SSC CGL 2025 (Held On: 12 Sept, 2025 Shift 1) (Previous Year Paper)

The logic follows here is:

Watt : Power → Watt is SI unit of Power.

Similarly,

Pascal : ? → Pascal  is SI unit of Pressure.

Hence, the correct answer is "Option 3"

The logic follows here, 

Peru, because the Mekong River originates in Tibet, similarly the Amazon River originates in the Andes mountains, primarily in Peru, making Peru the analogous origin point for the Amazon

Mekong : Tibet (Origin) :: Amazon : Peru (Origin)

Hence, the correct answer is "Option 2"

The pattern followed here is

Hence, the correct answer is "Option 3"

The pattern followed here is

Hence, the correct answer is "Option 3"

The pattern followed here is

Hence, the correct answer is "Option 4"

The pattern followed here is

Hence, the correct answer is "Option 1"

The pattern followed here is

Hence, the correct answer is "Option 3"

The logic follows here, 

Hence, the correct answer is "Option 2"

The logic followed here is: 

Given Word: STUDENT

 

According to the question, arraged in alphabetical order → D E N S T T U

 

So, Letter second from the left → E → 5

 

And,

 

Letter fourth from the right → S → 19

 

Thus, the number of letters between the letter that is second from the left and the one that is fourth from the right in the new letter-cluster formed → (S)19 − (E)5 − 1= 13

Hence, the correct answer is "Option 2"

The following addresses are identical

2. Arjun Mehta A-101, Emerald Tower, Surat, 395001

4. Arjun Mehta A-101, Emerald Tower, Surat, 395001

Hence, the correct answer is "Option 3"

Given: Meenal Gupta 102, Silver Oaks, Sector 12, Noida, 201301

1. Meenal Gupta 102, Silver Oaks, Sector 12, Noida, 201301 → Correct
2. Meenal Gupta 102, Silver Oaks, Sector-12, Noida, 201301 → Incorrect
3. Meenal Gupta 102, Silver Oaks, Sector 12, Noida 201301 → Incorrect
4. Meenal Gupta 102, Silver Oaks, Sector 12, Noida, 201302 → Incorrect

Hence, "Option 1" is the correct answer.

Alphabets Table

The pattern followed here is:

AG : IO

Similarly,

CM : ?

Hence, the correct answer is "Option 2"

Given: 

1. A is facing North.

As arrangement type (Linear, circular or any other polygon arrangement) is not mentioned, so we get:

A's right is east and A's left is west. 

2. B is seated second to the right of A.

As B's direction is not known yet, therefore B can face either in the north direction of south direction.

Case 1)

Case 2)

Thus, B's direction is not defined therefore the person who sits immediate left of B cannot be determined.

Hence, the correct answer is "Option 4"

Alphabet Table

The pattern followed here is

TIME : VJOG

Similarly,

WORD : ?

Hence, the correct answer is "Option 1"

The pattern followed here is

GNIDAER : READING

Similarly,

NOITULOS : ?

Hence, the correct answer is "Option 1"

The pattern followed here is

AYRRJC :: CATTLE

Similarly,

NCPDCAR : ?

Hence, the correct answer is "Option 3"

The logic follows here, 

• 2, 3, 5, 7, 11, 13, 17 → all are prime numbers
• 20 → not a prime number (it is composite)
• 20 is odd one.

Hence, the correct answer is "Option 3"

The logic follows here,

Option 1. 2, 3, 5 → all are prime numbers

Option 2. 11, 13, 17 → all are prime numbers

Option 3. 4, 6, 8 → all are composite numbers

Option 4. 7, 19, 23 → all are prime numbers

Hence, the correct answer is "Option 3"

Family Chart:

As per the given information:

Thus, the man is Rani's husband.

Hence, the correct answer is "Option 1"

The pattern followed here is

Option 1) K11 : I9 : G7

Option 2) M13 : K11 : I9

Option 3) O15 : M13 : K11

Option 4) N14 : K11 : H8

N14 : K11 : H8 - Not follows the same pattern.

Hence, the correct answer is "Option 4"

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Option 4 is the different one because it breaks the symbol progression. While the letters (J, K, L) and numbers (10, 11, 12) follow the established pattern, the symbol "@" is repeated in the second and third groups (K11@ and L12@). 

Hence, the correct answer is “Option 4”.

Decoding symbols for Family Tree:

Step-by-step Relationship Analysis:

Breakdown the statement made by the woman: "His (the man's) mother is the only daughter of my father."

• "The only daughter of my father" – Since the speaker is a woman, her father's only daughter must be herself.
• Now, replace that part in the sentence: "His mother is "me" (the woman)."
• If the woman is the mother of the man, then the man is her "Son".

Consolidated Family Structure:

The woman is the mother of the man. Therefore, the man is the woman's son.

Thus, the man is the Son of the woman.

Hence, the correct answer is "Option 1"

Decoding symbols for Family Tree:

Step-by-step Relationship Analysis:

Breakdown the statement made by John: "She is the wife of my uncle's only son."

• "My uncle's only son" refers to John's Cousin (male).
• "The wife of [John's Cousin]" refers to the woman in question.

Consolidated Family Structure:

Thus, the woman is the Sister-in-law of John.

Hence, the correct answer is "Option 3"

Step-by-step Relationship Analysis:

Breakdown the statement made by the man: "My mother's husband's only son is the father of your sister's brother."

• "My mother's husband" refers to the man's Father.
• "Father's only son" refers to the man himself (the speaker).
• "Your sister's brother" refers to your Brother (or you, if you are male).
• Now, replace the parts in the sentence: "I (the man) am the father of your Brother."

Consolidated Family Structure:

If the man is the father of your brother, he must also be your father.

Thus, the man is your Father.

Hence, the correct answer is "Option 2"

Given Equation: 9 # 2 @ 3 $ 1 = ?

BODMAS Rule:

Decoding the given information:

Now replacing the signs from left to right using BODMAS Rule, we get:

⇒ 9 × 2 - 3 + 1

⇒ 18 - 3 + 1

⇒ 19 - 3

⇒ 16

Hence, the correct option is "Option 3".

The Correct answer is The caves focus on Shaivite themes and feature sculptural depth through light and shadow.

Key Points

• The Elephanta Caves are located on the Elephanta Island, near Mumbai, Maharashtra.
• The caves primarily focus on Shaivite themes, highlighting the Hindu god Shiva in various forms such as Trimurti Shiva (three-faced Shiva), Ardhanarishvara (half-male, half-female form of Shiva), and Gangadhara (Shiva carrying the Ganga).
• They are renowned for their sculptural depth, achieved through intricate carvings that use light and shadow to create a sense of depth and realism.
• The caves date back to the 5th to 7th century CE and are considered significant for their artistic and architectural excellence.
• They represent the Gupta period's artistic style, showcasing highly detailed and expressive sculptures.
• The site is designated as a UNESCO World Heritage Site, emphasizing its cultural and historical importance.
• The artistic representation in the Elephanta Caves reflects the spiritual narratives and mythological episodes related to Shiva.

Additional Information

• Buddhist caves with large stupas
• This option refers to early Buddhist rock-cut architecture, such as the Ajanta Caves or Karle Caves, which are known for their large stupas and focus on Buddhist teachings.
• The Elephanta Caves are not Buddhist caves, as they primarily focus on Shaivite themes.
• Mix of Jain and Vaishnavite depictions in pillar halls
• This refers to sites such as the Ellora Caves, which have depictions of Hindu, Buddhist, and Jain art.
• The Elephanta Caves are focused exclusively on Shaivism and do not feature Jain or Vaishnavite depictions.
• Entirely monolithic structures from the Mauryan period
• Monolithic structures are carved from a single rock, such as the Barabar Caves, which belong to the Mauryan period.
• The Elephanta Caves, although rock-cut, belong to the Gupta period and are not entirely monolithic.

The Correct answer is Only 1 and 2.

Key Points

• The Goncha Festival is a famous festival celebrated in the Bastar region of Chhattisgarh.
• The festival is marked by the use of Tupki, which is a mock gun made of bamboo, and it uses the Goncha fruit as its bullets. This is a playful and symbolic activity during the festival.
• The chariot procession, a significant part of the Goncha Festival, was started during the rule of the Chalukya dynasty. This tradition is still carried out with grandeur and devotion.
• The festival reflects the rich cultural heritage and traditions of the region, highlighting the historical and religious significance of the event.

Additional Information

• Statement 3: "Rath Yatra begins on Ashadh Shukla Dashmi and ends on Dutiya."
• This statement is incorrect as it does not align with the traditional timeline of the Goncha Festival. While the Rath Yatra is part of the festival, the dates mentioned are not accurate for this specific festival.
• The Goncha Festival is celebrated with unique practices like the playful use of Tupki, which symbolizes the harmonious coexistence of people from different communities.
• The festival emphasizes regional identity, showcasing the historical and cultural richness of the Bastar region.

The Correct answer is Khanda Jaati.

Key Points

• In Carnatic music, rhythm plays a vital role, and it is structured using various rhythmic cycles called talas.
• A laghu is a rhythmic unit within a tala, and its beat count is determined by the jaati.
• The term Khanda Jaati refers to a laghu with five beats.
• In the Khanda Jaati, the rhythmic pattern consists of five syllables or beats, which can be represented as ta ka ta ki ta.
• This is one of the five types of jaatis in Carnatic music, which include Tishra (3 beats), Chaturashra (4 beats), Khanda (5 beats), Mishra (7 beats), and Sankeerna (9 beats).
• The usage of Khanda Jaati in talas adds complexity and richness to the rhythmic structure, showcasing the intricacy of South Indian classical music.
• Khanda Jaati is often employed in compositions to create distinctive and challenging rhythmic patterns that test the skill of performers.

Additional Information

• Tishra Jaati
• Tishra Jaati consists of three beats in the laghu.
• This jaati is represented as ta ki ta.
• It is one of the simplest jaatis and is widely used in basic rhythmic compositions in Carnatic music.
• Chaturashra Jaati
• Chaturashra Jaati consists of four beats in the laghu.
• The rhythmic pattern for Chaturashra Jaati is ta ka di mi.
• This is the most common jaati in Carnatic music and serves as the foundation for many talas.
• Mishra Jaati
• Mishra Jaati consists of seven beats in the laghu.
• The rhythmic syllables are represented as ta ki ta ta ka di mi.
• This jaati is more intricate and is used to add complexity to compositions.

The correct answer is Judo was introduced in 1882 by Jigoro Kano in Japan.

Key Points

• Judo was founded by Jigoro Kano in 1882 in Tokyo, Japan, through the establishment of the Kodokan. Hence, option 1 is correct.
• Statement 2: India's first National Judo Championship was held in 1966 at Hyderabad, not in 1970 at Delhi University. Hence, option 2 is incorrect.
• Statement 3: Indian judoka Kalpana Devi did not win a gold medal at the 2010 Judo World Cup. Hence, option 3 is incorrect.
• Statement 4: Judo became an Olympic sport in 1964 at the Tokyo Olympics, not in 1965. Hence, option 4 is incorrect.
• Therefore, only option 1 is correct.

Additional Information

• Jigoro Kano (1860–1938) developed Judo by modifying traditional Japanese martial arts, especially Jujutsu.
• The term Judo means "Gentle Way" and emphasizes technique, balance, and leverage rather than brute strength.
• Judo was included as an official sport for men at the 1964 Tokyo Olympics and for women at the 1992 Barcelona Olympics.
• The international governing body of Judo is the International Judo Federation (IJF), established in 1951.
• In India, Judo is governed by the Judo Federation of India (JFI), which promotes the sport at national and international levels.

Important Points

• Judo is both a martial art and an Olympic combat sport.
• The highest score in Judo is called an Ippon, which results in an immediate victory.
• Prominent Indian judokas include Tulika Maan, Garima Chaudhary, and Avtar Singh, who have represented India in major international competitions.

The correct answer is 12th January 2025, Meerut, Uttar Pradesh.

Key Points

• The 59th National Cross Country Championships is scheduled to be held on 12th January 2025.
• The event will take place in Meerut, Uttar Pradesh, a city known for its rich history and sports culture.
• Cross Country Championships are athletic events conducted over natural terrains such as grass, dirt trails, or hills, emphasizing endurance and strategy.
• The event is organized under the guidance of the Athletics Federation of India (AFI), which is the apex body for athletics in India.
• Meerut has a prominent reputation in sports equipment manufacturing and is a major contributor to the sports industry in India, making it a fitting choice for hosting such events.
• This championship attracts participants from across the nation, providing a platform for talented athletes to showcase their skills and gain recognition.
• Hosting the championship in Uttar Pradesh aligns with the state’s efforts to promote sports and athletics, further boosting regional development in this sector.

Additional Information

• 10th January 2025, Lucknow, Uttar Pradesh
• Lucknow, the capital city of Uttar Pradesh, is renowned for its historical monuments and cultural heritage.
• It has been a host to various national-level events and is equipped with modern sports infrastructure.
• 15th January 2025, Kanpur, Uttar Pradesh
• Kanpur is an industrial hub and one of the largest cities in Uttar Pradesh.
• The city has a growing focus on sports and athletics, with several recent initiatives to upgrade its sports facilities.
• 12th January 2025, Jaipur, Rajasthan
• Jaipur, the capital of Rajasthan, is known as the Pink City due to its distinct architectural style.
• Although primarily famous for its tourism, Jaipur has hosted various sports events in the past.

The Correct answer is Assures post-establishment investor confidence via standard and national treatment.

Key Points

• The 2024 India-UAE Bilateral Investment Treaty (BIT) focuses on post-establishment investor rights to ensure investor confidence.
• Key principles include standard treatment and national treatment, which ensure fair and equitable treatment of investments made by UAE investors in India and vice versa.
• This treaty aligns with India’s broader international investment strategy, which aims to create an investor-friendly environment while protecting national interests.
• It ensures that investments will not face arbitrary or discriminatory treatment, thereby promoting a secure investment climate.
• Such treaties are critical for strengthening bilateral economic ties and increasing foreign direct investment (FDI) inflows between the two nations.
• The BIT also aims to enhance transparency and provide a structured framework for resolving disputes through mechanisms such as mediation or arbitration.
• This approach helps in achieving a balance between investor protection and the host country’s regulatory autonomy.

Additional Information

• Proposes joint sovereign funds and links INR swap with UAE banks
• This option highlights potential financial mechanisms such as sovereign funds and INR swap arrangements, but these are not the core focus of the BIT.
• Such mechanisms are often discussed under separate financial agreements or trade pacts, not investment treaties.
• Focuses on pre-establishment rights and UAE-based arbitration
• The concept of pre-establishment rights involves granting foreign investors the right to invest even before they establish operations in a host country.
• However, the 2024 BIT primarily focuses on post-establishment rights, not pre-establishment rights.
• Additionally, UAE-based arbitration is not a major provision in this treaty; the treaty emphasizes balanced arbitration mechanisms.
• Aims at GCC-wide tax regulation under India-led digital framework
• This option refers to potential tax regulations across the Gulf Cooperation Council (GCC), but these are not the objectives of the BIT.
• Taxation agreements are usually part of separate double taxation avoidance agreements (DTAA) rather than investment treaties.

The correct answer is Riyadh.

Key Points

• The Santosh Trophy 2022-23 final was held in Riyadh, Saudi Arabia. This was the first time the tournament was organized outside India, making it a unique event in the history of the Santosh Trophy.
• The final match took place between Karnataka and Meghalaya. Karnataka defeated Meghalaya to win the title after a gap of 54 years.
• The match was hosted at the King Fahd International Stadium in Riyadh, a renowned venue for international football matches.
• The decision to hold the final in Riyadh was part of an effort to promote Indian football internationally and to engage with the Indian diaspora in Saudi Arabia.
• This victory marked Karnataka’s fifth Santosh Trophy title, with their last win being in 1968-69.

Additional Information

• Santosh Trophy:
• The Santosh Trophy is a prestigious inter-state football tournament in India, organized by the All India Football Federation (AIFF).
• It was established in 1941 and is named after the late Maharaja Sir Manmatha Nath Roy Chowdhary of Santosh, a prominent patron of football in India.
• Over the years, it has been a platform for discovering young and talented football players from across the country.
• Karnataka’s Performance:
• Karnataka has now won the Santosh Trophy title five times, with their first win in 1946.
• The 2022-23 win was a significant achievement as it ended a 54-year drought for the team in the tournament.
• King Fahd International Stadium:
• Located in Riyadh, Saudi Arabia, this stadium is a major venue for international football events.
• It has a seating capacity of over 68,000 spectators and is known for hosting significant matches, including the AFC Champions League and Saudi Pro League games.
• Indian Football Abroad:
• Hosting the Santosh Trophy final in Riyadh reflects the growing efforts to globalize Indian football.
• It aims to connect with the large Indian expatriate community in the Middle East and promote the sport beyond national borders.

The Correct answer is A study on drought's human and ecological impacts in India.

Key Points

• "Landscapes of Loss: The Story of an Indian Drought" by Kavitha Iyer focuses on the human and ecological consequences of droughts in India.
• The book sheds light on the socio-economic impact of droughts on rural communities, particularly farmers, and their families.
• It explores how droughts lead to migrations, loss of livelihoods, and challenges related to water scarcity.
• The narrative highlights the struggles faced by rural India, delving into the personal stories of individuals and communities.
• It discusses the ecological ramifications of droughts, including degradation of land and water resources.
• The book advocates for sustainable water management and policy reforms to address these recurring issues in India.
• Kavitha Iyer, as a journalist, uses her expertise to provide an in-depth analysis of drought's impact on India's agrarian landscape.

Additional Information

• Option 2: A fictional story about a family in a drought-hit area
• The book is not fictional. It is a non-fictional account based on real events and experiences.
• It uses journalistic tools to highlight the real plight of communities facing droughts in India.
• Option 3: A history of monsoon patterns and ancient agriculture in India
• While the book discusses water scarcity and droughts, it does not focus on the historical aspects of monsoon patterns or ancient agriculture.
• The primary focus is on modern-day droughts and their impact on communities.
• Option 4: A colonial-era policy analysis of water management
• The book does not explore colonial-era water policies; its emphasis is on contemporary issues related to drought and water scarcity.

The Correct answer is 1 and 2 are correct.

Key Points

• Hanging valleys are formed by tributary glaciers that join the main glacier at a higher elevation. This happens because the main glacier erodes deeper and more extensively than the tributary glacier.
• These valleys often open into main glacial valleys at a higher elevation, appearing as steep cliffs or waterfalls after the ice melts.
• The spurs of such hanging valleys are truncated into triangular facets due to glacial erosion. This truncation occurs as the glacier carves through the valley, cutting across the spurs and leaving behind triangular landforms.
• Hanging valleys are commonly associated with waterfalls, as the streams from the tributary valleys flow down into the main valley after the ice melts. A notable example is the Yosemite Valley in the United States.
• The processes involved in the formation of hanging valleys and triangular facets are examples of how glaciers reshape landscapes through both erosion and deposition.
• These features provide key evidence of the intensity and direction of glacial movement in an area, helping researchers understand past glacial environments.

Additional Information

• Glacial Landforms
• Glaciers create various landforms through erosion, transportation, and deposition. These include features like cirques, horns, aretes, U-shaped valleys, and moraines.
• The study of glacial landforms helps in understanding climatic changes and the extent of glacial advances and retreats during the Earth's history.
• Glacial erosion processes like plucking and abrasion are responsible for the characteristic shape of valleys and other landforms.

The Correct answer is To eject the crew module to safety during launch emergencies.

Key Points

• The Crew Escape System (CES) is a critical safety feature integrated into the ISRO's Human Rated LVM3 (HLVM3) rocket.
• Its primary function is to eject the crew module safely in case of any emergency during the launch or ascent phase.
• The CES ensures the safety of astronauts in scenarios such as rocket malfunctions, anomalies, or other emergencies.
• This system uses quick-acting escape motors to propel the crew module away from the rocket, thereby ensuring it avoids any potential danger.
• The CES operates with high precision and is designed to activate within milliseconds of detecting an anomaly.
• It is an integral part of making the Human Rated LVM3 rocket reliable and meeting international standards for crewed space missions.
• The system demonstrates ISRO’s commitment to ensuring astronaut safety during its upcoming human spaceflight missions, such as the Gaganyaan Mission.
• Such systems are standard in human-rated rockets globally, used by agencies like NASA, Roscosmos, and SpaceX.

Additional Information

• To guide the crew module into its designated Low Earth Orbit
• This is the function of the main rocket engines, not the Crew Escape System. The HLVM3 rocket is responsible for placing the crew module into the intended orbit.
• Once in orbit, the crew module performs its mission objectives, such as experiments or docking.
• To assist in docking the crew module with a space station
• Docking is a separate operation involving specialized systems like docking mechanisms and does not involve the Crew Escape System.
• Docking capabilities are used in missions where the crew module needs to connect with a space station or another spacecraft.
• To provide thermal shielding during re-entry into Earth's atmosphere
• The responsibility for thermal shielding lies with the heat shield of the crew module, not the Crew Escape System.
• The heat shield protects astronauts during re-entry by enduring extremely high temperatures generated due to friction with the Earth's atmosphere.

The correct answer is 1 and 2 only.

Key Points

• Justice Sanjiv Khanna became the 51st Chief Justice of India (CJI). Hence, statement 1 is correct.
• He succeeded Justice D.Y. Chandrachud, who demitted office after completing his tenure as the 50th CJI. Hence, statement 2 is correct.
• He did not serve as CJI from 2023. Justice D.Y. Chandrachud served as Chief Justice during 2022–2024. Hence, statement 3 is incorrect.
• Therefore, the correct option is 1 and 2 only.

Additional Information

• Chief Justice of India (CJI)
• Appointed under Article 124 of the Constitution of India.
• Appointed by the President of India following the convention of seniority.
• Retirement age: 65 years.
• Justice Sanjiv Khanna
• Elevated to the Supreme Court of India in January 2019.
• Previously served as a judge of the Delhi High Court.
• Belongs to a distinguished legal family; his uncle Justice H.R. Khanna was a renowned Supreme Court judge.
• Justice D.Y. Chandrachud
• Served as the 50th Chief Justice of India.
• Known for landmark judgments related to constitutional law, fundamental rights, and digital privacy.

The correct answer is Only 1, 3 and 4 are correct.

Key Points

• The National Population Policy (NPP) 2000 was formulated with the objective of stabilizing the population of India while ensuring sustainable development and improving the quality of life of its citizens.
• One of the key goals of the policy is providing free and compulsory education up to 14 years of age, as outlined in the Directive Principles of State Policy under the Indian Constitution. This helps address population issues through better awareness and education.
• The policy aims to reduce the infant mortality rate (IMR) below 30 per 1000 live births by improving healthcare services, immunization programs, and maternal health facilities.
• Promoting delayed marriage for girls is another critical goal of the policy. Encouraging marriage at a later age not only helps in reducing fertility rates but also allows women to pursue education and professional opportunities.
• The policy focuses on several other measures such as addressing unmet needs for contraception, improving maternal healthcare, and achieving population stabilization by 2045.

Additional Information

• Incorrect Option: Increasing fertility rate to ensure demographic dividend
• This is incorrect as the National Population Policy (NPP) 2000 focuses on reducing the fertility rate, not increasing it.
• Reducing fertility rates helps to stabilize population growth and improve socioeconomic indicators.
• Achieving a stable Total Fertility Rate (TFR) is one of the major goals of the policy, aiming for a replacement-level TFR of 2.1.
• Importance of Infant Mortality Rate Reduction
• Reducing the infant mortality rate (IMR) is a key indicator of healthcare quality in a country.
• It reflects improvements in areas such as nutrition, immunization, sanitation, and access to healthcare services.

The Correct answer is Electron Transport Chain.

Key Points

• The electron transport chain (ETC) is a crucial pathway in cellular respiration that generates the most ATP (adenosine triphosphate).
• It occurs in the inner membrane of the mitochondria in eukaryotic cells.
• The ETC uses high-energy electrons from molecules like NADH and FADH₂, which are produced during earlier stages of respiration.
• Electrons are transferred through a series of protein complexes, including cytochromes, which pump protons (H⁺) across the mitochondrial membrane, creating a proton gradient.
• This proton gradient powers the enzyme ATP synthase to synthesize ATP via a process called oxidative phosphorylation.
• The ETC is responsible for producing approximately 34 ATP molecules per glucose molecule, making it the most efficient pathway in energy production.
• Oxygen acts as the final electron acceptor in the ETC, combining with protons and electrons to form water, which is essential to the process.

Additional Information

• Glycolysis
• Glycolysis is the first step in cellular respiration, occurring in the cytoplasm of the cell.
• It breaks down glucose into two molecules of pyruvate, producing a net gain of 2 ATP molecules and 2 NADH molecules.
• Though it is an essential step, it generates far less ATP compared to the ETC.
• Krebs Cycle
• The Krebs cycle, also known as the citric acid cycle, occurs in the mitochondrial matrix.
• It produces NADH and FADH₂, which are used in the electron transport chain.
• The cycle directly generates only 2 ATP molecules per glucose molecule.
• Fermentation
• Fermentation is an anaerobic process that occurs in the absence of oxygen.
• It produces ATP through glycolysis and regenerates NAD+ for continued glycolysis.
• However, it generates only 2 ATP molecules per glucose molecule, making it far less efficient than aerobic respiration.

The correct answer is b-c-a.

Key Points

• The States Reorganisation Act was passed in 1956. It restructured India's states and territories, marking a significant moment in the political and administrative history of the country.
• The First Central Zonal Council meeting was held after the creation of zonal councils, which were established following the States Reorganisation Act. These councils aimed to promote cooperation and coordination between states.
• The Eastern Zonal Council meeting in 2022 occurred significantly later and focused on contemporary issues related to the states in the eastern region of India.
• The chronological order of the events is therefore: States Reorganisation Act passed (b), followed by the First Central Zonal Council meeting (c), and finally the Eastern Zonal Council meeting in 2022 (a).

Additional Information

• States Reorganisation Act
• The States Reorganisation Act, 1956 was a major reform that reorganized the boundaries of Indian states and territories based on linguistic lines.
• It led to the creation of 14 states and 6 union territories.
• This Act also provided the basis for the establishment of Zonal Councils under the States Reorganisation Commission.
• Zonal Councils
• The Zonal Councils were set up to foster interstate cooperation and coordination, as recommended by the States Reorganisation Commission.
• They are statutory bodies, established under the States Reorganisation Act, 1956.
• There are five Zonal Councils: Northern, Southern, Eastern, Western, and Central Zonal Councils.
• The Central Zonal Council includes states like Uttar Pradesh, Madhya Pradesh, Uttarakhand, and Chhattisgarh.
• Eastern Zonal Council
• The Eastern Zonal Council comprises the states of West Bengal, Odisha, Bihar, and Jharkhand.
• It focuses on issues like economic and social development, border disputes, and security concerns specific to the eastern region of India.
• The 2022 meeting of the Eastern Zonal Council aimed at resolving issues related to connectivity, infrastructure, and law and order in the eastern states.

The Correct answer is It is a constitutional legal right that permits deprivation only by authority of law.

Key Points

• Under Article 300A of the Indian Constitution, the right to property is no longer a fundamental right. It was demoted to a constitutional legal right by the 44th Constitutional Amendment Act, 1978.
• This article states that no person shall be deprived of their property except by the authority of law.
• This ensures that property can only be taken by the state through a legally established process, providing protection against arbitrary deprivation.
• As a constitutional legal right, this provision primarily ensures that property rights are safeguarded as long as the deprivation occurs through proper legislation.
• Unlike fundamental rights, violations of Article 300A cannot be directly challenged under Article 32 in the Supreme Court.
• However, if property is taken away without following the due process of law, remedies can be sought through the High Courts under Article 226 or other legal avenues.
• The transformation of the right to property from fundamental to constitutional legal right reflects the state's ability to regulate property for public welfare, subject to legal procedures.

Additional Information

• It is a fundamental right that guarantees compensation for all property acquisitions.
• Before the 44th Amendment Act, the right to property was a fundamental right under Articles 19(1)(f) and 31. However, post-amendment, Article 300A does not guarantee compensation for all acquisitions, and the right to property is now a constitutional legal right.
• It allows the State to deprive a person of property by any law, even without due process.
• This statement is incorrect as Article 300A explicitly requires deprivation to occur through the authority of law. Arbitrary deprivation without legal procedures violates the article.
• It permits citizens to claim property protection under Article 32 before the Supreme Court.
• Property rights under Article 300A cannot be enforced through Article 32, as they are not fundamental rights. Remedies for violations must be sought through High Courts under Article 226 or other legal mechanisms.

The Correct answer is The same for all particles.

Key Points

• In a rigid body, all particles are fixed relative to each other and move collectively during rotation.
• The angular velocity is a measure of the rate of rotation of a body about a given axis and is denoted as ω (omega).
• For a rigid body, the angular velocity of all particles is the same because they rotate together about the same axis at the same rate.
• While the linear velocity of particles depends on their distance from the axis of rotation, the angular velocity remains constant for all particles of the rigid body.
• This uniformity of angular velocity ensures that the body remains rigid and its shape does not change during rotation.
• Angular velocity is a vector quantity, having both magnitude and direction, where the direction is determined by the right-hand rule.
• The concept of angular velocity is widely used in mechanics, engineering, and physics to study rotational motion.

Additional Information

• Proportional to its distance from the axis
• The linear velocity of a particle in a rigid body is proportional to its distance from the axis of rotation. However, angular velocity is the same for all particles.
• This is because linear velocity (v) is calculated as v = ω × r, where r is the distance from the axis, and ω is the angular velocity.
• Inversely proportional to its distance from the axis
• This statement is incorrect because angular velocity does not depend on the distance from the axis. However, other properties, like torque, can depend inversely on certain factors.
• Always zero
• For a rigid body in rotational motion, angular velocity is never zero unless the body is at rest.
• If angular velocity were zero, the body would not exhibit any rotational motion.

The correct answer is Both A and R are true, and R is the correct explanation of A.

Key Points

• The One Nation One Ration Card (ONORC) scheme ensures the portability of food grains under the National Food Security Act (NFSA).
• Portability allows eligible beneficiaries to access their entitled food grains from any Fair Price Shop (FPS) in India, irrespective of their location.
• It particularly benefits migrant workers and their families who relocate to different states or regions for work or other reasons.
• The scheme uses Aadhaar-enabled biometric authentication to verify the identity of beneficiaries at FPS outlets. This ensures that food grains are delivered to the rightful beneficiaries.
• The integration of Aadhaar with the Public Distribution System (PDS) helps in preventing leakages, duplication, and fraud in the system.
• ONORC was introduced to support the vision of a unified India and address food security challenges faced by the migrant population.

Additional Information

• A is true, but R is false
• This option is incorrect because Reason (R) is true. The Aadhaar-enabled biometric authentication plays a crucial role in ensuring portability under the scheme.
• A is false, but R is true
• This option is incorrect because Assertion (A) is correct. The One Nation One Ration Card indeed ensures portability of food grains.
• Both A and R are true, but R is not the correct explanation of A
• This option is incorrect because Reason (R) directly supports Assertion (A). The Aadhaar-enabled system is a core component of ensuring portability.

The correct answer is Mizoram.

Key Points

• Cheraw, also known as the bamboo dance, is one of the most famous traditional dances of Mizoram.
• The dance involves the use of long bamboo sticks, which are held horizontally and tapped rhythmically on the ground by performers.
• The performers (usually women) move gracefully in and out of the bamboo sticks to the beat of the music without getting their feet caught.
• This dance holds cultural and religious significance for the Mizo community, as it is often performed during festivals and special occasions, such as weddings or harvest celebrations.
• The Cheraw dance reflects the rich heritage and traditions of the state of Mizoram.
• It symbolizes the harmony and coordination between nature and mankind through its intricate movements.
• Cheraw has gained international fame and is considered a symbol of Mizoram's cultural identity.

Additional Information

• Meghalaya
• Meghalaya is known for its rich tribal culture and several traditional dances, such as Wangala Dance, performed by the Garo tribe to celebrate the harvest festival.
• Another famous dance is the Shad Suk Mynsiem, performed by the Khasi tribe during the spring season.
• Arunachal Pradesh
• Arunachal Pradesh is famous for its diverse tribal dances such as Yak Dance, Buiya Dance, and Ajilamu Dance.
• These dances are often linked to religious rituals and seasonal celebrations.
• Sikkim
• Sikkim is known for its traditional dances like the Chu-Faat Dance and Mask Dance, performed during religious festivals.
• These dances are deeply rooted in Buddhist culture and depict various mythological stories and traditions.

The correct answer is Defense Budget.

Key Points

• The Global Firepower Military Strength Ranking evaluates the military capabilities of nations globally by analyzing several factors, including their defense budget.
• A country's defense budget directly impacts its ability to procure advanced weaponry, maintain military infrastructure, and invest in research and development for new technologies.
• The ranking considers the allocation of financial resources to defense-related activities as a critical element of a country's overall military strength.
• Countries with a larger and more consistent defense budget are typically better equipped to modernize their armed forces and maintain readiness.
• This factor is one of the most significant indicators of a nation's military might in terms of both quality and quantity of resources.
• Other elements of the ranking, such as manpower, equipment, and logistical capabilities, are often supported and enhanced by a robust defense budget.
• Leading nations like the United States, China, and India allocate substantial portions of their annual budgets to defense, which reflects their prioritization of national security.

Additional Information

• Economic Stability
• Economic stability refers to a country's ability to maintain a steady rate of economic growth and avoid inflation or deflation.
• Although related to national strength, it is not directly assessed in the Global Firepower Military Strength Ranking.
• Economic stability often indirectly supports military strength by ensuring the availability of resources for defense spending.
• Cultural Influence
• Cultural influence pertains to a nation's ability to impact others through its culture, values, and traditions.
• It is a component of soft power rather than military or hard power, making it irrelevant to the Global Firepower Military Strength Ranking.
• Healthcare Spending
• Healthcare spending involves a nation’s investment in the health and well-being of its citizens.
• While it contributes to a country's overall development and quality of life, it is not a parameter used in determining military strength.

The correct answer is Owned by workers or suppliers sharing profits and losses.

Key Points

• Cooperative sector industries are those owned and managed by groups of individuals who share common economic interests. These groups often consist of workers, suppliers, or consumers.
• The primary objective is to ensure mutual benefit, where profits and losses are shared equally among all members.
• These industries follow the principle of cooperation, which promotes economic equality and prevents exploitation.
• Examples of cooperative sector industries include milk cooperatives like Amul, handloom cooperatives, and agricultural cooperative societies.
• Cooperatives play a crucial role in empowering rural areas by providing employment, income stability, and promoting sustainable economic growth.
• They also adhere to the democratic principle of one member, one vote, ensuring equitable decision-making.

Additional Information

• Owned and operated by central government agencies
• Industries owned and operated by the central government fall under the category of public sector industries, not cooperative sector industries.
• These industries are managed by the government for purposes like national development, security, and providing essential services.
• Examples include Indian Railways, BHEL, and ONGC.
• Operated solely for export purposes
• Industries that primarily focus on exports are often classified as export-oriented industries.
• They aim to produce goods and services for international markets rather than domestic consumption.
• Examples include industries involved in textiles, pharmaceuticals, and IT services catering to global demand.
• Maintained by foreign companies with Indian partnerships
• Industries maintained by foreign companies in collaboration with Indian entities are referred to as joint ventures.
• They aim to combine resources, technology, and expertise from both parties for mutual benefit.
• Examples include Maruti Suzuki, a joint venture between India's Maruti and Japan's Suzuki.

The correct answer is Concurrent List.

Key Points

• The 42nd Amendment Act of 1976 is one of the most comprehensive amendments to the Indian Constitution. It brought about significant changes in various provisions.
• One of the key changes was the transfer of Education from the State List to the Concurrent List.
• By placing education in the Concurrent List, both the Union Government and the State Governments can legislate on matters related to education.
• This amendment was aimed at achieving a uniform educational policy across the country, ensuring better coordination and implementation of educational reforms.
• The Concurrent List is one of the three legislative lists under the Seventh Schedule of the Constitution of India. It contains subjects on which both the Union and State Governments can make laws.
• Other important subjects in the Concurrent List include criminal law, marriage and divorce, bankruptcy, and forests.

Additional Information

• Union List
• The Union List contains subjects on which only the Parliament has exclusive powers to make laws.
• Examples of subjects in the Union List include defense, foreign affairs, atomic energy, banking, and communications.
• It is mentioned in the Seventh Schedule of the Constitution and includes 100 subjects.
• State List
• The State List contains subjects on which only the State Legislatures have the authority to legislate.
• Examples of subjects in the State List include police, public health, agriculture, and local government.
• This list also falls under the Seventh Schedule and contains 61 subjects.

The Correct answer is To deliver sector-specific climate information services.

Key Points

• The National Framework for Climate Services (NFCS) was launched in 2024 to provide climate information tailored to specific sectors.
• This framework aims to enhance decision-making and improve resilience in areas such as agriculture, water resources, health, energy, and disaster management.
• Its primary objective is to ensure the delivery of timely, accurate, and actionable climate data to stakeholders across various sectors.
• The NFCS aligns with international frameworks, such as the Global Framework for Climate Services (GFCS), to promote better climate governance and collaboration.
• Sector-specific services include forecasting for crop yields, managing water resources, and planning for energy distribution based on climate patterns.
• By addressing the impacts of climate change, the NFCS supports sustainable development and helps mitigate risks associated with climate variability and extreme weather events.
• It also emphasizes capacity building and promotes collaboration between scientists, policymakers, and stakeholders.

Additional Information

• To set emission trading targets
• Emission trading, also known as cap-and-trade, is a market-based approach to control pollution by providing economic incentives for reducing emissions.
• This option relates to environmental economics rather than direct climate service delivery.
• India has previously introduced a carbon market mechanism, but it is not directly linked to the NFCS.
• To regulate groundwater quality
• Regulating groundwater quality involves policies to maintain water standards, often under environmental protection acts.
• While groundwater is affected by climate change, this is not the main objective of the NFCS.
• Groundwater regulation is generally managed by organizations like the Central Ground Water Authority (CGWA) in India.
• To mandate carbon offsetting in the private sector
• Carbon offsetting involves compensating for emissions by investing in projects that reduce greenhouse gases.
• This option primarily pertains to corporate social responsibility and environmental policy, not climate service frameworks.
• India has introduced carbon offset programs, but the NFCS focuses more on providing climate data and services rather than mandates for offsetting.

The correct answer is Decay of K-40.

Key Points

• Argon is a noble gas and is chemically inert, making it an important element in various industrial applications.
• On Earth, Argon is primarily produced through the radioactive decay of Potassium-40 (K-40).
• K-40, a naturally occurring isotope of potassium, undergoes beta decay to form Argon-40 (Ar-40).
• This process occurs deep within the Earth's crust and contributes significantly to the presence of argon in the atmosphere.
• The Earth's atmosphere contains approximately 0.93% argon, making it the third most abundant gas after nitrogen and oxygen.
• The decay of K-40 is a long-term geological process and is essential for understanding the Earth's isotopic composition and age.

Additional Information

• Volcanoes
• Volcanoes release various gases, including water vapor, carbon dioxide, sulfur dioxide, and sometimes traces of argon. However, argon from volcanic eruptions is minimal compared to its production through the decay of K-40.
• Volcanic activity contributes more significantly to the release of greenhouse gases like CO₂ rather than inert gases like argon.
• Photosynthesis
• Photosynthesis is a biological process performed by plants, algae, and cyanobacteria to convert sunlight, carbon dioxide, and water into glucose and oxygen.
• It does not involve the production of argon or any other noble gases.
• Cosmic rays
• Cosmic rays are high-energy particles from outer space. They can interact with the Earth's atmosphere to produce isotopes like Carbon-14, but they do not contribute significantly to the formation of argon in the Earth's crust.

The Correct answer is Fundamental Rights are justiciable, but DPSPs are not.

Key Points

• Fundamental Rights are explicitly mentioned in Part III of the Indian Constitution.
• They are enforceable by the courts, meaning individuals can approach the courts if their rights are violated. This makes them justiciable.
• The Directive Principles of State Policy (DPSPs), enshrined in Part IV of the Constitution, are not enforceable by the courts, making them non-justiciable.
• DPSPs act as guidelines for the government to achieve socio-economic goals and establish a welfare state.
• While Fundamental Rights focus on individual rights and liberties, DPSPs emphasize collective welfare and societal development.
• The Supreme Court of India has clarified that Fundamental Rights and DPSPs must be harmonized and not seen as conflicting entities.
• Examples of Fundamental Rights include the Right to Equality (Article 14-18) and the Right to Freedom (Article 19-22).
• Examples of DPSPs include the directive to promote equal justice and free legal aid (Article 39A) and to ensure living wages for workers (Article 43).

Additional Information

• Both are justiciable and enforceable by courts
• This option is incorrect because only Fundamental Rights are enforceable by courts, while DPSPs are not.
• DPSPs serve as principles for governance and cannot be legally upheld in courts.
• DPSPs override Fundamental Rights when in conflict
• The Supreme Court has ruled that Fundamental Rights hold a higher position in cases of conflict.
• However, efforts have been made to harmonize both, recognizing their complementary nature.
• DPSPs are guaranteed by the Constitution; Fundamental Rights are optional
• This is incorrect as both Fundamental Rights and DPSPs are integral parts of the Constitution.
• Fundamental Rights are guaranteed and enforceable, while DPSPs are guidelines that cannot be enforced legally.

Shortcut Trick

Convert the fractions into percentages to easily compare their values.

5/9 ≈ 55.55%, 4/7 ≈ 57.14%, 3/5 = 60%, 2/3 ≈ 66.67%

Arranging the percentages in ascending order: 55.55% < 57.14% < 60% < 66.67%

This exactly corresponds to the fractions: 5/9 < 4/7 < 3/5 < 2/3

∴ The correct answer is 5/9, 4/7, 3/5, 2/3.

Alternate Method

Given:

Fractions to arrange: 5/9, 4/7, 3/5, 2/3

Method Used:

LCM Equalization Method

Comparing Fractions (Percentage Value) 5/9 55.55% 4/7 57.14% 3/5 60.00% 2/3 66.67%

Calculations:

⇒ LCM of denominators (9, 7, 5, 3) = 9 × 7 × 5 = 315

⇒ Convert each fraction so that the denominator becomes 315:

⇒ 5/9 = (5 × 35) ÷ (9 × 35) = 175/315

⇒ 4/7 = (4 × 45) ÷ (7 × 45) = 180/315

⇒ 3/5 = (3 × 63) ÷ (5 × 63) = 189/315

⇒ 2/3 = (2 × 105) ÷ (3 × 105) = 210/315

⇒ Comparing the numerators: 175 < 180 < 189 < 210

⇒ This implies: 175/315 < 180/315 < 189/315 < 210/315

⇒ Resulting ascending order: 5/9 < 4/7 < 3/5 < 2/3

∴ The correct answer is 5/9, 4/7, 3/5, 2/3.

Additional Information

Cross-Multiplication Method

To compare two fractions a/b and c/d, cross-multiply to get a×d and b×c. If a×d < b×c, then the first fraction is smaller (a/b < c/d).

Decimal Conversion Method

Convert each fraction to its decimal equivalent by simply dividing the numerator by the denominator. Compare the resulting decimal numbers up to 2 to 3 decimal places for accurate results.

Difference Method

When the difference between the numerator and denominator is the exact same for a set of proper fractions, the fraction with the largest numerator is strictly the greatest.

Shortcut Trick

Apply the BODMAS rule and convert the fraction to a decimal directly.

Expression: (2½ + 3.6) − 1.9

⇒ (2.5 + 3.6) − 1.9

⇒ 6.1 − 1.9 = 4.2

∴ The correct answer is 4.2.

Alternate Method

Given:

Expression: (2½ + 3.6) − 1.9

Method Used:

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

Calculations:

⇒ First, convert the mixed fraction into a decimal:

⇒ 2½ = 2.5

⇒ Substitute this value back into the original expression:

⇒ (2.5 + 3.6) − 1.9

⇒ According to the BODMAS rule, perform the addition inside the brackets first:

⇒ 2.5 + 3.6 = 6.1

⇒ Finally, subtract 1.9 from the sum obtained:

⇒ 6.1 − 1.9 = 4.2

∴ The correct answer is 4.2.

Additional Information

BODMAS Rule

It defines the correct order of operations to solve an expression: Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction.

Fraction to Decimal Conversion

Common fractions should be converted to decimals to make addition and subtraction easier (e.g., 1/2 = 0.5, 1/4 = 0.25).

Decimal Arithmetic

Always align the decimal points vertically when adding or subtracting numbers to ensure correct place value calculation.

Shortcut Trick

Using the BODMAS rule, evaluate from the innermost brackets outwards.

Inner terms: (3/4 − 1/2) = 1/4 ⇒ 1/2 × 1/4 = 1/8

Curly brackets: {1/3 − 1/8} = 8/24 − 3/24 = 5/24

Square brackets: [5/6 ÷ 5/24] = 5/6 × 24/5 = 4

Final step: 7 1/4 − 4 = 3 1/4

∴ The correct answer is 3 1/4.

Alternate Method

Given:

Expression: 7 1/4 − [ 5/6 ÷ { 1/3 − ( 1/2 × ( 3/4 − 1/2 ) ) } ]

Concept Used:

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

Calculations:

⇒ 29/4 − [ 5/6 ÷ { 1/3 − ( 1/2 × ( 3/4 − 2/4 ) ) } ]

⇒ 29/4 − [ 5/6 ÷ { 1/3 − ( 1/2 × 1/4 ) } ]

⇒ 29/4 − [ 5/6 ÷ { 1/3 − 1/8 } ]

⇒ 29/4 − [ 5/6 ÷ { 8/24 − 3/24 } ]

⇒ 29/4 − [ 5/6 ÷ 5/24 ]

⇒ 29/4 − [ 5/6 × 24/5 ]

⇒ 29/4 − 24/6

⇒ 29/4 − 4

⇒ 29/4 − 16/4

⇒ 13/4 = 3 1/4

∴ The correct answer is 3 1/4.

Additional Information

BODMAS Rule

BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. It dictates the proper sequence to solve any mathematical expression systematically.

Fraction Division

To divide a number by a fraction, multiply the number by the reciprocal of the fraction: (a/b) ÷ (c/d) = (a/b) × (d/c).

Types of Brackets

Brackets are resolved in a specific order: first Line brackets (vinculum), then Round brackets ( ), followed by Curly brackets { }, and finally Square brackets [ ].

Shortcut Trick

Total engineers proficient in Python = Python only + Both = 70 + 50 = 120

Total engineers proficient in Java = Java only + Both = 60 + 50 = 110

Required Ratio = 120 : 110 = 12 : 11

∴ The correct answer is 12:11.

Alternate Method

Given:

Engineers proficient in both Python and Java = 50

Engineers proficient in Python only = 70

Engineers proficient in Java only = 60

Formula Used:

Total elements in a set = Elements exclusively in that set + Elements in intersection

Calculations:

⇒ Total engineers proficient in Python = Proficient in Python only + Proficient in both

⇒ Total engineers proficient in Python = 70 + 50 = 120

⇒ Total engineers proficient in Java = Proficient in Java only + Proficient in both

⇒ Total engineers proficient in Java = 60 + 50 = 110

⇒ Required Ratio = Total Python : Total Java

⇒ Required Ratio = 120 : 110 = 12 : 11

∴ The correct answer is 12:11.

Additional Information

Set Theory (Venn Diagram) Formula

For any two overlapping sets A and B, the total number of unique elements is given by: n(A ∪ B) = n(A) + n(B) − n(A ∩ B).

Total Elements vs 'Only' Elements

The total number of elements in Set A is the sum of elements exclusively in Set A and the elements shared with Set B: n(A) = n(Only A) + n(A ∩ B).

Simplifying Ratios

A ratio indicates how many times one number contains another. It is simplified by dividing both quantities by their Highest Common Factor (HCF).

Shortcut Trick

Profit Ratio = (Capital × Time)

Arvind : Bhavin : Chandan = (80 × 12) : (120 × 8) : (160 × 4)

⇒ Profit Ratio = 960 : 960 : 640 = 3 : 3 : 2

Total parts = 3 + 3 + 2 = 8 parts ≡ ₹1,05,000

Chandan's share (2 parts) = ₹1,05,000 × (2 ÷ 8) = ₹26,250.

∴ The correct answer is ₹26,250.

Alternate Method

Given:

Arvind's investment = ₹80,000 for 12 months

Bhavin's investment = ₹1,20,000 for (12 − 4) = 8 months

Chandan's investment = ₹1,60,000 for (12 − 8) = 4 months

Total profit = ₹1,05,000

Arvind ₹80k × 12m = 960k (3 parts) Bhavin ₹120k × 8m = 960k (3 parts) Chandan ₹160k × 4m = 640k (2 parts) Total Profit = ₹1,05,000 (8 parts)

Formula Used:

Profit Ratio = (C₁ × T₁) : (C₂ × T₂) : (C₃ × T₃)

Calculations:

⇒ Profit Ratio of A : B : C = (80,000 × 12) : (1,20,000 × 8) : (1,60,000 × 4)

⇒ Ratio = 9,60,000 : 9,60,000 : 6,40,000

⇒ Dividing by 3,20,000, we get the simplified Ratio = 3 : 3 : 2

⇒ Sum of profit ratios = 3 + 3 + 2 = 8 parts

⇒ Chandan's share = (2 ÷ 8) × Total Profit

⇒ Chandan's share = (1 ÷ 4) × 1,05,000

⇒ Chandan's share = ₹26,250

∴ The correct answer is ₹26,250.

Additional Information

Profit Ratio in Partnership

The profit share of any partner is directly proportional to the product of their capital invested and the time duration of the investment.

Working vs Sleeping Partner

A working partner actively manages the business and usually receives a fixed salary or percentage of total profit before the remaining profit is distributed among all partners based on their investments.

Joining Mid-way

When a partner joins a business mid-way, their effective time period is calculated from the date of joining to the end of the business cycle (typically 12 months).

Shortcut Trick

Profit Ratio = (Capital of A × Time of A) : (Capital of B × Time of B)

Profit Ratio = (80000 × 9) : (120000 × 6)

Profit Ratio = 720000 : 720000 = 1 : 1

B's share = (1 ÷ 2) × 45000 = 22500

∴ The correct answer is ₹22,500.

Alternate Method

Given:

Investment by A = ₹80,000

Time period of A = 9 months

Investment by B = ₹1,20,000

Time period of B = 6 months

Total Profit = ₹45,000

Formula Used:

Profit Ratio = (Investment × Time)

Partner A80k × 9mPartner B120k × 6mProfit: 720kProfit: 720kRatio A : B = 1 : 1

Calculations:

⇒ Equivalent Capital of A = 80000 × 9 = 7,20,000

⇒ Equivalent Capital of B = 120000 × 6 = 7,20,000

⇒ Profit Ratio (A : B) = 720000 : 720000 = 1 : 1

⇒ Total ratio parts = 1 + 1 = 2

⇒ B's share in profit = (1 ÷ 2) × Total Profit

⇒ B's share = (1 ÷ 2) × 45000 = 22500

∴ The correct answer is ₹22,500.

Additional Information

Simple Partnership

When partners invest their capital for the exact same duration, profits or losses are distributed directly in the ratio of their original investments.

Compound Partnership

When capital is invested for different time periods, the actual profit sharing ratio is derived by multiplying each partner's invested capital with the respective time period.

Working vs Sleeping Partner

A working partner actively manages the business and often draws a fixed salary from the profit before it is divided. A sleeping partner strictly provides capital and gets a pure proportional share based on investment and time.

Shortcut Trick

For an Arithmetic Progression, Average = (First term + Last term) ÷ 2

First multiple of 11 after 100 = 110

Last multiple of 11 before 250 = 242

Average = (110 + 242) ÷ 2 = 352 ÷ 2 = 176

∴ The correct answer is 176.

Alternate Method

100110121176242250Average = 176Arithmetic Progression (Common Difference = 11)

Given:

⇒ Range = Integers between 100 and 250.

⇒ The numbers must be exactly divisible by 11.

Calculations:

⇒ First integer divisible by 11 = 110 (since 11 × 10 = 110).

⇒ Last integer divisible by 11 = 242 (since 11 × 22 = 242).

⇒ The series is 110, 121, 132, ..., 242.

⇒ Total number of terms (n) = [(Last term − First term) ÷ Common Difference] + 1

⇒ n = [(242 − 110) ÷ 11] + 1

⇒ n = [132 ÷ 11] + 1 = 12 + 1 = 13 terms

⇒ Sum of an AP = (n ÷ 2) × (First term + Last term)

⇒ Sum = (13 ÷ 2) × (110 + 242)

⇒ Sum = (13 ÷ 2) × 352 = 13 × 176 = 2288

⇒ Average = Total Sum ÷ n

⇒ Average = 2288 ÷ 13 = 176

∴ The correct answer is 176.

Additional Information

Average of an Arithmetic Progression

If a series has a constant common difference (like multiples of a number), it forms an Arithmetic Progression (AP). Its average is always the exact mean of the first and last terms: Average = (First Term + Last Term) ÷ 2.

Sum of an Arithmetic Progression

The sum of n terms in an AP is calculated as: S_n = (n ÷ 2) × (First Term + Last Term).

Finding the Number of Terms

To find the total number of terms (n) in any given range for a specific sequence: n = [(Last Term − First Term) ÷ Common Difference] + 1.

Shortcut Trick

Net deviation of first 12 numbers = 6 × (72 − 80) + 6 × (90 − 80) = −48 + 60 = +12

Sum of the 13th, 14th, and 15th numbers = (3 × 80) − 12 = 228

Assuming the 15th number is x: (x + 8) + (x − 10) + x = 228 ⇒ 3x = 230

Average of 13th and 14th numbers = [(x + 8) + (x − 10)] ÷ 2 = x − 1

Required Average = 230/3 − 1 = 227/3 ≈ 75.67

∴ The correct answer is 75.67.

Alternate Method

Given:

Total numbers = 15 (Average = 80)

Average of first 6 numbers = 72

Average of next 6 numbers = 72 + 25% of 72 = 90

13th number = 15th number + 8

14th number = 15th number − 10

Formula Used:

Total Sum = Average × Total Observations

Total 15 numbers (Sum = 1200)First 6 (Avg 72)Sum: 432Next 6 (Avg 90)Sum: 540Last 3Sum: 22813th + 14th + 15th = 1200 − (432 + 540) = 228

Calculations:

⇒ Total sum of 15 numbers = 15 × 80 = 1200

⇒ Sum of the first 6 numbers = 6 × 72 = 432

⇒ Sum of the next 6 numbers = 6 × 90 = 540

⇒ Sum of remaining 3 numbers (13th, 14th, 15th) = 1200 − (432 + 540) = 228

⇒ Let the 15th number be x.

⇒ 13th number = x + 8

⇒ 14th number = x − 10

⇒ (x + 8) + (x − 10) + x = 228

⇒ 3x − 2 = 228

⇒ 3x = 230 ⇒ x = 230/3

⇒ Average of 13th and 14th = [(x + 8) + (x − 10)] ÷ 2

⇒ Average = (2x − 2) ÷ 2 = x − 1

⇒ Average = 230/3 − 1 = 227/3 = 75.666... ≈ 75.67

∴ The correct answer is 75.67.

Additional Information

Net Deviation Method

The sum of deviations of all observations from their arithmetic mean is always zero. The deviation trick helps compute missing elements by finding how much the known parts differ from the combined average.

Weighted Average

When combining separate groups with varying numbers of elements, the new average is calculated as (N₁A₁ + N₂A₂ + ...) ÷ (N₁ + N₂ + ...).

Successive Substitution

When elements relate to one unknown variable directly, convert the sum into an algebraic expression and solve for the unknown to simplify calculation of required parts directly.

Shortcut Trick

Monthly Return = (9% of ₹8,00,000) ÷ 12 = ₹72,000 ÷ 12 = ₹6,000

Monthly Rent = Monthly Return + Maintenance

Monthly Rent = ₹6,000 + ₹2,000 = ₹8,000

∴ The correct answer is ₹8,000.

Alternate Method

Given:

Investment (Cost of flat) = ₹8,00,000

Required annual return = 9%

Monthly maintenance = ₹2,000

Formula Used:

Monthly Rent = Monthly Net Return + Monthly Maintenance

Total Monthly Rent = ₹8,000

Maintenance ₹2,000

Net Return (9% p.a.) ₹6,000

9% of ₹8,00,000 ÷ 12 months

Calculations:

⇒ Annual Net Return = 9% of ₹8,00,000

⇒ Annual Net Return = (9 ÷ 100) × 8,00,000 = ₹72,000

⇒ Monthly Net Return = 72,000 ÷ 12 = ₹6,000

⇒ Total Monthly Rent = Monthly Net Return + Monthly Maintenance

⇒ Total Monthly Rent = 6,000 + 2,000 = ₹8,000

∴ The correct answer is ₹8,000.

Additional Information

Return on Investment (ROI)

ROI is a financial metric used to evaluate the profitability of an investment. It is calculated as the ratio of net profit to the initial investment cost, often expressed as an annual percentage.

Gross vs Net Income

Gross income refers to the total revenue generated (e.g., total rent collected), while net income is the profit remaining after deducting all operating expenses such as maintenance and taxes.

Annual to Monthly Equivalence

When cash flows or returns are uniform throughout the year, a monthly equivalent is obtained by simply dividing the annual expected value by 12. Monthly Return = Annual Return ÷ 12.

Shortcut Trick

If an amount becomes n times in t years at compound interest, it becomes n^m times in m × t years.

Given: The amount becomes 2 times (n = 2) in 5 years (t = 5).

We need it to become 8 times, which is 2³ times, so m = 3.

Required time = m × t = 3 × 5 = 15 years.

∴ The correct answer is 15 years.

Alternate Method

P

2P

4P

8P

5 years × 2

5 years × 2

5 years × 2

Total Time = 5 + 5 + 5 = 15 years

Given:

Amount doubles in 5 years at compound interest.

Let the initial principal be P.

Amount (A) = 2P, Time (t) = 5 years.

Formula Used:

A = P(1 + r/100)^t

Calculations:

⇒ 2P = P(1 + r/100)⁵

⇒ 2 = (1 + r/100)⁵

We need to find the time T when the amount becomes 8 times (A = 8P).

⇒ 8P = P(1 + r/100)^T

⇒ 8 = (1 + r/100)^T

Since 8 can be written as 2³:

⇒ 2³ = (1 + r/100)^T

Substituting the value of 2 from the first equation:

⇒ [(1 + r/100)⁵]³ = (1 + r/100)^T

⇒ (1 + r/100)¹⁵ = (1 + r/100)^T

Comparing the exponents on both sides:

⇒ T = 15

∴ The correct answer is 15 years.

Additional Information

Compound Interest Multiple Concept

If an amount becomes n times in t years at CI, it will become n^m times in m × t years.

Simple Interest Multiple Concept

If an amount becomes n times in t years at SI, it will become m times in [(m−1)/(n−1)] × t years.

Rule of 72

A quick formula to approximate the number of years required to double the principal at a fixed annual CI rate (Time ≈ 72 ÷ r).

Shortcut Trick

Multiplying factor for 1 year = Amount₃ ÷ Amount₂ = 7920 ÷ 6600 = 6/5

Since the sum amounts to ₹6,600 in 2 years at CI:

Principal × (6/5)² = 6600

⇒ Principal = 6600 × (25/36) ≈ 4583.33

∴ The correct answer is ₹4,583.33.

Alternate Method

Given:

Amount after 2 years (A₂) = ₹6,600

Amount after 3 years (A₃) = ₹7,920

Year 0 P = ? Year 2 ₹6,600 Year 3 ₹7,920

× (1 + R/100)² × (1 + R/100) Compound Interest Timeline

Formula Used:

A = P × (1 + R/100)ⁿ

Calculations:

⇒ A₃ ÷ A₂ = [P × (1 + R/100)³] ÷ [P × (1 + R/100)²]

⇒ 7920 ÷ 6600 = 1 + R/100

⇒ 1.2 = 1 + R/100

⇒ R = 20%

Now, substitute R into the 2nd year amount formula:

⇒ P × (1 + 20/100)² = 6600

⇒ P × (1.2)² = 6600

⇒ P × 1.44 = 6600

⇒ P = 6600 ÷ 1.44 = 4583.33

∴ The correct answer is ₹4,583.33.

Additional Information

Interest for 1 Year in CI

In compound interest, the amount accumulated at the end of a year acts as the principal for the next year. Thus, dividing the amount of any given year by the previous year's amount gives the direct multiplying factor for one year.

Simple Interest vs Compound Interest

For the first year (or the first compounding period), both Simple Interest and Compound Interest generate exactly the same interest. The difference arises from the second year onwards because Compound Interest charges interest on the previously accumulated interest.

Effective Rate for 2 Years

The effective compound interest rate for 2 consecutive years at R% per annum can be calculated directly using the successive percentage formula: R + R + (R × R) ÷ 100.

Shortcut Trick

Calculate the profit or loss per liter directly by comparing the cost prices with the final selling price of ₹48/liter.

Profit on the first quantity (25 liters) = 25 × (48 − 45) = 25 × 3 = +₹75

Loss on the second quantity (15 liters) = 15 × (48 − 50) = 15 × (−2) = −₹30

Net result = +75 − 30 = +₹45

Since the net result is positive, it represents an overall profit.

∴ The correct answer is Profit of ₹45.

Alternate Method

Given:

Quantity of first milk = 25 liters at ₹45/liter

Quantity of second milk = 15 liters at ₹50/liter

Selling price of the combined mixture = ₹48/liter

25 L @ ₹45/LCP = ₹112515 L @ ₹50/LCP = ₹750Total CP (40 L)₹1875Total SP @ ₹48₹1920Profit = ₹1920 − ₹1875 = ₹45

Formula Used:

Total CP = (Q₁ × CP₁) + (Q₂ × CP₂)

Total SP = Total Quantity × SP per liter

Profit = Total SP − Total CP

Calculations:

⇒ CP of 25 liters of milk = 25 × 45 = ₹1125

⇒ CP of 15 liters of milk = 15 × 50 = ₹750

⇒ Total CP of the mixture = 1125 + 750 = ₹1875

⇒ Total quantity of the mixture = 25 + 15 = 40 liters

⇒ Total SP of the mixture = 40 × 48 = ₹1920

⇒ Since Total SP > Total CP, Suman makes a profit.

⇒ Total Profit = 1920 − 1875 = ₹45

∴ The correct answer is Profit of ₹45.

Additional Information

Weighted Average (Mixtures)

The mean cost price of a mixture formed by mixing two distinct quantities can be calculated as: Mean CP = (Q₁ × P₁ + Q₂ × P₂) ÷ (Q₁ + Q₂).

Profit and Loss Fundamentals

A business transaction yields a profit when the Selling Price (SP) is greater than the Cost Price (CP). Conversely, it results in a loss if the CP exceeds the SP. The absolute profit is computed as: Profit = SP − CP.

Rule of Alligation

This rule provides a direct method to find the ratio in which two quantities of varying prices must be combined to yield a required average price: Quantity of Cheaper ÷ Quantity of Dearer = (Price of Dearer − Mean Price) ÷ (Mean Price − Price of Cheaper).

Shortcut Trick

Remaining cars after charity = 1200 − 200 = 1000.

Effective paid cars = 1000 × [8 ÷ (8 + 2)] = 800.

Selling Price (SP) per car = ₹120 − 10% = ₹108.

Total Revenue (SP) = 800 × ₹108 = ₹86,400.

Loss % = [(90,000 − 86,400) ÷ 90,000] × 100 = 4%.

∴ The correct answer is 4% loss.

Alternate Method

Given:

Total cost price (CP) = ₹90,000

Total toy cars produced = 1200

Cars given to charity = 200

Market price (MP) per car = ₹120

Discount = 10%

Total Produced = 1200 cars (Total CP = ₹90,000)DonatedFreePaid (800 cars)200200800Selling Price per paid car = ₹120 − 10% = ₹108Total Revenue (SP) = 800 × ₹108 = ₹86,400Loss = ₹90,000 − ₹86,400 = ₹3,600

Calculations:

⇒ Remaining cars left for sale = 1200 − 200 = 1000

⇒ Selling Price per car after discount = 120 − (10% of 120) = 120 − 12 = ₹108

⇒ The offer states 2 free cars for every 8 cars purchased. This means out of every 10 cars handed out, 8 are paid for.

⇒ Number of billed/paid cars = 1000 × (8 ÷ 10) = 800 cars

⇒ Total Selling Price (SP) = 800 × 108 = ₹86,400

⇒ Overall Loss = Total CP − Total SP = 90000 − 86400 = ₹3600

⇒ Loss % = (Loss ÷ CP) × 100

⇒ Loss % = (3600 ÷ 90000) × 100 = 4%

∴ The correct answer is 4% loss.

Additional Information

Buy X Get Y Free Concept

This means for a total of (X + Y) articles, the customer only pays for X articles. The effective discount percentage for the customer is calculated as: [Y ÷ (X + Y)] × 100.

Marked Price (MP) & Discount

Discount is always calculated on the Marked Price. Selling Price (SP) = MP − Discount. The final Selling Price can also be calculated directly using SP = MP × (100 − D%) ÷ 100.

Profit & Loss Percentage

Profit or loss is always calculated over the Cost Price (CP) unless explicitly stated otherwise. Loss % = (Loss ÷ CP) × 100 and Profit % = (Profit ÷ CP) × 100.

Shortcut Trick

Let the Cost Price be CP.

Fraction values: +80% markup = 180/100 = 9/5.

Fraction values: 25% discount = 3/4, and 10% discount = 9/10.

Final Selling Price = CP × 9/5 × 3/4 × 9/10 = CP × 243/200

⇒ 15552 = CP × 243/200 ⇒ CP = 15552 × 200 ÷ 243 = 12800

∴ The correct answer is ₹12,800.

Alternate Method

Given:

Markup = 80%, 1^st Discount = 25%, 2^nd Discount = 10%

Final Selling Price = ₹15,552

CP (100x)

+80%

MP (180x)

-25%

SP1 (135x)

-10%

Final SP (121.5x)

Final Selling Price (121.5x) = ₹15,552

Calculations:

⇒ Let the Cost Price (CP) be 100x.

⇒ Marked Price (MP) = 100x + 80% of 100x = 180x

⇒ Selling Price after 1^st discount (25%) = 180x × (1 − 25/100) = 135x

⇒ Final Selling Price after 2^nd discount (10%) = 135x × (1 − 10/100) = 121.5x

⇒ Given Final SP = ₹15,552

⇒ 121.5x = 15552

⇒ x = 15552 ÷ 121.5 = 128

⇒ Cost Price = 100x = 100 × 128 = 12800

∴ The correct answer is ₹12,800.

Additional Information

Marked Price (MP)

It is the price printed on the article. Markup percentage is always calculated on the base of Cost Price (CP).

Successive Discount

When multiple discounts are given sequentially, the final Selling Price is calculated by multiplying the successive discount factors: Final SP = MP × (1 − D₁/100) × (1 − D₂/100).

Equivalent Single Discount

If two successive discounts of x% and y% are given, the single equivalent discount is calculated using the formula: (x + y − xy/100)%.

Shortcut Trick

Since only water is added, the juice quantity is constant. Make juice units equal in both ratios:

Initial Juice : Water = 5 : 3 ⇒ (× 2) ⇒ 10 : 6

Final Juice : Water = 2 : 3 ⇒ (× 5) ⇒ 10 : 15

Initial quantity = 10 + 6 = 16 units = 40 L ⇒ 1 unit = 2.5 L.

Water added = 15 − 6 = 9 units ⇒ 9 × 2.5 = 22.5 L.

∴ The correct answer is 22.5 litres.

Alternate Method

Given:

Initial mixture = 40 liters | Initial ratio (Juice : Water) = 5 : 3

Final ratio (Juice : Water) = 2 : 3

Initial MixtureWater: 37.5%Added WaterWater: 100%Final60%100 − 60 = 4060 − 37.5 = 22.5Ratio of Quantities (Initial : Added) = 40 : 22.5Since Initial Mixture is 40 L   →   Added Water = 22.5 L

Calculations:

⇒ Quantity of Juice = (5 ÷ 8) × 40 = 25 liters

⇒ Quantity of Water = (3 ÷ 8) × 40 = 15 liters

Let the amount of water added be x liters, so the new amount of water = (15 + x) liters.

According to the new ratio of Juice to Water:

⇒ 25 ÷ (15 + x) = 2 ÷ 3

⇒ 75 = 30 + 2x

⇒ 2x = 45 ⇒ x = 22.5

∴ The correct answer is 22.5 litres.

Additional Information

Rule of Alligation

When two ingredients of different concentrations are mixed, the ratio of their quantities is: (Quantity of Cheaper) ÷ (Quantity of Dearer) = (Price of Dearer − Mean Price) ÷ (Mean Price − Price of Cheaper).

Constant Term Logic in Ratios

When only one component (like water) is added to a mixture, the quantity of the other component (like juice) remains unchanged. Equating the ratio units of the constant component naturally streamlines the calculation without needing algebra.

Replacement Formula

If V is the initial volume of pure liquid, and x volume is removed and replaced by water n times, the final volume of pure liquid left = V × (1 − x/V)ⁿ.

Shortcut Trick

Total work = LCM(15, 20) = 60 units.

Combined efficiency = (60 ÷ 15) + (60 ÷ 20) = 4 + 3 = 7 units/day.

Work done in 4 days = 7 × 4 = 28 units.

Remaining work = 60 − 28 = 32 units.

Fraction of work remaining = 32 ÷ 60 = 8/15.

∴ The correct answer is 8/15.

Alternate Method

Given:

Time taken by A to complete the task = 15 days

Time taken by B to complete the task = 20 days

Time they worked together = 4 days

⇒ Total efficiency of A and B = 4 + 3 = 7 units/day

⇒ Work done by A and B together in 4 days = 7 × 4 = 28 units

⇒ Remaining work = Total Work − Work Done

⇒ Remaining work = 60 − 28 = 32 units

⇒ Fraction of work remaining = Remaining Work ÷ Total Work

⇒ Fraction of work remaining = 32 ÷ 60 = 8/15

∴ The correct answer is 8/15.

Additional Information

Total Work & Efficiency

Efficiency is inversely proportional to the time taken. Total work is usually assumed as the LCM of the given individual days to avoid complex fractional calculations.

Work & Wages

Wages are completely distributed in proportion to the total actual work done by each person during the given period, not just by their efficiency ratios.

Pipes & Cisterns

This topic follows identical principles to Time & Work. The key difference is that filling pipes have a positive efficiency while emptying pipes (or leaks) have a negative efficiency.

Shortcut Trick

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

⇒ Mean CP = 144 × (100 ÷ 120) = ₹120/kg

Apply Alligation: Ratio = (Dearer Price − Mean Price) : (Mean Price − Cheaper Price)

⇒ Ratio = (150 − 120) : (120 − 90) = 30 : 30 = 1 : 1

∴ The correct answer is 1 : 1.

Alternate Method

Given:

Price of cheaper oil (C) = ₹90/kg

Price of dearer oil (D) = ₹150/kg

Selling price of mixture (SP) = ₹144/kg

Profit = 20%

Formula Used:

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

₹90 ₹150 ₹120 30 30

Cheaper Oil Dearer Oil Mean CP

Ratio = 30 : 30 = 1 : 1

Calculations:

⇒ Mean CP = 144 × [100 ÷ (100 + 20)]

⇒ Mean CP = 144 × (100 ÷ 120)

⇒ Mean CP = 144 × (5 ÷ 6) = ₹120/kg

⇒ By the rule of alligation:

⇒ Quantity of Cheaper : Quantity of Dearer = (150 − 120) : (120 − 90)

⇒ Quantity of Cheaper : Quantity of Dearer = 30 : 30

⇒ Ratio = 1 : 1

∴ The correct answer is 1 : 1.

Additional Information

Rule of Alligation

The ratio in which two ingredients are mixed to produce a mixture of a desired mean price is given by (Dearer Price − Mean Price) : (Mean Price − Cheaper Price).

Cost Price vs Selling Price in Mixtures

When applying alligation, all values must be of the same type. If the individual values are Cost Prices, the mean value must also be the Cost Price (CP), not the Selling Price (SP). CP = SP × 100 ÷ (100 + Profit%).

Weighted Average Method

The rule of alligation is a direct derivation of the weighted average formula: M = (Q₁ × C₁ + Q₂ × C₂) ÷ (Q₁ + Q₂), where Q represents quantity and C represents the respective cost.

Shortcut Trick

Total capacity = LCM(6, 8, 12) = 24 units.

Total efficiency of A, B and C = 4 + 3 + 2 = 9 units/hr.

Tank filled in 2 hours = 9 × 2 = 18 units.

Remaining capacity = 24 − 18 = 6 units.

Time taken by A and B to fill the rest = 6 ÷ (4 + 3) = 6/7 hours.

∴ The correct answer is 6/7 hours.

Alternate Method

Given:

Time taken by pipe A to fill the tank = 6 hours

Time taken by pipe B to fill the tank = 8 hours

Time taken by pipe C to fill the tank = 12 hours

Time all pipes operated together = 2 hours

Calculations:

⇒ Combined efficiency of A, B and C = 4 + 3 + 2 = 9 units/hr

⇒ Work done by A, B and C in 2 hours = 9 × 2 = 18 units

⇒ Remaining work = 24 − 18 = 6 units

⇒ Pipe C is closed, so the remaining work is done by pipes A and B.

⇒ Combined efficiency of pipes A and B = 4 + 3 = 7 units/hr

⇒ Additional time taken by A and B = Remaining work ÷ Combined efficiency

⇒ Additional time taken = 6/7 hours

∴ The correct answer is 6/7 hours.

Additional Information

Pipes and Cisterns Basics

If a pipe can fill a tank in x hours, the part filled in 1 hour is 1/x. This is analogous to the concept of Time and Work where efficiency is inversely proportional to time.

Inlet vs Outlet Pipes

An inlet pipe fills the tank and its work is considered positive. An outlet pipe empties the tank and its work is considered negative. Net work = 1/x − 1/y.

Alternate Working of Pipes

When pipes are opened in alternate hours, work is calculated in cycles (e.g., 2 hours if 2 pipes are working alternately) rather than directly summing their efficiencies per hour.

Shortcut Trick

Since the travel time remains constant (30 minutes) in both cases, Speed is directly proportional to Distance.

Because the distance increases by 20%, the required average speed must also increase by exactly 20%.

New Speed = 240 + (20% of 240)

New Speed = 240 + 48 = 288 km/h

∴ The correct answer is 288 km/h.

Alternate Method

Given:

Initial Average Speed (S₁) = 240 km/h

Initial Time (T₁) = 30 minutes = 0.5 hours

New Time (T₂) = 30 minutes = 0.5 hours

Initial Distance: 120 km Speed: 240 km/h | Time: 30 min

New Distance: 144 km (+20%) New Speed: 288 km/h | Time: 30 min

Formula Used:

Distance = Speed × Time

Speed = Distance ÷ Time

Calculations:

⇒ Initial Distance (D₁) = 240 × 0.5 = 120 km

⇒ The distance is increased by 20% due to track maintenance.

⇒ New Distance (D₂) = 120 + (20 ÷ 100) × 120

⇒ D₂ = 120 + 24 = 144 km

⇒ The train needs to arrive in the same exact time window.

⇒ New Time (T₂) = 0.5 hours

⇒ New Speed (S₂) = D₂ ÷ T₂

⇒ S₂ = 144 ÷ 0.5 = 288 km/h

∴ The correct answer is 288 km/h.

Additional Information

Direct and Inverse Proportionality

When Time is constant, Distance and Speed are directly proportional (S₁ ÷ S₂ = D₁ ÷ D₂). When Distance is constant, Time and Speed are inversely proportional.

Unit Conversions for Speed

To convert an object's speed from km/h to m/s, multiply it by 5 ÷ 18. To change m/s back to km/h, multiply by 18 ÷ 5.

Average Speed

Average Speed over an entire journey equals Total Distance ÷ Total Time. If two equal distances are traveled at speeds a and b, the Average Speed is 2ab ÷ (a + b).

Shortcut Trick

Relative speed in opposite direction = 360 ÷ 4 = 90 km/h

Relative speed in same direction = 360 ÷ 12 = 30 km/h

Speed of the faster car (X) = (Sum of relative speeds + Difference of relative speeds) ÷ 2

Speed of X = (90 + 30) ÷ 2 = 120 ÷ 2 = 60 km/h

∴ The correct answer is 60 km/h.

Alternate Method

Given:

Distance between X and Y = 360 km

Time to meet moving towards each other = 4 hours

Time to meet moving in the same direction = 12 hours

Formula Used:

Speed = Distance ÷ Time

Opposite Direction: Relative Speed = X + Y

Same Direction: Relative Speed = X − Y

Calculations:

⇒ X + Y = 360 ÷ 4

⇒ X + Y = 90     ... (Equation 1)

⇒ X − Y = 360 ÷ 12

⇒ X − Y = 30     ... (Equation 2)

⇒ Adding Equation 1 and Equation 2:

⇒ (X + Y) + (X − Y) = 90 + 30

⇒ 2X = 120

⇒ X = 60 km/h

∴ The correct answer is 60 km/h.

Additional Information

Relative Speed in Opposite Direction

When two bodies move towards each other, their relative speed is calculated as the sum of their individual speeds (S₁ + S₂).

Relative Speed in Same Direction

When two bodies move in the same direction, their relative speed is calculated as the difference of their individual speeds (S₁ − S₂).

Distance Constant Rule

If the distance to be covered remains constant, the speed of an object is inversely proportional to the time taken: S₁ ÷ S₂ = T₂ ÷ T₁.

Shortcut Trick

Remaining pizza percentage = 100% − 75% = 25% = 1/4 of total pizza.

Area remaining = (1/4) × π × r²

⇒ Area = (1/4) × (22/7) × 21 × 21

⇒ Area = (1/4) × 1386 = 346.5 cm²

∴ The correct answer is 346.5 cm².

Alternate Method

Given:

Radius of the circular pizza (r) = 21 cm

Percentage of pizza eaten = 75%

Formula Used:

Total Area of a circle = πr² (where π ≈ 22/7)

Remaining Area = Total Area × (Remaining Percentage / 100)

Eaten (75%) 25% Left r = 21 cm Pizza Area Remaining = 25%

Calculation:

⇒ Total Area of the pizza = (22/7) × 21 × 21

⇒ Total Area = 22 × 3 × 21 = 1386 cm²

⇒ Remaining Percentage = 100% − 75% = 25%

⇒ Remaining Area = 25% of Total Area

⇒ Remaining Area = (25 / 100) × 1386

⇒ Remaining Area = 1386 ÷ 4 = 346.5 cm²

∴ The correct answer is 346.5 cm².

Additional Information

Area of a Circle

The total area enclosed by a circle is given by A = πr², where r is the radius of the circle.

Area of a Sector

A sector is a portion of a circle enclosed by two radii and an arc. Its area is calculated as (θ/360) × πr², where θ is the central angle.

Percentage to Fraction Conversion

Converting standard percentages to fractions simplifies calculations. For example, 25% = 1/4, 50% = 1/2, and 75% = 3/4.

Shortcut Trick

Ratio of ring area to outer circle area = (R² − r²) : R²

⇒ Ratio = (10² − 7²) : 10² = (100 − 49) : 100

⇒ Exact Ratio = 51 : 100

⇒ Approximate Ratio ≈ 50 : 100 = 1 : 2

∴ The correct answer is 1:2.

Alternate Method

Given:

Outer radius (R) = 10 cm

Inner radius (r) = 7 cm

Formula Used:

Area of a circle = πR²

Area of a ring = π(R² − r²)

R = 10 cm

r = 7 cm

Ring-Shaped Disc

Calculations:

⇒ Area of the outer circle = π × (10)² = 100π cm²

⇒ Area of the inner circle = π × (7)² = 49π cm²

⇒ Area of the ring = Area of outer circle − Area of inner circle

⇒ Area of the ring = 100π − 49π = 51π cm²

⇒ Ratio of ring's area to outer circle's area = 51π : 100π

⇒ Exact ratio = 51 : 100

⇒ Approximating 51 to 50 for simplification

⇒ Approximate ratio ≈ 50 : 100 = 1 : 2

∴ The correct answer is 1:2.

Additional Information

Area of a Ring

The region bounded by two concentric circles of outer radius R and inner radius r is called a ring. Its area is calculated using the formula π(R² − r²).

Concentric Circles

Circles having the same center but different radii are called concentric circles. The perpendicular distance between the boundaries of these circles is uniform and equal to (R − r).

Area of a Sector

The area of a sector of a circle with radius r and central angle θ (in degrees) is calculated using the formula (θ ÷ 360) × πr².

Shortcut Trick

The percentage of circumference covered depends solely on the fraction of the turn, making the radius extraneous data.

A full turn (1 complete revolution) always covers exactly 100% of the circumference.

Therefore, a quarter turn covers exactly 1/4 of a full revolution.

Percentage covered = (1 ÷ 4) × 100% = 25%.

∴ The correct answer is 25%.

Alternate Method

Given:

Radius (r) = 35 cm

π = 22/7

Formula Used:

Circumference of a circle = 2 × π × r

Distance covered in a quarter turn = Circumference ÷ 4

90°

r = 35 cm Full Turn (360°) = 100% of Circumference Quarter Turn = 1/4 of Circle = 25% 1/4 Turn = 25% of Circumference

Calculations:

⇒ Total Circumference = 2 × (22/7) × 35

⇒ Total Circumference = 2 × 22 × 5 = 220 cm

⇒ Distance covered in a quarter turn = Total Circumference ÷ 4

⇒ Distance covered = 220 ÷ 4 = 55 cm

⇒ Percentage of circumference covered = (Distance ÷ Total Circumference) × 100

⇒ Percentage = (55 ÷ 220) × 100

⇒ Percentage = (1 ÷ 4) × 100 = 25%

∴ The correct answer is 25%.

Additional Information

Extraneous Data in Math Problems

When a question asks for a ratio, fraction, or percentage of a total, exact numerical measurements (like radius = 35 cm) are often not required to solve the problem and can be bypassed to save time.

Arc Length Formula

The length of an arc is proportional to its central angle: Arc Length = (θ ÷ 360) × 2 × π × r. A quarter turn has an angle of 90°, so the arc length is exactly 1/4 of the full circumference.

Distance and Rotations

The total linear distance covered by a rolling wheel equals the number of rotations multiplied by its circumference (Distance = n × 2 × π × r).

Shortcut Trick

If a line passes through a given point, the coordinates of the point directly satisfy the equation of the line.

Substitute the point (1, 8) into the line equation y = mx + 5.

⇒ 8 = m × 1 + 5

⇒ m = 8 − 5 = 3

∴ The correct answer is 3.

Alternate Method

Given:

Equation of the straight line: y = mx + 5

The line passes through the point (1, 8).

x y O

(0, 5)

(1, 8)

Δx = 1 Δy = 3

Line: y = mx + 5 y-intercept c = 5 → point (0, 5) Slope m = Δy ÷ Δx = 3 ÷ 1 = 3

Formula Used:

If a point (x, y) lies on a line, its values must satisfy the equation y = mx + c.

Calculations:

⇒ By placing x = 1 and y = 8 in the given equation y = mx + 5:

⇒ 8 = m(1) + 5

⇒ 8 = m + 5

⇒ m = 8 − 5

⇒ m = 3

∴ The correct answer is 3.

Additional Information

Slope-Intercept Form

The equation of a straight line is commonly written as y = mx + c, where m is the slope of the line and c is its y-intercept.

Calculating Slope

The slope m of a line passing through any two distinct points (x₁, y₁) and (x₂, y₂) is evaluated as m = (y₂ − y₁) ÷ (x₂ − x₁).

Point-Slope Form

If a line has a given slope m and passes through a specific point (x₁, y₁), its exact equation is found using y − y₁ = m(x − x₁).

X and Y Intercepts

The x-intercept is the point where the line touches the x-axis (y = 0). The y-intercept is the point where it crosses the y-axis (x = 0).

Shortcut Trick

Apply the Digital Sum (DS) method to solve the equation quickly.

DS of 31³ = 4³ = 64 ⇒ 1 | DS of 18³ = 9³ = 729 ⇒ 0.

DS of 37³ = 1³ = 1 | DS of 210 = 3.

Overall Expression DS = 1 + 0 − 1 + 3 = 3.

Check options: DS of −14820 = −(1+4+8+2) = −15 ⇒ −6. Add 9 to get positive DS: −6 + 9 = 3.

∴ The correct answer is -14820.

Alternate Method

Given:

Expression: 31³ + 18³ − 37³ + 210

Formula Used:

x³ = x × x × x

Calculations:

⇒ 31³ = 31 × 31 × 31 = 29791

⇒ 18³ = 18 × 18 × 18 = 5832

⇒ 37³ = 37 × 37 × 37 = 50653

Substitute the obtained values back into the expression:

⇒ Expression = 29791 + 5832 − 50653 + 210

⇒ Expression = 35623 − 50653 + 210

⇒ Expression = −15030 + 210

⇒ Expression = −14820

∴ The correct answer is -14820.

Additional Information

Simplification Rules

Always follow the proper order of operations (BODMAS). First evaluate powers and exponents before proceeding with addition and subtraction.

Digital Sum Concept

The digital sum of a number is the single-digit sum of its digits. The digital sum of the problem expression must equal the digital sum of its exact solution, making it an excellent verification tool.

Unit Digit Concept

The unit digit of an arithmetic expression relies purely on the unit digits of the numbers involved. For example, 1³ + 8³ − 7³ + 0 yields a unit digit calculation of 1 + 2 − 3 + 0 = 0.

The correct answer is: Treacherous.

Key Points

• The word "Perfidious" means deceitful and untrustworthy, especially in betraying someone who trusts you. (विश्वासघाती)
• Example: The spy revealed all the secrets to the enemy, proving to be perfidious to his country.
• "Treacherous" refers to someone or something that is guilty of betrayal or deception. It is synonymous with the word "perfidious." (विश्वासघाती)
• Example: The treacherous guide led them into a trap instead of the safe path.
• Hence, we can infer that the most appropriate synonym of 'Perfidious' is 'Treacherous'.

Therefore, the correct answer is: Treacherous.

Additional Information

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

• Honest (ईमानदार): Someone who is truthful and sincere in their actions or words.
• Example: She is known for being an honest person, always speaking the truth no matter the consequences.
• Faithful (वफादार): Someone who is loyal and devoted, especially to a person, cause, or belief.
• Example: The dog was faithful to its owner and never left his side.
• Loyal (निष्ठावान): Someone who is steadfast in allegiance or support to a person or cause.
• Example: He remained loyal to his friends even during difficult times.

The correct answer is: Option 3.

Key Points

• The idiom "Hobson's choice" means having no real choice at all; you must either accept what is offered or take nothing at all. (कोई वास्तविक विकल्प नहीं)
• Example: When it comes to the company's policies, employees often face Hobson's choice—either follow them or leave the job.
• It refers to a situation where only one option is available, and it can feel like an illusion of choice. (एक ऐसा विकल्प जो वास्तव में विकल्प नहीं है)
• Example: The restaurant offers Hobson's choice on its fixed menu—take it or leave it!

Therefore, the correct answer is: Option 3.

Additional Information

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

• Option 1: A dilemma between two evils (दो बुराइयों के बीच एक कठिनाई): Refers to choosing between two undesirable options.
• Example: She faced a dilemma between two evils—either betray her friend or lose her job.
• Option 2: A free and fair decision (एक स्वतंत्र और निष्पक्ष निर्णय): Refers to making a decision without pressure or bias.
• Example: The committee ensured that the decision-making process was free and fair.
• Option 4: A selection made under duress (दबाव में किया गया चयन): Refers to choosing something under pressure or force.
• Example: He signed the contract under duress, fearing repercussions.

The correct answer is: Extraordinary.

Key Points

• The word "Mundane" means lacking interest or excitement; dull and ordinary. (साधारण)
• Example: The job was mundane, consisting mainly of filing and answering the phone.
• "Extraordinary" refers to something very unusual or remarkable; exceptional. (असाधारण)
• Example: She has an extraordinary talent for playing the piano.
• Hence, we can infer that the opposite of 'Mundane' is 'Extraordinary'.

Therefore, the correct answer is: Extraordinary.

Additional Information

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

• Common (सामान्य): Occurring, found, or done often; prevalent.
• Example: It is a common misconception that all snakes are poisonous.
• Ordinary (साधारण): With no special or distinctive features; normal.
• Example: It was just an ordinary day at work.
• Boring (नीरस): Not interesting; tedious.
• Example: The lecture was so boring that many people fell asleep.

The correct answer is option 4.

Key Points

The misspelled word is 'Quintessance'.

• The correct spelling would be 'Quintessence'.
• The word 'quintessence' is a noun which means 'the most perfect or typical example of a quality or class'. (मूल तत्व)
• For Example -
• Sheep's milk cheese is considered the quintessence of traditional rural life.

Therefore, the correct answer would be 'Quintessence'.

Additional Information

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

• Vicereine - a woman who is a viceroy's wife.
• Floccinaucinihilipilification - the action or habit of estimating something as worthless.
• Defenestrate - to throw someone or something out of a window.

The correct answer is option 1.

Key Points

The correctly spelled term is 'Ventriculoperitoneal'.

• A ventriculoperitoneal (VP) shunt is a medical device that relieves pressure on the brain caused by fluid accumulation.
• The word 'ventriculoperitoneal' refers to the connection between the ventricles of the brain and the peritoneal cavity in the abdomen.

Therefore, the correct answer would be 'Ventriculoperitoneal'.

Additional Information

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

• Ventriculoperitoneal - The correct spelling and term related to the medical procedure involving a shunt.
• Ventriculoperitonal - Incorrect spelling.
• Ventriculaperitoneal - Incorrect spelling.
• Ventriculoperetoneal - Incorrect spelling.