DSSSB PRT Official Paper (Held On: 18 Feb, 2026 Shift 3) (Previous Year Paper)

The logic followed here is:

Position of Zoha from the right end = 25^th

Position of Piya from the right end = 34^th

Number of people between Zoha and Piya = 34 − 25 − 1 = 8

Since Piya is exactly between Zoha and Minal, the number of people between Piya and Minal is also 8.

Position of Minal from the right end = Position of Piya from the right end + Number of people between them + 1

= 34 + 8 + 1

= 43^rd

Position of Minal from the left end = 6^th (Given)

Total number of people in the row = (Position of Minal from the right end) + (Position of Minal from the left end) − 1

= 43 + 6 − 1

= 48

Hence, the correct answer is 'Option 1'.

The water image of ,

Hence, the correct answer is "Option 3 "

Preparing the family tree by using the following symbols:

1. A is the sister of B.
2. B is the son of C.
3. C is married to D.
4. D is the daughter of E.
5. E is the wife of F.
6. G is the brother of D

The family tree diagram,

From the family tree, it is evident that F is the father of D, and D is the mother of A. Therefore, F is the maternal grandfather or Mother’s father of A.

Hence, the correct answer is 'Option 4'.

Given: (left) 471 496 687 492 678 (right)

• The second digit of the highest number is: 8 (687)
• The second digit of the lowest number is: 7 (471)
• So, the addition of the second digit of the highest number and the second digit of the lowest number is: 8 + 7 = 15.

Hence, the correct answer is 'Option 1'.

The logic follows here, 

The code for P is 7. 

Hence, the correct answer is "option 1"

Given :  (Left) E B J E R A J N I D U R N L U H L T R (Right)

Required condition: Vowel → Consonant → Vowel

(Left) E B J E R A J N I D U R N L U H L T R (Right)

There are exactly 2 such consonants in the series.

Hence, the correct answer is "option 1"

BODMAS Rule:

The given mappings are:

Given Equation: 36 B 3 C 18 D 16 A 2 = ?

Replace the letters with their respective mathematical signs and using the BODMAS rule:

= 36 × 3 + 18 − 16 ÷ 2

= 36 × 3 + 18 − 8

= 108 + 18 − 8

= 126 − 8

= 118

Hence, the correct answer is "option 1"

The logic followed here is:

Option 1)  TV - WY,

Option 2) KM - NP,

Option 3) CE - GI

Option 4) HJ - KM,

Therefore, the letter-cluster pair that is different from the others is CE - GI.

Hence, the correct answer is 'Option 3'.

The logic followed here is:

Given Word : AWAITING

• Vowels (A, E, I, O, U) are replaced by the letter immediately preceding them in the English alphabetical order (Vowel − 1).
• Consonants are replaced by the letter immediately following them in the English alphabetical order (Consonant + 1).

• The new group of letters formed is: Z, X, Z, H, U, H, O, H.
• The letter that appears exactly twice is Z.

Hence, the correct answer is "option 1".

The logic followed here is:

• Total number of people in the row = 39
• Position of Lavanya from the left end = 17^th
• Rajat sits 5^th to the right of Lavanya.
• Position of Rajat from the left end = 17 + 5 = 22^nd

Position of Rajat from the right end = Total number of people − Position of Rajat from the left end + 1

= 39 − 22 + 1

= 17 + 1

= 18

So, Rajat is 18^th from the right end.

Hence, the correct answer is "Option 1".

The water image of the given figure,

Hence, the correct answer is "option 1".

Logic followed here is.

The pattern observed is: (First Number × 3) + 15.

For 16 is related to 63 ,

• (16 × 3) + 15 = 48 + 15 = 63

For 28 is related to 99,

• (28 × 3) + 15 = 84 + 15 = 99

Applying the same logic the number related to 12:

• (12 × 3) + 15 = 36 + 15 = 51

Therefore, the number related to 12 is 51.

Hence, the correct answer is "Option 2"

Given Series: (Left) R N R Y V I F E D H I T O J U E D S A B S I H R S A C (Right)

Required pattern: Consonant - Vowel - Vowel.

(Left) R N R Y V I F E D H I T O J U E D S A B S I H R S A C (Right)

Therefore, there is only One such vowel in the given series.

Hence, the correct answer is "option 1".

The logic followed here is:

For TRUE – RUTE – EURT .

WASH – ASWH – HSAW ,

Applying the same logic, 

Hence, the correct answer is "Option 2"

The logic followed here is:

Option 1) IB-EG,

Option 2) TM-PS,

Option 3) QJ-MO,

Option 4) NG-JL,

Therefore, the letter-cluster pair that is different from the others is TM-PS.

Hence, the correct answer is 'Option 2'.

Given: Seven people, D, A, N, U, B, E and S are sitting in a row, facing north.

1. No one sits to the right of S.
2. Only three people sit between S and B.
3. Only two people sit between B and A.
4. E sits third to the left of D.
5. U sits to the immediate right of D.

The Final Arrangement is, 

Three people sit between N and A

Hence, the correct answer is "Option 2".

Given number: 6543127

Arranged in ascending order from left to right, the new number formed is:

Left 1  2  3  4  5  6   7  Right 

• The second digit from the left in the new number is: 2 (1234567)
• The second digit from the right in the new number is: 6 (1234567)

So, the sum of the digit which is second from the left and the digit which is second from the right is : 2 + 6 = 8.

Hence, the correct answer is 'Option 1'.

The logic followed here is:

Combining the resulting letters from each position, we get ZCU.

Hence, the correct answer is  "option 4"

Given: Six people T, A, R, G, U, and S, live on floors 1 to 6.

1. S lives on the floor numbered 4.
2. Only two people live between S and G.
3. Only T lives between S and U.
4. A lives immediately below S

The Final Arrangement is,

Thus, R lives on floor 2.

Hence, the correct answer is "Option 4".

The logic followed here is

• 149 + 12 = 161
• 161 + 17 = 178
• 178 + 22 = 200
• 200 + 27 = 227
• 227 + 32 = 259

Thus, the missing term in the series is 259.

Hence, the correct answer is 'Option 3';

The correct answer is Akbar.

Key Points

• Akbar, the third Mughal Emperor, was the first ruler of the dynasty to abolish the Jizya tax in 1564. This tax was a discriminatory per capita levy imposed on non-Muslim subjects (known as Dhimmis).
• The abolition was a central part of his policy of Sulh-i-kul (universal peace) and was intended to bridge the divide between the Mughal Crown and his majority Hindu subjects, particularly the powerful Rajput clans.
• Before removing Jizya, Akbar had already abolished the Pilgrimage Tax in 1563, which was previously collected from Hindus at sacred sites like Prayagraj and Mathura.
• His inclusive administrative reforms helped transform the Mughal Empire from a foreign military state into a more integrated Indian Empire during his reign from 1556 to 1605.
• Though the tax was briefly reintroduced in 1575 due to pressure from the Ulema, Akbar permanently rescinded it again in 1579-1580 following his declaration of the Mahzar (Infallibility Decree).

 Additional Information

• Historical Context of Jizya:
• Qutb-ud-din Aibak first introduced Jizya in India, and later Firoz Shah Tughlaq became the first sultan to impose it on Brahmins.
• The tax was later reintroduced by Aurangzeb in 1679 as part of his orthodox Islamic policies to fund his Deccan Wars.
• Other Mughal Emperors:
• Babur: As the founder of the dynasty in 1526, he did not introduce significant social or tax reforms of this nature during his short reign.
• Jahangir and Shah Jahan: Both generally followed the liberal precedents set by Akbar, though Shah Jahan saw a gradual shift towards more traditional administrative practices.
• The tax was finally and permanently abolished by Muhammad Shah 'Rangeela' in 1720 at the request of the Sayyid Brothers.

The correct answer is National Education Policy 2020.

Key Points

• The National Sports Policy 2025 is strategically aligned with the National Education Policy 2020 (NEP 2020) to dismantle the traditional silos between curricular, co-curricular, and extra-curricular activities in Indian schools.
• The integration promotes sports-integrated pedagogy, an approach where physical movement and games are utilized as cross-curricular pedagogical tools to enhance cognitive development, socio-emotional skills, and physical health.
• Under this framework, sports are recognized as a formal subject within the National Curriculum Framework (NCF), allowing students to earn academic credits for sporting excellence and participation, ensuring it is no longer treated as a secondary interest.
• This synergy aims to achieve the goals of the Fit India Movement by embedding physical literacy into the daily lives of students starting from the foundational stage (ages 3 to 8) as defined in the 5+3+3+4 educational structure.
• The policy envisions a robust talent identification mechanism where educational institutions serve as the primary nurseries for identifying young athletes for the Olympic and Asian Games cycles.

 Additional Information

• National Education Policy 2020 (NEP 2020):
• Approved on July 29, 2020, based on the recommendations of the K. Kasturirangan Committee.
• It replaced the National Policy on Education, 1986, and aims to make India a global knowledge superpower.
• Key pillars include Access, Equity, Quality, Affordability, and Accountability.
• Ministry of Youth Affairs and Sports Initiatives:
• The Khelo India Programme works alongside NEP 2020 to provide infrastructure and financial support to schools for developing State-of-the-art sports facilities.
• The Target Olympic Podium Scheme (TOPS) complements these educational reforms by providing specialized training to elite athletes identified through the school system.

The correct answer is Uttarakhand.

Key Points

• The Hurka Baul is a prominent folk dance form primarily practiced in the Kumaon region of the hill state of Uttarakhand.
• This dance is intrinsically linked to agriculture, performed specifically during the manual cultivation of paddy and maize crops during the Kharif season.
• The performance gets its name from the Hurka, a small, hourglass-shaped percussion instrument similar to a Damru, which provides the rhythmic foundation for the singers and dancers.
• While the lead performer plays the drum and narrates heroic tales of valor and folklore, the agricultural workers move in synchronization, effectively turning the labor of transplanting crops into a rhythmic ritual.
• Geographically, it is most prevalent in the districts of Pithoragarh, Almora, Champawat, and Bageshwar, serving as a collective social activity to reduce the fatigue of farming.

 Additional Information

• Uttar Pradesh
• Home to the Classical dance Kathak and diverse folk forms such as Charkula, Raslila, Kajri, and Nautanki, which often depict stories of Lord Krishna.
• Punjab
• Characterized by high-energy performances like Bhangra, traditionally performed by men during the Baisakhi harvest, and Gidda, a graceful circle dance performed by women.
• West Bengal
• Known for the Chhau dance (specifically the Purulia style), which uses elaborate masks, as well as Gambhira, Brita, and the Baul musical tradition (distinct from the Hurka Baul of the hills).

The correct answer is 1627 AD.

Key Points

• The Dutch East India Company, historically known as the VOC (Vereenigde Oost-Indische Compagnie), established its first commercial presence in the Bengal region in 1627.
• The first Dutch settlement and trading factory were founded at Pipely (Pipli), which was situated at the mouth of the Subarnarekha River in the Balasore district of the then Bengal Subah.
• This strategic entry into Bengal was motivated by the high demand for commodities such as saltpeter, silk, cotton textiles, and opium in both European and East Asian markets.
• The establishment in 1627 allowed the Dutch to successfully challenge the Portuguese trade monopoly in the Bay of Bengal and expand their commercial network deeper into the Mughal Empire.
• Following their success at Pipely, the Dutch expanded further inland, establishing significant factories in Balasore, Kasimbazar, Patna, and Chinsurah.

 Additional Information

• Growth of the Dutch Presence:
• By 1655, the volume of trade became so significant that a separate Directorate of Bengal was officially formed to manage the Dutch operations in the region.
• The headquarters eventually shifted to Chinsurah (Chinsura) in 1656, where the Dutch constructed Fort Gustavus to protect their interests.
• Economic Impact:
• The Dutch were major exporters of Bengal saltpeter, which was a critical raw material for the manufacture of gunpowder in Europe.
• They also dominated the opium trade, shipping vast quantities from Bengal to the Indonesian Archipelago (Batavia).
• Decline and Cession:
• The political influence of the Dutch in Bengal suffered a decisive blow during the Battle of Bedara in 1759, where they were defeated by British forces under Robert Clive.
• The remaining Dutch territories in India, including Chinsurah, were finally ceded to the British under the terms of the Anglo-Dutch Treaty of 1824.

The correct answer is Giro d'Italia.

Key Points

• The Giro d'Italia is one of the three prestigious Grand Tours of professional road cycling, traditionally held over three weeks across Italy and neighboring regions.
• For the 2025 edition, which marks the 108th running of the race, organizers announced a historic passage through Vatican City, the smallest independent state in the world.
• This event marks the first time in the history of the race that the peloton will officially pass through the Vatican, specifically traversing St. Peter's Square.
• The inclusion of the Vatican is intended to coincide with the Jubilee Year 2025 (Holy Year), a major event in the Catholic Church expected to attract millions of pilgrims to Rome.
• The route highlights the symbolic connection between Italian sporting culture and the religious significance of the Holy See during the Jubilee celebrations.

 Additional Information

• Grand Tours of Cycling:
• Tour de France: The oldest and most famous of the three Grand Tours, primarily held in France during July.
• Vuelta a España: The final Grand Tour of the calendar year, held in Spain during late August and September.
• Giro d'Italia: Known for the Maglia Rosa (Pink Jersey), which is awarded to the overall leader of the general classification.
• Jubilee 2025:
• The theme for the 2025 Jubilee is Pilgrims of Hope, as designated by Pope Francis.
• Jubilees are special years of remission of sins and universal pardon, usually occurring every 25 years.
• Tour Down Under:
• Unlike the Grand Tours, this is a stage race held in and around Adelaide, South Australia, and is the first event of the UCI World Tour season.

The correct answer is Gita-Rahasya.

Key Points

• Bal Gangadhar Tilak, also known as Lokmanya Tilak, was arrested in July 1908 on charges of sedition for his articles published in his Marathi newspaper, Kesari.
• He was sentenced to six years of rigorous imprisonment and was deported to the Mandalay Jail in Burma (present-day Myanmar), where he remained until 1914.
• While in solitary confinement at Mandalay, Tilak authored his magnum opus, Gita-Rahasya (The Secret of the Bhagavad Gita), which he originally wrote in Marathi.
• In this work, also referred to as Karmayoga Shastra, Tilak provided a new interpretation of the Bhagavad Gita, arguing that its core message is Karma Yoga (the path of selfless action) rather than renunciation.
• He aimed to mobilize the Indian masses by teaching that performing one's duty without attachment to the results was the highest form of spiritual practice and essential for national service.

 Additional Information

• Scholarly Contributions:
• The Arctic Home in the Vedas: Written by Tilak in 1903, this book proposed the theory that the North Pole was the original home of the Aryans during the pre-glacial period.
• Orion: Published in 1893, this work investigated the antiquity of the Vedas using astronomical observations.
• Journalism and Organizations:
• Tilak founded two major newspapers: Kesari (in Marathi) and Mahratta (in English), which served as platforms for his nationalist ideology.
• He was a founding member of the Deccan Education Society (1884) and later played a pivotal role in the All India Home Rule League established in 1916.
• Social and Political Impact:
• Tilak is credited with popularizing the Ganpati Festival and Shivaji Jayanti to foster a sense of unity and national pride among Indians.
• He gave the famous slogan: 'Swaraj is my birthright, and I shall have it!' which became a rallying cry for the Indian independence movement.

The correct answer is Su-30 MKI.

Key Points

• The Defence Research and Development Organisation (DRDO) successfully conducted the release trials of the Gaurav long-range glide bomb from a Su-30 MKI fighter aircraft in April 2025.
• The trials were carried out at the Integrated Test Range (ITR) located off the coast of Odisha to evaluate the weapon's integration, separation, and guidance performance.
• Gaurav is an indigenously developed 1,000 kg class Long-Range Glide Bomb (LRGB), categorized as a precision-guided munition capable of hitting targets at significant standoff distances.
• The bomb is equipped with a GPS-aided Inertial Navigation System (GAINS), which allows it to navigate toward the coordinate-defined target with high accuracy even in the absence of continuous satellite signals.
• It features a winged configuration that provides the necessary lift to achieve a glide range of approximately 100 kilometers, enabling the launch aircraft to remain outside the envelope of enemy air defense systems.

 Additional Information

• Su-30 MKI:
• It is a twin-engine, multi-role air superiority fighter developed by Russia's Sukhoi and manufactured under license by Hindustan Aeronautics Limited (HAL) for the Indian Air Force (IAF).
• The aircraft acts as a versatile platform for various indigenous weapons including the BrahMos supersonic cruise missile and the Astra Beyond Visual Range Air-to-Air Missile.
• Research Centre Imarat (RCI):
• Located in Hyderabad, this DRDO laboratory is the lead agency responsible for the design and development of the Gaurav and Gautam glide bombs.
• LRGB Variants:
• While Gaurav is the winged version for long-range strikes, its counterpart Gautam is a non-winged version designed for high-precision strikes at shorter ranges.

The correct answer is Must be a citizen of India and at least 35 years old.

Key Points

• Article 157 of the Constitution of India explicitly specifies only two mandatory qualifications for a person to be eligible for appointment as the Governor of a state.
• The first qualification is that the person must be a citizen of India, which ensures the individual holds national allegiance.
• The second qualification is that the person must have completed the age of 35 years, which is consistent with the age requirement for the President and Vice-President of India.
• The Governor is appointed by the President of India by warrant under his hand and seal, as per the provisions of Article 155.
• These qualifications are strictly constitutional, and the Constitution does not prescribe any minimum educational qualification or professional background for the post.

 Additional Information

• Conditions of Office (Article 158):
• The Governor shall not be a member of either House of Parliament or a House of the Legislature of any state. if an MP or MLA is appointed, they must vacate their seat upon assuming the governorship.
• The appointee should not hold any other office of profit under the government.
• The emoluments and allowances of the Governor cannot be diminished during their term of office.
• Administrative Conventions:
• To ensure neutrality, a convention exists where the appointee is typically an outsider (not a resident of the state where they are appointed).
• The Union Government often consults the Chief Minister of the concerned state before the appointment, as recommended by the Sarkaria Commission, though this is not a constitutional mandate.
• Tenure and Role:
• The Governor holds office during the pleasure of the President, with a normal term of five years.
• The Governor acts as the Constitutional Head of the state and serves as a vital link between the Central Government and the State Government.

The correct answer is 2008.

Key Points

• The Prime Minister's Employment Generation Programme (PMEGP) was launched by the Government of India in the year 2008. It is a credit-linked subsidy scheme aimed at generating self-employment opportunities through the establishment of micro-enterprises in both non-farm rural and urban areas.
• The program was formed by merging two existing schemes, namely the Prime Minister’s Rozgar Yojana (PMRY) and the Rural Employment Generation Programme (REGP), which were in operation until March 2008.
• The Ministry of Micro, Small and Medium Enterprises (MSME) serves as the nodal ministry for this scheme, providing the policy framework and funding for its execution.
• At the national level, the Khadi and Village Industries Commission (KVIC) is the single nodal agency responsible for the implementation of the PMEGP across the country.

 Additional Information

• The implementation structure of the PMEGP involves several state-level agencies to ensure grassroots reach:
• State KVIC Directorates and State Khadi and Village Industries Boards (KVIBs) focus primarily on rural implementations.
• District Industries Centres (DICs) handle the scheme implementation in both rural and urban areas, coordinated by state governments.
• Financial Institutions: Public sector banks, regional rural banks, and cooperative banks play a critical role by providing the necessary bank credit and facilitating the margin money subsidy provided by the government.
• Eligibility Criteria: Any individual above 18 years of age is eligible to apply. For setting up manufacturing units costing above 10 lakh or service units costing above 5 lakh, the beneficiary must have passed at least the VIII standard.
• Objectives: The primary goal is to arrest the migration of rural youth to urban areas by providing them with sustainable employment opportunities locally and increasing the wage-earning capacity of traditional artisans.

The correct answer is Decreasing bank rate.

Key Points

• The Bank Rate is the official interest rate at which the central bank (such as the Reserve Bank of India) lends long-term funds to commercial banks without requiring any collateral.
• To increase the money supply in the economy, the central bank adopts an expansionary monetary policy, which involves lowering the Bank Rate.
• A reduction in the Bank Rate lowers the cost of borrowing for commercial banks, allowing them to acquire funds more cheaply from the central authority.
• As their cost of funds decreases, commercial banks pass this benefit to consumers by lowering their own lending rates, such as those for home, auto, and business loans.
• Lower interest rates stimulate demand for credit, leading to increased investment and consumption expenditure, which effectively boosts the total volume of money circulating in the economy.

 Additional Information

• Cash Reserve Ratio (CRR):
• It is the percentage of Net Demand and Time Liabilities (NDTL) that commercial banks are mandated to keep as cash reserves with the central bank.
• Increasing the CRR forces banks to keep more money parked with the RBI, thereby reducing their lending capacity and decreasing the money supply.
• Contractionary Monetary Policy:
• This involves increasing the bank rate or repo rate to curb inflation by making borrowing more expensive, which slows down the velocity of money.
• Statutory Liquidity Ratio (SLR):
• This is the minimum percentage of deposits that a commercial bank must maintain in the form of liquid assets like gold or government-approved securities.
• Lowering the SLR is another quantitative tool used to inject liquidity into the banking system.

The correct answer is Sub-tropical high.

Key Points

• The Sub-tropical high pressure belt, also known as the Horse Latitudes, is located approximately between 30° to 35° North and South latitudes in both hemispheres.
• This belt is formed due to the subsidence of air that rises at the Equatorial Low Pressure Belt. As the air reaches the upper troposphere and moves towards the poles, it cools and sinks around the 30° latitude mark.
• Descending air is compressed and undergoes adiabatic heating, which significantly lowers its relative humidity and prevents the formation of clouds.
• The high atmospheric stability and anticyclonic conditions created by this sinking air lead to dry climates and clear skies.
• Consequently, most of the world's major hot deserts, such as the Sahara in Africa, the Arabian Desert in Asia, and the Atacama in South America, are located within this pressure zone.

 Additional Information

• Equatorial Low
• Located near the 0° latitude, also known as the Doldrums or the Inter-Tropical Convergence Zone (ITCZ).
• It is characterized by intense heating, convectional currents, and high annual rainfall.
• Sub-polar Low
• Found around 60° to 65° latitudes in both hemispheres.
• This zone is created by the convergence of warm Westerlies and cold Polar Easterlies, resulting in cyclonic activity.
• Polar High
• Situated at the North and South Poles (90°).
• High pressure is maintained here due to extremely low temperatures causing the air to remain dense and sink permanently.

The correct answer is - $2H_{2}O \rightarrow 4H^{+} + 4e^{-} + O_{2}$

Key Points

• Photolysis of Water
• Photolysis is the process of the chemical decomposition of water molecules into protons (H⁺), electrons (e⁻), and oxygen (O₂) using light energy.
• This reaction takes place during the light-dependent stage of photosynthesis and is specifically associated with Photosystem II (PSII).
• The chemical equation for this process is: $2H_{2}O \rightarrow 4H^{+} + 4e^{-} + O_{2}$.
• It occurs on the inner side of the thylakoid membrane (thylakoid lumen) in the chloroplasts.
• Role in Photosynthesis
• The electrons released during photolysis are used to replace the electrons lost by the reaction center P680 of Photosystem II when it is excited by light.
• The protons generated accumulate in the thylakoid lumen, creating a proton gradient that powers ATP synthesis.
• Oxygen is released as a metabolic byproduct, which is essential for aerobic respiration in most living organisms.

Additional Information

• Oxygen Evolving Complex (OEC)
• Photolysis is facilitated by a protein complex known as the Oxygen Evolving Complex, which contains essential inorganic ions like Manganese (Mn), Calcium (Ca), and Chloride (Cl).
• Other Reactions in Photosynthesis
• Photophosphorylation: The reaction $ADP + Pi \rightarrow ATP$ represents the synthesis of energy molecules using light energy.
• NADP Reduction: Electrons and protons are finally used to reduce NADP⁺ to NADPH, which provides reducing power for the Calvin Cycle (Dark Reaction).
• Photorespiration: The reaction involving RuBP and O₂ to form 3-PGA and phosphoglycolate occurs when the enzyme Rubisco acts as an oxygenase, typically under conditions of high temperature or low carbon dioxide concentration.

The correct answer is A disqualified MP under the Tenth Schedule cannot be appointed as a minister under Article 75(1B) for a specified period..

Key Points

• Article 75(1B) was inserted into the Constitution of India by the 91st Constitutional Amendment Act, 2003. It mandates that any member of either House of Parliament belonging to any political party who is disqualified for being a member under the Tenth Schedule (Anti-Defection Law) shall also be disqualified to be appointed as a Minister until their term expires or they are re-elected. Hence, statement 1 is correct.
• The Fourth Schedule deals exclusively with the allocation of seats in the Rajya Sabha (Council of States) to the various States and Union Territories, while the collective responsibility of the Council of Ministers to the Lok Sabha is a constitutional mandate under Article 75(3). Hence, statement 2 is incorrect.
• According to Article 75(2), Ministers hold office during the pleasure of the President; however, the Ninth Schedule is reserved for acts and regulations (primarily concerning land reforms) that are protected from judicial review under Article 31B. Hence, statement 3 is incorrect.
• The forms of Oath or Affirmation for Union and State Ministers are explicitly prescribed in the Third Schedule, whereas the Second Schedule outlines the emoluments, allowances, and privileges of high-ranking officials such as the President, Governors, and Judges. Hence, statement 4 is incorrect.

 Additional Information

• Tenth Schedule:
• Introduced by the 52nd Amendment Act, 1985, it provides for the disqualification of members on grounds of defection.
• The 91st Amendment Act, 2003 strengthened this by removing the protection for one-third splits in political parties.
• Ministerial Strength:
• The 91st Amendment also stipulated that the total number of ministers, including the Prime Minister, in the Central Council of Ministers shall not exceed 15% of the total strength of the Lok Sabha.
• Constitutional Oaths:
• The Third Schedule covers oaths for Members of Parliament, Union Ministers, Supreme Court Judges, and the Comptroller and Auditor General (CAG).

The correct answer is Article 75.

Key Points

• According to Article 75(1) of the Indian Constitution, the Prime Minister shall be appointed by the President of India.
• The other Ministers of the Union Council of Ministers are also appointed by the President, but strictly on the advice of the Prime Minister.
• Article 75(3) establishes the principle of Collective Responsibility, stating that the Council of Ministers is collectively responsible to the Lok Sabha (House of the People).
• A Minister must be a member of either house of Parliament; if a person who is not a member is appointed, they must secure a seat within six consecutive months, as per Article 75(5).
• The 91st Amendment Act, 2003, amended this article to limit the size of the Council of Ministers to 15% of the total strength of the Lok Sabha.

 Additional Information

• Article 80:
• Dictates the Composition of the Council of States (Rajya Sabha).
• It stipulates a maximum strength of 250 members, where 12 members are nominated by the President for expertise in Literature, Science, Art, and Social Service.
• Article 60:
• Relates to the Oath or affirmation by the President.
• The oath is administered by the Chief Justice of India or, in their absence, the senior-most Judge of the Supreme Court.
• Article 62:
• Specifies the time of holding elections to fill a vacancy in the office of the President.
• An election to fill a vacancy caused by the expiration of the term must be completed before the term expires.

The correct answer is Hindustani.

Key Points

• Hindustani classical music is a major tradition of Indian classical music that originated and flourished in North India, eventually spreading across the northern, western, and eastern parts of the Indian subcontinent.
• It began to diverge from the unified Indian musical system around the 12th century CE, absorbing significant influences from Persian, Arabic, and Central Asian musical traditions during the Delhi Sultanate and Mughal Empire.
• The system is fundamentally based on Ragas (melodic frameworks) and Talas (rhythmic cycles), with a heavy emphasis on improvisation and the exploration of emotional nuances.
• It is categorized into several vocal styles, the most prominent being Dhrupad, which is characterized by its austere and spiritual nature, and Khayal, which allows for greater technical virtuosity and ornamentation.
• The tradition is preserved through Gharanas, which are specialized schools or lineages of music such as the Gwalior, Agra, Kirana, and Jaipur-Atrauli gharanas, each maintaining unique stylistic interpretations.

 Additional Information

• Carnatic Music
• This is the classical music tradition of South India, predominantly practiced in states like Tamil Nadu, Karnataka, Kerala, and Andhra Pradesh.
• Unlike the Hindustani tradition, it remained relatively free from external influences and is highly composition-focused, centering on the works of the Trinity of Carnatic Music: Tyagaraja, Muthuswami Dikshitar, and Syama Sastri.
• Folk Music
• Folk music refers to the diverse, regional musical styles of rural India, such as Baul of Bengal, Bhangra of Punjab, and Lavani of Maharashtra.
• It is primarily an oral tradition that reflects the cultural identity and social rituals of specific communities rather than following a strict codified classical theory.

The correct answer is Enhancement of income levels in industrial sectors.

Key Points

• Rural Development is an integrated and comprehensive process focusing on the social and economic upliftment of areas that lag behind in the overall development of the national economy, primarily the villages.
• The Enhancement of income levels in industrial sectors is generally associated with the secondary sector of the economy, which focuses on manufacturing, heavy industries, and urban-centric growth rather than the specific structural needs of the rural agrarian sector.
• Literacy and skill development are foundational to human resource development in rural areas, as they improve the quality of life and increase the productivity of the rural workforce in both farm and non-farm activities.
• Developing the productive resources of each locality ensures that rural communities can utilize their own natural and human capital, such as land, water, and local crafts, to create sustainable livelihoods.
• Infrastructure development, including the provision of rural roads, electricity, irrigation, and communication facilities, is essential for connecting rural markets and reducing the poverty gap through targeted economic measures.

 Additional Information

• Literacy and Skill Development:
• Focuses on female literacy and vocational training to empower marginalized sections.
• Enables the rural population to adopt modern agricultural technologies and diversify into service sectors.
• Productive Resources of Each Locality:
• Includes Land Reforms to ensure equitable distribution and optimal use of soil resources.
• Involves the development of allied activities such as fisheries, poultry, and horticulture.
• Infrastructure and Poverty Measures:
• Poverty Alleviation Programs like MGNREGA provide guaranteed wage employment to enhance rural purchasing power.
• Infrastructure such as rural godowns and cold storage prevents post-harvest losses and improves food security.

CONCEPT:

• Vinegar is a versatile liquid used in cooking, preservation, and cleaning, which primarily consists of water and acetic acid.
• It is produced through a two-step fermentation process where sugars are first converted into ethanol and then oxidized into acid.

EXPLANATION:

• The main acid component in vinegar is acetic acid (also systematically named ethanoic acid).
• In typical household vinegar, the concentration of acetic acid usually ranges from 4% to 8% by volume.
• The chemical formula for acetic acid is CH₃COOH. It is this carboxylic acid that gives vinegar its characteristic pungent smell and sour flavor.
• Other acids listed serve different roles:
• Nitric acid is a highly corrosive mineral acid used in fertilizers and explosives.
• Tannic acid is a type of polyphenol found in various plants, seeds, and tea.
• Citric acid is a weak organic acid found naturally in citrus fruits like lemons and oranges.
• Since acetic acid is the defining ingredient produced during the fermentation of ethanol, it is the primary acidic constituent of vinegar.

Therefore, the main acid component in vinegar is acetic acid.

The correct answer is Bihar.

Key Points

• According to the Census 2011, Bihar was identified as the state with the lowest literacy rate in India, recording a total literacy of 61.80%.
• The gender-wise breakdown of literacy in Bihar showed a significant disparity, with the male literacy rate at 71.20% and the female literacy rate at a mere 51.50%.
• The Census Commissioner of India defines the literacy rate as the percentage of the population aged 7 years and above who can both read and write with understanding in any language.
• While the National Literacy Rate of India stood at 74.04% in 2011, Bihar lagged significantly behind the national average, reflecting challenges in educational infrastructure and accessibility during that decade.
• Even among the bottom-performing states, Arunachal Pradesh (65.38%) and Rajasthan (66.11%) maintained higher literacy levels compared to Bihar.

 Additional Information

• Comparison with other states mentioned in options:
• Rajasthan: This state recorded a literacy rate of 66.11%. It is notable for having one of the lowest female literacy rates in the country at approximately 52.12%.
• Uttar Pradesh: As India's most populous state, it registered a literacy rate of 67.68%, with male literacy at 77.28% and female literacy at 57.18%.
• Madhya Pradesh: The literacy rate for this state was reported at 69.32% in the 2011 Census.
• National Extremes in 2011:
• Kerala: Achieved the highest literacy rate in India at 94.00%, followed by Mizoram at 91.33%.
• Lakshadweep: Held the highest literacy rate among all Union Territories at 91.85%.
• The 15th Indian Census (2011) revealed that the number of literates in India increased from 560.7 million in 2001 to 763.5 million in 2011.

The correct answer is 2024.

Key Points

• Aditya-L1 is the first dedicated Indian space mission for solar observation, designed and developed by the Indian Space Research Organisation (ISRO).
• The spacecraft was launched on September 2, 2023, from the Satish Dhawan Space Centre in Sriharikota aboard the PSLV-C57 rocket.
• Following a journey spanning approximately four months and covering nearly 1.5 million kilometers, the spacecraft successfully performed its final orbital maneuver on January 6, 2024.
• This maneuver successfully inserted Aditya-L1 into a halo orbit around the Sun-Earth Lagrange point 1 (L1), which is the year it officially reached its operational station.
• The L1 point provides a continuous, unobstructed view of the Sun without any occultation or eclipses, enabling real-time monitoring of solar activities and their effect on space weather.

 Additional Information

• Lagrange Point 1 (L1):
• It is one of five points in the Sun-Earth system where the gravitational forces of the two large masses balance the centripetal force required for a small object to move with them.
• The L1 point is located about 1 percent of the total distance from the Earth to the Sun.
• Scientific Payloads:
• The mission carries seven payloads to observe the photosphere, chromosphere, and the corona.
• Key instruments include the Visible Emission Line Coronagraph (VELC) for corona imaging and the Solar Ultraviolet Imaging Telescope (SUIT) for near-UV imaging.
• Mission Goals:
• To understand the problem of coronal heating, coronal mass ejections (CMEs), and the physics of the solar corona and its heating mechanism.

The correct answer is Liverpool.

Key Points

• The World Boxing Championships 2025 are scheduled to be hosted in the city of Liverpool, located in the United Kingdom, marking a major milestone for the sport.
• This event is the inaugural World Championships organized by World Boxing, the international federation established in 2023 to ensure boxing remains a part of the Olympic Games.
• The tournament is set to take place in September 2025 at the M&S Bank Arena, a prestigious venue on Liverpool's waterfront with a capacity to hold over 11,000 spectators.
• In a significant move toward gender equality, the 2025 Championships will feature both Elite Men and Elite Women competing simultaneously in the same tournament for the first time under this governing body.
• Liverpool was chosen due to its historical status as a boxing powerhouse, having produced numerous Olympic and World Champions, as well as its success in hosting events like the 2022 World Gymnastics Championships.
• The bid for the championships was a collaborative effort involving GB Boxing, England Boxing, and the Liverpool City Council, supported by National Lottery funding.
• Therefore, the correct option is 2.

 Additional Information

• World Boxing:
• Formed as a breakaway from the International Boxing Association (IBA) to address concerns regarding governance, refereeing, and financial transparency.
• It aims to achieve full recognition from the International Olympic Committee (IOC) to secure boxing's place in Los Angeles 2028.
• Venue Details:
• The M&S Bank Arena is part of the ACC Liverpool complex and has previously hosted high-profile events such as the Eurovision Song Contest 2023.
• Geographical Context:
• Liverpool is a major city in North West England known globally for its cultural impact and sporting excellence, particularly in football and combat sports.

Shortcut Trick

Slant height (l) = √(9² + 12²) = 15 m

Total Surface Area (including base) = πr(l + r)

⇒ Area = 3.14 × 9 × (15 + 9) = 3.14 × 9 × 24 = 678.24 m²

Total Cost = Area × Rate = 678.24 × 350 = ₹2,37,384

∴ The correct answer is ₹2,37,384.

Alternate Method

Given:

Radius (r) = 9 m

Height (h) = 12 m

Price of concrete = ₹350 per m²

π = 3.14

Formula Used:

Slant Height (l) = √(r² + h²)

Total Surface Area (TSA) = πrl + πr²

Calculations:

⇒ l = √(9² + 12²)

⇒ l = √(81 + 144) = √225 = 15 m

⇒ TSA = πr(l + r)

⇒ TSA = 3.14 × 9 × (15 + 9)

⇒ TSA = 3.14 × 9 × 24

⇒ TSA = 3.14 × 216 = 678.24 m²

⇒ Total Cost = Area × Rate per m²

⇒ Total Cost = 678.24 × 350

⇒ Total Cost = ₹2,37,384

∴ The correct answer is ₹2,37,384.

Additional Information

Pythagorean Triplet

The values 9, 12, and 15 form a Pythagorean triplet (3:4:5 ratio multiplied by 3), allowing for quick calculation of slant height.

Curved Surface Area (CSA)

The area of the conical part only is given by CSA = πrl. For this tower, CSA = 3.14 × 9 × 15 = 423.9 m².

Base Area of Cone

The base of a cone is a circle with area = πr². For this tower, Base Area = 3.14 × 81 = 254.34 m².

Volume of a Cone

If required to find the capacity or amount of concrete by volume, use V = (1/3) × πr²h.

Shortcut Trick

Downstream speed (D) = 12 / 1 = 12 km/hr

Upstream speed (U) = 12 / 1.2 = 10 km/hr (as 1 hr 12 min = 1.2 hr)

Speed in still water = (D + U) / 2 = (12 + 10) / 2 = 11 km/hr

∴ The correct answer is 11 km/hr.

Alternate Method

Given:

Downstream distance = 12 km, Time = 1 hr

Upstream distance = 12 km, Time = 1 hr 12 min

Formula Used:

Speed = Distance ÷ Time

Speed in still water (u) = (Downstream speed + Upstream speed) ÷ 2

Calculations:

⇒ Downstream Speed (x + y) = 12 / 1 = 12 km/hr

⇒ Upstream Time = 1 hr + (12 / 60) hr = 1 + 0.2 = 1.2 hr

⇒ Upstream Speed (x − y) = 12 / 1.2 = 10 km/hr

⇒ Speed in still water (x) = (12 + 10) / 2

⇒ x = 22 / 2 = 11 km/hr

∴ The correct answer is 11 km/hr.

Additional Information

Speed of Stream

The speed of the water current or stream is calculated as: Speed of stream = (Downstream Speed − Upstream Speed) ÷ 2.

Downstream vs Upstream

Downstream speed is the sum of boat speed and stream speed (u + v). Upstream speed is the difference between boat speed and stream speed (u − v).

Average Speed for Entire Journey

If a boat travels the same distance downstream and upstream, Average Speed = (Downstream Speed × Upstream Speed) ÷ Speed in Still Water.

Shortcut Trick

LCM of ratio parts 3 and 5 = 15 units.

Given LCM = 90 → 15 units = 90.

1 unit = 90 ÷ 15 = 6.

Required numbers = 3 × 6 and 5 × 6.

∴ The correct answer is 18, 30.

Alternate Method

Given:

Ratio of two numbers = 3 : 5

LCM of numbers = 90

Calculations:

Let the two numbers be 3x and 5x, where x is the HCF (Highest Common Factor).

Since 3 and 5 are co-prime numbers:

⇒ LCM(3x, 5x) = 3 × 5 × x

⇒ 15x = 90

⇒ x = 90 ÷ 15

⇒ x = 6

Now, calculate the numbers:

⇒ First number = 3x = 3 × 6 = 18

⇒ Second number = 5x = 5 × 6 = 30

∴ The correct answer is 18, 30.

Additional Information

LCM and HCF Relation

For any two numbers, the product of the numbers is equal to the product of their LCM and HCF: N₁ × N₂ = LCM × HCF.

Ratio and LCM Rule

If two numbers are in the ratio a : b and their HCF is x, then their LCM is given by a × b × x.

Co-prime Numbers

Two numbers are co-prime if their only common factor is 1. The LCM of two co-prime numbers is simply their product.

Shortcut Trick

Assume the Average is the base value: 21.

Deviation of 1st number (16) = 16 − 21 = −5

Deviation of 2nd number (23) = 23 − 21 = +2

Net deviation of known numbers = −5 + 2 = −3

To keep the Average 21, the third number must have a deviation of +3.

Third number = 21 + 3 = 24

∴ The correct answer is 24.

Alternate Method

Given:

Average of 3 numbers = 21

First number = 16

Second number = 23

Formula Used:

Average = Sum of all observations ÷ Total number of observations

Calculations:

⇒ Sum of 3 numbers = Average × 3

⇒ Sum of 3 numbers = 21 × 3 = 63

⇒ Sum of the two given numbers = 16 + 23 = 39

⇒ Third number = (Sum of 3 numbers) − (Sum of 2 numbers)

⇒ Third number = 63 − 39 = 24

∴ The correct answer is 24.

Additional Information

Properties of Average

The sum of deviations of all items from their arithmetic mean is always zero (Σ(x − x̄) = 0).

Change in Average

If every number in a set is increased or decreased by a constant value k, the new average also increases or decreases by k.

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Shortcut Trick

Net Simple Interest percentage = Rate × Time = 8% × 2 = 16%

According to the question: 16% of Principal = ₹1680

1% of Principal = 1680 ÷ 16 = 105

Total Principal (100%) = 105 × 100 = ₹10500

∴ The correct answer is ₹10500.

Alternate Method

Given:

Simple Interest (SI) = ₹1680

Rate of Interest (R) = 8% per annum

Time Period (T) = 2 years

Formula Used:

SI = (P × R × T) ÷ 100

Calculations:

⇒ 1680 = (P × 8 × 2) ÷ 100

⇒ 1680 = 16P ÷ 100

⇒ 1680 × 100 = 16P

⇒ 168000 = 16P

⇒ P = 168000 ÷ 16

⇒ P = ₹10500

∴ The correct answer is ₹10500.

Additional Information

Total Amount Formula

The total amount (A) in simple interest is given by A = Principal + SI = P × (1 + RT/100).

SI vs CI for 2 Years

The difference between Compound Interest and Simple Interest for 2 years is P × (R/100)².

Compound Interest Formula

For interest compounded annually, the Amount A = P(1 + R/100)ⁿ, where n is the number of years.

Given:

Expression = $\frac{\sqrt[3]{5832}}{\sqrt[4]{1296}} \times \frac{3}{54} \times 198$

Formula used:

Cube Root: √³a³ = a

Fourth Root: √⁴a⁴ = a

Calculations:

Simplifying the cube root part:

⇒ √³5832 = √³(18 × 18 × 18) = 18

Simplifying the fourth root part:

⇒ √⁴1296 = √⁴(6 × 6 × 6 × 6) = 6

Substituting these values back into the expression:

⇒ (18 / 6) × (3 / 54) × 198

⇒ 3 × (1 / 18) × 198

⇒ (3 / 18) × 198

⇒ (1 / 6) × 198

⇒ 33

∴ The correct answer is option (1).

Shortcut Trick

Monthly Savings = 12,000 − (5,000 + 3,000) = ₹4,000.

Since 1 month's savings is spent on birthday celebrations, savings occur for only 11 months.

Yearly Savings = 11 × 4,000 = ₹44,000.

∴ The correct answer is ₹44,000.

Alternate Method

Given:

Monthly Salary = ₹12,000

House Rent = ₹5,000

Bills = ₹3,000

Formula Used:

Monthly Savings = Monthly Salary − (Rent + Bills)

Yearly Savings = Monthly Savings × (Total Months − Spending Months)

⇒ Total Monthly Expenditure = ₹5,000 + ₹3,000 = ₹8,000

⇒ Monthly Savings = ₹12,000 − ₹8,000 = ₹4,000

⇒ Number of months in a year = 12

⇒ Savings for birthday month = ₹0 (as all savings were spent)

⇒ Effective savings months = 12 − 1 = 11 months

⇒ Yearly Savings = 11 × ₹4,000 = ₹44,000

∴ The correct answer is ₹44,000.

Additional Information

Income, Expenditure, and Savings

The basic relation is Income = Expenditure + Savings. To find total yearly values, multiply the monthly surplus by the number of contributing months.

Percentage Savings

It is the ratio of savings to income expressed as a percentage: (Savings ÷ Income) × 100.

Yearly vs Monthly Calculation

Always ensure all units are the same (either all monthly or all annual) before performing addition or subtraction to avoid calculation errors.

Shortcut Trick

Total Surface Area (TSA) of remaining part = Outer CSA of Cylinder + Base Area + Inner CSA of Cone.

TSA = 2πrh + πr² + πrl = πr(2h + r + l)

Given: Radius (r) = 31.5 cm, Height (h) = 25 cm.

Slant height (l) = √(31.5² + 25²) = √1617.25 ≈ 40.215 cm.

TSA = (22/7) × 31.5 × (2 × 25 + 31.5 + 40.215) = 99 × 121.715 = 12049.785 cm².

∴ The correct answer is 12,050 cm².

Alternate Method

Given:

Radius of Cylinder (r) = 31.5 cm

Height of Cylinder (h) = 25 cm

The Cone has the same Radius and Height.

Formula Used:

Slant height of cone (l) = √(r² + h²)

Remaining Surface Area = 2πrh + πr² + πrl

Calculations:

⇒ Slant height (l) = √(31.5² + 25²)

⇒ l = √(992.25 + 625) = √1617.25 ≈ 40.215 cm

⇒ Area of Cylinder CSA = 2 × (22/7) × 31.5 × 25 = 2 × 99 × 25 = 4950 cm²

⇒ Area of Bottom Base = (22/7) × 31.5 × 31.5 = 99 × 31.5 = 3118.5 cm²

⇒ Area of Conical Cavity (CSA) = (22/7) × 31.5 × 40.215 = 99 × 40.215 ≈ 3981.285 cm²

⇒ Total Surface Area = 4950 + 3118.5 + 3981.285 = 12049.785 cm²

⇒ Rounded to nearest tens = 12,050 cm²

∴ The correct answer is 12,050 cm².

Additional Information

Total Surface Area of a Solid Cylinder

The TSA includes the curved surface and two circular bases: TSA = 2πrh + 2πr² = 2πr(h + r).

Slant Height of a Cone

The slant height 'l' is the distance from the apex to any point on the base circle: l = √(r² + h²).

Surface Area of Conical Cavity

When a cone is carved out of a solid, the internal curved surface area added is πrl.

Rounding to Nearest Tens

If the last digit is 5 or more, round up the tens digit (e.g., 12049.7 → 12050).

Shortcut Trick

The second tap fills the cistern in 3 hr and the third tap empties it in 3 hr.

Their combined work per hour = 1/3 − 1/3 = 0.

Hence, only the first tap effectively fills the cistern.

Time taken by the first tap = 2 hr.

∴ The correct answer is 2 hr.

Alternate Method

Given:

Time taken by filling Tap A = 2 hr

Time taken by filling Tap B = 3 hr

Time taken by emptying Tap C = 3 hr

Formula Used:

Total Work = Time Taken × Efficiency

Net Efficiency = Efficiency of filling taps − Efficiency of emptying tap

⇒ Let Total Work = LCM of (2, 3, 3) = 6 units

⇒ Efficiency of Tap A = 6 ÷ 2 = +3 units/hr

⇒ Efficiency of Tap B = 6 ÷ 3 = +2 units/hr

⇒ Efficiency of Tap C = 6 ÷ 3 = −2 units/hr

⇒ Net Efficiency when all three taps are opened together = 3 + 2 − 2 = 3 units/hr

⇒ Time taken to fill the empty cistern = Total Work ÷ Net Efficiency = 6 ÷ 3 = 2 hr

∴ The correct answer is 2 hr.

Additional Information

Pipes and Cisterns Rule

If an inlet pipe fills a tank in x hours and an outlet pipe empties it in y hours, then the net part filled in 1 hour when both are open is (1/x − 1/y).

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete a work. If the ratio of time taken by two pipes is a : b, then the ratio of their efficiency is b : a.

Alternate Day Work

When pipes work on alternate hours, calculate the combined work done in a complete cycle of 2 hours, and then determine the total time required to finish the work.

Shortcut Trick

To find the percentage profit, compare the Cost Price (CP) and Selling Price (SP) for the same quantity (e.g., one dozen).

CP of 1 dozen = ₹ 3,750

SP of 1 dozen = 330 × 12 = ₹ 3,960

Profit % = [(SP − CP) ÷ CP] × 100 = (210 ÷ 3750) × 100 = 5.6%

∴ The correct answer is 5.6%.

Alternate Method

Given:

Cost Price (CP) of 1 dozen = ₹ 3,750

Selling Price (SP) of 1 individual item = ₹ 330

Formula Used:

Profit = SP − CP

Profit % = (Profit ÷ CP) × 100

Calculations:

⇒ Cost Price of 1 item = 3750 ÷ 12

⇒ Cost Price of 1 item = ₹ 312.5

⇒ Selling Price of 1 item = ₹ 330

⇒ Profit per item = 330 − 312.5 = ₹ 17.5

⇒ Profit % = (17.5 ÷ 312.5) × 100

⇒ Profit % = (1750 ÷ 312.5) = 5.6%

∴ The correct answer is 5.6%.

Additional Information

Profit and Loss Percentage

Profit % and Loss % are always calculated on the Cost Price (CP) unless stated otherwise. Profit % = (Profit/CP) × 100 and Loss % = (Loss/CP) × 100.

Unitary Method in Profit/Loss

Percentage profit remains the same whether calculated for a single item, a dozen, or the entire bulk (25 dozens), as long as the CP and SP rates are constant.

Relation between CP, SP and Discount

SP = CP + Profit or CP − Loss. Also, SP = Marked Price (MP) − Discount.

Shortcut Trick

When an object covers equal distances at different speeds x and y, the Average Speed is calculated using the formula: (2 × x × y) / (x + y).

Here, speed from A to B (x) = 96 km/hr and speed from B to A (y) = 94 km/hr.

Average Speed = (2 × 96 × 94) / (96 + 94)

Average Speed = 18048 / 190

Average Speed = 94.9894... ≈ 94.99 km/hr

∴ The correct answer is 94.99 km/hr.

Alternate Method

Given:

Distance between A and B = 752 km

Speed from A to B (v₁) = 96 km/hr

Speed from B to A (v₂) = 94 km/hr

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Time taken to go from A to B (t₁) = 752 / 96 hours

⇒ Time taken to return from B to A (t₂) = 752 / 94 hours

⇒ Total Distance = 752 + 752 = 1504 km

⇒ Total Time = (752 / 96) + (752 / 94)

⇒ Average Speed = 1504 ÷ [(752 / 96) + (752 / 94)]

⇒ Average Speed = 1504 ÷ [752 × (1/96 + 1/94)]

⇒ Average Speed = 2 ÷ [(94 + 96) / (96 × 94)]

⇒ Average Speed = (2 × 96 × 94) / 190

⇒ Average Speed = 18048 / 190 = 94.98947... km/hr

⇒ Rounding to two decimal places, we get 94.99 km/hr.

∴ The correct answer is 94.99 km/hr.

Additional Information

General Average Speed

For any journey with different distances d₁, d₂,... and speeds v₁, v₂,..., Average Speed = (d₁ + d₂ + ...) ÷ (d₁/v₁ + d₂/v₂ + ...).

Conversion of Speed Units

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

Relative Speed

When two objects move in the opposite direction, their relative speed is (v₁ + v₂). If they move in the same direction, it is |v₁ − v₂|.

Shortcut Trick

If b is the mean proportional between a and c, then b² = a × c.

Here, 48² = x × 192

2304 = 192 × x

x = 2304 ÷ 192 = 12

∴ The correct answer is 12.

Alternate Method

Given:

Mean proportional (b) = 48

First number (a) = x

Second number (c) = 192

Formula Used:

Mean proportional between two numbers a and c is given by √(a × c).

Calculations:

⇒ 48 = √(x × 192)

Squaring both sides:

⇒ 48² = x × 192

⇒ 48 × 48 = 192x

⇒ 2304 = 192x

⇒ x = 2304 ÷ 192

⇒ x = 12

∴ The correct answer is 12.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is a value x such that a/x = x/b, which simplifies to x = √(ab).

Third Proportional

For two numbers a and b, the third proportional c is such that a : b :: b : c, calculated as c = b²/a.

Fourth Proportional

For three numbers a, b, and c, the fourth proportional d is such that a : b :: c : d, calculated as d = (bc)/a.

Shortcut Trick

Ratio of shares of Mandar and Rupesh = (100 + r) : 100 (for 1 year age difference).

Ratio of Mandar : Rupesh = (100 + 8) : 100 = 108 : 100 = 27 : 25.

Total ratio parts = 27 + 25 = 52 units → ₹23,400.

1 unit = 23,400 ÷ 52 = ₹450.

Mandar's initial share = 27 × 450 = ₹12,150.

∴ The correct answer is ₹12,150.

Alternate Method

Given:

Total amount = ₹23,400

Rate of interest (r) = 8% p.a.

Current age of Rupesh = 12 years | Current age of Mandar = 13 years

Maturity age = 25 years

Formula Used:

Amount (A) = P(1 + r/100)ⁿ

Calculations:

Let Rupesh share = R and Mandar share = M.

Time period for Rupesh (n₁) = 25 − 12 = 13 years

Time period for Mandar (n₂) = 25 − 13 = 12 years

According to the question, Amount for Rupesh = Amount for Mandar:

⇒ R(1 + 8/100)¹³ = M(1 + 8/100)¹²

⇒ R(1.08)¹³ = M(1.08)¹²

⇒ R(1.08) = M

⇒ M/R = 1.08 / 1 = 108 / 100

⇒ M : R = 27 : 25

⇒ Total sum = 27 + 25 = 52 units

⇒ 52 units = ₹23,400

⇒ 1 unit = 23,400 ÷ 52 = ₹450

⇒ Mandar initial share = 27 × 450 = ₹12,150

∴ The correct answer is ₹12,150.

Additional Information

Ratio of Principals in Compound Interest

When amounts are equal after times t₁ and t₂, the ratio of principals is P₁ : P₂ = (1 + r/100)^t₂−t₁ : 1.

Compound Interest Formula

The amount A is calculated as A = P(1 + r/100)ⁿ, where P is the principal, r is the annual interest rate, and n is the number of years.

Successive Percentage Change

Compound interest is an application of successive percentage increases. For a rate r, the multiplying factor is (1 + r/100) each year.

Shortcut Trick

Sum of ratio parts for Length and Breadth = 8 + 7 = 15 units.

Semi-perimeter (L + B) = 90 ÷ 2 = 45 m.

Comparing ratio sum to semi-perimeter: 15 units = 45 m → 1 unit = 3 m.

Length corresponds to 8 units → 8 × 3 = 24 m.

∴ The correct answer is 24 m.

Alternate Method

Given:

Ratio of Length (L) to Breadth (B) = 8 : 7

Perimeter of the rectangular field = 90 m

Formula Used:

Perimeter (P) = 2 × (Length + Breadth)

Calculations:

⇒ Let the Length be 8x and the Breadth be 7x.

⇒ 2 × (8x + 7x) = 90

⇒ 2 × 15x = 90

⇒ 30x = 90

⇒ x = 90 ÷ 30 = 3

⇒ Length = 8x = 8 × 3 = 24 m.

∴ The correct answer is 24 m.

Additional Information

Area of Rectangle

The total space occupied by the rectangle is calculated as Length × Breadth (L × B).

Diagonal of Rectangle

The distance between opposite corners is given by the Pythagorean theorem: d = √(L² + B²).

Semi-Perimeter

The sum of one length and one breadth is exactly half of the total perimeter: Semi-perimeter = P ÷ 2 = L + B.

Given:

The total number of students in the school is 540. Based on the provided bar graph, the distribution of students according to their favourite sports is as follows:

Formula Used:

Ratio = (Value of First Category) ÷ (Value of Second Category)

To simplify a ratio A : B, divide both A and B by their Highest Common Factor (HCF).

Calculation:

According to the data extracted from the bar graph,

⇒ Number of students who like Cricket = 180

⇒ Number of students who like Badminton = 75

The required ratio between Cricket and Badminton is:

⇒ Ratio = 180 : 75

Now, simplify the ratio by dividing both terms by their common factor. Dividing by 5:

⇒ Ratio = (180 ÷ 5) : (75 ÷ 5)

⇒ Ratio = 36 : 15

Further simplifying by dividing both terms by 3:

⇒ Ratio = (36 ÷ 3) : (15 ÷ 3)

⇒ Ratio = 12 : 5

∴ The correct answer is 12 : 5, which corresponds to Option (3).

Shortcut Trick

Net filling rate per hour = (1/16) − (1/80)

Net filling rate = (5 − 1) / 80 = 4 / 80 = 1/20 of the tank per hour.

Time to fill full tank = 20 hours.

Time to fill 1/4^th of the tank = 20 ÷ 4 = 5 hours.

∴ The correct answer is 5 hr.

Alternate Method

Given:

Time taken by Filling Tap = 16 hr

Time taken by Emptying Tap = 80 hr

Total Work = LCM of 16 and 80 = 80 units

Calculations:

⇒ Combined Efficiency of (A + B) = 5 − 1 = 4 units/hr

⇒ Required work = 1/4 of Total Work = 80 ÷ 4 = 20 units

⇒ Time required = Required Work ÷ Combined Efficiency

⇒ Time = 20 ÷ 4 = 5 hr

∴ The correct answer is 5 hr.

Additional Information

Negative Work Concept

In Pipes and Cisterns, work done by an inlet pipe is positive, while work done by an outlet or leak is negative.

Net Rate Formula

If tap A fills in 'x' hours and tap B empties in 'y' hours, the net time 'T' to fill the tank is 1/T = 1/x − 1/y.

Partial Filling

To find the time for a fraction 'k' of the tank, simply multiply the total time by 'k': Time = k × (Total Time).

Shortcut Trick

If every number in a given set is increased by a constant value 'k', then the average of that set also increases by the same value 'k'.

Given Original Average = 45

Increase per number = 3

New Average = 45 + 3 = 48

∴ The correct answer is 48.

Alternate Method

Given:

The average of 8 numbers = 45

Each number is increased by 3.

Formula Used:

Average = Sum of all observations ÷ Number of observations

Sum of observations = Average × Number of observations

Calculations:

⇒ Total initial sum of 8 numbers = 45 × 8 = 360

⇒ Total increase across all numbers = 8 × 3 = 24

⇒ New total sum = 360 + 24 = 384

⇒ New average = 384 ÷ 8

⇒ New average = 48

∴ The correct answer is 48.

Additional Information

Property of Linear Transformation

If every observation is multiplied or divided by a constant 'k', the original average is also multiplied or divided by 'k' respectively.

Subtraction Property

If every term in a data set is decreased by a constant value 'x', the new average will be (Original Average − x).

Combined Average Formula

For two groups with averages A₁ and A₂ and sizes n₁ and n₂, the combined average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Shortcut Trick

The ratio of Cost Price (CP) to Selling Price (SP) is 1000 : 1250 = 4 : 5.

Profit unit = 5 − 4 = 1 unit on a base of 4 units.

Profit % = (1 ÷ 4) × 100 = 25%.

∴ The correct answer is 25%.

Alternate Method

Given:

Total Cost Price (CP) of 50 notebooks = ₹1000

Total Selling Price (SP) of 50 notebooks = ₹1250

Formula Used:

Profit = Selling Price (SP) − Cost Price (CP)

Profit Percentage = (Profit ÷ Cost Price) × 100

⇒ Profit = 1250 − 1000 = ₹250

⇒ Profit % = (250 ÷ 1000) × 100

⇒ Profit % = 1/4 × 100

⇒ Profit % = 25%

∴ The correct answer is 25%.

Additional Information

Loss Percentage

When CP > SP, Loss % = [(CP − SP) ÷ CP] × 100.

Selling Price Calculation

SP = CP × (100 + Profit %) ÷ 100 or SP = CP × (100 − Loss %) ÷ 100.

Cost Price Calculation

CP = [SP ÷ (100 + Profit %)] × 100.

Marked Price and Discount

Discount is always calculated on Marked Price (MP). SP = MP − Discount.

Shortcut Trick

Ratio of capital X : Y : Z = 5 : 2 : 8

Profit ratio = (5 × 6 + 2.5 × 6) : (2 × 12) : (8 × 12)

⇒ X : Y : Z = 45 : 24 : 96 ⇒ 15 : 8 : 32

Total units = 15 + 8 + 32 = 55 units

55 units = ₹55000 ⇒ 1 unit = ₹1000

Difference (X − Y) = (15 − 8) units = 7 × 1000 = ₹7000

∴ The correct answer is ₹7000.

Alternate Method

Given:

Initial investment ratio of X, Y, Z = 5 : 2 : 8

Total annual profit = ₹55000

Investment by Z = ₹19000 (used to establish base ratio)

Formula Used:

Profit Share ∝ (Capital × Time)

Calculations:

Let the initial capitals of X, Y, and Z be 5k, 2k, and 8k respectively.

⇒ X's equivalent capital for 1 year = (5k × 6) + (2.5k × 6) = 30k + 15k = 45k

⇒ Y's equivalent capital for 1 year = 2k × 12 = 24k

⇒ Z's equivalent capital for 1 year = 8k × 12 = 96k

⇒ Profit Ratio X : Y : Z = 45k : 24k : 96k = 15 : 8 : 32

⇒ Total profit units = 15 + 8 + 32 = 55 units

⇒ Total profit = 55 units = ₹55000

⇒ 1 unit = 55000 ÷ 55 = ₹1000

⇒ Profit of X = 15 × 1000 = ₹15000

⇒ Profit of Y = 8 × 1000 = ₹8000

⇒ Difference = 15000 − 8000 = ₹7000

∴ The correct answer is ₹7000.

Additional Information

Basic Partnership Rule

Profit is always distributed in the ratio of the product of capital and time: Profit = Capital × Time.

Variable Capital

If a partner changes their investment during the period, the total investment is calculated as the sum of (capital × duration) for each interval.

Working vs Sleeping Partner

A working partner may receive an additional percentage of profit as a salary before the remaining profit is divided according to the investment ratio.

Shortcut Trick

Equivalent discount % = 10 + 20 − (10 × 20)/100 = 28%

Since 28% discount = ₹140, then 100% (Marked Price) = (140 ÷ 28) × 100 = ₹500

Selling Price (SP) = Marked Price − Discount = 500 − 140 = ₹360

Profit = SP − CP = 360 − 288 = ₹72

Profit % = (72 ÷ 288) × 100 = 25%

∴ The correct answer is 25%.

Alternate Method

Given:

Two successive discounts = 10% and 20%

Equivalent single discount value = ₹140

Cost Price (CP) of the ruler = ₹288

Formula Used:

Equivalent Discount % = a + b − (a × b)/100

Profit % = [(SP − CP) / CP] × 100

⇒ Net Discount % = 10 + 20 − (10 × 20)/100

⇒ Net Discount % = 30 − 2 = 28%

⇒ 28% of Marked Price (MP) = 140

⇒ MP = (140 / 28) × 100 = ₹500

⇒ Selling Price (SP) = MP − Discount = 500 − 140 = ₹360

⇒ Profit = SP − CP = 360 − 288 = ₹72

⇒ Profit % = (72 / 288) × 100

⇒ Profit % = 1/4 × 100 = 25%

∴ The correct answer is 25%.

Additional Information

Successive Discounts

When multiple discounts are applied one after another, the effective discount is calculated using the formula: Total Discount = a + b − (ab/100).

Marked Price and Selling Price

Selling Price is the final price after subtracting the discount from the Marked Price: SP = MP × (100 − D%)/100.

Profit Percentage

Profit % is always calculated on the Cost Price (CP) unless stated otherwise: Profit % = (Profit/CP) × 100.

The correct answer is: inconsistant.

Key Points

• The word 'inconsistant' is the incorrectly spelled word in the given sentence. The correct spelling is 'inconsistent', ending with '-ent' rather than '-ant'. (गलत वर्तनी)
• Example: The report was rejected because it contained inconsistant figures.
• 'Inconsistent' refers to something that is not staying the same throughout, or having parts that contradict each other. (असंगत)
• Example: The witness was dismissed because his testimony was inconsistent with the evidence.
• Hence, we can infer that the incorrectly spelled word is 'inconsistant'.

Therefore, the correct answer is: inconsistant.

Additional Information

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

• concluded (निष्कर्ष निकाला): To bring something to an end or to arrive at a judgment or opinion by reasoning.
• Example: The investigators concluded that the fire was started accidentally.
• verification (सत्यापन): The process of establishing the truth, accuracy, or validity of something.
• Example: The system requires verification of your email address to complete the registration.
• committee (समिति): A group of people appointed for a specific function by a larger group.
• Example: The school committee is responsible for hiring the new principal.

The correct answer is 'Although'.

Key Points

• The conjunction 'Although' is used to introduce a subordinate clause that contains a statement which makes the main clause of the sentence seem surprising or unexpected.
• It is used to show a contrast between two clauses. In this context, it is surprising that the match continued despite the heavy rain.
• Options 2, 3, and 4 do not logically fit the relationship of contrast required by the sentence.

Therefore, the correct answer is Option 1.

Complete Sentence: 'Although it was raining heavily, the match continued.'

Additional Information

• Option 2: 'Unless' is a conditional conjunction meaning 'except if' (e.g., Unless it stops raining, the match will be cancelled).
• Option 3: 'Since' is used to indicate a reason or a starting point in time (e.g., Since it was raining, the match was cancelled).
• Option 4: 'While' is typically used to denote two actions happening at the same time or to present a comparison/contrast (e.g., While he likes cricket, she likes football).

The correct answer is implicit.

Key Points

• The term explicit is an adjective used to describe something that is stated clearly and in precise detail, leaving no room for confusion, ambiguity, or misinterpretation. In the given sentence, it suggests the instructions were straightforward and transparent.
• The word implicit serves as the direct antonym. It refers to something that is suggested or hinted at though not plainly expressed. It describes information that is inherent or tacit, requiring the listener or reader to infer the meaning from the context.
• While explicit content is unfolded and overt, implicit content is internalized and indirect. Therefore, if instructions are not explicit (clear), they are implicit (implied).

 Additional Information

• delicate:
• Refers to something fragile, easily broken, or requiring sensitive and tactful handling.
• It often describes textures, colors, or complex social situations.
• important:
• Denotes something of great significance, value, or consequence.
• It measures the weight or priority of a matter rather than the clarity of its expression.
• detailed:
• This is a synonym for explicit. It means including many specific particulars, items, or minutiae.
• A detailed report provides exhaustive information, similar to explicit instructions.

The correct answer is 'had addressed'.

Key Points

• The given sentence is an example of a third conditional sentence, which is used to describe a hypothetical situation in the past and its probable result.
• The grammatical structure for the third conditional is: If + past perfect (had + past participle), subject + would/might/could have + past participle.
• In the provided sentence, the main clause 'might have avoided' indicates that the 'if' clause must be in the past perfect tense.
• The past perfect form of the verb 'address' is 'had addressed'.

Therefore, the correct answer is Option 4.

Complete Sentence: 'If the manager had addressed the issue earlier, we might have avoided the delay.'

Additional Information

• Option 1: 'address' is the present tense base form, which does not fit the past hypothetical context.
• Option 2: 'addressed' is the simple past tense, which is used in second conditional sentences (e.g., If the manager addressed the issue, we would avoid the delay).
• Option 3: 'addresses' is the simple present form, typically used in zero or first conditional sentences.

The correct answer is Option (4) i.e. intervening.

Key Points

• The phrase 'coming in between' refers to something that occurs or exists in the time that separates two specific events or periods. (बीच में आने वाला)
• Example: They met last year, and much has happened in the coming in between months.
• The word 'intervening' is the most appropriate substitute as it specifically describes something that takes place between points of time or events. (अंतर्वर्ती/मध्यवर्ती)
• Example: During the intervening period between the two meetings, several important decisions were made.
• Hence, we can infer that 'intervening' correctly replaces the underlined phrase to make the sentence more concise and formal.

Therefore, the correct answer is- intervening.

Additional Information

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

• Suggesting (सुझाव देना/संकेत देना): To put forward an idea or plan for consideration, or to state something indirectly.
• Example: The evidence is suggesting that the fire was accidental.
• Abating (कम होना/शांत होना): Something that is becoming less intense, less active, or less widespread.
• Example: We waited for the heavy rain to show signs of abating before leaving the house.
• Skidding (फिसलना): An action where a vehicle or person slides, typically sideways or uncontrollably on a slippery surface.
• Example: The driver lost control, and the truck started skidding on the wet road.

The correct answer is 'The'.

Key Points

• In English grammar, the definite article 'the' is used before a common noun to give it the meaning of an abstract noun.
• In the given sentence, 'the patriot' does not refer to a person but rather to the patriotic feeling, spirit, or quality within the woman.
• The structure 'The + [Common Noun] + in + [Someone]' is a common idiomatic way to highlight a specific internal trait or emotion (e.g., 'The mother in her', 'The judge in him').

Therefore, the correct answer is Option 3.

Complete Sentence: "The patriot in her did not let her yield."

Additional Information

• Option 1: 'That' is a demonstrative used to identify a specific person or thing observed by the speaker, which does not fit the grammatical requirement for this abstract expression.
• Options 2 and 4: 'A' and 'An' are indefinite articles used for non-specific singular countable nouns. They cannot be used here because we are referring to a specific quality (the patriotic spirit) belonging to a specific person.

The correct answer is: obliterated.

Key Points

• The phrasal verb 'wiped out' means to erase, eliminate, or remove something completely so that no trace remains. (मिटा देना)
• Example: The memories of his childhood were nearly wiped out by the trauma of the accident.
• 'Obliterated' refers to the act of destroying something utterly or blotting it out such that it becomes invisible or indistinct. It is the most suitable synonym for 'wiped out' in the context of fading memories. (मिटा दिया/नष्ट कर दिया)
• Example: The intense sandstorm obliterated the tracks left by the vehicle within minutes.
• Hence, we can conclude that 'obliterated' is the correct substitute for the underlined phrase.

Therefore, the correct answer is: obliterated.

Additional Information

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

• Discriminated (भेदभाव किया): To recognize a distinction or to treat a person or particular group differently, especially in an unfair way.
• Example: The law ensures that no individual is discriminated against based on their background.
• Abided (पालन किया): To accept or act in accordance with a rule, decision, or recommendation.
• Example: Throughout the competition, all the players abided by the spirit of the game.
• Breached (उल्लंघन किया): To break or fail to observe a law, agreement, or code of conduct.
• Example: The construction project was halted because the builders breached safety regulations.

The correct answer is PQSR.

Key Points

• The sentence structure is initiated by S1 ('Once we have assessed'), which introduces a Dependent Adverbial Clause of time. The Transitive Verb 'assessed' logically requires a Direct Object to complete the thought.
• Part P ('the diverse patterns and') immediately follows S1 to provide that object. The presence of the conjunction and at the end of this part indicates that a second noun phrase is required to complete the list.
• Part Q ('shades at your disposal') serves as the second part of the Compound Object. The Idiomatic Phrase 'at your disposal' functions as an adjective modifying 'patterns and shades', signifying availability.
• Part S ('we will communicate our') acts as the start of the Main Independent Clause. It provides the subject ('we') and the future tense action that will occur once the assessment is finished.
• Part R ('specific preferences for you') follows S as the direct object of the verb communicate. It clarifies what is being sent and identifies the recipient ('for you').
• Part S6 ('to prepare samples accordingly') concludes the sentence with an Infinitive Phrase of Purpose. The adverb accordingly provides Syntactic Cohesion, linking the preparation task directly to the 'preferences' mentioned in part R.

 Additional Information

• Complex Sentence Structure:
• This sentence is Complex because it combines a Subordinate Clause (starting with 'Once') and a Main Clause. In formal writing, these are often separated by a comma when the subordinate clause comes first.
• Transitive Verbs like assess and communicate are essential here; they cannot stand alone without an object, which dictates the placement of P after S1 and R after S.
• The Infinitive of Purpose ('to prepare') is a grammatical construction used to show the intent or goal of the preceding action.
• The term at your disposal is a fixed Prepositional Phrase often used in professional contexts to mean 'available for use'.

The correct answer is humid.

Key Points

• The term arid refers to a specific climatic classification where there is a severe lack of available water, typically defined by receiving less than 250 millimeters of annual precipitation.
• In geography, arid regions like the Sahara or Thar Desert are characterized by high evaporation rates and dry soil, which prevents vegetation growth and makes agriculture difficult.
• The word humid serves as the direct antonym because it describes an environment with a high concentration of water vapor or moisture in the air.
• In meteorological terms, humidity is measured as relative humidity; a humid climate is the polar opposite of an arid climate in terms of atmospheric hydration and moisture availability.

 Additional Information

• Shiny:
• Describes optical properties where a surface reflects light with brightness.
• Used for polished surfaces or reflective materials, unrelated to climatic moisture.
• Rough:
• Pertains to physical texture or topography that is uneven or coarse.
• While arid land can be rough, the term does not describe the moisture content of the air.
• Windy:
• Relates to atmospheric movement and air currents.
• Refers to velocity rather than precipitation or dryness levels.

The correct answer is 'had studied'.

Key Points

• The sentence structure represents the Third Conditional, which is used to talk about hypothetical situations in the past that did not happen.
• The structure of a Third Conditional sentence is: If + past perfect (had + past participle), would have + past participle.
• In the given sentence, the main clause uses 'would have passed,' which is the perfect conditional. Therefore, the 'if' clause must be in the past perfect tense ('had studied').
• This indicates that the person did not study hard in the past and, as a result, did not pass the exam.

Therefore, the correct answer is Option 2.

Complete Sentence: 'If she had studied harder, she would have passed the exam.'

Additional Information

• Option 1: 'is studying' is in the Present Continuous tense and does not fit the conditional structure of this sentence.
• Option 3: 'study' is the base form of the verb and is grammatically incorrect in this context.
• Option 4: 'studies' is in the Simple Present tense, which is typically used in the First Conditional (e.g., 'If she studies, she will pass').

The correct answer is: took a leap in the dark.

Key Points

• The phrase 'took a risk' means to do something even though you know that something bad could happen as a result. (जोखिम उठाना)
• Example: He took a risk by investing his entire life savings into a single volatile stock.
• 'took a leap in the dark' is an idiom that means to take an action or make a decision without being certain of the outcome or the consequences; it perfectly substitutes the act of taking a risk in an uncertain situation. (बिना सोचे-समझे जोखिम उठाना)
• Example: Quitting his stable job to start his own firm was definitely taking a leap in the dark.
• Hence, we can infer that the most appropriate idiom to substitute the underlined segment is 'took a leap in the dark'.

Therefore, the correct answer is: took a leap in the dark.

Additional Information

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

• won laurels (यश या सम्मान प्राप्त करना): To achieve distinction, honor, or praise for one's accomplishments.
• Example: The young scientist won laurels for her groundbreaking research in renewable energy.
• took to his heels (दुम दबाकर भागना): To run away suddenly, often out of fear.
• Example: As soon as the burglar heard the dog bark, he took to his heels.
• took great pains (बहुत मेहनत करना): To make a significant effort to do something carefully and thoroughly.
• Example: The artist took great pains to ensure every detail of the portrait was accurate.

The correct answer is 'a'.

Key Points

• The choice between the indefinite articles 'a' and 'an' is determined by the sound of the following word, not just the first letter.
• The article 'a' is used before words that begin with a consonant sound.
• The word 'one' (as in 'one-year plan') starts with the consonant sound /w/ (like the word 'won'), despite starting with the vowel letter 'o'.
• Because it begins with a consonant sound, the correct article to use is 'a'.

Therefore, the correct answer is Option 1.

Complete Sentence: "The District Manager created a one-year plan to improve sanitation of the city."

Additional Information

• Option 2: 'an' is incorrect because it is only used before words starting with a vowel sound (e.g., an apple, an hour).
• Option 3: 'no article' is incorrect because 'plan' is a singular countable noun that requires an article in this context.
• Option 4: 'the' is generally used for specific or previously mentioned items. In this sentence, the plan is being introduced for the first time as a general initiative, making the indefinite article 'a' more appropriate.

The correct answer is hithreto.

Key Points

• The underlined word hithreto is misspelled within the context of the sentence.
• The correct orthographic spelling of the term is hitherto.
• Hitherto is an adverb that functions as a temporal marker, meaning until now or up to this time.
• The error in hithreto involves the incorrect placement and inclusion of the vowel 'e' before the 't'; the standard English spelling follows the sequence h-i-t-h-e-r-t-o.
• In the provided text, the word is used to describe how sophisticated arts like essay writing and literary criticism were historically less practiced by women until the specific period being discussed.

 Additional Information

• Sophisticated:
• Refers to something that is highly developed, complex, or refined through worldly experience.
• In a literary context, it describes arts that require specialized knowledge or intellectual maturity.
• Criticism:
• A literary genre and academic discipline involving the analysis, evaluation, and interpretation of works of art.
• It encompasses various theoretical frameworks such as historical criticism and formalism.
• Biography:
• A non-fiction narrative that provides a factual account of an individual's life history.
• It is distinct from an autobiography because it is written by a third-party author rather than the subject themselves.

The correct answer is: By leaps and bounds.

Key Points

• The word 'speedily' means at a high speed or very quickly. (तेज़ी से)
• Example: The emergency services responded speedily to the call.
• 'By leaps and bounds' is an idiom that means making rapid or spectacular progress; it is used to describe something that is happening very quickly and successfully. (दिन दूनी रात चौगुनी)
• Example: The technology sector is growing by leaps and bounds every year.
• Hence, the idiom 'by leaps and bounds' is the most appropriate replacement for 'speedily' in the given context.

Therefore, the correct answer is: By leaps and bounds.

Additional Information

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

• By fits and starts (रुक-रुक कर): Something that happens irregularly, with frequent interruptions or without a steady rhythm.
• Example: The renovation project proceeded by fits and starts due to a lack of funding.
• At the eleventh hr (अंतिम समय पर): Doing something at the last possible moment or just before it is too late.
• Example: The agreement was reached at the eleventh hour, preventing a nationwide strike.
• By hook or crook (किसी भी तरह से): By any possible means, whether honest or dishonest.
• Example: He was determined to win the competition by hook or crook.

The correct answer is RSPQ.

Key Points

• The sentence begins with the independent clause She quickly walked to the station, which establishes the primary subject and action.
• Part R (checking the time) is a present participle phrase that acts as an adverbial modifier, describing a secondary action performed by the subject simultaneously with the main verb. Hence, statement R is correct.
• Part S (on her phone) is a prepositional phrase that functions as a modifier for the participle in R, clarifying where the time was being checked. Hence, statement S is correct.
• Part P (trying to catch the train) introduces another participial phrase that explains the motive or reason for the subject’s haste and the preceding actions. Hence, statement P is correct.
• Part Q (before it departed) is a subordinate temporal clause introduced by the conjunction before, providing the specific time constraint for the action in P. Hence, statement Q is correct.

 Additional Information

• Sentence Structure and Syntax:
• Participial Phrases: These phrases start with a present participle (-ing) or past participle and function as adjectives or adverbs to add detail to the sentence without starting new clauses.
• Logical Flow: In sentence rearrangement, identifying the modifier-noun or modifier-verb relationship is crucial. Here, on her phone logically follows checking the time.
• Adverbial Clauses: Clauses like before it departed provide information about when, where, or how an action happens. Placing them at the end often helps maintain the natural cadence of English prose.
• Cohesion: The sequence RSPQ creates a cumulative sentence, where the main idea is joined by a series of modifying phrases that build detail step-by-step.

Therefore, the sequence RSPQ forms a meaningful and grammatically sound sentence.

The correct answer is Option 3.

Key Points

• The passage explicitly states that monks in medieval Europe dedicated long hours to the task of copying manuscripts by hand.
• This painstaking manual labor was a fundamental part of their religious life and was essential for the preservation of knowledge following the decline of the Roman Empire.
• By transcribing these works, they ensured the survival of classical texts in various disciplines such as philosophy, medicine, history, and theology.
• Consequently, the primary daily activity that defined the scholarly life of a monk was the hand-copying of these vital manuscripts.

Therefore, the correct answer is Option 3.

Supporting Quote: 'Monks devoted long hr to copying manuscripts by hand, ensuring the survival of classical texts in philosophy, medicine, history and theology.'

Additional Information

• Option 1: Conducting public debates – While medieval universities later became known for debates, the passage emphasizes monasteries as repositories of knowledge focused on preservation and study.
• Option 2: Creating fictional literature – The text mentions that monks produced commentaries, chronicles, and scientific observations, but it does not cite the creation of fiction as a major daily activity.
• Option 4: Translating foreign languages – Although translation occurred historically, the specific activity highlighted in the passage as occupying long hours of a monk's day is copying manuscripts.
• Monastic efforts served as a vital link between antiquity and the Renaissance, providing the foundational materials for the first European universities.

The correct answer is Option 2.

Key Points

• According to the passage, monks played a significant role in the preservation and evolution of knowledge during medieval Europe.
• The text explicitly mentions that monks produced commentaries, chronicles, and scientific observations based on ancient texts.
• In doing so, they were blending classical learning with Christian thought, rather than keeping the knowledge purely secular or strictly theological.
• This synthesis helped shape medieval scholarship and served as a bridge between antiquity and the later Renaissance.

Therefore, the correct answer is Option 2.

Reference Sentence: 'In addition to copying ancient works, monks produced commentaries, chronicles and scientific observations, blending classical learning with Christian thought.'

Additional Information

• Option 1 is incorrect because the passage says they blended the two, not that they replaced classical learning with theology.
• Option 3 is incorrect because the passage states they ensured the survival of classical texts in philosophy, meaning they did not remove those elements.
• Option 4 is incorrect because while they preserved the texts, they also produced commentaries and blended them with their own religious context, implying a degree of integration and interpretation rather than just static preservation.

The correct answer is Option 1.

Key Points

• The passage primarily focuses on how monasteries in medieval Europe served as vital intellectual centers for preserving knowledge.
• It highlights the efforts of monks who spent long hours copying manuscripts by hand, ensuring that classical texts in medicine, history, and philosophy were not lost.
• The narrative emphasizes that these monastic libraries acted as repositories that linked the intellectual past of antiquity to the Renaissance.
• The central theme revolves around the protection and maintenance of academic works during a time when formal education was scarce, making Monasteries as Keepers of Knowledge the most suitable title.

Therefore, the correct answer is Option 1.

Additional Information

• Option 2: The End of Classical Thought - This is incorrect because the passage explains how classical thought was preserved and blended with Christian ideas, rather than ending.
• Option 3: Religion and Medieval Power - This is too broad; while monasteries were religious, the text specifically addresses their scholarly and educational roles rather than general political or social power.
• Option 4: Decline of Learning in Europe - This title is misleading as the passage focuses on the survival and maintenance of learning through monastic efforts despite the collapse of other centers.

The correct answer is Option 3.

Key Points

• The word restricted in the passage describes the limited or controlled access to monastic knowledge and manuscripts during medieval Europe.
• An antonym is a word that carries the opposite meaning of another word.
• Restricted means kept within certain limits, confined, or not available to the general public.
• The word open means allowing access, not closed or blocked, and available for use by anyone, making it the direct opposite of restricted.
• Thus, open is the correct antonym for the given word.

Therefore, the correct answer is 3.

Contextual Usage: "While access to the library was previously restricted to scholars, it is now open to the general public."

Additional Information

• Cautious: This refers to being careful to avoid potential problems or dangers; it is unrelated to the concept of accessibility.
• Limited: This is a synonym for restricted, meaning kept within certain bounds or small in amount.
• Selective: This means relating to or involving the selection of the most suitable or best individuals or things; it implies a form of controlled access or restriction rather than an opposite.

The correct answer is Option 3.

Key Points

• The passage explicitly states that during medieval Europe, formal education was limited and literacy was rare among the general population.
• It highlights that monastic communities were the primary entities that valued and practiced reading, writing, and study.
• The text mentions that monastic schools were used to train clerics and administrators, which implies that literacy was a specialized skill reserved for those in specific religious or governance roles.
• Furthermore, the author notes that access to this knowledge remained restricted, reinforcing the idea that it was not accessible to the common public but confined to select groups.

Therefore, the correct answer is Option 3.

Inference Summary: 'Because the passage describes literacy as rare and knowledge as restricted to monks, clerics, and administrators, we can infer that literacy was limited to specific social or professional circles.'

Additional Information

• Option 1 is incorrect because the text suggests literacy was rare due to the collapse of learning centers, not because it was actively discouraged or forbidden.
• Option 2 is incorrect because the focus is on monasteries, which were often located in secluded or rural areas, and there is no mention of literacy being exclusive to urban regions.
• Option 4 is incorrect as the text clearly states that literacy was rare and education was limited, which is the opposite of being equally distributed.

'आगे कुआँ पीछे खाई' का सही उत्तर है: सभी ओर से विपत्ति का आना

Key Points

• 'आगे कुआँ पीछे खाई' लोकोक्ति का सही अर्थ 'सभी ओर से विपत्ति का आना' या 'दोनों ओर संकट होना' होगा।

• वाक्य प्रयोग - बेचारा सोहन नौकरी छोड़ता है तो भूखा मरता है और करता है तो अपमानित होता है, उसके लिए तो 'आगे कुआँ पीछे खाई' वाली स्थिति है।

• परिभाषा - लोकोक्ति का अर्थ है 'लोक में प्रचलित उक्ति'। जब कोई पूरा कथन किसी प्रसंग विशेष में उद्धृत किया जाता है, तो उसे लोकोक्ति कहते हैं। इसे कहावत भी कहा जाता है।

अन्य विकल्प-

Additional Information

कुछ महत्वपूर्ण संबंधित शब्द (लोकोक्तियाँ) -

दिए गए वाक्य में वर्तनी संबंधी अशुद्धि वाले भाग का सही उत्तर है: अधि कांस

मुख्य बिंदु

• 'अधि कांस' भाग में वर्तनी संबंधी अशुद्धि है, इसलिए सही उत्तर 'अधि कांस' होगा।

• 'अधिकांश' के संबंधित शब्द — अधिकतम, ज्यादातर, बहुधा।

• परिभाषा - लिखने की रीति को वर्तनी या अक्षरी कहते हैं। जब किसी शब्द में वर्णों का प्रयोग उचित क्रम में नहीं होता या गलत वर्णों का प्रयोग किया जाता है, तो उसे वर्तनी संबंधी अशुद्धि कहा जाता है। वाक्य में 'अधिकांश' को 'अधि कांस' लिखना त्रुटिपूर्ण है।

अन्य विकल्प-

अतिरिक्त जानकारी

कुछ महत्वपूर्ण वर्तनी सुधार -

दिए गए वाक्य का सही उत्तर है: ग्रामीण व्यक्तित्व

Key Points

• वाक्य के 'ग्रामीण व्यक्तित्व' वाले भाग में वर्तनी की अशुद्धि है।
• 'ग्रामीण' शब्द की शुद्ध वर्तनी में 'ण' का प्रयोग होता है, न कि 'न' का।
• 'व्यक्तित्व' शब्द ��ी शुद्ध वर्तनी में आधा 'क' और आधा 'त' का प्रयोग किया जाता है (व्य + क्ति + त्व)।
• परिभाषा - वर्तनी का अर्थ है शब्दों को लिखने के लिए वर्णों का सही क्रम। उच्चारण की अशुद्धि के कारण ही प्रायः लिखने में भी त्रुटि होती है।

अन्य विकल्प-

Additional Information

कुछ महत्वपूर्ण वर्तनी सुधार -

दिए गए वाक्य में अशुद्ध अंश है: का रूप-विश्लेषण

मुख्य बिंदु

• दिए गए वाक्य 'अध्यापक द्वारा साहित्यिक रचना का रूप-विश्लेषण किया गया' के भाग 'का रूप-विश्लेषण' में वर्तनी की त्रुटि है।

• इस वाक्यांश में 'विश्लेषण' शब्द का प्रयोग किया गया है। परीक्षा के दृष्टिकोण से अक्सर 'विश्लेषण' को अशुद्ध रूप में 'विष्लेषण' या 'विश्लेषन' लिखा जाता है, जो वर्तनी की दृष्टि से अशुद्ध है।

• परिभाषा - किसी तत्व या विषय के अंगों को अलग-अलग करके उनका सूक्ष्म अवलोकन व परीक्षण करने की प्रक्रिया को 'विश्लेषण' कहते हैं।

अन्य विकल्प-

अतिरिक्त जानकारी

कुछ महत्वपूर्ण शुद्ध-अशुद्ध वर्तनी वाले शब्द -

इस प्रश्न का सही उत्तर option 4 है , निचे दिए उत्तर के फॉ र्मेट मे html code में उत्तर दे , niche diya html code sirf sample demo hai

इसका सही उत्तर 'की' है।

Key Points

कारक और विभक्ति के नियमानुसार ,

• दिए गए वाक्य में 'शालू' और 'पुस्तक' के बीच सम्बन्ध दर्शाया जा रहा है, इसलिए यहाँ सम्बन्ध कारक का प्रयोग होगा।
• सम्बन्ध कारक के चिह्न 'का, के, की' होते हैं।
• चूँकि 'पुस्तक' एक स्त्रीलिंग संज्ञा शब्द है, इसलिए इसके साथ स्त्रीलिंग विभक्ति 'की' का प्रयोग उचित है।
• अतः, पूर्ण वाक्य होगा: 'यह शालू की पुस्तक है।'

Additional Information अन्य विकल्प:

पर -

• यह अधिकरण कारक का चिह्न है, जो क्रिया के आधार (स्थान या समय) को प्रकट करता है, जैसे- 'छत पर पक्षी बैठे हैं।'

को -

• यह कर्म कारक का चिह्न है, जिस पर क्रिया का फल पड़ता है, जैसे- 'उसने मोहन को बुलाया।'

हे -

• यह संबोधन कारक का चिह्न है, जिसका प्रयोग किसी को बुलाने या सचेत करने के लिए किया जाता है, जैसे- 'हे प्रभु! रक्षा करो।'

वाक्य 'सहज भाषा पाने के लिए कठोर तप अवश्यक है' के त्रुटिपूर्ण भाग का सही उत्तर है- अवश्यक है।

मुख्य बिंदु

• दिए गए वाक्य के भाग 'अवश्यक है' में वर्तनी संबंधी त्रुटि है। शब्द 'अवश्यक' अशुद्ध है, इसके स्थान पर 'आवश्यक' का प्रयोग होना चाहिए।
• हिंदी व्याकरण में शब्दों के वर्णों को सही क्रम में लिखना वर्तनी कहलाता है। यहाँ 'अ' स्वर के स्थान पर 'आ' स्वर का प्रयोग होना चाहिए था।
• शुद्ध वाक्य: सहज भाषा पाने के लिए कठोर तप आवश्यक है।
• अन्य वर्तनी उदाहरण: 'अगामी' के स्थान पर 'आगामी' और 'अहार' के स्थान पर 'आहार' शुद्ध रूप हैं।

अन्य विकल्प -

महत्वपूर्ण बिंदु 
 वर्तनी अशुद्धि के मुख्य प्रकार-

1. स्वर संबंधी अशुद्धियाँ (जैसे: अ/आ, इ/ई की त्रुटि)
2. व्यंजन संबंधी अशुद्धियाँ (जैसे: ण/न, ड/ड़ की त्रुटि)
3. अनुस्वार-अनुनासिक संबंधी अशुद्धियाँ
4. विसर्ग संबंधी अशुद्धियाँ

अतिरिक्त जानकारी

कंचन का सही उत्तर है: कनक

मुख्य बिंदु

• वाक्य में प्रयुक्त 'कंचन' शब्द का सही पर्यायवाची 'कनक' होगा।

• 'कंचन' के अन्य पर्यायवाची शब्द — सोना, स्वर्ण, कुंदन, हेम, हाटक।

• परिभाषा - पर्यायवाची शब्द उन शब्दों को कहते हैं जिनके अर्थ में समानता होती है, अर्थात एक ही वस्तु या भाव के लिए प्रयुक्त होने वाले भिन्न-भिन्न शब्द।

अन्य विकल्प-

अतिरिक्त जानकारी

कुछ महत्वपूर्ण पर्यायवाची शब्द -

'जो मन को हर ले' का सही उत्तर है: मनोहर

Key Points

• 'मनोहर' शब्द का सही अर्थ 'मन को हरने वाला' या 'सुंदर' होता है।

• 'मनोहर' के संबंधित शब्द — मनोरम, चित्ताकर्षक, ललित, मंजुल।

• परिभाषा - कम से कम शब्दों में अधिक से अधिक अर्थ प्रकट करना 'वाक्यांश के लिए एक शब्द' कहलाता है।