neeraj Chopra: Olympic gold medalist in Javelin throw, a modern icon.
• Milkha Singh: Legendary sprinter, known as "The Flying Sikh".
• Abhinav Bindra: India's first individual Olympic gold medalist (Shooting).
• P.T. Usha: Iconic track and field athlete, "Payyoli Express".

The correct answer is Ulaanbaatar, Mongolia.

Key Points

• The 17th edition of the joint India-Mongolia military exercise, Nomadic Elephant, was conducted in Ulaanbaatar, Mongolia.
• This exercise focuses on counter-insurgency and counter-terrorism operations under the United Nations mandate.
• The event aims to enhance mutual cooperation, interoperability, and camaraderie between the Indian Army and the Mongolian Armed Forces.
• Nomadic Elephant is an annual bilateral military exercise that alternates between India and Mongolia.
• The exercise strengthens defense ties and showcases India’s strategic outreach towards Mongolia under its Act East Policy.

Additional Information

• Key Aspects of Nomadic Elephant:
• Focus: Counter-terrorism, peacekeeping (UN mandate), mountain warfare, special forces tactics, and interoperability.
• Frequency: Annual, alternating locations.
• Participants: Indian Army special forces/units and Mongolian Armed Forces.
• Recent Edition: The 17th edition was held in Ulaanbaatar, Mongolia, in 2025.
• Training Modules: Include field training, reflex shooting, room intervention, cyber warfare, and drone operations.

The correct answer is Gumi, South Korea.

Key Points

• The Asian Athletics Championships 2025 is set to be hosted in Gumi, South Korea, a city known for its industrial development and modern infrastructure.
• The event will feature participation from over 40 Asian nations, highlighting the best talent from the continent in track and field events.
• The Asian Athletics Championships is organized by the Asian Athletics Association (AAA), which governs athletics activities in Asia.
• Gumi’s state-of-the-art sports facilities and its rich history of hosting international events make it an ideal venue for the Championships.
• The Championships serve as a significant platform for athletes to qualify for global events, including the World Athletics Championships and the Olympics.

Additional Information

• Busan, South Korea
• Busan is South Korea’s second-largest city and a major port known for its beaches and modern skyscrapers.
• It hosted the 2002 Asian Games and the 2002 FIFA World Cup in collaboration with Japan, showcasing its capability to organize large-scale sporting events.
• Seoul, South Korea
• Seoul, the capital city of South Korea, hosted the 1988 Summer Olympics, which played a significant role in putting South Korea on the global stage.
• It is a hub of culture, technology, and sports, with state-of-the-art stadiums and facilities for international events.
• Tokyo, Japan
• Tokyo, the capital city of Japan, recently hosted the 2020 Summer Olympics, which were delayed to 2021 due to the COVID-19 pandemic.
• The city is renowned for its advanced infrastructure and experience in organizing international sporting events.

The correct answer is Stories exploring immigrant life, cultural identity, and arranged marriage challenges..

Key Points

• "Arranged Marriage" by Chitra Banerjee Divakaruni is a critically acclaimed collection of short stories.
• The book addresses themes such as immigrant experiences, cultural identity, and the complexities of arranged marriages.
• Each story explores the struggles of Indian women navigating the traditional and modern worlds, often dealing with alienation, identity crises, and adaptation in foreign lands.
• The stories shed light on the cultural dilemmas and unique challenges faced by Indian immigrants, particularly women, in balancing their heritage with Western values.
• This collection has won several literary awards, including the American Book Award, and is widely praised for its emotional depth and nuanced storytelling.

Additional Information

• Key Novels of Chitra Banerjee:
• The Mistress of Spices (1997): A magical realism novel about a spice shop owner, later adapted into a film.
• Sister of My Heart (1999): Focuses on the bond between two cousins in Kolkata, navigating family secrets and cultural pressures.
• The Palace of Illusions (2008): A feminist retelling of the Mahabharata from Draupadi's perspective, a major bestseller.
• The Forest of Enchantments (2019): A retelling of the Ramayana, giving voice to Sita.
• Independence (2023): Her most recent novel, exploring the partition of India.
• Before We Visit the Goddess (2016): A multi-generational story of three Bengali women across India and the U.S..

The correct answer is It is an unsorted mix of materials deposited directly by ice..

Key Points

• Glacial till is characterized by its unsorted nature, meaning it contains particles of varying sizes ranging from clay and silt to large boulders.
• It is deposited directly by the movement or melting of glacial ice, without water sorting the materials.
• Unlike water-laid glacial sediments, glacial till often appears chaotic and lacks any layering or stratification.
• Glacial till is typically composed of angular particles, as the materials are broken and transported by ice rather than smoothed by water.
• It is a key indicator of past glacial activity and is commonly found in moraines, drumlins, and other glacial landforms.

Additional Information

• Glacial Deposits
• Glacial deposits include both till (unsorted materials directly deposited by ice) and stratified drift (sorted sediments deposited by meltwater).
• These deposits are essential in understanding past glacial movements, climate changes, and geological processes.
• Studying glacial deposits helps reconstruct the history of glaciated regions and provides insights into Earth's geomorphological evolution.

The correct answer is 1 and 2 only.

Key Points

• Gita Upadhyay is a noted Hindi writer from Assam who has contributed significantly to Hindi literature and literary translation. Hence, statement 1 is correct.
• She is known for translating several literary works, including “The Diary of Anne Frank”, into Indian languages to make the work accessible to a wider audience. Hence, statement 2 is correct.
• In 2025, she was honored with the Padma Shri, not the Padma Bhushan. Therefore, the statement mentioning Padma Bhushan is incorrect. Hence, statement 3 is not correct.
• Padma Awards are among the highest civilian honours in India and are announced annually on the eve of Republic Day.
• Statement-wise Analysis:
• Statement 1 – Correct.
• Statement 2 – Correct.
• Statement 3 – Incorrect.
• Hence, the correct answer is Statements 1 and 2 only.

Additional Information

• Padma Awards: India’s civilian awards include Bharat Ratna, Padma Vibhushan, Padma Bhushan, and Padma Shri.
• Padma Shri is awarded for distinguished service in fields such as literature, education, arts, science, social work, and public affairs.
• Anne Frank was a Jewish girl whose diary documented her experiences during the Second World War and the Nazi occupation.
• The Diary of Anne Frank is one of the world’s most translated and widely read autobiographical works.
• Assam has contributed significantly to Indian literature through works in Assamese, Hindi, Bengali, and regional dialects.

Important Points

• Translation literature plays an important role in spreading global literary works into regional Indian languages.
• Questions related to Padma Award recipients and notable literary personalities are frequently asked in competitive examinations.

The correct answer is A is true, but R is false.

Key Points

• The Population Enumeration phase of Census 2011 was conducted in most parts of India in February 2011, as per the scheduled timeline.
• The Census of India is conducted in two phases: the House Listing and Housing Census, and the Population Enumeration.
• The House Listing and Housing Census phase of Census 2011 was conducted earlier in 2010, not postponed, and served as the preparatory phase for Population Enumeration.
• The Population Enumeration phase collects critical information on the population's demographic, socio-economic, and cultural characteristics.
• Thus, the Assertion (A) is true, but the Reason (R) is false since House Listing and Housing Census was not postponed for simultaneous data collection.

Additional Information

• Census 2011:
• The Census 2011 was the 15th Census of India and the 7th Census after Independence.
• The Census was conducted under the Census Act, 1948, which provides the legal framework for the exercise.
• The Census process is carried out by the Office of the Registrar General and Census Commissioner, under the Ministry of Home Affairs, Government of India.
• It provides comprehensive data on the population size, distribution, literacy, gender ratio, economic activity, housing, and other critical socio-economic parameters.

The correct answer is Option 1: Only Statement 1 is correct.

Key Points

• Sun-synchronous orbits are designed to allow satellites to maintain consistent local solar time over a specific region. This is due to the synchronization of their orbital plane with the Earth's rotation and seasonal position of the Sun.
• These orbits are commonly used in Earth observation satellites to capture images under consistent lighting conditions, which enhances the accuracy of data collection and analysis.
• The inclination of a sun-synchronous orbit is typically between 96° to 98°, ensuring that the satellite crosses the equator at the same local solar time every day.
• Such orbits are highly beneficial for applications such as weather forecasting, environmental monitoring, and agricultural planning.
• Statement 2 is incorrect because geostationary orbits are not related to sun-synchronous functionality. Geostationary satellites remain fixed above a specific location on Earth, and their primary purpose is communication and broadcasting rather than maintaining consistent solar time.

Additional Information

• Geostationary orbits are located approximately 35,786 kilometers above Earth's equator and match the rotation of the Earth.
• Satellites in geostationary orbit are primarily used for telecommunications, weather monitoring, and broadcasting services.
• Unlike sun-synchronous orbits, geostationary satellites do not maintain consistent solar time. Instead, they remain stationary relative to a fixed point on Earth.
• Solar-powered satellites in geostationary orbit are effective due to constant sunlight exposure but are not related to the concept of sun-synchronous orbits.
• Geostationary vs. Sun-Synchronous Orbits:
• Geostationary orbits are fixed over one location, while sun-synchronous orbits move relative to the Earth's surface.
• Sun-synchronous orbits are ideal for Earth observation, while geostationary orbits are better suited for communication and weather satellites.

The correct answer is Hypothalamus.

Key Points

• The hypothalamus is a small region of the brain located below the thalamus and above the brainstem, playing a crucial role in maintaining the body’s internal balance (homeostasis).
• It regulates the circadian rhythm by controlling the suprachiasmatic nucleus (SCN), which is the brain’s master clock.
• The SCN receives light signals from the retina and adjusts the body’s internal clock according to the light-dark cycle of the environment.
• The hypothalamus influences several biological processes, including sleep-wake cycles, hormone release, temperature regulation, and other daily physiological rhythms.
• Disruption in the hypothalamus or SCN can lead to sleep disorders and abnormalities in circadian rhythm regulation.

Additional Information

• Cerebellum
• The cerebellum is primarily responsible for coordinating voluntary movements such as posture, balance, and speech.
• It does not regulate circadian rhythm but plays a key role in motor control and cognitive functions.
• Although it is not directly linked to circadian rhythms, research suggests it may indirectly influence motor activities during different times of the day.
• Medulla oblongata
• Located in the brainstem, the medulla oblongata controls vital autonomic functions such as respiration, heart rate, and blood pressure.
• It does not directly regulate circadian rhythms but ensures the continuous functioning of essential life-sustaining processes.
• The medulla is part of the brainstem, which communicates with other brain regions, including the hypothalamus, for integrated physiological control.
• Thalamus
• The thalamus acts as the brain’s relay center, transmitting sensory and motor signals to the cerebral cortex.
• It is involved in sleep regulation and consciousness but is not directly responsible for controlling circadian rhythms.
• The thalamus works closely with the hypothalamus in sleep-wake transitions and sensory processing during different states of alertness.

The correct answer is Option 1.

Key Points

• The Union Council of Ministers is collectively responsible to the Lok Sabha, as stated under Article 75(3) of the Indian Constitution.
• Collective responsibility means that the entire Council of Ministers shares responsibility for any decision or action taken by the government.
• They remain in office as long as they enjoy the confidence of the Lok Sabha. A vote of no-confidence can lead to their resignation.
• This principle ensures accountability of the executive (Council of Ministers) to the legislature (Lok Sabha) in a parliamentary system of government.
• Option 2 is incorrect because in states with bicameral legislatures, the State Council of Ministers is collectively responsible to the Legislative Assembly, not the Legislative Council, as per Article 164(2).

Additional Information

• Article 164(2): Responsibility of State CoM
• At the state level, the Council of Ministers is collectively responsible to the Legislative Assembly, not the Legislative Council, even in states with bicameral legislatures.
• This ensures that the executive at the state level remains accountable to the directly elected house of the legislature.
• Vote of No Confidence
• A government loses power if it fails to maintain the confidence of the Lok Sabha through a majority vote.
• A no-confidence motion can be moved against the government, and its passage results in the resignation of the entire Council of Ministers.
• Bicameral Legislature
• In India, a bicameral legislature refers to a legislative body with two houses: the Legislative Assembly (lower house) and the Legislative Council (upper house).
• The Legislative Assembly is the directly elected body, while the Legislative Council is partly elected and partly nominated.
• Collective responsibility applies only to the Legislative Assembly as it represents the will of the people.

The correct answer is Option 2: 1 & 3 correct.

Key Points

• Statement 1: The Governor's discretionary power to recommend President's Rule is indeed mentioned in Article 356(1) of the Indian Constitution.
• Article 356(1) allows the Governor to report to the President if the governance in a state cannot be carried out according to the provisions of the Constitution, thereby leading to the imposition of President's Rule.
• Statement 3: The Sarkaria Commission, which was constituted to examine the relationship between the Union and State governments, recommended that Governors should not be removed arbitrarily and must be allowed to complete their term unless there are rare and compelling reasons for their removal.
• The Sarkaria Commission's recommendations are widely recognized as a guiding framework for maintaining the independence and impartiality of the Governor's position.
• Statement 2 is incorrect as the 41st Constitutional Amendment did not curtail the Governor's term. The Governor's term remains five years, as per Article 156 of the Constitution.

Additional Information

• Article 356 of the Indian Constitution:
• It is also known as the "President's Rule" provision.
• The Governor of a state can report to the President if there is a failure of the constitutional machinery in the state.
• Based on this report, the President can assume control over the state's administration.
• It is considered a controversial article, as it has been invoked multiple times, often leading to debates about misuse.
• The Sarkaria Commission:
• Constituted in 1983 to review the working of the Centre-State relations in India and suggest improvements.
• Among its key recommendations was the advice that Governors should be apolitical and impartial.
• It emphasized that the Governor should be allowed to complete their five-year term except in exceptional circumstances.
• 42nd Constitutional Amendment:
• This amendment was passed in 1976 during the Emergency period in India.
• It extended the term of the Lok Sabha and State Legislative Assemblies from five years to six years.
• However, this was reversed by the 44th Constitutional Amendment in 1978, bringing the term back to five years.
• It had no impact on the term of Governors, which remains five years as per Article 156.

The correct answer is 25 cm.

Key Points

• The least distance of distinct vision for a normal human eye is approximately 25 cm.
• This is the minimum distance at which the eye can focus an object clearly without straining.
• The distance is determined by the ability of the eye lens to accommodate and focus the light on the retina.
• At distances shorter than 25 cm, the ciliary muscles of the eye experience strain, making it difficult to maintain a clear focus.
• This limit is applicable to individuals with normal vision and may vary for people with vision impairments such as myopia or hypermetropia.

Additional Information

• Concept of Least Distance of Distinct Vision:
• The least distance of distinct vision is also called the near point of the eye.
• It varies with age; for example, children may have a near point closer than 25 cm, while older individuals might have a farther near point due to presbyopia.
• The near point is critical for tasks requiring close focus, such as reading or sewing.

The correct answer is 60 days.

Key Points

• Under the Bharatiya Nagarik Suraksha Sanhita (BNSS), 2023, a Magistrate can authorize detention for a maximum period of 60 days for offences punishable with less than 10 years of imprisonment before default bail becomes applicable.
• Section 167 of the Code of Criminal Procedure (CrPC), which is mirrored in the BNSS, governs the detention period authorized by a Magistrate.
• The 60-day period applies to cases where the offence is not punishable with death, life imprisonment, or imprisonment exceeding 10 years.
• If the investigation is not completed within 60 days, the accused becomes entitled to default bail as per the provisions of the law.
• This provision ensures the protection of individual liberty and prevents unnecessary prolonged detention without trial.

Additional Information

• The Bharatiya Nagarik Suraksha Sanhita (BNSS), 2023, is a comprehensive legislation replacing the Code of Criminal Procedure (CrPC).
• It aims to streamline criminal procedures and ensure justice delivery while safeguarding the rights of the accused and victims.

The correct answer is A is true, but R is false.

Key Points

• SVAMITVA stands for Survey of Villages and Mapping with Improvised Technology in Village Areas, launched by the Government of India in April 2020.
• The scheme aims to map rural inhabited lands using drone technology and provides property cards to the owners of these lands.
• It is implemented by the Ministry of Panchayati Raj, in collaboration with State Revenue Departments.
• The property cards generated under this scheme serve as legal ownership documents for rural inhabitants.
• SVAMITVA focuses exclusively on rural areas and does not cover urban regions, making Reason (R) incorrect.

Additional Information

• Drone Technology in SVAMITVA:
• Drones are used to conduct surveys and create high-resolution maps of rural inhabited lands.
• The use of drones ensures accuracy and reduces disputes over property boundaries.
• This modern technology enables the creation of a robust digital land record system in rural India.
• Coverage of SVAMITVA:
• The scheme is limited to rural areas and is not extended to urban regions.
• The primary objective is to empower rural citizens by providing legal ownership of their properties.
• Urban areas are covered under separate land record programs.

The correct answer is Tamil Nadu.

Key Points

• Poikkal Kuthirai Aattam, also known as the dummy horse dance, is a traditional folk dance performed in Tamil Nadu, India.
• This dance is primarily showcased during religious festivals and cultural events, reflecting the rich heritage of Tamil Nadu.
• The performer wears a costume resembling a horse, which is constructed using lightweight materials like bamboo and cloth, giving the illusion of riding a horse.
• The dance is often accompanied by traditional Tamil music and percussion instruments such as thavil and nadaswaram, creating an energetic atmosphere.
• Poikkal Kuthirai Aattam has deep cultural and religious significance, often performed to honor deities during temple festivals.

Additional Information

• Kerala
• Kerala is renowned for its classical dance forms, including Kathakali and Mohiniyattam.
• These dances are deeply rooted in Kerala’s cultural and religious traditions, often narrating stories from Hindu mythology.
• While Kerala has a rich tradition of folk and classical performances, Poikkal Kuthirai Aattam is not a native dance form of the state.
• Karnataka
• Karnataka is famous for its traditional dances such as Yakshagana, a theatrical dance-drama that combines storytelling, music, and vibrant costumes.
• Yakshagana is performed in Kannada-speaking regions and is distinct from Tamil Nadu’s Poikkal Kuthirai Aattam.
• The state also has folk dances like Dollu Kunitha, showcasing the cultural diversity of Karnataka.
• Telangana
• Telangana is known for its folk dances, including Perini Shivatandavam, a dance performed as an offering to Lord Shiva.
• Bonalu and Bathukamma are popular festivals in Telangana that feature unique traditional performances.

The correct answer is More corruption.

Key Points

• The Corruption Perception Index (CPI) is developed by Transparency International, a global organization dedicated to combating corruption.
• The CPI ranks countries based on their perceived levels of public sector corruption, as determined by expert assessments and surveys.
• The CPI score ranges from 0 to 100, where 0 represents the highest level of perceived corruption and 100 indicates the lowest.
• A lower score (closer to 0) signifies more corruption and poor governance, lack of transparency, and inadequate measures to prevent corrupt practices.
• Countries with a lower CPI score often face challenges like weak institutions, lack of accountability, and limited enforcement of anti-corruption laws.

Additional Information

• Less corruption
• A higher CPI score (closer to 100) indicates less corruption and better governance.
• Countries with higher scores tend to have strong institutions, robust anti-corruption measures, and greater transparency in public administration.
• Examples of countries with high CPI scores include Denmark, Finland, and New Zealand.
• Higher transparency
• While transparency is closely related to corruption levels, the CPI primarily measures corruption perceptions rather than transparency.
• Higher transparency often correlates with lower corruption, but transparency alone does not encompass the full scope of corruption-related issues.
• Better governance
• Better governance typically leads to lower corruption levels, as it ensures accountability, rule of law, and ethical conduct in public administration.
• The CPI indirectly reflects governance quality, but its primary focus remains on corruption perceptions.

The correct answer is Cotton textiles and Sugar.

Key Points

• Agro-based industries are industries that primarily depend on agricultural raw materials for their production.
• Cotton textiles are an agro-based industry as they depend on cotton, which is an agricultural product, as the primary raw material.
• The sugar industry is also an agro-based industry since it relies on sugarcane, a crop grown widely in India, as its raw material.
• These industries play a significant role in the Indian economy, providing employment and contributing to exports.
• Both cotton textiles and sugar industries are part of agro-based industries because of their strong dependence on agricultural resources for raw materials.

Additional Information

• Cement and Petrochemicals:
• Cement and petrochemical industries are not agro-based; they rely on minerals and chemicals as raw materials.
• Cement is produced using limestone, clay, and gypsum, which are mineral-based resources.
• Petrochemicals are derived from crude oil and natural gas, making them part of the chemical industry rather than agro-based industries.
• Jute textiles and Steel:
• Jute textiles rely on jute, which is an agricultural product, and therefore jute textiles are considered an agro-based industry.
• However, steel production depends on iron ore and other minerals, making it a mineral-based industry rather than agro-based.
• This option is incorrect because steel is not agro-based.
• Edible oil and Aluminium:
• Edible oil production depends on agricultural products such as mustard, sunflower, and groundnuts and is considered agro-based.
• Aluminium production, however, depends on bauxite (a mineral), making it part of the mineral-based industries.
• This option is incorrect because aluminium is not agro-based.

The correct answer is Desert National Park.

Key Points

• Desert National Park is located in the state of Rajasthan, India, and is known for its vast expanse of sand dunes and desert ecosystems.
• The park is one of the last natural habitats of the critically endangered Great Indian Bustard, a species that is emblematic of India’s desert ecosystem.
• In recent years, conservation efforts, including the breeding and reintroduction programs, have been successfully implemented to save the dwindling population of the Great Indian Bustard.
• The park spans over 3162 square kilometers and includes unique geographical features such as salt lakes, craggy rocks, and fixed dunes, making it a thriving ecosystem for diverse flora and fauna.
• It is a designated UNESCO World Heritage Site under the category of natural heritage, emphasizing its ecological significance and the need for conservation.

Additional Information

• Sariska National Park
• Located in the Alwar district of Rajasthan, Sariska National Park is famous for its tiger reserve under Project Tiger.
• The park is home to Bengal tigers, leopards, and other wildlife such as hyenas, jackals, and various bird species.
• It is known for the successful relocation of tigers after the species was locally extinct in the park in the early 2000s.
• Kuno National Park
• Kuno National Park is located in Madhya Pradesh and is known for being the site of the Asiatic Cheetah reintroduction project in 2022.
• The park is home to diverse flora and fauna, including leopards, jackals, and antelopes.
• It has been proposed as an alternative site for relocating Asiatic lions from Gir National Park in Gujarat.
• Panna Tiger Reserve
• Panna Tiger Reserve is situated in Madhya Pradesh and is well-known for its tiger conservation efforts.
• The park was declared a Biosphere Reserve by UNESCO in 2020.
• The Ken-Betwa river interlinking project has drawn attention to the reserve due to its potential environmental impact on the local flora and fauna.
• Conservation of the Great Indian Bustard
• The Great Indian Bustard is listed as critically endangered by the IUCN and is protected under the Wildlife Protection Act of India, 1972.
• Its population has been declining due to habitat loss, hunting, and human-induced threats such as power lines and agricultural expansion.
• The Government of India has initiated the ‘Habitat Improvement and Conservation Breeding Programme’ to protect and increase the population of the species.

The correct answer is Right to Property.

Key Points

• The Right to Property was originally a Fundamental Right under Article 31 of the Indian Constitution.
• It was removed from the list of Fundamental Rights through the 44th Constitutional Amendment Act, 1978, and moved to the category of legal rights under Article 300A.
• The amendment was implemented to curb the misuse of property rights and facilitate equitable land reforms, ensuring that the state could acquire private property for public purposes by providing compensation.
• As a legal right, the Right to Property is enforceable through the courts, but it no longer enjoys the same elevated status and protection as Fundamental Rights.
• Currently, Article 300A states: "No person shall be deprived of his property save by authority of law."

Additional Information

• Right to Equality (Article 14-18)
• It ensures equality before the law and equal protection of laws for all citizens.
• Prohibits discrimination on grounds of religion, race, caste, sex, or place of birth (Article 15).
• Abolishes untouchability (Article 17) and titles except for military or academic distinctions (Article 18).
• Right to Freedom (Article 19-22)
• Guarantees six essential freedoms, including freedom of speech and expression, assembly, association, movement, residence, and profession (Article 19).
• Protects against arbitrary arrest and detention (Article 22).
• However, these rights are subject to reasonable restrictions for maintaining public order, sovereignty, and security.
• Right against Exploitation (Article 23-24)
• Prohibits human trafficking, forced labor, and other forms of exploitation (Article 23).
• Prohibits the employment of children below the age of 14 in hazardous jobs or industries (Article 24).
• Theme of the Question: Fundamental Rights
• Fundamental Rights are enshrined in Part III of the Constitution, from Articles 12 to 35, and are considered essential for the development of individuals and democracy.
• These rights include the Right to Equality, Right to Freedom, Right against Exploitation, Right to Freedom of Religion, Cultural and Educational Rights, and Right to Constitutional Remedies.
• They are justiciable, meaning citizens can approach courts if these rights are violated.

The correct answer is ASPEX.

Key Points

• ASPEX (Aditya Solar wind Particle Experiment) is a scientific payload onboard the Aditya-L1 mission designed to monitor the solar wind at the Lagrange point 1 (L1).
• The primary objective of ASPEX is to study the composition and energy distribution of solar wind particles, including protons, alpha particles, and heavy ions.
• The payload helps in understanding the interaction of solar wind with Earth’s magnetosphere and its impact on space weather.
• ASPEX provides critical data on the dynamics of solar wind, enabling scientists to predict geomagnetic storms and their potential effects on satellites, power grids, and communication systems.
• It plays a crucial role in enhancing our understanding of heliophysics and solar-terrestrial interactions by analyzing the solar wind in real-time from a vantage point at L1.

Additional Information

• SUIT (Solar Ultraviolet Imaging Telescope):
• SUIT is one of the key payloads of the Aditya-L1 mission, designed to capture full-disk images of the Sun in the ultraviolet (UV) spectrum.
• It studies the dynamics of the Sun’s photosphere and chromosphere, contributing to understanding solar activity and its influence on space weather.
• SUIT also measures solar irradiance variations in the UV band, which have implications for Earth’s climate and atmospheric processes.
• SoLEXS (Solar Low Energy X-ray Spectrometer):
• SoLEXS is a payload on Aditya-L1 that observes X-ray emissions from the Sun.
• It monitors solar flares and estimates their energy output, providing insights into the Sun’s high-energy processes.
• The data from SoLEXS help in understanding the heating mechanisms of the Sun’s corona and its impact on the heliosphere.
• HEL1OS (High Energy L1 Orbiting X-ray Spectrometer):
• HEL1OS is another payload on Aditya-L1 that studies high-energy X-rays emitted by the Sun.
• It focuses on detecting and characterizing solar flares, coronal mass ejections (CMEs), and other energetic solar phenomena.
• The instrument aids in understanding the acceleration of particles in the Sun’s atmosphere and their subsequent propagation through the solar system.

The correct answer is Only 1.

Key Points

• Indian federalism is considered biased towards the Centre because the Constitution of India establishes a quasi-federal structure, where the Centre has more power compared to the states.
• The Union List in the Seventh Schedule of the Constitution contains more items (97 subjects initially, now 100) compared to the State List (66 subjects initially, now 61), ensuring greater control for the Centre.
• The President of India has significant powers, such as the ability to impose President's Rule under Article 356, which allows the Centre to take over the administration of a state.
• Financial arrangements also favor the Centre, as it controls the major sources of revenue and allocates funds to the states, as per recommendations of the Finance Commission.
• However, the Constitution does not explicitly use the term "federal." Instead, it describes India as a "Union of States" in Article 1, emphasizing the indestructible nature of the Union.

Additional Information

• Federal Features of the Indian Constitution:
• Division of powers between the Union and the States through three lists: Union List, State List, and Concurrent List.
• Independent judiciary with the Supreme Court as the final arbiter in disputes between the Centre and the states.
• Bicameral legislature at the Centre, consisting of the Lok Sabha and the Rajya Sabha, representing both the people and the states.
• Unitary Features of the Indian Constitution:
• Emergency provisions allow the Centre to assume greater control over states during crises (Articles 352, 356, and 360).
• Centralized financial powers, as the Centre collects and allocates major sources of revenue.
• The Governor, appointed by the President, acts as the Centre's representative in states.

Calculation:

(3.2 - 1$\frac35$) + (2$\frac14$ ÷ 0.5)

⇒ (3.2 - $8\over5$) + ($9\over4$ ÷ 0.5)

⇒ (3.2 - 1.6) + (2.25 ÷ 0.5)

⇒ 1.6 + 4.5

⇒ 6.1

Hence the correct answer is option (2).

Shortcut Trick

Marketing department's share = ₹36,000 × [5 ÷ (4 + 5 + 3)] = ₹36,000 × (5/12) = ₹15,000

Remaining amount after deductions = ₹15,000 − ₹3,000 − ₹1,500 = ₹10,500

Ratio of top performers = 5 : 4, so the smaller share gets 4 parts out of 9.

Smaller share = ₹10,500 × (4/9) = ₹4,666.67

∴ The correct answer is ₹4,666.67.

Alternate Method

Total: 36k 5/12 Mktg: 15k - 4.5k Rem: 10.5k 5 parts 4 parts Smaller Share = 4/9 × 10500 = 4666.67

Given:

Total bonus pool = ₹36,000

Bonus ratio for Sales, Marketing, and Operations = 4 : 5 : 3

Marketing deductions = ₹3,000 (team building) and ₹1,500 (intern)

Top performers' allocation ratio = 5 : 4

Calculations:

⇒ Total initial ratio parts = 4 + 5 + 3 = 12 parts

⇒ Marketing department's share = (5 ÷ 12) × 36,000 = ₹15,000

⇒ Total fixed deductions = 3,000 + 1,500 = ₹4,500

⇒ Remaining amount for top performers = 15,000 − 4,500 = ₹10,500

⇒ The remaining amount is split into 5 + 4 = 9 parts.

⇒ The smaller share corresponds to the 4 parts ratio.

⇒ Value of the smaller share = (4 ÷ 9) × 10,500

⇒ Value = 42,000 ÷ 9 = ₹4,666.66...

∴ The correct answer is ₹4,666.67.

Additional Information

Ratio Distribution Rule

When a quantity Q is divided in the ratio a : b : c, the share of the first part is calculated directly as [a ÷ (a+b+c)] × Q.

Sequential Allocations

When solving hierarchical distribution problems, calculate the pool for each subsequent stage by subtracting any fixed amounts before applying the new ratio constraints.

Proportions in Partnerships

If profits, revenues, or bonuses are distributed among groups, the respective shares behave similarly to partnership accounts, where total allocation strictly bounds internal distributions.

Shortcut Trick

For continued fractions, always calculate from the bottommost nested denominator upwards.

Bottommost expression = 2 + 1/2 = 5/2

Middle expression = 2 + 1 / (5/2) = 2 + 2/5 = 12/5

Final top expression = 1 + 1 / (12/5) = 1 + 5/12 = 17/12

∴ The correct answer is 17/12.

Alternate Method

Given:

x = 1 + 1 / (2 + 1 / (2 + 1/2))

Calculations:

⇒ First, we simplify the innermost fraction at the bottom: 2 + 1/2

⇒ 2 + 1/2 = (4 + 1) / 2 = 5/2

⇒ Substitute this back into the expression:

⇒ x = 1 + 1 / (2 + 1 / (5/2))

⇒ Taking the reciprocal: 1 / (5/2) = 2/5

⇒ x = 1 + 1 / (2 + 2/5)

⇒ Now, simplify the new bottom fraction: 2 + 2/5

⇒ 2 + 2/5 = (10 + 2) / 5 = 12/5

⇒ Substitute this back into the expression:

⇒ x = 1 + 1 / (12/5)

⇒ Taking the reciprocal: 1 / (12/5) = 5/12

⇒ x = 1 + 5/12

⇒ x = (12 + 5) / 12 = 17/12

∴ The correct answer is 17/12.

Additional Information

Continued Fractions

A continued fraction is evaluated by working from the bottommost nested fraction upwards to the main fraction.

Reciprocal Rule

The reciprocal of a fraction a/b is b/a. This property is used repeatedly when resolving 1 ÷ (a/b).

BODMAS Rule

For nested expressions, calculations must always resolve the deepest levels first according to the standard order of operations.

Shortcut Trick

Profit ratio is directly proportional to Equivalent Capital (Capital × Time).

Kapil's equivalent capital = (10 × 6) + (6 × 6) = 60 + 36 = 96 units

Manish's equivalent capital = 8 × 9 = 72 units

Profit Ratio = 96 : 72 = 4 : 3

∴ The correct answer is 4:3.

Alternate Method

Given:

Kapil's initial investment = ₹1,00,000

Manish's investment after 3 months = ₹80,000

Kapil withdrew ₹40,000 after 3 more months (i.e., at the end of 6 months).

Formula Used:

Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂)

₹1,00,000 × 6m

₹60,000 × 6m

Kapil

₹80,000 × 9m

Manish

0m 3m 6m 12m

Profit Ratio = (100k × 6 + 60k × 6) : (80k × 9) = 960 : 720 = 4:3

Calculations:

⇒ Kapil invested ₹1,00,000 for the first 6 months.

⇒ After 6 months, his capital becomes = ₹1,00,000 − ₹40,000 = ₹60,000.

⇒ Kapil invested ₹60,000 for the remaining 6 months of the year.

⇒ Kapil's equivalent capital = (1,00,000 × 6) + (60,000 × 6)

⇒ Kapil's equivalent capital = 6,00,000 + 3,60,000 = 9,60,000

⇒ Manish joined after 3 months, so his money was invested for (12 − 3) = 9 months.

⇒ Manish's equivalent capital = 80,000 × 9 = 7,20,000

⇒ Profit Ratio = Kapil's equivalent capital : Manish's equivalent capital

⇒ Profit Ratio = 9,60,000 : 7,20,000

⇒ Profit Ratio = 96 : 72 = 4 : 3

∴ The correct answer is 4:3.

Additional Information

Compound Partnership

When partners invest for different time periods or change their capital mid-way, profit is distributed based on the product of Capital and Time (Equivalent Capital).

Simple Partnership

When all partners invest their capital for the exact same time period, the profit is divided purely in the ratio of their invested capitals.

Working vs Sleeping Partner

A working partner actively manages the business and usually receives a fixed salary or commission from the profit before the remaining profit is divided among all partners based on investment.

Shortcut Trick

Profit ratio of partners = Ratio of their (Capital × Time).

A's Profit : B's Profit = (60000 × 10) : (90000 × 8) = 600000 : 720000 = 5 : 6

Total profit ratio parts = 5 + 6 = 11 units, which corresponds to the total profit of ₹40,000.

A's share = (5 ÷ 11) × 40000 = 200000 ÷ 11 ≈ ₹18,181.82

∴ The correct answer is ₹18,181.82.

Alternate Method

Given:

A's investment = ₹60,000 | Time period = 10 months

B's investment = ₹90,000 | Time period = 8 months

Total Profit = ₹40,000

Formula Used:

Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂)

Partner A₹60,000× 10 months= 600,000Partner B₹90,000× 8 months= 720,000Profit Ratio → 600k : 720k = 5 : 6Total Profit = ₹40,000

Calculations:

⇒ Profit Ratio of A to B = (60000 × 10) : (90000 × 8)

⇒ Profit Ratio = 600000 : 720000

⇒ Simplifying the ratio by dividing by 120000, we get 5 : 6

⇒ Total parts in the profit ratio = 5 + 6 = 11

⇒ A's Share = (A's ratio ÷ Total ratio) × Total Profit

⇒ A's Share = (5 ÷ 11) × 40000

⇒ A's Share = 200000 ÷ 11 ≈ 18181.8181...

∴ The correct answer is ₹18,181.82.

Additional Information

Compound Partnership

When partners invest different amounts for different time periods, the profit ratio is calculated as the product of their investment and time: (Capital₁ × Time₁) : (Capital₂ × Time₂).

Simple Partnership

If all partners invest their capital for the exact same period of time, their profit is shared precisely in the ratio of their initial investments.

Active vs Sleeping Partner

An active partner manages the business and usually receives a fixed salary or a certain percentage of the total profit before the remaining profit is distributed based on the normal capital ratio. A sleeping partner only invests the capital.

Finding the Time Ratio

If the profit ratio and the investment capital ratio are both known, the time ratio can be directly found using: Time Ratio = Profit Ratio ÷ Capital Ratio.

Shortcut Trick

By using the Alligation Method on average salaries:

Ratio of Officers to Non-officers = (Overall Avg − Non-officers Avg) : (Officers Avg − Overall Avg)

Ratio = (16000 − 10000) : (28000 − 16000)

Ratio = 6000 : 12000 = 1 : 2

Since 1 ratio part = 15 officers, 2 ratio parts = 15 × 2 = 30 non-officers.

∴ The correct answer is 30.

Alternate Method

Given:

Average salary of officers = ₹28,000

Average salary of non-officers = ₹10,000

Overall average salary = ₹16,000

Number of officers = 15

Officers Non-Officers

28,000 10,000

Overall Avg 16,000

6,000 12,000

Ratio = 1 : 2

Calculations:

Let the number of non-officers be x.

Total Salary = Overall Average × Total Employees

⇒ (15 × 28000) + (x × 10000) = 16000 × (15 + x)

⇒ 420000 + 10000x = 240000 + 16000x

⇒ 16000x − 10000x = 420000 − 240000

⇒ 6000x = 180000

⇒ x = 180000 ÷ 6000

⇒ x = 30

∴ The correct answer is 30.

Additional Information

Weighted Average

When two or more groups are combined, the overall average is calculated as (n₁A₁ + n₂A₂) ÷ (n₁ + n₂), where n is the number of elements and A is the respective average of each group.

Alligation Rule

A rapid visual method to find the ratio in which two quantities are mixed to produce a mixture of known mean. The ratio equals (Dearer − Mean) : (Mean − Cheaper).

Average Deviation Method

The sum of net deviations of all the observations from their exact arithmetic mean is always mathematically equal to zero.

Shortcut Trick

The sum of the three given results is 210 + 198 + 192 = 600.

Each number is added twice as a full unit and once as a half unit across the three equations, giving a combined sum of 2.5 times the total sum of the three numbers.

Sum of the three numbers = 600 ÷ 2.5 = 240.

Required Average = 240 ÷ 3 = 80.

∴ The correct answer is 80.

Alternate Method

Given:

Let the three numbers be a, b, and c.

Calculations:

a + b + c/2=210b + c + a/2=198c + a + b/2=1922.5 × (a + b + c)=600Average = (a + b + c) ÷ 3 = 240 ÷ 3 = 80

According to the given conditions:

⇒ a + b + c/2 = 210

⇒ b + c + a/2 = 198

⇒ c + a + b/2 = 192

Adding all three equations:

⇒ (a + b + c/2) + (b + c + a/2) + (c + a + b/2) = 210 + 198 + 192

⇒ 2(a + b + c) + 0.5(a + b + c) = 600

⇒ 2.5 × (a + b + c) = 600

⇒ a + b + c = 600 ÷ 2.5

⇒ a + b + c = 240

The average of the three numbers is their sum divided by 3:

⇒ Average = (a + b + c) ÷ 3

⇒ Average = 240 ÷ 3 = 80

∴ The correct answer is 80.

Additional Information

Average (Arithmetic Mean)

The average of a given set of numbers is equal to the sum of all the observations divided by the total number of observations. Average = Sum of observations ÷ Total number of observations.

Properties of Average

If each observation in a dataset is increased, decreased, multiplied, or divided by a constant value 'k', the new average will also be correspondingly increased, decreased, multiplied, or divided by 'k'.

Weighted Average

If values x₁, x₂, ..., x_n have associated weights w₁, w₂, ..., w_n, the weighted average is calculated as (w₁x₁ + w₂x₂ + ... + w_nx_n) ÷ (w₁ + w₂ + ... + w_n).

Shortcut Trick

Target questions to pass = 60% of 120 = 72

Current correct questions = (70% of 20) + (50% of 50) + (30% of 50)

⇒ 14 + 25 + 15 = 54

Questions needed to pass = 72 − 54 = 18

∴ The correct answer is 18 questions.

Alternate Method

Given:

Total questions = 120

General Knowledge questions = 20, correctly answered = 70%

Reasoning questions = 50, correctly answered = 50%

English questions = 50, correctly answered = 30%

Minimum passing score = 60% of total questions

Total: 120 questionsCorrect: 5418NeededPassing Score: 72Target = 60% of 120 = 72

Calculations:

⇒ Passing score = 60% of 120 = (60 ÷ 100) × 120 = 72

⇒ Correct GK questions = 70% of 20 = (70 ÷ 100) × 20 = 14

⇒ Correct Reasoning questions = 50% of 50 = (50 ÷ 100) × 50 = 25

⇒ Correct English questions = 30% of 50 = (30 ÷ 100) × 50 = 15

⇒ Total correctly answered questions = 14 + 25 + 15 = 54

⇒ Additional questions needed = Passing score − Total correctly answered

⇒ Additional questions needed = 72 − 54 = 18

∴ The correct answer is 18 questions.

Additional Information

Passing Percentage

The minimum benchmark score set by examination bodies to qualify. Formula: Passing Marks = (Passing % ÷ 100) × Total Marks.

Aggregate Marks

The sum total of marks obtained across all sections or subjects. Formula: Aggregate % = (Total Marks Obtained ÷ Total Maximum Marks) × 100.

Weighted Average

Used when combining groups with different base values or sections with different maximum marks. Formula: Weighted Average = (N₁x₁ + N₂x₂ + ... ) ÷ (N₁ + N₂ + ... ).

Shortcut Trick

Rate for the 1st year = 9%

Rate for the next 8 months = 9% × (8/12) = 6%

Effective CI rate for 1 year 8 months = 9 + 6 + (9 × 6)/100 = 15.54%

Total Compound Interest = 15.54% of ₹7,000 = ₹1,087.80

∴ The correct answer is ₹1,087.80.

Alternate Method

Given:

Principal (P) = ₹7,000

Rate of Interest (R) = 9% p.a.

Time (T) = 1 year 8 months = 1 + (8/12) years = 1 + (2/3) years

Formula Used:

When time is in a fraction like n + a/b years:

Amount (A) = P × (1 + R/100)ⁿ × [1 + (R × a/b)/100]

Compound Interest (CI) = A − P

Start ₹7,000

End of 1 Year ₹7,630

End of 1 Yr 8 Mo ₹8,087.80

• 9% (₹630)

• 6% (₹457.80) Total CI = ₹630 + ₹457.80 = ₹1,087.80

Calculations:

⇒ Amount (A) = 7000 × (1 + 9/100)¹ × [1 + (9 × 2/3)/100]

⇒ A = 7000 × (109/100) × (1 + 6/100)

⇒ A = 7000 × 1.09 × 1.06

⇒ A = 7000 × 1.1554 = ₹8,087.80

⇒ CI = Amount − Principal

⇒ CI = 8087.80 − 7000 = ₹1,087.80

∴ The correct answer is ₹1,087.80.

Additional Information

Compound Interest Formula

When interest is compounded annually, the total amount is calculated as A = P × (1 + R/100)ⁿ, where P is the principal, R is the rate of interest, and n is the time in years.

Effective Rate of Interest

For two different continuous time periods with rates a% and b%, the combined effective rate is given by the successive percentage change formula: Effective Rate = a + b + (a × b)/100.

Compounding Half-Yearly

When the interest is compounded half-yearly, the rate of interest becomes half (R/2) and the number of time periods becomes double (2n).

Shortcut Trick

In compound interest, the amount from the previous year becomes the principal for the next year.

Interest for the 3rd year = Amount of 3rd year − Amount of 2nd year

⇒ Interest = 13200 − 12000 = ₹1200

Rate of Interest (R) = Interest ÷ Principal of that year

⇒ R = 1200 ÷ 12000 = 0.1

∴ The correct answer is 0.1.

Alternate Method

Year 0 Year 2 Year 3

P = ? ₹12,000 ₹13,200

CI = ₹1,200

Rate = R

Given:

Amount at the end of the 2nd year (A₂) = ₹12,000

Amount at the end of the 3rd year (A₃) = ₹13,200

Formula Used:

Amount for n years, A = P(1 + R)ⁿ

Calculations:

⇒ For 2 years: P(1 + R)² = 12000   --- (Equation 1)

⇒ For 3 years: P(1 + R)³ = 13200   --- (Equation 2)

⇒ Dividing Equation 2 by Equation 1:

⇒ [P(1 + R)³] ÷ [P(1 + R)²] = 13200 ÷ 12000

⇒ 1 + R = 1.1

⇒ R = 1.1 − 1

⇒ R = 0.1

∴ The correct answer is 0.1.

Additional Information

Compound Interest Formula

The amount after n years is given by A = P(1 + R)ⁿ, where P is the principal and R is the decimal rate of interest.

Simple vs Compound Interest

For the first year, both Simple Interest (SI) and Compound Interest (CI) are equal if compounded annually on a given principal.

Successive Amounts in CI

The ratio of amounts for any two consecutive years is always constant and equal to the multiplying factor (1 + R).

Shortcut Trick Let the quantities bought be 3, 4, and 3 respectively, making a total of 10 notebooks. Cost of 3 notebooks of Type 1 = 3 × (20 ÷ 5) = ₹12 Cost of 4 notebooks of Type 2 = 4 × (9 ÷ 2) = ₹18 and 3 notebooks of Type 3 = 3 × (45 ÷ 10) = ₹13.5 Total CP of 10 notebooks = 12 + 18 + 13.5 = ₹43.5 Total SP of 10 notebooks = 10 × (19 ÷ 4) = ₹47.5 Profit % = [(47.5 − 43.5) ÷ 43.5] × 100 = (4 ÷ 43.5) × 100 ≈ 9.2% Profit. ∴ The correct answer is Profit of 9.2%.

Alternate Method Given: CP of 5 notebooks of Type 1 = ₹20 CP of 2 notebooks of Type 2 = ₹9 CP of 10 notebooks of Type 3 = ₹45 Mixing ratio of Type 1, Type 2, and Type 3 = 3 : 4 : 3 SP of 4 notebooks = ₹19 Formula Used: Profit = Selling Price (SP) − Cost Price (CP) Profit % = (Profit ÷ CP) × 100

Type 1: 3 CP = ₹12

Type 2: 4 CP = ₹18

Type 3: 3 CP = ₹13.5

Total CP = ₹43.5

Total 10 Notebooks Sold @ ₹19 for 4 SP = 10 × (19 ÷ 4) = ₹47.5

Total SP = ₹47.5

Profit = ₹4

Profit % = (4 ÷ 43.5) × 100 ≈ 9.2%

Calculations: ⇒ Let the number of notebooks of Type 1, Type 2, and Type 3 be 3x, 4x, and 3x respectively. ⇒ Total number of notebooks = 3x + 4x + 3x = 10x ⇒ CP of 1 notebook of Type 1 = 20 ÷ 5 = ₹4 ⇒ Total CP of 3x notebooks of Type 1 = 3x × 4 = ₹12x ⇒ CP of 1 notebook of Type 2 = 9 ÷ 2 = ₹4.5 ⇒ Total CP of 4x notebooks of Type 2 = 4x × 4.5 = ₹18x ⇒ CP of 1 notebook of Type 3 = 45 ÷ 10 = ₹4.5 ⇒ Total CP of 3x notebooks of Type 3 = 3x × 4.5 = ₹13.5x ⇒ Total CP of all 10x notebooks = 12x + 18x + 13.5x = ₹43.5x ⇒ SP of 1 notebook = 19 ÷ 4 = ₹4.75 ⇒ Total SP of all 10x notebooks = 10x × 4.75 = ₹47.5x ⇒ Profit = Total SP − Total CP = 47.5x − 43.5x = ₹4x ⇒ Profit % = (Profit ÷ Total CP) × 100 ⇒ Profit % = (4x ÷ 43.5x) × 100 = 400 ÷ 43.5 = 800 ÷ 87 ≈ 9.195% ⇒ Profit % ≈ 9.2% ∴ The correct answer is Profit of 9.2%.

Additional Information Basic Profit & Loss Rule Profit occurs when Selling Price (SP) > Cost Price (CP). The fundamental formula to calculate the percentage is: Profit % = (Profit ÷ CP) × 100. Mixture Replacement / Combined Cost Price When different quantities or qualities of items are mixed, calculate the per-unit Cost Price of each type first. Then multiply them by their respective assumed ratio amounts to find the combined Total CP, ensuring accurate overall profit/loss estimation.

Shortcut Trick

Let the Selling Prices be 300, 400, and 500 units.

Total SP = 300 + 400 + 500 = 1200 units.

Total CP = (300 ÷ 1.25) + (400 ÷ 1.1) + (500 ÷ 0.8) = 240 + 363.63 + 625 = 1228.63 units.

Net Loss = Total CP − Total SP = 1228.63 − 1200 = 28.63 units.

Loss % = (28.63 ÷ 1228.63) × 100 ≈ 2.33%.

∴ The correct answer is loss of 2.33%.

Alternate Method

Given:

Ratio of Selling Prices (SP) = 3 : 4 : 5

Profit on C1 = 25%, Profit on C2 = 10%, Loss on C3 = 20%

Calculations:

⇒ The fractional values are: 25% = 1/4, 10% = 1/10, 20% = 1/5.

⇒ For C1, CP : SP = 4 : 5

⇒ For C2, CP : SP = 10 : 11

⇒ For C3, CP : SP = 5 : 4

⇒ We need SPs to be in ratio 3 : 4 : 5. First, make SP parts equal by multiplying with LCM(5, 11, 4) = 220.

⇒ Now multiply each SP by its ratio share: SP₁ = 3 × 220 = 660, SP₂ = 4 × 220 = 880, SP₃ = 5 × 220 = 1100.

⇒ Calculate corresponding CPs: CP₁ = 660 × (4 ÷ 5) = 528

⇒ CP₂ = 880 × (10 ÷ 11) = 800

⇒ CP₃ = 1100 × (5 ÷ 4) = 1375

⇒ Total CP = 528 + 800 + 1375 = 2703 units

⇒ Total SP = 660 + 880 + 1100 = 2640 units

Total Cost Price = 2703 units

Total Selling Price = 2640 units

Loss = 63

Transaction Summary

⇒ Loss = Total CP − Total SP = 2703 − 2640 = 63 units

⇒ Loss % = (Loss ÷ Total CP) × 100 = (63 ÷ 2703) × 100 = (2100 ÷ 901)% ≈ 2.33%

∴ The correct answer is loss of 2.33%.

Additional Information

Successive Profit or Loss

When multiple profits/losses are given successively, the effective percentage change is calculated as: Net % = a + b + (a × b) ÷ 100. Use positive sign for profit and negative for loss.

Cost Price from Selling Price

When Profit % is given: CP = (SP × 100) ÷ (100 + P%). When Loss % is given: CP = (SP × 100) ÷ (100 − L%).

Dishonest Dealer Concept

If a dealer claims to sell goods at CP but uses false weight, Profit % = [Error ÷ (True Weight − Error)] × 100.

Shortcut Trick

Let CP = 100 units ⇒ MP = 150 units (50% markup).

Price after 20% discount = 150 − 30 = 120 units.

Overall profit is 8% ⇒ Final SP = 100 + 8 = 108 units.

Second discount (y) reduces price from 120 to 108 ⇒ y = (12 ÷ 120) × 100 = 10%.

108 units = ₹4320 ⇒ 1 unit = 40 ⇒ CP (100 units) = ₹4000.

∴ The correct answer is CP = ₹4000, y = 10%.

Alternate Method

CP = 100u

MP = 150u

SP1 = 120u

SP2 = 108u

+50%

−20%

−y%

Profit = +8%

108u = ₹4320 → 1u = ₹40 → CP (100u) = ₹4000

Given:

Markup = 50%, First discount = 20%, Overall profit = 8%, Final SP = ₹4320.

Calculations:

Let the Cost Price (CP) be x.

⇒ Marked Price (MP) = x + (50% of x) = 1.5x

⇒ Price after 1st discount = 1.5x × (1 − 20÷100) = 1.5x × 0.8 = 1.2x

⇒ Price after 2nd discount = 1.2x × (1 − y÷100) = Final SP

⇒ Overall Profit = 8%, so Final SP = x + (8% of x) = 1.08x

Equating both expressions for Final SP:

⇒ 1.2x × (1 − y÷100) = 1.08x

⇒ 1 − y÷100 = 1.08 ÷ 1.2 = 0.9

⇒ y÷100 = 1 − 0.9 = 0.1

⇒ y = 10

Now, calculating CP using the Final SP:

⇒ 1.08x = 4320

⇒ x = 4320 ÷ 1.08 = 4000

⇒ CP = ₹4000

∴ The correct answer is CP = ₹4000, y = 10%.

Additional Information

Successive Discounts

When two discounts d₁% and d₂% are given one after another, the equivalent single discount is given by (d₁ + d₂ − d₁×d₂÷100)%.

Relation between CP and MP

When an item is sold at a profit of P% after offering a discount of D%, the ratio of Cost Price to Marked Price is given directly by: CP ÷ MP = (100 − D) ÷ (100 + P).

Markup Percentage

Markup percentage represents how much higher the marked price is compared to the cost price. It is calculated as: Markup% = (MP − CP) ÷ CP × 100.

Shortcut Trick

Let total work = LCM of 12 and 18 = 36 units.

Efficiencies: A = 36 ÷ 12 = 3 units/day, B = 36 ÷ 18 = 2 units/day.

Work done by A and B together in 4 days = (3 + 2) × 4 = 20 units.

Remaining work = 36 − 20 = 16 units.

Time taken by A to finish the remaining work = 16 ÷ 3 = 5¹/₃ days.

∴ The correct answer is 5¹/₃ days.

Alternate Method

Given:

Time taken by A to complete the task = 12 days

Time taken by B to complete the task = 18 days

Time A and B worked together = 4 days

Formula Used:

Total Work = LCM of individual days

Efficiency = Total Work ÷ Days

Time = Work ÷ Efficiency

Calculations:

⇒ Combined efficiency of A and B = 3 + 2 = 5 units/day.

⇒ Work completed by both in 4 days = 5 × 4 = 20 units.

⇒ Remaining work = 36 − 20 = 16 units.

⇒ Time taken by A for remaining work = Remaining work ÷ Efficiency of A.

⇒ Time taken = 16 ÷ 3 = 5¹/₃ days.

∴ The correct answer is 5¹/₃ days.

Additional Information

Pipes & Cisterns

Functions similarly to Time & Work. Inlets (filling pipes) have positive efficiency, while outlets (emptying pipes) have negative efficiency.

Work & Wages

Wages are distributed in direct proportion to the actual amount of work done by each individual.

Alternate Day Work

Work is done in turns. Calculate the total work done in a complete cycle (e.g., 2 days) and scale it up to reach close to the total work, then find the remainder for the next turn.

Shortcut Trick

By applying the Rule of Alligation directly:

Quantity Ratio = (Mean Price − Price of 2nd quality) / (Price of 1st quality − Mean Price)

⇒ 4 / 5 = (130 − x) / (150 − 130)

⇒ 4 / 5 = (130 − x) / 20

⇒ 130 − x = 16 ⇒ x = 114

∴ The correct answer is ₹114.

Alternate Method

Given:

Cost of the 1st quality tea = ₹150 per kg

Cost of the mixture (at no profit, no loss) = ₹130 per kg

Ratio of 1st to 2nd quality mixed = 4 : 5

Formula Used:

Total Cost = (Quantity₁ × Price₁) + (Quantity₂ × Price₂)

₹150 1st Quality

₹x 2nd Quality

130 Mixture Price

4 parts 130 − x

5 parts 150 − 130 = 20

Calculations:

Let the quantities of the 1st and 2nd quality tea be 4k and 5k respectively.

Let the cost of the 2nd quality tea be ₹x per kg.

⇒ Total quantity of the mixture = 4k + 5k = 9k

⇒ Total cost of the mixture = 9k × 130 = 1170k

⇒ Total cost of the 1st quality = 4k × 150 = 600k

⇒ Total cost of the 2nd quality = 5k × x = 5kx

Since the total cost of individual parts must equal the total mixture cost:

⇒ 600k + 5kx = 1170k

Dividing the entire equation by k:

⇒ 600 + 5x = 1170

⇒ 5x = 1170 − 600

⇒ 5x = 570

⇒ x = 570 ÷ 5 = 114

∴ The correct answer is ��114.

Additional Information

Rule of Alligation

It allows us to directly find the ratio in which two components at given prices must be mixed to obtain a specific mean price. Ratio = (Cheaper Quantity) : (Dearer Quantity) = (D − M) : (M − C).

Mean Price

The effective cost price of a unit quantity of the combined mixture is known as the mean price. It always lies strictly between the cost prices of the cheaper and dearer components being mixed.

Weighted Average Logic

Alligation is an alternative derivation of the weighted average formula: A_w = (w₁x₁ + w₂x₂) ÷ (w₁ + w₂), where w represents weights (quantities) and x represents values (prices).

Shortcut Trick

A working for 16 days and B working for 44 days is equivalent to A and B working together for 16 days, and B working alone for 28 days (44 − 16).

Work done by A and B together in 16 days = 16 ÷ 30 = 8/15 of total work.

Remaining work = 1 − 8/15 = 7/15, which B completes alone in 28 days.

Total time taken by B to complete the entire task = 28 × (15 ÷ 7) = 60 days.

∴ The correct answer is 60 days.

Alternate Method

Given:

Time taken by A and B together = 30 days

A works for 16 days and B finishes the remaining work in 44 days.

Formula Used:

Total Work = Efficiency × Time

Calculations:

⇒ Let Total Work = 30 units (LCM of 30).

⇒ Efficiency of (A + B) = 30 ÷ 30 = 1 unit/day.

⇒ Total work done = (A's work for 16 days) + (B's work for 44 days) = 30 units.

⇒ Grouping the work: (A + B) working for 16 days + B working alone for (44 − 16) days = 30 units.

⇒ 16 × (Efficiency of A + B) + 28 × (Efficiency of B) = 30

⇒ 16 × 1 + 28 × Efficiency of B = 30

⇒ 28 × Efficiency of B = 30 − 16

⇒ 28 × Efficiency of B = 14

⇒ Efficiency of B = 14 ÷ 28 = 0.5 units/day.

⇒ Time taken by B alone = Total Work ÷ Efficiency of B

⇒ Time = 30 ÷ 0.5 = 60 days.

∴ The correct answer is 60 days.

Additional Information

Pipes & Cisterns

Follows the exact same principles as Time & Work. Inlet pipes have positive efficiency as they fill the tank, while outlet pipes have negative efficiency as they empty the tank.

Work & Wages

Wages are always distributed in direct proportion to the actual amount of work done by each person. If people work for the exact same number of days, wages can be shared directly in the ratio of their efficiencies.

Alternate Day Work

When individuals work on alternate days, calculate the total work done in one complete cycle (e.g., 2 days) and multiply it to get close to the total work, then find the remaining work and assign it to the next person in sequence.

Shortcut Trick

Let the initial mixture be 16x. The initial parts are Orange = 5x, Apple = 7x.

Removing 24 litres takes out (5 / 16) × 24 = 7.5L Orange and (7 / 16) × 24 = 10.5L Apple.

Resultant Apple − Resultant Orange = (7x − 10.5) − (5x − 7.5 + 10) = 14.

⇒ 2x − 13 = 14 ⇒ 2x = 27.

Initial quantity = 16x = 27 × 8 = 216.

∴ The correct answer is 216 litres.

Alternate Method

Given:

Ratio of Orange : Apple : Guava = 5 : 7 : 4

Quantity of mixture taken out = 24 litres

Quantity of added juices = 10 litres Orange, 6 litres Guava

Resultant Apple juice − Resultant Orange juice = 14 litres

Initial Mix 16x Litres O : A : G 5 : 7 : 4

− 24L

Remaining 16x − 24 Ratio intact 5 : 7 : 4

• 10L Org
• 6L Guv

Final Mix Apple − Org = 14 Litres

Calculations:

⇒ Total ratio parts initially = 5 + 7 + 4 = 16 parts

⇒ Let the initial quantity of mixture be 16x litres.

⇒ The initial quantities are Orange = 5x, Apple = 7x, and Guava = 4x.

⇒ Quantity of Orange juice removed = (5 / 16) × 24 = 7.5 litres

⇒ Quantity of Apple juice removed = (7 / 16) × 24 = 10.5 litres

After taking out 24 litres and adding the respective juices, the new volumes are:

⇒ Resultant Orange juice = 5x − 7.5 + 10 = 5x + 2.5

⇒ Resultant Apple juice = 7x − 10.5

According to the given condition, the difference is 14 litres:

⇒ (7x − 10.5) − (5x + 2.5) = 14

⇒ 7x − 10.5 − 5x − 2.5 = 14

⇒ 2x − 13 = 14

⇒ 2x = 27

⇒ x = 13.5

⇒ Initial quantity of mixture = 16x = 16 × 13.5 = 216 litres.

∴ The correct answer is 216 litres.

Additional Information

Constant Ratio Property

When any volume of a mixture is drawn out, the remaining mixture still contains the original ingredients in the exact same ratio. Only adding or removing an individual component selectively will alter this final ratio.

Replacement Method

When a certain volume of mixture is replaced completely by one of its pure ingredients, the remaining quantity of the pure liquid left can be found using the formula: Final = Initial × (1 − Removed/Total)ⁿ.

Rule of Alligation

Used to find the required ratio when two ingredients at different prices or concentrations are mixed. Ratio = (Dearer − Mean) : (Mean − Cheaper).

Shortcut Trick

For a constant distance, Speed is inversely proportional to Time.

Initial time = 1 hr 45 min = 105 min.

New time = 105 + 15 = 120 min.

Time ratio = T₁ : T₂ = 105 : 120 = 7 : 8

∴ Speed ratio = S₁ : S₂ = 8 : 7

Decrease in speed = (8 − 7) ÷ 8 = 1/8 = 0.125 (or 12.5%)

∴ The correct answer is 12.5% (0.125).

Alternate Method

Given:

⇒ Initial speed (S₁) = 60 km/h

⇒ Initial time (T₁) = 1 hour 45 minutes = 105 minutes = 1.75 hours

⇒ New time (T₂) = 105 minutes + 15 minutes = 120 minutes = 2 hours

Distance = 105 km (Constant) Case 1: S = 60 km/h, T = 105 min

Case 2: S = 52.5 km/h, T = 120 min

Speed Decrease = 7.5 km/h Percentage Decrease = 12.5% (0.125)

Calculations:

⇒ Distance covered = S₁ × T₁ = 60 × 1.75 = 105 km

⇒ New speed (S₂) = Distance ÷ T₂ = 105 ÷ 2 = 52.5 km/h

⇒ Decrease in speed = S₁ − S₂ = 60 − 52.5 = 7.5 km/h

⇒ Fraction decrease = Decrease ÷ Original Speed

⇒ Fraction decrease = 7.5 ÷ 60 = 1/8 = 0.125

⇒ Percentage decrease = 0.125 × 100% = 12.5%

∴ The correct answer is 12.5% (0.125).

Additional Information

Inverse Proportionality of Speed and Time

When distance is kept constant, speed is inversely proportional to the time taken (S ∝ 1/T). If the time increases by a ratio of a : b, the required speed decreases by the ratio of b : a.

Average Speed

Average Speed = Total Distance ÷ Total Time. It must be noted that it is strictly calculated using this formula and is not merely the simple arithmetic average of individual speeds unless the travel times are identical.

Percentage Change

Percentage Change = (New Value − Initial Value) ÷ (Initial Value) × 100. A negative end result simply indicates a percentage decrease.

Shortcut Trick

Speed ratio = 4 : 6 = 2 : 3, so Time ratio = 3 : 2

Difference in time parts = 3 − 2 = 1 part

1 part = 15 min (late) + 5 min (early) = 20 mins = 1/3 hours

Time taken at 4 km/h (3 parts) = 3 × 1/3 = 1 hour

Distance = Speed × Time = 4 km/h × 1 hour = 4 km

∴ The correct answer is 4 km.

Alternate Method

Given:

Speed 1 (S₁) = 4 km/h (reaches 15 minutes late)

Speed 2 (S₂) = 6 km/h (reaches 5 minutes early)

Home

School

Distance = D km

Speed = 4 km/h | Time = t + 15 min

Speed = 6 km/h | Time = t - 5 min

Formula Used:

Time = Distance ÷ Speed

Calculations:

⇒ Let the distance from home to school be D km.

⇒ Time taken to cover D km at 4 km/h = D / 4 hours

⇒ Time taken to cover D km at 6 km/h = D / 6 hours

⇒ Time difference = 15 minutes (late) − (−5 minutes early) = 20 minutes

⇒ Convert time difference into hours = 20 / 60 = 1 / 3 hours

⇒ D / 4 − D / 6 = 1 / 3

⇒ (3D − 2D) / 12 = 1 / 3

⇒ D / 12 = 1 / 3

⇒ D = 12 / 3

⇒ D = 4 km

∴ The correct answer is 4 km.

Additional Information

Direct Formula for Early/Late Problems

Distance = [ (S₁ × S₂) ÷ (S₁ − S₂) ] × Total Time Difference in hours.

Average Speed

When a certain distance is covered at speed x and the same distance is covered at speed y, Average Speed = (2xy) ÷ (x + y).

Relative Speed

If two bodies move in opposite directions at speeds S₁ and S₂, Relative Speed = S₁ + S₂. In the same direction, Relative Speed = |S₁ − S₂|.

Shortcut Trick

Circumference of the ground = Total Cost ÷ Rate per meter

Circumference = 3768 ÷ 120 = 31.4 m

Since Circumference = 2 × π × r

2 × 3.14 × r = 31.4 ⇒ 6.28 × r = 31.4 ⇒ r = 5 m

∴ The correct answer is 5 m.

Alternate Method

Given:

Total cost of fencing = ₹3,768

Rate of fencing = ₹120/m

Formula Used:

Total Cost = Circumference × Rate

Circumference of a circle = 2πr (where r is the radius)

O

r = ? Circumference = Total Cost ÷ Rate Perimeter = 31.4 m

Total Cost ₹3768

Rate ₹120/m

Calculation:

⇒ Circumference = Total Cost ÷ Rate

⇒ Circumference = 3768 ÷ 120 = 31.4 m

⇒ 2 × π × r = 31.4

Taking π ≈ 3.14:

⇒ 2 × 3.14 × r = 31.4

⇒ 6.28 × r = 31.4

⇒ r = 31.4 ÷ 6.28

⇒ r = 5 m

∴ The correct answer is 5 m.

Additional Information

Area of a Circle

The area enclosed by a circle is given by the formula πr². If a question asks for the cost of levelling or plowing a circular field, the area must be calculated instead of the perimeter.

Perimeter of a Semi-Circle

The perimeter of a semi-circle includes both the curved arc and the straight diameter. The direct formula is πr + 2r.

Difference Between Fencing and Paving

Fencing always relates to the outer boundary (circumference of 2πr), whereas paving, painting, or laying grass relates to the inner flat surface (area of πr²).

Shortcut Trick

The unused area when a circle is perfectly inscribed in a square is directly given by the formula: r²(4 − π)

Substitute the given radius r = 14 cm, and use a precise value for π ≈ 3.1416:

Unused Area = 14² × (4 − 3.1416)

Unused Area = 196 × 0.8584 ≈ 168.25 cm²

∴ The correct answer is 168.25 cm².

Alternate Method

Given:

Radius of the circular logo (r) = 14 cm

Formula Used:

Side of the circumscribing square (a) = 2 × r

Area of square = a²

Area of circle = πr²

Unused square space = Area of square − Area of circle

r = 14 cm

Side = 28 cm Unused space (shaded blue)

Calculations:

⇒ Side of the square (a) = 2 × 14 = 28 cm

⇒ Area of the square = 28 × 28 = 784 cm²

⇒ Area of the circular logo = 3.1416 × 14 × 14 ≈ 615.75 cm²

⇒ Unused square space = 784 − 615.75 = 168.25 cm²

∴ The correct answer is 168.25 cm².

Additional Information

Area of Circumscribed Square

When a circle of radius r perfectly fits (is inscribed) inside a square, the side of the square is exactly the diameter of the circle (2r). The area of the square evaluates to 4r².

Area of Inscribed Square

Conversely, if a square is inscribed inside a circle of radius r, its diagonal matches the circle's diameter (2r), and its area calculates to 2r².

Inscribed Area Ratio

The ratio of the area of an inscribed circle to the area of its circumscribing square is π : 4. This implies the circle covers approximately 78.5% of the total square space.

Shortcut Trick

The minute hand covers a complete circle (360°) in 60 minutes.

In 30 minutes, it covers exactly half of the circular path.

Distance covered in 30 minutes = Half of circumference = π × r

Distance = (22/7) × 14 = 44 cm

∴ The correct answer is 44 cm.

Alternate Method

r = 14 cm 30 min (180°) 12 6

Given:

Radius of the clock face (r) = 14 cm

Time duration = 30 minutes

Formula Used:

Arc length = (θ ÷ 360°) × 2πr

Angle covered by minute hand in 1 minute = 360° ÷ 60 = 6°

Calculations:

⇒ Angle covered in 30 minutes (θ) = 30 × 6° = 180°

⇒ Arc length = (180° ÷ 360°) × 2 × (22/7) × 14

⇒ Arc length = (1/2) × 2 × 22 × 2

⇒ Arc length = 1 × 44 = 44 cm

∴ The correct answer is 44 cm.

Additional Information

Area of a Sector

The region bounded by two radii and an arc is called a sector. Formula: Area = (θ ÷ 360°) × πr².

Speed of Clock Hands

The minute hand moves at a speed of 6° per minute, while the hour hand moves at 0.5° per minute.

Circumference of a Circle

The total boundary length of a circular path is its circumference. Formula: C = 2πr or C = πd.

Shortcut Trick

The given line is in the form y = mx + c, giving slope m = -3.

For perpendicular lines, the product of their slopes is always -1.

So, perpendicular slope = -1 ÷ (-3) = 1/3.

∴ The correct answer is 1/3.

Alternate Method

Given:

Equation of the line: y = -3x + 7

XYy = -3x + 7Slope (m1) = -3Perpendicular LineSlope (m2) = ?90°

Formula Used:

Slope-intercept form of a line: y = mx + c, where m is the slope.

Condition for two perpendicular lines: m₁ × m₂ = -1

Calculations:

⇒ The given line is y = -3x + 7

⇒ Comparing with y = mx + c, we get the slope of the line, m₁ = -3

⇒ Let the slope of the perpendicular line be m₂

⇒ According to the condition for perpendicular lines, m₁ × m₂ = -1

⇒ -3 × m₂ = -1

⇒ m₂ = 1/3

∴ The correct answer is 1/3.

Additional Information

Parallel Lines

Lines which are parallel to each other have equal slopes (m₁ = m₂).

General Equation of a Line

For a line given by Ax + By + C = 0, the slope is m = -A/B.

Angle Between Two Intersecting Lines

If m₁ and m₂ are the slopes, the acute angle θ between them is given by tan(θ) = |(m₁ − m₂) ÷ (1 + m₁ × m₂)|.

Shortcut Trick

If x − 1/x = a, then x² + 1/x² = a² + 2

If x² + 1/x² = b, then x⁴ + 1/x⁴ = b² − 2

Here, a = 3 ⇒ b = 3² + 2 = 9 + 2 = 11

Now, x⁴ + 1/x⁴ = 11² − 2 = 121 − 2 = 119

∴ The correct answer is 119.

Alternate Method

Given:

x − 1/x = 3

Formula Used:

(a − b)² = a² − 2ab + b²

(a + b)² = a² + 2ab + b²

Calculations:

Squaring both sides of the given equation:

⇒ (x − 1/x)² = 3²

⇒ x² − 2 × x × 1/x + 1/x² = 9

⇒ x² − 2 + 1/x² = 9

⇒ x² + 1/x² = 9 + 2 = 11

Squaring both sides again:

⇒ (x² + 1/x²)² = 11²

⇒ x⁴ + 2 × x² × 1/x² + 1/x⁴ = 121

⇒ x⁴ + 2 + 1/x⁴ = 121

⇒ x⁴ + 1/x⁴ = 121 − 2 = 119

∴ The correct answer is 119.

Additional Information

Square Identity 1

If x + 1/x = a, then x² + 1/x² = a² − 2

Cube Identity 1

If x + 1/x = a, then x³ + 1/x³ = a³ − 3a

Cube Identity 2

If x − 1/x = a, then x³ − 1/x³ = a³ + 3a

Power 5 Identity

x⁵ + 1/x⁵ = (x² + 1/x²) × (x³ + 1/x³) − (x + 1/x)

Shortcut Trick

Convert the percentage to a fraction to simplify the calculation directly.

2.5% = 2.5 ÷ 100 = 1 ÷ 40

Multiply the fraction by the given number:

Value = (1 ÷ 40) × 200 = 5

∴ The correct answer is 5.

Alternate Method

Given:

Base number = 200

Percentage = 2.5%

Formula Used:

Percentage Value = (Percentage ÷ 100) × Base Number

5 195

Total = 200 (100%)

2.5%

Calculations:

⇒ Value = (2.5 ÷ 100) × 200

⇒ Value = 2.5 × 2

⇒ Value = 5

∴ The correct answer is 5.

Additional Information

Percentage to Fraction Conversion

To convert any percentage to a fraction, divide it by 100 and simplify. Example: 2.5% = 2.5 ÷ 100 = 25 ÷ 1000 = 1 ÷ 40.

Successive Percentage

When a value changes by x% and then by y%, the net percentage change is given by the formula: Net Change = x + y + (x × y) ÷ 100.

Percentage Change

To find the percentage change between two values, use the formula: % Change = (New Value − Old Value) ÷ Old Value × 100.

The correct answer is: Favorable.

Key Points

• The word "Propitious" means something that is favorable, promising, or indicating a high likelihood of success. (अनुकूल)
• Example: The sunny weather on the day of the picnic was certainly propitious.
• "Favorable" refers to conditions or circumstances that are advantageous or beneficial. (अनुकूल)
• Example: The team was given favorable odds of winning the championship.
• Hence, we can infer that the synonym of 'Propitious' is 'Favorable'.

Therefore, the correct answer is: Favorable.

Additional Information

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

• Doubtful (संदेहपूर्ण): Feeling uncertain or unsure about something.
• Example: The outcome of the experiment was doubtful due to insufficient data.
• Harmful (हानिकारक): Causing damage or injury.
• Example: Smoking is harmful to your health.
• Unlucky (अभाग्यशाली): Having bad luck or experiencing unfortunate events.
• Example: He was unlucky to miss the bus by just a few seconds.

The correct answer is: Option 2, i.e., "To waste time in trivialities during a crisis".

Key Points

• The idiom "Fiddle while Rome burns" means to waste time on unimportant matters while ignoring a significant or urgent crisis. (एक बड़े संकट के दौरान महत्वहीन चीजों में समय बर्बाद करना)
• Example: The manager was busy planning a party while the company was facing major financial losses. Truly, he fiddled while Rome burned.
• This idiom originates from the legend of Emperor Nero, who allegedly played the fiddle while Rome was burning in a great fire.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Option 1: To play music at night (रात में संगीत बजाना): This option refers to playing musical instruments during nighttime, which is unrelated to the idiom's meaning.
• Example: He often plays the guitar at night to relax after work.
• Option 3: To seek artistic approval (कलात्मक स्वीकृति प्राप्त करना): This means to look for recognition or validation of one's creative or artistic work.
• Example: The artist sought artistic approval by showcasing his work in galleries.
• Option 4: To incite rebellion (विद्रोह को भड़काना): This means to provoke or encourage people to rebel against authority.
• Example: The leader's fiery speeches were aimed at inciting rebellion among the oppressed workers.

The correct answer is: Defend.

Key Points

• The word "Oppugn" means to oppose, contradict, or challenge something. It refers to actively arguing against or questioning the validity of something. (विरोध करना)
• Example: The lawyer oppugned the witness's testimony, suggesting that it was inconsistent with the facts.
• "Defend" means to support or protect someone or something, especially by arguing in favor of it or shielding it from harm. (रक्षा करना)
• Example: The teacher defended her student, insisting that he had not cheated on the test.
• Hence, we can infer that the opposite of 'oppugn' is 'defend'.

Therefore, the correct answer is: Defend.

Additional Information

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

• Question (प्रश्न करना): To ask or inquire about something, or to doubt the truth of something.
• Example: The journalist questioned the politician about the recent policy changes.
• Dispute (विवाद करना): To argue or disagree over something, often resulting in a debate or conflict.
• Example: The two companies are in a legal dispute over the ownership of the patent.
• Challenge (चुनौती देना): To call into question or demand proof, or to contest something as invalid or incorrect.
• Example: The athlete challenged the referee's decision, claiming it was unfair.

The correct answer is option 2.

Key Points

The misspelled word is 'Occassionally'.

• The correct spelling would be 'Occasionally'.
• The word 'Occasionally' is an adverb which means 'at infrequent or irregular intervals; now and then'. (कभी-कभी)
• For Example -
• He occasionally goes for a walk in the morning.

Therefore, the correct answer would be 'Occassionally'.

Additional Information

Let's understand the meanings of the other marked words -

• Mnemonic - a device such as a pattern of letters, ideas, or associations that assists in remembering something (स्मृति-सहायक)
• Surveillance - close observation, especially of a suspected spy or criminal (निगरानी)
• Bureaucracy - a system of government in which most of the important decisions are made by state officials rather than by elected representatives (नौकरशाही)

The correct answer is option 1.

Key Points

The misspelled word is 'Serendipidous', 'Serendipitios', and 'Serendipetous'.

• The correct spelling would be 'Serendipitous'.
• The word 'Serendipitous' is an adjective which means 'occurring or discovered by chance in a happy or beneficial way'. (सौभाग्यशाली)
• For Example -
• The discovery of penicillin was a serendipitous accident.

Therefore, the correct answer would be 'Serendipitous'.

Additional Information

Let's understand some commonly confused spelling tips: 

• Serendipity - the occurrence of events by chance in a happy or beneficial way (सौभाग्य)
• Serendipitous - derived from serendipity, used as an adjective (सौभाग्यशाली)

The correct answer is: Option 2 (Ennui).

Key Points

• The word "Ennui" refers to a feeling of dissatisfaction and weariness that arises from a lack of excitement or purpose. (उदासी, मानसिक थकावट)
• Example: After months of doing the same repetitive tasks, she felt a deep sense of ennui.
• It describes a state of mental fatigue and boredom, often associated with monotony or lack of enthusiasm for life.

Therefore, the correct answer is: Option 2 (Ennui).

Additional Information

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

• Languor (सुस्ती): A state of physical or mental tiredness and lack of energy, often pleasant or dreamy.
• Example: She lay in the hammock, filled with a sense of languor on the warm summer afternoon.
• Torpor (अक्रियता): A state of reduced physical or mental activity, often caused by lethargy or laziness.
• Example: The bear entered a state of torpor during hibernation, conserving energy for months.
• Tedium (नीरसता): The state of being monotonous, boring, or tedious.
• Example: The tedium of doing the same task daily was starting to affect his motivation.

The correct answer is 'to'.

 

Key Points

• The correct preposition to use in this context is "to."
• The phrase "subordinated to" is commonly used to indicate that one thing is made secondary or less important compared to another.
• Options 1 (at), 2 (for), and 4 (with) are not appropriate prepositions in this context.

Therefore, the correct answer is Option 3.

 

Complete Sentence: "The architect argued that aesthetics should not be subordinated to functionality."

 

Additional Information

• Option 1: "at" is incorrect because "subordinated at" is not a valid collocation.
• Option 2: "for" is incorrect because it does not fit the meaning of subordination in this sentence.
• Option 4: "with" is incorrect because it does not convey the idea of one thing being secondary to another.

The correct answer is 'is'.

 

Key Points

• The verb "is" is used in the present tense to describe a condition or state of being.
• The sentence refers to a situation in the present where, if the security protocol is breached, the system responds immediately.
• Options 1, 3, and 4 are incorrect in this context because they do not align with the present tense and the intended meaning of the sentence.

Therefore, the correct answer is Option 2.

 

Complete Sentence: "If the security protocol is breached, the system alerts administrators instantly."

 

Additional Information

• Option 1: "were" is incorrect because it implies a hypothetical or past situation, which does not fit the given context.
• Option 3: "has" is incorrect because it does not grammatically fit the structure of the sentence.
• Option 4: "had been" is incorrect as it refers to a past perfect scenario, which is not relevant here.

The correct answer is 'undermined'.

 

Key Points

• The verb "undermined" means to weaken or reduce the effectiveness, power, or ability of something, which fits the context of the sentence.
• The sentence indicates that unforeseen variables negatively impacted the reliability of the experiment's conclusions, making "undermined" the appropriate choice.
• Options 2, 3, and 4 do not align with the intended meaning of the sentence.

Therefore, the correct answer is Option 1.

 

Complete Sentence: "Although the experiment had been meticulously designed, unforeseen variables undermined the reliability of its conclusions."

 

Additional Information

• Option 2: "bolstered" is incorrect because it means to support or strengthen, which is the opposite of the intended meaning.
• Option 3: "ratified" is incorrect because it means to formally approve or confirm, which does not fit the context.
• Option 4: "exacerbated" is incorrect because it means to make something worse, which does not align with the idea of impacting reliability.

The correct answer is Option 2.

 

Key Points

• The error lies in the construction of the phrase "or if the statement was merely a strategic ploy."
• The use of "if" is incorrect in this context. It should be replaced with "whether" to maintain parallelism with the earlier "whether" in the sentence.
• The corrected phrase should read: "whether the statement was merely a strategic ploy."
• This ensures proper grammatical structure and consistency in the sentence.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "It remains unclear whether the board intends to implement the proposal or whether the statement was merely a strategic ploy aimed at appeasing shareholders in light of the recent legal setbacks."

 

Additional Information

• Part 1: "It remains unclear whether the board intends to implement the proposal," – This part of the sentence is grammatically correct and does not require any changes.
• Part 3: "aimed at appeasing shareholders," – This part of the sentence is grammatically correct and does not require any changes.
• Part 4: "in light of the recent legal setbacks." – This part of the sentence is grammatically correct and does not require any changes.