SSC CGL 2025 (Held On: 19 Sept, 2025 Shift 2) (Previous Year Paper)

Given Statement:

The bank has introduced green bonds to fund eco-friendly projects.

Conclusions:

I. The bank is supporting sustainable development - True (Because, green bonds are specifically introduced to fund eco-friendly projects, which directly indicates support for sustainable development.)

II. Green bonds are more profitable than regular bonds - False (Because, no information is given in the statement regarding profitability comparison between green bonds and regular bonds.)

So, Only conclusion I follows.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: (First number)² + (Second number)² = 3rd number

Given,

For, 3 + 2

⇒ 3² + 2²

⇒ 9 + 4 = 13

For, 4 + 3

⇒ 4² + 3²

⇒ 16 + 9 = 25

Similarly, 5 + 4:

⇒ 5² + 4²

⇒ 25 + 16 = 41

Hence, the correct answer is "Option 1".

BODMAS Table: 

Given equation: 50 ÷ 5 + 8 - 6 × 2 = 56

Now, if ‘-’ and ‘×’ are interchanged, then:

⇒ 50 ÷ 5 + 8 × 6 - 2 = 56

⇒ 10 + 8 × 6 - 2 = 56

⇒ 10 + 48 - 2 = 56

⇒ 58 - 2 = 56

⇒ 56 = 56

Hence, the correct answer is "Option 4".

Family Chart:

Given: 

A is the daughter of B.

B is the son of C.

C is the father of D.

So, A is Niece of D.

Hence, the correct answer is "Option 2".

Family Chart:

Given: 

Raj's father's only son → Raj himself.

Grandmother of Raj → Raj's paternal grandmother.

Daughter-in-law of Raj's grandmother → wife of Raj's father.

So, the woman is Raj's mother.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: Each letter is shifted forward by +3 in the English alphabet.

Given, AC : DF

Now, GI:

So, GI : JL

Hence, the correct answer is "Option 1".

The logic followed here is:

thus, "364" will replace the question mark in the given series.

Hence, the correct option is "Option 1".

Given:

Statement:

Students often get distracted during online classes.

Action:

1. Introduce interactive tools and quizzes - Follows (Because, interactive tools and quizzes can actively engage students during online classes and directly help in reducing distraction.)
2. Ban online classes permanently - Does not follows (Because, banning online classes does not address the issue of distraction in a constructive way. The problem is distraction, not the existence of online classes themselves.)

So, Only 1 follows.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: In a correct modulo operation, the remainder should always be less than the divisor.

Checking each option:

Option 1: 6 % 3 = 2

→ Actually, 6 ÷ 3 = 2 remainder 0 (so 2 is wrong).

Option 2: 9 % 3 = 3

→ Actually, 9 ÷ 3 = 3 remainder 0 (so 3 is wrong).

Option 3: 8 % 2 = 4

→ Actually, 8 ÷ 2 = 4 remainder 0 (so 4 is wrong).

Option 4: 7 % 3 = 2

→ 7 ÷ 3 = 2 remainder 1 → This does not follow the pattern of exact division like the first three.

So, 7 % 3 = 2 violates the division pattern, and that makes it the odd one out.

Hence, the correct answer is "Option 4".

Given: Seven people A, B, C, D, E, F, and G live on seven different floors of a building.

The lowermost floor in the building is numbered 1 and the topmost floor is numbered 7.

A does not live on the topmost floor.

B lives immediately below F.

C lives on an even-numbered floor.

Three people live between F and C.

The number of people living between F and D is equal to the number of people living between D and C.

More than four people live between E and G.

B lives on one of the floors below G.

Two floors below A is E.

Hence, the correct answer is Option 3.

Given Statement:

All actors are professionals.

All professionals are creative.

Some creative people are lazy.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some actors are lazy - False (Because, although all actors are creative, and some creative people are lazy, there is no definite relation given between actors and lazy people. So it can be possible only.)

II. All actors are creative - True (Because, all actors are professionals and all professionals are creative, therefore all actors are definitely creative.)

So, Only conclusion II follows.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: All options except one are 2D shapes (flat shapes with area), while one is a 3D shape (has volume).

Square → 2D

Triangle → 2D

Rectangle → 2D

Sphere → 3D  

Pentagon → 2D

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: Each letter in the first word is replaced by a new letter pattern, preserving the same positional mapping.

Given: xxyzyy : ccbabb:

x → c

y → b

z → a

Now, xyyzzy:

x → c

y → b

y → b

z → a

z → a

y → b

So, xyyzzy → c b b a a b

Hence, the correct answer is "Option 4".

The logic followed here is:

FRIEND → F D N I R E

TICKET written?

So, TICKET → TTECIK

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: All options except one are economic measures/indicators, while one is an organization.

GDP → Economic measure

NNP → Economic measure

GNP → Economic measure

RBI → Central Bank / Organization 

Hence, the correct answer is "Option 4".

Given word: PROFESSION

Letters available: P, R, O, F, E, S, S, I, O, N

Option 1) PROVISION

→ Requires changing in F & E, and removing one S, so more than one change → Cannot be formed

Option 2) POSSESSION

→ Requires changing R → O and removing one F, so more than one change → Cannot be formed

Option 3) PROCESSION

→ Can be formed by changing F → C

Option 4) PROGRESSION

→ Requires changing F → G and adding R, more than one change → Cannot be formed

Hence, the correct answer is "Option 3".

The logic followed here is:

thus, "8.57" will replace the question mark in the given series.

Hence, the correct option is "Option 2".

The logic followed here is:

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

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: All options except one are political movements for India’s freedom, while one is a social reform/land donation movement.

Independence Movement → Political / Freedom struggle

Khilafat Movement → Political / Freedom struggle

Swadeshi Movement → Political / Freedom struggle

Bhoodan Movement → Social reform movement 

Hence, the correct answer is "Option 4".

The logic followed here is:

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

Hence, the correct answer is "Option 1".

BODMAS Table: 

Given equation: 20 + 8 - 5 = ?

Now, if ‘+’ = ‘-’ and ‘-’ = ‘+’, then:

⇒ 20 - 8 + 5 = ?

⇒ 12 + 5 = ?

⇒ 17

Hence, the correct answer is "Option 3".

Given:

Number of students sitting in a circle = 20

According to Question:

Each student shakes hands with exactly 3 neighbors.

Total handshakes = (Number of students × Handshakes per student) ÷ 2

= (20 × 3) ÷ 2

= 60 ÷ 2

= 30

Hence, the correct answer is Option 2.

The logic followed here is:

Logic: Each letter is shifted 1 position forward in the English alphabet.

Given,

MASTER → N B T U F S

Now, N B T U F S →

So, NBTUFS → O C U V G T

Hence, the correct answer is "Option 1".

Given: The 7th day of the month is three days earlier than Friday.

According to Question:

Three days earlier than Friday = Friday − 3 days = Tuesday

So, the 7th day of the month = Tuesday

Number of days between 7th and 20th = 20 − 7 = 13 days

Divide 13 by 7 to find weeks and extra days: 13 ÷ 7 = 1 week + 6 days

So, day of 20th = 7th day + 6 days = Tuesday + 6 days = Monday

Hence, the correct answer is Option 1.

The logic followed here is:

thus, "17" will replace the question mark in the given series.

Hence, the correct option is "Option 1".

The correct answer is Reduction in Earth's temperature.

Key Points

• The Gaganyaan mission is India's first human spaceflight mission, aimed at advancing the nation’s space technology and research capabilities.
• The mission primarily focuses on enhancing India's space exploration capabilities and human spaceflight technology, not on climate-related objectives like reducing Earth's temperature.
• Reduction in Earth's temperature is not a realistic or intended outcome of the Gaganyaan mission, as space missions do not directly influence global climate systems.
• Gaganyaan aims to develop indigenous technologies for human space travel, such as crew modules, life support systems, and space docking mechanisms, among others.
• The benefits of the mission are mainly technological, economic, and strategic, with no direct relation to environmental or climate control measures.

Additional Information

• Increased global collaborations in space science
• The Gaganyaan mission fosters international partnerships and collaborations in space science by working with countries like Russia, France, and the USA for training, technology sharing, and research.
• Such collaborations enhance India’s global standing in space exploration and encourage knowledge exchange with leading space agencies like NASA, Roscosmos, and ESA.
• Advancement in space-related R&D and technology
• The mission is expected to drive significant advancements in space technology, including innovations in materials, propulsion systems, life support, and spacecraft design.
• It will also boost research in artificial intelligence, robotics, and automation, which are critical for future space missions.
• The technologies developed for Gaganyaan have potential applications in defense, healthcare, communication, and disaster management sectors.
• Boost to India's human spaceflight capability
• The Gaganyaan mission is a major milestone in establishing India as a leader in human spaceflight capabilities.
• It aims to send a crew of Indian astronauts, also known as "vyomanauts," into a 300-400 km low Earth orbit for 5-7 days.
• This will make India the fourth country, after the USA, Russia, and China, to achieve independent human spaceflight capability.

The correct answer is USA.

Key Points

• The United States (USA) has the largest economy among the QUAD countries, with a nominal GDP of over $26.7 trillion as of 2023 (IMF data).
• The USA is the world’s largest economy overall, accounting for approximately 24% of global GDP.
• The country has a highly developed and technologically advanced economy, driven by sectors such as technology, finance, healthcare, and defense.
• It is a member of the QUAD (Quadrilateral Security Dialogue), along with Japan, India, and Australia, which focuses on strategic and economic cooperation in the Indo-Pacific region.
• The USA is a global leader in innovation, with major corporations like Apple, Microsoft, and Amazon headquartered there, contributing significantly to its economic strength.

Additional Information

• Japan
• Japan has the third-largest economy in the world, with a nominal GDP of approximately $4.4 trillion (as of 2023).
• It is a global leader in technology, automotive manufacturing, and robotics, with corporations like Toyota, Sony, and Panasonic based there.
• Japan is a key member of the QUAD alliance and plays a significant role in maintaining stability in the Indo-Pacific region.
• India
• India has the fifth-largest economy globally, with a nominal GDP of approximately $3.7 trillion (as of 2023).
• It is a rapidly growing economy, driven by sectors such as IT services, pharmaceuticals, agriculture, and renewable energy.
• India is a crucial member of the QUAD and contributes to the alliance's efforts to promote regional security and economic development.
• Australia
• Australia has a nominal GDP of approximately $1.9 trillion (as of 2023), making it the smallest economy among the QUAD nations.
• Its economy is heavily reliant on natural resources, agriculture, and services, with significant exports of coal, iron ore, and natural gas.
• Australia actively participates in the QUAD, emphasizing its commitment to a free and open Indo-Pacific region.
• The QUAD (Quadrilateral Security Dialogue)
• It is a strategic alliance between the USA, Japan, India, and Australia, aimed at promoting peace, security, and economic growth in the Indo-Pacific region.
• The QUAD focuses on collaboration in areas such as defense, climate change, critical technologies, and infrastructure development.
• As of recent years, the QUAD has gained prominence as a counterbalance to China's growing influence in the region.

The correct answer is To create public awareness about the economic, social, and cultural benefits of IPRs.

Key Points

• The National Intellectual Property Rights (IPR) Policy aims to promote awareness about IPRs among all sections of society, emphasizing their economic, social, and cultural significance.
• It focuses on enhancing the understanding of intellectual property rights to foster a culture of innovation and creativity in India.
• The policy encourages the active participation of stakeholders, including educational institutions, industries, and the public, in promoting IPR awareness.
• It seeks to integrate IPR education into the academic curriculum to build a knowledge-driven society.
• The goal is to increase the number of IPR filings in India by creating a more informed public and facilitating innovation-driven economic growth.

Additional Information

• Option 1: To discourage the filing of patents by domestic inventors to reduce bureaucratic hurdles
• This option is incorrect as the IPR policy aims to encourage, not discourage, the filing of patents by domestic inventors.
• The policy seeks to simplify and streamline procedures for filing patents and other IPRs to reduce bureaucratic hurdles.
• The government has introduced initiatives like the Startup Intellectual Property Protection (SIPP) scheme to assist startups in filing patents and trademarks.
• Option 3: To solely focus on strengthening the enforcement mechanisms against counterfeiting and piracy
• While strengthening enforcement mechanisms is a key component of the IPR policy, the policy does not focus solely on this aspect.
• It also emphasizes IPR awareness, capacity building, and innovation promotion to create a balanced IPR ecosystem.
• Measures include the establishment of Commercial Courts and the modernization of IPR offices to ensure timely and effective enforcement.
• Option 4: To advocate for the abolition of international treaties related to intellectual property
• This option is incorrect as the IPR policy supports India's active participation in international treaties and agreements related to intellectual property.
• The policy emphasizes aligning India's IPR framework with global standards while safeguarding national interests.
• India is a signatory to various international IPR treaties, such as the Paris Convention, Berne Convention, and TRIPS Agreement.
• Main Theme: National IPR Policy
• The National IPR Policy was adopted by the Government of India in May 2016 to create a robust IPR framework in the country.
• The policy is based on seven objectives, including IPR awareness, generation, legal and legislative framework, administration, commercialization, enforcement, and human capital development.
• It aims to position India as a global leader in innovation by building a dynamic and balanced IPR ecosystem.

The correct answer is The British monopoly on the manufacture and sale of salt.

Key Points

• The Salt Satyagraha, led by Mahatma Gandhi in 1930, was a nonviolent protest against the British monopoly on salt production and its taxation, which affected every Indian household.
• The British government imposed a salt tax and prohibited Indians from collecting or making their own salt, forcing them to buy it from government sources.
• On March 12, 1930, Gandhi and his followers began a 24-day march from Sabarmati Ashram to Dandi, covering 240 miles, to produce salt from seawater as an act of civil disobedience.
• The march and subsequent acts of defiance against the salt laws galvanized nationwide support, symbolizing the broader struggle for Indian independence.
• The Salt Satyagraha became a turning point in the Indian independence movement, showcasing the power of nonviolent resistance and gaining international attention.

Additional Information

• The imposition of heavy taxes on land revenue
• The British introduced systems like the Zamindari, Ryotwari, and Mahalwari to collect land revenue.
• These systems often resulted in exorbitant taxes, leading to widespread poverty and exploitation of farmers.
• While this issue caused significant unrest, it was not the direct cause of the Salt Satyagraha.
• The restrictions on the movement and assembly of Indians
• The British government implemented several restrictive laws, such as the Rowlatt Act, which curtailed civil liberties like freedom of assembly and movement.
• These restrictions led to protests like the Jallianwala Bagh massacre in 1919 but were not the primary focus of the Salt Satyagraha.
• The introduction of separate electorates for different communities
• The British introduced separate electorates for Muslims, Sikhs, and other minority communities through acts like the Government of India Act, 1919 and 1935.
• This policy was aimed at dividing Indian society along communal lines but was unrelated to the Salt Satyagraha.
• Overall Theme: The Salt Satyagraha
• The Salt Satyagraha was part of Gandhi's broader strategy of nonviolent resistance (Satyagraha) against British colonial rule.
• It demonstrated the ability of Indians to challenge unjust laws through peaceful means, inspiring similar movements worldwide.
• The movement emphasized self-reliance, unity, and the rejection of oppressive policies imposed by colonial rulers.

The correct answer is It must be accompanied by a valid digital signature.

Key Points

• Under the Bharatiya Sakshya Adhiniyam, 2023 (Indian Evidence Act), digital evidence must be accompanied by a valid digital signature to ensure its authenticity and integrity.
• A digital signature acts as a cryptographic mechanism that verifies the sender's identity and ensures that the data has not been altered during transmission.
• The requirement of a digital signature is in alignment with the provisions of the Information Technology Act, 2000, which governs digital transactions and electronic records in India.
• Courts accept digital evidence only when it has been properly authenticated and complies with the procedural requirements outlined in the Act.
• This measure ensures that the digital evidence presented in court is reliable and free from tampering or forgery.

Additional Information

• Option 1: It must be presented in hard copy form only
• Digital evidence does not need to be converted into hard copy form for submission in court as per modern evidence laws.
• The Bharatiya Sakshya Adhiniyam, 2023, recognizes electronic records, such as emails, videos, and data logs, as valid forms of evidence.
• Hard copies may be used for reference but are not mandatory for the admissibility of digital evidence.
• Option 2: It must come from a reliable, government-approved platform
• While platforms may be regulated or approved by the government for specific purposes, digital evidence does not have to originate from such platforms to be admissible.
• The authenticity of the evidence is determined by its compliance with legal requirements, including the presence of valid digital signatures and adherence to prescribed procedures.
• Option 4: It must be verified by a government official before submission
• Digital evidence does not necessarily need to be verified by a government official before submission in court.
• Instead, its admissibility depends on factors such as authenticity, relevance, and compliance with procedural requirements, including digital signatures.
• Verification may be required in specific cases, but it is not a blanket rule under the Bharatiya Sakshya Adhiniyam, 2023.
• Key Concepts Related to Digital Evidence:
• Digital evidence includes any information stored or transmitted in digital form that may be used in a court of law.
• Examples include emails, social media content, CCTV footage, electronic contracts, and mobile phone data.
• Authentication procedures, such as digital signatures and hash values, are crucial for ensuring the reliability of digital evidence.
• The Information Technology Act, 2000, and related amendments play a significant role in governing the use and admissibility of electronic records in India.

The correct answer is Rajeeva Laxman Karandikar.

Key Points

• Rajeeva Laxman Karandikar was appointed as the Chairperson of the National Statistical Commission (NSC) in December 2022.
• He is a renowned statistician and was formerly the Director of Chennai Mathematical Institute (CMI).
• Karandikar is well-known for his expertise in probability theory, statistical methods, and their applications in real-world problems.
• He has worked extensively in election forecasting, developing mathematical models to predict outcomes of elections based on data.
• As Chairperson of NSC, he oversees the development, implementation, and monitoring of statistical activities in India, ensuring data quality and transparency.

Additional Information

• Pronab Sen
• Pronab Sen is an Indian economist who served as the first Chief Statistician of India from 2007 to 2010.
• He played a key role in modernizing India’s statistical system and led the formulation of national accounts and price statistics.
• Sen was instrumental in the development of methodologies for economic surveys and improving data collection processes.
• Bimal Jalan
• Bimal Jalan is a prominent Indian economist and former Governor of the Reserve Bank of India (RBI).
• He has authored several books on economic policies and governance and played a significant role in India’s financial reforms during his tenure as RBI Governor.
• Jalan’s contributions are primarily in the field of monetary policy and macroeconomic stability.
• Arvind Virmani
• Arvind Virmani is an Indian economist who served as the Chief Economic Advisor to the Government of India from 2007 to 2009.
• He is known for his work on macroeconomic policy, international trade, and economic growth.
• Virmani has also represented India in several international organizations, including the International Monetary Fund (IMF).
• National Statistical Commission (NSC)
• NSC is an autonomous body established in 2006 to improve statistical systems and ensure the credibility of data in India.
• Its primary goal is to formulate policies and standards for statistical activities, ensuring data accuracy and reliability.
• The Commission consists of a Chairperson, members, and a Secretary to assist in its operations.
• NSC plays a pivotal role in guiding the statistical ecosystem in India, enabling evidence-based policymaking.

The correct answer is Option 1.

Key Points

• Option 1 is incorrect because both hematite and magnetite ores of iron are found in India, not just hematite.
• India is known for its significant iron ore resources, including hematite and magnetite, which account for a substantial portion of the country's mining output.
• Hematite is the most abundantly found iron ore in India, and it is extensively mined due to its high iron content.
• Magnetite is the second most prevalent iron ore in India, recognized for its higher iron content compared to hematite.
• This misrepresentation in Option 1 is why it is the correct answer to the question of incorrect statements.

Additional Information

• Option 2: In Odisha, iron ore occurs in a series of hill ranges in Sundargarh, Mayurbhanj, and Jhar.
• This statement is correct. Odisha is one of the leading producers of iron ore in India.
• The state is home to rich iron ore deposits in regions such as Sundargarh, Mayurbhanj, and Jhar.
• Odisha accounts for a significant share of India’s total iron ore production, contributing extensively to the steel industry.
• Option 3: India consists of the largest reserves of iron ore in Asia.
• This statement is correct. India is one of the leading countries in Asia in terms of iron ore reserves.
• With significant deposits in states like Odisha, Jharkhand, Chhattisgarh, Karnataka, and Goa, India plays a crucial role in the global iron ore trade.
• However, countries like China and Australia surpass India in terms of production and export volumes.
• Option 4: More than 90% of iron ore reserves are found in Jharkhand, Chhattisgarh, Karnataka, and Goa.
• This statement is correct. The majority of India’s iron ore reserves are concentrated in these four states.
• Jharkhand and Odisha have the largest hematite reserves, while Karnataka and Goa are known for both hematite and magnetite deposits.
• The Bellary-Hospet region in Karnataka and the Bailadila range in Chhattisgarh are particularly significant iron ore mining areas.
• Iron Ore in India:
• India is rich in iron ore resources, with hematite and magnetite being the two main types of iron ore found in the country.
• Hematite accounts for around 70% of India’s total iron ore reserves, while magnetite makes up the rest.
• Iron ore mining is a critical industry, as it forms the backbone of the steel industry, which is essential for infrastructure development.
• India exports a significant portion of its iron ore, primarily to countries like China and Japan.

The correct answer is Tambura.

Key Points

• Burrakatha is a traditional folk storytelling art form originating from Andhra Pradesh, India.
• The primary instrument used during Burrakatha performances is the Tambura, a string instrument that plays a pivotal role in setting the rhythm and tone.
• The Tambura is played by the main storyteller, referred to as the "Kathakudu", while narrating mythological, historical, or social stories.
• Burrakatha performances often involve three artists: the main storyteller (Kathakudu), an assistant who plays rhythm instruments like the dholak or kanjira, and another assistant who sings or provides commentary.
• The Tambura helps in maintaining the narrative flow by creating a consistent and captivating background melody.

Additional Information

• Dholak:
• The Dholak is a popular two-headed drum widely used in Indian folk and classical music.
• While the Dholak is commonly employed in folk performances, it is not the primary instrument for Burrakatha.
• In Burrakatha, the Dholak may be used as a supporting instrument to enhance rhythm.
• Noot:
• Noot refers to small cymbals or clappers used in some traditional Indian music performances.
• It is not associated with Burrakatha but may be used in other regional folk arts for rhythm accompaniment.
• Rabab:
• The Rabab is a plucked string instrument originating from Central Asia and is often used in Hindustani classical music.
• It is not relevant to Burrakatha performances, as it is not traditionally used in Andhra Pradesh's folk storytelling traditions.
• Burrakatha:
• Burrakatha is a unique folk art form characterized by its blend of storytelling, music, and commentary.
• The performances are often used to convey social messages, narrate epics, or recount historical events to educate and entertain audiences.
• This art form is deeply rooted in the cultural heritage of Andhra Pradesh, with its origins tracing back to early Telugu literature.

The correct answer is Daman and Diu.

Key Points

• According to the 2011 Census, Daman and Diu had the lowest sex ratio among all Indian States and Union Territories, with only 618 females per 1000 males.
• The low sex ratio in Daman and Diu is attributed to the influx of a male-dominated workforce, as the region has many industries attracting migrant workers.
• The sex ratio is a critical demographic indicator that reflects the number of females per 1000 males in a population.
• Efforts are being made to address the gender imbalance in such regions through awareness campaigns and policies promoting gender equality.
• In contrast, the national sex ratio of India in 2011 was recorded at 943 females per 1000 males, highlighting significant regional disparities.

Additional Information

• Haryana
• Haryana had the second-lowest sex ratio in 2011, with 879 females per 1000 males.
• The skewed sex ratio in Haryana is a result of long-standing issues such as female foeticide, gender-based discrimination, and son preference.
• To address this issue, the government introduced initiatives like Beti Bachao Beti Padhao to improve the status of women in the state.
• Punjab
• Punjab recorded a sex ratio of 895 females per 1000 males in 2011, making it one of the states with a low sex ratio.
• Similar to Haryana, Punjab also faces challenges like female infanticide and societal preference for male children.
• The state has implemented several awareness programs and campaigns to tackle this issue.
• Dadra and Nagar Haveli
• Dadra and Nagar Haveli recorded a sex ratio of 774 females per 1000 males in the 2011 Census.
• The low sex ratio in this Union Territory can also be attributed to the male-dominated migrant workforce in industrial and construction sectors.
• Efforts are being made to address the gender imbalance and improve the living standards of women in the region.
• Importance of Sex Ratio
• The sex ratio is a crucial social indicator that reflects the status of women in a society.
• It impacts various aspects of development, including education, health, and gender equality.
• Improving the sex ratio requires addressing deep-rooted cultural norms and practices, as well as ensuring effective implementation of laws and policies.

The correct answer is Bisht Doab - between Beas and Chenab.

Key Points

• The term Doab refers to the land lying between two rivers, derived from the Persian words "do" (two) and "ab" (water).
• The Bisht Doab is incorrectly stated as being between the Beas and Chenab rivers. This pairing does not geographically exist.
• The correct name for the doab between the Beas and Chenab rivers is nonexistent, as the Beas and Chenab are separated by the Ravi River.
• This makes Option 2 incorrect, as no such doab with this pairing is recognized in geographical terminology.
• The concept of doabs is primarily used for identifying fertile tracts of land in the Punjab region of India and Pakistan, which are irrigated by these river systems.

Additional Information

• Bari Doab (Option 1)
• The Bari Doab is the fertile land lying between the Beas River and the Ravi River.
• This region has significant agricultural importance and is part of the Punjab region in India and Pakistan.
• The word "Bari" comes from the Beas River, highlighting its geographical significance.
• Rachna Doab (Option 3)
• Rachna Doab refers to the land between the Ravi River and the Chenab River.
• This doab lies in the Punjab region of Pakistan and is known for its rich agricultural practices.
• The name "Rachna" is derived from the initial syllables of the rivers Ravi and Chenab.
• Jech Doab (Option 4)
• Jech Doab is the region between the Chenab River and the Jhelum River.
• It is another agriculturally rich area of the Punjab region, primarily situated in modern-day Pakistan.
• The name "Jech" combines the first letters of Jhelum and Chenab, reflecting the rivers it lies between.
• Doabs in the Punjab Region
• The Punjab region (meaning "Land of Five Rivers") is historically and geographically significant for its five rivers: Beas, Ravi, Chenab, Jhelum, and Sutlej.
• These rivers form fertile tracts of land known as doabs, which are vital for agriculture and settlement.
• Famous doabs include the Bari Doab, Rachna Doab, Jech Doab, Sindh Sagar Doab, and others, each named based on the rivers that define their boundaries.

The correct answer is Square base with curving walls.

Key Points

• The Nagara-style shikhara is a distinct feature of Hindu temple architecture, predominantly found in northern India.
• The simplest form of the Nagara-style shikhara is characterized by a square base, which serves as the foundation of the structure.
• The walls of the shikhara are curving inwards as they rise, creating a pyramidal or tower-like appearance.
• These curving walls give the structure its unique aesthetic, symbolizing a mountain or the cosmic axis (axis mundi).
• The Nagara-style is often adorned with intricate carvings and sculptures, representing deities, motifs, and mythological stories.
• This architectural style is most commonly associated with temples such as the Khajuraho Group of Monuments and other northern Indian temple complexes.

Additional Information

• Option 1: Circular base with domes
• This design is not characteristic of Nagara-style architecture but is more closely associated with Islamic architecture.
• Domes and circular bases are prominent features in structures like mosques and mausoleums, such as the Taj Mahal.
• Option 3: Triangular base with garden
• Triangular bases are not a feature of traditional Indian temple architecture.
• The inclusion of a garden is typically associated with Mughal architecture, which emphasizes symmetry and landscaping, as seen in structures like Humayun’s Tomb and the Taj Mahal.
• Option 4: Rectangular base with domes
• Rectangular bases with domes are associated with Indo-Islamic architecture rather than Nagara-style temples.
• This style is often seen in palaces, mosques, and forts built during the Mughal and Sultanate periods.
• Main Theme: Nagara-Style Architecture
• The Nagara style is one of the three main types of temple architecture in India, alongside Dravidian and Vesara styles.
• It is characterized by the vertical elevation of the shikhara and the absence of elaborate boundary walls or gateways.
• Nagara-style temples often have mandapas (pillared halls) leading to the garbhagriha (sanctum sanctorum), where the main deity resides.
• This style is widely prevalent in northern and central India, with notable examples including the Sun Temple at Konark and temples in Khajuraho.

The correct answer is Veneration of indigenous tribal deities.

Key Points

• The Kharchi festival is a significant cultural and religious festival in Tripura, primarily dedicated to the veneration of 14 indigenous tribal deities, collectively referred to as the "Chaturdasha Devata."
• It is observed annually at the Chaturdasha Devata Temple, located in Old Agartala, Tripura.
• The festival involves elaborate rituals, including the ceremonial bathing of the deities in the sacred river followed by their worship with traditional offerings like flowers, fruits, and animal sacrifices.
• The Kharchi Puja is deeply rooted in tribal traditions and signifies the cleansing of sins and the offering of gratitude to the deities for protecting the community and ensuring prosperity.
• The festival is celebrated over a period of seven days and attracts a large number of devotees, both tribal and non-tribal, symbolizing communal harmony and cultural integration in the state.

Additional Information

• Worship of Lord Jagannath:
• The worship of Lord Jagannath is associated with the famous Rath Yatra festival, primarily celebrated in Puri, Odisha.
• Rath Yatra involves the grand chariot procession of Lord Jagannath, his brother Balabhadra, and sister Subhadra, attracting millions of devotees.
• Lord Jagannath is a revered deity in Hinduism and is considered an incarnation of Lord Vishnu.
• Commemoration of Tripura's Statehood Day:
• Tripura's statehood day is celebrated on 21st January every year, marking the day Tripura became a full-fledged state in 1972 under the North-Eastern Areas (Reorganisation) Act, 1971.
• It is an occasion of pride for the people of Tripura, highlighting the state's rich cultural heritage and socio-economic progress.
• Worship of River Goddess Yamuna:
• The worship of Goddess Yamuna is commonly associated with the festival of Yamuna Jayanti or Yam Dwitiya, celebrated in certain parts of India.
• Yamuna is considered a sacred river goddess and the sister of Yama, the god of death, according to Hindu mythology.
• On this occasion, devotees perform rituals and offer prayers along the banks of the Yamuna River, seeking blessings for prosperity and purification of sins.

The correct answer is Devaputra.

Key Points

• The Kushana rulers adopted the title Devaputra, which translates to "Son of God," to assert their divine status and legitimacy as rulers.
• This title reflects their attempt to link their authority to divine origins, thereby elevating their status in the eyes of their subjects.
• The Kushanas were known for their syncretic culture, combining elements of Greek, Persian, Indian, and Central Asian traditions. The use of divine titles was part of this cultural synthesis.
• The title "Devaputra" was prominently used by rulers like Kanishka, who was one of the greatest Kushana emperors and is also known for his contributions to Buddhism.
• The adoption of divine titles helped the Kushana rulers to consolidate their empire and establish a sense of unity among diverse populations under their rule.

Additional Information

• Rajadhiraja:
• This term means "King of Kings" and was used by various Indian rulers to signify their paramount status among other rulers.
• It was a title often adopted by rulers of the Chola dynasty and other South Indian kingdoms to assert their dominance in the region.
• While the Kushanas were known for adopting titles with divine connotations, "Rajadhiraja" emphasized political supremacy rather than divine association.
• Chakravartin:
• The term "Chakravartin" refers to an ideal universal ruler or "one who rules the wheel" (symbolizing the wheel of dharma or sovereignty).
• It was a title used in ancient Indian texts to describe rulers who controlled vast territories and upheld dharma (moral law).
• Famous Mauryan emperor Ashoka is often referred to as a Chakravartin for his efforts to spread Buddhism and establish moral governance.
• The Kushana rulers, however, focused more on divine legitimacy rather than the concept of universal sovereignty implied by "Chakravartin."
• Maharajadhiraja:
• Maharajadhiraja means "Great King of Kings" and was a title used to denote supreme political authority in ancient India.
• It was commonly used by Gupta rulers, who were known for their administrative prowess and cultural achievements.
• While the Kushanas did use grand titles, their emphasis was on divine association through titles like "Devaputra" rather than political supremacy implied by "Maharajadhiraja."
• Main Theme:
• The Kushanas were a Central Asian dynasty that ruled over large parts of northern India, Central Asia, and Afghanistan during the 1st to 3rd centuries CE.
• Their rulers were known for adopting titles and practices that reflected their syncretic culture and political aspirations.
• The title "Devaputra" exemplifies their strategy of using divine legitimacy to strengthen their rule and create a unified empire.
• The Kushanas also played a significant role in the spread of Buddhism, with Kanishka convening the Fourth Buddhist Council and contributing to the development of Mahayana Buddhism.

The correct answer is option 2.

Key Points

• In Judo, a match ends immediately if a player scores an Ippon, which is equivalent to a full point, or receives a Hansoku-make, which signifies disqualification.
• Ippon is awarded when a player executes a perfect technique, such as a throw where the opponent lands on their back with force and control, or achieves a successful pin for 20 seconds.
• Hansoku-make refers to a serious violation of Judo rules, such as prohibited actions or dangerous techniques, which results in the immediate disqualification of the player.
• This rule ensures safety and adherence to the principles of Judo, emphasizing respect, discipline, and fair play during the match.
• The immediate termination of the match upon Ippon or Hansoku-make is a fundamental aspect of Judo competitions and aligns with the sport’s emphasis on decisive outcomes.

Additional Information

• Option 1: Shime-Waza are arm locks targeting the elbows
• This statement is incorrect. Shime-Waza refers to choking techniques in Judo, which involve restricting the opponent’s airflow or blood flow to induce submission.
• The arm locks targeting the elbows in Judo are categorized under Kansetsu-Waza, not Shime-Waza.
• Kansetsu-Waza techniques are designed to apply pressure on joints, particularly the elbows, forcing the opponent to submit.
• Option 3: Judoka can strike and kick but cannot attack joints other than elbows
• This statement is incorrect. Strikes and kicks are strictly prohibited in Judo as it is a grappling martial art focused on throws, pins, joint locks, and chokeholds.
• Judoka are allowed to attack joints only within the scope of Kansetsu-Waza, and even then, only the elbow joint is targeted.
• The prohibition of strikes and kicks reflects Judo’s emphasis on technique, control, and safety rather than brute force or aggression.
• Option 4: Hansoku-make is a minor penalty in Judo
• This statement is incorrect. Hansoku-make is not a minor penalty; it is the most severe penalty in Judo and leads to immediate disqualification.
• Minor penalties in Judo are referred to as Shido, which are warnings for less severe rule violations, such as passivity or improper gripping.
• Hansoku-make is awarded for major rule violations, such as dangerous techniques, unsportsmanlike behavior, or repeated minor penalties.
• Main Theme: Judo Techniques and Rules
• Judo is a modern martial art and Olympic sport developed by Jigoro Kano in Japan. It focuses on techniques such as throws (Nage-Waza), ground techniques (Ne-Waza), pins (Osaekomi-Waza), joint locks (Kansetsu-Waza), and chokes (Shime-Waza).
• The rules of Judo are designed to ensure fairness and safety, with penalties for violations and clear criteria for scoring.
• The emphasis is on skill, precision, and the use of an opponent’s energy and movement to execute techniques effectively.

The correct answer is Bhira.

Key Points

• Babur’s first conquest in India was the region of Bhira, located in Punjab, which was strategically important for establishing his foothold in India.
• This conquest occurred in 1519, during Babur’s early expeditions into the Indian subcontinent.
• Bhira provided Babur a base to secure his operations and enabled further campaigns in northern India.
• It was a well-fortified town, and its capture demonstrated Babur’s military strategy and organizational skills.
• The conquest of Bhira was part of Babur’s initial efforts to expand his empire and was a precursor to his later victories, such as the First Battle of Panipat in 1526.

Additional Information

• Panipat
• The First Battle of Panipat was fought on 21 April 1526, between Babur and Ibrahim Lodi.
• It marked the beginning of the Mughal Empire in India and was one of the earliest battles to use gunpowder firearms and field artillery in the subcontinent.
• Panipat was not Babur’s first conquest in India but was the decisive battle that established his dominance.
• Lahore
• Babur’s campaign in Lahore occurred later as part of his efforts to consolidate his empire after the First Battle of Panipat.
• Lahore was an important cultural and political center and played a significant role in the Mughal Empire’s administration.
• Sialkot
• Sialkot was another important city in Punjab, but it was not Babur’s first conquest during his campaigns in India.
• It became part of the Mughal Empire as Babur expanded his influence in the region.

The correct answer is By winning three repechage bouts after losing his opening match.

Key Points

• Sushil Kumar won the bronze medal in the 66 kg freestyle wrestling category at the 2008 Beijing Olympics.
• After losing his opening match to Andriy Stadnik of Ukraine, he entered the repechage round due to Stadnik advancing to the final.
• In the repechage round, Sushil Kumar secured victories in three consecutive bouts against Doug Schwab (USA), Albert Batyrov (Belarus), and Leonid Spiridonov (Kazakhstan).
• He defeated Leonid Spiridonov in the bronze medal match, making history as the first Indian wrestler to win an Olympic medal since Khashaba Dadasaheb Jadhav’s bronze in 1952.
• This achievement brought wrestling back into the spotlight in India and inspired a new generation of wrestlers.

Additional Information

• Option 1: By winning all his bouts consecutively without any loss
• This option is incorrect as Sushil Kumar lost his opening match against Andriy Stadnik. He did not have an undefeated run in the tournament.
• Winning all bouts consecutively is a rare occurrence in wrestling, especially at the Olympic level, due to tough competition.
• Option 3: By defeating the reigning champion in the finals
• This option is incorrect because Sushil Kumar did not compete in the final match of the tournament; he competed in the bronze medal bout.
• He faced Leonid Spiridonov in the repechage round for the bronze medal and not the reigning champion in the finals.
• Option 4: By receiving a walkover in the semifinals
• This option is incorrect as Sushil Kumar did not participate in the semifinals. He advanced through the repechage round after losing his first match.
• In Olympic wrestling, a walkover occurs when an opponent is unable to compete due to injury or other reasons, but this scenario did not apply to Sushil Kumar in the 2008 Olympics.
• Main Theme: Repechage System in Wrestling
• The repechage system gives wrestlers who lose to a finalist a second chance to compete for a bronze medal.
• This system ensures that wrestlers who face strong opponents early in the tournament still have a fair chance at securing a medal.
• It is commonly used in wrestling tournaments, including the Olympics, to maintain competitive fairness.

The correct answer is Banu Mushtaq & Deepa Bhasthi.

Key Points

• Banu Mushtaq & Deepa Bhasthi won the International Booker Prize in 2025 for their collaborative work, which has been recognized as a significant contribution to global literature.
• The International Booker Prize is awarded annually to a book translated into English and published in the UK or Ireland, with the prize money shared equally between the author and translator.
• The winning work by Banu Mushtaq & Deepa Bhasthi explores themes of identity, displacement, and cultural resilience, resonating with readers across linguistic and cultural boundaries.
• The jury for the International Booker Prize comprises prominent authors, critics, and literary figures who assess the shortlisted works based on originality, literary merit, and global impact.
• This recognition highlights the growing influence of South Asian authors and translators in international literary circles.

Additional Information

• Option 1: Samantha Harvey
• Samantha Harvey is a British author renowned for her works such as "The Wilderness" and "The Western Wind."
• Her novels often delve into themes of memory, morality, and existential questions, earning her several literary accolades but not the International Booker Prize in 2025.
• Option 3: Geetanjali Shree
• Geetanjali Shree, an Indian author, won the International Booker Prize in 2022 for her novel "Tomb of Sand," translated by Daisy Rockwell.
• This historic win marked the first time a work originally written in Hindi received this prestigious award.
• Her works explore themes of feminism, partition, and post-colonial identity, but she did not win the prize in 2025.
• Option 4: Vincenzo Latronico
• Vincenzo Latronico is an Italian author and translator known for his literary and philosophical works.
• While his contributions to literature are notable, he did not win the International Booker Prize in 2025.
• Main Theme: The International Booker Prize
• The International Booker Prize celebrates translated works of fiction, promoting cross-cultural understanding and appreciation.
• It underscores the importance of translators in bringing literary masterpieces to a global audience.
• The prize has significantly contributed to the recognition of diverse voices in literature from around the world.

The correct answer is Option 1: 1 and 2 only.

Key Points

• The 73rd Inter Services Water Polo Championship is an annual event conducted to foster sportsmanship and excellence among armed forces personnel.
• The event is organized by the Eastern Naval Command, which is responsible for promoting aquatic sports within the armed forces.
• In the 2024-25 edition, Visakhapatnam, a major naval base and city in Andhra Pradesh, served as the host city.
• The championship brings together top teams and athletes from the Indian Army, Navy, and Air Force, showcasing their skill and teamwork in water polo.
• There is no evidence or reliable source confirming that the tournament took place in April 2025, aligning with the armed forces' annual aquatic events calendar, making statement 3 incorrect.

Additional Information

• Statement 1: The Eastern Naval Command is a major formation of the Indian Navy that is headquartered in Visakhapatnam. It often takes the lead in hosting aquatic championships, such as the Inter Services Water Polo Championship, to encourage participation and excellence in water sports.
• Statement 2: Visakhapatnam is a significant location for the Indian Navy, hosting several naval facilities and events. Its infrastructure and proximity to the Eastern Naval Command headquarters make it an ideal venue for aquatic events.
• Statement 3: The claim that the tournament occurred in April 2025 is not substantiated. The annual events calendar of the armed forces typically schedules aquatic championships at various times during the year, but specific dates vary. Thus, this statement lacks confirmation and is incorrect.
• Importance of the Championship:
• The Inter Services Water Polo Championship provides a platform for armed forces personnel to demonstrate their physical endurance, teamwork, and strategic skills in water sports.
• Such events promote camaraderie and foster a sense of unity among the different branches of the armed forces.

The correct answer is Provides Inter-State Council framework.

Key Points

• Article 263 of the Indian Constitution empowers the President to establish an Inter-State Council if it appears to him that the public interests would be served by such a council.
• The primary role of the Inter-State Council is to facilitate coordination between the Union and State governments, ensuring harmonious decision-making.
• The Council can inquire into and discuss disputes or subjects of common interest between states or between the Union and one or more states.
• It provides a forum for discussing administrative issues and suggesting better methods for policy and implementation of decisions affecting Union-State relations.
• The Inter-State Council is an advisory body and does not have executive powers; its recommendations are not binding.

Additional Information

• Settles taxation disputes (Option 1)
• Taxation disputes between states or between the Union and states are primarily resolved through institutions such as the Goods and Services Tax (GST) Council, set up under Article 279A of the Constitution.
• The GST Council is responsible for making recommendations to the Union and States on issues related to GST, including tax rates and exemptions.
• Article 263 does not directly deal with settling taxation disputes.
• Creates Zonal Councils (Option 2)
• Zonal Councils are established under the States Reorganisation Act, 1956, and are not directly linked to Article 263.
• These councils aim to promote cooperation and coordination between states in each zone and with the Union government.
• There are five Zonal Councils: Northern, Southern, Eastern, Western, and Central, and they address regional issues like economic development, infrastructure, and border disputes.
• Enforces Emergency Provisions (Option 4)
• Emergency provisions are governed by Articles 352, 356, and 360 of the Constitution and are unrelated to Article 263.
• These provisions empower the President to declare a National Emergency, President’s Rule in a state, or a Financial Emergency under specific circumstances.
• Article 263 is focused on coordination and cooperation between the Union and states and does not deal with emergencies.

The correct answer is 2) 2 and 3 only.

Key Points

• Statement 2: The efficiency of an ideal heat engine depends only on the reservoir temperatures. This is in accordance with the Carnot theorem, which states that the efficiency of a reversible heat engine operating between two thermal reservoirs is solely a function of their absolute temperatures (T_H and T_C). The efficiency is given by the formula: η = 1 - (T_C/T_H).
• Statement 3: Heat flows from a colder body to a hotter body only when external work is applied. This is consistent with the second law of thermodynamics, which states that natural heat flow occurs from hot to cold, and reversing this process requires work (e.g., in refrigeration systems).
• The second law of thermodynamics governs both the efficiency of heat engines and the heat flow direction, ensuring these statements are scientifically accurate and interrelated.
• Both statements are fundamental principles in thermodynamics and are universally accepted in physics and engineering applications.
• Hence, both statements 2 and 3 are correct, making option 2 the correct answer.

Additional Information

• Statement 1: "Work done in irreversible expansion is greater than in quasi-static expansion."
• This statement is incorrect. In irreversible processes, work done is generally less than in quasi-static (reversible) processes because of factors like dissipation, friction, and rapid changes. Quasi-static processes maximize work output by maintaining equilibrium throughout the process.
• For example, in an isothermal reversible expansion of an ideal gas, the work done (W = nRT ln(V_f/V_i)) is higher compared to an irreversible expansion under similar conditions.
• Thermodynamic Processes:
• A thermodynamic process refers to the path through which a system changes its state (e.g., pressure, volume, temperature) due to interactions with its surroundings.
• Examples include isothermal, adiabatic, isobaric, and isochoric processes.
• Heat Engines:
• A heat engine is a device that converts heat energy into mechanical work by operating between two thermal reservoirs.
• Key components of a heat engine include the source (hot reservoir), the working substance, and the sink (cold reservoir).
• The Carnot cycle is the most efficient theoretical heat engine cycle, but real engines operate at efficiencies lower than Carnot efficiency due to irreversibilities.
• Second Law of Thermodynamics:
• The second law establishes the direction of natural processes, stating that entropy (disorder) in an isolated system tends to increase over time.
• It also explains why perpetual motion machines of the second kind are impossible, as no engine can be 100% efficient.

The correct answer is Arms.

Key Points

• Jhora dance is a traditional folk dance performed in the Kumaon region of Uttarakhand.
• The dance is typically performed during festivals, marriages, and other celebratory occasions, symbolizing joy and unity.
• Participants form a circle and hold each other by the arms, moving rhythmically to the beats of traditional music.
• Jhora dance involves synchronized movements and vibrant attire, reflecting the cultural heritage of the region.
• This dance is often accompanied by folk songs sung in the Kumaoni dialect, enhancing its cultural significance.

Additional Information

• Option 1: Shoulders
• While holding by the shoulders is a common style in various group dances globally, it is not a feature of the Jhora dance.
• In some folk dances, such as certain tribal dances, participants may hold each other by the shoulders to maintain formation and rhythm.
• Option 3: Waist
• Holding by the waist is typically seen in dances that require closer physical coordination, such as ballroom dancing or certain traditional couple dances.
• In Jhora dance, participants maintain a bit more distance by holding arms rather than the waist.
• Option 4: Wrists
• Holding by the wrists is common in some forms of folk dances and ceremonial dances where participants form chains or circles.
• However, the Jhora dance emphasizes holding by the arms for better movement synchronization.
• Main Theme: Jhora Dance
• Jhora is a significant cultural expression of the Kumaon region, showcasing the traditional values and festive spirit of the community.
• The dance fosters a sense of belonging and togetherness among participants and spectators alike.
• It is a reflection of the vibrant culture and traditions of Uttarakhand.

The correct answer is It uses over 60 factors including logistics and geography to calculate the PowerIndex.

Key Points

• The Global Firepower (GFP) review is an annual military strength ranking that evaluates nations based on their military capabilities.
• The PowerIndex (PwrIndx) score is calculated using over 60 individual factors, encompassing categories like manpower, equipment, natural resources, financial stability, and geography.
• The ranking methodology emphasizes diversity over quantity; for instance, having a balanced mix of naval assets is more favorable than having a large fleet of a single type.
• Geography plays a crucial role, as nations with strategic locations or extensive coastlines may gain an advantage in specific areas.
• Nuclear stockpiles are considered but do not dominate the ranking system, ensuring non-nuclear nations can also rank competitively.

Additional Information

• Option 1: It considers only the number of active military personnel
• This statement is incorrect because the GFP ranking is not solely based on manpower but evaluates a comprehensive range of factors.
• While active military personnel is an important component, other elements like reserve forces, equipment, and logistics are equally significant.
• Focusing only on manpower would ignore critical aspects like training, technology, and operational readiness.
• Option 2: It ranks nations solely based on nuclear capabilities
• This is incorrect as nuclear capability is only one of the factors considered in the GFP ranking.
• The review includes nuclear stockpiles but ensures that non-nuclear powers are not unfairly disadvantaged.
• The methodology focuses on overall military potential rather than singular factors like nuclear weapons.
• Option 4: It ranks countries alphabetically within continents
• This option is incorrect as the GFP ranking is based on calculated PowerIndex scores and not alphabetical or regional order.
• Countries are ranked globally, with their position determined by overall military strength rather than their location or name.
• Global Firepower (GFP) Overview
• The GFP review is widely recognized for its thorough and unbiased assessment of military strength.
• The ranking includes data from 145 nations, providing a comprehensive analysis of global military power.
• The PowerIndex score is inversely proportional, meaning a lower score indicates a stronger and more capable military.
• It excludes political or current conflict considerations, focusing purely on measurable military factors.

The correct answer is Andhra Pradesh.

Key Points

• India's first Green Hydrogen Hub is planned in Andhra Pradesh, which aims to lead the country's transition to clean energy.
• This initiative aligns with India’s National Hydrogen Mission, launched in 2021 to make India a global hub for green hydrogen production.
• Andhra Pradesh has been chosen due to its strategic location, abundant renewable energy resources, and proximity to ports, making it ideal for green hydrogen production and export.
• The state government is collaborating with private players and investors to establish facilities for green hydrogen production, focusing on decarbonizing industries like steel, cement, and transportation.
• The project is expected to promote sustainability, reduce carbon emissions, and enhance the energy security of India while boosting the regional economy.

Additional Information

• Punjab
• Punjab is a leading agricultural state in India but is not currently at the forefront of green hydrogen production.
• The state is, however, exploring renewable energy opportunities, particularly in solar and biomass energy, to reduce its carbon footprint.
• West Bengal
• West Bengal is an industrial hub with a strong focus on coal-based industries and thermal power plants.
• Efforts are being made to transition to cleaner energy sources, but the state is not a planned location for India's first Green Hydrogen Hub.
• Maharashtra
• Maharashtra, being an industrially advanced state, is actively working on renewable energy projects, including solar and wind energy.
• It has not yet been designated as a site for a Green Hydrogen Hub, but the state is exploring hydrogen-based technologies for decarbonization.
• Green Hydrogen and Its Importance
• Green hydrogen is produced using renewable energy sources like solar and wind power through electrolysis, making it environmentally friendly.
• It plays a vital role in decarbonizing sectors such as transportation, heavy industries, and energy storage.
• India aims to become a global leader in green hydrogen production under its National Hydrogen Mission, reducing dependence on fossil fuels and lowering greenhouse gas emissions.

The correct answer is Chandrayaan-1.

Key Points

• Chandrayaan-1, launched by the Indian Space Research Organisation (ISRO) in October 2008, was India’s first lunar mission.
• The mission made a significant breakthrough by discovering lunar hydration (water molecules) on the Moon’s surface using NASA’s Moon Mineralogy Mapper (M3) instrument onboard.
• This discovery confirmed the presence of hydroxyl (OH) and water (H2O) molecules in the polar regions of the Moon.
• Chandrayaan-1 provided evidence of water ice in permanently shadowed craters near the Moon's poles, revolutionizing our understanding of lunar resources.
• The mission successfully functioned for 312 days and significantly contributed to lunar science, including creating a detailed 3D atlas of the Moon's surface.

Additional Information

• Chandrayaan-2
• Launched in July 2019, Chandrayaan-2 aimed to explore the Moon’s south polar region for water ice and other resources.
• It consisted of an orbiter, a lander named Vikram, and a rover named Pragyan.
• While the lander lost communication during its descent, the orbiter continues to function, sending valuable data about the Moon’s surface and exosphere.
• Chandrayaan-2 further refined the findings of Chandrayaan-1 regarding the presence of water molecules.
• Chandrayaan-3
• As of October 2023, Chandrayaan-3 is ISRO’s latest lunar mission and focuses on demonstrating safe landing and roving capabilities.
• It is a follow-up mission to Chandrayaan-2, consisting of a lander and rover but no orbiter.
• The primary goal is to ensure a successful soft landing on the Moon and study its surface composition and seismic activity.
• Chandrayaan-4
• Chandrayaan-4 is not an officially announced mission by ISRO as of now. It is speculated to be a potential future lunar mission.
• ISRO is currently focusing on Chandrayaan-3 and other interplanetary missions like Gaganyaan and Aditya-L1.
• Lunar Hydration Discovery
• The discovery of water on the Moon is crucial for future human exploration, as it can support life, act as a resource for producing oxygen, and be used as rocket fuel.
• This finding has reshaped strategies for lunar exploration, making the Moon a potential hub for space missions.

The correct answer is Only 2.

Key Points

• Article 72 of the Indian Constitution empowers the President to grant pardons, reprieves, respites, or remissions of punishment, or to suspend, remit, or commute the sentence of any person convicted of an offense under certain circumstances, including in cases of death sentences.
• The Governor, under Article 161, has similar powers but does not have the authority to pardon a death sentence. The power to pardon a death sentence is exclusively vested in the President under Article 72.
• The second statement, "The Governor cannot pardon in cases of death sentence," is correct as the Governor can only commute or remit such sentences but cannot grant a full pardon.
• The first statement, "Both President and Governor can grant pardons under Article 72," is incorrect because the Governor does not exercise powers under Article 72. The Governor's pardoning power is provided under Article 161.
• Thus, the correct answer is Only 2.

Additional Information

• President's Pardoning Powers (Article 72):
• The President has the power to grant pardons, reprieves, respites, remissions, or commutations of punishments for offenses under:
• Union law.
• Matters concerning the executive power of the Union.
• Death sentences (exclusive power).
• This power is exercised on the advice of the Council of Ministers.
• Governor's Pardoning Powers (Article 161):
• The Governor can grant pardons, reprieves, respites, remissions, or commutations for offenses under:
• State law.
• The Governor cannot pardon a death sentence, as this power is exclusively reserved for the President.
• Key Differences Between Article 72 and 161:
• While both the President and Governor can grant pardons and similar reliefs, only the President can pardon death sentences.
• The jurisdiction of the President's power extends to offenses under Union laws, while the Governor's power is limited to State laws.

Shortcut Trick

For any two variables X and Y, if X + Y = A and X − Y = B, then X = (A + B) ÷ 2 and Y = (A − B) ÷ 2.

Here, treating X = √a and Y = √b:

⇒ √a = (5 + 1) ÷ 2 = 3 ⇒ a = 3² = 9

⇒ √b = (5 − 1) ÷ 2 = 2 ⇒ b = 2² = 4

∴ The correct answer is a = 9, b = 4.

Alternate Method

Given:

√a + √b = 5 .....(i)

√a − √b = 1 .....(ii)

Calculation:

Adding equation (i) and equation (ii), we get:

⇒ (√a + √b) + (√a − √b) = 5 + 1

⇒ 2√a = 6

⇒ √a = 3

Squaring both sides to find the value of a:

⇒ a = 3² = 9

Substituting the value of √a back into equation (i):

⇒ 3 + √b = 5

⇒ √b = 5 − 3

⇒ √b = 2

Squaring both sides to find the value of b:

⇒ b = 2² = 4

∴ The correct answer is a = 9, b = 4.

Additional Information

Properties of Surds

If √x = y, squaring both sides removes the square root to give x = y². Surds can be treated like standard algebraic variables when adding or subtracting like terms.

Difference of Squares

The identity a − b = (√a + √b)(√a − √b) links linear factors to square root terms. For this question, multiplying the equations gives a − b = 5 × 1 = 5, which perfectly matches 9 − 4 = 5.

Linear Equations

When provided with the sum and difference of the same two unknowns, adding the equations eliminates the second variable while subtracting them eliminates the first variable.

Shortcut Trick

A perfect square number can never end in the digits 2, 3, 7, or 8.

Looking at the given options, 100588, 100688, and 100788 all end in the digit 8.

Thus, they are instantly eliminated as they cannot be perfect squares.

Only 100489 ends in a valid perfect square unit digit (9).

∴ The correct answer is 100489.

Alternate Method

Given:

The smallest 6-digit number is 100000.

Method Used:

Find the approximate square root of the smallest 6-digit number, and square the next higher whole number to get the least perfect square.

Calculation:

⇒ Let us estimate the square root of 100000.

⇒ We know that 300² = 90000

⇒ Let us check 316: 316² = 99856 (This is a 5-digit number)

⇒ Since 99856 is less than 100000, 316 is the largest integer whose square is a 5-digit number.

⇒ To find the smallest 6-digit perfect square, we must square the next integer, which is 317.

⇒ Least 6-digit perfect square = 317²

⇒ 317² = (300 + 17)²

⇒ 317² = 300² + 2 × 300 × 17 + 17²

⇒ 317² = 90000 + 10200 + 289

⇒ 317² = 100489

∴ The correct answer is 100489.

Additional Information

Unit Digit Rule for Perfect Squares

Perfect squares can only end in the digits 0, 1, 4, 5, 6, or 9. Any number ending with 2, 3, 7, or 8 is never a perfect square.

Digital Root of Perfect Squares

The sum of the digits (reduced to a single digit) of a perfect square must always be 1, 4, 7, or 9. This serves as a quick check to eliminate non-squares.

Last Two Digits Check

The last two digits of any perfect square will always be the same as the last two digits of the square of some integer from 1 to 24 (e.g., 17² = 289, so 89 is a valid ending).

Shortcut Trick

Convert percentages into standard fractions directly: 12.5% = 1/8 and 50% = 1/2.

According to the given condition: (1/8) × p = (1/2) × q

Multiply both sides by 8: p = 4 × q

Rearranging the variables gives the ratio: p / q = 4 / 1

∴ The correct answer is 4 : 1.

Alternate Method

Given:

12.5% of p = 50% of q

Formula Used:

x% of A = (x ÷ 100) × A

Visualizing 12.5% of p = 50% of q p 12.5% Total p (100% = 8 × 12.5%) q 50% Total q (2 × 50%) = Ratio p : q = 320 : 80 = 4 : 1

Calculations:

⇒ (12.5 ÷ 100) × p = (50 ÷ 100) × q

⇒ 12.5 × p = 50 × q

⇒ p ÷ q = 50 ÷ 12.5

⇒ p ÷ q = 500 ÷ 125

⇒ p ÷ q = 4 ÷ 1

⇒ p : q = 4 : 1

∴ The correct answer is 4 : 1.

Additional Information

Percentage Definition

A percentage signifies a value out of 100. The basic equation to find x% of a number y is written mathematically as (x ÷ 100) × y.

Percentage to Fraction Shortcuts

Remembering standard fractions saves calculation time in exams: 12.5% = 1/8, 25% = 1/4, 37.5% = 3/8, 50% = 1/2, 62.5% = 5/8, and 87.5% = 7/8.

Properties of Proportions

If two quantities satisfy the equality equation a × x = b × y, the numerical ratio between the variables x and y directly equals b : a.

Shortcut Trick

Mean Cost Price (CP) = (Price₁ × Ratio₁ + Price₂ × Ratio₂) ÷ Total Ratio

⇒ Mean CP = (40 × 2 + 60 × 3) ÷ (2 + 3) = (80 + 180) ÷ 5 = ₹52/kg

Given Selling Price (SP) = ₹57.20/kg

⇒ Profit = SP − CP = 57.20 − 52.00 = ₹5.20/kg

⇒ Profit % = (Profit ÷ CP) × 100 = (5.20 ÷ 52) × 100 = 10% Gain

∴ The correct answer is 10% Gain.

Alternate Method

Given:

Cost Price (CP) of 1^st variety of rice = ₹40/kg

Cost Price (CP) of 2^nd variety of rice = ₹60/kg

Ratio of mixture = 2 : 3

Selling Price (SP) of the mixed variety = ₹57.20/kg

₹40/kg ₹60/kg

Mean CP ₹52/kg

2 Parts 3 Parts

SP = ₹57.20 → 10% Profit

Formula Used:

Mean Cost Price = (Quantity₁ × Price₁ + Quantity₂ × Price₂) ÷ (Quantity₁ + Quantity₂)

Profit Percentage = (Profit ÷ Cost Price) × 100

Calculations:

⇒ Let the exact quantity of the first variety be 2 kg and the second variety be 3 kg.

⇒ Total Cost Price of the mixture = (2 × 40) + (3 × 60)

⇒ Total Cost Price = 80 + 180 = ₹260

⇒ Total Quantity = 2 + 3 = 5 kg

⇒ Cost Price (CP) per kg of the mixed variety = 260 ÷ 5 = ₹52

⇒ The Selling Price (SP) of the mixture is ₹57.20 per kg.

⇒ Since SP > CP, the grocer makes a gain.

⇒ Gain per kg = SP − CP = 57.20 − 52.00 = ₹5.20

⇒ Gain Percent = (Gain ÷ CP) × 100

⇒ Gain Percent = (5.20 ÷ 52) × 100 = 0.10 × 100 = 10%

∴ The correct answer is 10% Gain.

Additional Information

Alligation Method

It is a rule that establishes the relationship between the quantities and prices of different ingredients. Ratio = (Dearer Price − Mean Price) : (Mean Price − Cheaper Price).

Weighted Average

When multiple elements are mixed in differing proportions, the net average value per unit is found using the weighted average formula: Total Value ÷ Total Units.

Profit and Loss Concept

Gain or Loss is strictly calculated over the overall average Cost Price (CP). If SP > CP, there is a profit, and Profit % = [(SP − CP) ÷ CP] × 100.

Shortcut Trick

Using the successive discount multiplying factor method:

Final SP = MP × (100 − D₁)% × (100 − D₂)%

Final SP = 600 × (90 ÷ 100) × (80 ÷ 100)

Final SP = 600 × 0.9 × 0.8 = 432

∴ The correct answer is ₹432.

Alternate Method

Given:

Original Marked Price (MP) = ₹600

First successive discount = 10%

Second successive discount = 20%

Formula Used:

Selling Price (SP) = MP − Discount Amount

Discount = Rate% of Base Price

₹600 Marked Price

−10%

₹540 After 1st Disc.

−20%

₹432 Final SP

Step-by-Step Discount Reduction

Calculations:

⇒ First discount amount = 10% of 600 = (10 ÷ 100) × 600 = ₹60

⇒ Price after first discount = 600 − 60 = ₹540

⇒ Second discount amount = 20% of 540 = (20 ÷ 100) × 540 = ₹108

⇒ Final Selling Price = 540 − 108 = ₹432

∴ The correct answer is ₹432.

Additional Information

Equivalent Successive Discount

When two successive discounts of a% and b% are given, the single equivalent discount is calculated as: D = a + b − (a × b) ÷ 100.

Marked Price vs Selling Price

Discounts are always evaluated on the Marked Price (MP). Hence, the base value changes after every applied discount, making Selling Price (SP) = MP − Discount.

Fraction Method for Discounts

A 10% discount implies the new price is 90% (or 9/10) of the original, while a 20% discount implies the new price is 80% (or 4/5) of the base value. Multiplying these fractions provides direct and accurate results.

Shortcut Trick

MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%)

120 ÷ 100 = (100 + 8) ÷ (100 − D)

6 ÷ 5 = 108 ÷ (100 − D)

100 − D = (108 × 5) ÷ 6 = 90

D = 10

∴ The correct answer is 10%.

Alternate Method

Given:

Markup Percentage = 20%

Profit Percentage = 8%

Formula Used:

MP = CP × (1 + Markup% ÷ 100)

SP = CP × (1 + Profit% ÷ 100)

Discount % = (MP − SP) ÷ MP × 100

CP 100

SP 108

MP 120

Markup = +20%

Profit = +8%

Discount = ?

Calculation:

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

⇒ The Marked Price (MP) is set at a 20% premium over the Cost Price.

⇒ Marked Price (MP) = 100 × (1 + 20 ÷ 100) = 120 units

⇒ The transaction ultimately yields an 8% profit on the Cost Price.

⇒ Selling Price (SP) = 100 × (1 + 8 ÷ 100) = 108 units

⇒ Discount given = Marked Price − Selling Price

⇒ Discount = 120 − 108 = 12 units

⇒ Discount % = (Discount ÷ MP) × 100

⇒ Discount % = (12 ÷ 120) × 100

⇒ Discount % = 10%

∴ The correct answer is 10%.

Additional Information

Direct Relation Between CP and MP

The direct ratio between Cost Price and Marked Price is always defined as: CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%). This allows for rapid calculation skipping the SP entirely.

Successive Discounts

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

Dishonest Dealer Concept

When a dealer pretends to sell goods at CP but uses a manipulated weight, the actual profit percentage is calculated as: [(True Weight − False Weight) ÷ False Weight] × 100.

Shortcut Trick

We can solve this quickly using the value-putting method by finding the integer factors of 6.

The possible factors of 6 are (1, 6) and (2, 3).

Let us test a = 2 and b = 3 ⇒ a³ + b³ = 2³ + 3³ = 8 + 27 = 35.

This matches the given condition perfectly.

Therefore, a + b = 2 + 3 = 5.

∴ The correct answer is 5.

Alternate Method

Given:

a³ + b³ = 35

ab = 6

Formula Used:

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculations:

Let the value of (a + b) be x.

⇒ x³ = 35 + 3 × 6 × x

⇒ x³ = 35 + 18x

⇒ x³ − 18x − 35 = 0

By hit and trial method, if we substitute x = 5:

⇒ 5³ − 18(5) − 35

⇒ 125 − 90 − 35 = 0

Since it perfectly satisfies the equation, we get a + b = 5.

∴ The correct answer is 5.

Additional Information

Algebraic Identity for Cubes

(a − b)³ = a³ − b³ − 3ab(a − b)

Sum of Cubes

a³ + b³ = (a + b)(a² − ab + b²)

Difference of Cubes

a³ − b³ = (a − b)(a² + ab + b²)

Shortcut Trick

Total Simple Interest (SI) generated in 4 years = 2520 − 2000 = ₹520.

Interest per year = 520 ÷ 4 = ₹130.

Rate % = (Interest per year ÷ Principal) × 100

Rate % = (130 ÷ 2000) × 100 = 6.5%.

∴ The correct answer is 6.5%.

Alternate Method

Given:

Principal (P) = ₹2,000

Amount (A) = ₹2,520

Time (T) = 4 years

Formula Used:

Simple Interest (SI) = Amount − Principal

Rate (R) = (SI × 100) ÷ (P × T)

Principal ₹2,000 Amount ₹2,520

Time = 4 Years

• SI = ₹520

Calculation:

⇒ SI = 2520 − 2000 = ₹520

⇒ R = (520 × 100) ÷ (2000 × 4)

⇒ R = 52000 ÷ 8000

⇒ R = 52 ÷ 8

⇒ R = 6.5%

∴ The correct answer is 6.5%.

Additional Information

Simple Interest (SI) vs Compound Interest (CI)

SI is calculated only on the principal amount for the entire period, while CI is calculated on the principal and also on the accumulated interest of previous periods.

Principal & Amount

Principal is the initial sum of money borrowed or invested. Amount is the total money paid back after the given time, which includes Principal and Interest (A = P + SI).

Finding Time (T)

If Principal (P), Rate (R), and Simple Interest (SI) are given, the time period can be calculated directly using the formula: T = (SI × 100) ÷ (P × R).

Shortcut Trick

Simple Interest for 1 year from the 1st scheme = 6% of ₹8,000 = ₹480

Simple Interest for 1 year from the 2nd scheme = 8% of ₹5,000 = ₹400

Total Simple Interest generated in 1 year = 480 + 400 = ₹880

Total time duration = Total Interest Received ÷ 1 Year Interest = 1760 ÷ 880 = 2 years

∴ The correct answer is 2 years.

Alternate Method

Given:

Principal of 1st investment (P₁) = ₹8,000

Rate of 1st investment (R₁) = 6%

Principal of 2nd investment (P₂) = ₹5,000

Rate of 2nd investment (R₂) = 8%

Total Simple Interest (SI) = ₹1,760

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Scheme 1 ₹8,000 @ 6% for T years

Scheme 2 ₹5,000 @ 8% for T years

Total SI = ₹1,760

Calculations:

Let the duration of the investments be T years.

⇒ Total SI = SI₁ + SI₂

⇒ 1760 = [(8000 × 6 × T) ÷ 100] + [(5000 × 8 × T) ÷ 100]

⇒ 1760 = 480T + 400T

⇒ 1760 = 880T

⇒ T = 1760 ÷ 880

⇒ T = 2 years

∴ The correct answer is 2 years.

Additional Information

Compound Interest (CI) Formula

When interest is compounded annually, the total amount is A = P × (1 + R ÷ 100)^T and Compound Interest = A − P.

Simple Interest vs Compound Interest

For the first year (or the first compounding period), Simple Interest and Compound Interest are exactly the same when calculated on the same principal at the same rate of interest.

Effective Total Simple Interest

If multiple principals P₁, P₂... are invested at rates R₁, R₂... for the same time duration T, the Total SI = (P₁R₁ + P₂R₂ + ...) × T ÷ 100.

Shortcut Trick

In any 30°-60°-90° right-angled triangle, the side opposite the 30° angle is exactly half of the hypotenuse.

⇒ Ramp Length = 2 × Height

⇒ Ramp Length = 2 × 1.5

⇒ Ramp Length = 3 m

∴ The correct answer is 3 m.

Alternate Method

A B C 1.5 m L (Ramp Length) 30°

Given:

Height of the platform (Opposite side) = 1.5 m

Angle of elevation of the ramp from the ground (θ) = 30°

Formula Used:

sin(θ) = Opposite ÷ Hypotenuse

Calculations:

Let the length of the ramp be L.

⇒ sin(30°) = 1.5 ÷ L

⇒ 1 ÷ 2 = 1.5 ÷ L

⇒ L = 1.5 × 2

⇒ L = 3 m

∴ The correct answer is 3 m.

Additional Information

Trigonometric Ratios

For a right-angled triangle, sin(θ) = Opposite ÷ Hypotenuse, cos(θ) = Adjacent ÷ Hypotenuse, and tan(θ) = Opposite ÷ Adjacent.

Angle of Elevation vs Depression

The angle of elevation is measured upwards from the horizontal line of sight, whereas the angle of depression is measured downwards. In parallel configurations, they are mathematically equal alternate interior angles.

30°-60°-90° Triangle Theorem

The sides of a 30°-60°-90° right triangle are always in the precise ratio 1 : √3 : 2, making geometrical height and distance calculations much faster without full trigonometric tables.

Shortcut Trick

The distance (d) from the foot of a building for a given angle of elevation θ is given by d = h × cot(θ).

Distance of point A from the foot = h × cot(30°) = h√3

Distance of point B from the foot = h × cot(60°) = h/√3

Ratio of distances = AF : BF = h√3 : (h / √3)

Ratio = √3 × √3 : 1 = 3 : 1

∴ The correct answer is 3 : 1.

Alternate Method

Given:

Angle of elevation from point A, θ₁ = 30°

Angle of elevation from point B, θ₂ = 60°

Formula Used:

In a right-angled triangle, tan(θ) = Perpendicular ÷ Base

30°

60°

T F A B h

AF = h√3

BF = h/√3

Calculation:

Let the height of the building be 'h' and its foot be 'F'.

Let the top of the building be 'T'.

⇒ In right-angled ΔTFA:

⇒ tan(30°) = TF ÷ AF

⇒ 1 / √3 = h ÷ AF

⇒ AF = h√3

⇒ In right-angled ΔTFB:

⇒ tan(60°) = TF ÷ BF

⇒ √3 = h ÷ BF

⇒ BF = h / √3

⇒ Required ratio = AF : BF

⇒ AF : BF = h√3 : (h / √3)

⇒ AF : BF = √3 × √3 : 1

⇒ AF : BF = 3 : 1

∴ The correct answer is 3 : 1.

Additional Information

Complementary Angles of Elevation

If the angles of elevation of the top of a tower from two points at distances 'a' and 'b' from its foot are complementary (sum to 90°), the height of the tower is given by h = √(a × b).

Angle of Elevation and Depression

The angle of elevation of an object as seen by an observer is numerically equal to the angle of depression of the observer as seen from the object, owing to alternating interior angles between parallel horizontal planes.

30°-60°-90° Triangle Theorem

In a right-angled triangle with angles 30°, 60°, and 90°, the sides opposite to these angles are strictly proportional to the ratio 1 : √3 : 2 respectively. This property frequently aids calculation speed in Heights and Distance problems.

Shortcut Trick

Diameter of hemisphere (d) = √(2 × CSA ÷ π)

⇒ d = √(2 × 154 × 7 ÷ 22)

⇒ d = √98 ≈ 9.9 cm

∴ The correct answer is 9.9 cm.

Alternate Method

 r    d = ? Curved Surface Area = 154 cm²

Given:

Curved Surface Area (CSA) of hemisphere = 154 cm²

Formula Used:

CSA = 2πr²

Diameter (d) = 2r

Calculations:

⇒ 2 × (22/7) × r² = 154

⇒ (44/7) × r² = 154

⇒ r² = (154 × 7) ÷ 44

⇒ r² = 24.5

⇒ r = √24.5 ≈ 4.95 cm

⇒ d = 2 × 4.95 = 9.9 cm

∴ The correct answer is 9.9 cm.

Additional Information

Total Surface Area of Hemisphere

The total surface area includes the curved surface and the flat circular base: TSA = 3πr².

Volume of a Hemisphere

The volume is exactly half of a full sphere: V = (2/3)πr³.

Relation between Areas

For a given radius, TSA of a hemisphere is 1.5 times its Curved Surface Area.

Shortcut Trick

For any cone, Volume ∝ r² × h.

New radius is 1/3 of the original, and new height is 1/2 of the original.

Ratio of new volume to original volume = (1/3)² × (1/2) = 1/9 × 1/2 = 1/18.

This means 1 part of the original volume is used out of 18 total parts.

Unused fraction = 1 − 1/18 = 17/18.

∴ The correct answer is 17/18.

Alternate Method

h r Original Cone

Melted

h/2 r/3 New Cone

Given:

Original cone height = h, radius = r

New smaller cone height = h/2, radius = r/3

Formula Used:

Volume of a cone = 1/3 × π × radius² × height

Calculations:

Let the volume of the original cone be V₁.

⇒ V₁ = 1/3 × π × r² × h

Let the volume of the new smaller cone be V₂.

⇒ V₂ = 1/3 × π × (r/3)² × (h/2)

⇒ V₂ = 1/3 × π × (r² / 9) × (h/2)

⇒ V₂ = (1/18) × (1/3 × π × r² × h)

⇒ V₂ = V₁ / 18

This means the new recast cone uses only 1/18th of the original volume.

Unused volume = Original volume − Used volume

⇒ Unused volume = V₁ − V₁ / 18

⇒ Unused volume = 17/18 × V₁

∴ The correct answer is 17/18.

Additional Information

Volume of Frustum of a Cone

When a cone is cut by a plane parallel to its base, the remaining solid is called a frustum. Volume = 1/3 × π × h × (R² + r² + R × r).

Melting and Recasting Principle

When a 3D solid is melted and recast into a different shape, the total volume remains constant unless some specific portion is explicitly stated as wasted or unused.

Scaling Factor in 3D Objects

If all linear dimensions of a standard 3D solid are uniformly scaled by a factor 'k', its total surface area is scaled by k² and its volume is scaled by k³.

Shortcut Trick

A regular hexagon is constructed by joining 6 identical equilateral triangles at its center point.

If the side length of the regular hexagon is 'a', then each of these 6 interior triangles will also have a side length of 'a'.

Therefore, the area of the regular hexagon is exactly 6 times the area of an equilateral triangle having the same side length.

∴ The correct answer is 6:1.

Alternate Method

Given:

Side length of the regular hexagon = a

Side length of the equilateral triangle = a

Formulas Used:

Area of an equilateral triangle = (√3 ÷ 4) × (side)²

Area of a regular hexagon = 6 × (√3 ÷ 4) × (side)²

Regular Hexagon Equilateral Triangle

1 2 3 4 5 6

Side = a

1 Side = a

Area = 6 × A Area = A

Calculations:

⇒ Area of the regular hexagon = 6 × (√3 ÷ 4) × a²

⇒ Area of the equilateral triangle = (√3 ÷ 4) × a²

⇒ Required Ratio = [6 × (√3 ÷ 4) × a²] ÷ [(√3 ÷ 4) × a²]

⇒ Required Ratio = 6 ÷ 1 = 6:1

∴ The correct answer is 6:1.

Additional Information

Properties of a Regular Hexagon

A regular hexagon has 6 equal sides and 6 equal interior angles (each measuring 120°). The sum of all its interior angles is exactly 720°.

Circumradius

The distance from the center of a regular hexagon to any of its outward vertices is exactly equal to its side length. Thus, its circumradius (R) = a.

Inradius

The perpendicular distance from the center to the midpoint of any side acts as the height of the internal equilateral triangles. The inradius (r) = (√3 ÷ 2) × a.

Perimeter to Area Efficiency

For a specifically given perimeter, a regular hexagon encloses a significantly larger internal area compared to a square or an equilateral triangle.

Shortcut Trick

Total height of the prism = Sum of 5 layers = 5 + 6 + 7 + 8 + 9 = 35 cm.

Area of equilateral triangular base = (√3 ÷ 4) × side² = (√3 ÷ 4) × 4² = 4√3 cm².

Total Volume = Base Area × Total Height = 4√3 × 35 = 140√3 cm³.

Substituting √3 ≈ 1.732, Volume = 140 × 1.732 = 242.48 cm³.

∴ The correct answer is 242.48 cm³.

Alternate Method

Given:

⇒ Base of the prism = Equilateral triangle with side (a) = 4 cm.

⇒ Heights of the 5 layers = 5 cm, 6 cm, 7 cm, 8 cm, and 9 cm.

Formula Used:

⇒ Area of an equilateral triangle = (√3 ÷ 4) × a²

⇒ Volume of a prism = Base Area × Total Height

4 cm 4 cm 4 cm Area = 4√3 cm² Equilateral Base

Height Layers

9 cm

8 cm

7 cm

6 cm

5 cm

Total = 35 cm

Calculation:

⇒ Total height of the prism (H) = 5 + 6 + 7 + 8 + 9 = 35 cm.

⇒ Base Area = (√3 ÷ 4) × 4²

⇒ Base Area = (√3 ÷ 4) × 16 = 4√3 cm².

⇒ Total Volume = 4√3 × 35 = 140√3 cm³.

⇒ Substituting the given value of √3 ≈ 1.732:

⇒ Total Volume = 140 × 1.732 = 242.48 cm³.

∴ The correct answer is 242.48 cm³.

Additional Information

Volume and Surface Area of a Prism

Volume = Base Area × Height. Total Surface Area = Lateral Surface Area + 2 × Base Area.

Equilateral Triangle Properties

For a side length 'a', Area = (√3 ÷ 4)a², Height = (√3 ÷ 2)a, and Perimeter = 3a.

Sum of an Arithmetic Progression

The sum of 'n' terms is given by S_n = (n ÷ 2)[2a + (n−1)d], or simply (n ÷ 2) × (First term + Last term).

Shortcut Trick

The equation of a line passing through a given point must satisfy the coordinates of that point.

Substitute x = −1 and y = −2 in the given options to verify.

Option 1: −3(−1) − 5 = 3 − 5 = −2 (Satisfies the point)

Other options will not yield −2.

∴ The correct answer is y = −3x − 5.

Alternate Method

Given:

Coordinates of the point = (−1, −2)

Slope of the line (m) = −3

Formula Used:

The equation of a line passing through point (x₁, y₁) with slope m is given by: y − y₁ = m(x − x₁)

X Y O (-1, -2) y = -3x - 5

Calculations:

⇒ y − y₁ = m(x − x₁)

⇒ y − (−2) = −3[x − (−1)]

⇒ y + 2 = −3(x + 1)

⇒ y + 2 = −3x − 3

⇒ y = −3x − 3 − 2

⇒ y = −3x − 5

∴ The correct answer is y = −3x − 5.

Additional Information

Slope-Intercept Form

The equation of a straight line with slope m and y-intercept c is given by the formula y = mx + c.

Two-Point Form

The equation of a line passing through two distinct points (x₁, y₁) and (x₂, y₂) is y − y₁ = [(y₂ − y₁) ÷ (x₂ − x₁)](x − x₁).

Intercept Form

A line that has x-intercept a and y-intercept b on the coordinate axes follows the equation x/a + y/b = 1.

Shortcut Trick

For any regular polygon, the sum of all exterior angles is always exactly 360°.

Number of sides = Sum of all exterior angles ÷ Measure of each exterior angle

⇒ Number of sides = 360° ÷ 60°

⇒ Number of sides = 6

∴ The correct answer is 6 sides.

Alternate Method

Given:

Measure of each exterior angle = 60°

Formula Used:

Interior Angle + Exterior Angle = 180°

Sum of interior angles of a polygon = (n − 2) × 180°, where n is the number of sides

Each interior angle = [(n − 2) × 180°] ÷ n

60° Exterior Angle

120° Interior Angle

Regular Hexagon (6 Sides)

Calculations:

⇒ Each interior angle = 180° − 60° = 120°

⇒ [(n − 2) × 180°] ÷ n = 120°

⇒ (n − 2) × 180° = 120°n

⇒ 180°n − 360° = 120°n

⇒ 180°n − 120°n = 360°

⇒ 60°n = 360°

⇒ n = 360° ÷ 60°

⇒ n = 6

∴ The correct answer is 6 sides.

Additional Information

Sum of Interior Angles

For a polygon with n sides, the sum of all interior angles is always given by (n − 2) × 180°.

Number of Diagonals

The total number of distinct diagonals that can be drawn within a polygon of n sides is given by the formula n(n − 3) ÷ 2.

Linear Pair Property

At any given vertex of a convex polygon, the interior angle and its adjacent exterior angle form a straight line, summing exactly to 180°.

Shortcut Trick

If G is the centroid of a triangle PQR, the coordinates of the third vertex R can be calculated directly using the relation: R = 3 × G − (P + Q)

x-coordinate = 3 × 1 − (3 − 2) = 3 − 1 = 2

y-coordinate = 3 × 2 − (−1 + 4) = 6 − 3 = 3

∴ The correct answer is (2, 3).

Alternate Method

Given:

Centroid of the triangle, G(x, y) = (1, 2)

Vertices, P(x₁, y₁) = (3, −1) and Q(x₂, y₂) = (−2, 4)

Let the third vertex be R(x₃, y₃).

Formula Used:

Centroid G(x, y) = [(x₁ + x₂ + x₃) ÷ 3, (y₁ + y₂ + y₃) ÷ 3]

G(1, 2)

Q(−2, 4)

P(3, −1)

R(x, y)

Calculation:

For the x-coordinate:

⇒ 1 = (3 − 2 + x₃) ÷ 3

⇒ 3 = 1 + x₃

⇒ x₃ = 2

For the y-coordinate:

⇒ 2 = (−1 + 4 + y₃) ÷ 3

⇒ 6 = 3 + y₃

⇒ y₃ = 3

∴ The correct answer is (2, 3).

Additional Information

1. Centroid of a Triangle

It is the intersection point of all three medians of the triangle. The centroid divides each median in the ratio 2:1. The formula is [(x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3].

2. Incenter of a Triangle

It is the point of intersection of internal angle bisectors. The coordinates are [(ax₁+bx₂+cx₃)/(a+b+c), (ay₁+by₂+cy₃)/(a+b+c)] where a, b, and c are side lengths.

3. Area of a Triangle

The area of a triangle given its three vertices is (1/2) × |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|.

Shortcut Trick

We know the direct algebraic identity: (a + b)² − (a − b)² = 4ab

Here, let a = √11 and b = √7

⇒ Result = 4 × √11 × √7

⇒ Result = 4√77

∴ The correct answer is 4√77.

Alternate Method

Given:

Expression: (√11 + √7)² − (√11 − √7)²

Formula Used:

(a + b)² = a² + b² + 2ab

(a − b)² = a² + b² − 2ab

Calculations:

⇒ Expand the first term: (√11 + √7)² = (√11)² + (√7)² + 2 × √11 × √7

⇒ (√11 + √7)² = 11 + 7 + 2√77 = 18 + 2√77

⇒ Expand the second term: (√11 − √7)² = (√11)² + (√7)² − 2 × √11 × √7

⇒ (√11 − √7)² = 11 + 7 − 2√77 = 18 − 2√77

⇒ Subtract the second expression from the first: (18 + 2√77) − (18 − 2√77)

⇒ 18 + 2√77 − 18 + 2√77

⇒ 4√77

∴ The correct answer is 4√77.

Additional Information

Sum of Squares Identity

Another useful variation is the sum of the squares: (a + b)² + (a − b)² = 2(a² + b²).

Difference of Squares

A very commonly used identity in simplification is a² − b² = (a + b)(a − b).

Square Root Properties

For any positive numbers x and y, the product of their square roots is √x × √y = √(xy) and squaring a root gives (√x)² = x.

Shortcut Trick The length of a Direct Common Tangent (DCT) is defined by the relation DCT2 = d2 − (r1 − r2)2. We are given that the length of the tangent is equal to the distance between the centers, which means DCT = d. For DCT2 to be equal to d2, the subtracted term (r1 − r2)2 must be exactly zero. This implies there is no difference between the lengths of their radii. ⇒ r1 − r2 = 0 ⇒ r1 = r2 ∴ The correct answer is r1 = r2.

Alternate Method Given: Radii of the two circles = r1 and r2 Distance between their centers = d Length of the Direct Common Tangent (L) = d Formula Used: The formula for the length of a Direct Common Tangent (L) is: L = √[d2 − (r1 − r2)2]

r₁ r₂ DCT = d d C₁ C₂

Calculations: ⇒ L = d (given in the question) ⇒ d = √[d2 − (r1 − r2)2] Squaring both sides: ⇒ d2 = d2 − (r1 − r2)2 ⇒ (r1 − r2)2 = d2 − d2 ⇒ (r1 − r2)2 = 0 Taking the square root on both sides: ⇒ r1 − r2 = 0 ⇒ r1 = r2 ∴ The correct answer is r1 = r2.

Additional Information Transverse Common Tangent (TCT) The length of a Transverse Common Tangent is given by TCT = √[d2 − (r1 + r2)2]. This tangent completely crosses the line segment joining the centers of the two circles. Number of Common Tangents When two circles do not touch or intersect (d > r1 + r2), they have exactly 4 common tangents (2 direct and 2 transverse). If they touch externally (d = r1 + r2), there are exactly 3 common tangents. Tangent Perpendicularity Theorem A line drawn from the center of a circle to the point of tangency makes a perpendicular angle (90 degrees) with the tangent line at that exact point.

Shortcut Trick

In a circle, the perpendicular from the center to a chord bisects it.

⇒ Half-chord = 2√21 ÷ 2 = √21 cm

⇒ Radius = √(Distance² + Half-chord²)

⇒ Radius = √(5² + (√21)²) = √(25 + 21)

⇒ Radius = √46 ≈ 6.78 cm

∴ The correct answer is 6.78 cm.

Alternate Method

O A B D

5 cm r √21 cm

2√21 cm

Given:

Length of the chord (AB) = 2√21 cm

Distance of the chord from the center (OD) = 5 cm

Formula Used:

The perpendicular drawn from the center of a circle to a chord bisects the chord.

By Pythagoras Theorem in right-angled ΔODB:

OB² = OD² + DB²

Calculations:

⇒ DB = AB ÷ 2 = 2√21 ÷ 2 = √21 cm

⇒ In ΔODB, OB is the radius (r)

⇒ r² = 5² + (√21)²

⇒ r² = 25 + 21

⇒ r² = 46

⇒ r = √46

⇒ r ≈ 6.78 cm

∴ The correct answer is 6.78 cm.

Additional Information

Perpendicular to a Chord

A perpendicular drawn from the center of a circle to a chord bisects it into two equal halves. The converse is also true.

Equal Chords Property

Chords of equal length in a circle are always equidistant from the center of the circle.

Pythagorean Triplet

In right-angled triangles inscribed in circles, the radius, half-chord, and perpendicular distance always form a Pythagorean relation: r² = d² + (L÷2)².

Shortcut Trick

The given expression is sin²A + cos²A + 2sinAcosA.

Notice that this is the direct algebraic expansion of (sinA + cosA)².

Since we are given sinA + cosA = x, directly substitute x into the expression.

Thus, (x)² = x².

∴ The correct answer is x².

Alternate Method

Given:

sinA + cosA = x

Formula Used:

(a + b)² = a² + b² + 2ab

Calculations:

⇒ sinA + cosA = x

Squaring both sides of the equation, we get:

⇒ (sinA + cosA)² = x²

Expanding the left-hand side using the algebraic identity:

⇒ sin²A + cos²A + 2sinAcosA = x²

This matches the required expression perfectly, giving the direct value.

∴ The correct answer is x².

Additional Information

Fundamental Trigonometric Identities

sin²θ + cos²θ = 1 | sec²θ − tan²θ = 1 | cosec²θ − cot²θ = 1

Important Algebraic Identities

(a + b)² = a² + b² + 2ab | (a − b)² = a² + b² − 2ab | a² − b² = (a − b)(a + b)

Double Angle Formulas

sin(2θ) = 2sinθcosθ | cos(2θ) = cos²θ − sin²θ = 2cos²θ − 1 = 1 − 2sin²θ

Shortcut Trick

Given, sin x = cos x ⇒ tan x = 1 ⇒ x = 45°

We need to find the value of sin⁴x + cos⁴x.

⇒ (sin 45°)⁴ + (cos 45°)⁴

⇒ (1/√2)⁴ + (1/√2)⁴

⇒ 1/4 + 1/4 = 1/2

∴ The correct answer is 1/2.

Alternate Method

Given:

sin x = cos x

Formula Used:

sin²x + cos²x = 1

Calculation:

⇒ sin x = cos x

Squaring both sides:

⇒ sin²x = cos²x

Substitute cos²x with sin²x in the standard trigonometric identity:

⇒ sin²x + sin²x = 1

⇒ 2sin²x = 1 ⇒ sin²x = 1/2

Similarly, cos²x = 1/2

Now evaluate the required expression:

⇒ sin⁴x + cos⁴x = (sin²x)² + (cos²x)²

⇒ (1/2)² + (1/2)²

⇒ 1/4 + 1/4 = 2/4 = 1/2

∴ The correct answer is 1/2.

Additional Information

Key Trigonometric Identities

sin²θ + cos²θ = 1 | 1 + tan²θ = sec²θ | 1 + cot²θ = cosec²θ

Double Angle Formulas

sin 2θ = 2 sin θ cos θ | cos 2θ = cos²θ − sin²θ = 1 − 2sin²θ = 2cos²θ − 1

Trigonometric Values at 45°

sin 45° = 1/√2 | cos 45° = 1/√2 | tan 45° = 1 | cot 45° = 1

Shortcut Trick

If a + b + c = 0, the standard algebraic identity yields a³ + b³ + c³ = 3abc.

Here, a + b + c = 0.1 + 0.2 − 0.3 = 0, so the condition is satisfied.

We can directly substitute 3abc in place of the numerator.

⇒ Expression = (3abc) ÷ (3abc) = 1

∴ The correct answer is 1.

Alternate Method

Given:

a = 0.1, b = 0.2, c = −0.3

a + b + c = 0

Formula Used:

a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)

Calculations:

⇒ We need to evaluate: (a³ + b³ + c³) ÷ (3abc)

⇒ From the given values, a + b + c = 0.1 + 0.2 + (−0.3) = 0

⇒ Substituting a + b + c = 0 into the identity formula:

⇒ a³ + b³ + c³ − 3abc = 0 × (a² + b² + c² − ab − bc − ca)

⇒ a³ + b³ + c³ − 3abc = 0

⇒ a³ + b³ + c³ = 3abc

⇒ Substitute a³ + b³ + c³ with 3abc in the given expression.

⇒ Value = (3abc) ÷ (3abc) = 1

∴ The correct answer is 1.

Additional Information

Standard Algebraic Identity

The foundational identity for sums of cubes is: a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca).

Special Case 1

If the sum of the variables is zero (a + b + c = 0), the right side simplifies to 0, which gives the direct result a³ + b³ + c³ = 3abc.

Alternative Form of the Identity

Another extremely useful form to quickly find values without extensive multiplication is: a³ + b³ + c³ − 3abc = 1/2 × (a + b + c) × [(a − b)² + (b − c)² + (c − a)²].

Shortcut Trick

In the given expression, we can simply factor out the constant from the numerator.

Expression = [(4p)³ + (4q)³] ÷ (p³ + q³)

⇒ [64p³ + 64q³] ÷ (p³ + q³)

⇒ 64 × (p³ + q³) ÷ (p³ + q³) = 64

Since the variable terms cancel out, the exact values of p and q are not required.

∴ The correct answer is 64.

Alternate Method

Given:

p = 0.8

q = 0.02

Formula Used:

(a × b)³ = a³ × b³

Calculation:

⇒ Expression = [(4p)³ + (4q)³] ÷ (p³ + q³)

⇒ Expression = [4³p³ + 4³q³] ÷ (p³ + q³)

⇒ Expression = [64p³ + 64q³] ÷ (p³ + q³)

⇒ Expression = 64(p³ + q³) ÷ (p³ + q³)

⇒ Expression = 64

∴ The correct answer is 64.

Additional Information

BODMAS Rule

Always follow the sequence of Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction while solving simplifications.

Algebraic Identities

a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²).

Indices Rule

When two variables are multiplied and raised to a power, the power applies to both: (ab)ⁿ = aⁿ × bⁿ.

The correct answer is: Cautious.

Key Points

• The word "circumspect" means being wary and unwilling to take risks; thinking carefully about possible risks before doing or saying something. (सावधान/सोच-समझकर)
• Example: She was circumspect about revealing her personal information to strangers.
• The word "cautious" means being careful to avoid potential problems or dangers. (सतर्क)
• Example: He took a cautious approach to investing his money in the stock market.
• Hence, "circumspect" and "cautious" share similar meanings, making "cautious" the most appropriate synonym.

Therefore, the correct answer is: Cautious.

Additional Information

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

• Reckless (लापरवाह): Acting without thinking or caring about the consequences.
• Example: Driving recklessly in heavy traffic can lead to serious accidents.
• Brash (अत्यधिक आत्मविश्वासी और आक्रामक): Being self-assertive in a rude, noisy, or overconfident way.
• Example: His brash attitude often annoyed his colleagues.
• Carefree (बिना चिंता के): Free from worries or responsibilities.
• Example: During their vacation, they enjoyed a carefree week on the beach.

The correct answer is: Yielding.

Key Points

• The word "Obdurate" means stubbornly refusing to change one's opinion or course of action, even in the face of reason or persuasion. (हठी, अडिग)
• Example: Despite numerous pleas for mercy, the obdurate judge refused to reduce the sentence.
• "Yielding" refers to being inclined to give way to the wishes of others or being flexible and accommodating. (झुकने वाला, लचीला)
• Example: She was yielding in her approach, always ready to adapt to others' needs.
• Hence, we can infer that the opposite of 'Obdurate' is 'Yielding'.

Therefore, the correct answer is: Yielding.

Additional Information

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

• Callous (निर्दयी): Insensitive and cruel disregard for others.
• Example: His callous comments about the tragedy upset everyone at the gathering.
• Adamant (अडिग): Refusing to be persuaded or to change one's mind.
• Example: She was adamant about finishing the project despite the challenges.
• Hardened (सख्त): Having become or made hard or unfeeling, especially as a result of experience.
• Example: Years of hardship had hardened him, making him less empathetic.

The correct answer is: Option 3 i.e. "Very closely associated".

Key Points

• The idiom "Hand and glove" means to be very closely associated, working in close cooperation, or in harmony with someone. (बहुत निकटता से संबंधित होना या सहयोग करना)
• Example: The two companies worked hand and glove to deliver the best customer experience.
• The correct meaning of the idiom "Hand and glove" is "very closely associated" (बहुत निकटता से संबंधित).
• Example: The detective and his assistant were hand and glove in solving the mystery.

Therefore, the correct answer is: Option 3 i.e. "Very closely associated".

Additional Information

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

• Option 1: Working in rivalry (प्रतिद्वंद्विता में काम करना):
• Explanation: This means competing against each other, which is contrary to the meaning of "hand and glove".
• Example: The two teams were working in rivalry to win the championship.
• Option 2: Acting carelessly (लापरवाही से कार्य करना):
• Explanation: This refers to behaving in a careless or inattentive manner, which does not align with the idiom's meaning.
• Example: He was acting carelessly and missed the important details in the report.
• Option 4: Openly suspicious (खुले तौर पर संदेह करना):
• Explanation: This means being openly doubtful or distrustful, which is unrelated to the meaning of "hand and glove".
• Example: She was openly suspicious of his intentions during the meeting.

The correct answer is: Option 2 i.e. Seeking approval through flattery.

Key Points

• The idiom "Currying favour" means seeking approval or advantage from someone through excessive flattery or trying to please them. (खुशामद करके पक्ष लेना)
• Example: He was currying favour with his boss by always complimenting her ideas.
• Explanation of the correct option: "Seeking approval through flattery" is the appropriate meaning of the idiom "currying favour." It represents the act of gaining someone’s favor by being overly pleasing or flattering. (खुशामद के माध्यम से स्वीकृति प्राप्त करना)
• Example: The employee tried currying favour with the manager to secure a promotion.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Option 1: Seeking emotional validation (भावनात्मक मान्यता प्राप्त करना): The act of wanting confirmation or approval for one’s emotions or feelings.
• Example: She constantly seeks emotional validation from her friends.
• Option 3: Avoiding direct confrontation (प्रत्यक्ष टकराव से बचना): Refers to steering clear of any direct conflict or argument.
• Example: Instead of addressing the issue, he avoided direct confrontation with his colleagues.
• Option 4: Asking for forgiveness subtly (धीरे-धीरे माफी मांगना): Refers to apologizing in an indirect or subtle way.
• Example: She asked for forgiveness subtly by leaving a heartfelt note on his desk.

The correct answer is option 1.

Key Points

The misspelled word is 'Pithey', 'Pithhy', and 'Pithie'.

• The correct spelling is 'Pithy'.
• The word 'pithy' is an adjective meaning 'concise and forcefully expressive' (संक्षिप्त और प्रभावशाली).
• For Example - She gave a pithy reply that ended the discussion.

Therefore, the correct spelling is 'Pithy'.

Additional Information

Let's understand the meanings of the other options:

• Pithey - Incorrect spelling of 'Pithy'.
• Pithhy - Incorrect spelling of 'Pithy'.
• Pithie - Incorrect spelling of 'Pithy'.