SSC GD Constable 2025 Official Paper (Held On: 06 Feb, 2025 Shift 2) (Previous Year Paper)

The logic followed here is

The word common to both phrases is "book", and the code common to both is "nk".

Therefore, the code for 'book' is 'nk'.

BODMAS Table: 

Given equation: 18 ÷ 90 − 5 × 11 + 2 = ?

Now, if ‘+’ and ‘ב and ‘−’ and ‘÷’ are interchanged, then:

⇒ 18 − 90 ÷ 5 + 11 × 2 = ?

⇒ 18 - 18 + 11 × 2 = ?

⇒ 18 - 18 + 22 = ?

⇒ 0 + 22 = 22.

Hence, the correct answer is "Option 4".

The logic followed here is:

For, SBFU is related to VDHX

For, HOXA is related to KQZD

Similarly, for 'ZEPI'

So, 'ZEPI' will be related to 'CGRL'

Hence, the correct answer is "Option 3".

Given Statements:

All balms are ears.

All balms are legs.

Some legs are fingers.

The least possible Venn diagram for the given statements is:

Conclusions:

I. Some fingers are balms. - False (From the diagram, there is no definite direct overlap between 'Fingers' and 'Balms'. It's a possibility, but not a definite conclusion.)

II. Some legs are ears. - True (Since all balms are ears and all balms are legs, the set of balms is common to both ears and legs. Therefore, some legs (which are balms) are definitely ears.)

So, Only conclusion II follows.

Hence, the correct answer is "Option 4".

Additional Information 

The logic followed here is:

So, 'HGMRU' will be the correct alternative that filled in the blanks in the same sequence will make the series logically complete.

Hence, the correct answer is "Option 3".

The image embedded in given figure is as shown below:

Hence, "Option 4" is the correct answer.

The logic followed here is:

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

Hence, the correct answer is "Option 4".

Family tree

Decoding the Symbols:

 

Given Expression: Q × R – S ÷ T + U

Let's break down the expression step-by-step:

Q × R: 'A × B' means ‘A is the wife of B’.

R – S: 'A – B' means ‘A is the brother of B’.

S ÷ T: 'A ÷ B' means ‘A is the father of B’.

T + U: 'A + B' means ‘A is the mother of B’.

Now, let's establish the family tree based on the derived relationships:

​

So, S is the mother's father of U.

Hence, the correct answer is "Option 4".

The logic followed here is,

To determine the code for 'you', we'll look for the common word and its corresponding code across the provided statements.

The word that appears in both phrases is 'you'.

The code that appears in both coded sequences is 'rc'.

Therefore, 'you' is coded as 'rc' in the given language.

Hence, the correct answer is "Option 3".

The paper after unfolded will be:

Hence, the correct answer is "Option 3".

The paper after unfolded will be:

Hence, the correct answer is "Option 1".

The logic followed here is:

For, 'NEYG' is related to 'PHBI'

For, 'LAVS' is related to 'NDYU'

Similarly, for 'HCTB'

So, 'HCTB' will be related to 'JFWD'

Hence, the correct answer is "Option 1".

Given, Eight people are sitting in two parallel rows containing 4 people each in such a way that there is equal distance between adjacent persons.

In row 1 – L, M, N and O are seated and all of them are facing south.

In row 2 – P, Q, R and S are seated and all of them are facing north.

Only one person sits between Q and P.

The one facing P sits at the second position from the left of the line.

 Only one person sits between N and M.

 N sits to the immediate left of O and faces S.

O does not face P. So case II is not possible

And R and L sit at the remaining place.

So, L and P are facing each other.

Hence, the correct answer is "Option 1".

The logic followed here is,

To select the Venn diagram that best illustrates the relationship among the classes: Mango, Fruit, Cauliflower, let's analyze their relationships:

• Mango is a type of Fruit. This means all Mangoes fall within the category of Fruits. In a Venn diagram, this is represented by one circle (Mango) being completely inside another larger circle (Fruit).
• Cauliflower is a vegetable and is not a fruit. Therefore, there is no overlap or inclusion between Cauliflower and either Mango or Fruit. In a Venn diagram, this is represented by a separate, non-overlapping circle for Cauliflower.

Based on this analysis, the correct Venn diagram should show:

Therefore, Option 1 best illustrates the relationship among Mango, Fruit, and Cauliflower.

The logic followed here is:

Option 1) QPT

Option 2) TTW

Option 3) ZYC

Option 4) EDH

Here, 'TTW' is odd among the given options.

Hence, the correct answer is "Option 2".

The logic followed here is,

Hence, the correct answer is "Option 2".

Given word: 'SYMPHONY'

After arranging in alphabetical order:

 

There is one alphabet "Y" at the 8^th position that remains unchanged when the letters in the word 'SYMPHONY' are arranged in English alphabetical order.

Hence, the correct answer is "Option 2".

Given, Six friends, E, F, G, X, Y and Z, are sitting in a row facing north (but not necessarily in the same order) .

No one sits to the left of F.

Only four people sit between F and E.

Only three people sit to the left of Z.

X sits to the immediate left of G.

And Y sits at the remaining place.

Three people sit between Y and F.

Hence, the correct answer is "Option 1".

The logic followed here is,

Hence, the correct answer is "Option 4".

The logic followed here is,

Hence, the correct answer is "Option 2".

The correct answer is 4.5.

Key Points

• The Second Five-Year Plan of India targeted a growth rate of 4.5% (0.045).
• It was formulated based on the Mahalanobis Model, focusing on rapid industrialization.
• The plan covered the period from 1956 to 1961.
• It emphasized the development of heavy industries, steel plants, and infrastructure to strengthen the industrial base of the economy.
• The actual achieved growth rate during the Second Plan period was approximately 4.27%, slightly below the targeted rate.

Additional Information

• Mahalanobis Model
• Developed by statistician P.C. Mahalanobis, this model emphasized the importance of the heavy industrial sector for long-term economic growth.
• It advocated for a higher allocation of resources to capital goods industries, such as steel, machinery, and infrastructure.
• Five-Year Plans
• India adopted the Five-Year Plan system in 1951 to achieve planned economic development.
• The plans were inspired by the Soviet model of centralized economic planning.
• The First Five-Year Plan (1951-1956) focused on agriculture, while the Second Plan shifted focus to industrialization.
• Planning Commission
• Established in 1950, the Planning Commission was responsible for formulating and monitoring Five-Year Plans.
• It was replaced by the NITI Aayog in 2015 under the government led by Prime Minister Narendra Modi.
• Heavy Industries
• The Second Five-Year Plan led to the establishment of steel plants in Bhilai, Rourkela, and Durgapur with the assistance of countries like the USSR, Germany, and the UK.
• It prioritized industries requiring high investment and long gestation periods for boosting overall economic growth.

The correct answer is Kumar Sanu.

Key Points

• Kumar Sanu, a renowned playback singer in India, set the Guinness World Record in 1993 for recording 28 songs in a single day.
• He achieved this feat during the peak of his career, showcasing his incredible vocal stamina and versatility.
• Kumar Sanu is known for his melodious voice and has sung in multiple languages, making him a household name in the Indian music industry.
• The record highlights his dedication and contribution to Indian music, particularly in the Bollywood industry.
• He received the prestigious Filmfare Award for Best Male Playback Singer for five consecutive years (1990-1994), further solidifying his legacy.

Additional Information

• Playback Singing:
• Playback singing is a unique feature of Indian cinema where singers record songs in advance, and actors lip-sync to them during filming.
• It allows the industry to leverage specialized vocal talents like Kumar Sanu for songs used in films.
• Guinness World Records:
• Guinness World Records is a global organization that verifies and catalogs extraordinary achievements across various fields.
• Kumar Sanu’s record for recording 28 songs in one day is a testament to his exceptional talent and work ethic.
• Bollywood Music Industry:
• Bollywood is one of the largest film industries in the world, known for its musical films and extensive use of songs.
• Kumar Sanu has been a key contributor to Bollywood music during the 1990s, often collaborating with legendary composers like Nadeem-Shravan.
• Legacy of Kumar Sanu:
• Born as Kedarnath Bhattacharya, Kumar Sanu is a Padma Shri awardee (2009) for his contribution to Indian music.
• He has sung over 20,000 songs in various Indian languages, making him one of the most prolific playback singers in history.

The correct answer is Bhangra.

Key Points

• Bhangra is one of the most popular and lively dance forms originating from Punjab, India.
• It is performed during harvest festivals like Baisakhi and other celebratory occasions.
• The dance form incorporates traditional Punjabi music using instruments like the dhol, tumbi, chimta, and tabla.
• Bhangra involves energetic and rhythmic movements, often reflecting the vibrancy and enthusiasm of Punjabi culture.
• Over time, Bhangra has gained global recognition and is now performed at international events and competitions.

Additional Information

• Ghumar: A traditional dance form of Rajasthan, performed by women in colorful attire during festivals and special occasions.
• Chhau: A semi-classical dance from eastern India (Odisha, Jharkhand, and West Bengal), often depicting themes from mythology and performed with masks.
• Garba: A folk dance from Gujarat performed during Navratri, characterized by circular movements and clapping.
• Punjabi Music: The energetic beats of the dhol and tumbi used in Bhangra reflect the agricultural roots and celebratory spirit of Punjab.
• Global Influence: Bhangra is widely recognized worldwide, with its fusion into modern music genres like hip-hop and electronic dance music.

The correct answer is Articles 36-51.

Key Points

• The Directive Principles of State Policy (DPSP) are enshrined in Part IV of the Constitution of India, covering Articles 36 to 51.
• DPSPs aim to create social and economic conditions under which citizens can lead a good life and are considered non-justiciable, meaning they are not legally enforceable.
• They are guidelines for the state to ensure socio-economic justice and establish a welfare state.
• These principles are inspired by the Irish Constitution and were included in the Indian Constitution to promote equitable development.
• Some important DPSPs include provisions for securing a uniform civil code, promoting cottage industries, ensuring equal pay for equal work, and protecting the environment.

Additional Information

• Fundamental Rights vs. DPSP:
• Fundamental Rights are justiciable and enforceable by courts, while DPSPs are non-justiciable and serve as moral obligations for the government.
• In case of conflict, courts strive to harmonize both; however, Fundamental Rights generally prevail.
• Classification of DPSPs:
• Socialistic Principles: Focus on social welfare, such as providing adequate means of livelihood and improving public health.
• Gandhian Principles: Reflect Mahatma Gandhi’s ideals, like promoting cottage industries and organizing village panchayats.
• Liberal-Intellectual Principles: Encourage economic and legal reforms, international peace, and protection of monuments.
• Significance of DPSPs:
• They act as a framework for governance and policymaking, guiding the government toward socio-economic justice.
• Though not enforceable, they often influence the judiciary in interpreting laws and policies.
• Amendments Related to DPSPs:
• The 42^nd Amendment Act, 1976, added new DPSPs, like promoting equal justice and free legal aid, and safeguarding forests and wildlife.
• The 86^th Amendment Act, 2002, made education for children a fundamental right but retained promoting free and compulsory education as a DPSP.

The correct answer is Shramshakti.

Key Points

• The title "Shramshakti" refers to the comprehensive report submitted by the National Commission on Self-Employed Women and Women in the Informal Sector.
• This report was presented during the Seventh Five-Year Plan (1985-1990) of India.
• The report highlighted the challenges faced by women working in the informal sector, emphasizing their contributions and socio-economic issues.
• The commission was headed by Dr. Ela Bhatt, a noted social activist and founder of SEWA (Self-Employed Women’s Association).
• The "Shramshakti" report laid the foundation for policy recommendations aimed at improving the working conditions and social security of women in the unorganized sector.

Additional Information

• Seventh Five-Year Plan (1985-1990):
• Focused on improving productivity and generating employment opportunities.
• Prioritized social justice and upliftment of marginalized groups, including women in the informal sector.
• Informal Sector:
• Comprises workers who are not covered by formal employment contracts, including domestic workers, street vendors, and agricultural laborers.
• Women form a significant proportion of the informal workforce, often lacking social security and legal protections.
• Dr. Ela Bhatt:
• A renowned social activist and founder of SEWA (Self-Employed Women’s Association), an organization aimed at empowering women workers in the informal sector.
• Instrumental in bringing attention to the issues of self-employed women through her leadership in preparing the "Shramshakti" report.
• Policy Impact:
• The "Shramshakti" report influenced various government policies aimed at improving the livelihood and social security of women in informal employment.
• It also led to the recognition of the informal sector as a crucial component of India’s economy.

The correct answer is Sukta.

Key Points

• The prayers and hymns in the Rigveda are known as Suktas, which means "well-said" or "beautifully constructed."
• Each Sukta is composed of several Richas (verses) that praise various deities, including Agni, Indra, Varuna, and others.
• The Rigveda contains 1,028 Suktas, which are further divided into 10 Mandalas (books or chapters).
• These Suktas form one of the oldest known collections of religious texts and reflect early Vedic culture and spirituality.
• The Rigveda is written in Vedic Sanskrit, an ancient Indo-Aryan language.

Additional Information

• Rigveda:
• It is the oldest of the four Vedas: Rigveda, Samaveda, Yajurveda, and Atharvaveda.
• The text is estimated to have been composed between 1500 BCE and 1200 BCE.
• The Rigveda primarily consists of hymns dedicated to natural forces and gods like Agni (fire), Indra (thunder), and Varuna (water).
• Richa:
• A Richa is a verse or mantra in Vedic literature.
• Each Sukta in the Rigveda is made up of multiple Richas.
• Richas are composed in a poetic meter and are used in Vedic rituals and ceremonies.
• Mandala Structure:
• The Rigveda is divided into 10 Mandalas (books).
• Each Mandala is further divided into Suktas, which are collections of hymns.
• The 10^th Mandala includes the famous Purusha Sukta, which describes the cosmic creation.
• Vedic Deities:
• The Rigveda mentions numerous deities, including Indra (king of gods), Agni (fire), and Varuna (cosmic order).
• These deities represent natural forces and cosmic principles.

The correct answer is The total amount paid by the government to its lenders.

Key Points

• Public debt refers to the total amount borrowed by the government from external or internal sources to finance its expenditures and obligations.
• It includes loans taken by the government from financial institutions, foreign governments, and private entities.
• The government pays interest on this borrowed amount, making public debt a financial liability for the country.
• Public debt is broadly categorized into internal debt (borrowed from domestic lenders) and external debt (borrowed from foreign lenders).
• It is a critical tool for managing economic growth, funding developmental projects, and addressing fiscal deficits.

Additional Information

• Internal Debt
• This refers to loans borrowed by the government from domestic sources like banks, financial institutions, and the public through bonds and securities.
• Internal debt is usually raised in the local currency and does not directly affect the foreign exchange reserves.
• External Debt
• External debt is borrowed from foreign governments, international organizations like the World Bank or IMF, or foreign private entities.
• It is denominated in foreign currencies, which makes it sensitive to exchange rate fluctuations.
• Gross Public Debt vs Net Public Debt
• Gross public debt includes all government borrowing, while net public debt accounts for the debt after subtracting government financial assets.
• Impact of Public Debt
• While public debt can fund infrastructure and development, excessive borrowing may lead to fiscal stress and inflationary pressures.
• Sustainable debt management is crucial for maintaining economic stability.

The correct answer is Bharat Rashtra Samiti (BRS).

Key Points

• K Chandrasekhar Rao (KCR) is the founder and leader of the Bharat Rashtra Samiti (BRS), a regional political party in India, formerly known as Telangana Rashtra Samithi (TRS).
• The party was renamed from Telangana Rashtra Samithi (TRS) to Bharat Rashtra Samiti (BRS) in December 2022 as part of KCR's efforts to expand its influence beyond Telangana.
• BRS, under KCR's leadership, played a significant role in the movement for the formation of the state of Telangana, which was officially created on June 2, 2014.
• KCR served as the first Chief Minister of Telangana after the state's formation and has been a prominent political figure in the region.
• The party's primary agenda includes promoting the welfare and development of Telangana while also aiming to expand its political presence nationwide.

Additional Information

• Telangana State Formation:
• Telangana was formed as the 29^th state of India on June 2, 2014, after bifurcation from Andhra Pradesh.
• The demand for a separate Telangana state was based on cultural, economic, and historical differences with Andhra Pradesh.
• Bharat Rashtra Samiti (BRS):
• The BRS is focused on regional development, addressing farmer issues, and providing welfare schemes for the people of Telangana.
• It has also initiated several flagship programs like the Rythu Bandhu Scheme and Mission Bhagiratha for rural development.
• K Chandrasekhar Rao (KCR):
• KCR played a pivotal role in the Telangana statehood movement and is known for his strong political strategy and governance style.
• He has been elected multiple times to the Telangana Legislative Assembly and Parliament of India.
• Renaming to BRS:
• The decision to rename TRS to BRS was taken to reflect the party's ambitions to expand its influence beyond Telangana and address national issues.
• The party's new focus includes a pan-India political vision under KCR's leadership.

The correct answer is 0.356.

Key Points

• As per the Employment Exchange Statistics 2023, the percentage of women jobseekers in the Live Register in India for the year 2022 was 35.6% (0.356).
• The Live Register refers to a dataset maintained by employment exchanges containing the number of jobseekers actively seeking employment.
• Women constituted a significant portion of jobseekers, reflecting the growing participation of women in the labor market.
• Despite the increase in women jobseekers, challenges like wage disparity, limited access to opportunities, and skill gaps persist in the Indian labor market.

Additional Information

• Live Register:
• A statistical measure maintained by employment exchanges to track the number of individuals actively seeking jobs.
• It provides insights into labor market trends, including gender-based jobseeking patterns.
• Employment Exchange Statistics:
• An annual report published by the Ministry of Labour and Employment, Government of India.
• It provides detailed data on employment trends, jobseeker demographics, and the performance of employment exchanges.
• Labor Force Participation Rate (LFPR):
• The percentage of the working-age population that is either employed or actively seeking employment.
• In India, LFPR for women remains lower compared to men, highlighting the need for targeted policies to enhance women's workforce participation.
• Skill Development Initiatives:
• Government schemes like the Pradhan Mantri Kaushal Vikas Yojana (PMKVY) aim to bridge skill gaps and improve employability.
• Such initiatives play a key role in empowering women jobseekers to compete in diverse sectors.
• Gender Equality in Employment:
• Promoting gender equality in the workforce is critical for achieving sustainable economic growth.
• Policymakers emphasize equal pay, safe workplaces, and access to professional opportunities to address gender disparities.

The correct answer is Manipur.

Key Points

• Cheiraoba is the traditional New Year festival celebrated in the state of Manipur, India.
• It is observed in the month of April, marking the beginning of the new year according to the traditional Manipuri lunar calendar.
• The festival involves ritualistic cleaning of houses and offering food to deities, symbolizing the renewal of life and prosperity.
• People prepare special dishes and offer them at hilltops, as a way to seek blessings for a better year ahead.
• Cheiraoba signifies unity and cultural pride among the Manipuri people, blending religious and social practices.

Additional Information

• Manipur’s Culture:
• Manipur is known for its rich cultural heritage, including classical dance forms like Ras Leela.
• The state is home to several indigenous festivals, such as Ningol Chakouba and Yaoshang.
• Geography of Manipur:
• Manipur is located in Northeast India and is bordered by Nagaland, Assam, Mizoram, and Myanmar.
• The state is famous for its scenic landscapes, such as Loktak Lake, the largest freshwater lake in northeastern India.
• Manipuri Lunar Calendar:
• The Manipuri lunar calendar governs traditional festivals and rituals observed in the state.
• It emphasizes alignment with natural cycles and the phases of the moon.
• Hilltop Rituals:
• Offering food at hilltops is a vital part of Cheiraoba, symbolizing the connection between humans and nature.
• It is believed to bring blessings, prosperity, and harmony for the year ahead.

The correct answer is 1953.

Key Points

• The Sangeet Natak Akademi was established in the year 1953 by the Government of India.
• It is India's apex cultural institution dedicated to the preservation and promotion of performing arts, including music, dance, and drama.
• The Akademi functions as an autonomous body under the Ministry of Culture and is headquartered in New Delhi.
• Its primary objectives include recognizing and honoring outstanding practitioners in the field of performing arts and providing financial assistance for the preservation of traditional art forms.
• The institution plays a pivotal role in showcasing India's rich cultural heritage through programs, festivals, and awards such as the Sangeet Natak Akademi Awards.

Additional Information

• Sangeet Natak Akademi Awards
• The awards are considered among the highest national recognition given to performing artists, teachers, and scholars of performing arts.
• It honors contributions in fields such as music, dance, theater, puppetry, and other traditional art forms.
• The awards were instituted in 1952 and are given annually.
• National Institutes under Sangeet Natak Akademi
• The Akademi supports several national institutions such as Kathak Kendra in New Delhi and Ravindra Rang Manch.
• These institutions focus on training, research, and promotion of specific art forms.
• Preservation of Traditional Arts
• The Akademi provides grants and organizes workshops to ensure the survival of endangered art forms.
• It emphasizes the documentation and archiving of rare performances and techniques for future generations.
• National Cultural Institutions
• Alongside Sangeet Natak Akademi, India has other apex institutions such as Lalit Kala Akademi (visual arts) and Sahitya Akademi (literature).
• These institutions collectively contribute to preserving India's diverse cultural heritage.

The correct answer is Mohammed Shami.

Key Points

• Mohammed Shami became the highest wicket-taker in the ICC Men's Cricket World Cup 2023 ODI tournament.
• Shami displayed exceptional bowling performance, taking a total of 23 wickets during the tournament.
• His best performance came against New Zealand, where he recorded impressive figures of 7 wickets for 57 runs.
• Shami's ability to deliver consistent breakthroughs in crucial matches played a key role in India's success in the tournament.
• He achieved this feat despite playing fewer matches compared to some other bowlers, showcasing his efficiency and skill.

Additional Information

• ICC Men's Cricket World Cup:
• The ICC Men's Cricket World Cup is the premier ODI cricket tournament organized by the International Cricket Council (ICC).
• It is held every four years, bringing together the best cricketing nations to compete for the coveted trophy.
• The 2023 edition was hosted by India, featuring 10 teams competing in a round-robin format followed by knockout stages.
• Bowling Terminology:
• Wicket-taking ability: Refers to a bowler's skill in dismissing batsmen and breaking partnerships.
• Economy rate: Indicates the average runs conceded per over, showcasing a bowler's control.
• Strike rate: Measures the average number of balls bowled per wicket taken, highlighting efficiency.
• Mohammed Shami's Career Highlights:
• Shami is one of India's premier fast bowlers, known for his ability to swing the ball both ways.
• He debuted for India in ODIs in January 2013 and has been an integral part of the team since then.
• Shami holds multiple records, including being the fastest Indian bowler to take 100 ODI wickets.
• India's Performance in ICC Men's Cricket World Cup 2023:
• India was one of the favorites in the tournament, finishing at the top of the group stage.
• Key players like Rohit Sharma, Virat Kohli, and Jasprit Bumrah contributed significantly to the team's success.
• The team's bowling attack, led by Mohammed Shami, was instrumental in securing crucial victories.

The correct answer is Puducherry.

Key Points

• According to the National Multidimensional Poverty Index 2023, Puducherry has the least percentage of population who are multidimensionally poor among all Union Territories.
• The Multidimensional Poverty Index (MPI) measures poverty based on multiple indicators, including education, health, and living standards, rather than just income.
• Puducherry's effective implementation of social welfare schemes and better access to healthcare and education have contributed to its low poverty levels.
• Data in the report highlights that Puducherry excels in most indicators of the MPI, including access to clean drinking water, sanitation, and electricity.
• The National MPI 2023 was developed by NITI Aayog in collaboration with Oxford Poverty and Human Development Initiative (OPHI) and United Nations Development Programme (UNDP).

Additional Information

• Multidimensional Poverty Index (MPI):
• The MPI is a measure that captures poverty using multiple factors, including education, health, and living standards.
• It is based on internationally recognized indicators and is used to assess poverty beyond income levels.
• The MPI considers factors like malnutrition, child mortality, years of schooling, access to clean water, electricity, and housing quality.
• Poverty Reduction in Puducherry:
• Puducherry has implemented various schemes, including free healthcare, subsidized housing, and education programs, to reduce poverty.
• The UT's small geographic area and relatively high urbanization rates also contribute to better management and delivery of public services.
• NITI Aayog's Role:
• NITI Aayog is the policy think tank of the Indian government, responsible for creating strategies to achieve sustainable development.
• It collaborates with international organizations like UNDP and OPHI to develop measures like the MPI.
• NITI Aayog’s focus on data-driven policymaking helps improve social welfare initiatives across India.
• Union Territories and MPI:
• Union Territories like Puducherry and Chandigarh typically perform better on MPI indicators due to concentrated governance and smaller populations.
• The MPI helps policymakers identify specific areas needing improvement to reduce poverty more effectively.

The correct answer is Chief Minister.

Key Points

• The Chief Minister is considered the real executive head of a state in India, as per the Constitution of India.
• While the Governor is the constitutional head of a state, the Chief Minister exercises real power and authority.
• The Chief Minister is the leader of the ruling party in the state legislature and plays a pivotal role in policy formulation and implementation.
• He or she is appointed by the Governor, but the appointment is based on the majority support in the legislative assembly.
• The Chief Minister heads the state council of ministers, which is responsible for advising the Governor and carrying out administrative duties.

Additional Information

• Governor:
• The Governor is the nominal or constitutional head of a state, similar to the role of the President at the national level.
• He or she acts on the advice of the Chief Minister and the council of ministers, except in specific discretionary powers.
• The Governor is appointed by the President of India and serves a term of five years.
• State Council of Ministers:
• It is headed by the Chief Minister and comprises ministers responsible for various portfolios such as health, education, and finance.
• The council collectively advises the Governor and is responsible for day-to-day administration of the state.
• Role of the Chief Minister:
• He or she is the chief spokesperson of the government in the state legislature.
• The Chief Minister coordinates the work of various ministries and ensures the implementation of policies and laws.
• He or she also represents the state in interactions with the central government.
• State Legislature:
• The state legislature consists of the legislative assembly (Vidhan Sabha) and in some states, the legislative council (Vidhan Parishad).
• The Chief Minister is usually a member of the legislative assembly and needs to maintain majority support to remain in office.

The correct answer is Andhra Pradesh state table tennis association.

Key Points

• The 50^th All India Inter-Institutional Table Tennis Championships 2023 was organized by the Andhra Pradesh state table tennis association.
• This prestigious event took place in Andhra Pradesh and is recognized for fostering national-level table tennis talent.
• The championship is conducted under the aegis of the Table Tennis Federation of India (TTFI), the governing body for table tennis in India.
• The event provides a platform for institutional teams across India to showcase their skills and compete for the championship title.
• It serves as a critical milestone for athletes aiming to represent India in international table tennis tournaments.

Additional Information

• Table Tennis Federation of India (TTFI):
• TTFI is the apex body for table tennis in India, responsible for organizing national and international tournaments in the country.
• Founded in 1926, it is affiliated with the International Table Tennis Federation (ITTF).
• TTFI works to promote the sport by organizing championships, training camps, and talent scouting programs.
• Significance of Inter-Institutional Championships:
• These tournaments bring together teams from various public and private institutions, fostering competitive spirit and skill enhancement.
• They also serve as a talent pool for identifying potential players for the national team.
• Andhra Pradesh and Sports:
• Andhra Pradesh has been actively involved in promoting sports, with a focus on creating world-class infrastructure and training facilities.
• The state has hosted several national and international sports events over the years.
• History of Table Tennis in India:
• Table tennis was introduced in India during the British era and has grown significantly in popularity since then.
• India has produced several notable players like Sharath Kamal, who have excelled in international competitions.

The correct answer is 2 kg.

Key Points

• The momentum (p) of an object is given by the formula: p = mv, where 'm' is the mass and 'v' is the velocity.
• In this problem, the final momentum of the body is 40 kg·m/s, and we need to calculate its mass 'm'.
• Using the equation of motion, the velocity (v) of the body just before hitting the ground can be calculated as:

v = √(2gh), where 'g' is the acceleration due to gravity (10 m/s²) and 'h' is the height (20 m). Thus, v = √(2 × 10 × 20) = √400 = 20 m/s.

• Substituting the values of momentum (p = 40 kg·m/s) and velocity (v = 20 m/s) into the momentum formula (p = mv):

40 = m × 20 → m = 40 / 20 = 2 kg.

• Thus, the mass of the body is 2 kg, which corresponds to Option 4.

Additional Information

• Momentum:
• Momentum is a vector quantity defined as the product of mass and velocity of an object: p = mv.
• It has both magnitude and direction, and its SI unit is kg·m/s.
• Free Fall:
• Free fall refers to the motion of a body under the sole influence of gravity, with negligible air resistance.
• In free fall, the acceleration of the body is equal to the acceleration due to gravity (g), typically 9.8 m/s² (approximated as 10 m/s² in calculations).
• Kinematic Equation for Velocity:
• The final velocity (v) of a body in free fall is calculated using the formula: v = √(2gh).
• Here, 'g' is the acceleration due to gravity, and 'h' is the height from which the body is dropped.
• Conservation of Momentum:
• The law of conservation of momentum states that in the absence of external forces, the total momentum of a system remains constant.
• This principle is fundamental in solving problems involving collisions and other interactions.

The correct answer is Arya Samaj.

Key Points

• The Arya Samaj was founded by Swami Dayananda Saraswati in 1875 in Bombay (now Mumbai).
• The movement aimed at promoting the purification and revival of Vedic principles and practices.
• Swami Dayananda advocated for the slogan "Back to the Vedas" (Vedo Ki Or Lauto) to revive ancient Indian culture and spirituality.
• The Arya Samaj opposed idol worship, caste-based discrimination, and superstitions, emphasizing the monotheistic teachings of the Vedas.
• It played a significant role in India’s social and cultural reform movements, including the promotion of women’s education and widow remarriage.

Additional Information

• Swami Dayananda Saraswati:
• He was a reformer and philosopher who sought to restore the Vedas as the ultimate source of knowledge and truth.
• He authored the book "Satyarth Prakash" (The Light of Truth), which became the doctrinal guide for the Arya Samaj.
• Swami Dayananda opposed rituals, priestly dominance, and practices like child marriage.
• Key Principles of Arya Samaj:
• Belief in the infallibility of the Vedas as the highest authority.
• Promotion of universal brotherhood and social equality.
• Advocacy for education for all, including women, and the establishment of educational institutions like the Dayanand Anglo-Vedic (DAV) schools and colleges.
• Social Impact:
• The Arya Samaj played a key role in the movement against untouchability and caste discrimination.
• It encouraged progressive reforms such as inter-caste marriages and widow remarriage.
• It also opposed foreign rule and contributed to India’s freedom struggle.
• Related Movements:
• The Brahmo Samaj, founded by Raja Ram Mohan Roy, also worked for reform but emphasized monotheism and modern education.
• The Prarthana Samaj promoted social reform but was more moderate in its approach compared to the Arya Samaj.

The correct answer is Calcium hydroxyapatite.

Key Points

• Calcium hydroxyapatite (Ca10(PO4)6(OH)2) is the primary mineral that forms the hard, protective outer layer of human teeth known as enamel.
• Tooth enamel is the hardest substance in the human body, and its durability is due to the crystalline structure of calcium hydroxyapatite.
• This mineral provides strength and resilience to teeth, enabling them to withstand the forces of chewing and grinding.
• Calcium hydroxyapatite also plays a role in maintaining the natural whiteness and smooth surface of enamel, which is critical for oral health.
• The presence of fluoride in dental products helps to convert hydroxyapatite into fluorapatite, which is more resistant to acid attacks from bacteria.

Additional Information

• Tooth Enamel:
• Tooth enamel is made up of 96% minerals, primarily calcium hydroxyapatite, with the remainder being water and organic matter.
• It is non-living tissue, which means it cannot regenerate or repair itself once damaged.
• Enamel erosion can occur due to exposure to acids from foods, drinks, or bacterial activity, leading to tooth sensitivity and cavities.
• Hydroxyapatite in Bones:
• Calcium hydroxyapatite is also a major component of bones, providing them with strength and structure.
• In bones, hydroxyapatite is embedded in a matrix of collagen, making them both strong and flexible.
• Role of Fluoride:
• Fluoride strengthens tooth enamel by forming fluorapatite, which is more resistant to decay.
• Fluoride is commonly added to toothpaste and drinking water to promote dental health.
• Dental Health Practices:
• Maintaining good oral hygiene, such as regular brushing and flossing, helps prevent enamel erosion and decay.
• Avoiding excessive consumption of acidic foods and drinks can protect enamel from damage.

The correct answer is Rainwater Harvesting.

Key Points

• Rainwater harvesting involves collecting and storing rainwater from rooftops, surfaces, or other catchment areas to use for irrigation, household use, and other purposes.
• This method reduces dependency on groundwater, which is depleting at an alarming rate due to over-extraction.
• It helps in recharging aquifers and improving the groundwater table, particularly in regions experiencing water scarcity.
• Rainwater harvesting is a sustainable and cost-effective water conservation method, widely promoted in urban and rural areas.
• Implementation of rainwater harvesting systems in residential, commercial, and industrial buildings can significantly reduce water wastage.

Additional Information

• Groundwater Depletion:
• Groundwater is a vital source of freshwater, but it is being depleted rapidly due to over-extraction and lack of recharge mechanisms.
• Rainwater harvesting can help mitigate this issue by replenishing aquifers.
• Traditional Water Conservation Practices:
• Many regions in India have traditional water conservation practices, such as stepwells and tanks, which emphasize the importance of rainwater collection.
• Reviving these practices can complement modern rainwater harvesting techniques.
• Environmental Benefits:
• Rainwater harvesting reduces surface runoff, minimizing soil erosion and waterlogging in urban areas.
• It also reduces dependency on municipal water supplies, lowering energy consumption for water pumping.
• Policy Support:
• Many state governments in India have made rainwater harvesting mandatory for new buildings to tackle water scarcity.
• Awareness campaigns and subsidies for installation are being provided to encourage adoption.

The correct answer is Central Government.

Key Points

• The Central Government has the authority to appoint a Census Commissioner for special population estimates, including Scheduled Tribes (ST).
• Such appointments are typically made under the provisions of relevant bills or legislations, such as the Readjustment of Representation of Scheduled Tribes in Assembly Constituencies of the State of Goa Bill, 2024.
• The Census Commissioner plays a crucial role in collecting and analyzing demographic data to ensure equitable representation for ST communities in legislative assembly constituencies.
• Population estimates of Scheduled Tribes are critical for implementing affirmative measures and ensuring compliance with constitutional provisions regarding representation.
• The Central Government oversees nationwide census operations, ensuring uniformity and accuracy in data collection.

Additional Information

• Census in India
• The Census in India is conducted every 10 years under the Census Act, 1948.
• The Registrar General and Census Commissioner of India under the Ministry of Home Affairs oversees the census operations.
• It is the most comprehensive source of demographic, social, and economic data in India.
• Scheduled Tribes (ST)
• Scheduled Tribes are recognized under Article 342 of the Indian Constitution.
• They are communities that are socially, economically, and educationally disadvantaged.
• Reservation and affirmative action policies aim to uplift ST communities in areas such as education, employment, and political representation.
• Representation in Assembly Constituencies
• Article 330 and 332 of the Constitution provide for reservation of seats for Scheduled Castes and Scheduled Tribes in the Lok Sabha and State Legislative Assemblies.
• Population data collected through census exercises is used to determine the proportionate representation of STs in legislative bodies.
• Key Legislative Processes
• Legislations like the Readjustment of Representation of Scheduled Tribes in Assembly Constituencies Bill aim to align representation with demographic changes.
• These bills are passed by Parliament and implemented through relevant government departments.

Shortcut Trick

Ratio of efficiencies of A and B = (1/2) ÷ (3/4) = 2 : 3.

Total combined efficiency = 2 + 3 = 5 units/day.

Total work = Combined efficiency × Total days = 5 × 66 = 330 units.

Time taken by B alone = Total work ÷ Efficiency of B = 330 ÷ 3 = 110 days.

∴ The correct answer is 110 days.

Alternate Method

Given:

A does half as much work as B in three-fourth of the time.

Together they complete the work in 66 days.

Formula Used:

Total Work = Efficiency × Time

Calculations:

⇒ Let B take x days to complete the whole work.

⇒ A completes half the work in (3/4)x days.

⇒ Time taken by A for full work = 2 × (3/4)x = 1.5x days.

⇒ Let Total work = LCM of 1.5x and x = 3x units.

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

⇒ Time taken together = Total work ÷ Combined efficiency

⇒ 66 = 3x ÷ 5

⇒ 3x = 66 × 5

⇒ 3x = 330

⇒ x = 110 days.

⇒ B alone takes x = 110 days.

∴ The correct answer is 110 days.

Additional Information

Time and Work Relation

Work = Efficiency × Time. Efficiency and time are inversely proportional when the total work is constant.

Work and Wages

Wages are distributed in direct proportion to the total amount of work done by each individual. If workers work for the same number of days, their wages are divided exactly in the ratio of their daily efficiencies.

Pipes & Cisterns

This concept is mathematically identical to Time & Work. The only difference is that an outlet pipe or leakage works with a negative efficiency (it empties the tank), while an inlet pipe works with a positive efficiency.

Shortcut Trick

The surface area of a sphere can be computed directly using its diameter (d) with the formula: SA = π × d².

⇒ SA = (22/7) × 21 × 21

⇒ SA = 22 × 3 × 21

⇒ SA = 66 × 21 = 1386

∴ The correct answer is 1386 cm².

Alternate Method

Given:

Diameter of the sphere (d) = 21 cm

Radius of the sphere (r) = d ÷ 2 = 21/2 cm

Formula Used:

Surface Area of a sphere = 4 × π × r²

d = 21 cm Sphere Surface Area

Calculations:

⇒ Surface Area = 4 × (22/7) × (21/2)²

⇒ Surface Area = 4 × (22/7) × (441/4)

⇒ Surface Area = (22/7) × 441

⇒ Surface Area = 22 × 63

⇒ Surface Area = 1386 cm²

∴ The correct answer is 1386 cm².

Additional Information

Volume of a Sphere

The amount of space occupied by a sphere is its volume. For a sphere of radius r, Volume (V) = (4/3) × π × r³.

Hemisphere

A hemisphere is an exact half of a sphere. Its Curved Surface Area (CSA) is 2 × π × r², and its Total Surface Area (TSA) is 3 × π × r².

Volume of a Hemisphere

Since it is half the size of a whole sphere, the volume of a hemisphere is given by V = (2/3) × π × r³.

Shortcut Trick

Cost Price (CP) is considered as the base value, which is 100%.

To make a profit of 26%, the Selling Price (SP) must be 100% + 26% = 126% of CP.

SP = 126% of 500

SP = 1.26 × 500 = 630

∴ The correct answer is ₹630.

Alternate Method

Given:

Cost Price of the article (CP) = ₹500

Desired Profit Percentage = 26%

Formula Used:

Profit = (Profit% ÷ 100) × CP

Selling Price (SP) = CP + Profit

CP = ₹500 (100%)

SP = ₹630 (126%)

• 26% Profit

Calculations:

⇒ Profit = (26 ÷ 100) × 500

⇒ Profit = 26 × 5 = ₹130

⇒ Selling Price = CP + Profit

⇒ Selling Price = 500 + 130 = ₹630

∴ The correct answer is ₹630.

Additional Information

Direct Selling Price Formula

When the profit percentage is given, SP = CP × (100 + Profit%) ÷ 100.

Calculation for Loss

When a loss percentage is given, SP = CP × (100 − Loss%) ÷ 100.

Profit/Loss Base

Unless otherwise stated, profit and loss percentages are always calculated on the Cost Price (CP).

Shortcut Trick

The third proportional of two numbers a and b is calculated directly using the formula: b² ÷ a.

Here, a = 36 and b = 42.

Third proportional = (42 × 42) ÷ 36

Third proportional = 1764 ÷ 36 = 49

∴ The correct answer is 49.

Alternate Method

Given:

First number (a) = 36

Second number (b) = 42

Formula Used:

If c is the third proportional to a and b, they form a continuous proportion such that a : b :: b : c.

⇒ a × c = b × b

⇒ c = b² ÷ a

Product of Extremes (36 × c)

Product of Means (42 × 42)

36

:

42

::

42

:

c

36 × c = 42 × 42   →   c = 49

Calculations:

⇒ c = (42 × 42) ÷ 36

⇒ c = (7 × 6 × 7 × 6) ÷ (6 × 6)

⇒ c = 7 × 7

⇒ c = 49

∴ The correct answer is 49.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(a × b).

Fourth Proportional

The fourth proportional to three numbers a, b, and c is d, such that a : b :: c : d, which simplifies to d = (b × c) ÷ a.

Compound Ratio

For two ratios a : b and c : d, their compound ratio is expressed as (a × c) : (b × d).

Duplicate Ratio

The duplicate ratio of a : b is defined as a² : b², and the sub-duplicate ratio is √a : √b.

Shortcut Trick

Ratio of shares (Raj : Varun) = (1 + 8/100)¹⁶⁻¹⁵ = 108/100 = 27/25.

Total parts = 27 + 25 = 52 parts.

52 parts = ₹1612 ⇒ 1 part = ₹31.

Raj's share = 27 parts = 27 × 31 = ₹837.

∴ The correct answer is ₹837.

Alternate Method

Total: ₹1612

Raj (R) 15 Years @ 8%

Varun (V) 16 Years @ 8%

Amounts are Equal

Given:

Total sum = ₹1612

Rate of interest (R) = 8% compounded annually

Time for Raj (T₁) = 15 years, Time for Varun (T₂) = 16 years

Formula Used:

Amount in Compound Interest, A = P(1 + R/100)ⁿ

Calculation:

⇒ Let the share of Raj be R and Varun be V.

⇒ R(1 + 8/100)¹⁵ = V(1 + 8/100)¹⁶

⇒ R / V = (1 + 8/100)¹⁶⁻¹⁵

⇒ R / V = (1 + 2/25)¹ = 27/25

⇒ The sum ₹1612 is divided in the ratio 27 : 25.

⇒ Total parts = 27 + 25 = 52

⇒ Value of 52 parts = ₹1612

⇒ Value of 1 part = 1612 ÷ 52 = ₹31

⇒ Raj's share = 27 parts = 27 × 31 = ₹837

∴ The correct answer is ₹837.

Additional Information

Equal Amounts in Compound Interest

When a sum is divided into two parts P₁ and P₂ invested at a rate R% for times T₁ and T₂ respectively such that their final amounts are equal, the ratio of their principals is given by P₁/P₂ = (1 + R/100)^T₂−T₁.

Effective Multiplying Factor

The multiplying factor (1 + R/100) acts as a geometric progression common ratio for every additional year the principal is invested in a compound interest scheme.

Time Difference Principle

To get equal amounts, the person who invests the money for a shorter duration must always start with a larger principal amount to compensate for the lesser interest gained over time.

Given:

E×pression: [(63 ÷ 9) × {96 ÷ 8 + (11 ÷ 4) × (9 − 5)}]

Calculation:

[(63 ÷ 9) × {96 ÷ 8 + (11 ÷ 4) × (9 − 5)}]

⇒ [(7) × {12 + (11/4) × (4)}]

⇒ [(7) × {12 + 11/4 × 4}]

⇒  [(7) × {12 + 11}]

⇒[(7) × {23}]

⇒ 7 × 23 = 161

∴ The final answer is: 161

Shortcut Trick

Relative speed in opposite directions = (50 + 110) × 5/18 = 160 × 5/18 = 400/9 m/s

Total distance covered in 12 s = (400/9) × 12 = 1600/3 ≈ 533.33 m

Length of second train = Total distance − Length of first train

Length of second train = 533.33 − 500 = 33.33 m

∴ The correct answer is 33.33 m.

Alternate Method

500 m 50 km/h

L m 110 km/h

Cross time = 12 s

Given:

Speed of first train, S₁ = 50 km/h

Speed of second train, S₂ = 110 km/h

Length of first train, L₁ = 500 m

Time taken to cross, T = 12 s

Formula Used:

Relative Speed = S₁ + S₂ (opposite directions)

Total Distance (L₁ + L₂) = Relative Speed × Time

Calculations:

⇒ Relative Speed = 50 + 110 = 160 km/h

⇒ Relative Speed in m/s = 160 × (5 / 18) = 400 / 9 m/s

⇒ Total Distance = Speed × Time = (400 / 9) × 12

⇒ Total Distance = 1600 / 3 m ≈ 533.33 m

⇒ L₁ + L₂ = 533.33 m

⇒ 500 + L₂ = 533.33

⇒ L₂ = 533.33 − 500

⇒ L₂ = 33.33 m

∴ The correct answer is 33.33 m.

Additional Information

Relative Speed (Opposite Direction)

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

Relative Speed (Same Direction)

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

Unit Conversion Rule

To convert km/h to m/s, multiply the speed by 5/18. To convert m/s to km/h, multiply by 18/5.

Crossing Stationary Objects

When a train crosses a pole or a standing man, the distance covered equals the length of the train itself.

Shortcut Trick

For compound interest questions where final amounts are equal, the ratio of principal invested is inversely proportional to the respective multiplying factors for the time difference.

Time difference = 18 − 17 = 1 year.

Ratio of Anand's share to Anil's share = (1 + 4/100)¹ = 104/100 = 26/25.

Total parts = 26 + 25 = 51 parts.

Anil's share (25 parts) = (25 ÷ 51) × 1224 = 25 × 24 = ₹600.

∴ The correct answer is ₹600.

Alternate Method

Given:

Total amount distributed = ₹1224

Rate of Interest (R) = 4% compounded annually

Time for Anand (t₁) = 17 years

Time for Anil (t₂) = 18 years

Formula Used:

Amount in Compound Interest, A = P(1 + R/100)ⁿ

Total: ₹1224

Anand (P1): 17 years Ratio: 26 parts

Anil (P2): 18 years Ratio: 25 parts

Equal Amount (A)

Calculations:

⇒ Let the principal sum given to Anand be P₁ and to Anil be P₂.

⇒ P₁(1 + 4/100)¹⁷ = P₂(1 + 4/100)¹⁸

⇒ P₁ / P₂ = (1 + 4/100)^{18 − 17}

⇒ P₁ / P₂ = (1 + 1/25)¹

⇒ P₁ / P₂ = 26 / 25

⇒ The sum of ₹1224 is divided in the ratio of 26 : 25.

⇒ Total ratio parts = 26 + 25 = 51 parts.

⇒ 51 parts = ₹1224

⇒ 1 part = 1224 ÷ 51 = 24

⇒ Anil's principal share (P₂) = 25 parts = 25 × 24 = 600

∴ The correct answer is ₹600.

Additional Information

Compound Interest Formula

The amount after n years at r% compound interest per annum is derived using A = P(1 + r/100)ⁿ.

Equal Amount Rule

When a sum is split into two parts P₁ and P₂ for n₁ and n₂ years respectively such that their end amounts are exactly equal, the initial parts hold the relation P₁ / P₂ = (1 + r/100)^{n2 − n1}.

SI vs CI Difference

The direct difference between CI and SI on the same principal is D = P(r/100)² for 2 years, and D = P(r/100)²(3 + r/100) for 3 years.

Shortcut Trick

Let SP of 1 chair be 1 unit.

Total SP = 152 units and Profit = 76 units.

Total CP = Total SP − Profit = 152 − 76 = 76 units.

Profit % = (Profit ÷ CP) × 100 = (76 ÷ 76) × 100 = 100%.

∴ The correct answer is 100%.

Alternate Method

Given:

Number of chairs sold = 152

Gain = Selling Price (SP) of 76 chairs

Formula Used:

Cost Price (CP) = SP − Profit

Profit % = (Profit ÷ CP) × 100

CP = 76 units

Profit = 76 units

Total SP = 152 units CP + Profit = Total SP

Calculations:

⇒ Let the SP of 1 chair be ₹1.

⇒ Total SP of 152 chairs = 152 × ₹1 = ₹152

⇒ Profit = SP of 76 chairs = 76 × ₹1 = ₹76

⇒ Total CP of 152 chairs = Total SP − Profit

⇒ Total CP = 152 − 76 = ₹76

⇒ Profit % = (Profit ÷ Total CP) × 100

⇒ Profit % = (76 ÷ 76) × 100

⇒ Profit % = 1 × 100 = 100%

∴ The correct answer is 100%.

Additional Information

Loss Scenario

If there is a loss equal to the SP of x articles, then CP = Total SP + Loss. The loss percentage is calculated as (Loss ÷ CP) × 100.

Profit/Loss based on CP

If profit or loss is given equal to the CP of x articles, let the CP of 1 article be 1 unit, and compute the total CP and profit/loss accordingly.

Marked Price & Discount

Discount is always given on the Marked Price (MP). SP = MP − Discount, and Discount % = (Discount ÷ MP) × 100.

Shortcut Trick

The mean proportional of two numbers a and b is √(a × b).

Mean proportional of x and 4x = √(x × 4x) = 2x.

Given 2x = 456976.

Therefore, x = 456976 ÷ 2 = 228488.

∴ The correct answer is 228488.

Alternate Method

Given:

The two numbers are x and 4x.

Their mean proportional = 456976.

Formula Used:

Mean proportional between a and b = √(a × b)

x

Mean (2x) = 456976

4x

× 2 × 2

Mean Proportional = √(a × b)

Calculations:

⇒ √(x × 4x) = 456976

⇒ √(4x²) = 456976

⇒ 2x = 456976

⇒ x = 456976 ÷ 2

⇒ x = 228488

∴ The correct answer is 228488.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(a × b). It implies that a : x :: x : b, where x is the mean proportional.

Third Proportional

The third proportional to two numbers a and b is c, such that a : b :: b : c. It is calculated as c = b² ÷ a.

Fourth Proportional

The fourth proportional to three numbers a, b, and c is d, such that a : b :: c : d. It is calculated as d = (b × c) ÷ a.

Shortcut Trick

Let assumed average be ₹30,000.

Net deviation = (28312 − 30000) + (32252 − 30000) + (25012 − 30000) + (33500 − 30000)

Net deviation = −1688 + 2252 − 4988 + 3500 = −924

Average deviation = −924 ÷ 4 = −231

Actual average = 30000 − 231 = 29769

∴ The correct answer is ₹29,769.

Alternate Method

Given:

Expenditure in January = ₹28,312

Expenditure in February = ₹32,252

Expenditure in March = ₹25,012

Expenditure in April = ₹33,500

Formula Used:

Average = Sum of all observations ÷ Total number of observations

28312 Jan

32252 Feb

25012 Mar

33500 Apr

Avg = 29769

Calculations:

⇒ Total expenditure = 28312 + 32252 + 25012 + 33500

⇒ Total expenditure = ₹119,076

⇒ Total number of months = 4

⇒ Average expenditure = 119076 ÷ 4

⇒ Average expenditure = ₹29,769

∴ The correct answer is ₹29,769.

Additional Information

Weighted Average

Used when different sets of data have varying frequencies. Formula: A_w = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Combined Average

When combining multiple groups, the total average can be found by summing all values across groups and dividing by the total number of combined items.

Effect of Arithmetic Operations on Average

If a constant number is added, subtracted, multiplied, or divided across all given observations, the overall average is also modified by the exact same mathematical operation.

Shortcut Trick

Relative speed = 75 − 30 = 45 km/hr = 45 × (5/18) = 12.5 m/s.

Total distance covered = Relative speed × Time = 12.5 × 108 = 1350 m.

Length of slow train = Total distance − Length of fast train.

Length of slow train = 1350 − 950 = 400 m.

∴ The correct answer is 400 m.

Alternate Method

Given:

Speed of fast train (v₁) = 75 km/hr

Speed of slow train (v₂) = 30 km/hr

Length of fast train (L₁) = 950 m

Time to cross (T) = 108 seconds

Formula Used:

Relative speed (same direction) = v₁ − v₂

Total distance = L₁ + L₂ = Relative speed × Time

Fast Train: 950 m

75 km/hr

Slow Train: L m

30 km/hr

Relative Speed = 75 − 30 = 45 km/hr

Calculations:

⇒ Relative speed = 75 − 30 = 45 km/hr

⇒ Convert km/hr to m/s: 45 × (5/18) = 12.5 m/s

⇒ Total Distance = 12.5 × 108 = 1350 m

⇒ Let the length of the slow train be L₂.

⇒ Total Distance = Length of fast train (L₁) + Length of slow train (L₂)

⇒ 1350 = 950 + L₂

⇒ L₂ = 1350 − 950 = 400 m

∴ The correct answer is 400 m.

Additional Information

Relative Speed in Opposite Directions

When two objects move in opposite directions, their relative speed is the sum of their individual speeds (v₁ + v₂).

Conversion of Speed Units

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

Trains Crossing a Stationary Object

When a train crosses a stationary object with length (like a platform or bridge), the total distance covered is the length of the train plus the length of the object.

Shortcut Trick Let the initial income be 100%, then initial savings = 23% and initial expenditure = 77%. New income = 100% + 27% = 127%. New expenditure = 77% + (50% of 77%) = 77% × 1.50 = 115.5%. New savings = 127% − 115.5% = 11.5%. Decrease in savings = 23% − 11.5% = 11.5% of the initial income. Decrease value = 11.5% of ₹75400 = (11.5 ÷ 100) × 75400 = ₹8671. ∴ The correct answer is decrease by ₹8671.

Alternate Method Given: Initial Income = ₹75400 Initial Savings % = 23% Income increase = 27% Expenditure increase = 50% Formula Used: Income = Expenditure + Savings

Original Income (100%)

Exp 77% Sav 23%

New Income (127%)

New Exp 115.5% Sav 11.5%

Decrease in Savings = 23% − 11.5% = 11.5% of Income

Calculations: ⇒ Initial Expenditure = (100% − 23%) of 75400 = 77% of 75400 = ₹58058 ⇒ Initial Savings = 23% of 75400 = ₹17342 ⇒ New Income = 75400 + (27% of 75400) = 75400 + 20358 = ₹95758 ⇒ New Expenditure = 58058 + (50% of 58058) = 58058 + 29029 = ₹87087 ⇒ New Savings = New Income − New Expenditure = 95758 − 87087 = ₹8671 ⇒ Change in Savings = Initial Savings − New Savings = 17342 − 8671 = ₹8671 ⇒ Since New Savings < Initial Savings, the total savings decreased by ₹8671. ∴ The correct answer is decrease by ₹8671.

Additional Information Income & Expenditure Concept Income is always equal to the sum of Expenditure and Savings. Any percentage change in overall income gets distributed between expenditure and savings based on their respective initial values. Percentage Change Formula Percentage Change = [(New Value − Initial Value) ÷ Initial Value] × 100. If the calculation yields a negative result, it clearly indicates a percentage decrease. Successive Percentage Changes When a value changes by a% and then further changes by b%, the net effective percentage change is evaluated as a + b + (a × b)÷100. This is highly useful for multi-stage problems.

Given:

Evaluate: 16 + 10 ÷ 5 - 2 × 4

Calculation:

Expression: 16 + 10 ÷ 5 - 2 × 4

⇒ 16 + (10 ÷ 5) - (2 × 4)

⇒ 16 + 2 - 8

⇒ 18 - 8 = 10

The correct answer is 10.

Shortcut Trick

Weight of Ram = (Sum of 2 overlapping groups) − (Total sum of all 3)

Weight of Ram = (39 × 2 + 49 × 2) − (46 × 3)

Weight of Ram = (78 + 98) − 138

Weight of Ram = 176 − 138 = 38

∴ The correct answer is 38 kg.

Alternate Method

Given:

Average weight of Mahesh, Ram, and Anwar = 46 kg

Average weight of Mahesh and Ram = 39 kg

Average weight of Ram and Anwar = 49 kg

Formula Used:

Total Value = Average × Number of entities

Mahesh + Ram + Anwar = 138 kg

Mahesh + Ram = 78 kg

Ram + Anwar = 98 kg

Overlap (Ram)

Calculations:

⇒ Total weight of Mahesh, Ram, and Anwar = 46 × 3 = 138 kg

⇒ Total weight of Mahesh and Ram = 39 × 2 = 78 kg

⇒ Total weight of Ram and Anwar = 49 × 2 = 98 kg

⇒ Sum of the two sub-groups = (Mahesh + Ram) + (Ram + Anwar) = 78 + 98 = 176 kg

⇒ Notice that in the sum above, Ram's weight is counted twice (Mahesh + 2 × Ram + Anwar = 176).

⇒ To find Ram's weight, subtract the total weight of all three distinct persons from this sum.

⇒ Weight of Ram = 176 − 138 = 38 kg

∴ The correct answer is 38 kg.

Additional Information

Average Concept

Average is defined as the sum of all observations divided by the total number of observations. Thus, Total Sum = Average × Number of Entities.

Overlapping Groups

When parts of a set overlap, adding the totals of the sub-groups causes the overlapping entity to be counted multiple times. Subtracting the total true sum of the set from the combined sub-groups isolates the value of the overlapping entity.

Weighted Average

To find the combined average of different groups without overlap, use the formula: Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Given:

Expression: \left[ (27 \times 3) \times \left{ 3 \div 3 \times \frac{(19 - 15)}{4} \right} \right]

Calculation:

\left[ (27 \times 3) \times \left{ 3 \div 3 \times \frac{(19 - 15)}{4} \right} \right]

⇒ \left[ (27 \times 3) \times \left{ 3 \div 3 \times \frac{4}{4} \right} \right]

⇒ \left[ (27 \times 3) \times \left{ 1 \times \frac{4}{4} \right} \right]

⇒ \left[ (27 \times 3) \times \left{ 1 \times 1 \right} \right]

⇒ $\left[ (27 \times 3) \times 1 \right]$

⇒ $\left[ 81 \times 1 \right]$

⇒ 81

∴ The value of the expression is 81.

Shortcut Trick

Effective Rate of Interest for 5 years = 9% × 5 = 45%.

So, 45% of Principal = ₹378

⇒ Principal = (378 ÷ 45) × 100

⇒ Principal = ₹840

∴ The correct answer is ₹840.

Alternate Method

Given:

Simple Interest (SI) = ₹378

Rate of interest (R) = 9% per annum

Time (T) = 5 years

Formula Used:

SI = (P × R × T) ÷ 100

Where P = Principal amount

Start P = ?

End

SI = ₹378 Time = 5 years Rate = 9% p.a. Total Interest = 45% of P = ₹378

Calculations:

By substituting the given values into the formula:

⇒ 378 = (P × 9 × 5) ÷ 100

⇒ 378 = (P × 45) ÷ 100

⇒ P = (378 × 100) ÷ 45

⇒ P = 37800 ÷ 45

⇒ P = 840

∴ The correct answer is ₹840.

Additional Information

Amount Formula

Total Amount = Principal + Simple Interest, or A = P × (1 + RT/100).

Compound Interest (CI)

Interest calculated on both the initial principal and the accumulated interest. A = P × (1 + R/100)^T.

Difference between CI and SI for 2 years

Difference = P × (R/100)². It is an important direct result for exam shortcuts.

Shortcut Trick

Using the property: Product of two numbers = LCM × HCF

⇒ Other Number = (LCM × HCF) ÷ Given Number

⇒ Other Number = (4158 × 54) ÷ 378

⇒ Other Number = 4158 ÷ 7 (since 378 ÷ 54 = 7)

⇒ Other Number = 594

∴ The correct answer is 594.

Alternate Method

Given:

LCM of the two numbers = 4158

HCF of the two numbers = 54

First number (N₁) = 378

Formula Used:

LCM × HCF = N₁ × N₂

Calculation:

⇒ 4158 × 54 = 378 × N₂

⇒ N₂ = (4158 × 54) ÷ 378

⇒ N₂ = (4158 × 54) ÷ (54 × 7)

⇒ N₂ = 4158 ÷ 7

⇒ N₂ = 594

∴ The correct answer is 594.

Additional Information

LCM and HCF of Fractions

LCM of fractions = LCM of Numerators ÷ HCF of Denominators. HCF of fractions = HCF of Numerators ÷ LCM of Denominators.

Co-prime Numbers

Two numbers are said to be co-prime if their HCF is 1. The LCM of two co-prime numbers is always equal to their product.

Product Rule Limitation

The standard formula (LCM × HCF = Product of numbers) is valid strictly for exactly two numbers. It does not hold true for three or more numbers.

Given:

2% of x = 276

Formula used:

2% of x = 276

Calculation:

2% of x = 276

⇒ $\dfrac{2}{100} \times x = 276$

⇒ $\dfrac{x}{50} = 276$

⇒ x = 276 × 50

⇒ x = 13800

∴ The correct answer is option (1).

Shortcut Trick

Net equivalent discount = A + B − (A × B) ÷ 100

⇒ Net discount = 30 + 20 − (30 × 20) ÷ 100 = 50 − 6 = 44%

Selling Price (SP) = 100% − 44% = 56% of Marked Price (MP)

⇒ 56% of Bill Amount = 840

⇒ Bill Amount = 840 × (100 ÷ 56) = 1500

∴ The correct answer is ₹1500.

Alternate Method

Given:

First discount (D₁) = 30%

Second discount (D₂) = 20%

Selling price (SP) = ₹840

Formula Used:

SP = MP × (1 − D₁/100) × (1 − D₂/100)

MP = ?

Inter. Price

SP = ₹840

−30%

−20%

MP × 0.7 × 0.8 = SP

Calculations:

⇒ 840 = MP × (1 − 30/100) × (1 − 20/100)

⇒ 840 = MP × (70/100) × (80/100)

⇒ 840 = MP × (7/10) × (8/10)

⇒ 840 = MP × (56/100)

⇒ MP = (840 × 100) ÷ 56

⇒ MP = 1500

∴ The correct answer is ₹1500.

Additional Information

Equivalent Discount

For two successive discounts of a% and b%, the single equivalent discount is given by [a + b − (a × b) ÷ 100]%.

Marked Price and Selling Price

Selling Price (SP) is the price paid by the customer after deducting the discount from the initial Marked Price (MP). SP = MP − Discount.

Successive Percentage Change

When a value is successively changed by x% and y%, the net percentage change is [x + y + (x × y) ÷ 100]%. For discounts, x and y are taken as negative values.

The correct answer is: Option 2 (Truce).

Key Points

• The word "Truce" refers to an agreement between opposing parties to stop fighting or arguing for a certain period. (युद्धविराम)
• Example: Both countries agreed to a truce to allow for peace negotiations.
• In the context of the sentence, "truce" is the most appropriate word because the meeting concluded on a temporary agreement, which is akin to a truce.

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

Additional Information

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

• Agenda (एजेंडा): A list of items to be discussed at a meeting.
• Example: The agenda for today's meeting includes budget planning and project updates.
• Fight (लड़ाई): A violent confrontation or struggle.
• Example: The fight between the two teams was intense and thrilling.
• Hot War (युद्ध): A conflict involving active military combat, as opposed to a cold war.
• Example: The region has been in a state of hot war for several years.

The correct answer is: Option 1 - An easy task.

Key Points

• The idiom "a piece of cake" means something that is very easy to do. (बहुत आसान)
• Example: Solving that math problem was a piece of cake for her because she is very good at math.
• In the given sentence, the use of the idiom refers to the fact that Jake and Emily found completing the project on time very easy.

​Therefore, the correct answer is: Option 1 - An easy task.

Additional Information

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

• Option 2 - A difficult task (कठिन कार्य): Something that requires a lot of effort or is hard to accomplish.
• Example: Climbing Mount Everest is a difficult task that requires years of preparation.
• Option 3 - Something enjoyable (आनंददायक): Something that provides happiness or pleasure.
• Example: Watching a comedy movie with friends is something enjoyable.
• Option 4 - Something annoying (परेशान करने वाला): Something that causes irritation or frustration.
• Example: The constant noise from the construction site is something annoying for the residents.

The correct answer is: Reject.

Key Points

• The word "Approbate" means to officially approve or sanction something. (स्वीकृत करना)
• Example: The committee approbated the new policy after thorough deliberation.
• "Reject" refers to the act of refusing to accept, believe, or approve something. (अस्वीकृत करना)
• Example: The board rejected the proposal due to insufficient evidence.
• Hence, we can infer that the opposite of 'approbate' is 'reject'.

Therefore, the correct answer is: Reject.

Additional Information

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

• Accept (स्वीकार करना): To consent to receive or agree to something.
• Example: She accepted the invitation to join the event.
• Permit (अनुमति देना): To allow something to happen or to give authorisation.
• Example: The teacher permitted the students to leave early.
• Supply (आपूर्ति करना): To provide something that is needed or desired.
• Example: The company supplies high-quality materials to construction firms.

The correct answer is: Option 1 (bite the bullet).

Key Points

• The idiom "bite the bullet" means to face a difficult or unpleasant situation with courage and determination. (मुश्किल या अप्रिय स्थिति का साहस और दृढ़ता के साथ सामना करना)
• Example: The athlete decided to bite the bullet and compete despite his injury.
• The sentence implies that the person faced their nervousness and delivered a fantastic speech, which aligns with the meaning of "bite the bullet."

Therefore, the correct answer is: Option 1 (bite the bullet).

Additional Information

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

• Option 2: Bite the tongue (अपनी जुबान पर काबू रखना): To stop yourself from saying something you want to say, often to avoid conflict or trouble.
• Example: She wanted to criticize her friend's decision but decided to bite her tongue.
• Option 3: Bite the dust (पराजित होना या मरना): To fail or be defeated, or to die.
• Example: Many startups bite the dust within their first year of operation.
• Option 4: Bite the pain (दर्द को सहन करना): This is not a standard idiom and does not fit the context of the sentence.

Question: Select the most appropriate idiom to substitute the underlined phrase in the given sentence.

The correct answer is: Option 1.

Key Points

• The word "queries" means questions or inquiries, especially those made to seek information or clarification. (प्रश्न)
• Example: The students asked several queries about the upcoming exam schedule.
• The correct word for the given context is "queries well", as it aligns with the teacher's role in resolving the students' doubts and questions effectively. (प्रश्नों का समाधान)
• Example: The teacher addressed the students' queries well during the interactive session.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Chapters slowly (अध्याय धीरे-धीरे): Refers to covering topics or lessons at a slow pace.
• Example: The teacher taught the chapters slowly to ensure every student understood the concepts.
• Solutions nicely (समाधान अच्छे से): Refers to providing answers or resolutions in a polite or pleasing manner.
• Example: He explained the solutions nicely to make them easier to understand.
• Parents respectfully (माता-पिता का आदरपूर्वक): Refers to interacting with parents in a respectful and courteous manner.
• Example: The teacher spoke to the parents respectfully during the parent-teacher meeting.

The correct answer is Option 1.

 

Key Points

• The phrase "I will have been studied" contains a grammatical error in the use of the verb form.
• For future perfect continuous tense, the correct structure is "will have been" + present participle (verb+ing), e.g., "will have been studying."
• The incorrect use of the past participle "studied" instead of "studying" violates the tense formation rules.
• Thus, the error is located in part 1 of the sentence.

Therefore, the correct answer is 1.

 

Correct Sentence: "At 6 p.m. tomorrow, I will have been studying for five hours straight."

 

Additional Information

• Part 4: "At 6 p.m. tomorrow," is a correct time phrase indicating a future reference point.
• Part 3: "for five hours straight." correctly expresses the duration of the action.
• No error option is incorrect as the sentence contains a clear tense error in part 1.

The correct answer is: Option 1 (Generous).

Key Points

• The word "stingy" refers to being unwilling to spend or share money or resources, often to an excessive degree. (कंजूस)
• Example: The stingy landlord refused to fix the broken heater despite repeated requests.
• "Generous" refers to someone who is willing to give or share freely, often more than expected or necessary. (उदार)
• Example: She is a generous donor who supports multiple charities.
• In the context of the sentence, the manager is "stingy" and does not appreciate the teammates. The opposite of "stingy" is "generous," which fits the sentence perfectly.

Therefore, the correct answer is: Option 1 (Generous).

Additional Information

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

• Aggressive (आक्रामक): Ready or likely to attack or confront; characterized by boldness or forcefulness.
• Example: The player was too aggressive and received a penalty for his actions.
• Strict (सख्त): Demanding that rules or standards are obeyed and observed.
• Example: The strict teacher ensured that all homework was submitted on time.
• Lazy (आलसी): Unwilling to work or use energy.
• Example: He is too lazy to clean his own room.

The correct answer is: Option 2 (Precarious).

Key Points

• The word "Precarious" means not securely held or in position; dangerously likely to fall or collapse. It also refers to a situation that is uncertain or risky. (अनिश्चित या खतरनाक स्थिति)
• Example: The climber was in a precarious position on the edge of the cliff.
• "Hazardous and perilous" indicates a dangerous or risky situation, which aligns perfectly with the meaning of "precarious." (अनिश्चित और जोखिमपूर्ण)

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

Additional Information

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

• Option 1: Guarded (सावधान): Cautious and reserved; not giving too much information or being careful about something.
• Example: She was guarded in her responses during the interview.
• Option 3: Reliable (विश्वसनीय): Something or someone you can depend on or trust.
• Example: He is a reliable friend who always helps in times of need.
• Option 4: Definite (स्पष्ट): Clearly stated or decided; not vague or doubtful.
• Example: We need a definite answer before proceeding with the project.

The correct answer is: Dull.

Key Points

• The word "Trenchant" means something that is very sharp, incisive, or forcefully effective, often used in the context of comments or arguments. (तीखा, प्रखर)
• Example: The critic’s trenchant review of the film highlighted its flaws with surgical precision.
• "Dull" refers to something that lacks sharpness or brightness, either literally or metaphorically, such as lacking intensity or excitement. (मंद, फीका)
• Example: The lecture was so dull that many students began to doze off.
• Hence, we can infer that the opposite of 'Trenchant' is 'Dull'.

Therefore, the correct answer is: Dull.

Additional Information

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

• Insightful (सूझ-बूझ वाला): Having or showing a deep understanding of something.
• Example: Her insightful comments during the debate impressed everyone.
• Acute (तीव्र, पैना): Extremely sharp or intense, often used to describe perceptions or conditions.
• Example: She has an acute sense of smell and can identify spices easily.
• Sharp (तेज, धारदार): Having a pointed edge or being keen in intellect or perception.
• Example: His sharp wit made him a popular speaker at events.

The correct answer is: Option 2 (Yielding).

Key Points

• The word "compliant" refers to someone or something that is willing to agree with others or obey rules. It describes a behavior that is accommodating, submissive, or conforming. (आज्ञाकारी)
• Example: The new employee was very compliant, following all instructions without hesitation.
• "Yielding" means being inclined to give way or comply with the wishes or demands of others. It denotes flexibility and an accommodating nature. (झुकनेवाला/समर्पणशील)
• Example: She had a yielding nature and was always ready to help her colleagues.
• Since "yielding" is a synonym for "compliant," it is the most appropriate choice.

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

Additional Information

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

• Difficult (कठिन): Something that is hard to deal with or does not yield easily to efforts.
• Example: The task was so difficult that it took hours to complete.
• Complaining (शिकायत करनेवाला): Frequently expressing dissatisfaction or annoyance about something.
• Example: He was always complaining about the food in the cafeteria.
• Adamant (जिद्दी): Refusing to be persuaded or to change one’s mind; stubborn or inflexible.
• Example: Despite the evidence, she remained adamant that her decision was correct.

The correct answer is: Option 2.

Key Points

• The word "Appropreately" is incorrectly spelt.
• The correct spelling is "Appropriately".
• Appropriately: It means in a manner suitable or proper in the circumstances. (उचित रूप से)
• Example: He was dressed appropriately for the formal dinner.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Analytically (विश्लेषणात्मक रूप से): In a way that involves detailed examination or analysis.
• Example: She approached the problem analytically to find the best solution.
• Apparently (जाहिर तौर पर): As far as one knows or can see; seemingly.
• Example: Apparently, he is not coming to the party tonight.
• Astonishingly (आश्चर्यजनक रूप से): In an astonishing or surprising manner.
• Example: The magician performed astonishingly well and left the audience amazed.

The correct answer is 'far-reaching'.

 

Key Points

• The collocation "far-reaching effect" means having a significant and extensive impact, especially over a long distance or time.
• In the given sentence, it refers to the CEO's influence that affects the future direction of the company, including global expansion.
• The other options do not collocate well with "effect" in this context:
• "grand effect" is not a common collocation.
• "broad effect" is less idiomatic than "far-reaching effect."
• "gorgeous effect" is inappropriate as "gorgeous" relates to appearance, not influence.

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

Complete Sentence: The CEO has a far-reaching effect on the future of the company, which includes global expansion.

Additional Information

• Grand: Usually describes something impressive in size or appearance, but does not commonly pair with "effect."
• Broad: Means wide in scope, but "broad effect" is less commonly used compared to "far-reaching effect."
• Gorgeous: Refers to something very beautiful, and is unrelated to the idea of influence or impact.

The correct answer is: Option 4.

Key Points

• The word "excruciating" means something that is intensely painful, either physically or emotionally. (बेहद पीड़ादायक)
• Example: The excruciating pain in his leg made it impossible for him to walk.
• The word "painful" refers to something that causes discomfort, distress, or suffering. (दर्दनाक)
• Example: It was a painful experience to recall those difficult moments from the past.
• Since the context of the sentence describes embarrassment and suffering, "painful" is the most appropriate synonym for "excruciating."

Therefore, the correct answer is: Option 4.

Additional Information

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

• Excited (उत्तेजित): Feeling very enthusiastic and eager.
• Example: She was excited to start her new job.
• Justified (सही ठहराया गया): Having a valid reason or explanation for something.
• Example: His anger was justified after being treated unfairly.
• Rational (तार्किक): Based on reason or logic.
• Example: He made a rational decision after carefully analyzing the situation.

The correct answer is Option 1.

 

Key Points

• The phrase "played rapidly" contains an error in adverbial usage.
• The verb "played" generally describes a leisurely or recreational activity, and the adverb "rapidly" (which means very fast) is inappropriate here.
• More suitable adverbs for "played" include "well," "happily," or "enthusiastically" depending on context.
• Thus, the error is located in part 1 of the sentence.

Therefore, the correct answer is 1.

 

Correct Sentence: "Michael and Robert played happily in the park near the apartment."

 

Additional Information

• Part 4: "Michael and Robert" correctly identifies the subjects of the sentence.
• Part 3: "in the park" correctly indicates the location where the action took place.
• Part 2: "near the apartment" correctly provides an additional location detail modifying "in the park."

The correct answer is: Option 3.

Key Points

• The word "Excited" means feeling or showing happiness and enthusiasm. (उत्साहित)
• Example: She was excited about her upcoming trip to Europe.
• The word "Receive" means to get or be given something. (प्राप्त करना)
• Example: He was thrilled to receive an award for his hard work.
• The word "Surprise" means something unexpected that causes amazement or wonder. (आश्चर्य)
• Example: The surprise party left him speechless.

Therefore, the correct answer is: Option 3.

Additional Information

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

• Option 1: "She was exicited to recieve a surprise gift from her friend on her birthday."
• Issue: The words "exicited" and "recieve" are misspelled. The correct spellings are "excited" and "receive". (उत्साहित और प्राप्त करना)
• Option 2: "She was excited to recieve a surprize gift from her friend on her birthday."
• Issue: The word "recieve" is misspelled; it should be "receive". Additionally, "surprize" is incorrect; the correct spelling is "surprise." (प्राप्त करना और आश्चर्य)
• Option 4: "She was exicited to recieve a surprize gift from her freind on her birthday."
• Issue: Multiple errors: "exicited" should be "excited," "recieve" should be "receive," "surprize" should be "surprise," and "freind" should be "friend." (उत्साहित, प्राप्त करना, आश्चर्य, मित्र)

The correct answer is 'in'.

 

Key Points

• The phrase "the sinking of the passenger-and-car ferry Estonia (1) ____ the Baltic" requires a preposition that indicates location or area where the sinking happened.
• "In the Baltic" is the correct collocation because it refers to the ferry sinking within the Baltic Sea.
• Other options such as "on the Baltic," "over the Baltic," and "up the Baltic" do not correctly describe the location in this maritime context.
• "On" typically refers to surfaces (e.g., "on the lake") but is less appropriate for naming seas; "over" implies movement above something; "up" implies direction, none of which fit the sentence meaning.

Therefore, the correct answer is 'Option 3'.

 

Complete Passage: Naval architects never claim that a ship is unsinkable, but the sinking of the passenger-and-car ferry Estonia in the Baltic surely (2) ______ never have happened. It was well designed and (3) ______ maintained. It carried the proper number of lifeboats. It (4)______ thoroughly inspected on the day of its fatal voyage. Yet hours later, the Estonia rolled over and (5) _______ in a cold and stormy night.

The correct answer is 'should'.

 

Key Points

• The phrase "surely (2) ______ never have happened" requires a modal verb that expresses strong certainty or expectation that the event should not have occurred.
• "Should never have happened" conveys a sense of expectation or moral obligation that the sinking was avoidable or ought not to have taken place.
• "Could," "might," and "would" express possibility or hypothetical situations, but lack the strong tone of certainty and expectation implied here.
• "Should" fits best to emphasize that the sinking was not expected or supposed to happen given the ship's design and maintenance.

Therefore, the correct answer is 'Option 4'.

 

Complete Passage: Naval architects never claim that a ship is unsinkable, but the sinking of the passenger-and-car ferry Estonia in the Baltic surely should never have happened. It was well designed and (3) ______ maintained. It carried the proper number of lifeboats. It (4)______ thoroughly inspected on the day of its fatal voyage. Yet hours later, the Estonia rolled over and (5) _______ in a cold and stormy night.

The correct answer is 'carefully'.

 

Key Points

• The phrase "It was well designed and (3) ______ maintained" requires an adverb that reflects positive, attentive maintenance.
• "Carefully" fits appropriately because it means maintenance done with attention and diligence, matching the positive context.
• "Awkwardly," "carelessly," and "haphazardly" imply negative or negligent maintenance, which contradicts the passage's emphasis on proper care.
• The passage highlights the ship's good design and proper lifeboat provision, supporting that the maintenance was done properly.

Therefore, the correct answer is 'Option 2'.

 

Complete Passage: Naval architects never claim that a ship is unsinkable, but the sinking of the passenger-and-car ferry Estonia in the Baltic surely should never have happened. It was well designed and carefully maintained. It carried the proper number of lifeboats. It (4)______ thoroughly inspected on the day of its fatal voyage. Yet hours later, the Estonia rolled over and (5) _______ in a cold and stormy night.

The correct answer is 'was'.

 

Key Points

• The sentence "It (4)______ thoroughly inspected on the day of its fatal voyage" requires the correct past tense passive form of the verb "inspect."
• "Was" is the correct auxiliary verb for simple past passive voice, fitting the sentence structure "was thoroughly inspected."
• "Has been" is present perfect passive, which is not suitable since the event happened in the past at a specific time.
• "Was been" is grammatically incorrect and does not exist in English.
• "Have been" is present perfect plural and incorrect here because the subject is singular ("It").

Therefore, the correct answer is 'Option 4'.

 

Complete Passage: Naval architects never claim that a ship is unsinkable, but the sinking of the passenger-and-car ferry Estonia in the Baltic surely should never have happened. It was well designed and carefully maintained. It carried the proper number of lifeboats. It was thoroughly inspected on the day of its fatal voyage. Yet hours later, the Estonia rolled over and (5) _______ in a cold and stormy night.

The correct answer is 'sank'.

 

Key Points

• The phrase "the Estonia rolled over and (5) _______ in a cold and stormy night" describes the final tragic event of the ferry.
• "Sank" is the correct verb to describe a ship going down below water.
• "Improved," "marched," and "upgraded" do not fit contextually or logically with the description of a ship's sinking.
• "Sank" is the past tense of "sink," which perfectly completes the description of the ship's fate.

Therefore, the correct answer is 'Option 4'.

 

Complete Passage: Naval architects never claim that a ship is unsinkable, but the sinking of the passenger-and-car ferry Estonia in the Baltic surely should never have happened. It was well designed and carefully maintained. It carried the proper number of lifeboats. It was thoroughly inspected on the day of its fatal voyage. Yet hours later, the Estonia rolled over and sank in a cold and stormy night.

सही उत्तर है - बहुत स्वादिष्ट

Key Points

• अशुद्ध वाक्य - दीपावली के अवसर पर बने सारे पकवान खाने में बहुत अच्छे लगते हैं।
• दिए गये वाक्य में शब्द-अर्थ प्रयोग की त्रुटि है,
• ​यहाँ 'खाने में बहुत अच्छे**'** सार्थक शब्द नहीं है और इससे सही अर्थ प्रकट नहीं हो रहा।
• ​अत: सार्थक शब्द 'बहुत स्वादिष्ट' होना चाहिए।
• शुद्ध वाक्य -  दीपावली के अवसर पर बने सारे पकवान बहुत स्वादिष्ट लगते हैं।

Additional Information 

  शब्द-अर्थ संबंधी अशुद्धियाँ - 

'प्रेम' का विलोम शब्द है - घृणा

Key Points

• 'प्रेम' शब्द का विलोम शब्द 'घृणा' होगा।
• 'प्रेम' का अर्थ- प्रीति, प्यार, स्नेह।
• 'घृणा' का अर्थ- नफ़रत, घिन।
• विलोम - जो शब्द किसी एक शब्द के विपरीत अर्थ को व्यक्त करते हैं, वे विलोम शब्द कहलाते हैं।

अन्य विकल्प-

Additional Information 

  कुछ अन्य महत्वपूर्ण विलोम शब्द -