SSC CGL 2025 (Held On: 14 Sept, 2025 Shift 1) (Previous Year Paper)

The logic followed here is:

Logic: The first word is an instrument used to measure the second word.

Here,

Clock : Time → A clock is used to measure time.

Similarly,

Thermometer : Temperature → A thermometer is used to measure temperature.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: The first word is the person who files or makes the second word.

Here,

Plaintiff : Complaint → A plaintiff is a person who files a complaint in a court of law.

Similarly,

Petitioner : Petition → A petitioner is a person who files a petition.

Hence, the correct answer is "Option 4.".

The logic followed here is:

So, 'LMN' will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

The logic followed here is:

So, 'STU' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

The logic followed here is:

So, 'XIN' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

The logic followed here is:

So, 'TPET' will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

The logic followed here is:

So, 'DMZJ' will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

The logic followed here is:

thus, "153" will replace the question mark in the given series.

Hence, the correct option is "Option 1".

Given: FRIENDLY

Alphabetically:  D, E, F, I, L, N, R, Y

Third from left → F

Second from right → R

Positions:

F = 6

R = 18

So, Letters between them = 18 − 6 − 1 = 11

Hence, the correct answer is "Option 4".

The address given in the problem is,

Amitabh S.

112/44 Block-B, Indira Nagar, Lucknow, 226016

Let's match this address with the given options one by one to figure out which ones are exactly the same.

So, addresses (2), and (3) are exactly identical, while address (1) and (4) is different due to the missing dot and hyphen.

Hence, the correct answer is option (2)

The address given in the problem is,

Dr Ruchi Jain

4/88, Skyline Residency, Jaipur, 302001

Let's match this address with the given options one by one to figure out which addresses are exactly identical.

From the comparison above, only options (2) and (3) are exactly identical to each other.

Hence, the correct answer is "2) 2 and 3".

The logic followed here is:

DINS : WRMH

Similarly,

EKPT : ?

Hence, the correct answer is "Option 3.

The logic followed here is:

Logic: Each letter is replaced by its alphabetical position, and the product is written in the same order.

Here, AxE : 1x5

A = 1

E = 5

So, AxE becomes 1 × 5.

Similarly, DxK : ?

D = 4

K = 11

So, DxK becomes 4 × 11.

Hence, the correct answer is "Option 2."

Given: 40 students.

Rahul is 13th from the left,

Kunal is 17th from the right.

So, students between Rahul and Kunal = 40 − 13 − 17 = 10.

So, there are '10' students standing between Rahul and Kunal.

Hence, the correct answer is "Option 3."

The logic followed here is:

PRINTING : RPNIITGN

Similarly, 

PROTOCOL : ?

Hence, the correct answer is "Option 4.

The logic followed here is:

HOUSE : GNTRD

Similarly, 

? : KHFGS

Hence, the correct answer is "Option 4."

Family Chart:

Given: 

B’s father’s wife → This is B’s mother (assuming no complication like remarriage).

B’s mother’s son → That is B himself (since B is the son of his parents).

 

So, “Your father's wife's son” = B = Sibling.

Hence, the correct answer is "Option 2".

The logic followed here is:

thus, "25" will replace the question mark in the given series.

Hence, the correct option is "Option 2".

The logic followed here is:

Given: 

Check each number:

Option 1) 21: Sum of digits = 2 + 1 = 3 → 21 ÷ 3 = 7 

Option 2) 30: Sum of digits = 3 + 0 = 3 → 30 ÷ 3 = 10 

Option 3) 36: Sum of digits = 3 + 6 = 9 → 36 ÷ 9 = 4 

Option 4) 39: Sum of digits = 3 + 9 = 12 → 39 ÷ 12 = 3.25 

So, 39 does not satisfy the condition.

Hence,The correct answer is "Option 4."

The pattern followed here is:

Option 1) A1 : D5 : G9

Option 2) B2 : E6 : H10

Option 3) C3 : F7 : I11

Option 4) D4 : G8 : K13

So, the odd group is D4 : G8 : K13.

Hence, the correct option is "Option 4".

The logic followed here is:

Logic: Letters increase by +3 positions and numbers increase by +3 in each step.

Now,

A1@ : D4# : G7$

Letters →

A → D (+3)

D → G (+3)

Numbers →

1 → 4 (+3)

4 → 7 (+3)

Follows the pattern

B2% : E5^ : H8&

Letters →

B → E (+3)

E → H (+3)

Numbers →

2 → 5 (+3)

5 → 8 (+3)

Follows the pattern

C3* : F6( : I9)

Letters →

C → F (+3)

F → I (+3)

Numbers →

3 → 6 (+3)

6 → 9 (+3)

Follows the pattern

D4_ : G8@ : K13$

Letters →

D → G (+3)

G → K (+4) Should be J if +3)

Numbers →

4 → 8 (+4)  (Should be +3)

8 → 13 (+5) 

Does NOT follow the pattern

So, the odd group is D4_ : G8@ : K13$.

Hence, the correct option is "Option 4".

Given: A said to B: "The woman I met yesterday at the park was the only daughter of the father of your brother."

 

So, The woman A met = B’s sister.

Hence, the correct answer is "Option 1".

Given: A man says, "My son's mother is the only child of your father."

 

So, the man is the husband of that person.

Hence, the correct answer is "Option 2".

Given: Introducing a man, Shruti said, "He is the husband of the granddaughter of the only son of my grandfather."

 

So, The man is Shruti’s daughter's husband or son-in-law.

Hence, the correct answer is "Option 1".

BODMAS Table: 

Given equation: 6 + 3 − 2 × 1 = ?

Now, if ‘+’ = ×, ‘−’ = +, and ‘×’ = ÷, then:

⇒ 6 × 3 + 2 ÷ 1 = ?

⇒ 18 + 2 ÷ 1 = ?

⇒ 18 + 2 = 20

Hence, the correct answer is "Option 1."

The correct answer is Only statement 2.

Key Points

• The security deposit of ₹15,000 is mandatory for candidates contesting the election for the President of India, as per Article 58 of the Constitution of India and the Presidential and Vice-Presidential Elections Act, 1952.
• The deposit is forfeited if the candidate fails to secure at least one-sixth of the votes cast in the election.
• The security deposit ensures that only serious candidates participate in the election process.
• The election of the President of India is conducted by an electoral college consisting of elected members of both Houses of Parliament and the Legislative Assemblies of States and Union Territories.
• As per the rules, the nomination paper must be supported by at least 50 proposers and 50 seconders to ensure legitimacy.

Additional Information

• Statement 1: Solicitor General of India is appointed by the president of India
• The Solicitor General of India is the second-highest law officer in the country after the Attorney General of India.
• Unlike the Attorney General, the Solicitor General is not appointed directly by the President of India. Instead, the appointment is made by the Union Government, specifically by the Ministry of Law and Justice.
• The Solicitor General assists the Attorney General in performing legal duties and advises the government on legal matters.
• Therefore, Statement 1 is incorrect.
• Concept of Presidential Elections in India:
• The President is elected by an electoral college through a proportional representation system using a single transferable vote.
• Every member of the electoral college casts their vote, and the candidate receiving the highest number of votes is elected.
• The process is governed by the provisions in Articles 52 to 62 of the Constitution.
• Other Important Facts:
• The President of India serves a term of five years and can be re-elected.
• The eligibility criteria for candidates contesting the Presidential elections include being a citizen of India, at least 35 years old, and qualified to be a member of the Lok Sabha.
• In case of vacancy, the election must be held within six months.

The correct answer is Option 2: Only Statement I is correct.

Key Points

• Statement I is correct: Mathura art was a significant school of art during the Kushana period, producing sculptures for both Indian and non-Indian patrons, including images of Buddha, Bodhisattvas, Yakshas, and Jain Tirthankaras.
• Mathura art is renowned for its syncretic style, blending indigenous Indian artistic traditions with Greco-Roman influences.
• It catered to diverse religious communities like Buddhists, Jains, and Hindus, reflecting its inclusive nature and wide patronage.
• Mathura art produced sculptures for Buddhist stupas in India and beyond, including regions such as Central Asia, showcasing its appeal to non-Indian patrons.

Additional Information

• Statement II is incorrect: Mathura art did not ignore nature-based themes. In fact:
• It prominently featured nature-inspired motifs such as trees, animals, and floral designs in its sculptures.
• Yakshas and Yakshinis, celestial beings associated with nature and fertility, were frequently depicted in Mathura sculptures.
• Nature was often used symbolically in Buddhist and Jain art, such as the Bodhi tree representing Buddha's enlightenment.
• Key Features of Mathura Art:
• Mathura art evolved during the Kushana period and served as a major center of artistic activity.
• It is characterized by red sandstone sculptures with intricate detailing and bold expressions.
• The art form emphasized realism and depicted human and divine figures with naturalistic features and elaborate ornamentation.
• Notable examples include the seated Buddha statues and images of Hindu deities like Vishnu and Shiva.
• Comparison with Gandhara Art:
• While Mathura art represented indigenous Indian styles, Gandhara art reflected strong Greco-Roman influences.
• Mathura sculptures were made of red sandstone, whereas Gandhara sculptures predominantly used grey schist stone.

The correct answer is It showcases martial arts, langars, and Nihang mock battles at Anandpur Sahib..

Key Points

• Hola Mohalla is a Sikh festival that was first introduced by Guru Gobind Singh, the tenth Sikh Guru, in 1701.
• The festival is celebrated a day after Holi and is marked by demonstrations of martial arts, mock battles by Nihang warriors, and traditional Sikh customs.
• The main celebrations are held at Anandpur Sahib, a significant Sikh pilgrimage site in Punjab.
• It is known for its community kitchens (langars), where free meals are served to all visitors as part of Sikh tradition.
• The festival also includes religious processions, poetry recitations, and devotional music, making it a vibrant cultural and spiritual event.

Additional Information

• It seems to be a misrepresentation of certain other cultural festivals in Punjab where women actively participate in folk activities like Giddha and Phulkari.
• In Punjab, Baisakhi is the prominent harvest festival celebrated in April to mark the wheat harvesting season.
• Hola Mohalla is celebrated a day after Holi and is distinct in its focus on martial traditions and Sikh spiritual values.

The correct answer is Vedic traditions.

Key Points

• Mārgi Sangita refers to the classical music tradition of ancient India, which is deeply rooted in the Vedic traditions.
• It was considered divine and sacred, often used in rituals, spiritual practices, and worship.
• The Samaveda, one of the four Vedas, provides the earliest references to music, including chants and hymns that were rhythmically structured.
• The concept of Mārgi Sangita was based on spiritual and philosophical ideals, aiming to elevate the human soul and connect it with higher consciousness.
• It contrasted with Desi Sangita, which referred to regional or folk music traditions and was meant for entertainment rather than spiritual elevation.

Additional Information

• Classical Music
• Hindustani (North India): Features instruments like sitar, sarod, and tabla, focusing on improvisation within complex melodic structures (ragas) and rhythmic cycles (talas).
• Carnatic (South India): Emphasizes vocal compositions, often devotional, using different structures and scales (swaras).
• Key Figures: Pandit Ravi Shankar (Sitar), Ustad Bismillah Khan (Shehnai), Pandit Bhimsen Joshi (Vocal).

The correct answer is Performing a successful takedown.

Key Points

• A takedown is a critical technique in freestyle wrestling that allows a wrestler to bring their opponent from a standing position to the mat and gain control.
• Performing a successful takedown awards the wrestler technical points, which depend on the skill level and execution of the move (usually 2 to 5 points).
• Common types of takedowns include single-leg takedown, double-leg takedown, and throws.
• In addition to scoring points, a takedown puts the wrestler in an advantageous position to attempt further scoring or pinning.
• Freestyle wrestling emphasizes both offensive and defensive techniques, with takedowns being one of the primary methods of scoring.

Additional Information

• Running out of the mat deliberately
• Running out of the mat is considered a form of passive wrestling or avoiding engagement, which can lead to penalties.
• Instead of gaining points, wrestlers may receive warnings or penalties for deliberately stepping out of the mat to escape an opponent’s hold or avoid engagement.
• In some cases, referees may award points to the opponent if this action is deemed intentional.
• Holding the opponent's singlet
• Grabbing the opponent's singlet, headgear, or other parts of their uniform is prohibited in freestyle wrestling.
• This action is considered illegal and results in penalties or warnings against the wrestler committing the foul.
• The purpose of this rule is to ensure fairness and maintain the integrity of the sport.
• Using an illegal headlock
• An illegal headlock occurs when a wrestler applies a headlock without an arm included in the hold.
• This technique is not allowed as it can cause serious injuries and is against the rules of freestyle wrestling.
• Wrestlers using illegal holds may face penalties, warnings, or even disqualification in extreme cases.

The correct answer is Carlos Góngora.

Key Points

• Vijender Singh defeated Carlos Góngora, a boxer from Ecuador, in the quarter-finals of the Men's Middleweight category at the 2008 Beijing Olympics.
• This victory secured Vijender Singh a medal in boxing, making him the first Indian boxer to win an Olympic medal.
• The match was intensely fought, with Vijender showcasing exceptional strategy, precision, and stamina to outclass Carlos Góngora.
• Vijender's performance at the Beijing Olympics marked a milestone for Indian boxing, elevating the sport's status in the country.
• He eventually secured the bronze medal in the Men's Middleweight (75 kg) category, creating history for Indian sports.

Additional Information

• Emilio Correa:
• Emilio Correa is a Cuban boxer who competed in the Middleweight category at the 2008 Beijing Olympics.
• He won the silver medal in the event, losing to James DeGale of Great Britain in the final.
• Correa was known for his aggressive fighting style and strong punches in the competition.
• Misha Aloyan:
• Misha Aloyan is a Russian boxer who specializes in the Flyweight category.
• He is a two-time world champion and an Olympic medalist, winning the bronze medal at the 2012 London Olympics.
• However, Aloyan did not compete in the same weight category or event as Vijender Singh during the 2008 Olympics.
• Vasyl Lomachenko:
• Vasyl Lomachenko is a celebrated Ukrainian boxer, widely regarded as one of the greatest amateur boxers of all time.
• He won gold medals in the Featherweight and Lightweight categories at the 2008 and 2012 Olympics respectively.
• Despite his legendary status, Lomachenko competed in a different weight category than Vijender Singh during the 2008 Beijing Olympics.

The correct answer is SAARC Currency Swap Framework (2024-27).

Key Points

• The SAARC Currency Swap Framework (2024-27) was operationalized by the Reserve Bank of India (RBI) to enhance financial cooperation and stability among SAARC member nations.
• Under this mechanism, India provides short-term financial assistance in foreign currency to SAARC member countries facing liquidity constraints.
• The total corpus for the framework is USD 2 billion, with each eligible member country allowed to withdraw up to USD 400 million within specified limits.
• The framework aims to strengthen regional financial resilience, mitigate balance of payment crises, and promote economic stability within the SAARC region.
• The currency swap facility is offered in major international currencies (e.g., USD, EUR) or Indian Rupees to support member nations in times of financial distress.

Additional Information

• SAARC Development Fund (SDF) capital increase:
• The SAARC Development Fund was established in 2010 to promote regional integration and economic development in SAARC member states.
• It primarily funds projects under its three windows: Social, Economic, and Infrastructure development.
• Although increasing the SDF's capital has been proposed, it is not directly linked to the financial resilience mechanisms implemented in 2024.
• About SAARC:
• The South Asian Association for Regional Cooperation (SAARC) was established in 1985 to promote economic, social, and cultural cooperation among its eight member states: Afghanistan, Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan, and Sri Lanka.
• SAARC initiatives aim to foster regional integration, address common challenges, and promote sustainable development within South Asia.

The correct answer is 23rd January 1973.

Key Points

• The National Institute of Sports (NIS) was established in 1961 within the premises of the historic Palace of the Maharaja of Patiala, Punjab.
• It was renamed as the Netaji Subhas National Institute of Sports (NSNIS) on 23rd January 1973.
• The renaming was done in honor of Netaji Subhas Chandra Bose, a prominent leader in India’s freedom struggle, whose birth anniversary falls on January 23rd.
• NSNIS is widely regarded as the "Mecca" of Indian sports, providing professional training and technical education in various sports disciplines.
• It functions under the aegis of the Sports Authority of India (SAI) and plays a pivotal role in nurturing and developing athletes and sports coaches in the country.

Additional Information

• National Institute of Sports (NIS) and its importance:
• The institute offers advanced training programs for athletes and coaches in a range of disciplines, including athletics, hockey, football, boxing, and wrestling.
• It also conducts diploma and certification courses in sports coaching, equipping individuals with the skills to train athletes effectively.
• NSNIS has played a key role in producing several Olympians and international-level athletes for India.
• It continues to be a hub for sports research and the development of modern training methodologies.

The correct answer is Option 1.

Key Points

• "The Vine of Desire" by Chitra Banerjee Divakaruni is a novel exploring the complexities of relationships, cultural conflicts, and identity within the context of Indian immigrant families.
• The book delves into themes of love, betrayal, reconciliation, and the challenges faced by immigrants in adapting to a new culture while holding onto traditional values.
• It primarily focuses on the lives of two cousins, Anju and Sudha, and their struggles to navigate personal and cultural dilemmas in the United States.
• The novel is known for its emotional depth and vivid portrayal of Indian-American immigrant life.
• Statement 1 is correct as it captures the essence of the book, which revolves around the cultural conflicts and generational challenges within an Indian immigrant family.

Additional Information

• Other notable works:
• The Mistress of Spices (1997): A bestseller about a woman who runs a spice shop and uses spices for magical, life-altering purposes.
• Sister of My Heart (1999): A story of two cousins and best friends in India, exploring deep bonds and fate.
• The Palace of Illusions (2008): A retelling of the Mahabharata from the perspective of the heroine, Panchaali (Draupadi).
• The Forest of Enchantments (2019) & The Last Queen (2021): Companion novels to The Palace of Illusions, continuing the epic mythological saga from other key female characters' viewpoints.
• Independence (2023): A powerful novel exploring the 1947 Partition of India through three generations of women.

The correct answer is Option 2: Only 2.

Key Points

• The Indian Desert, also known as the Thar Desert, is one of the most arid regions in India, and water scarcity is a defining feature of this landscape.
• Most streams in the Indian Desert are ephemeral in nature, meaning they flow only during the monsoon season and disappear into the sand due to high porosity and evaporation rates.
• Perennial streams are rare in the Thar Desert as the region receives an average annual rainfall of only 100-500 mm, which is insufficient to sustain year-round water flow.
• One notable exception is the Luni River, which is the largest river in the Thar Desert but even it becomes saline after flowing through the desert region, limiting its usability.
• The hydrological characteristic of the Thar Desert is such that most of the water from surface streams infiltrates into the sandy terrain or evaporates quickly due to the high temperatures.

Additional Information

• The Indian Desert:
• The Thar Desert covers approximately 200,000 square kilometers, making it the world's 17th largest desert.
• The region is characterized by sand dunes, rocky outcrops, and sparse vegetation.
• Oases in the Thar Desert, such as those in Jaisalmer, provide limited water resources for the local population.
• The region supports unique flora and fauna adapted to the arid environment, such as desert foxes and thorny shrubs.

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

Key Points

• Demographic statistics like birth and death rates depend heavily on accurate reporting from households to maintain the reliability of population data.
• Birth and death registration in India is governed by the Registration of Births and Deaths Act, 1969, which mandates recording these events.
• Despite the legal requirement, the implementation of birth and death registration varies widely across regions due to factors like literacy levels, infrastructure, and accessibility.
• The claim in the reason (R) that registration is "always accurately followed in all parts of India" is incorrect. Challenges such as lack of awareness, geographical inaccessibility, and resource constraints often result in underreporting or delayed registration.
• Thus, while the assertion (A) is correct, the reason (R) is false, as it does not accurately explain the situation of registration compliance in India.

Additional Information

• Importance of Birth and Death Registration
• Accurate registration is crucial for demographic analysis, policy-making, and resource allocation at both national and state levels.
• Birth certificates serve as proof of age, identity, and nationality, which are essential for accessing various benefits and rights.
• Death registration helps track mortality rates, causes of death, and contributes to public health planning.
• Efforts are being made to improve registration rates in India through awareness campaigns and the digitization of records.

The correct answer is Option 1: Gokul Chandra Das – Folk Music.

Key Points

• Gokul Chandra Das is a renowned artist in the field of Folk Music, recognized for his significant contributions to preserving and promoting traditional folk music in India.
• He was awarded the Padma Shri for his outstanding contribution to Folk Music, a category under Arts.
• The Padma Awards are one of the highest civilian honors in India, given in various fields such as art, literature, social work, and public affairs.
• The Padma Shri is the fourth highest civilian award in India, conferred to individuals for distinguished contributions in various fields.
• The recognition of individuals like Gokul Chandra Das highlights the importance of preserving and celebrating India’s rich cultural heritage.

Additional Information

• Dinesh Saini – Environment
• Dinesh Saini is not listed among the Padma awardees under the category of Environment.
• The Environment category in Padma Awards recognizes individuals for their work in environmental conservation, climate change mitigation, and ecological preservation.
• Farooq Ahmad Mir – Literature
• Farooq Ahmad Mir is not associated with receiving the Padma Award in the field of Literature.
• The Literature category in Padma Awards celebrates contributions to Indian literature, creative writing, and linguistic studies.
• Geeta Devi – Agriculture
• Geeta Devi is not listed among Padma awardees in the field of Agriculture.
• Agriculture-related Padma Awards are given to individuals who have contributed to advancements in farming techniques, sustainable agriculture, and rural development.
• Padma Awards Overview
• The Padma Awards are classified into three categories: Padma Vibhushan, Padma Bhushan, and Padma Shri, in decreasing order of prestige.
• These awards are announced annually on the eve of Republic Day in India.
• Fields covered include art, literature, science, sports, social work, public affairs, and more.
• The awards aim to recognize individuals from diverse backgrounds who have made exceptional contributions to society.

The correct answer is Autonomous high-speed landing under tough cross-range & wind.

Key Points

• ISRO's RLV-LEX3 mission on June 23, 2024, successfully demonstrated autonomous high-speed landing capabilities, a critical step in reusable launch vehicle technology development.
• The landing operation was conducted under challenging conditions, including tough cross-range and wind scenarios, showcasing the robustness of the vehicle's autonomous systems.
• This achievement marks a significant step forward in ISRO's plans to develop reusable space technology, which aims to reduce the cost of satellite launches and make space access more economical.
• The mission tested advanced technologies like precision navigation, guidance, and control systems, essential for enabling autonomous landing of spacecraft.
• The RLV (Reusable Launch Vehicle) program is part of ISRO's efforts to create a sustainable and cost-effective space ecosystem through reusable technologies.

Additional Information

• Reusable Launch Vehicle Technology
• Reusable launch vehicles are designed to be recovered and reused for multiple missions, significantly reducing the cost of satellite launches.
• The RLV program is a pioneering effort by ISRO to develop technologies such as autonomous landing, precision navigation, and reusability for space systems.
• These technologies are crucial for creating a sustainable and economically viable space exploration framework.

The correct answer is One gene affects multiple traits.

Key Points

• Pleiotropy refers to a situation where a single gene affects multiple phenotypic traits.
• This occurs because the gene encodes a product (such as a protein) that is involved in multiple biological processes.
• Examples of pleiotropy include the gene responsible for sickle-cell anemia, which affects red blood cell shape and provides resistance to malaria.
• Pleiotropic effects can be observed in both normal physiological processes and genetic disorders.
• Pleiotropy is a fundamental concept in genetics and demonstrates how genes can have far-reaching effects on an organism's phenotype.

Additional Information

• Option 2: Multiple genes affect one trait
• This describes a phenomenon known as polygenic inheritance, where a trait is governed by two or more genes.
• Examples include human height, skin color, and eye color, which result from the combined effect of several genes.
• Polygenic traits often show continuous variation, unlike pleiotropic traits, which are influenced by a single gene.
• Option 3: Gene mutation in one allele
• This refers to a mutation in one copy of a gene (allele) that can affect its function.
• Such mutations can lead to genetic disorders if the mutated allele is dominant or if the condition is recessive and both alleles are affected.
• While this is a distinct genetic concept, it does not describe pleiotropy.
• Option 4: Gene duplication
• Gene duplication is an evolutionary process where a segment of DNA containing a gene is copied, resulting in multiple copies of that gene in the genome.
• This can lead to the evolution of new gene functions or increased gene dosage but is unrelated to pleiotropy.
• Explanation of Pleiotropy:
• Pleiotropy is critical for understanding the complexity of genetic interactions and how single genes can have multiple impacts on an organism's physiology and development.
• It is also significant in studying diseases with pleiotropic effects, such as Marfan syndrome, where a single gene mutation affects the connective tissue throughout the body.

The correct answer is Rajya Sabha and Legislative Councils can only make recommendations within 14 days.

Key Points

• Under Article 110 of the Indian Constitution, a Money Bill can only be introduced in the Lok Sabha and not in the Rajya Sabha.
• Once the Lok Sabha passes a Money Bill, it is sent to the Rajya Sabha for its recommendations, but the Rajya Sabha cannot amend or reject it.
• The Rajya Sabha must return the Money Bill to the Lok Sabha with or without recommendations within a period of 14 days. If not returned within this period, the Bill is deemed passed by both Houses of Parliament.
• In the case of State Legislatures with bicameralism, the Legislative Council can only make recommendations to the Legislative Assembly on Money Bills and must return the Bill within 14 days.
• The powers of the Rajya Sabha and the Legislative Councils on Money Bills are limited to recommendations, and the final decision rests with the Lok Sabha and the Legislative Assembly, respectively.

Additional Information

• A Money Bill deals exclusively with matters listed in Article 110(1) of the Constitution, such as taxation, borrowing, expenditure, and matters incidental to these.
• The distinction between Money Bills and other financial Bills is significant because it limits the role of the Rajya Sabha and Legislative Councils in the legislative process.
• The Speaker of the Lok Sabha or the Legislative Assembly is the final authority to decide whether a Bill is a Money Bill.

The correct answer is Property of inertia.

Key Points

• Inertia is the property of matter that causes it to resist changes in its state of motion or rest unless acted upon by an external force.
• It is a fundamental concept of classical mechanics, based on Newton's First Law of Motion, which states that "an object at rest remains at rest, and an object in motion continues in motion with the same speed and direction unless acted upon by an external force."
• The difficulty in starting the motion of a heavy box is due to its inertia of rest, which resists any change from a stationary state.
• Similarly, the difficulty in stopping the box once it is moving is due to its inertia of motion, which resists any change in its current velocity.
• The larger the mass of an object, the greater its inertia, which is why heavier objects are harder to start or stop in motion.

Additional Information

• Concept of Power:
• Power is defined as the rate at which work is done or energy is transferred over time.
• The formula for power is given as P = W/t, where P is power, W is work, and t is the time taken.
• It is measured in Watts (W) in the SI system.
• Power is not directly related to the resistance to motion or stopping, and hence it is not the correct answer.
• Conservation of Energy:
• This principle states that energy cannot be created or destroyed; it can only change from one form to another.
• The total energy in an isolated system remains constant over time.
• While conservation of energy is a fundamental concept in physics, it does not directly explain the difficulty in starting or stopping the motion of a heavy object.
• Action-Reaction Principle:
• Based on Newton's Third Law of Motion, this principle states that "for every action, there is an equal and opposite reaction."
• It explains how forces act in pairs, such as when you push against a wall and the wall pushes back with an equal and opposite force.
• Although this principle is crucial in understanding motion, it does not account for the resistance to changes in motion, which is the domain of inertia.

The correct answer is Criminal Substantive Law.

Key Points

• The Bharatiya Nyaya Samhita (BNS), 2023, is aimed at consolidating and amending laws related to Criminal Substantive Law in India.
• BNS is designed as a replacement for the Indian Penal Code (IPC), 1860, which was drafted during British colonial rule in India.
• The primary objective of the BNS is to modernize and reform criminal laws to align with the changing socio-economic and technological landscape of the country.
• It seeks to simplify criminal laws, ensure speedy justice, and address contemporary challenges such as cybercrime and organized crime.
• The Bharatiya Nyaya Samhita Bill, 2023, was introduced in Parliament in August 2023 as part of a broader initiative to overhaul colonial-era legal frameworks, including the Code of Criminal Procedure (CrPC) and the Indian Evidence Act.

Additional Information

• Civil Procedure Law
• Civil Procedure Law governs the procedures and practices in civil courts, such as filing lawsuits, conducting trials, and enforcing judgments.
• The primary legislation governing this branch in India is the Civil Procedure Code (CPC), 1908.
• Civil laws deal with private disputes between individuals or organizations, such as property disputes, contracts, or family matters.
• Evidence Law
• The law of evidence deals with the rules and principles that determine what evidence is admissible in courts.
• The Indian Evidence Act, 1872, is the governing framework for evidence-related matters in Indian courts.
• It specifies the type and manner of evidence that can be presented in civil or criminal cases, including oral, documentary, and circumstantial evidence.
• Contract Law
• Contract law governs agreements between parties that are enforceable by law.
• The primary legislation in India is the Indian Contract Act, 1872, which outlines the essentials of a valid contract, including offer, acceptance, consideration, and capacity to contract.
• It also covers specific contracts such as indemnity, guarantee, bailment, agency, and partnership agreements.

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

Key Points

• The National Green Hydrogen Mission was approved by the Indian government in January 2023 with the aim of making India a global hub for green hydrogen production and export.
• The mission primarily focuses on reducing dependency on fossil fuels by promoting green hydrogen, a clean and sustainable energy source derived from renewable energy sources like solar and wind power.
• Through this mission, India aims to produce 5 million metric tonnes of green hydrogen annually by 2030, reducing carbon emissions and aiding the country's energy transition.
• The mission is led by the Ministry of New and Renewable Energy (MNRE), not the Ministry of Environment, Forest and Climate Change (MoEFCC).
• The mission also seeks to attract investments, create employment opportunities, and position India as a leader in the global green hydrogen economy.

Additional Information

• Key Focus of the National Green Hydrogen Mission:
• Promotes the use of green hydrogen in industries such as steel, chemicals, and transportation to reduce carbon footprints.
• Encourages research and development (R&D) to advance green hydrogen technologies and infrastructure.
• Aims to reduce import dependency on fossil fuels, supporting India's energy security.
• Ministry of Environment, Forest and Climate Change (MoEFCC):
• This ministry is responsible for implementing policies and programs related to the conservation of the environment, forests, and climate change mitigation.
• It oversees various environmental clearance processes, biodiversity conservation efforts, and initiatives to combat climate change.
• Although it plays a significant role in environmental sustainability, it is not directly involved in implementing the National Green Hydrogen Mission.

The correct answer is Fisherfolk.

Key Points

• Koli dance is a traditional folk dance performed by the Koli community, primarily comprising fisherfolk in Maharashtra, India.
• The dance represents the culture, lifestyle, and livelihood of the fishing community, symbolizing their connection with the sea and fishing activities.
• Koli dance is characterized by synchronized movements, vibrant costumes, and rhythmic music that depict the daily lives of fisherfolk, including fishing techniques and boat rowing.
• The dance is performed during community celebrations, festivals, and special occasions to express joy and unity.
• The Koli community has a rich cultural heritage, and their dance is an important representation of their identity and traditions.

Additional Information

• Popular Folk Dances of Maharashtra:
• Lavani: A dynamic dance with powerful rhythms, often performed by women in nine-yard sarees, narrating stories of love, society, and politics.
• Tamasha: A traditional folk theatre with dance, music, and drama, known for its entertainment and social commentary.
• Koli Dance: A lively dance of the Koli fishing community, reflecting their daily life and traditions.
• Lezim: An energetic dance performed with small cymbals (lezim), popular in processions and celebrations.
• Powada: A ballad form narrating the heroic tales of Chhatrapati Shivaji Maharaj.
• Dindi & Kala: Devotional dances performed during religious festivals, often honoring Lord Vithoba.
• Gondhal: A ritualistic dance performed for deities like Goddess Renuka.
• Dhangari Gaja: A dance performed solely by men, originating from the Dhangar (shepherd) community.

The correct answer is World Economic Forum.

Key Points

• The Global Energy Transition Index is released by the World Economic Forum (WEF), a Swiss-based international organization committed to improving the state of the world.
• This index assesses the energy systems of countries based on factors like environmental sustainability, energy security, and affordability, focusing on their readiness for energy transition.
• The index uses a unique framework called the Energy Transition Readiness Framework, considering both current performance and enabling conditions for energy transition.
• It ranks countries based on their ability to adopt clean energy technologies, reduce carbon emissions, and ensure reliable access to energy.
• The WEF works closely with governments, businesses, and other stakeholders to provide actionable insights for achieving sustainable energy transitions globally.

Additional Information

• IRENA (International Renewable Energy Agency)
• IRENA is an intergovernmental organization that supports countries in their transition to sustainable energy.
• It primarily focuses on promoting renewable energy sources like solar, wind, and hydroelectric power.
• Its reports and initiatives emphasize renewable energy deployment, innovation, and policy frameworks worldwide.
• While IRENA plays a key role in global energy discussions, it does not release the Global Energy Transition Index.
• IEA (International Energy Agency)
• IEA is an autonomous agency established in the framework of the Organisation for Economic Co-operation and Development (OECD).
• It focuses on energy security, economic development, and environmental sustainability across member countries.
• IEA releases reports like the World Energy Outlook and Energy Technology Perspectives.
• UNDP (United Nations Development Programme)
• UNDP is a global development network under the United Nations, focusing on sustainable development, poverty alleviation, and climate change.
• Its energy-related work often involves improving energy access and promoting clean energy solutions in developing countries.

The correct answer is Toothpaste.

Key Points

• Consumer goods industries produce goods that are directly consumed by customers, meaning they do not require further processing.
• Toothpaste is a prime example of a consumer goods product as it is manufactured for direct use by individuals for personal hygiene.
• It falls under the category of FMCG (Fast-Moving Consumer Goods), which are frequently purchased, low-cost items such as toiletries, beverages, and packaged food products.
• Consumer goods industries focus on manufacturing products that cater to everyday needs, including items like toothpaste, soap, cosmetics, and food products.
• Products from consumer goods industries are typically mass-produced to meet the demand of a large consumer base and distributed through retail outlets or e-commerce platforms.

Additional Information

• Iron and steel:
• The iron and steel industry is classified as a heavy industry as it deals with large-scale production of materials used in infrastructure, construction, and manufacturing.
• It provides raw materials for industries like automobile manufacturing, shipbuilding, and machinery production.
• Steel is not a consumer product but an intermediate good, which requires further processing to create consumer or industrial goods.
• Aluminium smelting:
• Aluminium smelting is an industrial process that involves the extraction of aluminium from its ore, bauxite, using electrolytic reduction.
• This industry is classified as a basic or heavy industry because aluminium is an intermediate product used in manufacturing sectors such as transportation, construction, and packaging.
• It does not directly produce goods for consumer use but supports other industries by providing raw materials.
• Copper smelting:
• Copper smelting involves the extraction of copper metal from its ores through heating and chemical processes.
• It is a heavy or basic industry, as the copper produced is used in electrical wiring, plumbing, and industrial machinery.
• Like aluminium and steel, copper is an intermediate product and not directly consumed by individuals.

The correct answer is Taxation of Goods and Services.

Key Points

• Article 246A of the Indian Constitution was introduced through the 101st Constitutional Amendment Act, 2016, which enabled the implementation of the Goods and Services Tax (GST).
• It grants concurrent powers to both the Parliament and State Legislatures to make laws with respect to GST.
• Under this article, the Parliament has exclusive power to make laws on inter-state trade or commerce of goods and services, while both Parliament and State Legislatures can legislate on intra-state transactions.
• GST subsumes multiple indirect taxes such as VAT, Service Tax, Excise Duty, and others, simplifying India's indirect taxation system.
• The introduction of Article 246A aimed to promote a unified market, enhance ease of doing business, and eliminate the cascading effects of taxes.

Additional Information

• Property Rights (Option 1):
• Property rights in India are addressed under Article 300A of the Indian Constitution, which states that no person shall be deprived of their property except by the authority of law.
• Initially, property rights were a fundamental right under Article 31, but it was abolished by the 44th Constitutional Amendment Act, 1978, and made a legal right under Article 300A.
• This provision ensures that private property cannot be taken away without due process of law or proper compensation.
• Emergency Provisions (Option 3):
• Emergency provisions are detailed under Part XVIII (Articles 352 to 360) of the Indian Constitution.
• These provisions enable the government to assume greater control during times of crisis and include three types of emergencies: National Emergency (Article 352), State Emergency/President’s Rule (Article 356), and Financial Emergency (Article 360).
• These provisions are invoked to safeguard the sovereignty, unity, and integrity of India during extraordinary situations.
• Criminal Law (Option 4):
• Criminal law in India is primarily governed by the Indian Penal Code (IPC), 1860, the Code of Criminal Procedure (CrPC), 1973, and various special laws.
• The Parliament and state legislatures can legislate on criminal law under the Concurrent List (List III) of the Seventh Schedule to the Constitution.
• Criminal law ensures the maintenance of public order, punishment for offenses, and the protection of citizens’ rights.

The correct answer is Sarsai Nawar Wetland, Uttar Pradesh.

Key Points

• Sarsai Nawar Wetland, located in Uttar Pradesh, is one of the wetlands recognized under the Ramsar Convention as a Ramsar Site.
• This wetland is renowned for hosting the largest population of Sarus Cranes in India, which are also the world's tallest flying birds.
• The Sarsai Nawar Wetland was designated as a Ramsar Site in 2019 for its ecological importance and contribution to biodiversity conservation.
• It serves as an important habitat for various bird species, including migratory birds, and plays a critical role in maintaining the ecological balance of the region.
• The wetland is also crucial for the local community, providing livelihood opportunities such as fishing and agriculture.

Additional Information

• Keoladeo National Park, Rajasthan:
• Keoladeo National Park, also known as Bharatpur Bird Sanctuary, is a UNESCO World Heritage Site and a Ramsar Site.
• It is a man-made wetland and is one of the richest bird areas in the world, serving as a wintering ground for thousands of migratory birds, including the endangered Siberian crane.
• The park is known for its role in providing ecological support and is an important site for avian biodiversity.
• Nalsarovar Bird Sanctuary, Gujarat:
• Nalsarovar Bird Sanctuary, located in Gujarat, is one of the largest wetlands in India and is a Ramsar Site.
• The sanctuary is home to a variety of migratory and resident bird species, including flamingos, pelicans, and herons.
• It also serves as an important stopover for migratory birds traveling along the Central Asian Flyway.
• Harike Wetland, Punjab:
• Harike Wetland, situated at the confluence of the Beas and Sutlej rivers, is the largest wetland in northern India and is designated as a Ramsar Site.
• The wetland supports a diverse range of flora and fauna, including several threatened and endangered species.
• It is an important ecological zone and acts as a critical habitat for migratory birds and aquatic species.
• Ramsar Convention:
• The Ramsar Convention is an international treaty signed in 1971 in Ramsar, Iran, aimed at the conservation and sustainable use of wetlands.
• It recognizes wetlands as ecosystems that are critical for biodiversity conservation and for the wellbeing of human communities.
• As of October 2023, there are over 2,500 Ramsar Sites worldwide, including more than 75 in India.

The correct answer is 21%.

Key Points

• The Earth's atmosphere contains approximately 21% oxygen, which is essential for the survival of most living organisms.
• Oxygen is the second most abundant gas in the atmosphere, after nitrogen, which makes up around 78% of the atmosphere.
• The high concentration of oxygen is maintained by processes like photosynthesis, where plants release oxygen as a byproduct.
• This oxygen concentration has remained relatively stable over millions of years, supporting life on Earth.
• Oxygen plays a critical role in cellular respiration, which is the process by which living organisms generate energy.

Additional Information

• Atmospheric Composition:
• The Earth's atmosphere is composed of approximately 78% nitrogen, 21% oxygen, 0.93% argon, and 0.04% carbon dioxide, along with trace amounts of other gases.
• These gases are essential for maintaining the Earth's climate, supporting life, and enabling processes like photosynthesis and respiration.

The correct answer is Both 1 and 2.

Key Points

• Statement 1: Supreme Court can transfer cases from one High Court to another – Article 139A of the Indian Constitution empowers the Supreme Court to transfer cases involving the same or substantially the same question of law from one High Court to another to ensure uniformity in decisions.
• This provision is aimed at eliminating conflicting judgments by different High Courts on the same legal matter, thereby ensuring consistency in the interpretation of laws across the country.
• Statement 2: Article 139A was introduced by the 42nd Amendment – The 42nd Amendment Act of 1976 added Article 139A to the Indian Constitution. This amendment is often referred to as the "mini-Constitution" due to the extensive changes it introduced.
• Article 139A allows the Supreme Court to withdraw cases from one or more High Courts if it feels that these cases involve a substantial question of law of general importance.
• Both statements are correct, as Article 139A was indeed introduced by the 42nd Amendment, and it authorizes the Supreme Court to transfer cases between High Courts.

Additional Information

• 42nd Amendment of 1976:
• Known as the "mini-Constitution," this amendment brought significant changes to the Indian Constitution.
• It added several articles, including Article 139A, and amended many existing provisions to strengthen the central government's powers.
• Key changes included the addition of the Fundamental Duties (Article 51A) and the insertion of the words "Socialist," "Secular," and "Integrity" into the Preamble.
• Supreme Court’s Powers under Article 139A:
• The Supreme Court has the authority to transfer cases between High Courts or withdraw cases from High Courts to itself if substantial questions of law are involved.
• This provision ensures uniformity in the interpretation of laws across different jurisdictions in India.
• Judicial Transfers under Article 139A:
• This article is critical for maintaining judicial discipline and consistency in legal interpretations by higher judiciary bodies.
• Such transfers are often considered in cases involving constitutional interpretation or significant questions of national importance.
• Role of High Courts:
• High Courts are the principal civil courts of original jurisdiction in India, but their decisions may differ based on regional contexts.
• Article 139A ensures that conflicting decisions on similar issues are avoided by centralizing the matter in the Supreme Court.

Shortcut Trick

Convert the fractions into decimals for faster and easier multiplication.

⇒ 2 ²/₅ = 2.4

⇒ ³/₄ = 0.75

⇒ Product = 1.2 × 2.4 × 0.75

⇒ Rearranging for ease: (1.2 × 0.75) × 2.4 = 0.9 × 2.4 = 2.16

∴ The correct answer is 2.16.

Alternate Method

Given:

Expression: 1.2 × 2 ²/₅ × ³/₄

Calculation:

⇒ Convert 1.2 to a decimal fraction: 1.2 = ¹²/₁₀ = ⁶/₅

⇒ Convert the mixed fraction into an improper fraction: 2 ²/₅ = (2 × 5 + 2) / 5 = ¹²/₅

⇒ Substitute these back into the expression:

⇒ ⁶/₅ × ¹²/₅ × ³/₄

⇒ Divide 12 by 4 to simplify:

⇒ (6 × 3 × 3) / (5 × 5)

⇒ ⁵⁴/₂₅

⇒ Multiply the numerator and denominator by 4 to get a base of 100 for immediate decimal conversion:

⇒ (54 × 4) / (25 × 4) = ²¹⁶/₁₀₀

⇒ 2.16

∴ The correct answer is 2.16.

Additional Information

Fraction to Decimal Conversion

Memorising standard fractions significantly speeds up calculation in exams: ¹/₄ = 0.25, ³/₄ = 0.75, ¹/₅ = 0.2, and ²/₅ = 0.4.

Simplification Trick for Base 100

When dividing any number by 25, simply multiply the numerator by 4 and place the decimal two spots from the right (effectively dividing by 100).

Mixed Fractions Rule

A mixed fraction represented as a(^b/_c) is converted into an improper fraction using the mathematical rule: (a × c + b) ÷ c.

Shortcut Trick

Observe the relationship between the numerator and the denominator.

Each term in the denominator is exactly 3 times the corresponding term in the numerator.

Expression = (0.1³ + 0.03³) ÷ [(3 × 0.1)³ + (3 × 0.03)³]

⇒ 1 ÷ 3³ = 1 ÷ 27

⇒ 1 ÷ 27 ≈ 0.037

∴ The correct answer is 0.037.

Alternate Method

Given:

Expression = (0.1 × 0.1 × 0.1 + 0.03 × 0.03 × 0.03) ÷ (0.3 × 0.3 × 0.3 + 0.09 × 0.09 × 0.09)

Formula Used:

(x × y)ⁿ = xⁿ × yⁿ

Calculations:

⇒ Numerator = 0.1³ + 0.03³

⇒ Denominator = 0.3³ + 0.09³

⇒ Denominator = (3 × 0.1)³ + (3 × 0.03)³

⇒ Denominator = 3³ × 0.1³ + 3³ × 0.03³

⇒ Denominator = 27 × (0.1³ + 0.03³)

⇒ Expression = (0.1³ + 0.03³) ÷ [27 × (0.1³ + 0.03³)]

⇒ Expression = 1 ÷ 27

⇒ 1 ÷ 27 = 0.037037...

∴ The correct answer is 0.037.

Additional Information

Laws of Exponents

When terms are multiplied and raised to a common power, the power distributes directly to both numbers: (xy)ⁿ = xⁿ × yⁿ. This allows easy extraction of common multiples from complex decimals.

Algebraic Simplification

In simplification problems involving decimals that look similar, always check if the denominator is a direct multiple of the numerator before calculating the actual cubes or squares.

Recurring Decimals

Fractions like 1 ÷ 27 result in non-terminating, repeating decimals. The value 1 ÷ 27 equals 0.037037037..., which is generally rounded off to 0.037 as given in the exam options.

Shortcut Trick Heights strictly less than 1.65 m are 1.55 m, 1.60 m, and 1.62 m. Students in Section A = 5 + 9 + 11 = 25 Students in Section B = 4 + 8 + 13 = 25 Required Ratio = 25 : 25 = 1 : 1 ∴ The correct answer is 1:1.

Alternate Method Given: A table containing the heights of students in two sections, A and B. We need the ratio of students with heights less than 1.65 metres in Section A to Section B. Calculations: ⇒ From the table, heights less than 1.65 m correspond to 1.55 m, 1.60 m, and 1.62 m. ⇒ Total number of students in Section A with height < 1.65 m = 5 + 9 + 11 ⇒ Total number of students in Section A = 25 ⇒ Total number of students in Section B with height < 1.65 m = 4 + 8 + 13 ⇒ Total number of students in Section B = 25 ⇒ Required Ratio = (Total students in Section A) : (Total students in Section B) ⇒ Required Ratio = 25 : 25 ⇒ Required Ratio = 1 : 1 ∴ The correct answer is 1:1.

Additional Information Ratio Comparison A ratio compares two quantities of the same kind. It is typically expressed in its simplest form by dividing both components by their highest common factor. Tabular Data Interpretation When verifying conditions such as 'less than a value', you only aggregate the frequencies of the categories strictly falling under that boundary condition.

Shortcut Trick

Profit Ratio = Ratio of (Capital × Time)

Since the time is the same (1 year), Profit Ratio = Capital Ratio

A : B : C = 40,000 : 60,000 : 80,000 = 2 : 3 : 4

B's share = [3 ÷ (2 + 3 + 4)] × 55,000 = (3 ÷ 9) × 55,000

B's share = 55,000 ÷ 3 = 18,333.33

∴ The correct answer is ₹18,333.33.

Alternate Method

Given:

A's investment = ₹40,000

B's investment = ₹60,000

C's investment = ₹80,000

Total time for each = 1 year

Total profit = ₹55,000

Formula Used:

Profit Ratio = (Investment of A × Time) : (Investment of B × Time) : (Investment of C × Time)

Share of a partner = (Partner's ratio part ÷ Total ratio parts) × Total Profit

₹40k A

₹60k B

₹80k C

Profit Ratio = 2 : 3 : 4

Calculations:

⇒ Ratio of profits of A, B, and C = 40000 : 60000 : 80000

⇒ Ratio of profits = 4 : 6 : 8

⇒ Simplifying the ratio further, we get A : B : C = 2 : 3 : 4

⇒ Sum of ratio parts = 2 + 3 + 4 = 9 parts

⇒ B's share in profit = (3 parts ÷ 9 parts) × Total Profit

⇒ B's share = (1 ÷ 3) × 55,000

⇒ B's share = 55,000 ÷ 3 = 18,333.33

∴ The correct answer is ₹18,333.33.

Additional Information

Simple Partnership

When all partners invest their capital for the same time period, the profits or losses are distributed exactly in the ratio of their original investments.

Compound Partnership

When partners invest their capital for different time periods, the profit sharing ratio is determined by multiplying each partner's capital by their respective time period (C₁T₁ : C₂T₂).

Sleeping Partner

A partner who only invests capital but does not actively participate in the management of the business. They still receive a share of the profit proportional to their investment unless explicitly stated otherwise.

Shortcut Trick

Total Capital = 60,000 + 90,000 = 1,50,000

Total Interest = 10% of 1,50,000 = 15,000

Remaining Profit = 25,000 − 15,000 = 10,000

Profit Ratio = 60,000 : 90,000 = 2 : 3

A's Total Share = (10% of 60,000) + (2/5 × 10,000) = 6,000 + 4,000 = 10,000

∴ The correct answer is ₹10,000.

Alternate Method

₹60,000 Ratio: 2 A

₹90,000 Ratio: 3 B

Given:

A's investment = ₹60,000

B's investment = ₹90,000

Total profit including interest = ₹25,000

Rate of interest on capital = 10% per annum

Formula Used:

Total Interest = Interest on A's capital + Interest on B's capital

Profit Ratio = (A's Investment × Time) : (B's Investment × Time)

Calculation:

⇒ Total investment = 60,000 + 90,000 = ₹1,50,000

⇒ Total interest to be paid = 10% of 1,50,000 = ₹15,000

⇒ Remaining profit = 25,000 − 15,000 = ₹10,000

⇒ Ratio of investments A:B = 60,000 : 90,000 = 2 : 3

⇒ A's share in remaining profit = (2 ÷ 5) × 10,000 = ₹4,000

⇒ A's interest amount = 10% of 60,000 = ₹6,000

⇒ A's total share = A's interest + A's share in profit

⇒ A's total share = 6,000 + 4,000 = ₹10,000

∴ The correct answer is ₹10,000.

Additional Information

Partnership Profit Division

Profits in a partnership are divided in the ratio of the product of capital invested and the time period of investment. Ratio = (C₁ × T₁) : (C₂ × T₂).

Active vs Sleeping Partner

An active partner manages the business and usually receives a fixed salary or commission from the profit before the remaining profit is distributed. A sleeping partner only invests capital.

Interest on Capital in Partnership

If the partnership deed specifies interest on capital, it is paid out of the total profit first. The leftover profit is then distributed in the standard capital ratio.

Shortcut Trick Since the number of months is the same (3) for all products, the product with the highest total sales will have the highest average. By simple observation of the table values: Sales of Product C (150, 160, 155) are strictly greater than those of Product A (100, 120, 110) and Product B (90, 85, 95) in every month. Thus, Product C clearly has the maximum sum and therefore the highest average without needing full calculations. ∴ The correct answer is Product C.

Alternate Method Given: Sales of Product A for Jan, Feb, Mar are 100, 120, and 110 respectively. Sales of Product B for Jan, Feb, Mar are 90, 85, and 95 respectively. Sales of Product C for Jan, Feb, Mar are 150, 160, and 155 respectively. Formula Used: Average = Total sum of values ÷ Number of values Calculations: ⇒ Average units sold for Product A = (100 + 120 + 110) ÷ 3 ⇒ Average for Product A = 330 ÷ 3 = 110 ⇒ Average units sold for Product B = (90 + 85 + 95) ÷ 3 ⇒ Average for Product B = 270 ÷ 3 = 90 ⇒ Average units sold for Product C = (150 + 160 + 155) ÷ 3 ⇒ Average for Product C = 465 ÷ 3 = 155 ⇒ Comparing the averages: 155 > 110 > 90 Product C clearly has the highest average. ∴ The correct answer is Product C.

Additional Information

1. Average and Sum Relationship For datasets with the same number of elements, the dataset with the largest sum will always have the largest arithmetic mean. This saves valuable calculation time in exams.
2. Data Comparison by Observation In data interpretation problems, if every element of Set X is greater than the corresponding elements of Sets Y and Z, no calculation is required to deduce that Set X has the highest sum and average.
3. Percentage Change A concept often requested along with averages in tabular data is percentage growth: % Change = ((New Value − Old Value) ÷ Old Value) × 100.

Shortcut Trick

Summing the three given results evaluates to 2 times the sum of the three numbers.

⇒ 2 × (Sum of three numbers) = 180 + 168 + 150 = 498

⇒ Sum of three numbers = 498 ÷ 2 = 249

⇒ Average of three numbers = 249 ÷ 3 = 83

∴ The correct answer is 83.

Alternate Method

Given:

Three numbers where the average of any two added to the third gives 180, 168, and 150 respectively.

Formula Used:

Average = Sum of all observations ÷ Total number of observations

a + b + 2c = 360

2a + b + c = 336

a + 2b + c = 300

4(a + b + c) = 996

Average = 83

Calculations:

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

⇒ (a + b) ÷ 2 + c = 180

⇒ a + b + 2c = 360     ... (Equation 1)

⇒ (b + c) ÷ 2 + a = 168

⇒ 2a + b + c = 336     ... (Equation 2)

⇒ (c + a) ÷ 2 + b = 150

⇒ a + 2b + c = 300     ... (Equation 3)

Adding Equation 1, Equation 2, and Equation 3 together:

⇒ 4a + 4b + 4c = 360 + 336 + 300

⇒ 4(a + b + c) = 996

⇒ a + b + c = 249

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

⇒ Average = (a + b + c) ÷ 3

⇒ Average = 249 ÷ 3 = 83

∴ The correct answer is 83.

Additional Information

Properties of Average

If a constant value is added, subtracted, multiplied, or divided by each observation in a dataset, the new average also changes exactly by the same arithmetic operation and constant.

Weighted Average

If quantities are divided into multiple groups with respective averages, the combined group average is evaluated as (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Average of Arithmetic Progression

For any sequence of numbers operating with a common difference, the average is strictly derived as (First Term + Last Term) ÷ 2, which also represents the exact middle term.

Shortcut Trick

Total items for students = 100 × (15% of 100) = 100 × 15 = 1500

Total items for chaperones = 10 × (25% of 100) = 10 × 25 = 250

Total items distributed = 1500 + 250 = 1750

∴ The correct answer is 1750 items.

Alternate Method

Given:

Total number of students = 100

Total number of chaperones = 10

Items per student's snack pack = 15% of total students

Items per chaperone's snack pack = 25% of total students

Formula Used:

Value = (Percentage ÷ 100) × Base Value

Students Count = 100 Items/pack = 15% of 100 = 15 Total = 100 × 15 = 1500

Chaperones Count = 10 Items/pack = 25% of 100 = 25 Total = 10 × 25 = 250

Total Snack Items = 1500 + 250 = 1750

Calculations:

⇒ Items in each student's pack = 15% of 100 = (15 ÷ 100) × 100 = 15 items

⇒ Total items given to 100 students = 100 × 15 = 1500 items

⇒ Items in each chaperone's pack = 25% of 100 = (25 ÷ 100) × 100 = 25 items

⇒ Total items given to 10 chaperones = 10 × 25 = 250 items

⇒ Total items distributed = Total student items + Total chaperone items

⇒ Total items distributed = 1500 + 250 = 1750

∴ The correct answer is 1750 items.

Additional Information

Percentage Calculation Rule

Percentage is fundamentally a fraction based on 100. To find x% of a quantity Y, the formula is (x ÷ 100) × Y. Always identify the correct base from the question text carefully before calculating.

Successive Distribution

When distinct items are given to multiple groups, compute the quantities for each group individually according to their independent rules, and then sum up the results.

Common Percentage Ratios

Memorizing basic percentage-to-fraction conversions helps solve equations faster in exams: 25% = 1/4, 20% = 1/5, 15% = 3/20, and 10% = 1/10.

Shortcut Trick

Effective CI rate for 2 years at 10% = 10 + 10 + (10 × 10)/100 = 21%

For the next 6 months (half-year), the rate becomes = 10% ÷ 2 = 5%

Net effective rate for 2.5 years = 21 + 5 + (21 × 5)/100 = 26 + 1.05 = 27.05%

Compound Interest = 27.05% of 10000 = 2705

∴ The correct answer is ₹2,705.

Alternate Method

Given:

Principal (P) = ₹10,000

Rate (R) = 10% per annum

Time (T) = 2 years 6 months = 2.5 years

Formula Used:

Amount (A) = P × [1 + R/100]ⁿ × [1 + (R × fraction of year)/100]

Compound Interest (CI) = A − P

Start ₹10k

Year 1 ₹11k

Year 2 ₹12.1k

Year 2.5 ₹12705

+10% (₹1000)

+10% (₹1100)

+5% (₹605)

Total CI = 1000 + 1100 + 605 = 2705

Calculations:

⇒ Full years (n) = 2, Fraction of year = 6/12 = 1/2 year

⇒ A = 10000 × [1 + 10/100]² × [1 + (10 × 1/2)/100]

⇒ A = 10000 × (11/10) × (11/10) × (105/100)

⇒ A = 10000 × (121/100) × (21/20)

⇒ A = 100 × 121 × (21/20)

⇒ A = 5 × 121 × 21

⇒ A = 121 × 105 = 12705

⇒ CI = 12705 − 10000 = 2705

∴ The correct answer is ₹2,705.

Additional Information

Effective Rate Method

For 2 years, the effective compound interest rate is calculated directly as A + B + (A × B)/100.

Half-Yearly Compounding

When interest is compounded half-yearly, the applied rate is halved (R/2) and the time periods are doubled (2T).

SI vs CI Difference

The exact difference between Compound Interest and Simple Interest for a 2-year period is given by the formula P(R/100)².

Shortcut Trick

Fraction value of 12% = 3/25 ⇒ Multiplying factor = 28/25.

For 2 years, Amount / Principal = (28/25)² = 784/625.

Given Amount = 784 parts = ₹3136 ⇒ 1 part = 4.

Principal = 625 parts = 625 × 4 = ₹2500.

140% of Principal = 1.4 × 2500 = ₹3500.

∴ The correct answer is ₹3500.

Alternate Method

Given:

Rate (R) = 12% per annum

Time (T) = 2 years

Amount (A) = ₹3136

Formula Used:

A = P(1 + R/100)^T

P = ? Year 1 ₹3136

+12% CI +12% CI

Equivalent to 25.44% Total Interest (Multiplier: 1.2544)

Calculation:

⇒ 3136 = P(1 + 12/100)²

⇒ 3136 = P(112/100)²

⇒ 3136 = P(28/25)²

⇒ 3136 = P × (784/625)

⇒ P = (3136 × 625) ÷ 784

⇒ P = 4 × 625

⇒ P = ₹2500

⇒ Required value = 140% of P

⇒ Required value = (140 ÷ 100) × 2500

⇒ Required value = 1.4 × 2500 = 3500

∴ The correct answer is ₹3500.

Additional Information

Effective Rate of Compound Interest

For 2 years at R%, the effective CI rate is given by R + R + (R × R)/100. For 12%, it is 12 + 12 + 1.44 = 25.44%.

Difference between CI and SI for 2 years

The difference between compound interest and simple interest for 2 years is calculated using the formula: Difference = P(R/100)².

Half-Yearly Compounding

When interest is compounded half-yearly, the rate is halved (R ÷ 2) and the time periods are doubled (2T).

Shortcut Trick

CP of first pulse = 72 × 100/120 = ₹60/kg

CP of second pulse = 60 × 100/125 = ₹48/kg

Net CP of mixture = (60 × 2 + 48 × 1) ÷ 3 = 168/3 = ₹56/kg

Overall Profit % = ((70 − 56) ÷ 56) × 100 = (14/56) × 100 = 25%

∴ The correct answer is Profit of 25%.

Alternate Method

Given:

⇒ SP of first variety = ₹72/kg, Profit = 20%

⇒ SP of second variety = ₹60/kg, Profit = 25%

⇒ Ratio of mixture (first : second) = 2 : 1

⇒ SP of mixture = ₹70/kg

Formula Used:

⇒ Cost Price (CP) = SP × 100 / (100 + Profit%)

⇒ Profit % = [(SP − CP) / CP] × 100

Type 1: 2 kg CP = ₹60/kg

Type 2: 1 kg CP = ₹48/kg

Mix CP: 3 kg Avg = ₹56/kg

Mix SP ₹70/kg

Profit = ₹14/kg (+25%)

Calculations:

⇒ Let the quantities of the two varieties be 2 kg and 1 kg respectively.

⇒ CP of 1st variety = 72 × 100 / (100 + 20) = 7200 / 120 = ₹60 per kg

⇒ Total CP for 2 kg of 1st variety = 60 × 2 = ₹120

⇒ CP of 2nd variety = 60 × 100 / (100 + 25) = 6000 / 125 = ₹48 per kg

⇒ Total CP for 1 kg of 2nd variety = 48 × 1 = ₹48

⇒ Total CP of 3 kg mixture = 120 + 48 = ₹168

⇒ Average CP of mixture = 168 ÷ 3 = ₹56 per kg

⇒ The SP of the mixture is given as ₹70 per kg

⇒ Overall Profit = SP − CP = 70 − 56 = ₹14 per kg

⇒ Profit Percentage = (Profit / CP) × 100 = (14 / 56) × 100 = (1 / 4) × 100 = 25%

∴ The correct answer is Profit of 25%.

Additional Information

Cost Price (CP)

The base price at which goods are purchased. It is the reference value for calculating profit or loss percentages. Formula: CP = SP × 100 / (100 + Profit%).

Mixtures & Alligation

A mathematical rule used to find the weighted average price of a mixture when two components with different prices are mixed in a specific ratio.

Profit & Loss Percentage

Profit and loss are always calculated over the overall Cost Price unless explicitly stated otherwise. Profit% = [(SP − CP) / CP] × 100.

Shortcut Trick

Let SP of dresses D₁, D₂, and D₃ be 5, 6, and 7 units respectively. (Total SP = 18)

Since profit is 20%, loss is 10%, and profit is 30% respectively, their multipliers are 1.2, 0.9, and 1.3.

Total CP = 5/1.2 + 6/0.9 + 7/1.3 = 25/6 + 20/3 + 70/13 = 65/6 + 70/13 = 1265/78

Total Profit = Total SP − Total CP = 18 − 1265/78 = 139/78

Profit % = (Total Profit ÷ Total CP) × 100 = (139/78 ÷ 1265/78) × 100 = 13900/1265 ≈ 10.98%

∴ The correct answer is profit of 10.98%.

Alternate Method

Given:

Selling Price (SP) ratio of D₁ : D₂ : D₃ = 5 : 6 : 7

Profit on D₁ = 20%, Loss on D₂ = 10%, Profit on D₃ = 30%

Formula Used:

Cost Price (CP) = [SP ÷ (100 ± Profit/Loss %)] × 100

Overall Profit % = [(Total SP − Total CP) ÷ Total CP] × 100

Calculations:

Let the Selling Prices of the three dresses be 500, 600, and 700 units respectively.

⇒ Total SP = 500 + 600 + 700 = 1800 units

Calculating the Cost Price of each dress:

⇒ CP of D₁ = (500 ÷ 120) × 100 = 5000/12 = 1250/3 units

⇒ CP of D₂ = (600 ÷ 90) × 100 = 6000/9 = 2000/3 units

⇒ CP of D₃ = (700 ÷ 130) × 100 = 7000/13 units

⇒ Total CP = 1250/3 + 2000/3 + 7000/13

⇒ Total CP = 3250/3 + 7000/13 = (42250 + 21000) ÷ 39 = 63250/39 units

Now, finding the overall profit margin:

⇒ Total SP = 1800 = 70200/39 units

⇒ Total Profit = Total SP − Total CP = (70200 − 63250) ÷ 39 = 6950/39 units

⇒ Profit % = [(6950/39) ÷ (63250/39)] × 100

⇒ Profit % = (6950 ÷ 63250) × 100

⇒ Profit % = (695 ÷ 6325) × 100 = (139 ÷ 1265) × 100 ≈ 10.988%

∴ The correct answer is profit of 10.98%.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount. The ratio SP / MP gives the multiplying factor for the exact discount applied.

Successive Percentage Changes

When applying successive profit, loss, or discounts, the net percentage change is evaluated by: A + B + (AB / 100)%, where profit is treated as positive and loss/discount as negative.

Dishonest Dealer Concept

When a dealer uses false weights, the actual cost is strictly based on the weight given, while the selling price is based on the claimed weight. Profit % = (Error ÷ True Value − Error) × 100.

Shortcut Trick

In successive chain transactions, the equivalent multiplying factor method is the fastest.

Net multiplying factor = 1.60 (wholesaler markup) × 0.85 (wholesaler discount) × 1.25 (retailer markup) × 0.90 (retailer discount)

Net factor = 1.60 × 0.85 × 1.25 × 0.90 = 1.53

14490 = Original CP × 1.53 ⇒ CP = 14490 ÷ 1.53 ≈ 9470.588

∴ The correct answer is ₹9,471.

Alternate Method

Wholesaler CP = 100x

Wholesaler MP = 160x

Retailer CP = 136x

Retailer MP = 170x

Final SP = 153x

+60% −15% +25% −10%

Final SP = 153x = ₹14,490

Given:

Final Selling Price (paid by customer) = ₹14,490

Let the original cost price of the microwave to the wholesaler be 100x.

Calculations:

⇒ Wholesaler's Marked Price (MP) = 100x + 60% of 100x = 160x

⇒ Trade discount given by wholesaler = 15% of 160x = 24x

⇒ Retailer's Cost Price (CP) = 160x − 24x = 136x

⇒ Retailer's Marked Price (MP) = 136x + 25% of 136x = 136x + 34x = 170x

⇒ Festival discount given by retailer = 10% of 170x = 17x

⇒ Final Selling Price (SP) = 170x − 17x = 153x

⇒ According to the given data, Final SP = 14490

⇒ 153x = 14490

⇒ x = 14490 ÷ 153 ≈ 94.7058

⇒ Wholesaler's Cost Price = 100x = 100 × 94.7058 = 9470.58

⇒ Approximate original cost price = ₹9,471

∴ The correct answer is ₹9,471.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price (MP). The formula used is: SP = MP × (1 − Discount / 100).

Markup Percentage

Markup is always calculated on the Cost Price (CP) before any discount is offered. The formula used is: MP = CP × (1 + Markup / 100).

Successive Transactions

When an article passes through multiple hands where percentage increases or decreases occur consecutively, the Final Value = Initial Value × (1 ± r₁/100) × (1 ± r₂/100) × ...

Shortcut Trick

Since only alcohol is added, the total quantity of water remains constant throughout the process.

Initial Water % × Initial Volume = Final Water % × Final Volume

20% × 60 = 15% × Final Volume

Final Volume = (20 × 60) ÷ 15 = 1200 ÷ 15 = 80 litres

Amount of alcohol added = Final Volume − Initial Volume = 80 − 60 = 20 litres.

∴ The correct answer is 20 litres.

Alternate Method

Given:

Initial volume of solution = 60 litres

Percentage of water initially = 20%

Target percentage of water finally = 15%

Formula Used:

We can solve this using the rule of Alligation on the alcohol percentage.

Initial alcohol % = 100% − 20% = 80%

Pure alcohol added % = 100%

Final mixture alcohol % = 100% − 15% = 85%

80% Initial 60 Litres

100% Added x Litres

85% Mixture

15

5

Ratio = 15 : 5 = 3 : 1

Calculations:

From the Alligation diagram, the ratio of the initial volume to the pure added alcohol is:

⇒ Initial Volume : Added Alcohol = 15 : 5

⇒ Initial Volume : Added Alcohol = 3 : 1

⇒ 3 ratio units = 60 litres

⇒ 1 ratio unit = 60 ÷ 3 = 20 litres

⇒ Added alcohol = 20 litres

∴ The correct answer is 20 litres.

Additional Information

Constant Component Principle

When one ingredient is added or removed from a mixture, the total quantity of the other ingredient remains constant. Equating the amount of the constant element (like water in this problem) gives a direct one-step equation.

Rule of Alligation

Used to find the ratio in which two mixtures or ingredients of given concentrations must be mixed to produce a mixture of a desired concentration. The cross-difference of concentrations directly provides the ratio of quantities.

Pure Substance Concentration

When applying alligation, pure substances like pure alcohol or pure milk are always taken as 100% concentration for that element, while pure water is taken as 0% of that active ingredient.

Shortcut Trick

Total Work = LCM(8, 12) = 24 units.

Efficiency of A = 24 ÷ 8 = 3 units/day, and Efficiency of B = 24 ÷ 12 = 2 units/day.

Combined efficiency = 3 + 2 = 5 units/day.

Work done in 3 days = 5 × 3 = 15 units.

Remaining work = 24 − 15 = 9 units, which is 9 ÷ 24 = 3/8 of the total work.

∴ The correct answer is 3/8.

Alternate Method

Given:

Time taken by A = 8 days

Time taken by B = 12 days

Time they worked together = 3 days

Formula / Method Used:

LCM Method: Total Work = LCM of given days, Efficiency = Total Work ÷ Days

Calculations:

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

⇒ Work done by A and B together in 3 days = 5 × 3 = 15 units

⇒ Remaining work = Total Work − Work Done

⇒ Remaining work = 24 − 15 = 9 units

⇒ Part of the work left = Remaining Work ÷ Total Work

⇒ Part of the work left = 9 ÷ 24 = 3/8

∴ The correct answer is 3/8.

Additional Information

Pipes & Cisterns

This topic follows the same logic as Time & Work. The only difference is that an emptying pipe has a negative efficiency. Net work in 1 hour for a filling pipe (x hours) and emptying pipe (y hours) = (1 ÷ x) − (1 ÷ y).

Work & Wages

Total wages are always distributed in proportion to the total work completed by each individual. If workers operate for the same number of days, their wages are directly proportional to their efficiencies.

Alternate Days Work

When individuals work consecutively on alternate days, group their efforts by calculating the combined work done in one complete cycle (e.g., 2 days) to easily track total completion time.

Shortcut Trick

Mean CP of the mixture = 75 ÷ 1.1 = 750/11 ₹/kg.

Applying alligation on CP: (80 − 750/11) : (750/11 − 65)

Ratio of Type 1 to Type 2 = 130/11 : 35/11 = 26 : 7

Given 26 parts = 40 kg ⇒ 1 part = 40 ÷ 26 = 20/13 kg.

Quantity of Type 2 = 7 parts = 7 × (20/13) = 140/13 ≈ 10.77 kg.

∴ The correct answer is 10.77 kg.

Alternate Method

Given:

Quantity of Type 1 lentils (Q₁) = 40 kg, Cost Price (CP₁) = ₹65/kg

Cost Price of Type 2 lentils (CP₂) = ₹80/kg

Selling Price of mixture (SP) = ₹75/kg, Profit = 10%

Formula Used:

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

Calculations:

⇒ Mean CP of the mixture = (75 × 100) ÷ 110 = 750/11 ₹/kg

⇒ Let the quantity of Type 2 lentils be x kg.

⇒ Total Cost Price = (65 × 40) + (80 × x) = 2600 + 80x

⇒ Total Selling Price = 75 × (40 + x) = 3000 + 75x

⇒ We know, SP = CP × 1.1 (for 10% profit)

⇒ 3000 + 75x = 1.1 × (2600 + 80x)

⇒ 3000 + 75x = 2860 + 88x

⇒ 88x − 75x = 3000 − 2860

⇒ 13x = 140

⇒ x = 140 ÷ 13 ≈ 10.77 kg

∴ The correct answer is 10.77 kg.

Additional Information

Alligation Rule

When two ingredients are mixed, their ratio is given by: (Quantity of Cheaper) / (Quantity of Dearer) = (Price of Dearer − Mean Price) / (Mean Price − Price of Cheaper).

Mean Price (Cost Price)

Alligation must always be applied on the Cost Price (CP) of the mixture. If the Selling Price (SP) and Profit/Loss percentages are given, first find the CP using: CP = (SP × 100) / (100 + Profit%).

Direct Algebraic Method

Alternatively, mixture problems can be solved directly using the total cost balance equation: Q₁ × CP₁ + Q₂ × CP₂ = (Q₁ + Q₂) × Mean CP.

Shortcut Trick

Total Work = LCM(12, 16) = 48 units. Efficiency: (A + B) = 4, (B + C) = 3.

Given: A works 5 days, B works 7 days, C works 13 days = Total Work.

Rewrite as: 5(A + B) + 2(B + C) + 11C = 48 units.

⇒ 5(4) + 2(3) + 11C = 48 ⇒ 26 + 11C = 48 ⇒ C = 2 units/day.

Time taken by C alone = Total Work ÷ Efficiency = 48 ÷ 2 = 24 days.

∴ The correct answer is 24 days.

Alternate Method

Given:

Time taken by (A + B) to complete the work = 12 days

Time taken by (B + C) to complete the work = 16 days

A works for 5 days, B works for 7 days, and C works for 13 days to complete the task.

Calculations:

Let the total work be 48 units (LCM of 12 and 16).

⇒ Efficiency of (A + B) = 48 ÷ 12 = 4 units/day

⇒ Efficiency of (B + C) = 48 ÷ 16 = 3 units/day

Let efficiency of A, B, and C be a, b, and c respectively.

⇒ a + b = 4

⇒ b + c = 3

According to the given condition, A works for 5 days, B for 7 days, and C for 13 days:

⇒ 5a + 7b + 13c = 48

We can group the terms to use the known combined efficiencies:

⇒ 5a + 5b + 2b + 2c + 11c = 48

⇒ 5(a + b) + 2(b + c) + 11c = 48

Substitute the values of (a + b) and (b + c):

⇒ 5 × 4 + 2 × 3 + 11c = 48

⇒ 20 + 6 + 11c = 48

⇒ 26 + 11c = 48

⇒ 11c = 48 − 26

⇒ 11c = 22

⇒ c = 2 units/day

Total time taken by C alone to complete the work = Total Work ÷ Efficiency of C

⇒ Time taken by C = 48 ÷ 2 = 24 days

∴ The correct answer is 24 days.

Additional Information

Time and Work Relation

Time taken to complete a work is inversely proportional to the efficiency. Work = Efficiency × Time.

Combined Efficiency Rule

When multiple people work together, their combined efficiency is the sum of their individual efficiencies: E_Total = E₁ + E₂ + ... + E_n.

Pipes and Cisterns

The concept is identical to Time & Work, but an emptying pipe has negative efficiency, decreasing the total work done per unit time.

MDH Formula

If M₁ men can do W₁ work in D₁ days working H₁ hours/day, then (M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂.

Shortcut Trick

When distance is constant, speed and time are inversely proportional: S₁ × T₁ = S₂ × T₂.

⇒ 20 × 4 = S₂ × 2.5

⇒ S₂ = 80 ÷ 2.5 = 32 km/h

Increase in speed = S₂ − S₁ = 32 − 20 = 12 km/h

∴ The correct answer is 12 km/h.

Alternate Method

Given:

Initial Speed (S₁) = 20 km/h

Initial Time (T₁) = 4 hours

Required Time (T₂) = 2.5 hours

Formula Used:

Distance = Speed × Time

Speed = Distance ÷ Time

City A

City B

Total Distance = 80 km

Case 1: S = 20 km/h, T = 4 hrs

Case 2: S = 32 km/h, T = 2.5 hrs

Calculations:

⇒ Total Distance = S₁ × T₁

⇒ Distance = 20 × 4 = 80 km

⇒ To cover the same distance in 2.5 hours, required New Speed (S₂) = Distance ÷ T₂

⇒ S₂ = 80 ÷ 2.5

⇒ S₂ = 32 km/h

⇒ Required increase in speed = New Speed − Initial Speed

⇒ Required increase = 32 − 20 = 12 km/h

∴ The correct answer is 12 km/h.

Additional Information

Proportionality of Speed, Time, and Distance

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

Average Speed

Average Speed = Total Distance Covered ÷ Total Time Taken. It is not always the simple average of speeds unless time intervals are equal.

Average Speed for Equal Distances

When a person travels equal distances at speeds x and y, the average speed for the whole journey is (2xy) ÷ (x + y).

Shortcut Trick

Distance covered by the first train in 2 hours (6:00 AM to 8:00 AM) = 60 × 2 = 120 km.

Remaining distance at 8:00 AM = 540 − 120 = 420 km.

Relative speed of both trains moving towards each other = 60 + 90 = 150 km/h.

Time taken to meet after 8:00 AM = 420 ÷ 150 = 2.8 hours = 2 hours 48 minutes.

Meeting time = 8:00 AM + 2 hours 48 minutes = 10:48 AM.

∴ The correct answer is 10:48 AM.

Alternate Method

Given:

Distance between Station A and Station B = 540 km

Speed of Train 1 (from Station A) = 60 km/h

Speed of Train 2 (from Station B) = 90 km/h

Formula Used:

Distance = Speed × Time

Relative Speed (Opposite Directions) = S₁ + S₂

Time = Distance ÷ Speed

A at 8:00 AM B

6:00 AM 8:00 AM

120 km

420 km

Total: 540 km

60 km/h →

← 90 km/h

2 hours

Calculations:

⇒ Train 1 starts at 6:00 AM and Train 2 starts at 8:00 AM. Hence, Train 1 travels alone for 2 hours.

⇒ Distance covered by Train 1 in 2 hours = 60 × 2 = 120 km.

⇒ Remaining distance between the two trains at 8:00 AM = 540 − 120 = 420 km.

⇒ At 8:00 AM, both trains are moving towards each other.

⇒ Relative Speed = Speed of Train 1 + Speed of Train 2

⇒ Relative Speed = 60 + 90 = 150 km/h.

⇒ Time required to meet = Remaining distance ÷ Relative speed

⇒ Time = 420 ÷ 150 = 14 ÷ 5 hours.

⇒ Converting hours into hours and minutes: (14 ÷ 5) hours = 2 hours and (4 ÷ 5) × 60 minutes.

⇒ Time taken to meet = 2 hours 48 minutes after 8:00 AM.

⇒ Meeting Time = 8:00 AM + 2 hours 48 minutes = 10:48 AM.

∴ The correct answer is 10:48 AM.

Additional Information

Relative Speed in Opposite Directions

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

Relative Speed in Same Direction

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

Average Speed

If an object covers equal consecutive distances at speeds S₁ and S₂, the average speed over the entire journey is given by (2 × S₁ × S₂) ÷ (S₁ + S₂).

Shortcut Trick

Initial radius (r) = 10 ÷ 2 = 5 m, New radius (R) = 5 + 1 = 6 m.

Percentage increase in radius = (1 ÷ 5) × 100 = 20%.

Since area is proportional to the square of the radius, apply successive percentage change: 2x + (x² ÷ 100).

Percentage increase in area = 2 × 20 + (20² ÷ 100) = 40 + 4 = 44%.

∴ The correct answer is 44%.

Alternate Method

Given:

Diameter of the circular garden = 10 m

Width of the concrete path = 1 m

Formula Used:

Area of a circle = πr²

Percentage Increase = [(New Area − Original Area) ÷ Original Area] × 100

r = 5 m

R = 6 m

1 m

Calculations:

⇒ Radius of the original garden (r) = 10 ÷ 2 = 5 m

⇒ Original Area of the garden = π × (5)² = 25π m²

⇒ New radius including the path (R) = 5 + 1 = 6 m

⇒ New Area including the path = π × (6)² = 36π m²

⇒ Increase in Area = 36π − 25π = 11π m²

⇒ Percentage Increase = (11π ÷ 25π) × 100

⇒ Percentage Increase = (11 ÷ 25) × 100 = 11 × 4 = 44%

∴ The correct answer is 44%.

Additional Information

Area of a Circular Path

The area of a uniform path of width w around a circle of inner radius r is formulated as π[(r + w)² − r²] = πw(2r + w).

Successive Percentage Change

When a parameter (like radius) increases by x%, quantities proportional to its square (like area) undergo successive increases. The net change is calculated using: (2x + x² ÷ 100)%.

Percentage Change Rule

Always calculate the percentage increase or decrease relative to the original base value using: % Change = (Absolute Difference ÷ Original Value) × 100.

Shortcut Trick

Total area of the circle = πr² = (22/7) × 14 × 14 = 616 cm².

Sector area as a fraction of the total area = 154 / 616 = 1/4.

Angle of the sector = Fraction of area × 360°.

Angle = (1/4) × 360° = 90°.

∴ The correct answer is 90°.

Alternate Method

Given:

Radius (r) = 14 cm

Area of the sector = 154 cm²

Formula Used:

Area of a sector = (θ / 360°) × πr²

O

r = 14 cm r = 14 cm

θ = ? Area = 154

Calculations:

⇒ 154 = (θ / 360°) × (22 / 7) × (14)²

⇒ 154 = (θ / 360°) × 22 × 2 × 14

⇒ 154 = (θ / 360°) × 616

⇒ θ / 360° = 154 / 616

⇒ θ / 360° = 1/4

⇒ θ = 360° / 4

⇒ θ = 90°

∴ The correct answer is 90°.

Additional Information

Length of an Arc

The length of an arc (l) of a circle can be calculated as: l = (θ / 360°) × 2πr.

Area of Sector using Arc Length

If the arc length is already known, the area of the sector can be found directly using the formula: Area = (1 / 2) × l × r.

Area of a Segment

The area of a segment of a circle is defined as: Area of the corresponding sector − Area of the corresponding triangle formed by the chord and the bounding radii.

Shortcut Trick

Total Cost = (Percentage Painted) × (Area of Circle) × Rate

⇒ Total Cost = 90% × (π × r²) × 60

⇒ Total Cost = 0.9 × 3.14 × 2² × 60

⇒ Total Cost = 0.9 × 12.56 × 60 = 678.24

⇒ Total Cost ≈ ₹678.2

∴ The correct answer is ₹678.2.

Alternate Method

90% Painted 10% r = 2 m Total Cost = Painted Area × Cost per m²

Given:

Radius of the circular signboard (r) = 2 m

Cost of painting = ₹60 per m²

Unpainted portion = 10%

Formula Used:

Area of a circle = πr²

Calculation:

⇒ Total area of the board = 3.14 × 2² = 12.56 m²

⇒ Painted portion = 100% − 10% = 90%

⇒ Area to be painted = 90% of 12.56 = 0.9 × 12.56 = 11.304 m²

⇒ Total cost of painting = Painted area × Cost per m²

⇒ Total cost = 11.304 × 60 = ₹678.24

⇒ Total cost ≈ ₹678.2

∴ The correct answer is ₹678.2.

Additional Information

Area of a Sector

A sector represents a fraction of the circle. The formula is Area = (θ ÷ 360°) × πr², where θ is the central angle.

Circumference of a Circle

The total length of the boundary of a circle is given by C = 2πr.

Percentage Application in Geometry

Instead of finding the excluded area and subtracting, directly calculate the effective percentage (e.g., 100% − 10% = 90%) and multiply it with the total area.

Shortcut Trick

For any linear equation in the standard form Ax + By = C, the y-intercept can be calculated directly by dividing the constant term by the y-coefficient.

Formula: y-intercept = C ÷ B

Here, the given equation is 4x + 5y = 20, where C = 20 and B = 5.

y-intercept = 20 ÷ 5 = 4

∴ The correct answer is 4.

Alternate Method

Given:

The linear equation of the line is 4x + 5y = 20.

Formula Used:

The y-intercept is the exact point where the graph of the line crosses the y-axis. At this specific point, the x-coordinate is always 0.

X Y O

(0, 4) y-intercept (5, 0) x-intercept

4x + 5y = 20

Calculations:

⇒ To find the y-intercept, substitute x = 0 in the given equation.

⇒ 4(0) + 5y = 20

⇒ 0 + 5y = 20

⇒ 5y = 20

⇒ y = 20 ÷ 5

⇒ y = 4

∴ The correct answer is 4.

Additional Information

Intercept Form of a Line

The equation of a straight line can be expressed as x/a + y/b = 1, where a represents the x-intercept and b represents the y-intercept.

Slope-Intercept Form

A line can be represented as y = mx + c, where m signifies the slope of the line and c represents the y-intercept.

Finding the x-intercept

The x-intercept is the exact point where the graph of the line intersects the x-axis. It is determined by setting y = 0 in the equation.

Shortcut Trick

For any given algebraic expression where x + 1/x = k, the value of x³ + 1/x³ is directly given by k³ − 3k.

Here, the given value is k = 4.

Substituting the value in the shortcut formula, we get: 4³ − 3 × 4

Value = 64 − 12 = 52

∴ The correct answer is 52.

Alternate Method

Given:

x + 1/x = 4

Formula Used:

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

⇒ Cubing both sides of the given equation, we get:

⇒ (x + 1/x)³ = 4³

⇒ x³ + 1/x³ + 3 × x × (1/x) × (x + 1/x) = 64

⇒ x³ + 1/x³ + 3 × 1 × 4 = 64

⇒ x³ + 1/x³ + 12 = 64

⇒ x³ + 1/x³ = 64 − 12

⇒ x³ + 1/x³ = 52

∴ The correct answer is 52.

Additional Information

Algebraic Identity 1

If x − 1/x = k, then the direct result is x³ − 1/x³ = k³ + 3k.

Algebraic Identity 2

If x + 1/x = k, then the square values relate as x² + 1/x² = k² − 2.

Algebraic Identity 3

If x − 1/x = k, then the square values relate as x² + 1/x² = k² + 2.

Shortcut Trick

When adding decimals with a single 1 in different place values, just position 1 in each corresponding decimal place.

0.1 has 1 in the tenths place.

0.01 has 1 in the hundredths place.

0.001 has 1 in the thousandths place.

⇒ Combining them directly gives 0.111

∴ The correct answer is 0.111.

Alternate Method

Given:

Expression: 0.1 + 0.01 + 0.001

Method Used:

Convert the given decimals into fractions with a common denominator of 1000, and then add them together.

Calculation:

⇒ 0.1 = 1 ÷ 10 = 100 ÷ 1000

⇒ 0.01 = 1 ÷ 100 = 10 ÷ 1000

⇒ 0.001 = 1 ÷ 1000

⇒ Sum = (100 ÷ 1000) + (10 ÷ 1000) + (1 ÷ 1000)

⇒ Sum = (100 + 10 + 1) ÷ 1000

⇒ Sum = 111 ÷ 1000

⇒ Sum = 0.111

∴ The correct answer is 0.111.

Additional Information

BODMAS Rule

It determines the correct sequence of operations in any mathematical expression: Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

Decimal Fractions

Fractions in which denominators are powers of 10 (like 10, 100, 1000) are known as decimal fractions. Example: 1 ÷ 10 = 0.1

Like Decimals

Decimals having the exact same number of decimal places are called like decimals. Adding trailing zeros converts unlike decimals to like decimals, making addition simpler (e.g., 0.100 + 0.010 + 0.001).

The correct answer is: Childish.

Key Points

• The word "Juvenile" refers to something related to young people, especially children or adolescents, or something immature. (नाबालिग/बालसुलभ)
• Example: The juvenile behavior of the students disrupted the class.
• "Childish" refers to behavior or actions that resemble those of a child and are often immature or silly. (बचकाना)
• Example: His childish argument showed a lack of seriousness.
• Hence, the word "Juvenile" closely relates to "Childish," making option 3 the correct answer.

Therefore, the correct answer is: Childish.

Additional Information

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

• Adult (वयस्क): Refers to a person who is fully grown or mature.
• Example: As an adult, he took full responsibility for his actions.
• Wise (बुद्धिमान): Having or showing experience, knowledge, and good judgment.
• Example: Her wise advice helped me solve the problem effectively.
• Mature (परिपक्व): Fully developed physically or mentally; showing maturity in behavior.
• Example: His mature response to the crisis impressed everyone.

The correct answer is: Option 1 i.e. To reconcile after a conflict.

Key Points

• The idiom "Bury the hatchet" means to end a dispute or conflict and restore friendly relations. (झगड़ा समाप्त करना और सुलह करना)
• Example: After years of rivalry, the two leaders decided to bury the hatchet and work together for the betterment of their people.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Option 2: To deepen hostility (शत्रुता बढ़ाना): This means to make a conflict or disagreement worse.
• Example: Her harsh words only served to deepen the hostility between the two groups.
• Option 3: To run away (भाग जाना): This means to flee or escape from a situation.
• Example: He decided to run away from his responsibilities instead of facing them.
• Option 4: To forget someone's name (किसी का नाम भूल जाना): This means being unable to recall a person's name.
• Example: I met her at the party, but I forgot her name shortly after.

The correct answer is: Establish.

Key Points

• The word "Extirpate" means to completely destroy or eradicate something, often referring to removing it from its roots. (जड़ से उखाड़ना)
• Example: Efforts were made to extirpate invasive species from the ecosystem.
• "Establish" is the opposite of extirpate as it refers to creating or setting up something permanently or firmly. (स्थापित करना)
• Example: The company plans to establish a new office in the city.
• Hence, we can infer that the antonym of "Extirpate" is "Establish".

Therefore, the correct answer is: Establish.

Additional Information

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

• Exterminate (समाप्त करना): To destroy completely, often used in the context of killing pests or enemies.
• Example: The government launched a campaign to exterminate mosquitoes carrying the disease.
• Uproot (जड़ से उखाड़ना): To pull out by the roots or completely remove something from its place.
• Example: The farmer uprooted the weeds from the field.
• Eradicate (समूल नष्ट करना): To destroy or eliminate completely.
• Example: Scientists are working to eradicate diseases from the world.

The correct answer is option 2.

Key Points

The misspelled word is 'Indispensible'.

• The correct spelling would be 'Indispensable'.
• The word 'indispensable' is an adjective which means 'absolutely necessary or essential'. (अत्यावश्यक)
• For Example -
• Good education is indispensable for a successful career.

Therefore, the correct answer would be 'Indispensable'.

Additional Information

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

• Embarrassment - a feeling of self-consciousness, shame, or awkwardness (शर्मिंदगी)
• Camouflage - the disguising of military personnel, equipment, or installations by painting or covering them to make them blend in with their surroundings (छलावरण)
• Rendezvous - a meeting at an agreed time and place, typically between two people (मिलन स्थल)

The correct answer is option 2.

Key Points

The correct spelling is 'Nitrocellulose'.

• Nitrocellulose is a compound used as an early film base and is also known as cellulose nitrate.
• It is highly flammable and was once widely used in photography and filmmaking.
• Over time, it was replaced by safer materials due to its tendency to degrade and pose fire hazards.

Therefore, the correct answer is 'Nitrocellulose'.

Additional Information

Interesting facts about Nitrocellulose:

• Nitrocellulose was initially used in the production of gunpowder and explosives before its application in film production.
• It is known for its glossy finish and is still used in some musical instrument coatings.
• The instability of nitrocellulose led to the development of safer, more durable alternatives for films.

The correct answer is: Glutton.

Key Points

• The word "Glutton" refers to a person who eats excessively or greedily. (पेटू व्यक्ति)
• Example: He is such a glutton that he finished the entire pizza by himself in just a few minutes.
• "Glutton" is the correct answer because it perfectly describes someone who overindulges in food or drink. (पेटू व्यक्ति)
• Example: The glutton at the party consumed more food than everyone else combined.
• Therefore, the correct answer is: Glutton.

Additional Information

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

• Gourmet (भोजन पारखी): A connoisseur of good food; someone who appreciates and knows the fine details of cuisine.
• Example: The gourmet chef prepared a meal that was both beautiful and delicious.
• Epicure (सुख-साधन प्रेमी): Someone who takes particular pleasure in fine food and drink.
• Example: She is an epicure who enjoys dining at Michelin-starred restaurants.
• Sybarite (भोग-विलासी): A person who is self-indulgent in their fondness for luxury and pleasure.
• Example: The sybarite spent his days lounging in luxury resorts.

The correct answer is 'which'.

 

Key Points

• The word "which" is used to refer to a specific item or subset from a group that was mentioned earlier.
• In this sentence, the phrase "none of ____ were explained" requires the relative pronoun "which" to refer to the caveats in the finance minister's statement.
• Options 1, 2, and 4 are grammatically incorrect in this context.

Therefore, the correct answer is Option 3.

 

Complete Sentence: "The finance minister's statement was laden with caveats, none of which were explained."

 

Additional Information

• Option 1: "that" is incorrect because "that" is not used to refer to specific items in this context.
• Option 2: "them" is incorrect because "them" is a pronoun and does not fit the grammatical structure of the sentence.
• Option 4: "whom" is incorrect because "whom" is used for people, not things.

The correct answer is 'opposed'.

 

Key Points

• The word "opposed" means being in direct conflict or contrast with something.
• The sentence indicates that the philosopher's stance was completely contrary to the prevailing orthodoxy, which aligns with the meaning of "opposed."
• Options 1, 2, and 3 do not fit the context. "Adverse" and "averse" have different meanings, and "converse" does not describe direct opposition.

Therefore, the correct answer is Option 4.

 

Complete Sentence:"The philosopher's stance was diametrically opposed to the prevailing orthodoxy."

 

Additional Information

• Option 1: "adverse" refers to something harmful or unfavorable, which does not fit the context here.
• Option 2: "averse" refers to a strong dislike, not a direct opposition.
• Option 3: "converse" means something reversed in position or order, which does not convey the intended meaning.

The correct answer is 'had'.

Key Points

• The correlative conjunction "No sooner... than" is used to indicate that one action happened immediately before another.
• When a sentence begins with "No sooner", it follows the structure: No sooner + had + subject + been + past participle + than + simple past.
• Thus, the correct sentence is: "No sooner had the findings been published than critics began questioning their legitimacy."
• Options 1, 3, and 4 are incorrect because they do not fit the required past perfect structure.

Therefore, the correct answer is Option 2.

Correct Sentence: *"*No sooner had the findings been published than critics began questioning their legitimacy."

Additional Information

• Common correlative conjunction patterns include:
• No sooner... than
• Hardly/Scarcely... when
• Examples:
• "No sooner had the train left than it started raining."
• "No sooner had the results been announced than the audience applauded."

The correct answer is Option 1.

 

Key Points

• The issue in this sentence is the incorrect placement of the correlative conjunction "neither...nor."
• The phrase "neither penalise first-time offenders" should be correctly placed to ensure parallel structure with "nor those who may have violated norms."
• The sentence should read: "The policy aims to penalise neither first-time offenders nor those who may have violated norms..."
• The error lies in part 1 of the sentence.

Therefore, the correct answer is Option 1.

 

Correct Sentence: "The policy aims to penalise neither first-time offenders nor those who may have violated norms due to systemic ambiguity rather than deliberate intent."

 

Additional Information

• Option 2: "nor those who may have violated norms" is grammatically correct and does not require any changes.
• Option 3: "due to systemic ambiguity" is grammatically correct and does not require any changes.
• Option 4: "rather than deliberate intent" is grammatically correct and does not require any changes.