SSC GD Constable 2026 Official Paper (Held On 27 Apr, 2026 Shift 2) (Previous Year Paper)

The logic followed in this pattern is a series of alphabetical shifts based on the positional values of the letters.

For 'LK' related to 'GE':

For 'FG' related to 'AA':

Applying the same logic to find the cluster related to 'YD':

Thus, DJ is the letter cluster that is related to YD.

Hence, the correct answer is 'Option 3'.

Given that the 2^nd of the current month is Monday.

The total number of days in the current month is 31 days.

Days remaining in the current month after the 2^nd = 31 − 2 = 29 days.

Days in the next month to reach the target date = 10 days.

Total days from the 2^nd of the current month to the 10^th of the next month = 29 + 10 = 39 days.

Number of odd days = 39 ÷ 7 ⇒ Remainder = 4 odd days

Now, add 4 days to the starting day (Monday):

Monday + 4 days = Friday

Hence, the 10^th of the next month will be Friday.

Hence, the correct answer is “Option 3”.

To find the first day of the year 1666, we need the day of the week on January 1, 1666.

Number of completed years = 1665 years

Breakdown of 1665 years = 1600 years + 65 years

Odd days in 1600 years = 0 (as 1600 is a multiple of 400)

In the remaining 65 years, number of leap years = 65 ÷ 4 = 16 (quotient)

Number of ordinary years = 65 − 16 = 49

Odd days in 65 years = (16 × 2) + (49 × 1) = 32 + 49 = 81 odd days

Converting 81 days into weeks: 81 ÷ 7 = 11 weeks and 4 odd days.

Total odd days until December 31, 1665 = 0 (from 1600 years) + 4 (from 65 years) = 4 odd days.

Number of odd days for January 1, 1666 = 4 (completed years) + 1 (current day) = 5 odd days.

According to the mapping, 5 odd days corresponds to Friday.

Hence, the first day of the year 1666 was Friday.

Key Points 

​Number of odd days in 100 years = 5

Number of odd days in 200 years = 3

Number of odd days in 300 years = 1

Number of odd days in 400 years = 0

An ordinary year has 1 odd day, and a leap year has 2 odd days.

Day code mapping: 0 = Sunday, 1 = Monday, 2 = Tuesday, 3 = Wednesday, 4 = Thursday, 5 = Friday, 6 = Saturday.

Alternate Method

Using the formula: Day = (Date + Month Code + Century Code + Year + Leap Year Code) ÷ 7

For January 1, 1666:

Date = 1

Month Code (January) = 0

Century Code (1600s) = 6

Year = 66

Leap Year Code (66 ÷ 4) = 16

Total = 1 + 0 + 6 + 66 + 16 = 89

Remainder of 89 ÷ 7 = 5

Day code 5 corresponds to Friday.

Hence, the correct answer is Friday.

Given the conditions for the runs scored by five boys R, B, C, L, and Q:

1. Runs of B are less than Q but more than C: 

Q > B > C.

2. Runs of L are more than R but less than C:

C > L > R.

By combining these two relationships, we get the complete descending sequence of runs:

Q > B > C > L > R

Now, let us evaluate the given sequences based on the combined chain:

I. Q > L > R → Correct (From the combined sequence Q > B > C > L > R, it is clear that Q is greater than L, and L is greater than R.)

II. B > L > C → Incorrect (From the combined sequence, we see that B > C and C > L, which means the order should be B > C > L.)

Since only the first sequence holds true, Only I is the correct conclusion.

Hence, the correct answer is 'Option 1'.

Given that there are 6 boys with different heights: M, N, O, P, Q, and R.

From the clues, we can deduce the following relationships:

1. Height of M is less than only Q and O.

→ So, the order is: O/Q > O/Q > M > _ > _ > _

2. O is the tallest boy among all.

→ Therefore, O > Q > M > _ > _ > _

3. Height of P is more than R but less than N.

→ N > P > R

4. Since M is already the 3^rd tallest, the remaining three positions below M must be occupied by N, P, and R.

Combining all the facts gives the final order from tallest to shortest:

→ O > Q > M > N > P > R

The boy whose height is less than M but more than P is N.

Hence, the correct answer is "Option 4".

Given Word: EAGLES

1. SAGE → The letters required are S, A, G, E. All these letters are available in EAGLES. Thus, SAGE can be formed.

2. LEGS → The letters required are L, E, G, S. All these letters are available in EAGLES. Thus, LEGS can be formed.

3. GALE → The letters required are G, A, L, E. All these letters are available in EAGLES. Thus, GALE can be formed.

Hence, the correct answer is “Option 4”.

Given:

'Pooja is older than Neha but younger than Rina':

Rina > Pooja > Neha.

'Seema is younger than Neha but older than Kiran': 

Neha > Seema > Kiran.

By combining both logical chains, we get the following sequence:

Rina > Pooja > Neha > Seema > Kiran.

Therefore, Kiran is the youngest person among them.

Hence, the correct answer is 'Option 4'.

Least possible Venn diagram,

​

Conclusions:

I. All the trains are bikes → Does not follow (The statements only tell us that all trains are cats. There is no information that all trains are bikes.)

II. Some bikes are trains → Does not follow (Although some bikes are cats and all trains are cats, there is no definite information that bikes and trains overlap.)

Neither conclusion I nor II follows.

Hence, the correct answer is "Option 4".

The logic followed in this pattern is based on specific alphabetical shifts for each letter in the group.

For 'CFI' related to 'HMO':

Applying the same logic to 'BDF':

Thus, CFI is related to HMO in the same way BDF is related to GKL.

Hence, the correct answer is 'Option 4'.

BEG : CFH

 

Similarly,

DFH : ?

 

Hence, the correct answer is 'Option 1'.

Given Statements:

1. L = F < D ≤ R

2. Y = T ≥ Q = L

Combined Statement: Y = T ≥ Q = L = F < D ≤ R

Conclusions:

I: T > F → False (Because T ≥ F)

II: F ≤ Y → True (Since Y = T and T > F, therefore F < Y, which means F ≤ Y.)

Therefore, Only conclusion II is true.

Hence, the correct answer is “Option 3”.

Logic followed here is,

840 − 20 = 820

820 − 40 = 780

780 − 60 = 720

720 − 80 = 640

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 2”.

The logic followed here is,

Revenue in January = 75,000

Revenue in February = 75,000 × 1.1 = 82,500

Revenue in March = 82,500 × 1.1 = 90,750

Revenue in April = 90,750 × 1.1 = 99,825

Revenue in May = 99,825 × 1.1 = 1,09,807.5

Revenue in June = 1,09,807.5 × 1.1 = 1,20,788.25

Thus, the monthly revenue in June will be ₹1,20,788.25.

Hence, the correct answer is 'Option 3';

The logic followed here is:

Logic: Second Number = (First Number)²

For the first pair 12 : 144

⇒ 12 × 12 = 144

For the second pair 9 : 81

⇒ 9 × 9 = 81

For the third pair 7 : 49

⇒ 7 × 7 = 49

Applying the same logic to the fourth pair

8 : ?

⇒ 8 × 8 = 64

Hence, the correct answer is 'Option 2'.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

TL210 : JV105 → 

EK320 : IG160 → 

Similarly,

DL500 : ? → 

Hence, the correct answer is “Option 3”.

Dictionary order of Given words:

3. Cycle

4. Cyclone

5. Cyclostyle

6. Cylinder

7. Cymbal

Correct order is : 32514

Hence, the correct answer is “Option 1”.

Dictionary order of given words:

2. Vinegar

3. Violaceous

4. Violate

5. Violence

6. Violent

Correct order is : 25134

Hence, the correct answer is “Option 4”.

CENT is coded as 168 →

Sum of positional values = 3 + 5 + 14 + 20 = 42

Code = 42 × 4 = 168

TAPE is coded as 168 →

Sum of positional values = 20 + 1 + 16 + 5 = 42

Code = 42 × 4 = 168

Similarly, let's find the code for PEACE:

Sum of positional values = 16 + 5 + 1 + 3 + 5 = 30

Code = 30 × 4 = 120

Hence, the correct answer is “Option 1”.

The correct answer is Finance Commission.

Key Points

• The Finance Commission is a constitutional body established by the President of India under Article 280 of the Indian Constitution.
• Its primary mandate is to define the financial relations between the Central Government and the State Governments, ensuring a balanced distribution of resources.
• The commission provides critical recommendations on the distribution of net proceeds of taxes between the Union and the States, a process known as vertical devolution.
• It also determines the principles for horizontal devolution, which is the allocation of tax proceeds among the various State Governments based on specific criteria like population, area, and fiscal capacity.
• Furthermore, it specifies the principles governing grants-in-aid to the States from the Consolidated Fund of India under Article 275.
• The First Finance Commission was constituted in 1951 under the chairmanship of K.C. Neogy, and typically, a new commission is formed every five years.

 Additional Information

• NITI Aayog:
• Established on January 1, 2015, it replaced the erstwhile Planning Commission.
• It serves as the premier policy think-tank of the Government of India, fostering cooperative federalism through a bottom-up approach.
• Unlike the Finance Commission, it does not possess the power to allocate or distribute funds to state governments.
• Planning Commission:
• Formed in 1950 as a non-constitutional and non-statutory body to formulate Five-Year Plans.
• It was responsible for central planning and resource allocation before being dissolved in 2014.
• Parliament:
• The supreme legislative body of India, comprising the President, Lok Sabha, and Rajya Sabha.
• It holds the authority to enact laws and pass the Union Budget, but it relies on the technical recommendations of the Finance Commission for tax sharing mechanisms.

The correct answer is President.

Key Points

• The Finance Commission is a quasi-judicial and constitutional body established by the President of India under Article 280 of the Indian Constitution.
• According to Article 280(1), the President is responsible for constituting the commission every five years or at such earlier time as he or she considers necessary.
• The commission consists of a Chairman and four other members, all of whom are officially appointed by the President by warrant under his hand and seal.
• The Chairman must be a person having experience in public affairs, while the other members are selected from among people who are High Court judges, have specialized knowledge of finance and accounts, or have wide experience in financial matters and economics.
• The primary function of the body is to provide recommendations to the President regarding the distribution of tax proceeds between the Union and the States and the principles governing grants-in-aid.

 Additional Information

• Parliamentary Role:
• While the President appoints the members, Article 280(2) grants Parliament the power to determine the qualifications and the manner of selection of the members.
• This led to the enactment of the Finance Commission (Miscellaneous Provisions) Act, 1951, which defines the eligibility criteria for the Chairman and members.
• Historical Context:
• The First Finance Commission was established in 1951 under the chairmanship of K.C. Neogy.
• The 15^th Finance Commission was chaired by N.K. Singh, and its recommendations cover the period up to 2025-26.
• The 16^th Finance Commission has recently been constituted with Arvind Panagariya as its Chairman.
• Reporting Mechanism:
• Under Article 281, the President must lay the recommendations of the Finance Commission, along with an explanatory memorandum on the action taken, before each House of Parliament.

The correct answer is Holi.

Key Points

• The Gaur dance is a world-renowned tribal folk dance performed by the Bison Horn Maria tribe, who primarily reside in the Bastar district of Chhattisgarh.
• This dance is predominantly performed during the spring festival of Holi (also known as Phagun) to celebrate the bounty of nature and the community's hunting traditions.
• The name of the dance is derived from the Gaur (Indian Bison), which is considered a symbol of strength and vitality by the tribe.
• Male performers wear a magnificent headdress made of bison horns, decorated with tufts of feathers and cowrie shells, mimicking the movements and spirit of a charging bull.
• The dance is characterized by energetic movements, rhythmic footwork, and the thunderous sound of large Dhol drums, which represent the heartbeat of the forest.

 Additional Information

• Maria Tribe:
• They are a major sub-group of the Gond community and are known for their distinct Ghotul system and rich artistic heritage.
• The Bison Horn Maria are specifically distinguished by their unique ritualistic use of animal horns in ceremonies.
• Significance of Other Festivals:
• Diwali: Known as the festival of lights, it is a pan-Indian festival but is not the primary occasion for the traditional Gaur dance.
• Navratri: This nine-night festival is dedicated to the Goddess Durga and is more famous for the Garba and Dandiya dances in Gujarat.
• Baisakhi: It is a major harvest and religious festival celebrated in Punjab and Haryana, marking the formation of the Khalsa Panth in 1699.
• Cultural Instruments: The performance relies heavily on traditional instruments like the Mandri, Tirududi (musical sticks), and brass flutes to maintain a high-energy tempo throughout the night.

The correct answer is Guru Granth Sahib.

Key Points

• Hola Mohalla is a prominent Sikh festival celebrated annually, typically in the month of March, one day after the Hindu festival of Holi.
• The festival was initiated by the tenth Sikh Guru, Guru Gobind Singh, in 1701 at Anandpur Sahib to transform the peaceful celebration of Holi into a display of martial spirit and military prowess.
• The Guru Granth Sahib, the central religious scripture of Sikhism, is the focal point of the celebrations; its verses are recited through Akhand Path (continuous reading) and Kirtan (devotional singing) throughout the event.
• During the festivities, Nihang Sikhs perform traditional martial arts known as Gatka, engage in mock battles, and demonstrate equestrian skills, all while maintaining the spiritual atmosphere through the recitation of Gurbani.

 Additional Information

• Guru Granth Sahib:
• It was first compiled as the Adi Granth by the fifth Guru, Guru Arjan Dev, in 1604 and later finalized by Guru Gobind Singh, who designated it as the eternal Guru.
• It contains 1,430 pages (Angs) and includes the teachings of six Sikh Gurus and various medieval saints like Kabir and Baba Farid.
• Bhagavad Gita:
• A sacred Hindu scripture consisting of 700 verses, it forms a part of the Indian epic Mahabharata and features a dialogue between Lord Krishna and Arjuna.
• Quran:
• The central religious text of Islam, believed by Muslims to be the verbatim word of God (Allah) as revealed to the Prophet Muhammad.
• Bible:
• The holy scripture of Christianity, comprised of the Old Testament and the New Testament, detailing the history of the faith and the life of Jesus Christ.

The correct answer is When it is in the direction of velocity.

Key Points

• Acceleration is defined as the rate at which an object changes its velocity. It is a vector quantity, meaning it possesses both magnitude and direction.
• The standard unit for measuring acceleration is meters per second squared (m/s²).
• Acceleration is considered positive when the change in velocity occurs in the same direction as the motion of the object. This typically results in the object speeding up.
• Mathematically, if the final velocity (v) is greater than the initial velocity (u) over a time period (t), the acceleration (a = (v − u) / t) yields a positive value.
• When the acceleration vector and the velocity vector point in the same direction, the magnitude of the velocity increases, confirming a positive acceleration relative to the direction of travel.

 Additional Information

• Negative Acceleration (Retardation):
• This occurs when the acceleration acts in the opposite direction to the velocity of the object.
• In such cases, the object slows down or undergoes deceleration. For example, applying brakes to a moving car produces negative acceleration.
• Zero Acceleration:
• An object has zero acceleration when it is at rest or moving with a constant velocity in a straight line.
• If there is no change in speed or direction, the acceleration is null.
• Directional Sign Conventions:
• The sign of acceleration (+ or −) depends on the chosen coordinate system.
• An object moving in a negative direction (e.g., left) that is slowing down actually has positive acceleration because the acceleration vector points in the positive direction (right) to oppose the motion.

The correct answer is Mary Shelley.

Key Points

• Mary Shelley was an English novelist who wrote the iconic novel Frankenstein; or, The Modern Prometheus, which was first published in 1818.
• The novel is frequently categorized as a masterpiece of Gothic horror and is widely regarded by scholars as the first true work of science fiction.
• The story was famously conceived during a competition to write ghost stories in 1816 at Villa Diodati in Switzerland, where Mary was staying with Percy Bysshe Shelley and Lord Byron.
• The plot centers on Victor Frankenstein, a scientist who animates a creature made from scavenged body parts, leading to an exploration of scientific responsibility and existential despair.

 Additional Information

• Bram Stoker
• An Irish author celebrated for his 1897 Gothic novel Dracula, which significantly shaped the modern vampire mythology in literature and film.
• H.G. Wells
• An English writer known as one of the 'fathers of science fiction' for his visionary works including The Time Machine (1895), The Invisible Man (1897), and The War of the Worlds (1898).
• Robert Louis Stevenson
• A Scottish novelist and poet famous for his psychological thriller Strange Case of Dr Jekyll and Mr Hyde (1886) and the adventure classic Treasure Island (1883).

The correct answer is Efficiency of the judicial system in resolving commercial disputes.

Key Points

• The Enforcing Contracts indicator is a core component of the World Bank Group's Ease of Doing Business (EODB) index, which evaluates the efficiency of the judicial system in handling commercial litigation.
• It measures the time and cost for resolving a commercial dispute through a local first-instance court, based on a standardized case study of a sales contract dispute between two domestic businesses.
• The Time metric calculates the duration in calendar days from the moment the plaintiff files the lawsuit until the final enforcement of judgment or actual payment.
• The Cost metric is expressed as a percentage of the claim value and includes court fees, attorney fees, and enforcement costs required to complete the litigation process.
• It also features a Quality of Judicial Processes Index, which uses a 0-18 scale to assess court structure, case management, court automation, and the availability of Alternative Dispute Resolution (ADR).
• A high ranking indicates that an economy has a transparent, predictable, and efficient legal framework, which reduces uncertainty and risks for entrepreneurs and investors.

 Additional Information

• Other key indicators within the Doing Business framework include:
• Paying Taxes: Measures the total tax rate, time taken to comply with tax laws, and the complexity of post-filing processes like audits or refunds.
• Labor Market Regulation: Analyzes the flexibility of employment contracts, including regulations on hiring, working hours, and severance pay.
• Resolving Insolvency: Focuses on the efficiency and outcome of bankruptcy proceedings, measuring recovery rates and the strength of the insolvency framework.
• Registering Property: Tracks the number of procedures, time, and cost involved in transferring a land title from one company to another.
• In 2021, the World Bank announced the discontinuation of the Doing Business report, replacing it with a more comprehensive project titled Business Ready (B-READY).

The correct answer is Helsinki, 1983.

Key Points

• The inaugural World Athletics Championships were held in Helsinki, Finland, between August 7 and August 14, 1983.
• The event was organized by the International Association of Athletics Federations (IAAF), which is now known as World Athletics.
• The primary venue for the competition was the Helsinki Olympic Stadium, which had previously hosted the 1952 Summer Olympics.
• This championship marked a significant shift in track and field history, as it was the first time a standalone global competition was conducted independently of the Olympic Games.
• A total of 1,333 athletes from 153 nations participated, competing across 41 sports events, including 24 for men and 17 for women.
• The United States emerged as the most successful nation in terms of the medal tally, securing 24 medals, including 8 golds, with the Soviet Union and East Germany following closely.
• American sprinter and long jumper Carl Lewis was the standout athlete of the meet, winning three gold medals in the 100 meters, long jump, and the 4×100 meters relay.

 Additional Information

• The World Athletics Championships followed a quadrennial cycle (every four years) until 1991, after which it transitioned to a biennial cycle (every two years).
• Rome, 1987:
• This was the second edition of the championships held at the Stadio Olimpico in Italy.
• It featured 43 events and saw the introduction of the 10,000 meters and 10 km walk for women.
• Tokyo, 1991:
• The third edition was hosted in Japan and is widely remembered for Mike Powell breaking Bob Beamon's long-standing long jump world record with a leap of 8.95 meters.
• Stuttgart, 1993:
• The fourth edition took place in Germany (the option mentions Berlin, but the 1993 event was actually in Stuttgart).
• It was the first championship where the biennial schedule was fully implemented.

The correct answer is 58 days.

Key Points

• To find the time taken for the journey, we use the fundamental kinematic formula: Time = Distance ÷ Speed.
• The distance to be covered is 1 Astronomical Unit (AU), which is defined as approximately 150,000,000 kilometers.
• The constant speed of the spacecraft is provided as 30 km/s.
• First, calculate the total time in seconds: 150,000,000 km ÷ 30 km/s = 5,000,000 seconds.
• To convert this duration into a more standard unit like days, we determine the number of seconds in one day: 24 hours × 60 minutes × 60 seconds = 86,400 seconds.
• Finally, divide the total seconds by the seconds per day: 5,000,000 ÷ 86,400 ≈ 57.87 days.
• When rounded to the nearest whole number, the duration equals 58 days.

 Additional Information

• Astronomical Unit (AU)
• It serves as a standard unit of measurement in astronomy to describe distances within the Solar System.
• It represents the mean distance between the center of the Earth and the center of the Sun, approximately 93 million miles.
• Relative Speeds in Space
• A speed of 30 km/s is comparable to the orbital velocity of Earth, which moves at about 29.78 km/s around the Sun.
• In comparison, light travels at 299,792 km/s, meaning it takes only about 8 minutes and 20 seconds for sunlight to reach Earth.
• Man-made probes like the Voyager 1 travel at roughly 17 km/s, whereas the Parker Solar Probe has reached record-breaking speeds exceeding 150 km/s during its solar approach.

The correct answer is 2021.

Key Points

• India officially assumed the BRICS Chairship from the Russian Federation on January 1, 2021.
• The year 2021 marked the third time India headed the group, after previously holding the presidency in 2012 and 2016.
• Under its chairship, India hosted the 13^th BRICS Summit on September 9, 2021, which was chaired by Prime Minister Narendra Modi in a virtual format.
• The chairship of BRICS (Brazil, Russia, India, China, and South Africa) rotates annually among the members in accordance with the acronym B-R-I-C-S; thus, Russia handed over the baton to India.
• The primary theme selected by India for its 2021 tenure was 'BRICS @ 15: Intra-BRICS Cooperation for Continuity, Consolidation and Consensus'.

 Additional Information

• BRICS Formation and Evolution:
• The grouping was originally formed as BRIC following a meeting of the leaders of Brazil, Russia, India, and China in 2006.
• It was expanded to BRICS in 2010 with the formal induction of South Africa during the Sanya Summit in China.
• The BRICS nations together represent about 41 percent of the global population, 24 percent of the global GDP, and over 16 percent of global trade share.
• One of the most significant achievements of the group is the establishment of the New Development Bank (NDB), headquartered in Shanghai, which was formalized during the 6^th BRICS Summit in Fortaleza, Brazil (2014).
• The grouping serves as a platform for South-South cooperation and seeks to reform multilateral institutions like the United Nations and the IMF to reflect contemporary global realities.

The correct answer is They restricted economies of scale and technological upgrading.

Key Points

• The reservation policy for Small-Scale Industries (SSIs) was primarily designed to protect small producers from the competition of large-scale manufacturers and to promote employment generation.
• A significant drawback was the investment limit placed on plant and machinery; firms that expanded their capital beyond a specific threshold lost their SSI status and associated government incentives.
• This policy created a perverse incentive for entrepreneurs to keep their units small, which prevented them from achieving economies of scale, leading to higher marginal costs of production.
• Due to the fear of losing protection, these industries avoided technological upgrading and modernization, resulting in technological obsolescence and lower productivity compared to global standards.
• The lack of scale and modern technology eventually made these units uncompetitive in the international market, as they could not match the quality or price of goods produced by large-scale global firms.

 Additional Information

• Karve Committee (1955):
• Also known as the Village and Small-Scale Industries Committee, it first suggested using small-scale industries as a tool for rural development and social justice.
• Abed Hussain Committee:
• This committee later recommended the de-reservation of items, arguing that reservation hindered the export potential and growth of the manufacturing sector.
• Industrial Policy Resolution 1956:
• It laid the foundation for the Public Sector and provided various fiscal concessions, like lower excise duties and bank loans at lower interest rates, to the SSI sector.
• Post-1991 Reforms:
• Following Liberalization, the government began a phased de-reservation process to allow Market Competition to drive efficiency and innovation within the industry.

The correct answer is Harrod-Domar model.

Key Points

• The First Five-Year Plan was launched for the period of 1951 to 1956 under the leadership of India's first Prime Minister, Jawaharlal Nehru.
• The plan was based on the Harrod-Domar model, which posits that economic growth depends on the level of savings and the capital-output ratio; specifically, it suggests that higher savings lead to higher investment and thus higher growth.
• The primary focus of this plan was the development of the primary sector, with a heavy emphasis on agriculture, irrigation, and power to address the food shortages caused by the partition of India.
• Significant investments were made in large-scale multipurpose projects, including the Bhakra-Nangal, Hirakud, and Damodar Valley dams, to improve irrigation and power generation.
• The plan was highly successful, achieving a growth rate of 3.6%, which significantly exceeded the target growth rate of 2.1%.

 Additional Information

• Mahalanobis Model
• Formulated by statistician Prasanta Chandra Mahalanobis, this model served as the blueprint for the Second Five-Year Plan (1956-1961).
• It shifted the economic focus from agriculture to rapid industrialization, specifically emphasizing heavy and basic industries like steel and chemicals.
• Solow Model
• Developed by Robert Solow, this is an exogenous growth model that analyzes long-run economic growth by looking at capital accumulation, labor growth, and technological progress.
• Unlike the Harrod-Domar model, it accounts for diminishing returns to capital and emphasizes that technological change is the ultimate driver of growth.
• Keynesian Model
• Originating from John Maynard Keynes, this macroeconomic theory focuses on how aggregate demand (total spending) influences output and inflation.
• It advocates for government intervention through fiscal and monetary policies to manage economic cycles, particularly to mitigate recessions and unemployment.

The correct answer is 91.4 m.

Key Points

• A standard field hockey pitch is a rectangular playing surface with a specific length of 91.40 meters (equivalent to 100 yards) and a width of 55.00 meters (equivalent to 60 yards).
• The dimensions and markings are strictly regulated by the International Hockey Federation (FIH), which is the global governing body for the sport.
• The total area of a regulation field is approximately 5,027 square meters, and it is divided by a center line and two 23-meter lines (historically 25-yard lines).
• The pitch is marked with white lines that are 75 mm wide, and these lines are considered part of the playing area.

 Additional Information

• Specific Field Markings:
• Shooting Circle (D): A semi-circular area formed by two quarter-circles with a radius of 14.63 meters (16 yards) from the inner front corner of each goal post.
• Penalty Spot: A circular mark with a diameter of 150 mm, positioned 6.40 meters (7 yards) from the center of the goal line.
• Penalty Corner Markings: Markers are placed on the backline at 5 meters and 10 meters from the goal posts to facilitate set plays.
• Playing Surfaces:
• Modern high-level hockey is played almost exclusively on artificial turf, which provides a fast and consistent ball roll.
• Water-based pitches are the standard for Olympic Games and World Cups, requiring a layer of water to reduce friction and prevent player injury.
• Sand-dressed or sand-filled artificial grass is commonly used at club and school levels for durability.

The correct answer is Urban infrastructure and water supply.

Key Points

• The Atal Mission for Rejuvenation and Urban Transformation (AMRUT) was launched by the Ministry of Housing and Urban Affairs (MoHUA) in June 2015 to improve the quality of life in urban areas.
• The primary objective of the mission is to ensure that every household has access to a functional tap with an assured supply of water and a sewerage connection to manage waste effectively.
• It prioritizes the development of urban infrastructure, specifically focusing on stormwater drainage to reduce flooding and the promotion of non-motorized urban transport like cycling and walking.
• The mission aims to increase the amenity value of cities by developing and maintaining green spaces, parks, and well-designed open spaces, especially for children.
• AMRUT covers 500 cities across India, including those with a population of over one lakh, capital cities, and identified heritage cities or cities on the banks of main rivers.

 Additional Information

• AMRUT 2.0:
• Launched in October 2021, this subsequent phase aims to make Indian cities water secure and provide 100% coverage of water supply to all households in about 4,700 Urban Local Bodies (ULBs).
• It promotes the circular economy of water through the development of City Water Balance Plans focusing on recycle/reuse of treated sewage and rejuvenation of water bodies.
• Related Urban Schemes:
• Smart Cities Mission: Focused on driving economic growth and improving quality of life through local development and technology.
• Swachh Bharat Mission-Urban: Concentrates on making cities garbage-free and open defecation free (ODF).

The correct answer is EXIM Bank.

Key Points

• The Export-Import Bank of India, popularly known as EXIM Bank, is the premier export finance institution in India, established in 1982 under the Export-Import Bank of India Act, 1981.
• It was set up for the purpose of financing, facilitating, and promoting foreign trade in India and is the principal financial institution for coordinating the working of institutions engaged in financing export and import of goods and services.
• The bank is fully owned by the Government of India and plays a vital role in providing Lines of Credit (LOC) to overseas financial institutions and sovereign governments to encourage the purchase of Indian goods.
• It provides a wide range of financial products such as Buyer's Credit, Supplier's Credit, and Pre-shipment Credit to assist Indian exporters in operating in the competitive global market.
• Beyond financing, EXIM Bank offers value-added services including market research, advisory services, and technical assistance to help Indian companies establish a global footprint.

 Additional Information

• NABARD (National Bank for Agriculture and Rural Development):
• Established on July 12, 1982, based on the recommendations of the B. Sivaraman Committee.
• It is the apex development bank in India specifically for agriculture and rural development.
• SIDBI (Small Industries Development Bank of India):
• Established on April 2, 1990, under an Act of Parliament to serve as the principal financial institution for the MSME (Micro, Small and Medium Enterprises) sector.
• It focuses on the promotion, financing, and development of small-scale industries and coordinates the functions of similar institutions.
• World Bank:
• An international financial organization established at the 1944 Bretton Woods Conference, headquartered in Washington, D.C.
• It consists of the IBRD and IDA, providing loans and grants to low and middle-income countries for capital projects and poverty reduction.

The correct answer is Jahangir.

Key Points

• Emperor Jahangir explicitly recorded the economic and logistical contributions of the Banjaras in his personal memoirs, titled Tuzuk-i-Jahangiri.
• He described how these trader-nomads transported grain on their bullocks from various regions to be sold in urban markets, highlighting their role in the Mughal trade network.
• The Banjaras were the most prominent nomadic community in medieval India, moving in large caravans known as tandas, which often comprised thousands of bullocks and entire families.
• During major military campaigns, the Mughal army depended on the Banjaras for food supplies; Jahangir noted that a single army could be accompanied by as many as 100,000 bullocks carrying grain.
• They functioned as a vital logistics chain, purchasing grain where it was plentiful and cheap and transporting it to areas where demand was high, thereby stabilizing food distribution across the empire.

 Additional Information

• Tuzuk-i-Jahangiri:
• This autobiography, written in Persian, provides comprehensive details on the administrative, social, and cultural aspects of 17^th-century India.
• It reflects Jahangir’s keen interest in the daily lives of his subjects and the practicalities of governance, including the movements of nomadic tribes.
• Babur:
• He authored the Baburnama (Tuzk-e-Babri) in Chaghatai Turkic, focusing on the flora, fauna, and geography of India, but it does not contain specific accounts of the Banjaras transporting grain.
• Sher Shah Suri:
• Although he is credited with the development of the Grand Trunk Road (Sadak-e-Azam) to facilitate trade and travel, he did not write personal memoirs documenting the Banjaras.
• Historical Precedence:
• While Alauddin Khalji of the Delhi Sultanate was the first ruler to systematically employ Banjaras for city grain supplies, Jahangir is the one who provided a first-hand account in his own memoirs.

The correct answer is Brahmachari.

Key Points

• The term Brahmachari identifies a student during the Brahmacharya stage, which is the first of the four Ashramas (stages of life) in ancient Hindu philosophy.
• This stage typically commenced between the ages of 8 and 12 following the Upanayana ceremony, which symbolized the initiation into formal Vedic education.
• A Brahmachari resided in a Gurukula (teacher's household), where they served the Guru and learned various subjects including the Vedas, philosophy, grammar, and ethics.
• The core values of this stage included strict celibacy, self-discipline, and the practice of Bhiksha (seeking alms) to cultivate a sense of humility and social equality.
• The duration of this stage was intended to prepare the individual for their future responsibilities in society by building a strong foundation of Dharma (righteousness).

 Additional Information

• The Ashrama system, or Chaturashrama, outlines the progression of human life toward spiritual liberation:
• Grihastha: The second stage (householder), where an individual marries, raises a family, and fulfills social and economic duties through Artha (wealth) and Kama (desire).
• Vanaprastha: The third stage (forest-dweller), which begins as one transitions from worldly attachments toward a more secluded, contemplative life of spiritual study.
• Sannyasin: The final stage of renunciation, where the individual abandons all material ties and social status to focus entirely on achieving Moksha (liberation from birth and death).

The correct answer is 12%.

Key Points

• A working paper titled 'Not Everyone is Migrating: Measuring Domestic Migration in India' was released by the Economic Advisory Council to the Prime Minister (EAC-PM) in 2024.
• The report indicates that the internal migration rate in India witnessed a sharp decline from 33% in 2011 to 21% during the 2022-23 period.
• This absolute difference of 12% (33% − 21%) suggests that the overall propensity of the Indian population to migrate domestically has significantly lowered over the last decade.
• The study utilized data from the Census 2011 and compared it with the latest Periodic Labour Force Survey (PLFS) data to track the movement of citizens across state and district boundaries.
• The findings challenge the common perception of mass distress migration and suggest that more people are finding livelihood opportunities within their home regions.

 Additional Information

• Economic Advisory Council to the Prime Minister (EAC-PM)
• It is a non-constitutional, non-permanent, and independent body constituted to provide economic advice to the Government of India.
• The council is currently chaired by Dr. Bibek Debroy, with members like Shamika Ravi who authored the migration study.
• Factors Contributing to the Decline
• The report attributes the lower migration rate to improved rural-urban connectivity and the saturation of basic amenities in rural areas.
• Government flagship schemes such as MGNREGA, PM-Kisan, and PMAY-G have played a crucial role in providing local employment and social security, reducing the need for forced migration.
• The COVID-19 pandemic also triggered a temporary reverse migration, which influenced the data collection period for the PLFS 2022-23.
• Periodic Labour Force Survey (PLFS)
• Conducted by the National Sample Survey Office (NSSO), the PLFS is the primary source of high-frequency data on employment, unemployment, and demographic shifts in the absence of a recent national census.

The correct answer is 1994.

Key Points

• The Pre-Conception and Pre-Natal Diagnostic Techniques (PCPNDT) Act was enacted by the Parliament of India in 1994 to provide for the prohibition of sex selection, before or after conception.
• The act aims to regulate the use of pre-natal diagnostic techniques, such as ultrasound and amniocentesis, by restricting them to the detection of genetic abnormalities, metabolic disorders, or certain congenital malformations.
• The legislation was a critical response to the social menace of female foeticide and the rapidly declining child sex ratio in India, which was observed during the 1991 Census.
• It mandates that no person, including the specialist conducting the procedure, shall communicate the sex of the foetus to the pregnant woman or her relatives by words, signs, or any other method.

 Additional Information

• Evolution and Implementation:
• The Act officially came into force on January 1, 1996, and was later amended in 2003 to improve its implementation and encompass pre-conception sex selection techniques.
• It established the Central Supervisory Board (CSB), chaired by the Union Minister of Health and Family Welfare, to advise the Central Government on policy matters.
• Under the Act, all Genetic Counselling Centres, Genetic Laboratories, and Genetic Clinics must be registered with the Appropriate Authority to operate legally.
• Non-compliance or violation of the provisions can result in imprisonment for a term up to 3 years and a fine up to 10,000 rupees for the first conviction.

The correct answer is Bahadur Shah Zafar.

Key Points

• On May 10, 1857, the rebellion began in Meerut when sepoys refused to use the new Enfield rifle cartridges, leading to a violent breakout against British officers.
• The rebel soldiers of the Meerut Regiment marched through the night and reached Delhi on the morning of May 11, 1857, crossing the Yamuna river.
• The soldiers gathered at the Red Fort and demanded to meet Bahadur Shah Zafar, the last Mughal Emperor, to seek his leadership and blessing for the uprising.
• Despite his initial hesitation due to his advanced age of 82 years and lack of resources, the Emperor was proclaimed Shahenshah-e-Hindustan (Emperor of India) by the sepoys.
• The choice of Bahadur Shah Zafar was symbolic, as the Mughal Dynasty still carried historical legitimacy across various regions and communities in India, serving as a unifying figure against the British East India Company.

 Additional Information

• Nana Saheb
• He was the adopted son of the late Peshwa Baji Rao II and led the rebellion in Kanpur.
• He declared himself Peshwa but notably acknowledged Bahadur Shah Zafar as the supreme Emperor of India.
• Rani Lakshmibai
• The Queen of Jhansi who joined the rebellion after her kingdom was annexed under the Doctrine of Lapse.
• She became one of the most formidable leaders of the revolt, fighting alongside Tantia Tope.
• Peshwa Baji Rao II
• The last Peshwa of the Maratha Empire who was exiled to Bithoor by the British after the Third Anglo-Maratha War.
• He passed away in 1851, several years before the Revolt of 1857 began.
• Consequences for the Emperor
• After the British recaptured Delhi in September 1857, the Emperor was tried for treason and exiled to Rangoon (Burma), where he died in 1862.

Shortcut Trick

Solve the bracket and multiplication simultaneously for speed.

Product: 72 × 2 = 144

Bracket: 61 − 28 = 33

Combine: 144 − 19 + 33 + 35 = 125 + 68 = 193

∴ The correct answer is 193.

Alternate Method

Given: 72 × 2 − 19 + (61 − 28) + 35

Formula Used: BODMAS Rule

⇒ 72 × 2 − 19 + (33) + 35 (Solving Bracket)

⇒ 144 − 19 + 33 + 35 (Solving Multiplication)

⇒ 125 + 33 + 35 (Solving first Subtraction)

⇒ 158 + 35 (Solving first Addition)

⇒ 193

∴ The correct answer is 193.

Additional Information

BODMAS Rule Priority

The order of operations is Brackets (B), Orders (O), Division (D), Multiplication (M), Addition (A), and Subtraction (S). Note that DM and AS have equal priority and are solved from left to right.

Types of Brackets

Brackets are solved in the order: Bar/Vinculum, Parentheses ( ), Braces { }, and then Square Brackets [ ].

Shortcut Trick

Solve the expression using the VBODMAS priority order.

⇒ 76 − 33 + (28 × 2) + (36 ÷ 3) − 22 + 19

⇒ 76 − 33 + 56 + 12 − 22 + 19

⇒ (76 + 56 + 12 + 19) − (33 + 22) = 163 − 55 = 108

∴ The correct answer is 108.

Alternate Method

Given:

76 − 33 + 28 of 2 + 36 ÷ 3 − (22) + 19

Formula Used:

Follow the BODMAS rule: Brackets, Of, Division, Multiplication, Addition, Subtraction.

Calculations:

⇒ 76 − 33 + (28 × 2) + (36 ÷ 3) − 22 + 19 (Solving Of and Division)

⇒ 76 − 33 + 56 + 12 − 22 + 19

⇒ 43 + 56 + 12 − 22 + 19 (Solving Subtraction/Addition from left to right)

⇒ 99 + 12 − 22 + 19

⇒ 111 − 22 + 19

⇒ 89 + 19

⇒ 108

∴ The correct answer is 108.

Additional Information

BODMAS Rule

It specifies the order of operations: Brackets ((), {}, []), Orders (powers/roots), Division, Multiplication, Addition, and Subtraction.

The 'Of' Operator

The word 'of' represents multiplication but must be performed before regular division and multiplication in the hierarchy.

Addition and Subtraction Grouping

For faster calculation, group all positive numbers and all negative numbers separately, then find the final difference.

Shortcut Trick

Solve the expression following the BODMAS priority: Bracket, Of, Division, Multiplication, Addition, and Subtraction.

Step 1: Of → 17 × 2 = 34

Step 2: Division → 44 ÷ 4 = 11

Step 3: Multiplication → 29 × 1 = 29

Step 4: 78 − 33 + 29 + 11 + 34 − 19 = 152 − 52 = 100

∴ The correct answer is 100.

Alternate Method

Given: 78 − 33 + 29 × 1 + 44 ÷ 4 + (17 of 2) − 19

Following the BODMAS rule step-by-step:

⇒ 78 − 33 + 29 × 1 + 44 ÷ 4 + 34 − 19

⇒ 78 − 33 + 29 × 1 + 11 + 34 − 19

⇒ 78 − 33 + 29 + 11 + 34 − 19

⇒ (78 + 29 + 11 + 34) − (33 + 19)

⇒ 152 − 52

⇒ 100

∴ The correct answer is 100.

Additional Information

BODMAS Rule

It is an acronym to help remember the order of mathematical operations: Brackets, Of (orders/powers), Division, Multiplication, Addition, and Subtraction.

The 'Of' Operation

In simplification, the term of is treated as multiplication but is prioritized higher than division and standard multiplication symbols.

Calculation Tip

While performing addition and subtraction, it is often faster to group all positive terms and negative terms separately before the final subtraction.

Shortcut Trick

Identify and solve BODMAS components mentally: Bracket (18 − 14 = 4), Of (21 × 2 = 42), and Division (33 ÷ 3 = 11).

Notice the cancellation: The expression contains −42 and + (21 of 2), which is −42 + 42 = 0.

Remaining calculation: 96 + 11 + 4 = 111.

∴ The correct answer is 111.

Alternate Method

Given: 96 − 42 + 33 ÷ 3 + 21 of 2 + (18 − 14)

Formula Used: Apply the VBODMAS rule (Vinculum, Bracket, Of, Division, Multiplication, Addition, Subtraction).

⇒ 96 − 42 + 33 ÷ 3 + 21 of 2 + 4 (Solving Bracket: 18 − 14)

⇒ 96 − 42 + 33 ÷ 3 + 42 + 4 (Solving Of: 21 × 2)

⇒ 96 − 42 + 11 + 42 + 4 (Solving Division: 33 ÷ 3)

⇒ 54 + 11 + 42 + 4 (Solving Subtraction: 96 − 42)

⇒ 65 + 42 + 4 (Solving Addition: 54 + 11)

⇒ 107 + 4 = 111

∴ The correct answer is 111.

Additional Information

BODMAS Hierarchy

The rule ensures a unique solution to mathematical expressions by following the sequence: Brackets, Orders/Of, Division, Multiplication, Addition, and Subtraction.

Sign Convention

When multiple addition and subtraction operations are present, they are performed from left to right, although results remain the same if all additions are grouped first.

Of Operator Significance

The 'of' operator acts like multiplication but holds a higher precedence than division, meaning it must be calculated before any division in the expression.

Shortcut Trick

In a parallelogram, the sum of any two adjacent angles is always 180° (they are supplementary).

Adjacent Angle = 180° − Given Angle

Adjacent Angle = 180° − 60° = 120°

∴ The correct answer is 120°.

Alternate Method

Given: One angle of the parallelogram = 60°

Formula Used: Consecutive interior angles formed by a transversal crossing parallel lines are supplementary. For a parallelogram ABCD, ∠A + ∠B = 180°.

Calculations:

⇒ Let the angles of the parallelogram be ∠A, ∠B, ∠C, and ∠D.

⇒ Given ∠A = 60°.

⇒ Since AD || BC and AB || DC, the adjacent angles are supplementary.

⇒ ∠A + ∠B = 180°

⇒ 60° + ∠B = 180°

⇒ ∠B = 180° − 60°

⇒ ∠B = 120°

∴ The correct answer is 120°.

Additional Information

Opposite Angles Property

In any parallelogram, the opposite angles are always equal in measure. If one angle is 60°, its opposite angle is also 60°.

Angle Sum Property

The sum of all four interior angles of a parallelogram (or any quadrilateral) is always 360°.

Consecutive Angles

Any two consecutive angles of a parallelogram are supplementary, meaning their sum is 180°.

Shortcut Trick

The Least Common Multiple (LCM) of a set of numbers can be found by taking the LCM of the LCMs of its subsets.

LCM(A, B, C, D) = LCM[LCM(A, B), LCM(C, D)]

Given: LCM(A, B) = 15 and LCM(C, D) = 25

Required LCM = LCM(15, 25)

LCM(15, 25) = 75

∴ The correct answer is 75.

Alternate Method

Given:

LCM of A and B = 15

LCM of C and D = 25

Formula Used:

The Associative Property of LCM states: LCM(a, b, c, d) = LCM(LCM(a, b), LCM(c, d)).

Calculations:

⇒ To find the LCM of 15 and 25, we use Prime Factorization.

⇒ 15 = 3¹ × 5¹

⇒ 25 = 5 × 5 = 5²

⇒ LCM is the product of the highest power of all prime factors involved.

⇒ LCM(15, 25) = 3¹ × 5²

⇒ LCM = 3 × 25

⇒ LCM = 75

∴ The correct answer is 75.

Additional Information

Fundamental LCM Property

The Least Common Multiple (LCM) is the smallest positive integer that is perfectly divisible by every number in the given set.

LCM and HCF Relationship

For any two numbers x and y, the product of their HCF and LCM is equal to the product of the numbers: HCF(x, y) × LCM(x, y) = x × y.

LCM of Co-prime Numbers

If two numbers are co-prime (having no common factors other than 1), their LCM is simply the product of the two numbers.

Shortcut Trick

To find the LCM of three numbers A, B, and C, we use the property: LCM(A, B, C) = LCM[LCM(A, B), C].

Given LCM(A, B) = 30 and C = 18.

We need to find the LCM of 30 and 18.

Check the multiples of the larger number (30): 30 × 1 = 30 (not divisible by 18), 30 × 2 = 60 (not divisible by 18), 30 × 3 = 90 (divisible by 18).

∴ The correct answer is 90.

Alternate Method

Given:

LCM of A and B = 30

Value of C = 18

Formula Used:

The Least Common Multiple (LCM) of three numbers is the LCM of the LCM of any two of those numbers and the third number.

Calculations:

⇒ Prime factorization of 30 = 2 × 3 × 5

⇒ Prime factorization of 18 = 2 × 3 × 3 = 2 × 3²

⇒ To find the LCM, take the highest power of each prime factor present in both numbers:

⇒ Highest power of 2 = 2¹

⇒ Highest power of 3 = 3²

⇒ Highest power of 5 = 5¹

⇒ LCM(30, 18) = 2¹ × 3² × 5¹

⇒ LCM = 2 × 9 × 5 = 90

∴ The correct answer is 90.

Additional Information

LCM and HCF Relation

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

LCM of Fractions

To calculate the LCM of fractions, use the formula: LCM = LCM(Numerators) ÷ HCF(Denominators).

Divisibility Rule

The HCF of a set of numbers always completely divides their LCM.

Shortcut Trick

The Highest Common Factor (HCF) of any set of numbers must always be a factor of their Least Common Multiple (LCM).

Given LCM = 150.

Check the options to see which number divides 150 exactly: 150 ÷ 15 = 10 (Integer).

Other options (20, 35, 28) do not divide 150 without leaving a remainder.

∴ The correct answer is 15.

Alternate Method

Given:

LCM = 150

Property: In any pair of numbers, the LCM is always a multiple of the HCF. Conversely, the HCF must divide the LCM completely.

Let us test each option:

⇒ Option (1): 150 ÷ 15 = 10 (Divisible)

⇒ Option (2): 150 ÷ 20 = 7.5 (Not divisible)

⇒ Option (3): 150 ÷ 35 = 4.28 (Not divisible)

⇒ Option (4): 150 ÷ 28 = 5.35 (Not divisible)

⇒ Since only 15 is a factor of 150, it can be the HCF.

∴ The correct answer is 15.

Additional Information

Product Rule of LCM and HCF

For any two numbers A and B, the product of the numbers is equal to the product of their HCF and LCM: A × B = HCF(A, B) × LCM(A, B).

HCF of Coprime Numbers

The Highest Common Factor of two coprime numbers is always 1, and their LCM is simply the product of the two numbers.

Range of HCF and LCM

The HCF is always less than or equal to the smallest number in the set, while the LCM is always greater than or equal to the largest number in the set.

Shortcut Trick

Loss of 18% = ₹81

1% = 81 ÷ 18 = 4.5

Selling Price (SP) = 100% − 18% = 82%

Selling Price (SP) = 82 × 4.5 = ₹369

∴ The correct answer is ₹369.

Alternate Method

Given:

Loss = ₹81

Loss Percentage = 18%

Formula Used:

Loss % = (Loss ÷ Cost Price) × 100

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

Calculations:

⇒ 18 = (81 ÷ CP) × 100

⇒ CP = (81 × 100) ÷ 18

⇒ CP = 4.5 × 100 = ₹450

⇒ SP = 450 − 81

⇒ SP = ₹369

∴ The correct answer is ₹369.

Additional Information

Cost Price (CP)

The price at which an article is purchased. It is the base for calculating Profit % or Loss %.

Profit Percentage Formula

Profit % = [(Selling Price − Cost Price) ÷ Cost Price] × 100.

Selling Price for Profit

To find SP when Profit % is given: SP = CP × (100 + Profit %) ÷ 100.

Shortcut Trick

Ratio of Smaller number (S) to Larger number (L) is inversely proportional to their percentage values.

S : L = 20% : 40% = 1 : 2

Sum of ratios = 1 + 2 = 3 units

3 units = 750 ⇒ 1 unit = 250

Larger number = 2 units = 2 × 250 = 500

∴ The correct answer is 500.

Alternate Method

Given: Sum of numbers = 750, 40% of Smaller = 20% of Larger.

Formula Used: Percentage = (Value / Total) × 100

Let the smaller number be S and the larger number be L.

⇒ 40% × S = 20% × L

⇒ (40/100) × S = (20/100) × L

⇒ 2 × S = 1 × L ⇒ L = 2S

⇒ S + L = 750

⇒ S + 2S = 750

⇒ 3S = 750 ⇒ S = 250

⇒ Larger number (L) = 2 × 250 = 500

∴ The correct answer is 500.

Additional Information

Percentage Equivalence

If x% of A = y% of B, then the ratio of the numbers is A : B = y : x. This is a common shortcut for direct ratio conversion.

Dividing a Sum into Ratios

To divide a total sum T into ratio a : b, the parts are calculated as [a / (a + b)] × T and [b / (a + b)] × T.

Linear Equations in Two Variables

Problems involving the sum of two numbers can always be modeled using x + y = Total and solved by substituting one variable in terms of the other.

Shortcut Trick

Let the initial Cost Price be 100 units, then the initial Selling Price is 75 units (25% loss).

New Cost Price = 100 + 40% = 140 units.

New Selling Price at 15% loss = 140 × 0.85 = 119 units.

Required percentage increase in Selling Price (y) = [(119 − 75) ÷ 75] × 100.

y = (44 ÷ 75) × 100 = 176 ÷ 3 = 58.67.

∴ The correct answer is 58.67.

Alternate Method

Given:

Initial Loss = 25%

Increase in Cost Price = 40%

New Loss = 15%

Formula Used:

Selling Price (SP) = Cost Price (CP) × (100 − Loss%)/100

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

Calculations:

⇒ Assume initial Cost Price = 100

⇒ Initial Selling Price = 100 − 25% of 100 = 75

⇒ New Cost Price = 100 + 40% of 100 = 140

⇒ New Selling Price = 140 × (100 − 15)/100

⇒ New Selling Price = 140 × 85/100 = 119

⇒ Increase in Selling Price = 119 − 75 = 44

⇒ Percentage increase (y) = (44 ÷ 75) × 100

⇒ y = (44 × 4) ÷ 3 = 176 ÷ 3

⇒ y = 58.666... ≈ 58.67

∴ The correct answer is 58.67.

Additional Information

Profit and Loss Relationship

Selling Price is calculated as CP × (100 + P%)/100 for profit and CP × (100 − L%)/100 for loss.

Percentage Change

The percentage change between two values is always calculated using the original value as the base: [(New − Old) ÷ Old] × 100.

Effective Change

When both CP and SP change, the new profit/loss percentage depends on the final ratio of the updated SP and CP values.

Shortcut Trick

Time for S to complete 3/4 work = 18 days

Time for S to complete full work = 18 × (4/3) = 24 days

Since R is 3 times as efficient as S, he takes 1/3^rd of the time.

Time taken by R = 24 ÷ 3 = 8 days

∴ The correct answer is 8 days.

Alternate Method

Given:

S completes 3/4 part of work in 18 days.

R's Efficiency = 3 × S's Efficiency.

Formula:

Total Time = (Time taken for fraction) ÷ (Fraction of work)

Efficiency × Time = Total Work

⇒ Total days for S = 18 × (4 ÷ 3) = 24 days.

⇒ Let Efficiency of S = 1 unit/day.

⇒ Total Work = Efficiency × Days = 1 × 24 = 24 units.

⇒ Efficiency of R = 3 × Efficiency of S = 3 × 1 = 3 units/day.

⇒ Days taken by R alone = Total Work ÷ Efficiency of R

⇒ Days taken by R alone = 24 ÷ 3 = 8 days.

∴ The correct answer is 8 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a work. If the ratio of efficiency is x : y, then the ratio of time taken is y : x.

Total Work Calculation

Total Work = Number of Days × Efficiency. For fractional work, Full Work Time = (Time for Part) × (Reciprocal of the Part).

Combined Efficiency

When multiple people work together, their efficiencies are added: E_total = E₁ + E₂ + ... + E_n.

Shortcut Trick

Total work = LCM(18, 24, 36) = 72 units.

2(M + R + P) combined efficiency = (72 ÷ 18) + (72 ÷ 24) + (72 ÷ 36) = 4 + 3 + 2 = 9.

Combined efficiency of M, R, and P = 9 ÷ 2 = 4.5 units/day.

Work done in 4 days = 4.5 × 4 = 18 units.

Required part of work = 18 ÷ 72 = 1/4.

∴ The correct answer is 1/4.

Alternate Method

Given: M and R = 18 days, R and P = 24 days, P and M = 36 days.

Formula Used: Efficiency = Total Work ÷ Time; Total work done = Combined Efficiency × Time.

⇒ Sum of efficiencies = 2 × (M + R + P) = 4 + 3 + 2 = 9 units/day.

⇒ Efficiency of (M + R + P) working together = 9 ÷ 2 = 4.5 units/day.

⇒ Work completed in 4 days = 4.5 × 4 = 18 units.

⇒ Part of work done = 18 ÷ 72 = 1/4.

∴ The correct answer is 1/4.

Additional Information

Combined Efficiency of Pairs

When people work in pairs (AB, BC, CA), the sum of their individual efficiencies is found by dividing the sum of pair efficiencies by 2.

Work & Wages Principle

Wages are distributed based on the Efficiency × Time product for each person, which represents the actual work done.

Fractional Work

The part of work done in 'n' days is calculated as (Combined Efficiency × n) ÷ Total Work.

Shortcut Trick

Speed of boat in still water is the average of downstream and upstream speeds.

Speed = (Downstream + Upstream) ÷ 2

Speed = (42 + 36) ÷ 2 = 78 ÷ 2 = 39 km/hr

∴ The correct answer is 39 km/hr.

Alternate Method

Given:

Downstream Speed (D) = 42 km/hr

Upstream Speed (U) = 36 km/hr

Formula Used:

Speed of boat in still water (x) = (D + U) ÷ 2

Speed of stream (y) = (D − U) ÷ 2

Calculations:

⇒ x = (42 + 36) ÷ 2

⇒ x = 78 ÷ 2

⇒ x = 39 km/hr

∴ The correct answer is 39 km/hr.

Additional Information

Speed of Stream

The rate at which the water flows is given by y = (Downstream speed − Upstream speed) ÷ 2. In this case, y = (42 − 36) ÷ 2 = 3 km/hr.

Downstream and Upstream Logic

Downstream Speed = Speed of boat (x) + Speed of stream (y). Upstream Speed = Speed of boat (x) − Speed of stream (y).

Unit Conversion

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

Shortcut Trick

Speed of Stream = Still Water Speed − Upstream Speed

⇒ Speed of Stream = 23 − 17

⇒ Speed of Stream = 6 km/hr

∴ The correct answer is 6 km/hr.

Alternate Method

Given:

Speed of the boat in still water (u) = 23 km/hr

Upstream speed of the boat (u − v) = 17 km/hr

Formula Used:

Upstream Speed = Speed in Still Water − Speed of Stream

Calculations:

Let the speed of the stream be v km/hr.

⇒ 17 = 23 − v

⇒ v = 23 − 17

⇒ v = 6 km/hr

∴ The correct answer is 6 km/hr.

Additional Information

Downstream Speed

It is the net speed of the boat when it travels in the direction of the stream: Downstream Speed = u + v.

Speed in Still Water

If downstream and upstream speeds are known: u = (Downstream + Upstream) ÷ 2.

Speed of Stream

If downstream and upstream speeds are known: v = (Downstream − Upstream) ÷ 2.

Shortcut Trick

Upstream Speed = Downstream Speed − 2 × Stream Speed

Upstream Speed = 35 − 2(5) = 25 km/hr

Total Time = (350 ÷ 35) + (150 ÷ 25) = 10 + 6 = 16 hr

∴ The correct answer is 16 hr.

Alternate Method

Given: Downstream Speed = 35 km/hr, Stream Speed = 5 km/hr, Downstream Distance = 350 km, Upstream Distance = 150 km.

Formula Used: Time = Distance ÷ Speed | Boat Speed (u) = Downstream − Stream | Upstream = u − Stream

⇒ Boat Speed in Still Water (u) = 35 − 5 = 30 km/hr

⇒ Upstream Speed (v) = 30 − 5 = 25 km/hr

⇒ Time taken for Downstream = 350 ÷ 35 = 10 hr

⇒ Time taken for Upstream = 150 ÷ 25 = 6 hr

⇒ Total Time = 10 + 6 = 16 hr

∴ The correct answer is 16 hr.

Additional Information

Boat Speed and Stream Speed Calculation

Boat speed in still water (u) = (Downstream Speed + Upstream Speed) ÷ 2. Stream speed (v) = (Downstream Speed − Upstream Speed) ÷ 2.

Average Speed in Boats and Streams

When the boat covers the same distance downstream and upstream, the Average Speed = (u² − v²) ÷ u, where u is boat speed and v is stream speed.

Upstream and Downstream Logic

Downstream speed is always greater than upstream speed because the stream supports the boat movement in the former and opposes it in the latter.

Shortcut Trick

Use the ratio of Marked Price (MP) to Cost Price (CP):

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

MP / 10000 = (100 + 40) / (100 − 30) = 140 / 70 = 2 / 1

MP = 10000 × 2 = ₹20000

∴ The correct answer is ₹20000.

Alternate Method

Given:

Cost Price (CP) = ₹10000

Profit Percentage = 40%

Discount Percentage = 30%

Formula Used:

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

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

Calculations:

⇒ SP = 10000 × (100 + 40) / 100

⇒ SP = 10000 × 140 / 100 = ₹14000

⇒ 14000 = MP × (100 − 30) / 100

⇒ 14000 = MP × 70 / 100

⇒ MP = (14000 × 100) / 70

⇒ MP = 200 × 100 = ₹20000

∴ The correct answer is ₹20000.

Additional Information

Relationship between CP and MP

The direct formula is CP / MP = (100 − Discount%) / (100 + Profit%). If there is a loss, use (100 − Loss%).

Markup Percentage

Markup % is the percentage by which the cost price is increased to set the marked price. Markup % = [(MP − CP) / CP] × 100.

Successive Discounts

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

Shortcut Trick

The Marked Price (MP) is calculated as SP ÷ (1 − d), where d is the discount in decimal form.

Compare denominators: 0.9, 0.75, 0.55, and 0.8. A smaller denominator increases the final value.

Option 3: 6000 ÷ 0.55 ≈ 10909.09 (Highest SP with the highest discount %).

Option 4: 6250 ÷ 0.8 = 7812.5 (High SP but much lower discount %).

By inspection, Case 3 has the lowest multiplier (0.55) relative to its high base price.

∴ The correct answer is Rs. 6000 and 45% discount.

Alternate Method

Given: Selling Price (SP) and Discount Percentage for four different cases.

Formula Used: Marked Price (MP) = (SP × 100) ÷ (100 − Discount %)

⇒ Case 1: MP = (4000 × 100) ÷ (100 − 10) = 400000 ÷ 90 ≈ ₹4444.44

⇒ Case 2: MP = (5000 × 100) ÷ (100 − 25) = 500000 ÷ 75 ≈ ₹6666.67

⇒ Case 3: MP = (6000 × 100) ÷ (100 − 45) = 600000 ÷ 55 ≈ ₹10909.09

⇒ Case 4: MP = (6250 × 100) ÷ (100 − 20) = 625000 ÷ 80 = ₹7812.50

Comparing all the results, Case 3 has the highest value.

∴ The correct answer is Rs. 6000 and 45% discount.

Additional Information

Marked Price and Discount

The Marked Price (MP) is also known as the list price or tag price. Discount is always calculated on the MP, and SP = MP − Discount.

Discount Percentage Formula

The percentage of discount is given by: Discount % = (Discount ÷ Marked Price) × 100.

Successive Discounts

When two discounts a% and b% are given, the Effective Discount = (a + b − (a × b) ÷ 100)%.

Shortcut Trick

Net discount % = a + b − (a × b)/100

Net discount = 20 + 30 − (20 × 30)/100 = 50 − 6 = 44%

Selling Price (SP) = 100% − 44% = 56% of Marked Price

56% = Rs. 4480 ⇒ 1% = 80 ⇒ 100% = Rs. 8000

∴ The correct answer is Rs. 8000.

Alternate Method

Given:

First discount (d₁) = 20%

Second discount (d₂) = 30%

Selling Price (SP) = Rs. 4480

Formula Used:

SP = MP × (100 − d₁)/100 × (100 − d₂)/100

Calculations:

⇒ SP = MP × (80/100) × (70/100)

⇒ 4480 = MP × (4/5) × (7/10)

⇒ 4480 = MP × (28/50)

⇒ 4480 = MP × (14/25)

⇒ MP = (4480 × 25) ÷ 14

⇒ MP = 320 × 25

⇒ MP = Rs. 8000

∴ The correct answer is Rs. 8000.

Additional Information

Successive Discount Formula

For two successive discounts of x% and y%, the single equivalent discount is (x + y − xy/100)%.

Relationship between MP, CP and Profit/Discount

The ratio of Marked Price to Cost Price is given by: MP/CP = (100 + Profit%)/(100 − Discount%).

Marked Price (MP) Definition

It is the price displayed on the label of an article, also known as the list price. Discount is always calculated on this price.

Shortcut Trick

Ratio of Height to Shadow is constant at the same time.

Boy's Ratio = 1.8 : 1.2 = 3 : 2

For the Building, Shadow = 8 m (which is 2 × 4)

Building Height = 3 × 4 = 12 m

∴ The correct answer is 12 m.

Alternate Method

Given:

Height of the Boy (H₁) = 1.8 m

Shadow of the Boy (S₁) = 1.2 m

Shadow of the Building (S₂) = 8 m

Formula Used:

In Similar Triangles (formed by sun rays), Height₁ / Shadow₁ = Height₂ / Shadow₂

Calculations:

⇒ H₁ / S₁ = H₂ / S₂

⇒ 1.8 / 1.2 = H₂ / 8

⇒ 3 / 2 = H₂ / 8

⇒ H₂ = (3 × 8) / 2

⇒ H₂ = 24 / 2

⇒ H₂ = 12 m

∴ The correct answer is 12 m.

Additional Information

Angle of Elevation

At any given time, the Sun's angle of elevation is the same for all objects in the same vicinity, making the triangles formed by objects and their shadows mathematically similar.

Properties of Similar Triangles

For two triangles to be similar, their corresponding sides must be in the same proportion. Here, Height/Shadow = tan(θ), where θ is the sun's altitude.

Ratio and Proportion

If a : b = c : d, then the product of means equals the product of extremes (ad = bc). This is used to find the unknown height directly.

The correct answer is: Option (1) i.e. Problems are about to begin.

Key Points

• The idiom 'The fat is in the fire' means that something has been said or done that will definitely cause trouble or make a difficult situation even worse; it implies that an angry reaction or conflict is now inevitable. (मुसीबत शुरू हो जाना या स्थिति बिगड़ जाना)
• Example: When she told the boss that the project was a failure, the fat was in the fire.
• 'Problems are about to begin' refers to a situation where difficulties, complications, or conflicts are starting to emerge as a result of a specific action. (समस्याएं शुरू होने वाली हैं)
• Example: With the new tax regulations being announced, many businesses feel that problems are about to begin.
• Hence, we can infer that the meaning of the idiom 'The fat is in the fire' is 'Problems are about to begin'.

Therefore, the correct answer is: Problems are about to begin.

Additional Information

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

• To be subject to intense criticism or judgment (कड़ी आलोचना या निर्णय का पात्र होना): To be in a situation where people are attacking or scrutinizing your actions severely.
• Example: The director was under fire from the board for the company's poor financial performance.
• The misery that one faces in hell (नरक में होने वाला कष्ट): A literal or hyperbolic expression referring to extreme suffering or torment.
• Example: The poet described the misery that one faces in hell to warn people against bad deeds.
• A final effort or attempt (एक अंतिम प्रयास): Often referred to as a 'last-ditch effort', it is a desperate try to achieve something or avoid defeat.
• Example: In a final effort to save the sinking ship, the crew started throwing the cargo overboard.

The correct answer is "Blithe".

Key Points

• The correctly spelt word is "Blithe".
• "Blithe" means cheerful, carefree, and light-hearted. (प्रसन्नचित्त / बेफिक्र)
• Example: She had a blithe and cheerful attitude despite the difficulties.
• The other options are incorrectly spelt:
• Biffurcate → Correct spelling: Bifurcate
• Beseach → Correct spelling: Beseech
• Berreft → Correct spelling: Bereft

Therefore, the correct answer is "Option 4".

Additional Information

• Bifurcate: To divide or split into two branches or parts. (दो भागों में विभाजित करना)
• Beseech: To ask or request earnestly. (विनती करना / प्रार्थना करना)
• Bereft: Deprived of or lacking something, especially because of a loss. (वंचित / शोकाकुल)

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

Key Points

• The word 'weary' means feeling or showing extreme tiredness, especially as a result of excessive exertion, lack of sleep, or boredom. (थका हुआ)
• Example: She gave a weary sigh and leaned back in her chair after the long meeting.
• 'Tired' refers to the state of being in need of sleep or rest; it is the most direct synonym for weary as it describes a similar physical or mental state of exhaustion. (थका हुआ)
• Example: He was far too tired to continue driving and decided to pull over for the night.
• Hence, we can infer that the synonym of 'weary' is 'tired'.

Therefore, the correct answer is- Tired.

Additional Information

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

• Fresh (ताज़ा): Full of energy and vigor; not tired or fatigued.
• Example: After a quick nap, I felt fresh and ready to start working again.
• Excited (उत्साहित): Feeling or showing great enthusiasm and eagerness.
• Example: The children were very excited about their upcoming trip to the zoo.
• Awake (जागृत): Not asleep; conscious and alert.
• Example: I was still wide awake at midnight because of the loud music outside.

The correct answer is: Hygeinic.

Key Points

• The word 'Hygeinic' is a misspelt word; the correct spelling is 'Hygienic', which refers to conditions or practices conducive to maintaining health and preventing disease, especially through cleanliness. (स्वच्छता संबंधी)
• Example: Maintaining a hygienic environment in hospitals is essential to prevent infections.
• 'Hygienic' is the correctly spelled term that follows the rule of placing 'i' before 'e' in this specific context (h-y-g-i-e-n-i-c). (स्वास्थ्यकर)
• Example: The health inspector checked if the kitchen followed hygienic standards.
• Hence, we can infer that 'Hygeinic' is the incorrectly spelled word among the given options.

Therefore, the correct answer is- Hygeinic.

Additional Information

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

• Excruciating (अत्यंत कष्टदायक): Something that is intensely painful or mentally agonizing.
• Example: She was in excruciating pain after falling from the stairs.
• Foreigner (विदेशी): A person who comes from a different country.
• Example: The foreigner enjoyed the local cuisine and culture.
• Fascinating (आकर्षक/दिलचस्प): Something that is extremely interesting or charming.
• Example: The history of the ancient ruins was absolutely fascinating to the tourists.

The correct answer is: Hide.

Key Points

• The word 'discover' means to find something unexpectedly or in the course of a search; it involves bringing something to light that was previously unknown. (खोजना)
• Example: Scientists discover new species of plants in the Amazon rainforest every year.
• 'Hide' refers to the act of putting or keeping something out of sight or concealing it, ensuring it is not easily found or seen; this is the opposite of discovering. (छिपाना)
• Example: The children decided to hide the birthday gift so that their mother would be surprised.
• Hence, we can infer that the opposite of 'discover' is 'hide'.

Therefore, the correct answer is- Hide.

Additional Information

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

• Find (पाना): To discover something by chance or effort; it is often used as a synonym for discover.
• Example: I need to find my lost keys before I can leave for work.
• Explore (अन्वेषण करना): To travel in or through an unfamiliar area in order to learn about it or discover new things.
• Example: We decided to explore the old ruins near the village to see what we could find.
• Learn (सीखना): To gain or acquire knowledge or skill in something through study, experience, or being taught.
• Example: It is never too late to learn a new language or a new skill.

The correct answer is Option(3) i.e. Tiny.

Key Points

• The word 'Enormous' means very large in size, quantity, or extent; it describes something that is huge or vast. (विशाल)
• Example: The enormous elephant walked slowly through the thick jungle.
• 'Tiny' refers to something that is very small or minute in size; it is the direct opposite of enormous. (बहुत छोटा)
• Example: I found a tiny seed in the bottom of the bag.
• Hence, we can infer that the opposite of 'Enormous' is 'Tiny'.

Therefore, the correct answer is- Tiny.

Additional Information

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

• Huge (बहुत बड़ा): Extremely large in size or scale; a synonym for enormous.
• Example: There was a huge rock blocking the path to the cave.
• Immense (अत्यधिक/विशाल): Extremely large or great, especially in scale or degree.
• Example: The artist put an immense amount of detail into the painting.
• Massive (बड़ा और भारी): Consisting of a large mass; exceptionally large and heavy.
• Example: The castle was protected by massive stone walls.

Question: Choose the most suitable one-word substitution for the following. A group of people who travel with an important or famous person.

The correct answer is: Entourage.

Key Points

• The phrase 'A group of people who travel with an important or famous person' refers to a retinue of attendants or associates who accompany a high-profile individual. (किसी महत्वपूर्ण या प्रसिद्ध व्यक्ति के साथ चलने वाला अनुचर वर्ग)
• Example: The famous singer arrived at the hotel with a large entourage of bodyguards and stylists.
• 'Entourage' refers to a group of people attending or surrounding an important person to provide support, security, or status. (अनुचर-वर्ग)
• Example: The billionaire rarely goes anywhere without his full entourage.
• Hence, we can infer that the most suitable one-word substitution for the given phrase is 'entourage'.

Therefore, the correct answer is- Entourage.

Additional Information

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

• Gambit (चाल/पहला कदम): An opening move or remark in a game or conversation, typically one that involves a risk but is intended to gain an advantage.
• Example: His opening gambit in the debate was to question his opponent's previous record.
• Cohorts (साथी/सहकर्मी): A group of people who share a common characteristic or are treated as a group, often used for a group of supporters or companions.
• Example: The professor and his cohorts spent years studying the effects of the new law.
• Caravan (काफ़िला): A group of people, especially traders or pilgrims, traveling together across a desert or through hostile territory.
• Example: The merchant caravan stopped at the oasis to rest before continuing their long journey.

The correct answer is Our wardrobe will be cleaned out before Christmas.

Key Points

• The given sentence 'We will clean out our wardrobe before Christmas' is in the Active Voice and uses the Future Simple Tense (Subject + will + Base Verb + Object).
• To convert a sentence from Active to Passive Voice in the Future Simple, the object of the active sentence ('our wardrobe') becomes the subject of the passive sentence.
• The grammatical structure for the Future Simple Passive is: Subject + will + be + Past Participle (V3) + [by agent].
• The main verb 'clean' must be converted into its Past Participle form, which is 'cleaned'.
• In this transformation, the original subject 'We' becomes the agent 'by us'. However, in passive constructions, the agent is often omitted if it is obvious or unimportant to the context of the sentence.
• Therefore, the sentence correctly transforms to 'Our wardrobe will be cleaned out before Christmas'.

 Additional Information

• Passive Voice Rules for Different Tenses:
• Future Simple: Uses the auxiliary 'will be' followed by the V3 form. Option 2 is incorrect because it misses the auxiliary verb 'be'.
• Present Simple: Uses 'is/am/are' followed by the V3 form. Option 3 ('is cleaned') is incorrect because it changes the future intent to a habitual or current action.
• Participle Usage: The passive voice strictly requires the Past Participle. Option 4 ('will be clean') is incorrect because 'clean' is used as a base verb or adjective instead of the required V3 'cleaned'.
• Phrasal Verbs: In the passive voice, the preposition ('out') must stay immediately after the verb ('cleaned').

The correct answer is Has your new invention been patented?.

Key Points

• The given sentence is an Interrogative Sentence in the Present Perfect Tense. The active structure is: Have/Has + Subject + Past Participle (V3) + Object?
• To convert it into Passive Voice, the object of the active sentence (your new invention) must become the subject of the passive sentence.
• The verb form in the Present Perfect Passive must follow the structure: Has/Have + Subject + been + Past Participle (V3) + (by agent)?
• In the active sentence, the auxiliary verb Have is used because the subject is you. In the passive voice, the new subject your new invention is singular, necessitating the use of the singular auxiliary verb Has.
• The past participle form of the verb patent remains patented in both active and passive forms.
• Combining these elements, the correct passive construction is: Has (Auxiliary) + your new invention (New Subject) + been (Passive Marker) + patented (V3).

 Additional Information

• Subject-Verb Agreement:
• The choice between Has and Have depends entirely on the number and person of the new subject. Singular nouns like invention always take Has, whereas Have is reserved for plural nouns and pronouns like I, we, you, and they.
• Tense Consistency:
• Voice conversion must preserve the original tense. Options using Is or Are change the tense to Simple Present, which is grammatically incorrect for this transformation.
• The inclusion of been is mandatory in all Perfect Tense passive structures to distinguish them from simple or continuous forms.

The correct answer is Option 2.

 

Key Points

• The primary error in the sentence is the incorrect use of the preposition of after the noun decrease.
• When describing a reduction in the level, amount, or quantity of something, the noun decrease should be followed by the preposition in.
• The phrase decrease of is generally used to indicate the specific magnitude or amount of the reduction (e.g., a decrease of 5%).
• In this context, since we are referring to the category being reduced (direct taxes), the correct phrase is decrease in direct taxes.
• Thus, the error is located in part (2) of the sentence.

Therefore, the correct answer is Option 2.

 

Correct Sentence: 'The unprecedented decrease in direct taxes has increased the earning potential of the capitalists.'

 

Additional Information

• (1) The unprecedented – This part is correct; unprecedented is an adjective meaning never done or known before, appropriately modifying the noun decrease.
• (3) increased the earning – This part is grammatically correct as the present perfect tense (has increased) is used correctly with the singular subject decrease.
• (4) potential of the capitalists. – This part is grammatically sound and functions correctly as the object of the verb.
• Subject-Verb Agreement: The singular noun decrease correctly agrees with the singular auxiliary verb has.

The correct answer is 'about'.

 

Key Points

• The preposition 'about' is used to indicate the subject or topic of a conversation, discussion, or book.
• In the given sentence, the devotees are having a discussion regarding the topic of 'Brahminical thoughts' and their application.
• The noun 'discussion' is commonly followed by the prepositions 'about' or 'on' to introduce the matter being discussed.

Therefore, the correct answer is Option 4.

 

Complete Sentence: 'The devotees held a long discussion about Brahminical thoughts and their application in real-life situations.'

 

Additional Information

• Option 1: 'for' is generally used to indicate purpose, reason, or duration (e.g., 'waiting for someone').
• Option 2: 'in' is used to indicate location, position, or time periods (e.g., 'in the room', 'in the morning').
• Option 3: 'upon' is a more formal version of 'on' and is typically used to indicate position or immediacy (e.g., 'once upon a time', 'based upon').

The correct answer is 'to'.

 

Key Points

• The verb 'agree' is followed by the preposition 'to' when it refers to a proposal, suggestion, or request.
• In the given sentence, the object is 'the marriage proposal', which is a specific offer or suggestion. Therefore, the preposition 'to' is grammatically correct.
• The other options (on, with, about) do not fit the context of accepting a proposal in this specific grammatical structure.

Therefore, the correct answer is Option 2.

 

Complete Sentence: "Ritika did not agree to the marriage proposal of Suvankar."

 

Additional Information

• Agree with: This is used when you are in accord with a person, an opinion, or a statement (e.g., I agree with you).
• Agree on: This is used when multiple parties reach a mutual decision or consensus regarding a topic (e.g., They agreed on a price).
• Agree about: This is often used when discussing a subject or matter of debate (e.g., We agree about the need for change).

The correct answer is Option 4.

Key Points

• The paragraph describes a physical descent into a deep location, likely a river valley or a canyon, using various sensory details to build a picture of the arrival at the floor of the world.
• Sentence C is the first sentence to follow S1 as it elaborates on the nature of the descent mentioned in 'We circled down':
• 'The track had come down deep as a tunnel.'
• Sentence B follows next by introducing the first sensory experience of the destination—the sound of water:
• 'The sounds of the river tossing and dizzying and teasing its great trash could be heard through the dark now.'
• Sentence D is the third sentence because it uses the pronoun 'It' to refer back to the sound or the river described in Sentence B, providing more detail:
• 'It made the noise of a moving wall, and up it fishes and reptiles and uprooted trees and man's throwaways played and climbed all alike in a splashing like innocence.'
• Sentence A is the fourth sentence, providing the final sensory input (smell) as the descent reaches its conclusion:
• 'A great wave of smell beat at my face.'
• The paragraph concludes with S2: 'We were on the floor of the world.'
• The correct sequence is CBDA.

Coherent paragraph after rearrangement:

'We circled down. The track had come down deep as a tunnel. The sounds of the river tossing and dizzying and teasing its great trash could be heard through the dark now. It made the noise of a moving wall, and up it fishes and reptiles and uprooted trees and man's throwaways played and climbed all alike in a splashing like innocence. A great wave of smell beat at my face. We were on the floor of the world.'

The correct answer is Option 3.

Key Points

• The paragraph describes a journey to North America and the process of cultural adaptation through reading a guidebook.
• Sentence D is the first sentence as it provides the specific itinerary following the mention of plane travel in S1:
• 'I flew first to Calcutta, to attend my wedding, and a week later to Boston, to begin my new job.'
• Sentence A follows because it describes the narrator’s activity during the flights mentioned in D:
• 'During the flight I read The Student Guide to North America, for although I was no longer a student, I was on a budget all the same.'
• Sentence C is the third sentence as it details the initial cultural and linguistic facts the narrator learned from the guidebook:
• 'I learned that Americans drove on the right side of the road, not the left, and that they called a lift an elevator and an engaged phone busy.'
• Sentence B is the fourth sentence as it introduces a direct quote about the pace of life, setting the stage for the continuation of that quote in S2:
• 'The pace of life in North America is different from Britain as you will soon discover, the guidebook informed me.'
• The correct sequence is DACB.

Coherent paragraph after rearrangement:

'By then I had enough money to go by plane. I flew first to Calcutta, to attend my wedding, and a week later to Boston, to begin my new job. During the flight I read The Student Guide to North America, for although I was no longer a student, I was on a budget all the same. I learned that Americans drove on the right side of the road, not the left, and that they called a lift an elevator and an engaged phone busy. The pace of life in North America is different from Britain as you will soon discover, the guidebook informed me. Everybody feels he must get to the top. Don’t expect an English cup of tea.'

The correct answer is Option 1.

 

Key Points

• The original sentence uses the word phenomenal, which is an adjective, to describe the action performed.
• In English grammar, adjectives are used to modify nouns or pronouns, while adverbs are used to modify verbs, adjectives, or other adverbs.
• Since the word needs to describe how the dancers performed (a verb), we must use the adverbial form, which is phenomenally.
• Therefore, the underlined part should be replaced with the dancers performed phenomenally to ensure grammatical accuracy.

Therefore, the correct answer is Option 1.

 

Correct Sentence: 'The audience couldn't stop applauding as the dancers performed phenomenally.'

 

Additional Information

• Option 2: This option is grammatically incorrect because was (a linking verb) should be followed by an adjective (phenomenal) to describe the subject (performance), not an adverb (phenomenally).
• Option 3: This option is logically flawed. The dancers themselves are people; they are not a performance. They gave or delivered a performance.
• Option 4: This is incorrect because the original sentence contains a grammatical error by using an adjective instead of an adverb.

The correct answer is Option 1.

 

Key Points

• The passage explicitly defines ecotourism in its opening sentence as a practice that promotes responsible travel to natural areas.
• The primary objective of this type of travel is biodiversity conservation, ensuring that the environment is protected while being visited.
• According to the text, ecotourism helps in advancing national heritage and conservation efforts through initiatives like anti-poaching patrols and habitat preservation.
• Therefore, the description provided in Option 1 aligns perfectly with the definition given in the passage.

Therefore, the correct answer is Option 1.

 

Additional Information

• Option 2: This describes luxury tourism, which focuses on comfort and leisure rather than the ecological responsibility and conservation required for ecotourism.
• Option 3: This describes urban or cultural tourism, which centers on city infrastructure and human traditions rather than natural wildlife habitats.
• Option 4: Adventure sports may take place in nature, but they are focused on recreation and thrill-seeking, which does not inherently imply the conservation goals of ecotourism.