DSSSB PRT Official Paper (Held On: 17 Feb, 2026 Shift 3) (Previous Year Paper)

The logic followed here is based on the positional values of the letters in the English alphabetical order.

Logic: (1st letter + 2 = 3rd letter) and (2nd letter + 4 = 4th letter).

Option 1) DE - FI,

Option 2) PQ - RU,

Option 3) VW - XZ,

This pair does not follow the rule.

Option 4) IJ - KN,

Therefore, the letter-cluster pair that is different from the others is VW - XZ.

Hence, the correct answer is 'Option 3'.

Given:

• L is the mother of E.
• E is the sister of M.
• O is the father of N.
• N is the husband of M.

The Family Tree Diagram,

Therefore, O is the father of N, and N is the husband of L's daughter (M). So, O is L's Daughter's husband's father.

Hence, the correct answer is 'Option 1'.

Given (Left) B K C A L Q R V G T N J E N E J W Y C G R L A M I U (Right)

The required pattern is: Consonant → Consonant → Vowel

(Left) B K C A L Q R V G T N J E N E J W Y C G R L A M I U (Right)

There are exactly three such consonants.

• KCA
• NJE
• RLA

Hence, the correct answer is "option 3"

The logic followed here is:

Logic: Second Number = First Number − 729

For the first pair 1003 : 274

⇒ 1003 − 729 = 274

For the second pair 987 : 258

⇒ 987 − 729 = 258

Applying the same logic to the third pair

1105 : ?

⇒ 1105 − 729 = 376

Hence, the correct answer is "Option 3".

Given: Seven boxes, F, I, L, T, E, R and S, are kept one over the other but not necessarily in the same order

1. Only R is kept above E.
2. Only two boxes are kept between E and T.
3. Only I is kept below L.
4. F is not kept immediately above T.

Final Arrangement:

Thus, there are two boxes (T and L) kept between S and I.

Hence, the correct answer is 'Option 2'.

Given : (Left) E D U J Y H B V G T I O J U E D S A I B C A D E Y I O L B S M C (Right)

Required Pattern: Consonant → Vowel → Consonant

(Left) E D U J Y H B V G T I O J U E D S A I B C A D E Y I O L B S M C (Right)

The three occurrences satisfying the condition are:

• D U J
• C A D
• D E Y

Therefore, there are three such vowels in the given series.

Hence, the correct answer is "Option 2."

The logic followed here is based on the positional rearrangement of letters in each word within the triads.

Analysis of the given triads:

1. AMID − MIAD − DIMA

EAST − ASET − TSAE

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Applying the same logic to the correct option

WEAR − EAWR − RAEW

Hence, the correct answer is "Option 4"

The logic followed here is:

Option 1) AN - GS

Option 2) TC - ZH

Option 4) UP - AU

Option 3) YR - EV

Therefore, the letter-cluster pair that is different from the others is YR - EV.

Hence, the correct answer is 'Option 3'.

The logic followed here is:

Given Word: PRAYING

 

Therefore, the number of letters whose positions remain unchanged is Zero.

Hence, the correct answer is "option 3"

BODMAS Rule:

Sign Interchange:

 

Given equation: 46 + 2 × 4 − 6 ÷ 20 = ?

After interchanging the signs, using the BODMAS rule the equation becomes:

= 46 ÷ 2 − 4 × 6 + 20

= 23 − 4 × 6 + 20

= 23 + 20 − 24

= 43 − 24

= 19

Hence, the correct answer is "option 1"

Given : S, U, B, M, E, R and G are sitting around a circular table facing the centre of the table.

1. B sits to the immediate left of M.
2. U sits to the immediate left of E.
3. E sits second to the left of G.
4. R sits third to the left of M.

The final arrangement is, 

G sits fourth to the right of S

Hence, the correct answer is G.

The logic followed here is ,

The code for ‘D’ is 3.

Hence, the correct answer is "option 4"

The logic followed here is,

BODMAS Rule:

Given Equation: 424 ÷ 2 + 966 × 3 − 23 = ?

Signs to be interchanged:

After interchanging the signs,and using the BODMAS rule the new equation becomes:

= 424 × 2 − 966 ÷ 3 + 23

= 848 - 322 + 23

= 848 + 23 - 322  

= 871 − 32

= 549.

Hence, the correct answer is "option 4"

Given: Seven people (H, U, S, B, A, N, D) have exams from Monday to Sunday.

1. Only three people have exams between B and H.
2. Only three people have exams between A and S.
3. D has an exam on some day before U and on some day after N.
4. Only S has an exam after H

The Final Arrangement is,

 

The total number of people after A is 4.

Hence, the correct answer is "Option 2".

The logic followed here is here, 

The question figure is perfectly embedded in option 1.

 

Hence, the correct answer is "option 1".

Given: Each of A, B, C, D, I, J and K has an exam on a different day of a week starting from Monday and ending on Sunday of the same week.

1. Only three people have exams between C and I.
2. Only three people have exams between J and D.
3. B has exam on some day before K and on some day after A.
4. Only D has exam after I

Final Arrangement:

There are 4 (Four) people who have exams after J.

Hence, the correct answer is "Four".

The water image of the given figure,

Hence, the correct answer is "option 1"

The logic followed here is:

Pattern:

• 14 + 9 = 23
• 23 + 9 = 32
• 32 + 9 = 41
• 41 + 9 = 50
• 50 + 9 = 59

Thus, the missing term in the series is 59.

Hence, the correct answer is 'Option 4'.

The logic followed here is:

• From the above table, it is clear that only the position of the letter N remains unchanged when the letters are arranged alphabetically.
• Therefore, the number of letters that remain unchanged is one.

Hence, the correct answer is option 4

The logic followed here is:

 

The next word in the series is MQOH.

Hence, the correct answer is "option 4"

The correct answer is Nirmala Sitharaman.

Key Points

• The Union Budget of India for the financial year 2025-2026 was presented by Nirmala Sitharaman, who serves as the Union Minister of Finance and Corporate Affairs.
• Following the established parliamentary tradition, the budget was tabled in the Lok Sabha on February 1, 2025.
• With the presentation of this budget, Nirmala Sitharaman achieved the milestone of presenting seven consecutive Union Budgets (including one interim budget in 2024), surpassing the record previously held by Morarji Desai.
• The budget for 2025-2026 focuses on the roadmap for Viksit Bharat @ 2047, prioritizing sustainable economic growth, infrastructure development, and technological advancement.
• Under Article 112 of the Constitution of India, the central government is mandated to present the Annual Financial Statement, which outlines estimated receipts and expenditures.

 Additional Information

• Other notable cabinet ministers:
• Amit Shah: He currently holds the portfolio of the Union Minister of Home Affairs and the Minister of Cooperation.
• Rajnath Singh: He serves as the Union Minister of Defence and has previously held the Home Ministry portfolio.
• Piyush Goyal: He is the Minister of Commerce and Industry. Although he presented the Interim Budget in 2019 while holding temporary charge of the Finance Ministry, he did not present the 2025-2026 budget.
• The Union Budget is divided into two parts: the Revenue Budget and the Capital Budget, ensuring a comprehensive overview of the nations financial health.

The correct answer is Krishna I.

Key Points

• The Kailasha temple, also known as Cave 16 at Ellora, is a colossal structure dedicated to Lord Shiva and is widely considered the pinnacle of Rashtrakuta architecture.
• It was constructed under the patronage of King Krishna I (reigned approximately 756 to 774 CE), who was a powerful ruler of the Rashtrakuta Dynasty.
• The monument is famous for being monolithic, meaning it was carved from a single, massive basalt cliff, starting from the top and working downwards to the base.
• The temple design is heavily influenced by the Dravidian style, featuring a multi-storeyed Vimana (tower), a large courtyard, and intricate sculptures depicting scenes from the Ramayana and Mahabharata.
• Engineering estimates suggest that over 200,000 tonnes of rock were excavated over several decades to create this masterwork, which was intended to symbolize Mount Kailash.

 Additional Information

• Rashtrakuta Dynasty:
• The dynasty was founded by Dantidurga, who overthrew the Chalukyas of Badami. Krishna I, his uncle, succeeded him and expanded the empire across central and southern India.
• The Rashtrakutas were great patrons of art and literature, supporting various religious traditions including Hinduism, Buddhism, and Jainism.
• Ellora Caves:
• Located in the Sambhaji Nagar (formerly Aurangabad) district of Maharashtra, Ellora is a UNESCO World Heritage Site.
• The site comprises 34 caves: 12 Buddhist, 17 Hindu, and 5 Jain, showcasing the religious harmony and cultural synthesis of ancient India.
• Context of Other Options:
• Krishna II: He was a later Rashtrakuta king (grandson of Krishna I) known for his long reign and military engagements with the Eastern Chalukyas, but he is not the patron of the main Kailasha monument.
• Vikramaditya: This name refers to several rulers, most notably from the Western Chalukya or Gupta dynasties. While Vikramaditya II of the Chalukyas built temples in Pattadakal that influenced the Kailasha temple's design, he was not its patron.

The correct answer is A - IV, B - I, C - II, D - III.

Key Points

• Visveswaraya Iron and Steel Plant (VISL) is located in Bhadravati, Karnataka. Originally established as the Mysore Iron Works in 1923 by Sir M. Visveswaraya, it became a unit of the Steel Authority of India Limited (SAIL) in 1989. It is renowned for producing high-quality alloy and special steels. Hence, A matches with IV.
• The Indian Aluminium Company Ltd. (INDAL), which later merged with Hindalco Industries, commissioned its primary aluminium smelter at Hirakud, Odisha, in 1959. The plant benefits from the hydroelectric power generated by the Hirakud Dam on the Mahanadi River, which is critical for energy-intensive aluminium smelting. Hence, B matches with I.
• The Fertiliser Corporation of India Ltd. (FCI) established its landmark unit at Sindri, Jharkhand. Commissioned in 1951, it was the first major public sector fertilizer plant in India, playing a pivotal role in the country's Green Revolution by manufacturing Ammonium Sulphate. Hence, C matches with II.
• Hindustan Antibiotics Ltd. (HAL) is headquartered in Pimpri, Pune. Founded in 1954 with technical assistance from WHO and UNICEF, it was the first public sector company in India to manufacture Penicillin and other essential life-saving drugs. Hence, D matches with III.

 Additional Information

• Industrial Importance of Locations:
• Bhadravati: Known as the industrial capital of Shimoga, it also houses the Mysore Paper Mills.
• Hirakud: Apart from aluminium, the region is a hub for thermal power and heavy engineering industries.
• Sindri: Historically significant as the 'Fertilizer City', it was chosen due to its proximity to coalfields in the Damodar Valley.
• Pimpri: Part of the Pune industrial belt, it is now one of the largest automobile and manufacturing hubs in Asia.

The correct answer is Vector quantities because they have both magnitude and direction.

Key Points

• A vector quantity is a physical quantity that is completely specified by both a magnitude (numerical value with unit) and a direction.
• The Electric Field ($\vec{E}$) at a point is defined as the electrostatic force per unit positive charge. Its direction is the same as the direction of the force exerted on a positive test charge placed at that point.
• The Magnetic Field ($\vec{B}$) is a region around a magnetic material or a moving electric charge within which the force of magnetism acts. It has a specific direction at every point, typically indicated by the way a north pole of a compass needle points.
• Both electric and magnetic fields obey the principle of superposition, meaning the resultant field at any point is the vector sum of the individual fields produced by various sources.
• Since these fields cannot be fully described without mentioning which way they point (outward, inward, clockwise, etc.) in three-dimensional space, they are classified as vector quantities.

Additional Information

• Scalar Quantities: Unlike vectors, scalars like Electric Potential, Energy, and Charge only have magnitude and no specific spatial direction.
• SI Units: The SI unit for the Electric Field is Newtons per Coulomb (N/C) or Volts per meter (V/m), while the SI unit for the Magnetic Field is the Tesla (T).
• Lorentz Force: The vector nature of these fields is fundamental to the Lorentz Force equation, $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$, where the cross product ($\times$) specifically requires vector inputs.
• Field Lines: These fields are visually represented using field lines, where the tangent to the line at any point gives the direction of the field at that point.

The correct answer is Pulakeshin I.

Key Points

• Pulakeshin I is historically recognized as the real founder and the first sovereign ruler of the Chalukya dynasty, specifically the Badami Chalukyas (Vatapi Chalukyas).
• He established his independent kingdom by fortifying the hill of Vatapi (modern-day Badami in the Bagalkot district of Karnataka) around 540 CE and making it his capital.
• To proclaim his supreme sovereignty and independence from the Kadambas, he performed significant Vedic rituals, including the Ashvamedha (horse sacrifice), Hiranyagarbha, and Agishtoma.
• He assumed grand imperial titles such as Satyashraya (the refuge of truth), Ranavikrama (the valorous in war), and Shri Prithvi-vallabha (the favorite of the Goddess of Fortune and Earth).
• While records mention his ancestors Jayasimha and Ranaraga, they are believed to have been feudatory chiefs; the dynasty achieved true imperial status only under Pulakeshin I.

 Additional Information

• Kirtivarman I
• He was the son and successor of Pulakeshin I.
• He is credited with the territorial expansion of the kingdom by defeating the Kadambas of Banavasi and the Mauryas of Konkan.
• Vikramaditya I
• A later ruler of the Badami Chalukyas and the son of Pulakeshin II.
• He is famous for restoring the prestige of the dynasty after the Pallava occupation of Vatapi and capturing the Pallava capital, Kanchi.
• Rajendra II
• He was a powerful monarch of the Medieval Chola dynasty, not the Chalukya dynasty.
• He is renowned for his victory in the Battle of Koppam against the Western Chalukyas and his coronation on the battlefield.

The correct answer is Kuala Lumpur Peace Accord.

Key Points

• The Kuala Lumpur Peace Accord was officially signed on 26 October 2025, representing a historic milestone in Southeast Asian diplomacy aimed at resolving complex territorial sovereignty and border delimitation issues.
• The agreement was designed to settle long-standing maritime boundary disputes and overlapping claims in resource-rich zones, fostering a spirit of regional stability and economic integration within the ASEAN framework.
• Key provisions of the accord included the establishment of Joint Development Areas (JDAs) for the equitable sharing of natural resources, such as oil and natural gas, found along the contested borders.
• The negotiations leading to the Kuala Lumpur Peace Accord were facilitated by international mediators and adhered strictly to the principles laid out in the United Nations Convention on the Law of the Sea (UNCLOS).
• By signing this accord, the involved Southeast Asian nations committed to peaceful dispute resolution mechanisms, effectively reducing the risk of naval confrontations and enhancing maritime security in the region.

 Additional Information

• Minsk Peace Protocol
• This refers to a series of international agreements, specifically Minsk I (2014) and Minsk II (2015), which sought to end the war in the Donbas region of Ukraine.
• It involved the Trilateral Contact Group consisting of Ukraine, Russia, and the OSCE, and is unrelated to Southeast Asian border disputes.
• Kyoto Peace Protocol
• Commonly referred to as the Kyoto Protocol, this was an international treaty adopted in 1997 in Kyoto, Japan.
• Its primary objective was the reduction of greenhouse gas emissions to combat global warming, rather than settling geopolitical borders.
• Schengen Peace Agreement
• The Schengen Agreement, signed in 1985, led to the creation of the Schengen Area in Europe.
• Its main function is the abolition of internal border checks among European countries to facilitate free movement of people, not the resolution of territorial disputes.

The correct answer is Jodha Bai Palace.

Key Points

• Jodha Bai Palace is the largest and most significant residential structure in the Fatehpur Sikri complex, commissioned by the Mughal Emperor Akbar in the late 16th century.
• The building is considered a masterpiece of syncretic architecture, as it heavily incorporates ancient Indian architectural elements from Hindu and Jain traditions.
• Architecturally, the palace utilizes the Trabeate (post-and-lintel) system rather than the Arcuate (arched) system, which is a hallmark of indigenous Indian craftsmanship.
• The interior is decorated with traditional motifs such as the Lotus, Swan, Srivatsa mark, and Ghant-mala (bell and chain), all of which are rooted in ancient temple architecture.
• Structural features like Chhatris (canopied pavilions), Jharokhas (overhanging balconies), and ornate carved brackets demonstrate the influence of Gujarati and Rajasthani styles.
• Therefore, Jodha Bai Palace is the correct answer as it represents the fusion of medieval Mughal needs with ancient Indian architectural principles.

 Additional Information

• Fatehpur Sikri:
• Founded in 1569 by Akbar, it served as the capital of the Mughal Empire from 1571 to 1585 and was declared a UNESCO World Heritage Site in 1986.
• The city was built to honor the Sufi saint Sheikh Salim Chishti, whose tomb is located within the Jama Masjid courtyard.
• Hawa Mahal:
• A prominent palace in Jaipur, Rajasthan, built in 1799 by Maharaja Sawai Pratap Singh; it is not located in the Fatehpur Sikri complex.
• Raja Mahal:
• Often refers to the 16th-century palace built by the Bundela Rajput kings in Orchha, Madhya Pradesh, known for its grand towers and murals.

The correct answer is New Delhi.

Key Points

• The Khelo India Para Games 2025 represents the second edition of this massive sporting event, designed specifically to promote inclusivity and provide a national platform for divyang athletes.
• New Delhi was designated as the host city to utilize the existing international-standard infrastructure, including the Indira Gandhi Stadium complex, which is equipped with specialized accessibility features for para-athletes.
• The event is a flagship initiative of the Ministry of Youth Affairs and Sports, aiming to identify and nurture talent for global competitions such as the Paralympic Games and Asian Para Games.
• The games include various disciplines such as para-athletics, para-badminton, para-powerlifting, para-table tennis, and para-archery, drawing participants from across all States and Union Territories of India.

 Additional Information

• Khelo India Programme:
• Introduced in 2018, this central sector scheme focuses on building a strong sports ecosystem in India.
• The Para Games were added to the Khelo India calendar to ensure that differently-abled sportspersons receive the same level of support, funding, and recognition as their able-bodied counterparts.
• Lucknow:
• While a major sports hub in Uttar Pradesh, it hosted the Khelo India University Games in 2023 but is not the venue for the 2025 Para Games.
• Bengaluru:
• Known for the Sports Authority of India (SAI) Netaji Subhas Southern Centre, it frequently hosts training camps for Olympic athletes but was not selected as the primary host for this specific edition.
• Jaipur:
• The capital of Rajasthan has produced several high-profile para-shooters like Avani Lekhara, yet the central organization of the 2025 Para Games remains consolidated in the national capital.

The correct answer is To provide financial support to street vendors for their business growth.

Key Points

• The PM SVANidhi (PM Street Vendor’s AtmaNirbhar Nidhi) scheme was launched by the Ministry of Housing and Urban Affairs on June 1, 2020, to provide affordable working capital loans to street vendors.
• Its core objective is to offer a collateral-free loan of up to ₹10,000 to help street vendors restart their livelihoods which were adversely impacted by the COVID-19 pandemic and subsequent lockdowns.
• The scheme targets urban street vendors, including those from peri-urban and rural areas, who were engaged in vending operations on or before March 24, 2020.
• It promotes financial discipline by offering an interest subsidy of 7% per annum on timely or early repayment, which is credited directly to the beneficiary's bank account via Direct Benefit Transfer (DBT).
• The scheme also encourages digital transactions by providing monthly cashback incentives, thereby integrating street vendors into the formal digital economy and improving their credit profile.

 Additional Information

• Implementation and Lending:
• The Small Industries Development Bank of India (SIDBI) acts as the implementation partner. Lending institutions include Scheduled Commercial Banks, Regional Rural Banks, Small Finance Banks, Cooperative Banks, and Non-Banking Financial Companies (NBFCs).
• Loan Tranches:
• Vendors are eligible for a second loan tranche of up to ₹20,000 and a third tranche of up to ₹50,000 upon the successful and timely repayment of the preceding loans, facilitating business expansion.
• SVANidhi se Samriddhi:
• An additional component launched to map the socio-economic profile of PM SVANidhi beneficiaries and their families to link them to various central welfare schemes such as PM Jan Dhan Yojana and PM Suraksha Bima Yojana.

The correct answer is Open defecation free villages.

Key Points

• The Swachh Bharat Mission (Gramin) or SBM-G was launched on 2nd October 2014 by the Government of India to accelerate efforts to achieve universal sanitation coverage and focus on safe sanitation.
• The primary objective of the mission was to make rural India Open Defecation Free (ODF) by 2nd October 2019, as a tribute to the 150th birth anniversary of Mahatma Gandhi.
• It aimed to improve the general quality of life in rural areas by promoting cleanliness, hygiene, and eliminating the practice of open defecation through the construction of Individual Household Latrines (IHHL) and Community Sanitary Complexes.
• The program utilized a demand-driven approach, emphasizing behavioral change through Information, Education, and Communication (IEC) strategies to ensure sustainable usage of toilets.
• Following the successful declaration of all villages as ODF in 2019, Phase II of SBM-G was launched (2020-21 to 2024-25) to focus on ODF Plus, which includes ODF sustainability and Solid and Liquid Waste Management (SLWM).

 Additional Information

• Providing irrigation:
• This is the core objective of the Pradhan Mantri Krishi Sinchayee Yojana (PMKSY), which aims to enhance physical access to water on farms and expand the cultivable area under assured irrigation.
• Providing gas connections:
• The Pradhan Mantri Ujjwala Yojana (PMUY) was launched in 2016 specifically to provide LPG (Liquefied Petroleum Gas) connections to women from Below Poverty Line (BPL) households to replace unhealthy cooking fuels.
• Rural electrification:
• This is addressed through schemes like the Deen Dayal Upadhyaya Gram Jyoti Yojana (DDUGJY) and the Saubhagya Scheme (Pradhan Mantri Sahaj Bijli Har Ghar Yojana), focusing on 100 percent electrification of all rural households.

The correct answer is Worker Population Ratio (WPR).

Key Points

• The Worker Population Ratio (WPR) is defined as the percentage of employed persons in the total population, serving as a primary indicator to assess the employment situation in India.
• It is calculated using the formula: (Total number of workers / Total population) × 100.
• The National Statistical Office (NSO), under the Ministry of Statistics and Programme Implementation (MoSPI), is responsible for collecting and releasing this data.
• Data for WPR is disseminated through the Periodic Labour Force Survey (PLFS), which was launched in April 2017 to provide more frequent labor force statistics.
• A high WPR signifies that a substantial part of the population is actively engaged in economic activities, contributing to the production of goods and services.
• The index provides insights into the demand for labor and the capacity of the economy to generate employment opportunities for its citizens.

 Additional Information

• Consumer Price Index (CPI):
• It measures the weighted average of prices of a basket of consumer goods and services, such as transportation, food, and medical care.
• In India, it is used by the Reserve Bank of India (RBI) as the key indicator for measuring Inflation and formulating Monetary Policy.
• Gini Coefficient:
• A statistical measure used to represent the income distribution of a nation’s residents.
• It ranges from 0 to 1, where 0 represents perfect equality and 1 represents perfect inequality.
• Human Development Index (HDI):
• A composite statistic developed by the United Nations Development Programme (UNDP) to rank countries by level of human development.
• It considers three main dimensions: Life expectancy (Health), Expected/Mean years of schooling (Education), and Gross National Income per capita (Standard of living).

CONCEPT:

Colligative properties are the properties of a dilute solution that depend only on the total number of solute particles (molecules or ions) present in the solution, regardless of their nature. There are four primary colligative properties:

• Relative lowering of vapour pressure
• Elevation of boiling point
• Depression of freezing point
• Osmotic pressure

EXPLANATION:

• Relative lowering of vapour pressure: When a non-volatile solute is added to a solvent, the vapour pressure of the solution becomes lower than that of the pure solvent. The ratio of this decrease to the vapour pressure of the pure solvent is a colligative property.
• Elevation of boiling point: Adding a solute decreases the vapour pressure, which means a higher temperature is required for the vapour pressure to equal the atmospheric pressure. Thus, the boiling point of the solution increases (elevates).
• Depression of freezing point: The presence of solute particles prevents the solvent molecules from easily forming a solid crystal lattice. As a result, the freezing point of the solution is lower than that of the pure solvent.
• Elevation of freezing point: This is not a colligative property. In fact, the freezing point of a solvent always decreases (depresses) upon the addition of a non-volatile solute; it is never elevated under standard conditions for a solution.

Therefore, the property that is NOT a colligative property is Elevation of freezing point.

The correct answer is They advise the Governor on governmental affairs.

Key Points

• The primary relationship between the State Council of Ministers and the Governor is established under Article 163 of the Indian Constitution, which states that there shall be a Council of Ministers with the Chief Minister at the head to aid and advise the Governor in the exercise of his functions.
• This advisory role covers the broad spectrum of governmental affairs, including administrative decisions and legislative proposals, ensuring that the Governor, as the nominal executive head, acts according to the will of the elected representatives.
• While the Council provides advice, Article 163 also specifies that the Governor may exercise certain functions in his discretion; however, for all other matters, the advice of the Council is generally binding in a parliamentary democracy.
• Under Article 164, the Chief Minister is appointed by the Governor, and other ministers are appointed by the Governor on the advice of the Chief Minister, further cementing the advisory nature of their relationship.
• The Council of Ministers acts as the real executive, and their advice is the mechanism through which the State Government operates in the name of the Governor.

 Additional Information

• They hold office at the pleasure of the Governor:
• This is a constitutional fact under Article 164(1), which states that ministers hold office during the pleasure of the Governor.
• However, this 'pleasure' is not arbitrary; as per constitutional conventions and the S.R. Bommai case, the Governor cannot dismiss a Council that enjoys a majority in the Legislative Assembly.
• This clause primarily relates to the tenure of the ministers rather than the daily functional relationship of governance.
• They assist the Governor in drafting state laws:
• This is conceptually incorrect as the drafting of laws is a function of the Legislature (Vidhan Sabha and Vidhan Parishad).
• While the Council of Ministers (Executive) initiates Government Bills and determines the legislative agenda, the formal drafting and enactment process is a legislative function.
• They supervise the Governor’s actions:
• The Council does not 'supervise' the Governor; rather, the Governor acts as a Constitutional sentinel.
• The relationship is one of cooperation and advice, where the Governor has the right to be informed of all cabinet decisions under Article 167.

The correct answer is Drain-of-Wealth theory.

Key Points

• The Drain-of-Wealth theory was conceptualized by Dadabhai Naoroji to describe the systematic transfer of India's resources and capital to Britain without any equivalent return.
• Naoroji first presented this economic critique in 1867 in his paper titled 'England's Debt to India', argued before the East India Association in London.
• The concept was later expanded in his seminal book, 'Poverty and Un-British Rule in India', published in 1901, where he meticulously documented how colonial policies were impoverishing the subcontinent.
• He argued that this economic drain prevented the accumulation of domestic capital, which was necessary for India's industrial growth, leading to recurring famines and mass poverty.
• The Indian National Congress officially endorsed this theory at its Calcutta Session in 1896, marking it as a foundational pillar of the Indian nationalist movement against British economic imperialism.

 Additional Information

• Dadabhai Naoroji:
• Known as the Grand Old Man of India, he was a teacher, cotton trader, and a founding member of the Indian National Congress.
• In 1892, he became the first Indian to be elected as a Member of Parliament in the British House of Commons representing Central Finsbury.
• Mechanisms of the Drain:
• Home Charges: These included salaries, pensions, and administrative expenses of the India Office in London, paid entirely from Indian revenues.
• Interest on Public Debt: India was forced to pay interest on loans taken for railway expansion and military expeditions conducted by the British Empire outside India.
• Private Remittances: The savings and profits earned by British officials, merchants, and planters were regularly sent back to Britain, further depleting the Indian treasury.

The correct answer is Article 164.

Key Points

• Article 164 of the Indian Constitution outlines various provisions regarding the Council of Ministers in states, including their appointment, salary, and responsibilities.
• The proviso to Article 164(1) specifically mandates that there shall be a Minister in charge of tribal welfare in the states of Chhattisgarh, Jharkhand, Madhya Pradesh, and Odisha.
• This minister may additionally hold portfolios for the welfare of Scheduled Castes and backward classes or any other relevant administrative work.
• The requirement for a specialized tribal welfare minister ensures that the interests of significant tribal populations in these states are represented at the highest executive level.
• The 94th Constitutional Amendment Act, 2006 updated this provision to include the newly formed states of Chhattisgarh and Jharkhand, while removing the state of Bihar from the list.

 Additional Information

• Article 170:
• Relates to the Composition of the Legislative Assemblies in the states.
• It specifies that each assembly shall have a maximum of 500 members and a minimum of 60 members, directly elected from territorial constituencies.
• Article 168:
• Provides for the Constitution of Legislatures in States.
• It establishes that every state legislature consists of the Governor and one or two Houses (Legislative Assembly and, in some states, a Legislative Council).
• Article 166:
• Deals with the Conduct of business of the Government of a State.
• It mandates that all executive actions of the State Government shall be expressed to be taken in the name of the Governor.

The correct answer is Divanshi.

Key Points

• Divanshi emerged as a star performer at the ISSF Junior World Championship 2024, which was hosted in Lima, Peru.
• She secured her second individual gold medal of the competition by winning the women's 25m standard pistol event, finishing with a score of 564.
• Prior to this victory, she had already clinched her first individual gold medal in the women's 25m pistol event at the same championship.
• Her performance in the 25m standard pistol led an Indian sweep of the medals, where she was followed by Parisha Gupta (Silver) and Khushi Kapoor (Bronze).
• These individual successes were pivotal in India topping the overall medal tally at the 2024 Junior World Championships, reflecting the country's depth in junior shooting talent.

 Additional Information

• Manu Bhaker:
• A high-profile Indian shooter who made history by winning two Bronze medals at the Paris 2024 Olympics.
• She has won numerous gold medals at the ISSF World Cup, Commonwealth Games, and Youth Olympics in both 10m Air Pistol and 25m Pistol categories.
• Apurvi Chandela:
• An elite Indian Rifle shooter who specialized in the 10m air rifle event and reached the World Number 1 ranking in 2019.
• She is a recipient of the Arjuna Award and won the gold medal at the 2014 Commonwealth Games in Glasgow.
• Heena Sidhu:
• The first Indian pistol shooter to be ranked World Number 1 by the International Shooting Sport Federation (ISSF) in 2014.
• She was the first Indian to win a gold medal in an ISSF World Cup Final (2013) in the 10m Air Pistol event.

The correct answer is Age and sex structure of the population.

Key Points

• A population pyramid, also referred to as an age-sex pyramid, is a graphical illustration that represents the distribution of various age groups within a specific population.
• The vertical axis (Y-axis) displays age cohorts, typically in five-year intervals (e.g., 0-4, 5-9, 10-14), while the horizontal axis (X-axis) represents the total number or percentage of males (usually on the left) and females (usually on the right).
• It serves as a visual tool to analyze demographic trends, including fertility rates, mortality rates, and life expectancy, providing a snapshot of the historical and future growth potential of a nation.
• The structure effectively identifies the dependency ratio, highlighting the balance between the working-age population (typically 15 to 64 years) and the dependent population (children under 15 and seniors over 65).

 Additional Information

• The shape of the pyramid provides insights into the economic development stage of a country:
• Expansive Pyramids: Feature a wide base and narrow peak, indicating high birth rates and high death rates, characteristic of developing countries with rapid growth.
• Constrictive Pyramids: Narrower at the bottom, reflecting declining birth rates and an aging population, common in highly industrialized nations.
• Stationary Pyramids: Maintain a relatively rectangular shape, suggesting stable population growth with balanced birth and death rates.
• Policy Planning: Governments utilize these pyramids to allocate resources for maternal health, primary education, vocational training, and pension systems based on which age bracket is dominant.
• Demographic Dividend: A bulge in the middle section suggests a large labor force, which can lead to rapid economic growth if the country provides sufficient employment and training.

The correct answer is Dancing Girl.

Key Points

• The Dancing Girl is a world-renowned bronze statuette created approximately in 2500 BCE, serving as a primary specimen of the Indus Valley Civilization's artistic excellence.
• It was discovered in 1926 by the British archaeologist Ernest Mackay in the HR area of Mohenjo-daro, a major urban center of the Harappan culture.
• The sculpture is approximately 10.5 centimeters tall and was manufactured using the Lost Wax Casting (Cire Perdue) technique, indicating an advanced understanding of metallurgy and bronze alloying.
• The figure is depicted in a standing position with her right hand on her hip and her left arm, which is heavily laden with 24 bangles, resting on her thigh.
• This artifact is significant because it provides evidence of the Harappan people's mastery over metal casting and their sophisticated sense of aesthetic expression and fashion.

 Additional Information

• Bearded Priest:
• This is a famous steatite (soapstone) sculpture rather than bronze, found at Mohenjo-daro, depicting a male figure with a trefoil-patterned shawl.
• Bull Seal:
• Harappan seals, such as the Humped Bull seal, were primarily carved from steatite or made of terracotta and were used for trade and administrative purposes.
• Mother Goddess:
• These are typically terracotta figurines characterized by elaborate fan-shaped headgear and were likely used for religious or fertility worship.
• Lost Wax Process:
• This ancient method involved coating a wax model with clay, heating it to remove the wax, and then pouring molten metal into the hollow cavity to create a solid sculpture.

The correct answer is 1992.

Key Points

• In February 1992, the National Bank for Agriculture and Rural Development (NABARD) launched the pilot project for the Self-Help Group (SHG) Bank Linkage Programme.
• The primary mandate of this pilot project was to establish a formal credit channel by linking 500 SHGs with the mainstream banking system to promote microfinance and financial inclusion.
• The program was initiated following the recommendations of the S.K. Kalia Committee, which recognized the efficacy of informal groups in delivering credit to the rural poor.
• The success of this pilot phase led the Reserve Bank of India (RBI) to issue guidelines in 1996, mainstreaming SHG lending as a priority sector activity for commercial banks.
• This initiative is historically significant as it evolved into the world's largest community-based microfinance project, empowering millions of rural women through thrift and credit services.

 Additional Information

• 1995:
• The Rural Infrastructure Development Fund (RIDF) was established within NABARD during the 1995-96 fiscal year.
• It focuses on providing low-cost capital to state governments for completing irrigation, road, and bridge projects in rural areas.
• 1990:
• This period marked the conceptualization stage where NABARD, in collaboration with various Non-Governmental Organizations (NGOs), conducted field studies to validate the group-lending model.
• 2000:
• In the Union Budget of 2000-01, the Microfinance Development Fund (MFDF) was created with a corpus of 100 crore rupees to scale up the SHG-Bank Linkage movement across India.
• This period also saw the expansion of Kisan Credit Cards (KCC), another flagship scheme of NABARD introduced in 1998.

The correct answer is Ensuring Everyday Essentials: Public Services and Dignity for All.

Key Points

• The National Conference on Human Rights Day 2025 was organized by the National Human Rights Commission (NHRC) of India to commemorate the anniversary of the Universal Declaration of Human Rights (UDHR).
• The specific title for the 2025 conference, Ensuring Everyday Essentials: Public Services and Dignity for All, was chosen to emphasize the transition from theoretical rights to the practical delivery of basic amenities.
• The conference focused on the intersection of governance and human rights, highlighting that access to clean water, sanitation, healthcare, and education is fundamental to maintaining human dignity.
• Discussions during the event underscored the role of State authorities and local bodies in ensuring that marginalized sections of society receive uninterrupted access to essential public services without discrimination.
• The event served as a platform for policymakers, legal experts, and civil society to evaluate the progress of welfare schemes and their impact on the lived reality of citizens.

 Additional Information

• Human Rights Day:
• Celebrated globally on December 10 every year, marking the day the United Nations General Assembly adopted the UDHR in 1948.
• The year 2025 marked the 77th anniversary of this landmark document.
• National Human Rights Commission (NHRC):
• Established on October 12, 1993, under the Protection of Human Rights Act (PHRA).
• It serves as the 'watchdog of human rights' in India, dealing with violations related to life, liberty, equality, and dignity.
• The commission is headquartered in New Delhi and consists of a Chairperson (who has been a Chief Justice of India or a Judge of the Supreme Court) and other members.
• Other Related Themes:
• Dignity, Freedom, and Justice for All was the global theme used by the United Nations for the 75th Anniversary of the UDHR in 2023.
• Themes such as Equality and Inclusion are frequently adopted as core pillars for various human rights campaigns to address systemic barriers and promote social justice.

Shortcut Trick

When the Selling Price (SP) of two articles is the same, and one is sold at x% gain and the other at x% loss, there is always a total loss.

Net Loss % = x² ÷ 100 = 25² ÷ 100 = 6.25%

Total SP = 1,200 + 1,200 = ₹2,400

Since Net Loss = 6.25% = 1/16, it means CP = 16 units, Loss = 1 unit → SP = 15 units.

15 units = ₹2,400 ⇒ 1 unit (Loss) = 2,400 ÷ 15 = ₹160.

∴ The correct answer is ₹160.

Alternate Method

Given:

SP of first article = ₹1,200, Gain% = 25%

SP of second article = ₹1,200, Loss% = 25%

Calculations:

⇒ Cost Price of 1^st article (CP₁) = SP × [100 ÷ (100 + Gain%)]

⇒ CP₁ = 1,200 × [100 ÷ 125] = 1,200 × (4/5) = ₹960

⇒ Cost Price of 2^nd article (CP₂) = SP × [100 ÷ (100 − Loss%)]

⇒ CP₂ = 1,200 × [100 ÷ 75] = 1,200 × (4/3) = ₹1,600

⇒ Total CP = 960 + 1,600 = ₹2,560

⇒ Total SP = 1,200 + 1,200 = ₹2,400

⇒ Total Loss = Total CP − Total SP = 2,560 − 2,400 = ₹160

∴ The correct answer is ₹160.

Additional Information

Case: SP same and x% profit / y% loss

If percentages are different, use the formula: Net % = [100(x − y) − 2xy] ÷ (200 + x − y).

Direct Loss Amount Formula

When x% gain and x% loss with same SP, Total Loss = (Total SP × x²) ÷ (100² − x²).

CP same, same gain/loss %

If the Cost Price of two articles is the same, and one is sold at x% profit and another at x% loss, there is neither profit nor loss.

Shortcut Trick

The inner curved surface area of a pipe is given by the formula: π × d × h

Given inner diameter (d) = 6 cm and length (h) = 42 cm.

Area = (22/7) × 6 × 42

Area = 22 × 6 × 6 = 792 cm².

∴ The correct answer is 792 cm².

Alternate Method

Given:

Length of the metal pipe (h) = 42 cm

Inner diameter = 6 cm

Outer diameter = 6.4 cm

Formula Used:

Inner Curved Surface Area (CSA) = 2 × π × r × h

Where r is the inner radius (diameter ÷ 2).

Calculations:

⇒ Inner radius (r) = 6 ÷ 2 = 3 cm

⇒ Inner CSA = 2 × (22/7) × 3 × 42

⇒ Inner CSA = 2 × 22 × 3 × (42 ÷ 7)

⇒ Inner CSA = 44 × 3 × 6

⇒ Inner CSA = 132 × 6

⇒ Inner CSA = 792 cm²

∴ The correct answer is 792 cm².

Additional Information

Outer Curved Surface Area

It is the area of the external side of the pipe, calculated as 2 × π × R × h, where R is the outer radius.

Total Surface Area of Hollow Pipe

TSA = Inner CSA + Outer CSA + 2 × Area of base rings = 2πh(R + r) + 2π(R² − r²).

Volume of Metal in Pipe

The volume of the material used to make the pipe is π × h × (R² − r²).

Shortcut Trick

Equate Area of rectangle and circle: πr² = Length × Width

(22/7) × r² = 198 × 175

r² = (198 × 175 × 7) ÷ 22 ⇒ r² = 9 × 175 × 7 = 11025

Radius (r) = √11025 = 105 m

Perimeter (Circumference) = 2 × (22/7) × 105 = 660 m

∴ The correct answer is 660 m.

Alternate Method

Given:

Length (L) of rectangular field = 198 m

Width (W) of rectangular field = 175 m

Area of circle = Area of rectangle

Formula Used:

Area of Rectangle = L × W

Area of Circle = πr²

Perimeter (Circumference) = 2πr

Calculations:

⇒ Area of rectangular field = 198 × 175 = 34650 m²

⇒ Area of circular field = (22/7) × r² = 34650

⇒ r² = (34650 × 7) ÷ 22

⇒ r² = 1575 × 7 = 11025

⇒ r = √11025 = 105 m

⇒ Perimeter (Circumference) = 2 × (22/7) × 105

⇒ Perimeter = 44 × 15 = 660 m

∴ The correct answer is 660 m.

Additional Information

Circle Properties

The Area is πr² and the Circumference (Perimeter) is 2πr or πd, where d is the Diameter.

Rectangle Properties

The Area is Length × Width and the Perimeter is 2(Length + Width).

Radius from Area

If Area (A) is known, the Radius r = √(A/π).

Unit Conversion

Ensure all dimensions are in the same unit (meters in this case) before equating Areas or Perimeters.

Given:

x = 22^0.32

y = 22^0.89

x^z = y⁸

Formula used:

(a^m)ⁿ = a^{m × n}

Calculations:

Substitute values of x and y in the given equation:

(22^0.32)^z = (22^0.89)⁸

⇒ 22^{0.32 × z} = 22^{0.89 × 8}

⇒ 22^0.32z = 22^7.12

On comparing the powers because the bases are equal:

⇒ 0.32z = 7.12

⇒ z = 7.12 ÷ 0.32

⇒ z = 712 ÷ 32

⇒ z = 22.25

∴ The correct answer is option (3).

Given:

Formula Used:

Percentage Increase = [(Value in Final Year − Value in Initial Year) ÷ Value in Initial Year] × 100

Calculation:

From the given data in the line graph,

⇒ Number of students who joined the school in the academic year 2018 = 190

⇒ Number of students who joined the school in the academic year 2019 = 250

⇒ Increase in the number of students from 2018 to 2019 = 250 − 190 = 60

⇒ Percentage increase = (60 ÷ 190) × 100

⇒ Percentage increase = (6 ÷ 19) × 100

⇒ Percentage increase = 600 ÷ 19

⇒ Percentage increase ≈ 31.578%

⇒ Rounding to the nearest value provided in the options, the approximate percentage increase is 31.5%.

∴ The correct answer is 31.5%.

Shortcut Trick

Downstream Speed = Speed of boat + Speed of stream = 21 + 3 = 24 km/hr.

Time taken = Total distance ÷ Downstream speed = 48 ÷ 24 = 2 hr.

∴ The correct answer is 2 hr.

Alternate Method

Given:

Speed of the boat in still water (u) = 21 km/hr

Speed of the stream (v) = 3 km/hr

Total distance (D) = 48 km

Formula Used:

Downstream Speed (S_d) = u + v

Time taken (T) = Distance (D) ÷ Speed (S_d)

Calculations:

⇒ Downstream speed (S_d) = 21 + 3 = 24 km/hr

⇒ Time taken = 48 ÷ 24

⇒ Time taken = 2 hours

∴ The correct answer is 2 hr.

Additional Information

Upstream Speed

The net speed of a boat moving against the stream: S_u = Speed of boat − Speed of stream.

Speed in Still Water

Calculated from downstream and upstream speeds: u = (Downstream speed + Upstream speed) ÷ 2.

Speed of Stream (Current)

Calculated as: v = (Downstream speed − Upstream speed) ÷ 2.

Shortcut Trick

The Surface Area (S) of a sphere can be expressed directly in terms of its diameter (d) as S = πd².

Given, Surface Area = 81π cm².

⇒ π × d² = 81π

⇒ d² = 81

⇒ d = √81 = 9 cm.

∴ The correct answer is 9 cm.

Alternate Method

Given: Surface Area of the sphere = 81π cm².

Formula Used: Surface Area of sphere = 4πr², where r is the radius and Diameter (d) = 2r.

⇒ 4πr² = 81π

⇒ 4r² = 81

⇒ r² = 81 ÷ 4

⇒ r = √(81 ÷ 4)

⇒ r = 9 ÷ 2 = 4.5 cm

⇒ Diameter (d) = 2 × r

⇒ d = 2 × 4.5 = 9 cm

∴ The correct answer is 9 cm.

Additional Information

Volume of a Sphere

The volume of a sphere is the capacity it can hold, calculated as V = (4/3)πr³.

Surface Area of a Hemisphere

The Curved Surface Area (CSA) is 2πr² and the Total Surface Area (TSA) is 3πr².

Radius vs Diameter

The radius is half the diameter. For any sphere, d = 2r.

Shortcut Trick

Assume a base value (Assumed Mean) of 50 kg.

Find deviations: (40−50), (49−50), (57−50), (77−50), (36−50) → −10, −1, +7, +27, −14.

Net deviation = −10 − 1 + 7 + 27 − 14 = +9.

Average deviation = 9 ÷ 5 = 1.8.

Final Average = Assumed Mean + Average deviation = 50 + 1.8 = 51.8 kg.

∴ The correct answer is 51.8 kg.

Alternate Method

Given:

Weights of 5 family members: 40 kg, 49 kg, 57 kg, 77 kg, and 36 kg.

Number of members (n) = 5.

Formula Used:

Average = (Sum of all observations) ÷ (Total number of observations)

Calculations:

⇒ Sum of weights = 40 + 49 + 57 + 77 + 36

⇒ Sum of weights = 259 kg

⇒ Average weight = 259 ÷ 5

⇒ Average weight = 51.8 kg

∴ The correct answer is 51.8 kg.

Additional Information

Arithmetic Mean

The arithmetic mean or average is the central value of a set of numbers, calculated by dividing the total sum by the count of numbers.

Property of Deviations

The sum of deviations of all observations from their arithmetic mean is always zero.

Effect of Change in Observations

If each observation is increased or decreased by a constant value 'k', the new average will also increase or decrease by 'k'.

Shortcut Trick

Let Total Work (LCM of 45 and 60) = 180 units.

Efficiency: A = 180 ÷ 45 = 4; B = 180 ÷ 60 = 3.

Work done by Pipe A in 18 min = 18 × 4 = 72 units.

Remaining work = 180 − 72 = 108 units.

Additional time for both = 108 ÷ (4 + 3) = 15.42... min → 16 min (rounded to next min).

∴ The correct answer is 16 min.

Alternate Method

Given:

Time taken by Pipe A = 45 min

Time taken by Pipe B = 1 hr = 60 min

Pipe A works alone for 18 min.

Calculations:

⇒ Total capacity of the tank = 180 units.

⇒ Work done by Pipe A in 18 minutes = 18 × 4 = 72 units.

⇒ Remaining tank capacity = 180 − 72 = 108 units.

⇒ Combined efficiency of A and B = 4 + 3 = 7 units/min.

⇒ Time required for both pipes to fill the remaining part = 108 ÷ 7 = 15.428... minutes.

⇒ Rounding off to the next minute, we get 16 minutes.

∴ The correct answer is 16 min.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to time. If Pipe A is twice as efficient as Pipe B, it will take half the time to fill the same tank.

Total Work Concept

Total Work = Efficiency × Time. In Pipes and Cisterns, total work is often assumed as the LCM of individual times to simplify calculations.

Inlet and Outlet Pipes

Inlet pipes have positive efficiency (filling), while outlet pipes (leaks) have negative efficiency (emptying) in calculations.

Shortcut Trick

When the Selling Price of 'x' items equals the Cost Price of 'y' items:

Gain/Loss % = ((Items with CP − Items with SP) ÷ Items with SP) × 100

Here, Items with CP = 27 and Items with SP = 25.

Gain % = ((27 − 25) ÷ 25) × 100 = (2 ÷ 25) × 100 = 8%.

∴ The correct answer is 8% gain.

Alternate Method

Given: Selling Price (SP) of 25 books = Cost Price (CP) of 27 books.

Let the Cost Price (CP) of 1 book be ₹1.

⇒ Cost Price (CP) of 27 books = ₹27.

⇒ Selling Price (SP) of 25 books = ₹27 (Given).

⇒ Cost Price (CP) of 25 books = ₹25.

Now, we calculate the Gain on 25 books:

⇒ Gain = SP of 25 books − CP of 25 books

⇒ Gain = ₹27 − ₹25 = ₹2.

The Gain Percentage is calculated on the Cost Price:

⇒ Gain % = (Gain ÷ CP) × 100

⇒ Gain % = (2 ÷ 25) × 100

⇒ Gain % = 2 × 4 = 8%.

∴ The correct answer is 8% gain.

Additional Information

Profit and Loss Basic Formulas

Profit = SP − CP (when SP > CP). Loss = CP − SP (when CP > SP). Both percentages are calculated on CP.

Quantity Based Shortcut

If CP of m articles = SP of n articles, then Profit/Loss % = ((m − n) ÷ n) × 100. Positive result indicates Gain, negative indicates Loss.

Effective Gain with Discounts

If a trader uses faulty weights of g grams instead of 1 kg, Gain % = ((1000 − g) ÷ g) × 100.

Shortcut Trick

Apply the direct property: Product of two numbers = HCF × LCM

Let the second number be x.

90 × x = 18 × 360

x = (18 × 360) ÷ 90 = 18 × 4

x = 72

∴ The correct answer is 72.

Alternate Method

Given:

HCF of two numbers = 18

LCM of two numbers = 360

One number (a) = 90

Formula Used:

First Number × Second Number = HCF × LCM

Calculations:

⇒ 90 × Second Number = 18 × 360

⇒ Second Number = (18 × 360) ÷ 90

⇒ Second Number = 6480 ÷ 90

⇒ Second Number = 72

∴ The correct answer is 72.

Additional Information

Fundamental Property of HCF and LCM

For any two positive integers a and b, the product of the numbers is always equal to the product of their Highest Common Factor and Least Common Multiple: a × b = HCF(a, b) × LCM(a, b).

HCF (Highest Common Factor)

It is the largest positive integer that divides each of the integers without leaving a remainder. It is also known as GCD (Greatest Common Divisor).

LCM (Least Common Multiple)

It is the smallest positive integer that is divisible by both a and b.

Co-prime Numbers

Two numbers are called co-prime if their HCF is 1. For co-prime numbers, the LCM is simply the product of the two numbers.

Shortcut Trick

Total interest percentage for 6 years = Rate × Time

Effective SI % = 7% × 6 = 42%

Simple Interest = 42% of ₹3500

Interest = 42 × 35 = 1470

∴ The correct answer is ₹1470.

Alternate Method

Given:

Principal (P) = ₹3500

Rate of Interest (R) = 7% per annum

Time (T) = 6 years

Formula Used:

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

Calculations:

⇒ SI = (3500 × 7 × 6) ÷ 100

⇒ SI = 35 × 7 × 6

⇒ SI = 35 × 42

⇒ SI = ₹1470

∴ The correct answer is ₹1470.

Additional Information

Total Amount Formula

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

Finding Other Variables

From the SI formula, we can derive: P = (SI × 100) ÷ (R × T), R = (SI × 100) ÷ (P × T), and T = (SI × 100) ÷ (P × R).

Nature of Simple Interest

Simple Interest remains constant for every year if the principal and rate remain unchanged, unlike Compound Interest where interest is calculated on the accumulated amount.

Shortcut Trick

Apply the direct ratio formula: CP/MP = (100 − Discount%)/(100 + Profit%)

Given Marked Price (MP) = ₹1,620, Discount = 10%, Profit = 20%

CP/1620 = (100 − 10)/(100 + 20) = 90/120 = 3/4

CP = 1620 × (3/4) = 405 × 3 = 1215

∴ The correct answer is ₹1,215.

Alternate Method

Given:

Marked Price (MP) of the article = ₹1,620

Discount percentage = 10%

Profit percentage = 20%

Formula Used:

Selling Price (SP) = Marked Price × (100 − Discount%)/100

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

Calculations:

⇒ Selling Price (SP) = 1620 × (100 − 10)/100

⇒ SP = 1620 × 90/100

⇒ SP = 162 × 9 = ₹1,458

⇒ Cost Price (CP) = 1458 × 100/(100 + 20)

⇒ CP = 1458 × 100/120

⇒ CP = 1458 × 5/6

⇒ CP = 243 × 5

⇒ CP = ₹1,215

∴ The correct answer is ₹1,215.

Additional Information

Relation between CP and MP

The most efficient way to solve mark-up and discount problems is using the ratio CP/MP = (100 − D%)/(100 + P%).

Markup Percentage

Markup % = [(MP − CP)/CP] × 100. In this case, Markup = 1620 − 1215 = 405, so Markup % = (405/1215) × 100 = 33.33%.

Successive Discounts

If two successive discounts d₁ and d₂ are given, the single equivalent discount is (d₁ + d₂ − d₁d₂/100)%.

Shortcut Trick

Net effective rate for successive Interest Rates = R₁ + R₂ + (R₁ × R₂) ÷ 100

Given: R₁ = 4% and R₂ = 4% + 3% = 7%

Net Rate = 4 + 7 + (4 × 7) ÷ 100 = 11 + 0.28 = 11.28%

Total Compound Interest = 57,500 × 11.28% = 575 × 11.28 = 6,486

∴ The correct answer is 6,486.

Alternate Method

Given:

Principal (P) = ₹57,500

Rate for 1^st year (R₁) = 4%

Rate for 2^nd year (R₂) = 4% + 3% = 7%

Step-by-step Calculation:

⇒ Interest for the 1^st year = Principal × R₁ ÷ 100

⇒ Interest₁ = 57,500 × 4 ÷ 100 = ₹2,300

⇒ Amount after the 1^st year (A₁) = Principal + Interest₁

⇒ A₁ = 57,500 + 2,300 = ₹59,800

⇒ Interest for the 2^nd year = A₁ × R₂ ÷ 100

⇒ Interest₂ = 59,800 × 7 ÷ 100 = ₹4,186

⇒ Total Compound Interest = Interest₁ + Interest₂

⇒ Total CI = 2,300 + 4,186 = 6,486

∴ The correct answer is 6,486.

Additional Information

Variable Interest Rate CI Formula

When rates differ each year, Amount (A) = P × (1 + R₁/100) × (1 + R₂/100) ... × (1 + R_n/100).

Successive Percentage Method

For two years, the total interest percentage is R₁ + R₂ + (R₁R₂)/100. This is the fastest way to solve for 2-year compounding.

Difference between CI and SI

The difference between CI and SI for the first year is always zero (when compounding annually), as both are calculated on the same principal.

Shortcut Trick

Using the Alligation Method to find the mixing ratio of two pulses.

Ratio = (Cost of Dearer − Mean Price) : (Mean Price − Cost of Cheaper)

Ratio = (120 − 106.50) : (106.50 − 105)

Ratio = 13.50 : 1.50 = 135 : 15 = 9 : 1

∴ The correct answer is 9 : 1.

Alternate Method

Given:

Cost of Variety 1 (C₁) = ₹105 per kg

Cost of Variety 2 (C₂) = ₹120 per kg

Desired Mean Price (M) = ₹106.50 per kg

Formula Used:

Quantity of Cheaper / Quantity of Dearer = (CP of Dearer − Mean Price) / (Mean Price − CP of Cheaper)

Calculations:

⇒ Ratio = (120 − 106.50) / (106.50 − 105)

⇒ Ratio = 13.50 / 1.50

⇒ Ratio = 135 / 15

⇒ Ratio = 9 / 1

∴ The correct answer is 9 : 1.

Additional Information

Rule of Alligation

It is a rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a specified price.

Mean Price (M)

The cost price of a unit quantity of the mixture is called the mean price. It always lies between the cost prices of the cheaper and dearer ingredients.

Weighted Average Formula

The mean price M can also be calculated as M = (n₁C₁ + n₂C₂) / (n₁ + n₂), where n represents the quantities and C represents the costs.

Shortcut Trick

Calculate the 30% of 80 directly by multiplying the tens digits: 3 × 8 = 24.

Calculate the 20% of 50 similarly: 2 × 5 = 10.

Find the difference: 24 − 10 = 14.

∴ The correct answer is 14.

Alternate Method

Given: First value is 30% of 80 and the second value is 20% of 50.

Formula Used: Percentage value = (Percentage / 100) × Base Value

⇒ First Number = (30 / 100) × 80

⇒ First Number = 3 × 8 = 24

⇒ Second Number = (20 / 100) × 50

⇒ Second Number = 2 × 5 = 10

⇒ Difference = 24 − 10

⇒ Difference = 14

∴ The correct answer is 14.

Additional Information

Percentage Calculation

To find x% of y, the general formula is (x × y) / 100. This can also be written as y% of x.

Decimal Conversion

A percentage can be converted to a decimal by dividing by 100 (e.g., 30% = 0.30). Multiplying the decimal by the total gives the value.

Percentage Change

Percentage change is calculated as [ (Difference) / (Original Value) ] × 100.

Shortcut Trick

Let the average speed be V km/h. Speed for the last segment = 1.2V.

Total time ratio: (0.3 ÷ 40) + (0.4 ÷ 60) + (0.3 ÷ 1.2V) = 1 ÷ V

⇒ (3 ÷ 400 + 4 ÷ 600) + 1 ÷ 4V = 1 ÷ V

⇒ (9 + 8) ÷ 1200 = 1 ÷ V − 1 ÷ 4V = 3 ÷ 4V

⇒ 17 ÷ 1200 = 3 ÷ 4V ⇒ V = (1200 × 3) ÷ (4 × 17) = 900 ÷ 17 ≈ 52.94 km/h.

∴ The correct answer is 53 km/h.

Alternate Method

Given:

Total Distance = 250 km

Segment 1: Distance = 30% of 250 = 75 km | Speed = 40 km/h

Segment 2: Distance = 40% of 250 = 100 km | Speed = 60 km/h

Segment 3: Distance = 30% of 250 = 75 km | Speed = 1.2 × Average Speed (V)

Formula Used:

Average Speed (V) = Total Distance ÷ Total Time

Calculations:

⇒ Time for segment 1 (t₁) = 75 ÷ 40 = 1.875 hr

⇒ Time for segment 2 (t₂) = 100 ÷ 60 = 5 ÷ 3 hr ≈ 1.667 hr

⇒ Time for segment 3 (t₃) = 75 ÷ 1.2V = 62.5 ÷ V hr

⇒ V = 250 ÷ (1.875 + 5/3 + 62.5/V)

⇒ V(1.875 + 1.666...) + V(62.5/V) = 250

⇒ V × (15/8 + 5/3) + 62.5 = 250

⇒ V × (45 + 40) ÷ 24 = 250 − 62.5 = 187.5

⇒ V × 85 ÷ 24 = 187.5

⇒ V = (187.5 × 24) ÷ 85 = 4500 ÷ 85

⇒ V = 900 ÷ 17 ≈ 52.941 km/h

Rounding off to the nearest integer, we get V = 53 km/h.

∴ The correct answer is 53 km/h.

Additional Information

General Average Speed Formula

Average Speed = (Total Distance) ÷ (Total Time taken for all parts of the journey).

Average Speed for Equal Distances

If a journey is divided into two equal distances with speeds x and y, the Average Speed = 2xy ÷ (x + y).

Unit Conversion

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

Shortcut Trick

Capital Ratio X : Y = 85,737 : 57,158 = 3 : 2.

Management Fee for X = 8% of ₹37,875 = ₹3,030.

Remaining Profit = 92% of ₹37,875 = ₹34,845.

X's share in remaining profit = 3/5 × 34,845 = ₹20,907.

Total amount X receives = ₹3,030 + ₹20,907 = ₹23,937.

∴ The correct answer is ₹23,937.

Alternate Method

Given:

Investment of X = ₹85,737

Investment of Y = ₹57,158

Total Profit = ₹37,875

Management Fee = 8% of Total Profit

Calculations:

⇒ Ratio of Capitals (X : Y) = 85,737 : 57,158

⇒ Dividing both by 28,579 → X : Y = 3 : 2

⇒ Management allowance for X = 8% × 37,875 = (8/100) × 37,875 = ₹3,030

⇒ Remaining profit = 37,875 − 3,030 = ₹34,845

⇒ X’s share from remaining profit = (3 / (3+2)) × 34,845

⇒ X’s share = (3/5) × 34,845 = 3 × 6,969 = ₹20,907

⇒ Total amount X gets = Management Fee + Ratio Share

⇒ Total for X = 3,030 + 20,907 = ₹23,937

∴ The correct answer is ₹23,937.

Additional Information

Partnership Profit Distribution

Profit is distributed based on the product of Capital and Time. If time is constant, Profit Ratio = Capital Ratio.

Working vs. Sleeping Partner

A working partner receives a management fee or salary before the remaining profit is divided according to investment ratios.

Ratio Simplification

To simplify large numbers, find the HCF of the investments to determine the basic ratio parts.

Shortcut Trick

In a continued proportion A : B :: B : C, the value of the third proportional C is given by B² ÷ A.

Identify terms: A = x³y and B = xy. We need to find C = a.

∴ a = (xy)² ÷ (x³y)

∴ a = (x²y²) ÷ (x³y) = y/x

∴ The correct answer is y/x.

Alternate Method

Given:

The proportion is x³y : xy :: xy : a.

Formula Used:

For any proportion A : B :: C : D, the Product of Extremes is equal to the Product of Means (A × D = B × C).

Calculations:

⇒ (x³y) × a = (xy) × (xy)

⇒ x³y × a = x²y²

⇒ a = (x²y²) ÷ (x³y)

⇒ a = (x² ÷ x³) × (y² ÷ y)

⇒ a = (1/x) × y

⇒ a = y/x

∴ The correct answer is y/x.

Additional Information

Fourth Proportional

In a proportion a : b :: c : d, the term d is the fourth proportional, calculated as d = (b × c) ÷ a.

Third Proportional

When three quantities a, b, and c are in continued proportion (a : b :: b : c), then c is the third proportional, where c = b² ÷ a.

Mean Proportional

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

Properties of Proportion

Key properties include Invertendo (b:a = d:c), Alternando (a:c = b:d), and Componendo-Dividendo.

Shortcut Trick

व्युत्क्रमानुपाती संबंध (Inverse Proportion) का प्रयोग करें: M₁D₁ = M₂D₂

यहाँ 1204 × 24 = 2064 × D₂

D₂ = 28896 ÷ 2064 = 14

∴ The correct answer is 14 days.

Alternate Method

दिया गया है:

सैनिकों की प्रारंभिक संख्या (M₁) = 1204

राशन के प्रारंभिक दिन (D₁) = 24

सैनिकों की नई संख्या (M₂) = 2064

प्रयुक्त सूत्र:

जब कुल कार्य (या कुल राशन) समान हो: M₁ × D₁ = M₂ × D₂

गणना:

⇒ 1204 × 24 = 2064 × D₂

⇒ D₂ = (1204 × 24) ÷ 2064

⇒ D₂ = 28896 ÷ 2064

⇒ D₂ = 14

∴ The correct answer is 14 days.

Additional Information

व्युत्क्रमानुपाती नियम (Inverse Proportion)

यदि काम करने वालों की संख्या बढ़ती है, तो उसी काम को पूरा करने में लगने वाला समय घट जाता है। सूत्र: M × D = स्थिरांक।

मिश्र समानुपात (Compound Proportion)

यदि कार्य के घंटे (H) और कार्य की मात्रा (W) भी दी गई हो, तो (M₁D₁H₁) / W₁ = (M₂D₂H₂) / W₂ का उपयोग किया जाता है।

प्रति व्यक्ति राशन की खपत

यदि प्रति व्यक्ति खपत अलग-अलग दी गई हो, तो उसे व्यक्तियों की संख्या के साथ गुणा (M × D × C) किया जाता है।

The correct answer is: extremly.

Key Points

• The word 'extremly' is the misspelt word in the given sentence. The correct spelling is 'extremely', which means to a very great degree or very much. (अत्यधिक)
• Example: The project was extremely challenging, but the team managed to complete it on time.
• 'Extremely' is an adverb used to emphasize the intensity of an adjective or another adverb. It is formed by adding the suffix '-ly' to the base word 'extreme'. (अत्यंत)
• Example: It is extremely important to follow the safety guidelines while working in the lab.
• Hence, we can infer that the misspelt word among the options is 'extremly'.

Therefore, the correct answer is- extremly.

Additional Information

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

• Knowledgeable (जानकार): Having or showing a great deal of information or understanding about a particular subject.
• Example: She is highly knowledgeable about ancient history and architecture.
• Young (युवा): Being in the early stage of life, growth, or development.
• Example: The young entrepreneur started his first company at the age of eighteen.
• Intern (प्रशिक्षु): A student or trainee who works in an organization, sometimes without pay, in order to gain work experience or satisfy requirements for a qualification.
• Example: As an intern at the hospital, he learned how to handle emergency situations.

The correct answer is 'the'.

 

Key Points

• The definite article 'the' is used to refer to specific or particular nouns.
• In the given sentence, the speaker is referring to a specific, well-known individual, Charlie Chaplin.
• When a noun (like 'actor') is used as an appositive to identify or describe a specific famous person already mentioned by name, the definite article 'the' is required to emphasize their unique identity.
• Therefore, the word 'the' correctly completes the sentence.

Therefore, the correct answer is Option 1.

 

Complete Sentence: "Do you mean Charlie Chaplin, the actor?"

 

Additional Information

• Option 2: 'that' is a demonstrative adjective and is grammatically less appropriate than the definite article in this specific appositive construction.
• Option 3: 'a' is an indefinite article used for non-specific items; it would imply he is just one of many actors, which contradicts the specific naming of a famous person.
• Option 4: 'an' is also an indefinite article used before vowel sounds. While 'actor' starts with a vowel, the indefinite nature makes it incorrect for identifying a specific person like Charlie Chaplin.

The correct answer is QPSR.

Key Points

• Segment Q (she missed the morning bus,) functions as the primary independent clause that establishes the initial context. It identifies the subject and the predicament, which is the logical starting point for the narrative sequence. Hence, statement Q is correct.
• Segment P (but by taking a rickshaw,) introduces an adversative conjunction 'but' to signal a contrast or a shift in the situation. The following prepositional phrase 'by taking a rickshaw' describes the instrumental method used to overcome the previous problem. Hence, statement P is correct.
• Segment S (she managed to reach school on time,) provides the resolution of the sentence. This clause naturally follows the action in segment P, showing the successful outcome of the subject's effort to reach her destination despite the initial delay. Hence, statement S is correct.
• Segment R (showing her punctuality) acts as a participial phrase that modifies the preceding main clause. It serves as a concluding observation that characterizes the subject's behavioral trait based on the actions described in the earlier segments. Hence, statement R is correct.

 Additional Information

• Logical Sentence Structuring:
• Narrative Coherence: Coherent statements often follow a Problem-Action-Result structure. Here, missing the bus (problem), taking a rickshaw (action), and arriving on time (result) create a logical chronological flow.
• Conjunction Usage: The coordinating conjunction 'but' is used to connect two contrasting ideas. It bridges the negative event of missing a bus with the positive resolution of reaching on time.
• Grammatical Modifiers: Present participle phrases (like 'showing...') are frequently placed at the end of sentences to provide supplementary information or a resultant attribute concerning the main subject.

The correct answer is indiscipline.

Key Points

• The word indiscipline is the correct spelling of the misspelled term indisipline found in the provided sentence.
• Etymologically, the term is derived from the negative prefix in- (meaning 'not' or 'lack of') and the Latin root disciplina (meaning 'instruction' or 'knowledge'). It specifically refers to a lack of control or the refusal to obey rules and authority.
• In English orthography, the sequence -sc- is a common digraph found in words like discipline, science, and scented; the error in the sentence occurs because the letter c was omitted.
• Contextually, the sentence describes a head of a school (principal) dealing with behavioral issues, making indiscipline the most appropriate noun to describe the subject of the address.

 Additional Information

• Analysis of other terms:
• principle: This is a homophone of principal. It refers to a fundamental truth, doctrine, or moral law. While spelled correctly as a word, it does not replace the misspelled word in the sentence.
• adressed: This is an incorrect spelling of the verb addressed. In English, the verb address (meaning to speak to or deal with) requires a double d and a double s.
• asembly: This is an incorrect spelling of the noun assembly. A correct spelling requires a double s (assembly) to refer to a formal gathering or congregation of people.

The correct answer is Cibophobia.

Key Points

• Cibophobia is defined as the pathological or irrational fear of food. The term originates from the Latin word 'cibus', meaning food, and the Greek word 'phobos', meaning fear.
• Unlike eating disorders like anorexia, which are driven by body image concerns, cibophobia is a specific phobia where the individual fears the food items themselves, often due to concerns about contamination, food poisoning, or expiration dates.
• Individuals with this condition often avoid highly perishable items such as meat, dairy, or seafood. They may also develop an obsession with ingredient labels or cooking temperatures to ensure the food is safe.
• This phobia can lead to significant nutritional deficiencies and social isolation, as eating in public or communal settings becomes a source of intense anxiety.

 Additional Information

• Mysophobia:
• It is the extreme fear of germs, bacteria, dirt, and contamination.
• The term was first introduced by Dr. William Hammond in 1879 when describing a case of Obsessive-Compulsive Disorder (OCD) manifested through excessive handwashing.
• Cynophobia:
• This is the clinical fear of dogs. It is categorized as a zoophobia (fear of animals).
• It is one of the most common animal phobias and usually develops during childhood after a traumatic encounter with a canine.
• Phonophobia:
• It is the fear of sound or loud noises. This is not a hearing disorder but a psychological phobia.
• Sufferers may fear sudden, unexpected noises like firecrackers or balloons popping, which can trigger panic attacks.

The correct answer is: Bibliophile.

Key Points

• The phrase 'individual who has a great love for books' describes a person who enjoys reading, collecting, and possessing books. (वह व्यक्ति जिसे पुस्तकों से बहुत अधिक प्रेम हो)
• Example: With shelves reaching the ceiling in every room, it was obvious he was an individual who has a great love for books.
• 'Bibliophile' is the one-word substitute for a person who collects or has a great love of books. (पुस्तक प्रेमी)
• Example: As a dedicated bibliophile, she was thrilled to find a rare first edition at the local estate sale.
• Hence, the highlighted segment can be appropriately replaced by the term 'bibliophile'.

Therefore, the correct answer is- Bibliophile.

Additional Information

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

• Horticulturist (बागवानी विशेषज्ञ): An expert in the science and art of growing fruits, vegetables, flowers, or ornamental plants.
• Example: The horticulturist advised the community on which plants would thrive in the local climate.
• Stoic (सहनशील/वैराग्यवादी): A person who can endure pain or hardship without showing their feelings or complaining.
• Example: Despite the grueling nature of the marathon, he remained stoic and focused on the finish line.
• Pedestrian (पैदल यात्री): A person walking rather than traveling in a vehicle.
• Example: The city installed a new signal to ensure pedestrian safety at the busy intersection.

The correct answer is 'the, the'.

 

Key Points

• The definite article 'the' is used before nouns that are unique, specific, or have been previously mentioned.
• In the first blank, 'the' is used with 'stars' because it refers to the specific celestial bodies visible to the observer in the context of the sentence.
• In the second blank, 'the' is used with 'sky' because the sky is considered a unique entity (there is only one sky surrounding the Earth).
• Common examples of this rule include: the sun, the moon, the earth, and the universe.

Therefore, the correct answer is Option 4.

 

Complete Sentence: 'When you look at the stars in the sky, do you ever wonder about life elsewhere?'

 

Additional Information

• Indefinite Articles (a/an): Used for non-specific, singular countable nouns. Since 'stars' is plural, 'a' or 'an' cannot be used.
• Zero Article: Sometimes used for general statements, but when referring to physical entities like the sky or stars in a descriptive sense, the definite article is preferred.

The correct answer is: depletion.

Key Points

• The word 'proliferation' means a rapid increase in the number or amount of something. (तेजी से वृद्धि)
• Example: The proliferation of digital technology has completely transformed the modern workplace.
• 'Depletion' refers to the reduction in the number or quantity of something; it involves the exhaustion of resources or supplies. (रिक्तीकरण)
• Example: The depletion of natural resources like groundwater is a major global concern for future generations.
• Hence, we can infer that the opposite of 'proliferation' is 'depletion'.

Therefore, the correct answer is: depletion.

Additional Information

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

• Extension (विस्तार): A part that is added to something to enlarge or prolong it.
• Example: The company requested an extension for the submission of the final report.
• Accession (पद-ग्रहण): The attainment or acquisition of a position of rank or power.
• Example: The historical archives documented the king's accession to the throne in detail.
• Distension (फैलाव): The state of being swollen or stretched, often due to internal pressure.
• Example: Severe abdominal distension can be a symptom of various underlying medical conditions.

The correct answer is ABCDE.

Key Points

• The sentence follows a logical chronological progression of disaster management, starting with the immediate aftermath when floodwaters receded. Hence, the introductory clause is correctly placed.
• Segment A focuses on restoring clean water and sanitation, which is the primary medical priority to prevent the spread of waterborne diseases like cholera after a flood. Hence, statement A is correct.
• Segment B transitions to the next vital need, food security, by distributing emergency rations to isolated households that lack access to supplies. Hence, statement B is correct.
• Segment C completes the list of immediate survival needs by coordinating shelter for displaced families, maintaining parallelism with the previous gerund phrases. Hence, statement C is correct.
• Segment D introduces a simultaneous administrative action using the conjunction while, focusing on the technical assessment of physical assets. Hence, statement D is correct.
• Segment E provides the necessary teleological purpose for the assessment, linking the current damage evaluation to the future goal of long-term rebuilding. Hence, statement E is correct.

 Additional Information

• Humanitarian Relief Priorities:
• WASH (Water, Sanitation, and Hygiene): In flood scenarios, contamination of groundwater is common; thus, water purification and waste management are prioritized to halt pathogen transmission.
• Logistics and Rations: Relief teams often use geospatial mapping to identify isolated clusters and deliver non-perishable food items.
• Infrastructure Assessment: This involves civil engineers checking the load-bearing capacity of bridges and pavement integrity of highways before heavy reconstruction equipment can be deployed.
• Disaster Recovery Framework: The transition from relief (short-term) to reconstruction (long-term) requires a systematic Post-Disaster Needs Assessment (PDNA) to ensure resilience against future climate events.

The correct answer is: temporary.

Key Points

• The word eternal means lasting or existing forever; without end or beginning and often used to describe something that is permanent. (अनंत)
• Example: The poet wrote about the eternal beauty of the mountains.
• Temporary refers to something that lasts for only a limited period of time and is not permanent; it is the direct opposite of something that is everlasting. (अस्थायी)
• Example: They found a temporary solution to the leak until the plumber arrived.
• Hence, we can infer that the opposite of eternal is temporary.

Therefore, the correct answer is: temporary.

Additional Information

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

• Perpetual (निरंतर): Never ending or changing; occurring so frequently as to seem ceaseless.
• Example: The perpetual noise of the traffic made it difficult to concentrate.
• Immortal (अमर): Living forever; never dying or decaying.
• Example: In the stories, the gods are immortal and do not age.
• Enduring (स्थायी): Lasting over a long period of time; durable or persistent.
• Example: The treaty created an enduring peace between the two nations.

The correct answer is 'quickly'.

 

Key Points

• The word quickly is an adverb of manner that describes an action performed at a high speed or in a short time.
• The phrase to meet the submission deadline indicates that time was a critical factor and the task needed to be completed fast.
• Among the given options, quickly is the most appropriate adverb to address the urgency implied by a deadline.

Therefore, the correct answer is Option 1.

 

Complete Sentence: 'She typed the report quickly to meet the submission deadline.'

 

Additional Information

• Option 2: Neatly refers to the cleanliness or organized appearance of the work.
• Option 3: Accurately refers to performing the task correctly and without errors.
• Option 4: Efficiently refers to working in a way that achieves maximum productivity with minimum wasted effort.

The correct answer is: the squeaky wheel gets the grease.

Key Points

• The phrase 'the loudest complainer gets the attention' means that people who complain the most or make their needs known loudly are the ones who receive help or service. (सबसे अधिक शिकायत करने वाले को ही ध्यान या सहायता मिलती है)
• Example: In a busy restaurant, the customer who keeps calling the waiter is served first; truly, the loudest complainer gets the attention.
• 'The squeaky wheel gets the grease' is a proverb which implies that the most noticeable problems or the people who make the most noise are the ones most likely to get attention or be fixed. (जो पहिया आवाज़ करता है, उसे ही तेल मिलता है)
• Example: I had to keep calling customer service for a week before they resolved my issue; it is a classic case of the squeaky wheel gets the grease.
• Hence, we can infer that the proverb 'the squeaky wheel gets the grease' is the best substitute for the underlined part.

Therefore, the correct answer is: the squeaky wheel gets the grease.

Additional Information

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

• Every cloud has a silver lining (निराशा में भी आशा की किरण होती है): This means that every difficult or unpleasant situation has some positive aspect or potential for good.
• Example: Although she failed the exam, it made her realize she wanted to study a different subject; every cloud has a silver lining.
• The pen is mightier than the sword (कलम की शक्ति तलवार से बड़ी होती है): This proverb suggests that writing and communication are more effective tools for change than physical force or violence.
• Example: The author's books changed the laws of the country, showing that the pen is mightier than the sword.
• The early bird catches the worm (जो जल्दी शुरुआत करता है वही सफल होता है): This means that someone who arrives early or acts promptly will have the best chance of success.
• Example: If you want to get the best seats for the concert, you should buy them now because the early bird catches the worm.

The correct answer is 'bury'.

 

Key Points

• The phrase 'bury the hatchet' is a well-known English idiom.
• It means to make peace, end a quarrel, or settle a conflict. (पुरानी दुश्मनी भुला देना)
• The sentence mentions ending their differences after a discussion, which perfectly fits the context of this idiomatic expression.
• Idioms use specific words that cannot usually be replaced by synonyms; therefore, 'bury' is the only word that completes the fixed expression 'bury the hatchet'.

Therefore, the correct answer is 'Option 4'.

Complete Sentence: After a lot of discussion, they finally decided to bury the hatchet and end their differences.

Additional Information

• Settle: Means to reach an agreement or resolve a dispute (e.g., settle a score), but it does not collocate with 'hatchet'.
• Resolve: To find a solution to a problem or contentious matter.
• Fix: To repair something that is broken or damaged.

The correct answer is 'regardless of'.

 

Key Points

• The phrase 'regardless of' is a prepositional phrase that means 'without regard to' or 'notwithstanding'.
• In the context of workplace policies, it is the standard idiom used to indicate that equal opportunities are provided to everyone without being influenced by factors such as background, experience, race, or gender.
• The sentence implies a policy of inclusivity where every employee is treated the same way.
• Options 2, 3, and 4 do not convey the intended meaning of a neutral, fair policy.

Therefore, the correct answer is Option 1.

 

Complete Sentence: 'The organisation ensures equal opportunities for all employees regardless of their background or experience level.'

 

Additional Information

• Option 2: 'in spite of' is used to show a contrast or when something happens despite a hindrance (e.g., We went out in spite of the rain).
• Option 3: 'because of' is used to indicate a reason or cause for something.
• Option 4: 'instead of' is used to suggest an alternative or substitution.

The correct answer is 'but'.

 

Key Points

• The word "but" is a coordinating conjunction used to introduce a statement that contrasts with or contradicts what has been mentioned before.
• In this sentence, there is a contrast between the positive action ("studied diligently") and the negative feeling ("felt unprepared").
• The use of the word "still" in the second clause further emphasizes the unexpected nature of the feeling, making "but" the most appropriate logical connector.

Therefore, the correct answer is Option 3.

 

Complete Sentence: "She studied diligently for weeks, but she still felt unprepared on the day of the exam."

 

Additional Information

• Option 1: "and" is used for addition or to connect similar ideas, which does not fit the contrast here.
• Option 2: "so" is used to show a result or consequence. Feeling unprepared is not the logical result of studying hard.
• Option 4: "yet" is also a conjunction for contrast, but "but" is the standard choice provided in the official answer key for this grammatical structure.

The correct answer is Option 2.

 

Key Points

• The passage states that sustainable resource management is a method used to mitigate risks associated with water security and unsustainable consumption.
• It explicitly defines the aim of this management style as balancing present needs with long-term availability.
• This approach ensures that freshwater resources remain accessible for future generations while meeting the current requirements for drinking water, food production, and public health.
• Thus, Option 2 directly aligns with the primary objective provided in the text.

Therefore, the correct answer is Option 2.

 

Correct Sentence: 'Sustainable resource management seeks to address these risks by balancing present needs with long-term availability.'

 

Additional Information

• Option 1: 'Over-extraction of groundwater' – The passage identifies this as a cause of recurring shortages and a challenge to be overcome, rather than a goal of sustainable management.
• Option 3: 'Increase in urban sanitation systems' – While improved sanitation is related to water management, the text does not cite it as the central aim of sustainable resource management.
• Option 4: 'Centralising water ownership and distribution' – The text emphasizes effective governance, transparent policies, and the involvement of local communities, which implies a more inclusive and decentralized framework than a purely centralized one.

The correct answer is Data-driven monitoring.

 

Key Points

• The passage explicitly discusses the growing role of technology in addressing water security and resource management.
• According to the text, specific technological tools include data-driven monitoring, efficient irrigation systems, and early-warning tools for droughts and floods.
• These tools are designed to optimise water use and reduce waste, making data-driven monitoring the correct technological tool listed in the options.
• The passage emphasizes that while technology is helpful, it must be combined with social equity and behavioural change to be fully effective.

Therefore, the correct answer is Data-driven monitoring.

 

Additional Information

• Traditional irrigation channels – While the passage mentions irrigation, it focuses on efficient irrigation systems as a modern technological improvement rather than traditional methods.
• Seasonal migration patterns – This concept is not mentioned in the text as a strategy or tool for water management.
• Market forecasting tools – The passage focuses on environmental sustainability and governance rather than economic market forecasting.

The correct answer is Option 3.

 

Key Points

• The passage highlights that while technology is a helpful tool, it is not enough on its own to ensure water security.
• It explicitly states that without behavioural change and equitable access, improvements in water management may only benefit a limited few.
• This suggests that for water resources to be managed effectively for the whole population, the distribution and availability must be fair and inclusive.
• Therefore, the most logical inference is that water access must be equitable to achieve long-term security.

Therefore, the correct answer is Option 3.

 

Key Quote: 'Without behavioural change and equitable access, improvements may benefit only a few.'

 

Additional Information

• Option 1: The text mentions effective governance and local community involvement, which leans towards public and social responsibility rather than privatisation.
• Option 2: The requirement for sustainable resource management, rainwater harvesting, and watershed protection indicates that water access does not improve automatically.
• Option 4: While the passage mentions climate change, it also discusses groundwater, wastewater reuse, and governance, showing that access depends on many factors, not only on rainfall.

The correct answer is Sustainable management is essential for water security.

Key Points

• The passage highlights water security as a critical global concern and argues that sustainable resource management is the primary method to address risks by balancing present needs with long-term availability. Hence, statement 1 is correct.
• While the text identifies climate change as a pressure on freshwater resources, it describes its impact broadly on water security rather than limiting its effects strictly to rainfall patterns. Hence, statement 2 is incorrect.
• The author explicitly states that technology alone cannot ensure water security and must be coupled with behavioural change and social equity to be effective for the whole society. Hence, statement 3 is incorrect.
• The passage does not describe water scarcity as unavoidable; instead, it provides various strategies like rainwater harvesting and watershed protection to mitigate it through integrated management. Hence, statement 4 is incorrect.

 Additional Information

• Sustainable Resource Management:
• Focuses on the circular economy of water, including the reuse of treated wastewater.
• Aligns with the United Nations Sustainable Development Goal 6 (SDG 6), which aims for clean water and sanitation for all by 2030.
• Involves Integrated Water Resources Management (IWRM), a framework for coordinating water, land, and related resources.
• Governance and Community:
• Transparent policies and sectoral coordination are vital for reducing inefficient irrigation.
• Local communities are key stakeholders as they possess indigenous knowledge essential for managing regional watersheds.
• Technological Tools:
• Includes data-driven monitoring and early-warning tools for disaster management like droughts and floods.

The correct answer is Analytical.

Key Points

• An Analytical tone is characterized by a logical, objective, and systematic examination of a subject. The author breaks down the complex issue of water security into its causes (such as population growth and climate change), its impacts (on public health and food production), and potential solutions. Hence, the tone is Analytical.
• The passage evaluates various methods like sustainable resource management, governance, and technology. It does not just present facts but analyzes how these elements interact—for instance, noting that technology alone is insufficient without social equity and behavioural change. Hence, the passage reflects an analytical approach.
• The Emotional option is incorrect because the passage maintains a neutral, fact-based stance without using language intended to evoke strong personal feelings, bias, or dramatic appeal. Hence, the tone is not Emotional.
• The Narrative option is incorrect because the text does not follow a story arc, characters, or a chronological sequence of events; it is expository and structural in nature. Hence, the tone is not Narrative.
• The Sarcastic option is incorrect as there is no evidence of irony, mockery, or humor used to criticize the subject matter or stakeholders. Hence, the tone is not Sarcastic.

 Additional Information

• Sustainable Resource Management
• It seeks to ensure that freshwater resources are available for future generations while meeting current needs.
• The text emphasizes that effective governance requires transparent policies and the involvement of local communities, providing a comprehensive view of the problem.
• Key technological tools mentioned include data-driven monitoring and efficient irrigation systems, which are analyzed as part of a broader strategy for resource optimization.
• The final inference of the passage is that water access must be equitable to truly achieve security, reinforcing the analytical depth of the writing.

सही उत्तर है- नन्हें

Key Points

• दिए गए वाक्य के लिए नन्हें सबसे उपयुक्त विशेषण है क्योंकि यह चिड़िया के बच्चों के आकार या अवस्था (गुण) की विशेषता बता रहा है।
• विशेषण वह शब्द होते हैं जो किसी संज्ञा या सर्वनाम की विशेषता (गुण, दोष, संख्या, परिमाण आदि) बताते हैं। यहाँ 'बच्चे' विशेष्य है जिसकी विशेषता 'नन्हें' शब्द से प्रकट हो रही है।
• अन्य उदाहरण: नन्हा पौधा, नन्ही चींटी।

अन्य विकल्प -

Important Points 
 विशेषण के भेद-

1. गुणवाचक विशेषण (जैसे- नन्हा, सुंदर, काला)
2. परिमाणवाचक विशेषण (जैसे- दो किलो, थोड़ा)
3. संख्यावाचक विशेषण (जैसे- चार, कुछ, दस)
4. सार्वनामिक विशेषण (जैसे- वह आदमी, यह घर)

Additional Information

इसका सही उत्तर 'पर' है।

Key Points

वाक्य के अनुसार:

• रिक्त स्थान के लिए सही कारक चिह्न 'पर' है। पूर्ण वाक्य होगा - 'छत पर सामान रख दो।'
• यहाँ 'पर' अधिकरण कारक का विभक्ति चिह्न (परसर्ग) है।
• अधिकरण कारक: संज्ञा के जिस रूप से क्रिया के आधार, स्थान या समय का बोध होता है, उसे अधिकरण कारक कहते हैं।
• इस वाक्य में 'छत' वह स्थान या आधार है जहाँ सामान रखने की क्रिया हो रही है। इसलिए, 'पर' सही उत्तर है।

Additional Informationअन्य विकल्पों का विवरण:

ने:

• यह कर्ता कारक का चिह्न है। इसका प्रयोग क्रिया करने वाले के साथ होता है (जैसे - राम ने खाना खाया)। यह यहाँ अनुपयुक्त है।

के लिए:

• यह संप्रदान कारक का चिह्न है। इसका प्रयोग तब किया जाता है जब क्रिया किसी के लिए की जाती है (जैसे - वह फल के लिए गया)।

से:

• यह करण कारक (साधन के अर्थ में) या अपादान कारक (अलग होने के अर्थ में) का चिह्न है। छत से सामान गिर गया (अपादान) हो सकता है, लेकिन 'रख दो' क्रिया के साथ आधार की आवश्यकता है।

उत्थान का सही उत्तर है: पतन

Key Points

• 'उत्थान' शब्द का समानार्थी शब्द 'उन्नति' या 'प्रगति' है।
• 'उत्थान' शब्द का सही विलोम शब्द 'पतन' होगा।
• 'उत्थान' शब्द का अर्थ है — ऊपर उठना, उन्नति या विकास की प्रक्रिया।
• 'पतन' शब्द का अर्थ — नीचे गिरना, अवनति या गिरावट।
• विलोम - जो शब्द किसी शब्द का विपरीत अर्थ प्रकट करते हैं, उन्हें विलोम या विपरीतार्थक शब्द कहा जाता है।

अन्य विकल्प-

Additional Information कुछ अन्य महत्वपूर्ण विलोम शब्द -

दिए गए वाक्य में मौन का पर्यायवाची है: निस्तब्ध

Key Points

• 'मौन' शब्द का सही पर्यायवाची शब्द- 'निस्तब्ध' होगा।
• 'मौन' के अन्य प्रमुख पर्यायवाची शब्द - निस्तब्ध, चुप्पी, शांत, मूक, खामोश, नि:शब्द, अवाक, मुनित्व, तूष्णीं, अभाषी।
• पर्यायवाची - ऐसे शब्द जिनके अर्थ समान हों, पर्यायवाची शब्द कहलाते हैं। इन्हें 'समानार्थी' शब्द भी कहा जाता है।

अन्य विकल्प-

Additional Information कुछ महत्वपूर्ण पर्यायवाची शब्द -

इसका सही उत्तर 'दिलवाई' है।

Key Points

वाक्य के अनुसार:

• रिक्त स्थान के लिए सबसे उपयुक्त शब्द 'दिलवाई' है। पूर्ण वाक्य: अधिकारियों ने नगरपालिका से सड़कों की मरम्मत के लिए कर्मचारियों को सामग्री दिलवाई।
• जब कर्ता स्वयं कार्य न करके किसी दूसरे को कार्य करने के लिए प्रेरित करता है या किसी के माध्यम से कार्य करवाता है, तो उसे प्रेरणार्थक क्रिया कहते हैं।
• यहाँ 'देना' मूल क्रिया है, जिसका प्रथम प्रेरणार्थक 'दिलाना' और द्वितीय प्रेरणार्थक 'दिलवाना' होता है। वाक्य के संदर्भ में अधिकारियों ने नगरपालिका के माध्यम से सामग्री उपलब्ध कराई, इसलिए 'दिलवाई' सही विकल्प है।

Additional Information अन्य विकल्प:

बनवाई -

• यह 'बनाना' क्रिया का प्रेरणार्थक रूप है। यह निर्माण के संदर्भ में उपयोग होता है (जैसे: अधिकारियों ने सड़क बनवाई), लेकिन सामग्री के साथ यह सटीक नहीं बैठता।

करवायी -

• यह 'करना' क्रिया का प्रेरणार्थक रूप है। यदि वाक्य में 'मरम्मत' के बाद रिक्त स्थान होता (जैसे: मरम्मत करवायी), तो यह सही होता, किन्तु सामग्री के बाद इसका प्रयोग अनुचित है।

सुझाई -

• इसका अर्थ 'सुझाव देना' या विचार प्रस्तुत करना होता है। यह वाक्य के क्रियात्मक प्रवाह और 'नगरपालिका से सामग्री...' वाले संदर्भ में उपयुक्त नहीं है।

दिए गए वाक्य में त्रुटिपूर्ण भाग का शुद्ध रूप है- लेखनी की परीक्षा

Key Points

• वाक्य के भाग 'लेखनी की परिक्षा' में वर्तनी संबंधी अशुद्धि है। यहाँ 'परिक्षा' शब्द गलत लिखा गया है, इसका शुद्ध वर्तनी रूप 'परीक्षा' होता है।
• वाक्य शुद्धि का तात्पर्य वाक्य को व्याकरण के नियमों और शब्दों की शुद्ध वर्तनी के अनुसार लिखने से है। एक सार्थक वाक्य में शब्दों का शुद्ध रूप और सही स्थान पर होना अनिवार्य है।
• उदाहरण 1: 'उसकी आध्यात्मिक (शुद्ध वर्तनी) उन्नति हुई।'
• उदाहरण 2: 'हमें उज्ज्वल (शुद्ध वर्तनी) भविष्य की कामना करनी चाहिए।'

अन्य विकल्प -

Important Pointsवाक्य अशुद्धि के मुख्य भेद-

1. वर्तनी संबंधी अशुद्धि
2. शब्द-चयन संबंधी अशुद्धि
3. कारक संबंधी अशुद्धि
4. लिंग और वचन संबंधी अशुद्धि
5. पुनरुक्ति संबंधी अशुद्धि

Additional Information

वाक्य में रेखांकित शब्द मीन का सही पर्यायवाची शब्द मत्स्य है।

Key Points

• 'मीन' शब्द का पर्यायवाची शब्द 'मत्स्य' होगा।
• 'मीन' के अन्य प्रमुख पर्यायवाची शब्द - मछली, झष, जलजीवन, सफरी, अंडभव, विसार, शफरी, झख, जलतोरि, पाठीन।
• पर्यायवाची - वे शब्द जिनका अर्थ समान होता है, उन्हें पर्यायवाची शब्द या समानार्थी शब्द कहते हैं।
• वाक्य का अर्थ: पानी के बीच में रहते हुए भी मछली प्यासी है (यह कबीर दास जी की एक प्रसिद्ध पंक्ति है)।

अन्य विकल्प-

Additional Information कुछ महत्वपूर्ण पर्यायवाची शब्द -

दिए गए वाक्य के रिक्त स्थान के लिए सही शब्द अचानक है। पूर्ण वाक्य: 'रीमा आज अचानक कार्यालय से चली गयी।'

Key Points

• 'रीमा आज अचानक कार्यालय से चली गयी' वाक्य में 'अचानक' शब्द मूल क्रिया-विशेषण है। यह शब्द क्रिया (चली गयी) के होने के आकस्मिक ढंग या रीति को सूचित कर रहा है।
• मूल क्रिया-विशेषण: वे क्रिया-विशेषण जो किसी दूसरे शब्द के मेल से नहीं बनते, बल्कि स्वतंत्र होते हैं, उन्हें मूल क्रिया-विशेषण कहते हैं।
• जैसे- अचानक, ठीक, दूर, फिर, नहीं, सदा, सहसा, कल, आज, प्रायः आदि।
• उदाहरण - वह सहसा बोल पड़ा।

Important Pointsअर्थ के आधार पर क्रिया-विशेषण के भेद-

• स्थानवाचक क्रिया-विशेषण
• कालवाचक क्रिया-विशेषण
• परिमाणवाचक क्रिया-विशेषण
• रीतिवाचक क्रिया-विशेषण

Additional Information

इसका सही उत्तर 'को' है।

Key Points

कारक और विभक्ति के अनुसार:

• दिए गए वाक्य 'रणधीर को मार पड़ी है' में रिक्त स्थान के लिए 'को' सबसे उपयुक्त कारक चिह्न है।
• यहाँ 'मार पड़ना' एक ऐसी क्रिया है जिसका प्रभाव या अनुभव रणधीर पर हो रहा है। हिंदी व्याकरण में अनुभवकर्ता (Experiencer) के साथ अक्सर 'को' विभक्ति का प्रयोग किया जाता है।
• पूर्ण वाक्य: 'रणधीर को मार पड़ी है।'
• इसलिए, सही उत्तर को है।

Additional Information अन्य विकल्पों का विश्लेषण:

ने (कर्ता कारक) -

• इसका प्रयोग प्रायः सकर्मक क्रिया के साथ भूतकाल में किया जाता है (जैसे: रणधीर ने खाना खाया)। 'मार पड़ी' के साथ 'ने' का प्रयोग व्याकरणिक रूप से अशुद्ध है।

का (संबंध कारक) -

• यह दो पदों के बीच संबंध स्थापित करता है (जैसे: रणधीर का घर)। यहाँ यह क्रिया के साथ जुड़कर कोई सार्थक अर्थ नहीं देता।

में (अधिकरण कारक) -

• यह क्रिया के आधार, स्थान या समय का बोध कराता है (जैसे: कमरे में)। 'रणधीर में मार पड़ी' कहना अर्थहीन है।

दिए गए वाक्य में वर्तनी संबंधी त्रुटि वाला शब्द और शुद्ध वाक्य का रूप है- सास्त्रीजी (शुद्ध रूप: शास्त्रीजी)

Key Points

• वाक्य का शुद्ध रूप: 'शास्त्रीजी, अपने सादगीपूर्ण जीवन और दृढ़ राष्ट्रभक्ति से देशवासियों के हृदय में अमिट स्थान बना चुके हैं।'
• दिए गए वाक्य में 'सास्त्रीजी' शब्द की वर्तनी अशुद्ध है। इसमें 'स' के स्थान पर 'श' का प्रयोग होना चाहिए, जिससे सही शब्द 'शास्त्रीजी' बनेगा। साथ ही 'चूके' के स्थान पर 'चुके' का प्रयोग व्याकरणिक दृष्टि से उचित है।
• वाक्य शुद्धि का अर्थ है वाक्य को व्याकरण के नियमों (जैसे- वर्तनी, लिंग, वचन, कारक आदि) के अनुसार शुद्ध करना ताकि अर्थ स्पष्ट हो सके।
• उदाहरण 1: 'अतिथी' (अशुद्ध) - 'अतिथि' (शुद्ध)।
• उदाहरण 2: 'प्रदर्शिनी' (अशुद्ध) - 'प्रदर्शनी' (शुद्ध)।

अन्य विकल्प -

Important Pointsवाक्य अशुद्धि के मुख्य भेद-

1. वर्तनी संबंधी अशुद्धि: शब्दों के वर्णों को गलत लिखने पर होने वाली त्रुटि।
2. मात्रा संबंधी अशुद्धि: स्वरों की छोटी या बड़ी मात्राओं का गलत प्रयोग।
3. लिंग संबंधी अशुद्धि: कर्ता के अनुसार क्रिया का लिंग सही न होना।
4. वचन संबंधी अशुद्धि: एकवचन और बहुवचन का अनुचित प्रयोग।
5. पदक्रम संबंधी अशुद्धि: वाक्य में शब्दों का सही स्थान पर न होना।

Additional Information

अतः सही उत्तर विकल्प 3 (सास्त्रीजी) है।