DSSSB TGT (Social Science) Official Paper (Held On: 07 Nov, 2025 Shift 1) (Previous Year Paper)

Logic: (1^st number ÷ 2) - 2 = 2^nd number.

Now,

For, 52 : 24

⇒ (52 ÷ 2) - 2 = 26 - 2 = 24.

For, 28 : 12

⇒ (28 ÷ 2) - 2 = 14 - 2 = 12.

Similarly, checking options:

Option (3) 34 : 15

⇒ (34 ÷ 2) - 2 = 17 - 2 = 15.

Hence, the correct answer is "Option 3".

BODMAS Table: 

Given equation: 64 C 4 D 12 B 3 A 4 = ?

Now, replacing the symbols:

A = ÷, B = ×, C = +, D = -

⇒ 64 + 4 - 12 × 3 ÷ 4 = ?

⇒ 64 + 4 - 12 × 3 ÷ 4 = ?

⇒ 64 + 4 - 36 ÷ 4 = ?

⇒ 64 + 4 - 9 = ?

⇒ 64 + 4 - 9 = ?

⇒ 68 - 9 = 59

Hence, the correct answer is "Option 3".

According to the given information,

 

Given equation: Q + U – E + V × F ÷ N → Q is mother of U, U is brother of E, E is mother of V, V is wife of F and F is father of N.

E is N's mother's mother.

Hence, the correct answer is “Option 2”.

(1) UNG

U - 7 = N

N - 7 = G

(2) OHA

O - 7 = H

H - 7 = A

(3) SLO

S - 7 = L 

L + 3 = O

(4) MFY

M - 7 = F

F - 7 = Y

Hence, the correct answer is “Option 3”.

Concept:

Vowels (A, E, I, O, U) → replaced by next letter

Consonants → replaced by previous letter

Given words: ZIP, CUP, HAT, HYP

Step 1: Apply the rule

ZIP → Z→Y, I→J, P→O → YJO

CUP → C→B, U→V, P→O → BVO

HAT → H→G, A→B, T→S → GBS

HYP → H→G, Y→X, P→O → GXO

YJO → contains vowel O

BVO → contains vowel O

GBS → contains no vowel

GXO → contains vowel O

Groups without vowels = 1

Hence, the correct answer is “Option 2”.

Logic: (Number × 2) ÷ 3 = Result

Now,

For 84 : 56

⇒ (84 × 2) ÷ 3 = 168 ÷ 3 = 56

For 36 : 24

⇒ (36 × 2) ÷ 3 = 72 ÷ 3 = 24

Similarly, for 144 : ?

⇒ (144 × 2) ÷ 3 = 288 ÷ 3 = 96

Hence, the correct answer is "Option 3".

Least possible Venn diagram,

Conclusions:

(I): Some princes are generals → Follow (Some princes are ministers and all ministers are generals. so, some princes which are ministers are definitely generals).

(II): Some kings are generals → Does not follow (There is no direct relation given between kings and generals. so, it is possible not definite).

Only conclusion (I) follows.

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Hence, the correct answer is “Option 3”.

BETH’ is coded as ‘7463’

And

‘ECHT’ is coded as ‘6741.’ 

Code for "C" is " 1".

Hence, the correct answer is “Option 1”.

Six friends, Amar, Bindu, Carol, Don, Isha, and Fazal, are sitting around a round table, facing the center.

1. Bindu sits third to the right of Amar.
2. Fazal sits to the immediate left of Bindu.
3. Carol is the immediate neighbor of both Don and Bindu.

Amar sits to the immediate left of Isha.

Hence, the correct answer is “Option 1”.

BODMAS Table: 

Given equation: 77 A 36 B 6 D 5 C 9 = ?

Replace symbols:

A = +, B = ÷, C = ×, D = −

⇒ 77 + 36 ÷ 6 − 5 × 9 = ?

⇒ 77 + 36 ÷ 6 − 5 × 9 = ?

⇒ 77 + 6 − 45 = ?

⇒ 77 + 6 − 45 = ?

⇒ 83 − 45 = 38

Hence, the correct answer is "Option 3".

Pattern followed here is,

Hence, the correct answer is “Option 3”.

E, F, G, H, K, L and M each have their exam on a different day of the week, starting from Monday and ending on Sunday of the same week.

1. No one has an exam after L.
2. Only two people have an exam between E and H.
3. Only two people have an exam between G and K.
4. Only two people have an exam between L and K.
5. F has an exam on a day before M.
6. H has an exam immediately after M.

F has an exam on Tuesday.

Hence, the correct answer is “Option 4”.

Statements:

I) The director of organization Y issued show-cause notices to some employees. - Effect (This is an action taken in response to some wrongdoing.)

II) Some employees of organization Y were found involved in objectionable activities. - Cause (This is the reason that could lead to disciplinary action.)

Statement II is the cause, and statement I is its possible effect.

Hence, the correct answer is "Option 1".

According to the given information,

To reach point A again, he should walk 8 - 5 = 3 km in Eest direction.

Hence, the correct answer is “Option 4”.

Seven boxes, C, D, E, F, G, H, and Y, are placed one above the other, but not necessarily in the same order.

1. Only H is placed above Y.
2. Only D is placed between Y and C.
3. Only E is placed below F. 

Three boxes are placed between G and H.

Hence, the correct answer is “Option 2”.

(1) PTS

P + 4 = T

T - 1 = S

(2) IML

I + 4 = M

M - 1 = L

(3) VZY

V + 4 = Z

Z - 1 = Y

(4) CGE

C + 4 = G

G - 2 = E

Hence, the correct answer is “Option 4”.

AD 9 is related to GA 4,

And 

HK 22 is related to NH 17,

Similarly,

DO 3 is related to,

Hence, the correct answer is “Option 3”.

Concept:

Vowels (A, E, I, O, U) → replaced by next letter

Consonants → replaced by previous letter

Given words: GOD, TEN, WAS, CUP

Step 1: Apply the rule

GOD → G→F, O→P, D→C → FPC

TEN → T→S, E→F, N→M → SFM

WAS → W→V, A→B, S→R → VBR

CUP → C→B, U→V, P→O → BVO

FPC → contains no vowel

SFM → contains no vowel

VBR → contains no vowel

BVO → contains vowel O

Groups without vowels = 3

Hence, the correct answer is “Option 4”.

Logic followed here is,

24 - 5 = 19

19 - 4 = 15

15 - 3 = 12

12 - 2 = 10

10 - 1 = 9

Hence, the correct answer is “Option 1”.

The correct answer is Money Market.

Key Points

• The Money Market is a component of the financial market where short-term borrowing and lending take place, primarily dealing with debt securities with a maturity period of one year or less. Hence, Option C is correct.
• It provides a platform for liquidity management, allowing banks, financial institutions, and corporations to bridge the gap between short-term cash requirements and excess funds.
• The primary function of this market is to facilitate the working capital needs of industries and provide the government with short-term funds to manage fiscal deficits.
• In India, the Money Market is regulated and controlled by the Reserve Bank of India (RBI) to maintain monetary stability and influence interest rates in the economy.
• Instruments traded here are considered near-money assets because they are highly liquid, carry low financial risk, and can be converted into cash quickly with minimal transaction costs.

Additional Information

• Capital Market:
• The Capital Market is designed for long-term investments, where equity and debt securities with a maturity exceeding one year are traded.
• It is regulated by the Securities and Exchange Board of India (SEBI) and helps in capital formation and wealth creation for investors. Hence, Statement B is incorrect.
• Primary Market:
• This is the section of the capital market where new securities are issued for the first time.
• Commonly associated with Initial Public Offerings (IPOs), it allows companies to raise fresh capital directly from investors. Hence, Statement A is incorrect.
• Secondary Market:
• Commonly known as the stock market or stock exchange (e.g., BSE, NSE), it is the platform where previously issued securities are traded among investors.
• It provides liquidity to existing shareholders but does not provide additional capital to the issuing company. Hence, Statement D is incorrect.

Important Points

• Treasury Bills (T-Bills): These are short-term debt instruments issued by the Government of India in three tenors: 91 days, 182 days, and 364 days. They are issued at a discount and redeemed at par.
• Commercial Paper (CP): Introduced in 1990, it is an unsecured money market instrument issued in the form of a promissory note by highly rated corporate entities to meet short-term liabilities.
• Certificates of Deposit (CD): These are negotiable money market instruments issued by Scheduled Commercial Banks and Financial Institutions against funds deposited for a specific period.
• Call Money: This refers to short-term finance repayable on demand, with a maturity ranging from 1 day to 14 days. It is used by commercial banks to maintain their Cash Reserve Ratio (CRR).
• Commercial Bill: A bill of exchange used to finance the working capital of business firms. It is a self-liquidating, negotiable instrument used for credit sales of goods.

The correct answer is Fossil fuels.

Key Points

• Advanced Chemistry Cells (ACC) are the new generation of advanced storage technologies that can store electric energy either as electrochemical or as chemical energy and convert it back to electric energy as and when required.
• The primary objective of promoting ACC manufacturing is to reduce the heavy reliance on Fossil fuels such as petrol, diesel, and coal by enabling the transition to Electric Vehicles (EVs) and Renewable Energy storage.
• In May 2021, the Cabinet approved the Production Linked Incentive (PLI) Scheme for the National Programme on Advanced Chemistry Cell (ACC) Battery Storage to achieve a manufacturing capacity of 50 Giga Watt Hour (GWh).
• The shift towards ACC batteries helps in lowering Crude Oil imports, which significantly improves India’s Trade Balance and Energy Security. Hence, the option related to fossil fuels is correct.
• By storing power from intermittent sources like Solar and Wind, these batteries ensure a steady supply of green energy, further displacing the need for thermal power generated from fossil fuels.

Additional Information

• PLI Scheme for ACC: The government allocated an outlay of  ₹18,100 crore for this program to incentivize domestic and foreign investment in Giga-scale manufacturing facilities.
• Environmental Impact: This initiative is a cornerstone of India's commitment to the Paris Agreement and the goal of achieving Net Zero emissions by the year 2070. It directly addresses the reduction of Greenhouse Gas (GHG) emissions from the transportation and power sectors.
• Technology Neutrality: The National Programme on ACC is technology-agnostic, meaning it supports various chemistries such as Lithium-Ion, Sodium-Ion, Solid-State batteries, and Flow batteries, provided they meet specific performance criteria.
• Economic Benefits: It is estimated that the scheme will lead to direct investment of around  ₹45,000 crore and result in import substitution of around  ₹20,000 crore to  ₹25,000 crore every year.
• Application Areas: Apart from Electric Vehicles, ACC batteries find critical applications in consumer electronics, solar rooftops, telecom towers, and smart grids for load leveling.

Important Points

• Supply Chain Security: By localized manufacturing, India aims to reduce its dependence on specific countries for battery cells, which are currently dominated by China and South Korea.
• FAME-II Linkage: The ACC program works in tandem with the Faster Adoption and Manufacturing of Hybrid and Electric Vehicles (FAME-II) scheme, which provides subsidies to consumers for purchasing electric two-wheelers, three-wheelers, and buses.
• Research and Development: The program encourages R&D in battery chemistry to find alternatives to scarce minerals like Lithium and Cobalt, exploring abundant materials available within the country.
• Niche ACC: The program also includes a 5 GWh capacity for Niche ACC technologies that may have higher energy density or specialized applications but are not yet produced on a commercial scale.

The correct answer is Prevention of Money Laundering Act (PMLA).

Key Points

• On May 16, 2024, the Supreme Court of India (SCI) delivered a landmark judgment in the case of Tarsem Lal v. Directorate of Enforcement, significantly limiting the arrest powers of the Enforcement Directorate (ED) under the Prevention of Money Laundering Act (PMLA), 2002.
• A bench comprising Justice Abhay S. Oka and Justice Ujjal Bhuyan ruled that if the ED has not arrested an accused during the investigation until the filing of the complaint, it cannot arrest the person under Section 19 once the Special Court takes cognizance of the complaint.
• The court clarified that after cognizance is taken, if the accused appears before the Special Court pursuant to a summons, they are considered to be in the custody of the court, and thus the ED must seek specific permission from the court if they wish to take the person into custody.
• The ruling specifies that the stringent "twin conditions" for bail under Section 45 of the PMLA would not apply in cases where the accused appears in court following a summons, as they are not being "arrested" in the traditional sense at that stage.
• This decision emphasizes that the power of arrest under Section 19 is not an arbitrary tool and cannot be exercised once the matter has transitioned from the investigative stage to the judicial stage through the filing of a prosecution complaint.

Additional Information

• Prevention of Money Laundering Act (PMLA), 2002:
• The PMLA was enacted by the Parliament of India in 2002 to prevent money laundering and provide for the confiscation of property derived from money laundering.
• It came into force on July 1, 2005. The Act is designed to meet India's international obligations under the Vienna Convention and the Financial Action Task Force (FATF) guidelines.
• Section 19 of the Act empowers authorized ED officers to arrest a person if they have "reason to believe" (recorded in writing) that the person is guilty of an offense.
• Enforcement Directorate (ED):
• The ED is a specialized financial investigation agency under the Department of Revenue, Ministry of Finance, Government of India.
• Its primary function is to enforce two key laws: the Foreign Exchange Management Act (FEMA), 1999, and the Prevention of Money Laundering Act (PMLA), 2002.
• The agency is headquartered in New Delhi and was established on May 1, 1956, originally as an 'Enforcement Unit' in the Department of Economic Affairs.
• Section 45 and Twin Conditions:
• Section 45 of PMLA makes the offenses cognizable and non-bailable. It imposes twin conditions for bail: the Public Prosecutor must be given an opportunity to oppose the bail, and the court must be satisfied that the accused is not guilty and is unlikely to commit any offense while on bail.
• The Supreme Court had struck down these conditions in 2017 (Nikesh Tarachand Shah case), but the Parliament reinstated them through an amendment in 2018, which was upheld by the SCI in the Vijay Madanlal Choudhary case in 2022.

Important Points

• Constitutional Context: This judgment is seen as a major protection for personal liberty under Article 21 of the Constitution of India, preventing potential misuse of power by investigative agencies.
• Legal Procedure: The court noted that when an accused is not arrested during the probe, the Special Court should normally issue a summons and not a warrant at the first instance.
• Scope of Summons: If an accused appears before the court in response to a summons, they can furnish a bond for appearance under Section 88 of the Code of Criminal Procedure (CrPC) (now replaced by Section 91 of the Bharatiya Nagarik Suraksha Sanhita, 2023), and this does not amount to applying for bail.
• Impact on Future Cases: This ruling limits the ED's ability to use the threat of arrest as a means of coercion once the formal judicial proceedings have commenced, ensuring a balance between the State's power to investigate and the citizen's right to a fair trial.

The correct answer is P. R. Sreejesh.

Key Points

• The legendary former Indian hockey goalkeeper, P. R. Sreejesh, was honored with the Padma Bhushan award in January 2025. This is the third-highest civilian award in India, conferred for his distinguished service to Indian sports.
• The announcement was made on the eve of the 76^th Republic Day of India in 2025. Sreejesh retired from professional hockey following the Paris 2024 Olympics, where he played a monumental role in India winning the Bronze Medal.
• Known as the "The Wall" or the "Great Wall of Indian Hockey", he served the national team for nearly 18 years, making over 300 international appearances since his debut in 2006.
• His leadership as a former captain and his heroics at the goalpost were instrumental in India’s historic Bronze Medal win at the Tokyo 2020 Olympics, which ended a 41-year Olympic medal drought for the country in hockey.
• In 2025, the government recognized his consistent excellence and his contribution to revitalizing the popularity of hockey in India, particularly after he successfully guarded the goal in back-to-back Olympic medal-winning campaigns (Tokyo 2020 and Paris 2024).

Additional Information

• Major Awards and Honors: P. R. Sreejesh has a decorated trophy cabinet, including the Arjuna Award in 2015, the Padma Shri (India's fourth-highest civilian award) in 2017, and the Major Dhyan Chand Khel Ratna Award in 2021. He was also named the World Games Athlete of the Year in 2021, becoming only the second Indian to receive this global honor.
• Olympic Career: He represented India in four consecutive Olympic Games: London 2012, Rio 2016, Tokyo 2020, and Paris 2024. His performance in the penalty shootout against Great Britain in the Paris 2024 quarterfinals is considered one of the greatest goalkeeping displays in hockey history.
• Post-Retirement Role: Following his retirement in August 2024, Hockey India appointed him as the Head Coach of the Junior India Men's Hockey Team. He aims to mentor the next generation of players and goalkeepers to maintain India's standing in world hockey.
• Biographical Details: Born on 8 May 1988 in Kizhakkambalam, Kochi, Kerala, Sreejesh initially started in athletics (sprinting and long jump) before switching to hockey as a student at the GV Raja Sports School in Thiruvananthapuram.
• Asian Games Success: He was a key member of the gold-medal-winning teams at the 2014 Incheon Asian Games and the 2022 Hangzhou Asian Games (held in 2023). His save in the 2014 final shootout against Pakistan remains a career highlight.

Important Points

• Padma Awards Overview: These awards are conferred by the President of India at ceremonial functions held at Rashtrapati Bhawan. The awards are given in three categories: Padma Vibhushan (exceptional and distinguished service), Padma Bhushan (distinguished service of high order), and Padma Shri (distinguished service).
• 2025 Sports Contingent: The 2025 Padma Awards list featured several prominent sports personalities. P. R. Sreejesh being promoted from Padma Shri to Padma Bhushan signifies the highest level of national appreciation for his career longevity and impact on the sport.
• Legacy in Kerala: Sreejesh is the first sportsperson from Kerala to win two Olympic medals, making him an icon in his home state where the Kerala Government has also honored him with several state-level rewards and a road named after him in his hometown.

The correct answer is Demand for Money.

Key Points

• Liquidity preference is a fundamental economic theory that describes the Demand for Money, specifically why individuals choose to hold liquid assets (cash) rather than illiquid assets like bonds or real estate.
• The concept was pioneered by the famous British economist John Maynard Keynes in his seminal 1936 work, "The General Theory of Employment, Interest, and Money".
• Keynes argued that the interest rate is not a reward for saving, but rather the price paid to induce people to part with their liquidity for a certain period.
• There is an inverse relationship between the interest rate and the liquidity preference; as interest rates rise, the opportunity cost of holding cash increases, leading to a decrease in the demand for money.
• The liquidity preference curve is typically downward sloping, indicating that at lower interest rates, people desire to hold more cash because the returns on other investments are less attractive.

Additional Information

• Three Motives for Holding Money:
• Transactions Motive: People hold money to bridge the interval between the receipt of income and its expenditure for daily requirements.
• Precautionary Motive: This refers to the desire to hold cash for unforeseen contingencies, such as medical emergencies, accidents, or unemployment.
• Speculative Motive: This is the desire to hold cash to take advantage of future changes in market interest rates or bond prices. If investors expect interest rates to rise, they will hold cash to buy bonds later at a lower price.
• Liquidity Trap:
• This is a specific economic situation where interest rates are so low (near zero) that monetary policy becomes ineffective.
• In a liquidity trap, the liquidity preference becomes perfectly elastic (horizontal), meaning people prefer to hold cash regardless of how much money supply is increased by the central bank.
• Money Supply vs. Demand for Money:
• While Demand for Money is determined by the public's preference, the Money Supply is typically controlled by a country's central bank, such as the Reserve Bank of India (RBI) or the Federal Reserve in the USA.
• In India, money supply is measured through aggregates like M1 (Narrow Money), M2, M3 (Broad Money), and M4, based on their liquidity levels.

Important Points

• Determinants of Liquidity Preference:
• Income Level: As nominal income increases, the transactions demand for money also increases because people engage in more volume of trade.
• Price Level: Higher inflation or prices increase the demand for money because more currency is needed to purchase the same basket of goods.
• Uncertainty: Higher socio-economic uncertainty increases the precautionary demand for liquid cash.
• Impact on Bonds:
• There is an inverse relationship between bond prices and interest rates. When the demand for money is high, people sell bonds, causing bond prices to fall and interest rates to rise.
• The liquidity preference theory helps policymakers understand how interest rates are determined in the money market by the equilibrium of money supply and money demand.

The correct answer is National Commission for Women.

Key Points

• In February 2025, the National Commission for Women (NCW) officially urged the Ministry of Information and Broadcasting (MIB) to take immediate and stringent action against the rising trend of obscene and vulgar content on Over-the-Top (OTT) platforms and social media streaming sites.
• The Commission expressed deep concern over the depiction of women in a manner that is derogatory and indecent, noting that such content violates the dignity of women and has a detrimental effect on societal values and the younger generation.
• The Chairperson of the NCW, Vijaya Rahatkar, emphasized that while creative freedom is important, it cannot be used as a pretext to bypass the laws of the land, specifically the Indecent Representation of Women (Prohibition) Act, 1986.
• The NCW highlighted the necessity for a more robust regulatory framework or pre-certification process for digital content, similar to the Central Board of Film Certification (CBFC) which regulates theatrical releases.
• The commission's demand follows numerous complaints regarding the use of explicit language, sexual violence, and degrading portrayals that are easily accessible to minors on various streaming applications.

Additional Information

• National Commission for Women (NCW):
• Established in January 1992 under the National Commission for Women Act, 1990, it is a statutory body of the Government of India.
• The NCW is mandated to review the constitutional and legal safeguards for women, recommend legislative measures, and facilitate redressal of grievances.
• The NCW consists of a Chairperson, five members, and a Member-Secretary, all nominated by the Central Government.
• IT Rules 2021:
• The Information Technology (Intermediary Guidelines and Digital Media Ethics Code) Rules, 2021, provide a three-tier grievance redressal mechanism for OTT platforms and digital news.
• Tier I involves self-regulation by the platform; Tier II is an independent self-regulating body headed by a retired judge; and Tier III is an Oversight Mechanism by the Central Government.
• Indecent Representation of Women (Prohibition) Act, 1986:
• This Act prohibits the indecent representation of women through advertisements, publications, writings, or in any other manner.
• The government has proposed amendments to this Act to include digital forms of communication and electronic media to keep pace with technological advancements.

Important Points

• Regulatory Challenges: Unlike traditional cinema, OTT platforms are not subject to the Cinematograph Act, 1952, which requires mandatory certification before public exhibition.
• Information Technology Act, 2000: Section 67 of the IT Act provides for punishment for publishing or transmitting obscene material in electronic form, carrying a penalty of imprisonment and fines.
• Ministry of Information and Broadcasting (MIB): Under the Allocation of Business Rules updated in 2020, digital/online media, including OTT platforms, were brought under the direct jurisdiction of the MIB.
• Constitutional Context: Article 19(1)(a) of the Constitution of India guarantees freedom of speech and expression, but Article 19(2) allows reasonable restrictions in the interest of decency or morality.

The correct answer is Maharashtra.

Key Points

• The Savalda culture is an early Chalcolithic (Copper-Stone Age) culture primarily located in the state of Maharashtra, specifically concentrated in the Tapi River valley.
• It is named after the type-site Savalda, which is situated in the Dhule district of Maharashtra.
• Chronologically, the Savalda culture is dated between 2300 BCE and 2000 BCE, predating the famous Jorwe culture in the region.
• The culture is characterized by its unique Savalda ware, which is a sturdy pottery made on a slow-turning wheel and decorated with various geometric and naturalistic motifs.
• Excavations at the site of Daimabad in Ahmednagar district revealed that the Savalda culture represents the earliest occupational phase (Phase I) in the regional Chalcolithic sequence.

Additional Information

• Savalda Pottery Features: The pottery is typically chocolate-colored or red-slipped. Notable decorations include depictions of arrows, harpoons, fish, and antelopes, which reflect the hunter-gatherer influence alongside early farming.
• Settlement Pattern: The people of this culture lived in mud houses that were either rectangular or circular in shape. The site of Kaothe in Dhule district is one of the most extensive settlements identified for this culture.
• Economy and Subsistence: Evidence suggests a mixed economy involving agriculture (cultivating wheat, barley, and lentils), animal husbandry (rearing cattle, sheep, and goats), and fishing.
• Tools and Technology: They utilized copper for making simple tools like rings and beads, though the use of stone tools (microliths) made from chalcedony and agate remained predominant.
• Geographic Range: While centered in Maharashtra, traces of the culture and its pottery styles have been identified in parts of the North Deccan, showing interactions with contemporary Neolithic and early Chalcolithic communities.

Important Points

• Relation to Harappan Civilization: The Savalda culture was roughly contemporary with the Mature Harappan phase. Interestingly, at Daimabad, the Savalda phase is followed by a Late Harappan influence, indicating a complex transition of cultures in Western India.
• Distinctive Sites: Apart from Savalda and Daimabad, other important sites include Arawada and Bahurupa. These sites have provided crucial data regarding the pre-Jorwe cultural landscape of Maharashtra.
• Cultural Evolution: The discovery of Savalda culture shifted the historical understanding of Maharashtra, proving that the region had well-established copper-using farming communities long before the Iron Age or the peak of the Jorwe period.
• Archaeological Significance: The pottery of Savalda is often cited as one of the most artistically distinct among regional Chalcolithic styles in India, specifically due to its symbolic paintings which are not as common in the later Malwa or Jorwe phases.

The correct answer is Triangular.

Key Points

• The Deccan Plateau is a triangular landmass that lies to the south of the Narmada River. This shape is defined by its physical boundaries, which taper towards the south. Hence, the statement regarding its triangular shape is correct.
• In the north, its broad base is flanked by the Satpura Range, while the Mahadev, the Kaimur Hills, and the Maikal Range form its eastern extensions. Hence, the description of its northern and eastern boundaries is correct.
• The Deccan Plateau is higher in the West and slopes gently eastwards. This specific gradient causes most of its major rivers to flow toward the Bay of Bengal. Hence, the statement regarding its eastward slope is correct.
• An extension of the Plateau is also visible in the Northeast, locally known as the Meghalaya, Karbi-Anglong Plateau, and North Cachar Hills. It is separated by a fault from the Chotanagpur Plateau. Hence, the statement regarding its northeastern extension is correct.
• The plateau covers an area of approximately 5,00,000 square kilometers and is one of the oldest and most stable landmasses of India, being part of the ancient Gondwanaland.

Additional Information

• Geographical Boundaries: The western edge of the plateau is marked by the Western Ghats (also known as Sahyadris), while the eastern edge is marked by the Eastern Ghats. The Western Ghats are higher, with an average elevation of 900 to 1,600 meters, whereas the Eastern Ghats are lower, averaging about 600 meters.
• Geological Composition: One of the distinct features of the Deccan Plateau is the black soil area known as the Deccan Trap. This is of volcanic origin, consisting of igneous rocks (basalt). The rocks have denuded over time and are responsible for the formation of black soil, which is highly suitable for cotton cultivation.
• States Covered: The plateau spans across eight Indian states, with the majority of the area falling in Maharashtra, Karnataka, Telangana, and Andhra Pradesh. Portions also extend into Kerala and Tamil Nadu in the south.
• Major Rivers: The region is drained by several large perennial rivers such as the Godavari, Krishna, and Kaveri. The Godavari is the longest river in the peninsula and is often referred to as the Dakshin Ganga.

Important Points

• Highest Peaks: The highest peak in the Deccan Plateau and the entire South India is Anamudi, located in the Anaimalai Hills of Kerala, with an elevation of 2,695 meters. Doda Betta is the second-highest peak at 2,637 meters, located in the Nilgiri Hills.
• Formation: The plateau was formed during the late Cretaceous period (roughly 66 million years ago) due to massive fissure-type volcanic eruptions. These eruptions laid down thick layers of lava, creating a "step-like" topography, hence the name "trap" (from the Swedish word 'trappa' meaning stairs).
• Climate: Due to its elevation and location, the plateau experiences a semi-arid climate in its central parts, as the Western Ghats act as a barrier to the Southwest Monsoon winds, creating a rain-shadow area.

The correct answer is December 12, 2019.

Key Points

• The Citizenship (Amendment) Bill, 2019 was passed by the Lok Sabha on December 9, 2019. It was subsequently introduced and passed in the Rajya Sabha on December 11, 2019.
• The Bill officially became an Act after it received the assent of the President of India, Shri Ram Nath Kovind, on December 12, 2019. Hence, the correct option is B.
• The Citizenship (Amendment) Act (CAA), 2019 aims to amend the Citizenship Act, 1955, specifically to provide a path to Indian citizenship for persecuted religious minorities.
• The Act applies to migrants from six specific religious communities: Hindus, Sikhs, Buddhists, Jains, Parsis, and Christians who arrived in India on or before December 31, 2014.
• These migrants must have originated from three neighboring countries: Afghanistan, Bangladesh, and Pakistan. The primary objective is to protect those who fled due to religious persecution or the fear of such persecution.

Additional Information

• Effective Date: While the Presidential assent was granted in 2019, the Ministry of Home Affairs issued a notification stating that the provisions of the Act would come into force on January 10, 2020. Hence, the date in option C represents the commencement date, not the assent date.
• Residency Requirement: Under the original Citizenship Act, 1955, one of the requirements for citizenship by naturalization was that the applicant must have resided in India for at least 11 years. The 2019 Amendment reduced this period to 5 years for the specified categories of migrants.
• Exemptions: The CAA 2019 does not apply to the tribal areas of Assam, Meghalaya, Mizoram, and Tripura as included in the Sixth Schedule of the Constitution of India. It also excludes areas regulated under the Inner Line Permit (ILP) system, which currently includes Arunachal Pradesh, Mizoram, Manipur, and Nagaland.
• OCI Cancellation: The Act also introduced provisions allowing the Central Government to cancel the registration of Overseas Citizen of India (OCI) cardholders if they violate any law notified by the government.

Important Points

• Constitutional Basis: The power to legislate on citizenship is exclusively vested in the Parliament under Article 11 of the Constitution of India. Citizenship falls under the Union List (Entry 17) of the Seventh Schedule.
• The Citizenship Act, 1955: This is the parent legislation that prescribes five ways to acquire Indian citizenship: Birth, Descent, Registration, Naturalization, and Incorporation of Territory.
• CAA Rules 2024: Although the Act was passed in 2019, the specific Citizenship (Amendment) Rules, 2024, were officially notified by the Government of India on March 11, 2024, enabling the actual application process for eligible individuals.
• Illegal Migrants: Before this amendment, "illegal migrants" were prohibited from acquiring Indian citizenship. The 2019 Act ensures that the specified group of persons shall not be treated as illegal migrants for the purpose of the Act.

The correct answer is 5 years.

Key Points

• Article 243E of the Constitution of India explicitly states that every Panchayat, unless dissolved sooner under any law for the time being in force, shall continue for a period of 5 years from the date appointed for its first meeting and no longer. Hence, the statement regarding the 5-year duration is correct.
• The 73^rd Constitutional Amendment Act, passed in 1992, provided a statutory and constitutional framework for the Panchayati Raj Institutions (PRIs), making the 5-year term a mandatory requirement across the country.
• As per the Constitution, an election to constitute a Panchayat must be completed before the expiration of its duration of 5 years. Hence, the statement regarding completion before expiration is correct.
• In the event of the dissolution of a Panchayat before the completion of its full term, the election to constitute a new Panchayat must be completed before the expiration of a period of 6 months from the date of its dissolution. Hence, the statement regarding the 6-month window after dissolution is correct.
• It is important to note that if the remainder of the period for which the dissolved Panchayat would have continued is less than 6 months, it is not obligatory to hold an election for that short remaining duration.

Additional Information

• The 73^rd Amendment Act, 1992, added a new Part IX to the Constitution of India, entitled "The Panchayats", and consists of provisions from Article 243 to 243O.
• The Act also added the Eleventh Schedule, which contains 29 functional items of the Panchayats, including agriculture, land improvement, poverty alleviation programs, and education.
• It mandates a three-tier system of Panchayati Raj: the Gram Panchayat at the village level, the Panchayat Samiti at the intermediate or block level, and the Zila Parishad at the district level.
• The State Election Commission is the designated authority responsible for the superintendence, direction, and control of the preparation of electoral rolls and the conduct of all elections to the Panchayats.
• Reservation of seats is provided for Scheduled Castes (SCs) and Scheduled Tribes (STs) in every Panchayat based on their population ratio, and at least one-third of the total number of seats must be reserved for women.

Important Points

• The minimum age required for a person to be eligible to contest an election for a Panchayat is 21 years, which is lower than the age requirement for the Legislative Assembly or Lok Sabha (25 years).
• The Gram Sabha is the primary and permanent body of the Panchayati Raj system, consisting of all persons registered in the electoral rolls of a village within the Panchayat area.
• To ensure financial viability, the Governor of a state is required to constitute a State Finance Commission every 5 years to review the financial position of the Panchayats and recommend the distribution of revenues.
• The provisions of the 73^rd Amendment do not apply to the states of Nagaland, Meghalaya, and Mizoram, and certain other scheduled areas or tribal areas, which are governed by different administrative laws.
• The Panchayati Raj system aims to promote decentralization and local self-government, enabling people's participation in the development process at the grassroots level.

The correct answer is Malayalam.

Key Points

• My Dear Kuttichathan is a landmark Indian fantasy film released in 1984, and it is widely recognized as India's first 3D film.
• The film was originally written and filmed in the Malayalam language, directed by Jijo Punnoose and produced by M. C. Punnoose (popularly known as Navodaya Appachan).
• The film utilized stereoscopic 3D technology, which was a revolutionary feat for the Indian film industry during the 1980s.
• The story focuses on a mystical spirit called Kuttichathan, who is released from the bondage of a cruel magician by three children, leading to various magical adventures.
• It was produced under the banner of Navodaya Studio, based in Kerala, which was at the forefront of technical innovation in regional cinema.

Additional Information

• Chhota Chetan: Due to its immense popularity, the film was dubbed into Hindi and released as Chhota Chetan in 1998. This version included new scenes featuring Urmila Matondkar and Satish Kaushik to appeal to a wider national audience.
• Regional Impact: Apart from Hindi, the film was also dubbed into Tamil as Chutti Chathan and Telugu as Chinnari Chethana, showcasing its cross-cultural appeal across India.
• Technical Prowess: The film's success is attributed to the use of Chris Condon’s StereoVision 3D lens system. The cinematography was handled by Ashok Kumar, who successfully captured the depth required for a 3D experience.
• Cast and Crew: The film featured notable actors such as Kottarakkara Sreedharan Nair as the cruel magician, along with child actors Sonia, Master Aravind, and Master Mukesh.
• Legacy: Even decades after its release, it remains a cult classic in Malayalam cinema and is frequently re-released in theaters with upgraded digital 3D technology.

Important Points

• National Recognition: The film won the National Film Award for Best Children's Film at the 32^nd National Film Awards in 1985, cementing its status as a high-quality production for young audiences.
• Navodaya Studio Achievements: Before making the first 3D film, Navodaya Studio also produced Padayottam (1982), which was India's first indigenously shot 70mm film. This established the studio's reputation for pioneering technological advancements in South Indian cinema.
• Box Office Success: My Dear Kuttichathan was a massive commercial success, reportedly earning many times its original production budget. Its 1998 re-release in Hindi alone collected over ₹60 crore, a significant amount at that time.
• Genre: It falls under the Children's Fantasy genre, blending elements of Indian folklore (the spirit Kuttichathan is a figure in Kerala's local myths) with modern cinematic techniques.

The correct answer is Variable rate technology.

Key Points

• Variable Rate Technology (VRT) is a key component of Precision Agriculture that allows for the automated, site-specific application of agricultural inputs.
• It enables farmers to apply fertilizers, pesticides, herbicides, and seeds at different rates across a single field, matching the specific nutrient requirements or soil conditions of each zone.
• The technology functions using Global Positioning System (GPS) to track the machinery's exact location and Geographic Information Systems (GIS) to analyze spatial data.
• There are two primary types of VRT: Map-based VRT, which uses pre-generated prescription maps derived from soil samples or satellite imagery, and Sensor-based VRT, which uses real-time sensors on the machinery to measure crop health or soil properties on the fly.
• The main objective of VRT is to increase input efficiency, ensuring that crops receive exactly what they need for optimal growth while avoiding the waste associated with blanket application methods.

Additional Information

• Precision Farming: This is a management strategy that uses Information Technology (IT) to ensure that crops and soil receive exactly what they need for optimum health and productivity. It relies on Big Data, drones, and satellite imagery.
• Economic Impact: By utilizing VRT, farmers can see a significant reduction in input costs. For example, by applying nitrogen only where the soil is deficient, a farmer can save thousands of dollars in chemical fertilizers over a large area.
• Environmental Benefits: VRT plays a crucial role in environmental sustainability by reducing chemical runoff. Excess fertilizers often leak into groundwater or nearby streams; VRT minimizes this risk by preventing over-saturation of chemicals.
• Soil Variability: Factors such as topography, organic matter, moisture content, and pH levels can vary significantly within a few meters. VRT is designed specifically to address this spatial heterogeneity.
• Yield Monitoring: This involves using sensors to measure the harvested weight of the crop in real-time, which provides the data necessary to create the prescription maps used in future VRT cycles.

Important Points

• Equipment Requirements: To implement VRT, machinery must be equipped with a Variable Rate Controller, a GPS receiver, and an on-board computer capable of processing digital maps.
• NDVI Sensors: The Normalized Difference Vegetation Index (NDVI) is a common metric used in sensor-based VRT to determine plant vigor and greenness, which informs the machinery how much fertilizer to spray at that exact moment.
• Indian Context: In India, the Indian Council of Agricultural Research (ICAR) and various Agri-tech startups are working to make VRT more accessible to small-scale farmers to improve resource use efficiency.
• Data Management: A challenge of VRT is the high volume of data generated. Farmers often need to work with agronomists or data scientists to interpret soil health reports and translate them into actionable machine instructions.

The correct answer is Nanda.

Key Points

• The Mauryan Empire was founded by Chandragupta Maurya in 322 BCE after he overthrew the last ruler of the Nanda Dynasty, Dhana Nanda.
• Chandragupta Maurya was assisted by his mentor and strategist, Chanakya (also known as Kautilya or Vishnugupta), who sought to end the oppressive rule of the Nandas.
• The Nanda Dynasty ruled the Magadha region in northern India during the 4^th century BCE, with their capital at Pataliputra (modern-day Patna, Bihar).
• The fall of the Nanda Dynasty marked the beginning of the first great pan-Indian empire, as the Mauryas expanded their territory across almost the entire Indian subcontinent.
• According to historical accounts and the play Mudrarakshasa, the transition of power involved complex political maneuvering and a decisive military campaign against the Nanda capital.

Additional Information

• Haryanka Dynasty:
• This was the first important dynasty of Magadha, founded by Bimbisara in 544 BCE.
• Bimbisara used matrimonial alliances and conquests to expand his kingdom. His son, Ajatashatru, is famous for the First Buddhist Council held in 483 BCE.
• Shishunaga Dynasty:
• Founded by Shishunaga in 413 BCE, who was previously a minister under the Haryanka rulers.
• They are notable for temporarily shifting the capital to Vaishali and for Kalasoka, who convened the Second Buddhist Council in 383 BCE.
• Nanda Dynasty:
• Established by Mahapadma Nanda (often called the "Uprooter of all Kshatriyas") in 345 BCE.
• They maintained a massive army consisting of 200,000 infantry, 20,000 cavalry, and 3,000 elephants, which reportedly discouraged Alexander the Great from advancing further into India in 326 BCE.
• Kanva Dynasty:
• A much later dynasty, founded by Vasudeva Kanva in 73 BCE after overthrowing the Shunga Dynasty.
• They were a short-lived Brahmin dynasty that ruled from Magadha until approximately 28 BCE before being replaced by the Satavahanas.

Important Points

• The rise of the Mauryas is well-documented in several historical texts, including the Indica by Megasthenes (a Greek ambassador to Chandragupta’s court) and the Arthashastra by Kautilya.
• The Mauryan administration was highly centralized and efficient, featuring a sophisticated system of municipal administration and espionage.
• Ashoka the Great, the grandson of Chandragupta Maurya, brought the empire to its zenith, famously embracing Buddhism after the Kalinga War in 261 BCE.
• The Mauryan Empire eventually declined and was succeeded by the Shunga Dynasty in 185 BCE when Pushyamitra Shunga assassinated the last Mauryan king, Brihadratha.

The correct answer is Raghupathi Venkaiah Naidu.

Key Points

• Raghupathi Venkaiah Naidu (born 1887 – died 1941) is widely regarded as the "Father of Telugu Cinema" due to his pioneering contributions to the film industry in Southern India. He was born in Machilipatnam, Andhra Pradesh. Hence, this option is correct.
• In 1914, he established the Gaiety Showplace, which was the first permanent cinema hall in Madras (now Chennai). This initiative laid the foundation for the film exhibition industry in the region.
• He was a multi-faceted personality, working as a photographer, filmmaker, and exhibitor. He traveled across Asia, including Japan, Burma (Myanmar), and Sri Lanka, to screen silent films and promote the medium of cinema.
• Venkaiah Naidu was instrumental in producing some of the earliest silent films in India, such as Bhisma Pratigna (1921), which he co-directed with his son R. S. Prakash.
• To honor his legacy, the Government of Andhra Pradesh instituted the Raghupathi Venkaiah Award in 1989. It is the highest award in Telugu cinema, presented for lifetime achievement and outstanding contribution to the industry.

Additional Information

• NT Rama Rao (NTR):
• Nandamuri Taraka Rama Rao (1923–1996) was a legendary actor, filmmaker, and politician. He appeared in over 300 films and is famous for portraying deities like Lord Krishna and Lord Rama.
• He served as the 10^th Chief Minister of Andhra Pradesh for three terms and founded the Telugu Desam Party (TDP) in 1982. While he is an icon of the industry, he is not the "father" of the cinema. Hence, this option is incorrect.
• Chittoor Nagaiah:
• Vuppadutadiyam Nagaiah (1904–1973) was a veteran actor, composer, and director. He was the first South Indian actor to be honored with the Padma Shri in 1965.
• He was known as the "Paul Muni of India" for his method acting. His famous works include Vemana and Thyagayya. Hence, this option is incorrect.
• LV Prasad:
• Akkineni Lakshmi Vara Prasada Rao (1908–1994) was a renowned film producer, director, and actor. He established Prasad Studios in 1956 and Prasad's Group, which became a cornerstone for film post-production in India.
• He received the prestigious Dadasaheb Phalke Award in 1982. Although he was a giant in the industry, the title of "father" belongs to Naidu. Hence, this option is incorrect.

Important Points

• First Telugu Talkie: The first Telugu sound film, Bhakta Prahlada, was released on February 6, 1932. It was directed by H. M. Reddy, who is also a significant figure in early South Indian cinema.
• Transition of Hub: Initially, Telugu cinema was based in Madras. It gradually shifted its base to Hyderabad, Telangana, in the 1990s, leading to the establishment of the massive Ramoji Film City, which is the world's largest integrated film studio complex according to the Guinness World Records.
• Regional Impact: Telugu cinema, often referred to as Tollywood, has grown to become one of the largest film industries in India by the number of films produced and box office revenue, especially after the global success of films like Baahubali and RRR.

The correct answer is 3.

Key Points

• The 74^th Constitutional Amendment Act, which was passed in 1992, provides a constitutional framework for Urban Local Bodies (ULBs) in India. This act came into force on June 1, 1993.
• According to Article 243-Q of the Constitution of India, the act mandates the constitution of three types of municipalities in every state. Hence, the act divides municipalities into 3 parts.
• Nagar Panchayat: This is constituted for a transitional area, which refers to an area that is currently transitioning from a rural area to an urban area.
• Municipal Council: This body is established for a smaller urban area. These are often referred to as Municipalities or Nagar Palikas in various states.
• Municipal Corporation: This is the highest tier, created for a larger urban area. Major cities like Mumbai, Delhi, and Kolkata are governed by these corporations, often called Mahanagar Palikas.
• The classification of these areas (transitional, small, or large) is decided by the Governor of the state based on factors like population, density of population, revenue generated, and percentage of employment in non-agricultural activities.

Additional Information

• Constitutional Status: The 74^th Amendment Act added Part IXA to the Constitution of India, titled 'The Municipalities', covering Articles 243-P to 243-ZG. It also added the 12^th Schedule, which contains 18 functional items of municipalities.
• Reservation of Seats: Under Article 243-T, the act provides for the reservation of seats for Scheduled Castes (SC) and Scheduled Tribes (ST) in proportion to their population. Crucially, it mandates that not less than one-third (33%) of the total number of seats must be reserved for women.
• Duration of Municipalities: Article 243-U provides for a fixed five-year term for every municipality. If a municipality is dissolved before the expiry of its term, elections to constitute a new one must be completed within a period of six months.
• State Election Commission: The superintendence, direction, and control of the preparation of electoral rolls and the conduct of all elections to the municipalities are vested in the State Election Commission.
• Finance Commission: Under Article 243-Y, the State Finance Commission (constituted under Article 243-I) reviews the financial position of the municipalities and makes recommendations regarding the distribution of taxes and grants-in-aid between the State and the municipalities.

Important Points

• District Planning Committee (DPC): According to Article 243-ZD, every state is required to constitute a District Planning Committee at the district level to consolidate the plans prepared by the Panchayats and the Municipalities in the district.
• Metropolitan Planning Committee (MPC): Article 243-ZE provides for the creation of an MPC in every metropolitan area (an area having a population of 10 lakhs (1 million) or more) to prepare a draft development plan for the metropolitan area as a whole.
• Historical Context: The first Municipal Corporation in India was set up in Madras (now Chennai) in the year 1688. Later, in 1726, municipal corporations were set up in Bombay and Calcutta.
• Lord Ripon’s Resolution: The resolution of 1882 by Lord Ripon is hailed as the Magna Carta of local self-government in India. He is known as the 'Father of Local Self-Government' in India.
• Types of Urban Governments: Apart from the three mentioned in the 74^th Act, other types of urban local bodies include Notified Area Committees, Town Area Committees, Cantonment Boards, Townships, Port Trusts, and Special Purpose Agencies.

The correct answer is Manipur.

Key Points

• Sanamahism is the ancient indigenous religion of the Meitei people, who are the primary ethnic group in the Indian state of Manipur.
• The religion is centered around the worship of Lainingthou Sanamahi, the deity considered the creator and the supreme household god.
• It is one of the oldest practiced traditions in Southeast Asia and Northeast India, with a history spanning several millennia in the Imphal Valley.
• While Vaishnavite Hinduism became the state religion of Manipur in the 18^th century under King Pamheiba, Sanamahism continued to be practiced within households, leading to a unique syncretic religious culture.
• In the 20^th century, a strong revivalist movement emerged to protect and promote the original Meitei identity, culture, and the Meitei Mayek script, which is closely linked to Sanamahi scriptures.

Additional Information

• Deities and Spirits: Apart from Lainingthou Sanamahi, the pantheon includes Leimarel Sidabi (the mother goddess), Ibudhou Pakhangba (often depicted as a serpentine dragon representing royalty), and Panthoibi (the goddess of war and love).
• Festivals: The most significant religious festival is Lai Haraoba, which translates to "the pleasing of the gods." It features traditional dances, music, and rituals that reenact the Meitei creation myth.
• Geographical Location: The practice of Sanamahism is concentrated in the Imphal Valley of Manipur, though Meitei diaspora in Assam, Tripura, Myanmar, and Bangladesh also follow these traditions.
• Census Data: According to the 2011 Census, although many Meiteis are counted under Hinduism, there has been an increasing trend of individuals officially registering their religion as Sanamahi to assert their indigenous heritage.
• Functions: The religion governs various aspects of life, including birth, marriage, and death rituals, emphasizing the harmony between humans, nature, and ancestral spirits.

Important Points

• Puya: These are the sacred archaic Meitei manuscripts that contain the philosophical, historical, and ritualistic foundations of Sanamahism. Many of these texts were preserved despite historical attempts at suppression.
• Meitei Mayek: The revival of the Meitei script in the year 2005 in educational institutions is deeply tied to the preservation of Sanamahi religious texts and hymns.
• Cheiraoba: The Meitei New Year, celebrated in the month of March or April, involves climbing nearby hills and offering special food to Sanamahi at the household altar to ensure prosperity for the coming year.
• Comparison with other states: Unlike Rajasthan, Maharashtra, or Tamil Nadu, where Brahmanical Hinduism or Dravidian traditions are dominant, Manipur presents a distinct Tibeto-Burman cultural and religious legacy through Sanamahism.

The correct answer is Bharti Airtel.

Key Points

• Bharti Airtel emerged as the largest bidder in the 5G spectrum auction conducted in June 2024, committing a total of ₹6,856.76 crore. The company acquired 97 MHz of spectrum to strengthen its mid-band and sub-GHz holdings. Hence, the option identifying Bharti Airtel is correct.
• The Department of Telecommunications (DoT), under the Ministry of Communications, offered a total of 10,522.35 MHz of spectrum across eight different bands, ranging from 800 MHz to 26 GHz.
• Vodafone Idea (Vi) was the second-highest bidder, committing ₹3,510.40 crore to acquire spectrum in the 900 MHz, 1800 MHz, and 2100 MHz bands. This acquisition was aimed at enhancing its 4G and 5G coverage across several circles.
• Reliance Jio, despite being the largest operator in India by subscriber base, placed a relatively modest bid of ₹973.62 crore. Its primary focus was on renewing its existing spectrum in the 800 MHz band to maintain service continuity.
• The total value of the winning bids in the 2024 auction stood at ₹11,340.78 crore. This was a significant decrease compared to the landmark 2022 auction, which saw bids worth ₹1.5 lakh crore, as most companies had already secured substantial 5G airwaves previously.

Additional Information

• Spectrum Bands and Uses:
• The June 2024 auction included airwaves in the 800 MHz, 900 MHz, 1800 MHz, 2100 MHz, 2300 MHz, 2500 MHz, 3300 MHz, and 26 GHz bands.
• Lower bands like 900 MHz are preferred for wide coverage and indoor penetration, while higher bands like 3300 MHz and 26 GHz (millimeter wave) are essential for high-speed 5G data transmission.
• Financial Terms:
• Successful bidders like Bharti Airtel and Vodafone Idea have the flexibility to pay the auction amount in 20 equal annual installments.
• The interest rate for these installments was set at 8.65% by the Government of India.
• Regulatory Framework:
• The Telecom Regulatory Authority of India (TRAI) provides recommendations on spectrum pricing, while the Department of Telecommunications (DoT) manages the actual bidding process.
• The spectrum rights acquired in this auction are valid for a duration of 20 years.
• Operator Strategies:
• Reliance Jio: Focused on capital conservation after heavy spending in 2022.
• Bharti Airtel: Focused on "filling gaps" in its spectrum portfolio to improve efficiency.
• Vodafone Idea: Used the auction to signal long-term commitment following its recent Follow-on Public Offer (FPO).

Important Points

• BSNL Participation: The state-owned Bharat Sanchar Nigam Limited (BSNL) did not participate in the June 2024 auction. This is because the government has already reserved and administratively allocated spectrum for BSNL for its 4G and 5G rollout.
• Economic Impact: While the auction proceeds were lower than expected, they contribute to the Non-Tax Revenue of the Government of India for the financial year 2024-25.
• Circle-Wise Allocation: Bharti Airtel acquired airwaves in various telecom circles, including Airtel's strategic wins in the 900 MHz band in circles like Assam, Bihar, and Odisha to improve rural connectivity.

The correct answer is Chitra Banerjee Divakaruni.

Key Points

• The book 'The Palace of Illusions: A Novel' was written by Chitra Banerjee Divakaruni, a renowned Indian-American author and poet.
• The novel was published in the year 2008 and provides a modern reimagining of the ancient Indian epic, the Mahabharata.
• The story is uniquely narrated from the first-person perspective of Panchaali (also known as Draupadi), the wife of the five Pandava brothers.
• It explores themes of patriarchy, feminism, and destiny, shifting the focus from the traditional male-centric narrative of the epic to a woman's internal journey.
• The book follows Panchaali from her birth in fire through her marriage, the Kurukshetra War, and finally her path toward the Himalayas.

Additional Information

• Chitra Banerjee Divakaruni:
• She was born in Kolkata, India, in 1956 and later moved to the United States for higher education.
• Her literary career includes famous works like 'The Mistress of Spices' (1997) and 'Sister of My Heart' (1999).
• She received the American Book Award in 1996 for her collection of short stories titled 'Arranged Marriage'.
• Alka Joshi:
• She is a New York Times bestselling author known for her debut novel 'The Henna Artist', published in 2020.
• Her works often focus on the socio-cultural landscape of post-independence India, specifically the 1950s.
• Sarah Nisha Adams:
• She is a British-Indian author whose debut novel 'The Reading List' was released in 2021.
• Her writing often highlights the power of literature and community in modern London settings.
• Retellings of Epics:
• Retellings like 'The Palace of Illusions' are part of a genre that seeks to give voice to marginalized characters in mythology.
• Divakaruni also wrote 'The Forest of Enchantments' in 2019, which retells the Ramayana from Sita's point of view.

Important Points

• Literary Impact:
• The novel is widely studied for its feminist interpretation of classical texts, bringing the domestic and emotional aspects of mythological figures to the forefront.
• It humanizes grand historical figures like Karna, Krishna, and Bhishma through the eyes of a contemporary female narrator.
• Other Notable Works:
• 'The Last Queen' (2021): A historical novel by Divakaruni based on the life of Rani Jindan Kaur, the youngest wife of Maharaja Ranjit Singh.
• 'The Independence' (2022): A story set during the Partition of India in 1947, focusing on three sisters in Bengal.

The correct answer is Manipur.

Key Points

• Manipur topped the medal tally at the inaugural Khelo India Beach Games (KIBG) 2025, which were held in the Union Territory of Dadra and Nagar Haveli and Daman and Diu from May 19 to May 24, 2025.
• The games took place primarily at Ghoghla Beach in Diu, with Diu Beach hosting the Sepaktakraw events.
• The mascot was 'Pearl', a happy and energetic dolphin representing Diu's coastal spirit and marine heritage.
• Athletes competed in six medal sports: Beach Soccer, Beach Volleyball, Sepaktakraw (kick volleyball), Beach Kabaddi, Pencak Silat, and Open Water Swimming.
• Mallakhamb and Tug-of-War were included as non-medal demonstration sports to showcase India's traditional athletic heritage.
• The official tagline for the games was "Khel ke Sitare, Diu ke Kinare" (Stars of the Game, Shores of Diu).
• This Indonesian martial art had the highest impact on the medal tally, with 28 of the 46 total gold medals awarded in this discipline. Manipur secured 4 of its 5 gold medals in this sport alone.
• This was the first-ever multi-sport beach event under the Indian government's Khelo India banner, aimed at promoting coastal sports tourism.
• Manipur was declared the overall winner over Maharashtra despite having fewer total medals because the ranking was decided first by Gold count, and then by Silver count (Manipur had 6 silvers to Maharashtra's 5).

Additional Information

• Overview of Khelo India Beach Games:
• The Khelo India Beach Games is a new addition to the Khelo India initiative, which was originally launched in 2018 by the Government of India to strengthen the grassroots sports culture.
• The Ministry of Youth Affairs and Sports organized this event to provide a platform for athletes to excel in beach sports, which have high potential in international competitions like the Asian Beach Games.
• The 2024 games featured a total of 8 sports disciplines, including Beach Soccer, Beach Boxing, Beach Kabaddi, Sea Swimming, and the traditional Indian sport of Mallakhamb.
• Participation and Scale:
• More than 1200 athletes from 28 states and Union Territories across India participated in this multi-sport event.
• The venue, Ghoghla Beach, is notably one of the Blue Flag certified beaches in India, ensuring high environmental and safety standards for the number of participants involved.

Important Points

• Strategic Objectives: The introduction of beach games aims to boost sports tourism in coastal areas and UTs like Dadra and Nagar Haveli and Daman and Diu.
• Organizational Support: The games were executed with the support of the Sports Authority of India (SAI) and the local administration of Diu, ensuring international-level facilities for the year 2024.
• Medal Distribution: Landlocked states like Madhya Pradesh showed surprising dominance, proving that geographical location does not limit success in beach sports when proper training is provided. Maharashtra, with its vast coastline, continues to be a powerhouse in the Khelo India ecosystem.
• Future Implications: Success in these games serves as a selection criterion for national camps, preparing India for global events in the 2025 and 2026 international sports cycles.

The correct answer is Making India a Developed Nation by 2047.

Key Points

• Viksit Bharat 2047 is the visionary plan of the Government of India to transform the country into a developed nation by the year 2047, which marks the centenary of India's independence (100 years). Hence, the option Making India a Developed Nation by 2047 is correct.
• Prime Minister Narendra Modi launched the initiative "Viksit Bharat @2047: Voice of Youth" on December 11, 2023, via video conferencing to involve the younger generation in the national planning process.
• The vision encompasses several dimensions of development, including economic growth, social progress, environmental sustainability, and good governance.
• The roadmap for this initiative focuses on four major pillars: Yuva (Youth), Garib (Poor), Mahila (Women), and Annadata (Farmers), ensuring inclusive growth across all sections of society.
• It aims to bridge the gap between rural and urban areas through improved infrastructure, digital connectivity, and employment opportunities.

Additional Information

• Economic Transformation: Under this initiative, India aspires to become a $30 trillion economy by 2047, moving from its current status as the world's fifth-largest economy to one of the top three global powers.
• Infrastructure and Technology: The government is focusing on projects like PM Gati Shakti for integrated infrastructure and the expansion of the Digital India mission to ensure that Artificial Intelligence (AI) and 5G technology empower every citizen.
• Education and Skill Development: The National Education Policy (NEP) 2020 serves as a foundation for this mission by restructuring the education system to focus on skill development, research, and innovation.
• Health and Wellness: The goal includes achieving Universal Health Coverage through schemes like Ayushman Bharat, ensuring that quality healthcare is accessible and affordable for all 1.4 billion citizens.
• Sustainability: While pursuing development, India remains committed to climate action, aiming for Net Zero emissions by 2070 and significantly increasing the share of renewable energy in the total energy mix.

Important Points

• NITI Aayog: The National Institution for Transforming India (NITI Aayog) is the nodal agency responsible for preparing the "Viksit Bharat @2047" document, coordinating with various ministries, state governments, and industry experts.
• Youth Engagement: The "Voice of Youth" portal was created to crowd-source ideas from students and academicians in higher education institutions, making them active stakeholders in the nation-building process.
• Global Leadership: The vision also positions India as a "Vishwa Mitra" (friend of the world), emphasizing cooperation, peace, and leadership in solving global challenges such as supply chain resilience and cybersecurity.
• Ease of Living: A significant portion of the goal focuses on Ease of Living and Ease of Doing Business, reducing compliance burdens and promoting entrepreneurship through the Start-up India initiative$.

Shortcut Trick

Since both percentages are of the same number, they can be compared directly as values.

Let the 3% value be the base (denominator) and the 5% value be the numerator.

Required percentage = (5 ÷ 3) × 100

Required percentage = 1.6666... × 100 = 166.67%

∴ The correct answer is 166.67%.

Alternate Method

Given:

Value 1 = 5% of a number

Value 2 = 3% of the same number

Formula Used:

Required Percentage = (Value 1 ÷ Value 2) × 100

5% (5 units) 3% (3 units) Comparison: 5 is what % of 3?

Calculations:

⇒ Let the number be x.

⇒ 5% of x = 0.05x

⇒ 3% of x = 0.03x

⇒ Required % = (0.05x ÷ 0.03x) × 100

⇒ Required % = (5 ÷ 3) × 100

⇒ Required % = 500 ÷ 3

⇒ Required % = 166.666...%

⇒ Required % ≈ 166.67%

∴ The correct answer is 166.67%.

Additional Information

Basic Percentage Formula

To find X% of Y, use the formula: (X × Y) ÷ 100.

Percentage Comparison

To find what percent A is of B, use the formula: (A ÷ B) × 100. Always place the 'of' value in the denominator.

Fraction to Percentage Conversion

Common fractions like 1/3 = 33.33%, 2/3 = 66.67%, and 5/3 = 166.67% are useful for quick calculations.

Shortcut Trick

Marked Price = ₹225

Price after 20% discount = 225 × 0.8 = ₹180

Target Selling Price = ₹108

Additional reduction needed = 180 − 108 = ₹72

Additional Discount % = (72 ÷ 180) × 100 = 40%

∴ The correct answer is 40%.

Alternate Method

Given: Marked Price (MP) = ₹225, First Discount = 20%, Final Selling Price (SP) = ₹108.

Formula: SP = MP × (100 − D₁)/100 × (100 − D₂)/100

MP = ₹225 −20% Price: ₹180 D2 = ? SP = ₹108

⇒ Price after 1^st discount = 225 − (20% of 225)

⇒ Price after 1^st discount = 225 − (225 × 20 ÷ 100) = 225 − 45 = ₹180

⇒ Let additional discount be x%

⇒ Final SP = Price after 1^st discount × (100 − x) ÷ 100

⇒ 108 = 180 × (100 − x) ÷ 100

⇒ 108 ÷ 1.8 = 100 − x

⇒ 60 = 100 − x

⇒ x = 100 − 60 = 40%

∴ The correct answer is 40%.

Additional Information

Successive Discount Formula

A single discount equivalent to two successive discounts d₁% and d₂% is given by [d₁ + d₂ − (d₁ × d₂) ÷ 100]%.

Relation between MP and SP

The Selling Price is calculated by applying discount on the Marked Price: SP = MP × (100 − Discount%) ÷ 100.

Marked Price Definition

MP is the price printed on the label of an article. Discount is always calculated on the MP unless otherwise stated.

Shortcut Trick

Compare % increase of X over Y each year

2016: (40−30)/30 = 33.33%

2017: (55−45)/45 ≈ 22.22%

2018: (60−50)/50 = 20%

2019: (60−65) → negative

2020: (65−70) → negative

∴ The correct answer is 2016.

Alternate Method

Given:

2016 → X=40, Y=30

2017 → X=55, Y=45

2018 → X=60, Y=50

2019 → X=60, Y=65

2020 → X=65, Y=70

Formula Used:

% more = (X − Y) ÷ Y × 100

Calculation:

⇒ 2016: (40−30)/30 ×100 = 10/30 ×100 = 33.33%

⇒ 2017: (55−45)/45 ×100 = 10/45 ×100 ≈ 22.22%

⇒ 2018: (60−50)/50 ×100 = 10/50 ×100 = 20%

⇒ 2019: (60−65)/65 ×100 = negative

⇒ 2020: (65−70)/70 ×100 = negative

∴ The correct answer is 2016.

Additional Information

Percentage Difference Formula

% change = (difference ÷ base value) × 100, base is Y here.

DI Shortcut

Compare differences first, then divide by smaller Y for quick estimation.

Negative Values

If X < Y, percentage becomes negative, so ignore for maximum.

Exam Tip

Largest ratio comes when denominator is smallest for same difference.

Shortcut Trick

HCF must divide all numbers. Check options for divisibility.

252 is not divisible by 25 (ends in 52), 59 (59 × 4 = 236), or 47 (47 × 5 = 235).

252 ÷ 12 = 21 | 1092 ÷ 12 = 91 | 1800 ÷ 12 = 150.

Since 12 is the only option that divides all three numbers, it is the HCF.

∴ The correct answer is 12.

Alternate Method

Given numbers: 252, 1092, 1800

Formula: HCF = Product of common prime factors with the lowest power.

252 1092 1800 12 Common Factor (HCF)

Prime Factorization:

⇒ 252 = 2 × 2 × 3 × 3 × 7 = 2² × 3² × 7

⇒ 1092 = 2 × 2 × 3 × 7 × 13 = 2² × 3¹ × 7¹ × 13

⇒ 1800 = 2 × 2 × 2 × 3 × 3 × 5 × 5 = 2³ × 3² × 5²

⇒ Common factors are 2 and 3.

⇒ HCF = 2^min(2,2,3) × 3^min(2,1,2)

⇒ HCF = 2² × 3¹ = 4 × 3 = 12

∴ The correct answer is 12.

Additional Information

HCF Difference Rule

The HCF of two or more numbers is always a factor of the difference between any two of those numbers.

Relationship between LCM and HCF

For two numbers a and b, HCF(a, b) × LCM(a, b) = a × b.

HCF of Fractions

HCF of Fractions = (HCF of Numerators) ÷ (LCM of Denominators).

Shortcut Trick

Volume of a cone is proportional to r² × h.

10% increase means multiplier is 1.1.

New Volume = 1.1 × 1.1 × 1.1 = 1.331 times the original volume.

% Increase = (1.331 − 1) × 100 = 33.1%.

∴ The correct answer is 33.1%.

Alternate Method

Given: Initial radius (r₁) increase = 10%, Initial height (h₁) increase = 10%.

Formula Used: Volume (V) = (1/3) × π × r² × h

h r Initial    1.1h 1.1r Final  +10% each

⇒ Let original r = 10 and h = 10.

⇒ Original Volume V₁ = (1/3) × π × (10)² × 10 = 1000π/3

⇒ New radius r₂ = 10 + 10% of 10 = 11.

⇒ New height h₂ = 10 + 10% of 10 = 11.

⇒ New Volume V₂ = (1/3) × π × (11)² × 11 = 1331π/3

⇒ Percentage increase in Volume = [(V₂ − V₁) / V₁] × 100

⇒ Percentage increase = [(1331π/3 − 1000π/3) / (1000π/3)] × 100

⇒ Percentage increase = (331 / 1000) × 100 = 33.1%

∴ The correct answer is 33.1%.

Additional Information

Volume of a Cone

The volume is given by V = (1/3)πr²h. If only radius changes by x%, Volume changes by (1 + x/100)² − 1.

Successive Percentage Formula

For two successive changes x% and y%, net change = x + y + (xy/100). For three changes, apply this twice.

Curved Surface Area of Cone

The CSA is πrl, where l = √(r² + h²) is the slant height.

Shortcut Trick

Area of Rhombus = 1/2 × (Product of Diagonals)

Area = 1/2 × 88 × 78

Area = 44 × 78 = 3432 cm2

∴ The correct answer is 3432 cm².

Alternate Method

Given:

Diagonal 1 (d₁) = 88 cm

Diagonal 2 (d₂) = 78 cm

Formula Used:

Area of Rhombus = (d₁ × d₂) / 2

90° d2 = 78 cm d1 = 88 cm A B C D Rhombus Area = 1/2 × d1 × d2

Calculations:

⇒ Area = (88 × 78) / 2

⇒ Area = 44 × 78

⇒ Area = 44 × (80 − 2)

⇒ Area = 3520 − 88

⇒ Area = 3432 cm²

∴ The correct answer is 3432 cm².

Additional Information

Properties of Rhombus

All sides are equal, and diagonals bisect each other at 90°. Opposite angles are equal, and adjacent angles are supplementary (sum to 180°).

Side and Diagonal Relationship

The relationship between the side (a) and diagonals (d₁, d₂) is given by: 4a² = d₁² + d₂².

Perimeter of Rhombus

The perimeter (P) of a rhombus with side length 'a' is: P = 4 × a.

Area using Base and Height

If the base (b) and height (h) are known, Area = b × h. This is applicable since a rhombus is also a parallelogram.

Shortcut Trick

Effective interest percentage = Rate × Time

Effective SI% = 4% × 4 = 16%

Simple Interest = 16% of Principal = 16% of 3,00,000

SI = 16 × 3000 = 48000

∴ The correct answer is ₹48000.

Alternate Method

Given:

Principal (P) = ₹3,00,000

Time (T) = 4 years

Rate of Interest (R) = 4% per annum

Formula Used:

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

Start (Year 0) End (Year 4)  P = ₹3,00,000  Rate = 4% per year Simple Interest Calculation

Calculations:

⇒ SI = (300000 × 4 × 4) ÷ 100

⇒ SI = 3000 × 4 × 4

⇒ SI = 3000 × 16

⇒ SI = ₹48,000

∴ The correct answer is ₹48000.

Additional Information

Total Amount Formula

The total amount (A) payable after the time period is the sum of the Principal and the Simple Interest: A = P + SI.

Principal from Amount

If the total amount is given, the principal can be calculated as: P = (100 × A) ÷ (100 + R × T).

Rate or Time Calculation

To find the Rate: R = (SI × 100) ÷ (P × T). To find the Time: T = (SI × 100) ÷ (P × R).

Shortcut Trick

Net Percentage Change = x + y + (x × y / 100)

Here, x = −30 (loss) and y = +62 (profit).

Net Change = −30 + 62 + [(−30 × 62) / 100]

Net Change = 32 − 18.6 = 13.4%

∴ The correct answer is 13.4%.

Alternate Method

Given: Initial CP = ₹363, First Loss = 30%, Second Profit = 62%

Formula: Final SP = Initial CP × (1 − Loss%/100) × (1 + Profit%/100)

CP: ₹363 -30% SP1: ₹254.1 +62% SP2: ₹411.64 Overall Profit = 13.4%

⇒ SP₁ (after 30% loss) = 363 × (70 ÷ 100) = ₹254.1

⇒ Final SP (after 62% profit) = 254.1 × (162 ÷ 100) = ₹411.642

⇒ Net Profit Value = 411.642 − 363 = ₹48.642

⇒ Overall Profit % = (48.642 ÷ 363) × 100 = 13.4%

∴ The correct answer is 13.4%.

Additional Information

Successive Percentage Change

When a value is changed by x% and then by y%, the net change is given by [x + y + (xy/100)]%.

Multiplier Method

Final value = Initial value × M₁ × M₂, where M is the multiplier (e.g., 0.7 for 30% loss and 1.62 for 62% profit).

Profit and Loss Dependency

Overall percentage profit or loss is independent of the actual cost price if all transactions are based on the subsequent selling prices.

Shortcut Trick

For 2 years, the difference between CI and SI is given by P × (R/100)².

Difference = 98,200 × (7/100) × (7/100)

Difference = 98,200 × (49 / 10,000) = 9.82 × 49

Difference = 481.18 ≈ ₹481.2

∴ The correct answer is ₹481.2.

Alternate Method

Given: Principal (P) = ₹98,200, Rate (R) = 7%, Time (T) = 2 years.

Formula: Difference (D) = P × (R/100)²

 Start (P) Year 1 Year 2  R = 7%  R = 7%  Principal: ₹98,200 Difference = Interest on SI for 1<sup>st</sup> year

⇒ Simple Interest (SI) for 2 years = (P × R × T) ÷ 100

⇒ SI = (98,200 × 7 × 2) ÷ 100 = 982 × 14 = ₹13,748

⇒ Compound Interest (CI) for 2 years: Amount (A) = P × (1 + R/100)²

⇒ A = 98,200 × (1.07) × (1.07) = 98,200 × 1.1449

⇒ A = ₹112,429.18

⇒ CI = Amount − Principal = 112,429.18 − 98,200 = ₹14,229.18

⇒ Difference = CI − SI = 14,229.18 − 13,748 = ₹481.18

⇒ Rounding to one decimal place ≈ ₹481.2

∴ The correct answer is ₹481.2.

Additional Information

CI − SI for 2 years

The difference is always given by D = P(R/100)², which represents the interest earned on the first year's interest.

CI − SI for 3 years

The difference for a 3-year period is given by the formula: D = P(R/100)² × (3 + R/100).

Effective Rate Method

For 2 years, the effective rate of CI is x + y + (xy/100)%. Since for SI it is just (x+y)%, the difference in % is (R²/100)% of Principal.

Shortcut Trick

Compare the first and third terms: 88 is exactly 2 times 44 (44 × 2 = 88).

In a proportion, the same multiplier applies to the second and fourth terms.

Therefore, y = 91 × 2 = 182.

∴ The correct answer is 182.

Alternate Method

Given: 44, 91, 88, and y are in proportion.

Formula Used: If a, b, c, and d are in proportion (a : b :: c : d), then Product of Extremes = Product of Means (a × d = b × c).

44 91 = 88 y × 2 × 2 Proportion Scale

Calculations:

⇒ 44 ÷ 91 = 88 ÷ y

⇒ 44 × y = 91 × 88

⇒ y = (91 × 88) ÷ 44

⇒ y = 91 × 2

⇒ y = 182

∴ The correct answer is 182.

Additional Information

Fourth Proportional

If four quantities a, b, c, d are in proportion, then d is called the fourth proportional of a, b, and c, calculated as d = (b × c) ÷ a.

Mean Proportional

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

Third Proportional

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

Shortcut Trick

कुल दूरी = (8 × 8) + (2 × 2) = 64 + 4 = 68 km

कुल समय = 8 + 2 = 10 घंटे

औसत चाल = कुल दूरी ÷ कुल समय

औसत चाल = 68 ÷ 10 = 6.8 = 6 4/5 km/hr

∴ The correct answer is 6 4/5 km/hr.

Alternate Method

दिया गया है:

पहली स्थिति: चाल (s₁) = 8 km/hr, समय (t₁) = 8 घंटे

दूसरी स्थिति: चाल (s₂) = 2 km/hr, समय (t₂) = 2 घंटे

सूत्र: औसत चाल = (कुल दूरी) ÷ (कुल समय)

 प्रारंभ मध्य अंत  दूरी 1 = 8 × 8 = 64 km समय 1 = 8 घंटे  दूरी 2 = 4 km समय 2 = 2 hr कुल दूरी = 68 km | कुल समय = 10 hr

गणना:

⇒ पहली दूरी (d₁) = 8 km/hr × 8 hr = 64 km

⇒ दूसरी दूरी (d₂) = 2 km/hr × 2 hr = 4 km

⇒ कुल दूरी = d₁ + d₂ = 64 + 4 = 68 km

⇒ कुल समय = t₁ + t₂ = 8 + 2 = 10 hr

⇒ औसत चाल = 68 ÷ 10

⇒ औसत चाल = 6.8 km/hr

⇒ भिन्न रूप में: 6.8 = 68/10 = 34/5 = 6 4/5 km/hr

∴ The correct answer is 6 4/5 km/hr.

Additional Information

समान दूरी के लिए औसत चाल

यदि कोई व्यक्ति दो समान दूरियों को x और y चालों से तय करता है, तो औसत चाल = 2xy ÷ (x + y) होती है।

सापेक्ष चाल (Relative Speed)

समान दिशा में सापेक्ष चाल = |s₁ − s₂| और विपरीत दिशा में सापेक्ष चाल = s₁ + s₂ होती है।

इकाई परिवर्तन (Unit Conversion)

km/hr को m/s में बदलने के लिए 5/18 से गुणा करें और m/s को km/hr में बदलने के लिए 18/5 से गुणा करें।

Shortcut Trick

जब समय समान होता है, तो चाल का अनुपात दूरी के अनुपात के बराबर होता है।

D : U = 25 : 15 ⇒ 5 : 3

धारा की चाल = (5 − 3) ÷ 2 = 1 इकाई = 3 km/h

धारा के अनुकूल चाल (D) = 5 × 3 = 15 km/h और धारा के प्रतिकूल चाल (U) = 3 × 3 = 9 km/h

कुल समय = (30 ÷ 15) + (33 ÷ 9) = 2 + 3 (2/3) घंटे = 5 घंटे 40 मिनट

∴ The correct answer is 5 घंटे 40 मिनट.

Alternate Method

दिया गया है:

धारा की चाल (v) = 3 km/h

सूत्र:

समय = दूरी ÷ चाल

धारा के अनुकूल चाल (D) = u + v | धारा के प्रतिकूल चाल (U) = u − v

नदी का प्रवाह (v = 3 km/h) बोट (u) अनुकूल (u+3) प्रतिकूल (u−3) नाव और धारा की स्थिति

माना शांत जल में नाव की चाल u km/h है।

⇒ 25 ÷ (u + 3) = 15 ÷ (u − 3)

⇒ 5 ÷ (u + 3) = 3 ÷ (u − 3)

⇒ 5u − 15 = 3u + 9

⇒ 2u = 24

⇒ u = 12 km/h

⇒ अनुकूल चाल (D) = 12 + 3 = 15 km/h

⇒ प्रतिकूल चाल (U) = 12 − 3 = 9 km/h

⇒ कुल समय = (30 ÷ 15) + (33 ÷ 9)

⇒ कुल समय = 2 + 11/3 = 17/3 घंटे

⇒ कुल समय = 5 घंटे + (2/3 × 60) मिनट = 5 घंटे 40 मिनट

∴ The correct answer is 5 घंटे 40 मिनट.

Additional Information

शांत जल में नाव की चाल

नाव की चाल (u) = (अनुकूल चाल + प्रतिकूल चाल) ÷ 2

धारा की चाल

धारा की चाल (v) = (अनुकूल चाल − प्रतिकूल चाल) ÷ 2

सापेक्ष गति

धारा के अनुकूल सापेक्ष चाल बढ़ जाती है जबकि धारा के प्रतिकूल यह कम हो जाती है।

Shortcut Trick

माना कि संख्या 100% है।

प्रश्न के अनुसार: 20% + 360 = 100%

⇒ 80% = 360

⇒ 1% = 360 ÷ 80 = 4.5

⇒ संख्या का 60% = 4.5 × 60 = 270

∴ The correct answer is 270.

Alternate Method

दिया गया है:

माना संख्या x है।

x का 20% + 360 = x

प्रयुक्त सूत्र:

संख्या का n% = (n ÷ 100) × संख्या

20% भाग शेष 80% भाग = 360 कुल संख्या (100%) 20% 80% (360 के बराबर)

गणना:

⇒ (20 ÷ 100) × x + 360 = x

⇒ 0.2x + 360 = x

⇒ x − 0.2x = 360

⇒ 0.8x = 360

⇒ x = 360 ÷ 0.8

⇒ x = 450

अब, संख्या का 60% ज्ञात करना है:

⇒ 60% of 450 = (60 ÷ 100) × 450

⇒ 0.6 × 450 = 270

∴ The correct answer is 270.

Additional Information

प्रतिशत परिवर्तन (Percentage Change)

यदि किसी संख्या को r% से बढ़ाया जाता है, तो नई संख्या = मूल संख्या × (1 + r/100) होती है।

प्रतिशत से भिन्न (Percentage to Fraction)

गणना को आसान बनाने के लिए प्रतिशत को भिन्न में बदलें: 20% = 1/5, 60% = 3/5, 80% = 4/5।

आधार परिवर्तन का नियम

यदि A, B से r% अधिक है, तो B, A से [r ÷ (100 + r)] × 100% कम होगा।

Shortcut Trick

According to the question, First/2 = Second/4 = Third/8.

Ratio of First : Second : Third = 2 : 4 : 8 = 1 : 2 : 4.

Total ratio units = 1 + 2 + 4 = 7 units.

7 units = 2961 ⇒ 1 unit = 2961 ÷ 7 = 423.

Third part (4 units) = 4 × 423 = 1692.

∴ The correct answer is 1692.

Alternate Method

Given: Total sum = 2961.

Let the three parts be A, B, and C.

Condition: (1/2) × A = (1/4) × B = (1/8) × C.

A (1 unit) B (2 units) C (4 units) - Target Total = 7 Units = 2961

⇒ Let A/2 = B/4 = C/8 = k.

⇒ A = 2k, B = 4k, C = 8k.

⇒ Sum: A + B + C = 2k + 4k + 8k = 14k.

⇒ 14k = 2961.

⇒ k = 2961 ÷ 14 = 211.5.

⇒ Third part (C) = 8k = 8 × 211.5 = 1692.

∴ The correct answer is 1692.

Additional Information

Direct Proportion in Division

If x/a = y/b = z/c, then the quantities x, y, and z are directly proportional to a, b, and c. The ratio x : y : z = a : b : c.

Dividing a Quantity into a Ratio

To divide a total S into the ratio a : b : c, the share of the third part is calculated as S × [c ÷ (a + b + c)].

Reciprocal Property

If m × A = n × B = p × C, then the ratio A : B : C = (1/m) : (1/n) : (1/p). Multiply by the LCM to simplify into integers.

Shortcut Trick

कुल कार्य इकाइयाँ (मानव-दिवस) = श्रमिकों की सं���्या × दिनों की संख्या

कुल इकाइयाँ = 5 × 2 = 10 इकाइयाँ

एक श्रमिक की दैनिक मजदूरी = कुल मजदूरी ÷ कुल इकाइयाँ

दैनिक मजदूरी = 1720 ÷ 10 = 172

∴ The correct answer is ₹172.

Alternate Method

दिया गया है:

श्रमिकों की संख्या = 5

दिनों की संख्या = 2

कुल मजदूरी = ₹1,720

कुल मजदूरी वितरण (₹1,720) दिन 1 (5 श्रमिक) दिन 2 (5 श्रमिक) कुल 10 भाग  1 भाग = 1720 ÷ 10 = ₹172

गणना:

⇒ 5 श्रमिकों की 2 दिन की मजदूरी = ₹1,720

⇒ 5 श्रमिकों की 1 दिन की मजदूरी = 1720 ÷ 2

⇒ 5 श्रमिकों की 1 दिन की मजदूरी = ₹860

⇒ 1 श्रमिक की 1 दिन की मजदूरी = 860 ÷ 5

⇒ 1 श्रमिक की दैनिक मजदूरी = ₹172

∴ The correct answer is ₹172.

Additional Information

कार्य और मजदूरी का नियम

मजदूरी हमेशा किए गए कार्य के अनुपात में वितरित की जाती है। सूत्र: कुल मजदूरी = दर × समय × श्रमिकों की संख्या।

श्रृंखला नियम (Chain Rule)

यदि M₁ व्यक्ति D₁ दिनों में W₁ मजदूरी कमाते हैं, तो (M₁ × D₁) / W₁ = (M₂ × D₂) / W₂।

दैनिक मजदूरी दर

प्रति व्यक्ति प्रति दिन मजदूरी निकालने के लिए कुल मजदूरी को कुल मानव-दिवस (Man-days) से विभाजित करें।

Shortcut Trick

यदि किसी समूह की प्रत्येक संख्या को एक नियत मान 'k' से गुणा किया जाता है, तो उनका औसत भी 'k' गुना हो जाता है।

यहाँ, पुराना औसत = 13 और प्रत्येक संख्या को 8 से गुणा किया गया है।

नया औसत = पुराना औसत × 8

नया औसत = 13 × 8 = 104

∴ The correct answer is 104.

Alternate Method

दिया गया है:

संख्याओं की कुल संख्या = 13

पुराना औसत = 13

सूत्र: औसत = संख्याओं का योग ÷ कुल संख्या

पुराना औसत: 13 प्रत्येक पद × 8 नया औसत: 104 नया औसत = 13 × 8

⇒ 13 संख्याओं का कुल योग = 13 × 13 = 169

⇒ प्रत्येक संख्या को 8 से गुणा करने पर, नया कुल योग = 169 × 8

⇒ नया कुल योग = 1352

⇒ नया औसत = नया कुल योग ÷ कुल संख्या

⇒ नया औसत = 1352 ÷ 13 = 104

∴ The correct answer is 104.

Additional Information

औसत पर संक्रियाओं का प्रभाव

यदि प्रत्येक संख्या में 'n' जोड़ा या घटाया जाता है, तो नया औसत = पुराना औसत ± n होता है।

विभाजन का नियम

यदि प्रत्येक संख्या को 'n' से विभाजित किया जाता है, तो नया औसत = पुराना औसत ÷ n होता है।

औसत का मूल सूत्र

औसत = (पदों का कुल योग) ÷ (पदों की कुल संख्या)

Shortcut Trick

Subtract remainders from given numbers: 2246 − 10 = 2236 and 1429 − 12 = 1417.

The largest number is the HCF of 2236 and 1417.

Calculate the difference: 2236 − 1417 = 819.

The HCF must be a factor of 819; check options: only 13 divides 819 (819 ÷ 13 = 63).

∴ The correct answer is 13.

Alternate Method

Given:

Numbers = 2246, 1429 | Remainders = 10, 12

Formula Used:

Required number = HCF(N₁ − R₁, N₂ − R₂)

Number 1: 2246 − 10 = 2236 Number 2: 1429 − 12 = 1417 Highest Common Factor (HCF) = 13

Calculations:

⇒ First number = 2246 − 10 = 2236

⇒ Second number = 1429 − 12 = 1417

⇒ Using division method for HCF(2236, 1417):

⇒ 2236 = 1 × 1417 + 819

⇒ 1417 = 1 × 819 + 598

⇒ 819 = 1 × 598 + 221

⇒ 598 = 2 × 221 + 156

⇒ 221 = 1 × 156 + 65

⇒ 156 = 2 × 65 + 26

⇒ 65 = 2 × 26 + 13

⇒ 26 = 2 × 13 + 0

⇒ Since the last divisor is 13, HCF = 13.

∴ The correct answer is 13.

Additional Information

HCF (Highest Common Factor)

It is the greatest number that divides two or more integers without leaving any remainder. It is also known as Greatest Common Divisor (GCD).

Difference Rule for HCF

The HCF of two numbers always divides their difference. This is a very useful shortcut when numbers are large.

Divisibility by 13

A number is divisible by 13 if the sum of 4 × (unit digit) and the remaining part of the number is divisible by 13.

Shortcut Trick

कुल कार्य = ल.स.प.(14, 19) = 266 units.

क्षमता: P = 19, Q = 14. 2-दिन का चक्र (P + Q) = 33 units.

16 दिन (8 चक्र) में पूर्ण कार्य = 33 × 8 = 264 units.

शेष 2 units P द्वारा 2/19 दिन में पूरा किया जाएगा।

कुल समय = 16 + 2/19 = 16 2/19 दिन।

∴ The correct answer is 16 2/19 दिन.

Alternate Method

Given:

P द्वारा लिया गया समय = 14 दिन

Q द्वारा लिया गया समय = 19 दिन

Formula Used:

कुल कार्य = क्षमता × समय

⇒ कुल कार्य (14 और 19 का ल.स.प.) = 266 units.

⇒ P की दक्षता = 266 ÷ 14 = 19 units/day.

⇒ Q की दक्षता = 266 ÷ 19 = 14 units/day.

⇒ 1 चक्र (2 दिन: P + Q) में किया गया कार्य = 19 + 14 = 33 units.

⇒ 8 चक्रों (16 दिनों) में किया गया कार्य = 33 × 8 = 264 units.

⇒ शेष कार्य = 266 − 264 = 2 units.

⇒ 17वें दिन P कार्य करेगा। P द्वारा लिया गया समय = 2 ÷ 19 दिन।

⇒ कुल लिया गया समय = 16 + 2/19 = 16 2/19 दिन।

∴ The correct answer is 16 2/19 दिन.

Additional Information

एकांतर दिन कार्य (Alternate Day Work)

जब व्यक्ति बारी-बारी से काम करते हैं, तो कार्य को एक चक्र (Cycle) के रूप में माना जाता है। कुल समय = (पूर्ण चक्र × दिनों की संख्या) + (शेष कार्य ÷ अगले व्यक्ति की दक्षता)।

कार्य और दक्षता (Work and Efficiency)

दक्षता समय के व्युत्क्रमानुपाती होती है। यदि कार्य समान है, तो समय का अनुपात a:b होने पर दक्षता का अनुपात b:a होता है।

नल और हौज (Pipes and Cisterns)

यही सिद्धांत पाइप और टंकी वाले प्रश्नों में भी लागू होता है, जहाँ पानी निकालने वाले पाइप की दक्षता को ऋणात्मक (negative) माना जाता है।

Shortcut Trick

Ratio CP : MP = (100 − Discount%) : (100 + Profit%)

CP : MP = (100 − 16) : (100 + 16) = 84 : 116

Simplified Ratio CP : MP = 21 : 29

Markup = 29 − 21 = 8 units ⇒ Markup % = (8 ÷ 21) × 100

Markup % ≈ 38.10%

∴ The correct answer is 38.10%.

Alternate Method

Given: Discount = 16%, Profit = 16%

Formula: SP = MP × (1 − D/100) = CP × (1 + P/100)

 CP (100) SP (116) MP (138.10)  Profit 16%  Discount 16%  Markup % = 38.10%

⇒ Let CP = ₹100

⇒ Profit = 16% ⇒ SP = 100 + 16 = ₹116

⇒ Discount = 16% ⇒ SP = MP × (100 − 16) ÷ 100

⇒ 116 = MP × 84 ÷ 100

⇒ MP = (116 × 100) ÷ 84 = 11600 ÷ 84

⇒ MP ≈ ₹138.095

⇒ Markup % = [(138.095 − 100) ÷ 100] × 100

⇒ Markup % ≈ 38.10%

∴ The correct answer is 38.10%.

Additional Information

CP, SP, and MP Relation

The direct ratio is given by CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%). This bypasses calculating SP entirely.

Markup Percentage

Markup % = [(MP − CP) ÷ CP] × 100. It represents how much the price is increased over the cost price before offering a discount.

Effective Discount for Successive Rates

If two successive discounts d₁% and d₂% are given, the single equivalent discount = d₁ + d₂ − (d₁ × d₂ ÷ 100).

Shortcut Trick

मान लीजिए कि आधार औसत 7 है।

भारित विचलन = (2 × 4) + (−1 × 5) + (0 × 3) + (1 × 6) = 8 − 5 + 0 + 6 = 9

कुल भार = 4 + 5 + 3 + 6 = 18

औसत में समायोजन = 9 ÷ 18 = 0.5

भारित औसत = 7 + 0.5 = 7.5

∴ The correct answer is 7.5.

Alternate Method

दिया गया है:

भौतिकी (अंक: 9, भार: 4), गणित (अंक: 6, भार: 5), रसायन विज्ञान (अंक: 7, भार: 3), जीव विज्ञान (अंक: 8, भार: 6)

प्रयुक्त सूत्र:

भारित औसत = Σ(अंक × भार) ÷ Σभार

भौतिकी 9  गणित 6  रसायन 7  जीव वि. 8  औसत: 7.5

गणना:

⇒ कुल भारित अंक = (9 × 4) + (6 × 5) + (7 × 3) + (8 × 6)

⇒ कुल भारित अंक = 36 + 30 + 21 + 48 = 135

⇒ कुल भार = 4 + 5 + 3 + 6 = 18

⇒ भारित औसत = 135 ÷ 18

⇒ भारित औसत = 7.5

∴ The correct answer is 7.5.

Additional Information

भारित औसत (Weighted Average)

यह औसत का एक प्रकार है जिसमें डेटा सेट के प्रत्येक तत्व को एक निश्चित भार दिया जाता है। सूत्र: x_w = Σ(w_i × x_i) ÷ Σw_i

सरल औसत बनाम भारित औसत

सरल औसत में सभी संख्याओं का महत्व समान होता है, जबकि भारित औसत में अधिक महत्व (भार) वाली संख्या का औसत पर अधिक प्रभाव पड़ता है।

भारित औसत की सीमा

भारित औसत हमेशा डेटा सेट के न्यूनतम और अधिकतम मानों के बीच स्थित होता है।

The correct answer is 'Option 3'.

 

Key Points

• Option 3: Homogenisation of cultural practices
• This is correct as the passage states that a major effect of globalisation is the homogenisation of cultural practices, where Western ideals and consumer goods often dominate, overshadowing indigenous traditions.
• Option 1: Increased protection of local customs
• This is incorrect as the passage describes challenges to cultural preservation, not increased protection.
• Option 2: Preservation of traditional agricultural methods
• This is incorrect because the passage does not mention agricultural methods.
• Option 4: Strengthening of indigenous languages
• This is incorrect as the passage notes the decline, not the strengthening, of indigenous languages due to globalisation.

Therefore, the correct answer is Option 3.

 

Additional Information

• Option 3: Correct, as it directly reflects a key point from the passage about the effects of globalisation.
• Option 1: Incorrect, as there is no mention of increased protection.
• Option 2: Incorrect, as the passage does not discuss agriculture.
• Option 4: Incorrect, as the passage discusses the decline of indigenous languages.

The correct answer is 'Option 2'.

 

Key Points

• Option 2: By leading to the dominance of Western media and consumer goods
• This is correct as the passage explains that globalisation spreads Western ideals, entertainment, and products, which often overshadow and erode local traditions, languages, and cultural practices.
• Option 1: By providing resources for the preservation of languages and customs
• This is incorrect because, while globalisation can offer opportunities for preservation, the erosion discussed in the passage is linked to dominance, not preservation.
• Option 3: By promoting the revitalisation of indigenous art forms
• This is incorrect as revitalisation is mentioned as a positive effect, not as a cause of erosion.
• Option 4: By encouraging local governments to support cultural diversity
• This is incorrect as the passage does not mention this as a cause of erosion.

Therefore, the correct answer is Option 2.

 

Additional Information

• Option 2: Correct, as the passage highlights the overshadowing effect of Western media and goods.
• Option 1: Incorrect, since this describes a positive effect, not erosion.
• Option 3: Incorrect, as revitalisation is a benefit, not a cause of erosion.
• Option 4: Incorrect, as there is no mention of local government encouragement leading to erosion.

The correct answer is 'Option 1'.

 

Key Points

• Option 1: Social media provides a platform for the global sharing and awareness of traditional cultures.
• This is correct as the passage mentions that social media and digital technologies enable communities to share their customs, art, and languages globally, fostering awareness and appreciation.
• Option 2: Social media only helps in promoting modern global trends at the cost of traditional cultures.
• This is incorrect because the passage highlights the positive role of social media in cultural preservation, not just in promoting global trends.
• Option 3: Social media helps in diminishing the appreciation of indigenous cultures.
• This is incorrect as the passage suggests the opposite, emphasizing increased awareness and appreciation.
• Option 4: Social media has no role in the exchange of cultural practices.
• This is incorrect because the passage specifically mentions the role of social media in cultural exchange.

Therefore, the correct answer is Option 1.

 

Additional Information

• Option 1: Correct, as it aligns with the passage's statement on the positive role of social media in sharing and preserving traditional cultures.
• Options 2, 3, and 4: Incorrect, as they contradict the passage's main ideas about the beneficial impact of social media on cultural preservation.

The correct answer is: Option 4 i.e. Standardisation.

Key Points

• The term "homogenisation" refers to the process of making things uniform or similar.
• "Standardisation" most closely aligns with this meaning, as it involves establishing standards or consistency across different elements.
• The other options, namely fragmentation, innovation, and diversification, do not convey the sense of making things uniform or consistent.
• Fragmentation: The process or state of breaking or being broken into small or separate parts.
• Innovation: The process of creating new ideas, products, or methods.
• Diversification: The process of becoming varied or different.

Therefore, the term 'homogenisation' most closely means: Standardisation.

Additional Information

Here are the other options and their meanings:

• Fragmentation (खंडित): The process or state of breaking or being broken into small or separate parts.
• Innovation (नवोन्मेष): The process of creating new ideas, products, or methods.
• Diversification (विविधीकरण): The process of becoming varied or different.

The correct answer is 'Option 1'.

 

Key Points

• Option 1: Reflective and analytical
• This is correct as the passage thoughtfully examines both the challenges and opportunities globalisation presents for traditional cultures. It analyses the positive and negative impacts, weighing the complexities and encouraging balance.
• Option 2: Critical and pessimistic
• This is incorrect because while the passage discusses challenges, it also highlights positive aspects and does not focus solely on criticism or negativity.
• Option 3: Descriptive and neutral
• This is partly correct, as the passage describes effects, but the overall approach is more reflective and analytical, considering implications and solutions.
• Option 4: Enthusiastic and optimistic
• This is incorrect because the passage maintains a balanced perspective, not an overly enthusiastic one.

Therefore, the correct answer is Option 1.

 

Additional Information

• Option 1: Correct, as it captures the thoughtful and analytical approach of the passage in discussing both sides of globalisation's impact on culture.
• Option 2: Incorrect, as the tone is not solely negative or critical.
• Option 3: Not fully correct, as the passage goes beyond description to analyse and reflect.
• Option 4: Incorrect, as the passage remains balanced rather than optimistic.

The correct answer is Option 2.

Key Points

• The paragraph revolves around an example of bad habits and systems that lead to repetitive problems.
• Sentence D sets the context by introducing the example of a messy room and the goal to clean it:
• "Imagine you have a messy room and you set a goal to clean it."
• Sentence E logically follows as it describes the immediate result of summoning energy to clean the room:
• "If you summon the energy to tidy up, then you will have a clean room for now."
• Sentence C comes next as it highlights the problem of not addressing the root cause, leading to the reappearance of clutter:
• "But if you maintain the same sloppy pack rat habits that led to a messy room in the first place, soon you’ll be looking at a new pile of clutter."
• Sentence A follows logically as it explains the consequence of not changing the underlying system:
• "You’re left chasing the same outcome because you never change the system behind it."
• Sentence B concludes the paragraph by summarizing the issue of addressing symptoms but not the cause:
• "You treated a symptom without addressing the cause."
• The correct sequence is DECAB.

Coherent paragraph after rearrangement:

"Imagine you have a messy room and you set a goal to clean it. If you summon the energy to tidy up, then you will have a clean room for now. But if you maintain the same sloppy pack rat habits that led to a messy room in the first place, soon you’ll be looking at a new pile of clutter. You’re left chasing the same outcome because you never change the system behind it. You treated a symptom without addressing the cause."

The correct answer is: Option 4 i.e. Globophobia.

Key Points

• Globophobia refers to an extreme or irrational fear of balloons. (गुब्बारे का अत्यधिक या तर्कहीन डर)
• Example: The child refused to enter the party hall because of his globophobia.
• The fear can stem from traumatic experiences, such as the popping sound of balloons causing discomfort or fear.

Correct word: Globophobia (गुब्बारे का डर) is the appropriate choice here as the child has an extreme fear of balloons due to past experiences of loud popping sounds.

• Example: The doctor suggested therapy sessions to help him overcome his globophobia.

Therefore, the correct answer is: Option 4 i.e. Globophobia.

Additional Information

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

• Ablutophobia (स्नान का डर): The irrational fear of bathing, washing, or cleaning.
• Example: Her ablutophobia made it difficult for her to maintain hygiene.
• Chiroptophobia (चमगादड़ का डर): The irrational fear of bats.
• Example: She screamed and ran away due to her chiroptophobia when she saw a bat in the attic.
• Porphyrophobia (बैंगनी रंग का डर): The irrational fear of the color purple.
• Example: His porphyrophobia made him avoid anything that was purple in color.

The correct answer is: 3) To reveal confidential information.

Key Points

• The idiom "Spill the beans" means to reveal confidential or secret information, often unintentionally. (गुप्त जानकारी प्रकट करना)
• Example: He accidentally spilled the beans about the surprise party during the meeting.

Additional Information

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

• 1) To celebrate success (सफलता का जश्न मनाना): Refers to rejoicing or commemorating an achievement.
• Example: The team celebrated their success with a party after winning the tournament.
• 2) To work hard (कड़ी मेहनत करना): Refers to putting in great effort to achieve something.
• Example: She worked hard to secure a place in the national team.
• 4) To clean up (सफाई करना): Refers to making a place neat and tidy by removing dirt or unwanted items.
• Example: They cleaned up the entire house before the guests arrived.

The correct answer is '1' i.e. the.

 

Key Points

• The definite article "the" is used before the names of mountain ranges, oceans, rivers, and other unique geographical entities.
• In the given sentence, "Himalayas" is a proper noun referring to a specific mountain range, which makes the use of "the" necessary.
• Other options (2: "a", 3: "an", and 4: "No article required") are grammatically incorrect in this context.

Therefore, the correct answer is Option 1.

 

Complete Sentence: "Hiking across the Himalayas is going to be difficult."

 

Additional Information

• Option 2: "a" is incorrect because "a" is used before singular countable nouns starting with a consonant sound, and "Himalayas" is plural.
• Option 3: "an" is incorrect because "an" is used before singular countable nouns starting with a vowel sound, and "Himalayas" is plural.
• Option 4: "No article required" is incorrect because proper nouns like "Himalayas" require the definite article "the" when referring to a specific entity.