Given:

Seven people, E, F, G, H, K, L and M, are sitting in a row, facing north.

Only two people sit to the right of G. Only two people sit between G and L.

Only two people sit between E and M. M sits to the immediate left of G.

H sits to the immediate right of K.

Thus, F sits at the third position from the left end of the line.

Hence, the correct answer is "Option 4".

The pattern followed here is:

Logic: 

 and 

 moving anti-clockwise direction, skipping one block.

Hence, the correct answer is "Option 3".

The logic followed here is:

Option (1): OQN

Option (2): HJG

Option (3): YXV

Option (4): MOL

The letter-cluster that DOES NOT belong to the group is: YXV

Hence, the correct answer is "Option 3".

Given word:

LANGUID

First, we arrange the letters of the word LANGUID in English alphabetical order.

The letters are: L, A, N, G, U, I, D

Arranged in alphabetical order, the new cluster is: A D G I L N U.

We identify the letter which is third from the left end and the one which is first from the right end.

The third letter from the left end is G.

The first letter from the right end is U.

The letters between G and U are: H, I, J, K, L, M, N, O, P, Q, R, S, T.

Thus, there are 13 letters.

Hence, the correct answer is "Option 4".

The logic followed here is:​

For 'ESAW' related to 'GVCZ':

For 'TIPD' related to 'VLRG':

 

Applying the same logic to 'XUNC':

Thus, 'XUNC' will be coded as ZXPF.

Hence, the correct answer is "Option 2".

The logic followed here is:

Hence, the correct answer is "Option 2".

The least possible venn diagram is:

Conclusions:

(I): Some apples are cucumbers → False (As, there is no direct relation between apples and cucumbers. so it can be a possibility)

(II): Some beans are carrots → True (As,  All cucumbers are carrots, All cucumbers are beans. so, Some beans are carrots holds true)

Thus, Only conclusion (II) follows.

Hence, the correct answer is "Option 2".

The paper look when unfolded:

Hence, the correct answer is "Option 3".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 2".

The logic followed here is:​

For 'RN 20' related to 'SI 4':

For 'MK 5' related to 'NF -11':

Applying the same logic to 'QV 3':

Thus, QV 3 is related to RQ -13.

Hence, the correct answer is "Option 3".

The logic followed here is:

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: Total number of letter × 4 = Number.

For 'MCOPT' is coded as '20' 

Total letters is 5

5 × 4 = 20

For  'VSB' is coded as '12'

Total letters is 3

3 × 4 = 12

Similarly,

For 'JIGETY'

Total letters is 6

6 × 4 = 24.

Hence, the correct answer is "Option 3".

Given:

Pizza, Pasta, and Noodles are all considered types of food, but they are distinct from each other.

Hence, the correct answer is "Option 4".

The logic followed here is:

Thus, 'PML' will be the next in the series.

Hence, the correct answer is "Option 1".

The given dice:

As T is common in both the dice then moving clockwise or anti-clockwise direction from T we get opposite pairs.

Opposite pairs

P ⇔ A

M ⇔ D

T ⇔ I

This, T is opposite to I.

Hence, the correct answer is "Option 2".

Given:

Six people, B, C, D, E, F and S, are sitting in a row facing north.

Only two people sit to the left of S. Only two people sit between S and F.

Only one person sits between F and C. D sits to the immediate left of E.

Thus, One person sits to the right of B.

Hence, the correct answer is "Option 2".

The logic followed here

Given Series: _XRLQ_PJOT_HMRL_ KPJ_

Option 1 (SVNFD) by sequentially placing its letters in the blanks:

Resulting series: SXRL QV PJ OTNH MRLF KPJD

Hence, the correct answer is "Option 1".

The given code language is:

Thus, 'K' is coded as '0'.

Hence, the correct answer is "Option 1".

BODMAS Rule:

The given equation is:

50 × 3 + 12 × 5 – (66 ÷ 2) + 11 × 4 – 22 = 160

1) Interchange 22 and 2

New Equation: 50 × 3 + 12 × 5 – (66 ÷ 22) + 11 × 4 – 2 = ?

⇒ 50 × 3 + 12 × 5 – (66 ÷ 22) + 11 × 4 – 2

⇒ 150 + 60 – 3 + 44 – 2

⇒ 210 – 3 + 44 – 2

⇒ 207 + 44 – 2

⇒ 251 – 2   

⇒ 249 ≠ 160 (Incorrect)

2) Interchange 5 and 3

New Equation: 50 × 5 + 12 × 3 – (66 ÷ 2) + 11 × 4 – 22 = ?

⇒ 50 × 5 + 12 × 3 – (66 ÷ 2) + 11 × 4 – 22

⇒ 250 + 36 – 33 + 44 – 22

⇒ 286 – 33 + 44 – 22

⇒ 253 + 44 – 22

⇒ 297 – 22   

⇒ 275 ≠ 160 (Incorrect)

3) Interchange 12 and 11

New Equation: 50 × 3 + 11 × 5 – (66 ÷ 2) + 12 × 4 – 22 = ?

⇒ 50 × 3 + 11 × 5 – (66 ÷ 2) + 12 × 4 – 22

⇒ 150 + 55 – 33 + 48 – 22

⇒ 205 – 33 + 48 – 22

⇒ 172 + 48 – 22

⇒ 220 – 22   

⇒ 198 ≠ 160 (Incorrect)

4) Interchange 3 and 2

New Equation: 50 × 2 + 12 × 5 – (66 ÷ 3) + 11 × 4 – 22 = ?

Perform operations according to BODMAS:

⇒ 50 × 2 + 12 × 5 – (66 ÷ 3) + 11 × 4 – 22

⇒ 100 + 60 – 22 + 44 – 22

⇒ 160 – 22 + 44 – 22 

⇒ 138 + 44 – 22   

⇒ 182 – 22

⇒ 160

160 = 160 (Correct)

Hence, the correct answer is "Option 4".

Given Expression: U * F - L # M

U * F: U is the mother of F.

F - L: F is the father of L.

L # M: L is the brother of M.

According to the given information Family Tree Representation:

Thus, L is the Grandson (Son's son) of U.

Hence, the correct answer is "Option 3"

The correct answer is Atishi Marlena.

Key Points

• Atishi Marlena took charge as the Chief Minister of Delhi in September 2024, succeeding Arvind Kejriwal.
• She is a prominent member of the Aam Aadmi Party (AAP) and has been a key figure in Delhi's politics.
• Atishi has been recognized for her contributions to education reforms in Delhi, including the transformation of government schools.
• Her appointment marks a significant milestone, as she is the first woman Chief Minister of Delhi from the AAP.
• She played a crucial role in the conceptualization and implementation of initiatives like the "Happiness Curriculum" in schools.

Additional Information

• Delhi's Administrative Framework
• Delhi is a Union Territory with a Legislative Assembly, and its Chief Minister oversees areas such as education, health, and public works.
• However, certain powers such as law enforcement fall under the jurisdiction of the Lieutenant Governor.
• Aam Aadmi Party (AAP)
• AAP was founded in 2012 by Arvind Kejriwal and others, focusing on anti-corruption and governance reforms.
• The party has been in power in Delhi since 2015, with significant focus areas such as education, healthcare, and public welfare.
• Education Reforms in Delhi
• Under AAP’s governance, Delhi saw major overhauls in its education system, including infrastructure improvements and teacher training programs.
• Initiatives like the "Happiness Curriculum" and "Entrepreneurship Mindset Curriculum" have garnered international attention.
• Women in Leadership
• Atishi's appointment as Chief Minister adds to the growing number of women in leadership roles in Indian politics.
• Her leadership is expected to inspire more women to enter public administration and governance.

The correct answer is three.

Key Points

• The FIFA U-17 Women's World Cup 2022 was hosted by India from October 11 to October 30, 2022.
• The tournament matches were held at three venues across the country: Bhubaneswar (Kalinga Stadium), Goa (Pandit Jawaharlal Nehru Stadium, Fatorda), and Navi Mumbai (DY Patil Stadium).
• This was the seventh edition of the FIFA U-17 Women's World Cup and the first time India hosted the tournament.
• A total of 16 teams participated in the event, including India as the host nation.
• The tournament aims to provide a platform to showcase young female football talent globally, promoting women's football.

Additional Information

• FIFA U-17 Women's World Cup:
• It is an international football competition organized by FIFA for female players under the age of 17.
• The tournament began in 2008 and is held every two years.
• The 2022 edition marked the first time India hosted the tournament, underscoring its growing importance in global women's football.
• Host Venues in India (2022):
• Kalinga Stadium, Bhubaneswar: A prominent venue in Odisha known for hosting major sporting events.
• Pandit Jawaharlal Nehru Stadium, Fatorda: Located in Goa, it is one of the best football stadiums in India.
• DY Patil Stadium, Navi Mumbai: A multi-purpose stadium that has hosted several international sports events.
• Women's Football Development:
• The tournament promotes the development of women's football globally by providing a platform for young players.
• FIFA and host nations also organize grassroots programs to encourage local participation in women's football.
• India's Participation:
• As the host nation, India automatically qualified for the tournament.
• This was a significant opportunity to showcase Indian women's football talent on a global stage.

The correct answer is Nagaland.

Key Points

• Bushu, Yemshe, and Tokhu Emong are major cultural festivals celebrated by the tribal communities of Nagaland.
• Tokhu Emong is celebrated by the Lotha Naga tribe as a post-harvest festival to mark the end of the agricultural season.
• Bushu is a festival of the Kachari tribe, celebrated to mark the end of the paddy cultivation cycle.
• Yemshe is observed by the Pochury tribe as a harvest festival, signifying a time of joy and thanksgiving.
• Nagaland is known as the ‘Land of Festivals’ due to its diverse tribal communities, each having unique cultural practices and traditions.

Additional Information

• Nagaland's Tribal Diversity
• Nagaland is home to 16 major tribes, including Ao, Angami, Sumi, Lotha, Chakhesang, and Konyak tribes, among others.
• Each tribe has its unique dialect, attire, customs, and festivals, contributing to the state's rich cultural heritage.
• Hornbill Festival
• This is the most famous cultural festival of Nagaland, celebrated annually in December.
• It showcases the cultural vibrancy of all tribes and is often referred to as the ‘Festival of Festivals’.
• The festival includes traditional dance, music, handicrafts, and cuisine, attracting tourists from around the world.
• Geography of Nagaland
• Nagaland is located in Northeast India and shares its borders with Assam, Arunachal Pradesh, Manipur, and Myanmar.
• Kohima is the state capital, while Dimapur is the largest city and a major commercial hub.
• Traditional Practices
• Many festivals in Nagaland are closely linked to agricultural cycles, emphasizing the importance of farming in their livelihood.
• Traditional attire, dances, and songs during festivals reflect the deep-rooted cultural identity of the tribes.

The correct answer is Palaeolithic.

Key Points

• Ostrich fossils and eggshell fragments have been discovered in several archaeological sites across India, particularly in the Palaeolithic period.
• Evidence of ostriches in India has been primarily found in regions such as Rajasthan, Gujarat, and Madhya Pradesh.
• These fossils suggest that ostriches were once a part of the Indian subcontinent's fauna during the late Pleistocene epoch.
• The Palaeolithic period, which spans from approximately 2.5 million years ago to 10,000 years ago, is marked by the use of stone tools and the emergence of early human behavior.
• Ostrich remains in India have been studied using radiocarbon dating and other scientific methods to establish their Palaeolithic context.

Additional Information

• Palaeolithic Period:
• The Palaeolithic period is also known as the Old Stone Age.
• It is characterized by the use of crude stone tools and the subsistence lifestyle of hunter-gatherers.
• This period is divided into three phases: Lower, Middle, and Upper Palaeolithic.
• Ostrich Evidence in India:
• Ostrich eggshells and fossilized bones have been unearthed in sites such as Bhimbetka and Patne in India.
• These findings indicate the presence of ostriches in the Indian subcontinent during the Pleistocene epoch.
• Scientific Techniques Used:
• Techniques such as radiocarbon dating and isotopic analysis are used to analyze ostrich remains.
• These methods help determine the age and environmental conditions of the period.
• Pleistocene Epoch:
• The Pleistocene epoch (2.58 million to 11,700 years ago) is a geological timeframe that witnessed significant climatic changes and the evolution of early humans.
• It coincides with the Palaeolithic period in archaeological terms.

The correct answer is Anahat Singh.

Key Points

• Anahat Singh, a 15-year-old squash player, became the youngest medalist for India at the Asian Games 2023.
• She won a bronze medal in the women’s squash team event, showcasing her exceptional talent at a young age.
• Anahat Singh has previously gained recognition at international levels, including winning the Asian Junior Squash Championship.
• Her contribution to the Indian squash team was pivotal in securing a medal at the prestigious event held in Hangzhou, China.
• Anahat’s achievement highlights the rise of young athletes in India, especially in sports like squash, which are gaining prominence.

Additional Information

• Asian Games 2023:
• The 19^th edition of the Asian Games was held in Hangzhou, China from 23 September to 8 October 2023.
• India achieved its best-ever medal tally at the event, securing 107 medals, including 28 golds, 38 silvers, and 41 bronzes.
• It was a landmark event for Indian sports, with new records set in athletics, shooting, and other disciplines.
• Squash in India:
• Squash is an emerging sport in India, with players like Saurav Ghosal and Joshna Chinappa paving the way for young talents.
• The Squash Rackets Federation of India (SRFI) governs the sport in the country.
• India has consistently performed well in squash at the Asian Games, winning medals across multiple editions.
• Youth in Indian Sports:
• India has witnessed a surge in young athletes competing at international levels in various sports.
• Programs such as the Khelo India initiative aim to nurture young talent and provide them with opportunities to excel.
• Talented young players like Anahat Singh and Neeraj Chopra symbolize the bright future of Indian sports.
• Asian Games History:
• The Asian Games, also known as Asiad, is a continental multi-sport event organized by the Olympic Council of Asia.
• The first Asian Games were held in 1951 in New Delhi, India.
• It is held every four years, showcasing the top athletes from across Asia.

The correct answer is Butane.

Key Points

• Butane is a straight-chain alkane composed of 4 carbon atoms (C4H10).
• It is commonly used as a fuel in lighters and as an aerosol propellant in various industries.
• Butane is a highly flammable hydrocarbon gas and is part of the liquefied petroleum gas (LPG) used for cooking and heating.
• It exists in two structural isomers: n-butane (straight chain) and isobutane (branched chain), but the question refers specifically to the straight-chain form.
• Due to its energy density and portability, butane is widely used in both industrial and household applications.

Additional Information

• Alkanes:
• Alkanes are saturated hydrocarbons containing only single bonds between carbon atoms.
• They follow the general formula CnH2n+2, where "n" represents the number of carbon atoms.
• Examples of alkanes include methane (CH4), ethane (C2H6), and propane (C3H8).
• Liquefied Petroleum Gas (LPG):
• LPG is a mixture of hydrocarbons, primarily propane and butane.
• It is used as a fuel for cooking, heating, and in vehicles.
• LPG is stored under pressure in liquid form and vaporizes when released.
• Aerosol Propellants:
• Butane is widely used as a propellant in aerosol sprays due to its flammability and ability to vaporize quickly.
• It is used in products like deodorants, air fresheners, and spray paints.
• Isomers of Butane:
• Butane has two isomers: n-butane (straight chain) and isobutane (branched chain).
• Isobutane is used in the petrochemical industry to produce high-octane gasoline components.

The correct answer is 0.086.

Key Points

• As per Census 2011, the percentage of Scheduled Tribes (ST) in India’s total population was 8.6%.
• The total Scheduled Tribe population in India was approximately 10.45 crore out of the total population of 121 crore.
• Scheduled Tribes are officially recognized indigenous communities in India, identified under Article 342 of the Indian Constitution.
• Madhya Pradesh has the largest population of Scheduled Tribes in India, followed by Maharashtra and Odisha.
• Among the states, Lakshadweep has the highest proportion of Scheduled Tribe population at 94.8%.

Additional Information

• Definition of Scheduled Tribes: Scheduled Tribes are socio-economically disadvantaged indigenous groups that have been granted constitutional recognition and protection under Article 342 of the Constitution of India.
• Reservation Policy: Scheduled Tribes benefit from reservation in education, employment, and political representation to promote their development and inclusion.
• Tribal Sub-Plan (TSP): TSP is a strategy adopted by the Indian government to allocate funds and resources specifically for the socio-economic development of tribal communities.
• Geographical Distribution: Scheduled Tribes are primarily concentrated in central, northeastern, and southern regions of India, including states like Madhya Pradesh, Odisha, Chhattisgarh, and Jharkhand.
• Notable Tribes: Some of the prominent Scheduled Tribes in India include the Gond, Bhil, Santhal, Oraon, and Khasi tribes.

The correct answer is Writs Issuing powers.

Key Points

• The Governor of a state in India does not have the power to issue writs. Writ-issuing powers are exclusively vested in the Supreme Court and High Courts under Articles 32 and 226 of the Indian Constitution, respectively.
• The writs include Habeas Corpus, Mandamus, Prohibition, Certiorari, and Quo Warranto, designed to ensure the protection of fundamental rights and maintain justice.
• Governors exercise various powers, including Legislative, Financial, Executive, and Discretionary powers, but lack judicial powers like issuing writs.
• Writ jurisdiction is a crucial judicial function and cannot be delegated to executive authorities like the Governor.
• This separation of powers ensures checks and balances in governance, safeguarding the independence of the judiciary.

Additional Information

• Article 32:
• Known as the "Right to Constitutional Remedies," it empowers the Supreme Court to issue writs to enforce fundamental rights.
• It is considered the heart and soul of the Indian Constitution, as stated by Dr. B.R. Ambedkar.
• Article 226:
• Empowers High Courts to issue writs for the enforcement of fundamental rights as well as other legal rights.
• The scope of writ jurisdiction under Article 226 is broader than under Article 32.
• Governor's Powers:
• Legislative Powers: Includes summoning, proroguing, and dissolving the state legislature and reserving bills for the President.
• Financial Powers: Includes ensuring the presentation of the state budget and recommending money bills.
• Discretionary Powers: Includes decision-making in cases such as hung assemblies or reserved bills.
• Judiciary's Independence:
• The judiciary in India is an independent body, separate from the executive and legislative branches.
• This ensures the fair and impartial administration of justice and the protection of constitutional rights.

The correct answer is Primary Industry.

Key Points

• Primary industries focus on the extraction and harvesting of natural resources directly from nature, such as agriculture, forestry, fishing, and mining.
• These industries operate with minimal human intervention and rely heavily on natural processes.
• Examples include farming, logging, fishing, and mineral extraction, which form the base for secondary and tertiary industries.
• Primary industries are integral to the economy as they provide raw materials for manufacturing and other industrial sectors.
• They are characterized by their direct interaction with nature, making them highly dependent on environmental conditions and sustainability practices.

Additional Information

• Types of Industries:
• Primary Industry: Focuses on the extraction of natural resources (e.g., agriculture, fishing, forestry).
• Secondary Industry: Involves manufacturing and processing of raw materials into finished goods.
• Tertiary Industry: Provides services such as retail, transportation, and healthcare.
• Quaternary Industry: Focuses on knowledge-based services, including information technology, research, and consultancy.
• Natural Resources:
• Materials provided by nature that are used in economic activities, such as water, minerals, forests, and soil.
• Renewable resources (e.g., solar energy, wind energy) can replenish naturally, while non-renewable resources (e.g., fossil fuels, metals) are finite.
• Environmental Dependency:
• Primary industries depend heavily on environmental factors like climate, soil fertility, and water availability.
• Sustainable practices are crucial to ensure long-term viability and prevent resource depletion.
• Role in Economy:
• Primary industries are foundational to the economy, providing essential inputs for secondary and tertiary sectors.
• They contribute significantly to employment, especially in rural areas, and are critical for food security and resource supply.

The correct answer is Third Plan.

Key Points

• The Third Five-Year Plan (1961-1966) aimed to achieve self-reliance in food production and industrial growth in India.
• This plan was interrupted due to the Indo-China War of 1962 and the Indo-Pak War of 1965, causing economic turmoil.
• The government shifted focus from planned economic development to defense and emergency management.
• Severe droughts in 1965-1966 also further disrupted the objectives of the plan, leading to a crisis in agricultural production.
• The economic challenges during this period necessitated a deviation from the planned targets and resulted in the introduction of annual plans or "Plan Holidays" from 1966 to 1969.

Additional Information

• Five-Year Plans in India
• India's Five-Year Plans were a series of centralized economic and social development strategies implemented from 1951 to 2017.
• The Planning Commission was responsible for formulating these plans until its replacement by the NITI Aayog in 2015.
• The plans aimed to boost economic growth, improve the standard of living, and address social inequalities.
• Plan Holidays (1966-1969)
• Plan Holidays were introduced after the Third Five-Year Plan due to financial constraints caused by wars and droughts.
• During this period, the government adopted annual plans to address short-term goals and stabilize the economy.
• Impact of Indo-Pak War on Economy
• The 1965 Indo-Pak War strained India's financial resources, diverting funds from developmental activities to defense expenditures.
• It disrupted trade and led to inflation, further complicating economic recovery efforts.
• Green Revolution
• The Green Revolution, initiated in the late 1960s, was a response to the agricultural crisis during the Third Plan era.
• It focused on high-yield crop varieties, modern irrigation techniques, and the use of fertilizers to increase agricultural productivity.

The correct answer is Ram Nath Kovind.

Key Points

• The Union Cabinet approved the One Nation, One Poll recommendations proposed by a committee led by former President Ram Nath Kovind in September 2023.
• This initiative seeks to synchronize the timing of Lok Sabha and State Assembly elections to reduce the frequency of elections and associated costs.
• The government formed the committee under Ram Nath Kovind's chairmanship to examine the feasibility of implementing the "One Nation, One Poll" policy.
• The proposal aims to enhance administrative efficiency, reduce the burden on security forces, and ensure seamless governance by avoiding frequent imposition of the Model Code of Conduct.
• The committee includes legal experts, political leaders, and representatives from various government bodies to ensure the recommendations are comprehensive and inclusive.

Additional Information

• One Nation, One Poll:
• This concept refers to holding simultaneous elections for the Lok Sabha, State Legislative Assemblies, and local bodies across the country.
• It aims to reduce election-related expenses and frequent disruptions to development activities caused by repeated imposition of the Model Code of Conduct.
• The idea was first proposed during the tenure of Prime Minister Atal Bihari Vajpayee and has been discussed multiple times in recent years.
• Committee Formation:
• In 2023, the Union Government set up a high-level committee under the chairmanship of Ram Nath Kovind to deliberate on the feasibility of implementing this electoral reform.
• The committee includes members from political parties, legal experts, and representatives from the Election Commission of India (ECI).
• Advantages of One Nation, One Poll:
• Reduction in the cost of conducting frequent elections.
• Minimization of policy paralysis and disruptions in governance caused by repeated elections.
• Streamlining of security personnel deployment and efficient management of resources.
• Challenges:
• Constitutional amendments are required to synchronize the terms of various legislative bodies.
• Political consensus is necessary to implement the reform successfully.
• Logistical challenges such as voter education, preparedness of the Election Commission, and managing simultaneous elections on a large scale.

The correct answer is Tropical.

Key Points

• Tropical climate zones are characterized by hot and humid conditions throughout the year.
• They are located near the Equator, between the Tropic of Cancer and Tropic of Capricorn.
• These regions receive a high amount of solar radiation, resulting in consistently warm temperatures and minimal seasonal variation.
• Tropical zones experience significant rainfall due to their proximity to Intertropical Convergence Zones (ITCZ), which facilitates frequent precipitation.
• Examples of tropical climates include the Amazon rainforest, the Congo Basin, and Southeast Asia.

Additional Information

• Intertropical Convergence Zone (ITCZ)
• A region near the Equator where trade winds converge, leading to frequent thunderstorms and heavy rainfall.
• The ITCZ shifts seasonally, influencing precipitation patterns in tropical regions.
• Rainforest Ecosystem
• Tropical rainforests are characterized by high biodiversity, with millions of species of plants, animals, and microorganisms.
• They serve as the Earth's lungs by producing oxygen and absorbing carbon dioxide.
• Temperature Range
• In tropical climates, the average monthly temperature typically stays above 18°C (64°F) year-round.
• This contrasts with other climate zones where seasonal temperature variations are more pronounced.
• Subtypes of Tropical Climate
• Tropical rainforest climate: High rainfall throughout the year.
• Tropical monsoon climate: Seasonal shifts between wet and dry periods.
• Tropical savanna climate: Wet summers and dry winters.

The correct answer is biome.

Key Points

• A biome is a large geographic area characterized by specific climatic conditions, flora, and fauna.
• Biomes are classified based on their distinct ecosystems, such as forests, deserts, grasslands, tundra, and aquatic environments.
• Factors like temperature, precipitation, altitude, and latitude play a significant role in determining the type of biome.
• Examples of biomes include the Amazon rainforest (tropical rainforest biome) and the Sahara Desert (desert biome).
• Unlike ecosystems, which focus on interactions within a smaller area, biomes represent broader climatic and ecological patterns.

Additional Information

• Ecosystem
• An ecosystem is a community of living organisms in conjunction with non-living components like air, water, and soil.
• It focuses on the interactions and energy flow between biotic (living) and abiotic (non-living) components within a specific area.
• Examples include ponds, forests, coral reefs, and grasslands.
• Biosphere
• The biosphere is the global sum of all ecosystems and includes all life forms on Earth.
• It extends to the atmosphere, lithosphere, and hydrosphere where living organisms exist.
• The biosphere supports life by cycling nutrients, water, and energy.
• Climate
• Climate refers to the long-term average weather conditions in a particular region.
• It is determined by factors like temperature, humidity, wind patterns, and precipitation over decades.
• Climate greatly influences the type of biome that forms in a specific area.
• Organism
• An organism is any individual living entity, such as a plant, animal, fungus, or microbe.
• Organisms are the basic unit of life in biology, interacting within ecosystems and biomes.
• They adapt to their environment to survive and reproduce.

The correct answer is Assam.

Key Points

• Garima Hazarika is a well-known exponent of the classical Indian dances, Sattriya and Odissi.
• The Sattriya dance form is native to the state of Assam and has significant cultural and religious importance.
• Garima Hazarika has received the prestigious Sangeet Natak Akademi Award for her contributions to Indian classical dance.
• She is recognized for her efforts in promoting and preserving Assam's Sattriya dance, which was introduced by the Vaishnavite saint Srimanta Sankardeva.
• Hazarika has been a prominent figure in showcasing Assamese culture on national and international platforms.

Additional Information

• Sattriya Dance
• Sattriya is one of the eight classical dance forms of India and originates from Assam.
• It was introduced in the 15^th century by the saint-scholar Srimanta Sankardeva as a medium of religious expression.
• Sattriya is performed in monasteries called Satras and often narrates mythological stories.
• In 2000, Sattriya was recognized as a classical dance form by the Sangeet Natak Akademi.
• Odissi Dance
• Odissi is one of the oldest surviving dance forms, originating from the state of Odisha.
• It is characterized by its graceful and lyrical movements, expressing devotion to Lord Jagannath and other deities.
• Key features include tribhangi (three-bend posture) and intricate hand gestures called mudras.
• Odissi has a deep connection with temple rituals and is performed as an offering to gods and goddesses.
• Sangeet Natak Akademi
• It is India's national academy for music, dance, and drama, established in 1953.
• The Akademi recognizes and promotes the performing arts through awards, scholarships, and fellowships.
• The Sangeet Natak Akademi Award is one of the highest honors for artists in the field of performing arts in India.
• Srimanta Sankardeva
• He was a 15^th-century saint-scholar, social reformer, and cultural icon of Assam.
• Sankardeva is credited with the creation of Sattriya dance and the establishment of the Neo-Vaishnavite movement in Assam.
• He used art forms like dance, music, and drama to propagate his teachings and promote unity.

The correct answer is Debendranath Tagore.

Key Points

• Debendranath Tagore founded the Tattwabodhini Sabha in Bengal in 1839.
• The Sabha aimed to revive the principles of the Brahmo Samaj, emphasizing monotheism and the Upanishadic philosophy.
• The Tattwabodhini Sabha became a hub for discussions on social and religious reforms in Bengal.
• It also played a significant role in promoting Bengali language and literature by publishing the "Tattwabodhini Patrika," a journal that propagated reformist ideas.
• Debendranath Tagore, often referred to as the "Maharshi," was a key figure in the Bengal Renaissance and contributed significantly to the intellectual awakening in India.

Additional Information

• Brahmo Samaj:
• Founded by Raja Ram Mohan Roy in 1828, it was a socio-religious reform movement that opposed idol worship and emphasized monotheism.
• The Brahmo Samaj sought to reform Hinduism by eliminating practices like sati, caste discrimination, and child marriage.
• Tattwabodhini Patrika:
• This journal was the official publication of the Tattwabodhini Sabha.
• It served as a medium to disseminate the Sabha's reformist ideas and foster intellectual debates.
• Debendranath Tagore:
• He was the father of Rabindranath Tagore, a Nobel laureate in literature.
• He joined the Brahmo Samaj in 1843 and later played a pivotal role in its revival.
• Bengal Renaissance:
• A cultural, social, and intellectual awakening in 19^th-century Bengal, spearheaded by luminaries like Raja Ram Mohan Roy, Ishwar Chandra Vidyasagar, and Debendranath Tagore.
• It aimed to reform traditional Indian society by adopting progressive ideas while retaining the essence of Indian culture.

The correct answer is Bharatanatyam.

Key Points

• The Thanjavur Quartet refers to four brothers—Chinnayya, Ponnayya, Sivanandam, and Vadivelu—renowned for their contribution to Bharatanatyam.
• They were instrumental in reviving, codifying, and systematizing Bharatanatyam as a classical art form during the early 19^th century.
• They composed numerous dance pieces, including varnams and padams, that became integral to the Bharatanatyam repertoire.
• The brothers served in the court of King Serfoji II of Thanjavur and were deeply influenced by his patronage of the arts.
• Their efforts laid the foundation for the margam (traditional sequence of Bharatanatyam performance), which is still followed today.

Additional Information

• Bharatanatyam:
• Bharatanatyam is one of the oldest classical dance forms of India, originating in Tamil Nadu.
• It combines bhava (expression), raga (melody), tala (rhythm), and natyam (dramatic art).
• Traditionally performed in temples as an offering to deities, it is deeply rooted in spiritual and religious themes.
• The dance is accompanied by Carnatic music, and its movements are characterized by intricate footwork and graceful gestures.
• Thanjavur Quartet's Legacy:
• The Quartet's compositions are still widely performed and respected in Bharatanatyam recitals.
• They introduced innovations such as integrating music with dance and enhancing the use of abhinaya (expressive storytelling).
• Margam:
• Margam is the traditional sequence of a Bharatanatyam performance, consisting of pieces like alarippu, jatiswaram, varnam, padam, and tillana.
• This structure was formalized by the Thanjavur Quartet, making it a hallmark of Bharatanatyam.
• King Serfoji II:
• King Serfoji II of Thanjavur was a major patron of the arts, encouraging the development of Bharatanatyam under the Thanjavur Quartet.
• His reign saw a flourishing of Tamil classical music, dance, and literature.

The correct answer is government revenue equates government expenditure.

Key Points

• A balanced budget occurs when government revenue is equal to its expenditure, ensuring no deficit or surplus in the budget.
• This fiscal arrangement reflects efficient financial management by the government, maintaining economic stability.
• Balanced budgets are often preferred as they avoid excessive borrowing and ensure sustainability of public finances.
• Such budgets are typically used as a tool to prevent inflation or deflation in the economy.
• While balanced budgets are ideal, they may not always be feasible, especially during times of economic recession or financial crises.

Additional Information

• Budget Deficit:
• A situation where government expenditure exceeds its revenue.
• It often requires borrowing or issuing bonds to cover the gap.
• Budget Surplus:
• Occurs when government revenue exceeds expenditure.
• Surpluses can be used for debt repayment or saved for future use.
• Fiscal Policy:
• A government strategy for managing its budget through revenue collection (taxes) and expenditure.
• Fiscal policy plays a crucial role in regulating economic growth and stability.
• Types of Government Budgets:
• Balanced Budget: Revenue equals expenditure.
• Surplus Budget: Revenue exceeds expenditure.
• Deficit Budget: Expenditure exceeds revenue.
• Implications of a Balanced Budget:
• Promotes fiscal discipline and long-term economic stability.
• May limit the government’s ability to invest in large-scale projects during critical times.

The correct answer is Sarod.

Key Points

• Arnab Chakrabarty is a renowned Indian classical musician and one of the most prominent Sarod players of his generation.
• He is known for his profound grasp of Indian classical ragas and his ability to blend traditional styles with contemporary interpretations.
• Arnab Chakrabarty has trained under distinguished gurus, including Pandit Brij Narayan and Pandit Buddhadev Dasgupta, both legends in the Sarod tradition.
• His performances have gained global acclaim, especially for their technical brilliance and emotional depth.
• Arnab Chakrabarty is also dedicated to reviving the authentic construction and sound of the Sarod, often working with instrument makers to refine its tonal quality.

Additional Information

• Sarod
• The Sarod is a prominent stringed instrument used in Indian classical music, known for its deep, resonant, and soulful tone.
• It is played using a plectrum called a jawa and does not have frets, allowing for smooth glides between notes (meend).
• The Sarod is believed to have evolved from the Afghan Rabab and was further adapted in India.
• It is primarily associated with Hindustani classical music and features prominently in solo and ensemble performances.
• Notable Sarod Players
• Ustad Amjad Ali Khan, a legendary Sarod maestro and one of the most celebrated names in Indian classical music.
• Ali Akbar Khan, another iconic Sarod virtuoso, was instrumental in popularizing Indian classical music in the West.
• Sharan Rani, one of the first female Sarod players, earned the title "Sarod Rani."
• Construction of Sarod
• The Sarod is made from a single block of wood, typically teak or tun wood, with a goat skin-covered resonator.
• It has between 17 and 25 strings, divided into melody, drone, and sympathetic strings, enhancing its rich tonal quality.
• The metal fingerboard allows for intricate sliding techniques unique to the Sarod.
• Comparison with Sarangi
• The Sarangi, another Indian classical instrument, is a bowed string instrument, unlike the plucked Sarod.
• While the Sarangi is primarily used for accompaniment in vocal performances, the Sarod is a dominant solo instrument in classical music.

The correct answer is Union of States.

Key Points

• According to Article 1 of the Indian Constitution, India is defined as a "Union of States."
• The term "Union of States" signifies that India is not a federation created by an agreement among states but rather an indestructible union.
• The Indian Constitution does not describe India as a federation, although it has federal features. It is instead called a "quasi-federal" system.
• The central government holds more power compared to the states, ensuring a strong unitary character.
• This structure aims to maintain the unity and integrity of India while allowing states to function within their designated powers under the Constitution.

Additional Information

• Federal Features of the Indian Constitution:
• Division of powers between the Union and States through the Union List, State List, and Concurrent List.
• Independent judiciary with the Supreme Court as the guardian of the Constitution.
• Written Constitution with rigid provisions requiring special procedures for amendments.
• Bicameral legislature at the central level (Lok Sabha and Rajya Sabha).
• Unitary Features:
• Strong central authority with residuary powers vested in the Union Government.
• Emergency provisions that convert India into a unitary state during crises.
• Single citizenship for all Indians, emphasizing unity.
• Integrated judiciary and administrative system across the country.
• Terminology:
• "Union of States" reflects the emphasis on the unity of the nation despite regional diversities.
• "Quasi-federal" refers to the blend of federal and unitary characteristics in the Indian political system.
• Historical Context:
• The framers of the Constitution chose the term "Union" to prevent the possibility of secession by states, unlike in some federations.
• This was influenced by the partition of India and the need to ensure national integration.

The correct answer is 12.

Key Points

• The National Multidimensional Poverty Index (MPI) 2021 of India is based on 12 indicators.
• These indicators are grouped under three dimensions: Health, Education, and Standard of Living.
• The MPI report is prepared by NITI Aayog in collaboration with Oxford Poverty and Human Development Initiative (OPHI) and United Nations Development Programme (UNDP).
• Indicators include nutrition, child mortality, years of schooling, school attendance, cooking fuel, sanitation, drinking water, electricity, housing, assets, and others.
• The MPI aims to provide a comprehensive measure of poverty beyond income-based metrics.

Additional Information

• Multidimensional Poverty Index (MPI)
• It is a measure developed by OPHI and UNDP to capture multidimensional aspects of poverty.
• MPI complements income-based poverty measures by assessing deprivations across multiple dimensions like health, education, and living standards.
• It uses household-level data to analyze poverty trends and identify areas requiring policy intervention.
• NITI Aayog
• It is the policy think tank of the Government of India, established in 2015 to replace the Planning Commission.
• NITI Aayog is responsible for promoting cooperative federalism and providing strategic and technical advice to states and central governments.
• Key Dimensions of MPI in India
• Health: Includes indicators like nutrition and child mortality.
• Education: Covers years of schooling and school attendance.
• Living Standards: Includes indicators like access to electricity, sanitation, drinking water, housing, cooking fuel, and assets.
• Global MPI
• The Global Multidimensional Poverty Index is published annually by OPHI and UNDP.
• It covers more than 100 countries and provides global insights into poverty trends.

Shortcut Trick

To find the LCM of numbers given in exponential form, identify all the distinct bases.

Then, take the highest power of each distinct base present across all the given expressions.

The highest powers present for each base are: 2³, 9³, 13², and 19².

Multiply these highest powers together to get the final LCM directly.

∴ The correct answer is 2³ × 9³ × 13² × 19².

Alternate Method

Given:

First expression = 2³ × 9² × 13

Second expression = 2² × 13² × 19

Third expression = 9³ × 13² × 19²

Formula Used:

LCM of exponential expressions = Product of the highest power of each distinct factor present in the expressions.

Calculations:

⇒ Maximum power of base 2 = max(3, 2, 0) = 3 ⇒ 2³

⇒ Maximum power of base 9 = max(2, 0, 3) = 3 ⇒ 9³

⇒ Maximum power of base 13 = max(1, 2, 2) = 2 ⇒ 13²

⇒ Maximum power of base 19 = max(0, 1, 2) = 2 ⇒ 19²

⇒ LCM = 2³ × 9³ × 13² × 19²

∴ The correct answer is 2³ × 9³ × 13² × 19².

Additional Information

HCF of Exponential Numbers

To find the Highest Common Factor (HCF) of numbers in exponential form, select and multiply the lowest powers of only the common bases present in all expressions.

LCM and HCF of Fractions

LCM of fractions = (LCM of Numerators) ÷ (HCF of Denominators) | HCF of fractions = (HCF of Numerators) ÷ (LCM of Denominators).

Relation between HCF and LCM

For any two numbers a and b, the product of their HCF and LCM is strictly equal to the product of the numbers themselves: HCF(a, b) × LCM(a, b) = a × b.

Shortcut Trick

For equal successive percentage increase and decrease of x%, there is always a net decrease.

Net percentage change = −(x² ÷ 100)%

Here, x = 8%

Net change = −(8² ÷ 100)% = −(64 ÷ 100)% = −0.64%

∴ The correct answer is 0.64%.

Alternate Method

Given:

Initial percentage increase = +8%

Subsequent percentage decrease = −8%

100 Initial Salary

+8%

108

−8%

99.36 Final Salary

Net Change: 100 → 99.36 (−0.64%)

Calculations:

⇒ Let the initial salary of the worker be 100 units.

⇒ After an 8% increase, salary = 100 + 8 = 108 units.

⇒ After an 8% decrease on the new salary, decrease amount = 108 × (8 ÷ 100) = 8.64 units.

⇒ Final salary = 108 − 8.64 = 99.36 units.

⇒ Net decrease in salary = Initial salary − Final salary = 100 − 99.36 = 0.64 units.

⇒ Percentage change = (0.64 ÷ 100) × 100% = 0.64%.

∴ The correct answer is 0.64%.

Additional Information

Successive Percentage Change

When a value is changed successively by x% and y%, the effective percentage change is given by the formula: [x + y + (x × y) ÷ 100]%.

Equal Increase and Decrease

If a number is first increased by x% and then decreased by x%, there is always an overall net decrease equal to (x² ÷ 100)%.

Multiplier Method

For multiple changes, Final Value = Initial Value × (1 ± x ÷ 100) × (1 ± y ÷ 100). The plus (+) sign is used for an increase and the minus (−) sign is used for a decrease.

Given:

The value of 40 - 3 × [10 + 6 × {20 - 10 (6 - 5) × 2} ÷ 47]

Formula used:

Follow BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction).

Calculation:

40 - 3 × [10 + 6 × {20 - 10 (6 - 5) × 2} ÷ 47]

⇒ 40 - 3 × [10 + 6 × {20 - 10 × 1 × 2} ÷ 47]

⇒ 40 - 3 × [10 + 6 × {20 - 20} ÷ 47]

⇒ 40 - 3 × [10 + 6 × 0 ÷ 47]

⇒ 40 - 3 × [10 + 0]

⇒ 40 - 3 × 10

⇒ 40 - 30

⇒ 10

∴ The correct answer is option (3).

Shortcut Trick

Convert member counts to ratio: 30 : 76 : 44 = 15 : 38 : 22 (Total parts = 75).

Let the assumed average be ₹250. The deviations for each group are −1, −82, and +248.

Net deviation = (15 × −1) + (38 × −82) + (22 × 248) = −15 − 3116 + 5456 = +2325.

Average deviation = 2325 ÷ 75 = +31.

Actual average = 250 + 31 = ₹281.

∴ The correct answer is ₹281.

Alternate Method

Given:

Members in groups A, B, and C are 30, 76, and 44 respectively.

Average amounts spent are ₹249, ₹168, and ₹498 respectively.

Formula Used:

Combined Average = Total Amount Spent ÷ Total Number of Members

Group A 30 × ₹249

Group B 76 × ₹168

Group C 44 × ₹498

Combined Average 150 Members → ₹281

Calculations:

⇒ Total members = 30 + 76 + 44 = 150

⇒ Total amount spent by Group A = 30 × 249 = 7470

⇒ Total amount spent by Group B = 76 × 168 = 12768

⇒ Total amount spent by Group C = 44 × 498 = 21912

⇒ Total combined amount spent = 7470 + 12768 + 21912 = 42150

⇒ Combined Average = 42150 ÷ 150 = 281

∴ The correct answer is ₹281.

Additional Information

Weighted Average Formula

Combined Average = (N₁A₁ + N₂A₂ + N₃A₃) ÷ (N₁ + N₂ + N₃), where N represents the quantity count and A represents the average for each group.

Assumed Mean / Deviation Method

To avoid large multiplications, select a base average close to the given numbers. Compute the net sum of deviations, divide by total parts, and adjust the base average accordingly.

Ratio Simplification

When base counts are exceptionally large, simplify them into their lowest ratio before applying the assumed mean method. The final average remains mathematically identical.

Shortcut Trick

We can use the successive percentage formula to find the overall effect: Net Profit % = a + b + (a × b) ÷ 100

Here, markup a = +60% and discount b = −25%.

⇒ Net Profit % = 60 − 25 + [60 × (−25)] ÷ 100

⇒ Net Profit % = 35 − 1500 ÷ 100

⇒ Net Profit % = 35 − 15 = 20%

∴ The correct answer is 20%.

Alternate Method

Given:

Marked Price (MP) = 60% above Cost Price (CP)

Discount = 25% on MP

Formula Used:

Selling Price (SP) = MP × (100 − Discount%) ÷ 100

Profit% = [(SP − CP) ÷ CP] × 100

Profit and Discount Relationship CP → MP → SP

CP: 100

MP: 160

SP: 120

+60% Markup

−25% Discount

+20% Profit

Calculations:

Let the Cost Price (CP) of the goods be 100 units.

⇒ Marked Price (MP) = 100 + 60% of 100 = 160

⇒ Discount = 25% of 160 = (25 ÷ 100) × 160 = 40

⇒ Selling Price (SP) = MP − Discount = 160 − 40 = 120

⇒ Profit = SP − CP = 120 − 100 = 20

⇒ Profit% = (20 ÷ 100) × 100 = 20%

∴ The correct answer is 20%.

Additional Information

Marked Price & Discount Relation

Discount is always calculated strictly on the Marked Price (MP), not on Cost Price (CP). The final transaction price is Selling Price (SP) = MP − Discount.

Successive Discount

When two successive discounts of a% and b% are given, the equivalent single discount can be calculated using the formula: [a + b − (a × b) ÷ 100]%.

Dishonest Dealer Concept

If a merchant sells goods at CP but uses a false weight, the actual Profit % is calculated as: [Error ÷ (True Weight − Error)] × 100.

Shortcut Trick

The total effective interest rate for simple interest is calculated as R × T.

Effective interest rate = 2% × 5 = 10%.

We are given that 10% of the Principal equals ₹191.

To find the total Principal amount (which represents 100%), we multiply the given interest by 10.

Principal = 191 × 10 = 1910

∴ The correct answer is ₹1910.

Alternate Method

Given:

Simple Interest (SI) = ₹191

Time period (T) = 5 years

Rate of interest (R) = 2% per annum

Principal P = ?

Simple Interest ₹191

Time = 5 Years Rate = 2% p.a.

Total Interest = P × R × T ÷ 100

Formula Used:

SI = (P × R × T) ÷ 100

Calculations:

⇒ 191 = (P × 2 × 5) ÷ 100

⇒ 191 = (P × 10) ÷ 100

⇒ 191 = P ÷ 10

⇒ P = 191 × 10

⇒ P = 1910

∴ The correct answer is ₹1910.

Additional Information

Simple Interest (SI)

In simple interest, the interest is calculated only on the initial principal amount throughout the entire period. The fundamental formula is SI = (P × R × T) ÷ 100.

Total Amount (A)

The total amount paid or received at the end of the time period is the sum of the borrowed principal and the interest earned. Formula: A = P + SI.

Compound Interest (CI)

Unlike simple interest, compound interest is calculated on both the initial principal and the accumulated interest from previous periods. Formula: A = P(1 + R/100)^T.

Shortcut Trick

Total Distance = 1320 + 1760 + 2095 = 5175 km.

Total Time = (1320 ÷ 528) + (1760 ÷ 352) + (2095 ÷ 419) = 2.5 + 5 + 5 = 12.5 hours.

Average Speed = Total Distance ÷ Total Time = 5175 ÷ 12.5 = 414 km/h.

∴ The correct answer is 414 km/h.

Alternate Method

Given:

Distance D₁ = 1320 km, Speed S₁ = 528 km/h

Distance D₂ = 1760 km, Speed S₂ = 352 km/h

Distance D₃ = 2095 km, Speed S₃ = 419 km/h

1320 km 1760 km 2095 km

528 km/h 352 km/h 419 km/h

T = 2.5 h T = 5 h T = 5 h

Total Distance = 5175 km

Avg Speed = 5175 ÷ 12.5 = 414 km/h

Formula Used:

Time = Distance ÷ Speed

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance = 1320 + 1760 + 2095 = 5175 km

⇒ Time T₁ = 1320 ÷ 528 = 2.5 hours

⇒ Time T₂ = 1760 ÷ 352 = 5 hours

⇒ Time T₃ = 2095 ÷ 419 = 5 hours

⇒ Total Time = 2.5 + 5 + 5 = 12.5 hours

⇒ Average Speed = 5175 ÷ 12.5

⇒ Average Speed = 51750 ÷ 125 = 414 km/h

∴ The correct answer is 414 km/h.

Additional Information

Average Speed

When multiple parts of a journey are covered at different speeds, Average Speed = Total Distance ÷ Total Time. If the distance covered in two equal parts is the same, Average Speed = (2 × S₁ × S₂) ÷ (S₁ + S₂).

Relative Speed

When two objects travel in opposite directions, their relative speed is S₁ + S₂. When travelling in the same direction, their relative speed is |S₁ − S₂|.

Speed Conversions

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

Shortcut Trick

Time for Rodney = 22 − 15 = 7 years and Time for Amit = 22 − 16 = 6 years.

Time difference = 1 year. Since Amit's money compounds for 1 year less, his principal must be larger by the 1-year interest multiplier.

Ratio of shares (Amit : Rodney) = (100 + 8) : 100 = 108 : 100 = 27 : 25.

Total ratio parts = 27 + 25 = 52 parts → ₹23400.

Amit's share (27 parts) = (23400 ÷ 52) × 27 = 450 × 27 = ₹12150.

∴ The correct answer is ₹12150.

Alternate Method

Total Wealth = ₹23400

Rodney (15 yrs) Time = 7 years

Amit (16 yrs) Time = 6 years

Rate = 8% CI p.a.

Equal Amount at 22 yrs

Given:

Total money distributed = ₹23400

Rate of interest (R) = 8% per annum compounded annually.

Time for Rodney = 22 − 15 = 7 years.

Time for Amit = 22 − 16 = 6 years.

Formula Used:

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

Calculation:

⇒ Let Amit's initial share be ₹A and Rodney's share be ₹(23400 − A).

⇒ Amount received by Amit after 6 years = A × (1 + 8/100)⁶

⇒ Amount received by Rodney after 7 years = (23400 − A) × (1 + 8/100)⁷

⇒ Since both receive the exact same amount when they turn 22, we equate the two values:

⇒ A × (1 + 8/100)⁶ = (23400 − A) × (1 + 8/100)⁷

⇒ A ÷ (23400 − A) = (1 + 8/100)¹

⇒ A ÷ (23400 − A) = 108 / 100

⇒ A ÷ (23400 − A) = 27 / 25

⇒ 25 × A = 27 × (23400 − A)

⇒ 25A = 631800 − 27A

⇒ 25A + 27A = 631800

⇒ 52A = 631800

⇒ A = 631800 ÷ 52 = 12150

∴ The correct answer is ₹12150.

Additional Information

Ratio of Shares for Equal Amount (CI)

If a given sum is divided into two parts P₁ and P₂ such that their amounts are equal after t₁ and t₂ years respectively at R% compound interest, then P₁ / P₂ = (1 + R/100)^{t₂ − t₁}.

Effective Rate of Compound Interest

For 2 years, the effective compound interest rate is calculated using the successive percentage formula: R + R + (R × R)/100 = 2R + (R²/100) %.

Difference Between CI and SI

The difference between compound interest and simple interest for exactly 2 years on a principal P at a given rate R% per annum is given by PR² / 10000.

Shortcut Trick

When the distance covered is the same for two parts of a journey, the actual distance is not required.

Average Speed = 2xy ÷ (x + y)

⇒ Average Speed = (2 × 77 × 63) ÷ (77 + 63)

⇒ Average Speed = 9702 ÷ 140 = 69.3 km/hr

∴ The correct answer is 69.3 km/hr.

Alternate Method

Given:

Forward Speed (x) = 77 km/hr

Return Speed (y) = 63 km/hr

Distance (D) = 97 km

Chandigarh

Ludhiana

x = 77 km/hr

y = 63 km/hr

D = 97 km Average Speed = 2xy ÷ (x + y)

Formula Used:

Average Speed = Total Distance ÷ Total Time

Total Distance = D + D = 2D

Total Time = (D ÷ x) + (D ÷ y)

Calculations:

⇒ Average Speed = 2D ÷ [D × (1/x + 1/y)]

⇒ Average Speed = 2xy ÷ (x + y)

⇒ Average Speed = (2 × 77 × 63) ÷ (77 + 63)

⇒ Average Speed = (2 × 77 × 63) ÷ 140

⇒ Average Speed = (77 × 63) ÷ 70

⇒ Average Speed = (11 × 63) ÷ 10

⇒ Average Speed = 693 ÷ 10 = 69.3 km/hr

∴ The correct answer is 69.3 km/hr.

Additional Information

Average Speed for 3 Equal Distances

When three equal distances are covered at speeds x, y, and z, the Average Speed = 3xyz ÷ (xy + yz + zx).

Average Speed for Constant Time

If two different speeds x and y are maintained for exactly the same duration of time, the Average Speed = (x + y) ÷ 2.

Relative Speed

For two moving bodies traveling in the same direction, relative speed = (x − y). For two moving bodies traveling in opposite directions, relative speed = (x + y).

Shortcut Trick

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

⇒ a = 4 + √5, b = 12 − 2√20 = 12 − 4√5

⇒ a × b = (4 + √5) × 4(3 − √5)

⇒ a × b = 4(12 − 4√5 + 3√5 − 5) = 4(7 − √5)

⇒ Mean proportional = √[4(7 − √5)] = 2√(7 − √5)

∴ The correct answer is 2√(7 − √5).

Alternate Method

Given:

First number (a) = 4 + √5

Second number (b) = 12 − 2√20

Formula Used:

Mean proportional (x) between two numbers a and b is x = √(a × b)

a = 4 + √5 b = 12 − 2√20 a × b

x x x² Mean Proportional: x = √(a × b)

Calculations:

⇒ First, simplify the second number:

⇒ b = 12 − 2√(4 × 5) = 12 − 2 × 2√5 = 12 − 4√5

⇒ Multiply both numbers a and b:

⇒ a × b = (4 + √5) × (12 − 4√5)

⇒ a × b = 48 − 16√5 + 12√5 − 20

⇒ a × b = 28 − 4√5

⇒ Take 4 common from the terms:

⇒ a × b = 4(7 − √5)

⇒ Now calculate the mean proportional x:

⇒ x = √(a × b) = √[4(7 − √5)]

⇒ x = 2√(7 − √5)

∴ The correct answer is 2√(7 − √5).

Additional Information

Mean Proportional

For any two numbers a and b, their mean proportional is the square root of their product, given by x = √(a × b).

Third Proportional

If a, b, and c are in continued proportion (a : b :: b : c), then c is the third proportional, calculated as c = b² ÷ a.

Fourth Proportional

For three given numbers a, b, and c, the fourth proportional d satisfies a : b :: c : d, calculated as d = (b × c) ÷ a.

Shortcut Trick

Total work = LCM(18, 24) = 72 units.

Efficiency: A = 4 units/day, B = 3 units/day.

Work done in one 3-day cycle (A, A, B) = 4 + 4 + 3 = 11 units.

6 cycles (18 days) complete = 6 × 11 = 66 units. Remaining = 72 − 66 = 6 units.

Day 19: A does 4 units. Remaining = 2 units. Day 20: A takes 2 ÷ 4 = 1/2 day.

∴ The correct answer is 19 ¹/₂ days.

Alternate Method

Given:

Time taken by A = 18 days

Time taken by B = 24 days

Working cycle: A works for 2 consecutive days, and B works on the 3^rd day.

Method Used:

We use the LCM method to find the total work and the efficiency of each person.

Calculations:

⇒ Work done in a single 3-day cycle = (Work by A for 2 days) + (Work by B for 1 day)

⇒ Work done in 3 days = (2 × 4) + (1 × 3) = 8 + 3 = 11 units

⇒ Number of full cycles required to approach the total work = 72 ÷ 11 ≈ 6 cycles

⇒ Work done in 6 cycles (18 days) = 6 × 11 = 66 units

⇒ Remaining work = 72 − 66 = 6 units

⇒ On the 19^th day (start of the 7^th cycle), A works and completes 4 units of work.

⇒ Work remaining after the 19^th day = 6 − 4 = 2 units

⇒ On the 20^th day, A works again. Time taken by A to complete the remaining 2 units = 2 ÷ 4 = 1/2 day.

⇒ Total time taken to complete the entire work = 18 + 1 + 1/2 = 19 ¹/₂ days.

∴ The correct answer is 19 ¹/₂ days.

Additional Information

LCM Method for Time & Work

Total work is assumed as the Least Common Multiple (LCM) of the given individual times. Efficiency represents the work done per day, calculated as (Total Work ÷ Total Days).

Cyclic or Alternate Day Work Pattern

For repetitive work patterns, group the days into a single block or cycle where the pattern repeats. Multiply the total work done in one cycle to get as close to the overall work as possible without exceeding it. Then calculate the remaining units manually day-by-day based on who is scheduled to work.

Given:

Evaluate: (-9) - (-60) ÷ (-15) + (-3) × 9

Formula used:

Follow BODMAS rule: Brackets, Orders (exponents), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

Calculation:

Expression: (-9) - (-60) ÷ (-15) + (-3) × 9

⇒ (-9) - [(-60) ÷ (-15)] + [(-3) × 9]

⇒ (-9) - [4] + [-27]

⇒ (-9) - 4 - 27

⇒ -9 - 4 = -13

⇒ -13 - 27 = -40

∴ The correct answer is option (2).

Shortcut Trick

If a group is divided into two parts and the overall percentage is equal to the percentage in one part, then the percentage in the second part must be exactly the same.

⇒ Overall literate population = 71%

⇒ Literate males = 71%

⇒ Literate females must also be = 71%

∴ The correct answer is 71%.

Alternate Method

Given:

⇒ Total population = 333000

⇒ Number of males = 213000

⇒ Overall literate population = 71%

⇒ Literate males = 71%

Total Population = 333,000 Literate = 71%

Males = 213,000 Literate = 71%

Females = 120,000 Literate = ? %

Total Literate = Literate Males + Literate Females

Calculations:

⇒ Total females = Total population − Total males

⇒ Total females = 333000 − 213000 = 120000

⇒ Literate population = (71 ÷ 100) × 333000 = 236430

⇒ Literate males = (71 ÷ 100) × 213000 = 151230

⇒ Literate females = Total literate − Literate males

⇒ Literate females = 236430 − 151230 = 85200

⇒ Percentage of literate females = (Literate females ÷ Total females) × 100

⇒ Percentage = (85200 ÷ 120000) × 100

⇒ Percentage = 0.71 × 100 = 71%

∴ The correct answer is 71%.

Additional Information

Weighted Average in Mixtures

When a group is divided into components A and B, the overall percentage is given by the weighted average formula: Overall % = (Value_A × %_A + Value_B × %_B) ÷ (Value_A + Value_B).

Constant Percentage Rule

If two different groups have the exact same percentage of a specific characteristic, any combination or total mixture of these groups will naturally possess that exact same percentage without needing further calculation.

Shortcut Trick

The required number when increased by 5 must be perfectly divisible by all the given numbers.

Instead of calculating the LCM, add 5 to the given options and check for divisibility by 18 (i.e., by 9 and 2).

Option 1: 355 + 5 = 360 (Divisible by 9 and 2)

No other option yields a number that is perfectly divisible by 9 and 2 when increased by 5.

∴ The correct answer is 355.

Alternate Method

Given:

The numbers are 18, 30, 36, and 24.

Formula Used:

Required Number = LCM(18, 30, 36, 24) − 5

Calculations:

⇒ Prime factorization of the given numbers:

⇒ 18 = 2 × 3²

⇒ 30 = 2 × 3 × 5

⇒ 36 = 2² × 3²

⇒ 24 = 2³ × 3

⇒ The LCM is the product of the highest powers of all prime factors.

⇒ LCM = 2³ × 3² × 5

⇒ LCM = 8 × 9 × 5 = 360

⇒ The required number is 5 less than the LCM.

⇒ Required number = 360 − 5 = 355

∴ The correct answer is 355.

Additional Information

LCM (Least Common Multiple)

The smallest number that is a multiple of two or more given numbers. It contains the highest power of each prime factor involved.

Divisibility Rule of 9

A number is divisible by 9 if the sum of its digits is perfectly divisible by 9. This rule is extremely helpful for quick option elimination without calculating the LCM.

Number System Rule for Remainders

The smallest number which when divided by x, y, z leaves a remainder R in each case is calculated as: LCM(x, y, z) + R.

Shortcut Trick

Since the population increases by 25% (fractional value = 1/4), it becomes 5/4 times each year.

To find the previous years' population, we multiply by the inverse factor 4/5.

Population 2 years ago = 100000 × (4/5) × (4/5) = 64000

Population 3 years ago = 64000 × (4/5) = 51200

Difference = 64000 − 51200 = 12800

∴ The correct answer is 12800.

Alternate Method

Given:

Current population (P₀) = 100000

Rate of increase (R) = 25% = 1/4

Multiplying factor for 25% increase = 1 + 1/4 = 5/4

P-3 P-2 P-1 100k

+25% +25% +25%

3 yrs ago 2 yrs ago 1 yr ago Current

Difference = ?

Calculations:

⇒ Let the population 2 years ago be P₋₂.

⇒ P₋₂ × (5/4) × (5/4) = P₀

⇒ P₋₂ × (25/16) = 100000

⇒ P₋₂ = 100000 × (16/25) = 64000

⇒ Let the population 3 years ago be P₋₃.

⇒ P₋₃ × (5/4) = P₋₂

⇒ P₋₃ × (5/4) = 64000

⇒ P₋₃ = 64000 × (4/5) = 51200

⇒ Difference = P₋₂ − P₋₃ = 64000 − 51200 = 12800

∴ The correct answer is 12800.

Additional Information

Population After n Years

If the current population is P and the annual rate of increase is R%, the population after n years = P × (1 + R/100)ⁿ.

Population n Years Ago

If the current population is P and the annual rate of increase is R%, the population n years ago = P ÷ (1 + R/100)ⁿ.

Fractional Equivalent

Using fractional values of percentages (e.g., 25% = 1/4) simplifies successive change calculations. An increase of 1/4 means the new value becomes 5/4 of the original value.

Shortcut Trick

In cases of dishonest weighing where goods are sold at cost price:

Profit % = [Error ÷ (True Value − Error)] × 100

Here, Error = 37% and True Value = 100%

Profit % = [37 ÷ (100 − 37)] × 100 = (37 ÷ 63) × 100

Profit % = 3700 ÷ 63 = 58 ⁴⁶/₆₃%

∴ The correct answer is 58 ⁴⁶/₆₃%.

Alternate Method

Given:

Promised selling price = Cost price (CP)

Weight used = 37% less than the actual written weight

Promised Weight (SP) = 100 units

Actual Weight given = 63 units Cost Price (CP) = ₹63

Cheated = 37 units Profit = ₹37

Total Amount Received (SP) = ₹100

Calculations:

⇒ Let the true weight be 100 units and its Cost Price (CP) be ₹100.

⇒ The shopkeeper promises to sell at CP, so his Selling Price (SP) for 100 units is ₹100.

⇒ However, he uses a weight that is 37% less, meaning he gives 100 − 37 = 63 units.

⇒ The actual Cost Price (CP) of the 63 units given is ₹63.

⇒ So, the shopkeeper spends ₹63 but receives ₹100 from the customer.

⇒ Profit = SP − CP = 100 − 63 = ₹37

⇒ Profit % = (Profit ÷ CP) × 100

⇒ Profit % = (37 ÷ 63) × 100 = 3700 ÷ 63

⇒ 3700 ÷ 63 = 58 with a remainder of 46, which is 58 ⁴⁶/₆₃%

∴ The correct answer is 58 ⁴⁶/₆₃%.

Additional Information

Dishonest Dealer Selling at CP

When a dealer claims to sell at Cost Price but uses false weight: Profit % = [Error ÷ (True Weight − Error)] × 100.

Dishonest Dealer Selling at Markup

If the dealer marks up the price by x% and also uses a false weight, calculate the overall profit by combining the price ratio and weight ratio (Overall Ratio = True Weight ÷ False Weight × Markup Price ÷ Base Price).

Successive Percentage Change

Net Change = a + b + (a × b) ÷ 100. This is useful when multiple percentage changes occur, such as when markup is followed by discount before applying the false weight.

Shortcut Trick

Relative speed of trains in opposite directions = 80 + 70 = 150 km/h.

Relative speed in m/s = 150 × (5/18) = 125/3 m/s.

Total distance covered in 19 seconds = Speed × Time = (125/3) × 19 = 2375/3 m ≈ 791.66 m.

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

Length of the second train = 791.66 − 180 = 611.66 m.

∴ The correct answer is 611.66 m.

Alternate Method

Given:

Speed of Train 1 (S₁) = 80 km/h

Speed of Train 2 (S₂) = 70 km/h

Length of Train 1 (L₁) = 180 m

Time taken to cross (T) = 19 s

Formula Used:

Total Distance = Relative Speed × Time

When moving in opposite directions, Relative Speed = S₁ + S₂

180 m

80 km/h

L2 = ?

70 km/h

Opposite Directions → Speeds Add Up Relative Speed = 150 km/h Time to Cross = 19 s

Calculations:

⇒ Relative Speed = 80 + 70 = 150 km/h

⇒ Relative Speed in m/s = 150 × (5 / 18) = 125 / 3 m/s

⇒ Total Distance = (125 / 3) × 19

⇒ Total Distance = 2375 / 3 m

⇒ L₁ + L₂ = 791.66 m

⇒ 180 + L₂ = 791.66 m

⇒ L₂ = 791.66 − 180

⇒ L₂ = 611.66 m

∴ The correct answer is 611.66 m.

Additional Information

Relative Speed in Same Direction

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

Relative Speed in Opposite Direction

When two objects move in opposite directions, their relative speed is the sum of their individual speeds. Relative Speed = S₁ + S₂.

Crossing a Stationary Object

To cross a stationary pole or a standing man, the distance covered is exactly equal to the length of the train (L). Time taken = L ÷ S.

Speed Conversion

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

Shortcut Trick

Perimeter of a square = 4 × √Area

Perimeter = 4 × √252

Perimeter = 4 × √(36 × 7)

Perimeter = 4 × 6√7 = 24√7 m

∴ The correct answer is 24√7 m.

Alternate Method

Given:

Area of the square field = 252 m²

Formula Used:

Area of a square = a² (where a is the side of the square)

Perimeter of a square = 4a

Side (a) = 6√7 m a Area = 252 m² Perimeter = 4 × a = 24√7 m

Calculations:

⇒ a² = 252

⇒ a = √252

⇒ a = √(36 × 7)

⇒ a = 6√7 m

⇒ Perimeter = 4 × a

⇒ Perimeter = 4 × 6√7

⇒ Perimeter = 24√7 m

∴ The correct answer is 24√7 m.

Additional Information

Diagonal of a Square

The diagonal 'd' of a square with side 'a' is given by d = a√2.

Area in terms of Diagonal

The area of a square can also be calculated directly from its diagonal using the formula Area = d² ÷ 2.

Incircle and Circumcircle

For a square of side 'a', the radius of the inscribed circle is a ÷ 2, and the radius of the circumscribed circle is a ÷ √2.

Shortcut Trick

Difference between the two selling prices = ₹4,000 − ₹2,790 = ₹1,210.

Ratio of Profit to Loss = 10 : 1. Total parts = 10 + 1 = 11 parts.

11 parts = 1,210 ⇒ 1 part (Loss) = 1,210 ÷ 11 = ₹110.

Cost Price (CP) = ₹2,790 + ₹110 = ₹2,900.

Selling Price for 20% profit = ₹2,900 × 1.20 = ₹3,480.

∴ The correct answer is ₹3,480.

Alternate Method

Given:

Selling Price 1 (SP₁) = ₹2,790 (Loss incurred)

Selling Price 2 (SP₂) = ₹4,000 (Profit earned)

Profit = 10 × Loss

SP1 = 2790 CP SP2 = 4000

Loss (L) Profit (10L)

Total Gap = 11L = 1210

Formula Used:

Profit = SP − CP

Loss = CP − SP

Calculations:

⇒ Let the Cost Price be CP.

⇒ Profit = 4000 − CP

⇒ Loss = CP − 2790

⇒ According to the given condition: Profit = 10 × Loss

⇒ 4000 − CP = 10 × (CP − 2790)

⇒ 4000 − CP = 10CP − 27900

⇒ 11CP = 31900

⇒ CP = 31900 ÷ 11 = ₹2,900

⇒ Desired profit = 20%

⇒ New Selling Price = CP × (100 + Profit%) ÷ 100

⇒ New SP = 2900 × (120 ÷ 100) = ₹3,480

∴ The correct answer is ₹3,480.

Additional Information

Profit and Loss Basics

Profit occurs when Selling Price > Cost Price (Profit = SP − CP). Loss occurs when Cost Price > Selling Price (Loss = CP − SP).

Percentage Calculations

Profit % = (Profit ÷ CP) × 100. Loss % = (Loss ÷ CP) × 100. Both are always calculated taking the Cost Price as the base.

Selling Price Formula

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

Shortcut Trick

In direct variation, q is a constant multiple of p.

Constant multiple = q₁ ÷ p₁ = 630 ÷ 15 = 42

Therefore, q₂ = p₂ × 42

⇒ q₂ = 6 × 42 = 252

∴ The correct answer is 252.

Alternate Method

Given:

p₁ = 15, q₁ = 630

p₂ = 6

Formula Used:

If p varies directly to q, then p ∝ q

⇒ p₁ / q₁ = p₂ / q₂

p₁ = 15 p₂ = 6 q₁ = 630 q₂ = ?

=

Direct Variation : p₁ / q₁ = p₂ / q₂

Calculation:

⇒ 15 / 630 = 6 / q₂

⇒ 1 / 42 = 6 / q₂

⇒ q₂ = 42 × 6

⇒ q₂ = 252

∴ The correct answer is 252.

Additional Information

Direct Variation

When two variables change in the same direction at a constant rate, it is direct variation (e.g., p ∝ q ⇒ p / q = k).

Inverse Variation

When an increase in one variable results in a proportional decrease in the other, it is inverse variation (e.g., p ∝ 1 / q ⇒ p × q = k).

Joint Variation

When a quantity varies directly with the product of two or more other quantities, it is called joint variation (e.g., p ∝ q × r ⇒ p = k × q × r).

The correct answer is: Complex.

Key Points

• The word "convoluted" means something that is extremely complex, intricate, or difficult to understand. (जटिल)
• Example: The professor's explanation was so convoluted that even the brightest students struggled to understand.
• "Complex" refers to something that is composed of many interconnected parts, making it complicated or intricate. (जटिल)
• Example: The plot of the movie was so complex that it required multiple viewings to fully grasp.
• Hence, we can infer that the synonym of 'convoluted' is 'complex'.

Therefore, the correct answer is: Complex.

Additional Information

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

• Straightforward (सीधा-सादा): Something simple, clear, and easy to understand.
• Example: The instructions were straightforward, so we completed the task without any issues.
• Neutral (तटस्थ): Not supporting or favoring any side in a conflict or disagreement.
• Example: The mediator remained neutral during the heated argument between the two parties.
• Direct (प्रत्यक्ष): Something that is straight and without deviation.
• Example: She gave a direct answer to the question without any hesitation.

The correct answer is: Option 4.

Key Points

• The idiom "The proof of the pudding is in the eating" means that the real value or quality of something can only be determined by putting it to the test or experiencing it firsthand. (इसका असली मूल्य या गुणवत्ता केवल इसे आजमाने से पता चल सकता है।)
• Example: He claimed his new recipe was amazing, but the proof of the pudding is in the eating, so I had to taste it to believe him.
• Explanation of the correct meaning: The idiom suggests that a person can only know if something is good or bad by trying or experiencing it. (किसी चीज़ की अच्छाई या बुराई को केवल अनुभव करके ही जाना जा सकता है।)
• Example: The new software looks promising, but the proof of the pudding is in the eating; let's use it in real-world scenarios to see how well it works.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Option 1: One has the evidence if they are alert (यदि वे सतर्क हैं, तो उनके पास सबूत होता है।)
• Explanation: This statement is unrelated to the given idiom.
• Example: Being alert is important to gather evidence during an investigation.
• Option 2: Trust is built by sharing good food (भरोसा अच्छे भोजन को साझा करके बनाया जाता है।)
• Explanation: While food can help people bond, this interpretation does not match the idiom.
• Example: A warm meal can bring people together, but trust goes beyond just sharing food.
• Option 3: It's better to be well-fed than to go hungry (भूखे रहने से अच्छा है कि भरपेट खाएं।)
• Explanation: This option focuses on hunger and does not explain the idiom's true meaning.
• Example: It's always wise to plan meals so that no one goes hungry.

The correct answer is: Option 4 (Contemporary).

Key Points

• The word "traditional" means something that adheres to established customs or long-standing practices. (पारंपरिक)
• Example: The traditional dress of the region reflects its rich cultural heritage.
• "Contemporary" refers to something modern or current, often in contrast to traditional practices or styles. (आधुनिक)
• Example: The artist's contemporary techniques brought a fresh perspective to the classic themes.
• Hence, the opposite of "traditional" is "contemporary."

Therefore, the correct answer is: Option 4 (Contemporary).

Additional Information

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

• Unique (अद्वितीय): Being the only one of its kind; unlike anything else.
• Example: Her unique style makes her paintings stand out from the rest.
• Stale (बासी): Something that is no longer fresh or appealing.
• Example: The bread had gone stale after being left out overnight.
• Ancient (प्राचीन): Something very old, often belonging to a distant past.
• Example: The museum houses ancient artifacts from centuries ago.

The correct answer is Option 2.

 

Key Points

• The word "strenuous" is an adjective, not an adverb. It describes something that requires a lot of effort or energy (e.g., "a strenuous task").
• In the sentence, the verb "worked" requires an adverb to describe how the students worked. Therefore, "strenuous" is grammatically incorrect in this context.
• A grammatically correct usage would be: "worked strenuously."

Therefore, the correct answer is Option 2.

 

Correct Usage: "The teacher noticed that all students worked strenuously to complete the project on time."

 

Additional Information

• Option 1: "laboriously" – Correct adverb; means with great effort. (कड़ी मेहनत से)
• Option 3: "hard" – Correct adverb; irregular form of “hardly.” Means with intensity or diligence. (मेहनत से)
• Option 4: "meticulously" – Correct adverb; means with great attention to detail. (बारीकी से)

The correct answer is 'Option 3' i.e. actively.

 

Key Points

• "Actively involved" is a common collocation, meaning someone is consistently and energetically participating in an activity. (सक्रिय रूप से शामिल)
• It fits naturally with the phrase “involved in social service,” implying regular and enthusiastic contribution.
• Example: She has been actively involved in community health programs for decades.

Therefore, the correct answer is 'Option 3'.

Complete Sentence: Ramesh has been actively involved in social service for 30 years.

Additional Information

• Exactly (सटीक रूप से): Used for precision or accuracy, not suitable before “involved.”
• Example: That’s exactly what I meant.
• Brightly (चमकते हुए): Refers to light or color — unrelated to participation.
• Example: The stars shone brightly in the sky.
• Gently (धीरे से): Describes a soft or mild manner — doesn't suit the context of social service involvement.
• Example: She spoke gently to calm the child.

The correct answer is Option 4.

 

Key Points

• The phrase "more too faster" is grammatically incorrect because it contains a redundancy.
• The word "faster" is already a comparative form of "fast" and does not require "more" or "too" before it simultaneously.
• You can say either "too fast" or "much faster", but "more too faster" is incorrect.
• The corrected sentence should read: "that he sings too fast" or "that he sings much faster."

Therefore, the correct answer is Option 4.

 

Correct Sentence: "In the Director’s party, everyone noticed that he sings too fast."

 

Additional Information

• Option 1: "everyone noticed" – grammatically correct.
• Option 2: "In the Director’s party," – grammatically correct prepositional phrase.
• Option 3: "No error" – incorrect, as Option 4 clearly contains an error.

The correct answer is: Modest.

Key Points

• The word "Haughty" refers to being arrogantly superior and disdainful, often showcasing a sense of excessive pride or self-importance. (अहंकारी)
• Example: Her haughty attitude made it difficult for others to approach her.
• "Modest" is characterized by humility, not being overly proud or arrogant, and being unassuming. (विनम्र)
• Example: Despite his great achievements, he remained modest and approachable.
• Hence, the antonym of 'Haughty' is 'Modest'.

Therefore, the correct answer is: Modest.

Additional Information

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

• Distracted (विचलित): Unable to concentrate or focus due to interruptions or disturbances.
• Example: He seemed distracted during the meeting and missed the key points.
• Ample (पर्याप्त): Describes something that is plentiful or more than enough.
• Example: They had ample time to prepare for the presentation.
• Transient (क्षणिक): Refers to something temporary or not lasting for a long time.
• Example: The transient nature of fame means it can disappear quickly.

The correct answer is: Option 4.

Key Points

• The word "neccessary" is spelled incorrectly. The correct spelling is "necessary".
• "Neccessary" is not a valid word in English and does not exist in the dictionary. (गलत वर्तनी)
• Example: The word "neccessary" does not convey any meaning as it is incorrectly spelled.
• The correct word "necessary" means something that is essential or required. (आवश्यक)
• Example: It is necessary to bring your identification card for the meeting.
• Hence, the incorrect spelling "neccessary" should be replaced with the correct spelling "necessary".

Therefore, the correct answer is: Option 4.

Additional Information

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

• Process (प्रक्रिया): A series of actions or steps taken to achieve a particular end.
• Example: The application process requires careful attention to detail.
• Required (आवश्यक): Needed or essential for a particular purpose.
• Example: A passport is required for international travel.
• Application (आवेदन): A formal request or form for something, such as a job or admission.
• Example: The application for the scholarship must be submitted by next week.

The correct answer is: Option 4.

Key Points

• The word "comforble" is incorrectly spelt. It should be "comfortable." (आरामदायक)
• English Meaning: Providing physical ease and relaxation; free from stress or discomfort.
• Hindi Meaning: आरामदायक
• Example: The sofa in the living room is very comfortable to sit on.
• The correct word is "comfortable."
• English Meaning: Providing physical ease and relaxation; free from stress or discomfort.
• Hindi Meaning: आरामदायक
• Example: The hotel provided comfortable accommodations during our stay.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Option 1: The team worked hard to complete the project. (टीम ने परियोजना को पूरा करने के लिए कड़ी मेहनत की।)
• Hindi Meaning: कोई गलत वर्तनी नहीं है।
• Example: The team showed great dedication while completing the project.
• Option 2: We visited several historical sites during our trip. (हमने अपनी यात्रा के दौरान कई ऐतिहासिक स्थलों का दौरा किया।)
• Hindi Meaning: कोई गलत वर्तनी नहीं है।
• Example: The Taj Mahal is one of the historical sites we visited during our trip.
• Option 3: She enjoyed the delicious dinner and dessert. (उसने स्वादिष्ट रात के खाने और मिठाई का आनंद लिया।)
• Hindi Meaning: कोई गलत वर्तनी नहीं है।
• Example: The chocolate cake was the perfect dessert after dinner.

The correct answer is: Succinct.

Key Points

• The word "succinct" means clearly and briefly expressed, without unnecessary words. (संक्षिप्त)
• Example: The professor gave a succinct explanation of the complex topic, making it easy for everyone to understand.
• In the given sentence, the term "compact and precise summary" is best described by the word "succinct." (संक्षिप्त)
• Example: Her succinct presentation covered all the main points in just five minutes.

Therefore, the correct answer is: Succinct.

Additional Information

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

• Redundant (अतिरिक्त): Something that is unnecessary, repetitive, or no longer needed.
• Example: The report was filled with redundant information, making it unnecessarily long.
• Verbose (शब्दाडंबरपूर्ण): Using more words than necessary; wordy.
• Example: His verbose speech made it difficult to focus on the main point.
• Diffuse (फैलाना): Spread over a large area; not concentrated or concise.
• Example: The article was so diffuse that it was hard to understand the key message.

The correct answer is: Meticulous.

Key Points

• The word "sloppy" means careless, untidy, or lacking attention to detail. (असावधान, अस्त-व्यस्त)
• Example: The sloppy handwriting made the document hard to read.
• "Meticulous" refers to showing great attention to detail; being very careful and precise. (अत्यंत सावधान, सूक्ष्म दृष्टि वाला)
• Example: She is meticulous in her work, ensuring everything is done perfectly.
• Hence, we can infer that the opposite of "sloppy" is "meticulous".

Therefore, the correct answer is: Meticulous.

Additional Information

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

• Untidy (अस्त-व्यस्त): Not neat or organized; messy.
• Example: His untidy room made it difficult to find anything.
• Shabby (घिसा-पिटा, जीर्ण): Showing signs of wear and tear; neglected or in poor condition.
• Example: The shabby sofa had been in the family for generations.
• Messy (गंदा, अव्यवस्थित): Disorganized or dirty.
• Example: The messy table was covered with books and papers.

The correct answer is 'to leave'.

 

Key Points

• The phrase "ordered someone to do something" is the correct grammatical structure used after reporting verbs like "order", "tell", "ask", etc.
• Therefore, the verb should be in the infinitive form: to leave, not "left", "leaving", or "to left".
• This maintains subject-verb agreement and sentence clarity.

Therefore, the correct answer is Option 4.

 

Complete Sentence: "The security officer ordered the group to leave the premises immediately."

 

Additional Information

• Option 1: "Left" is the simple past tense, but it doesn’t follow the correct pattern after "ordered".
• Option 2: "to left" is grammatically incorrect; "left" cannot follow "to".
• Option 3: "leaving" is the present participle and does not fit the construction with "ordered".

The correct answer is Option 1.

 

Key Points

• The subject "Somebody" is a singular indefinite pronoun, so it must be followed by a singular verb.
• The correct singular verb form of "have" is "has", making the correct phrase: "Somebody has left".
• The original sentence incorrectly uses the plural verb "have" with a singular subject.

Therefore, the correct answer is Option 1.

 

Correct Sentence: "Somebody has left dirty clothes on the bed."

 

Additional Information

• Option 2: "have been left" – Incorrect as it is passive voice and also mismatches with the singular subject "Somebody".
• Option 3: "was left" – Incorrect tense and passive voice; also doesn’t match with the plural object "dirty clothes".
• Option 4: "were left" – Also passive and does not match with the singular subject "Somebody".

The correct answer is 'that'.

 

Key Points

• The word "that" is a relative pronoun used to introduce a defining clause, giving essential information about the noun it follows — in this case, "technology."
• The clause "that promises to very quickly create anything people can design" describes the function of 3D printing.
• Thus, "that" correctly connects the noun "technology" with the action it performs.

Therefore, the correct answer is Option 4.

 

Complete Sentence: "3D printing is an exciting new technology that promises to very quickly create anything people can design."

 

Additional Information

• Option 1: "the" – Incorrect article; does not connect clauses.
• Option 2: "then" – An adverb used for sequencing, not for introducing a relative clause.
• Option 3: "than" – Used in comparisons, not appropriate here.

The correct answer is: Ruthless.

Key Points

• The word "Brutal" means harsh, cruel, or extremely violent. It is used to describe actions or behavior lacking compassion or mercy. (क्रूर)
• Example: The dictator's brutal policies led to widespread suffering among the people.
• "Ruthless" refers to showing no pity or compassion for others. It is synonymous with "Brutal" as both imply a lack of mercy or kindness. (निर्दयी)
• Example: The ruthless leader crushed any opposition to his rule without hesitation.
• Hence, we can infer that the synonym of "Brutal" is "Ruthless".

Therefore, the correct answer is: Ruthless.

Additional Information

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

• Active (सक्रिय): Energetic or involved in action.
• Example: She is very active in community service and volunteers regularly.
• Heroic (वीरता): Showing courage and determination, often in challenging situations.
• Example: His heroic efforts saved many lives during the disaster.
• Notable (उल्लेखनीय): Worthy of attention or significant.
• Example: The scientist made notable contributions to the field of medicine.

The correct answer is 'up'.

 

Key Points

• The correct phrasal verb is "eat up", which means to consume something completely or greedily.
• In the context of the passage, the birds were eating all the harvested grains, leaving none behind — hence, “eat up” is the most appropriate choice.
• Other options do not form appropriate or meaningful phrasal verbs with "eat" in this context:
• Eat away: implies gradual erosion, not fast consumption of food.
• Eat off: means to eat from the surface of something (like a plate).
• Eat on: not a standard phrasal verb in this context.

Therefore, the correct answer is 'Option 1'.

 

Complete Sentence: The farmers in our village were fed up with the birds that used to eat up all their harvested grains.

 

Additional Information

• Eat up: To consume completely — most suitable in this food-related agricultural context.
• Eat away: To erode or corrode — more suited to gradual damage.
• Eat off: To consume food from a surface — incorrect here.
• Eat on: Not a recognized or meaningful phrasal verb here.

The correct answer is 'but'.

 

Key Points

• The sentence contrasts two ideas: the farmers made an effort to guard the crops, but their efforts failed.
• In such a scenario, a contrast conjunction like “but” is required to connect the two opposing outcomes.
• Other options do not convey the contrast appropriately:
• As: implies cause or reason — not suitable here.
• For: also gives reason — not appropriate for contrast.
• Because: denotes causality — incorrect in this context of failure despite effort.

Therefore, the correct answer is 'Option 3'.

 

Complete Sentence: They tried to take turns watching, but still, they were not able to save the crops.

 

Additional Information

• But: Used to show contrast — correct choice in this context.
• As: Indicates time or reason — incorrect.
• For: Means "because" — does not express contrast.
• Because: Used to state a reason — doesn't fit the contrast needed here.

The correct answer is 'were used'.

 

Key Points

• The passage is narrated in the simple past tense (e.g., "were fed up", "tried", "suggested", "was made", "was accessorised").
• To maintain tense consistency, the correct form for the blank is also in the simple past passive voice: "were used".
• "Bundles of straw" is the subject receiving the action (being used), so the passive form is appropriate.
• Other options:
• Has been used: Present perfect tense — mismatched with past narration.
• Are used: Simple present — incorrect with the past narrative.
• Had been used: Past perfect — implies a past-before-past scenario, unnecessary here.

Therefore, the correct answer is 'Option 2'.

 

Complete Sentence: The face of the scarecrow was made using an earthen pot, while bundles of straw were used to create its arms.

 

Additional Information

• Were used: Simple past passive — correct and consistent with the rest of the passage.
• Has been used: Present perfect — tense mismatch.
• Are used: Present tense — does not fit past narration.
• Had been used: Past perfect — unnecessary complexity in this context.