SSC GD Constable 2026 Official Paper (Held On 06 May, 2026 Shift 2) (Previous Year Paper)

Logic followed here is,

(−89 × 2) + 2 = −178 + 2 = −176

(−176 × 2) + 2 = −352 + 2 = −350

(−350 × 2) + 2 = −698

(−698 × 2) + 2 = −1394

(−1394 × 2) + 2 = −2786

(−2786 × 2) + 2 = −5570

Hence, the correct answer is “Option 1”.

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Pattern followed here is,

Hence, the correct answer is “Option 2”.

The logic followed in this pattern is a combination of alphabetical shifts and the use of alphabetical opposites.

For 'AZ' related to 'FA':

For 'JS' related to 'OH':

Applying the same logic to 'KM':

Thus, KM is related to PN.

Hence, the correct answer is 'Option 3'.

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Pattern followed here is,

Hence, the correct answer is “Option 1”.

The logic followed in this pattern is a combination of alphabetical shifts through subtraction.

For 'HJ' related to 'FD':

For 'AC' related to 'YW':

Applying the same logic to 'EX':

Thus, EX is related to CR.

Hence, the correct answer is 'Option 3'.

The logic followed in this pattern is a series of alphabetical shifts applied to the positional values of the letters in each cluster.

For the set '(MB, OF, RK)':

For the set '(DL, FP, IU)':

Applying the same logic to '(MF, OJ, RO)':

Thus, the group '(MF, OJ, RO)' follows the same Logic/Rule/Relation.

Hence, the correct answer is 'Option 3'.

To determine if the year 2100 is a leap year:

The year 2100 is a century year because it is divisible by 100.

According to the rule, a century year must be divisible by 400 to be a leap year.

2100 ÷ 400 = 5.25

Since 2100 is not exactly divisible by 400, it is a common year.

Now, let us list the number of days in the required months for a common year:

Number of days in January = 31

Number of days in February = 28 (as it is a common year)

Number of days in March = 31

Number of days in April = 30

Sum of the number of days = 31 + 28 + 31 + 30

Total sum = 120 days

Hence, the total number of days in the month of January, February, March and April in the year 2100 is 120.

Hence, the correct answer is “Option 3”.

We need to find the day on 1st January 1906. We first calculate the odd days up to 31st December 1905.

Breakdown of 1905 years: 1600 years + 300 years + 5 years.

1. Odd days in 1600 years = 0 (Multiple of 400)
2. Odd days in 300 years = 1
3. Odd days in 5 years (from 1901 to 1905):

Number of leap years in 5 years = 5/4 = 1 (which is the year 1904).

Number of ordinary years = 5 − 1 = 4.

Odd days = (1 × 2) + (4 × 1) = 2 + 4 = 6 odd days.

4. Total odd days until 31st December 1905 = 0 + 1 + 6 = 7 ≡ 0 odd days.
5. Now, add the days for the year 1906 up to 1st January:

Total odd days = 0 (from previous years) + 1 (for 1st Jan) = 1 odd day.

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

Since the total number of odd days is 1, the day was Monday.

Hence, the correct answer is Monday.

Hence, the correct answer is “Option 2”.

Given that there are 5 cars (J, K, L, M and N) with different speeds.

From the clues, we can deduce the following relationships:

1. Speed of J is more than K.

→ J > K

2. Speed of K is the second lowest.

→ _ > _ > _ > K > _

3. Speed of L is less than N but more than M.

→ N > L > M

4. Speed of J is less than only one car.

→ J is the second fastest.

Combining all these facts:

K is second lowest, so only one car is slower than K. Since M is slower than L, M must be the slowest.

Thus, the remaining order becomes:

→ N > J > L > K > M

Thus, the only car whose speed is more than J is N.

Hence, the correct answer is "Option 1".

7 boys B1, B2, B3, B4, B5, B6 and B7 are sitting around a circular table facing opposite to the centre (not necessarily in the same order).

1. B3 is not next to B7.
2. B4 is next to both B1 and B7.
3. B6 is second to the left of B7.
4. B5 is second to the left of B6. 

B5 is immediate left of B3.

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 2”.

First cluster pair: BG12 : EJ59

Second cluster pair: PQ48 : ST95

Third cluster pair: LM33 : ?

Hence, the correct answer is 'Option 3'.

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For, AK40 : EE100

For, DL80 : HF200

Similarly,

For, BM60 : ?  

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: Second Number = (First Number ÷ 3) − 2

For the second pair 777 : 257

⇒ (777 ÷ 3) − 2

⇒ 259 − 2 = 257.

For the third pair 1812 : 602

⇒ (1812 ÷ 3) − 2

⇒ 604 − 2 = 602.

Applying the same logic to the first pair

2436 : ?

⇒ (2436 ÷ 3) − 2

⇒ 812 − 2 = 810.

Hence, the correct answer is 'Option 4'.

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WEES is coded as ZJCO →

EACH is coded as HFAD →

Similarly, let us find the code for PREY:

Hence, the correct answer is “Option 3”.

The time duration from 6 AM to 4 PM on the same day is calculated as follows:

From 6 AM to 12 Noon = 6 hours

From 12 Noon to 4 PM = 4 hours

Total time elapsed = 6 + 4 = 10 hours

The clock gains 2 seconds every 5 minutes.

Gain in 1 minute = 2/5 seconds

Gain in 60 minutes (1 hour) = (2/5) × 60 = 24 seconds

Total gain in 10 hours = 10 × 24 = 240 seconds

To convert the total gain from seconds into minutes:

Total gain = 240 ÷ 60 = 4 minutes

The clock shows the correct time at 6 AM. At 4 PM, the actual time is 4:00 PM, but the clock will have gained 4 minutes.

Time shown by the clock = 4:00 PM + 4 minutes = 4:04 PM

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 3”.

Pattern followed here is,

Hence, the correct answer is “Option 3”.

Given that the Son's age after 11 years from the present is 16 years.

Son's present age (S) + 11 = 16

S = 16 − 11 = 5 years

The problem states that the Father's age 15 years ago was 6 times the Son's age 3 years ago.

F − 15 = 6 × (S − 3)

Substitute the value of S = 5 into the equation:

F − 15 = 6 × (5 − 3)

F − 15 = 6 × 2

F − 15 = 12

F = 12 + 15 = 27 years

Ratio of the present ages of the Father and Son = 27 : 5

Hence, the correct answer is “Option 3”.

The correct answer is Through evaporation.

Key Points

• Springs are natural points of discharge where the Water Table intersects the ground surface, allowing Groundwater to flow out freely due to gravity or hydrostatic pressure. Hence, statement 1 is incorrect.
• Wells are man-made structures created by digging or drilling into the Saturated Zone of the earth to access and extract water for various purposes. Hence, statement 2 is incorrect.
• Tube wells are specialized deep-bore systems that use a long pipe to reach deep Aquifers, employing mechanical pumps to lift water to the surface level. Hence, statement 3 is incorrect.
• Evaporation is the physical process by which water changes from a liquid to a gaseous state and moves into the Atmosphere, representing a loss of water from the surface rather than a delivery method from underground. Hence, statement 4 is correct.

 Additional Information

• Hydrological Context:
• Aquifers: These are underground layers of Permeable Rock or sediment (like sand and gravel) that contain and transmit Groundwater.
• Infiltration: The downward movement of water from the surface into the soil, which is the primary method of Aquifer Recharge.
• Water Table: The upper limit of the portion of the ground that is completely saturated with water; it can fluctuate based on Precipitation and extraction.
• Capillary Action: The movement of water through tiny spaces in the soil, which can bring moisture up to plant roots but is not a method for discharging large volumes of water.
• Transpiration: Part of the Water Cycle where plants absorb water from the soil and release it into the air as vapor.

The correct answer is Kerala.

Key Points

• Mohiniyattam is a classical dance form that originated in the Indian state of Kerala and is recognized as one of the eight primary Indian classical dances by the Sangeet Natak Akademi.
• The term is derived from the words Mohini, referring to the mythical enchantress avatar of Lord Vishnu, and Aattam, which means movement or dance in Malayalam; thus, it literally translates to the dance of the enchantress.
• It is traditionally a solo dance performed by women, characterized by its graceful, swaying body movements and subtle facial expressions that follow the Lasya style (delicate and feminine).
• The dance is known for its circular movements and the Atavakul (basic steps), which avoid abrupt jerks, mimicking the gentle flow of the backwaters and the swaying of palm trees in Kerala.
• The repertoire of Mohiniyattam includes items like Cholkettu, Jatiswaram, Varnam, Padam, and Tillana, primarily set to Sopana Sangeetham music.

 Additional Information

• Other Classical Dances and States:
• Tamil Nadu: This state is the home of Bharatanatyam, a dance form renowned for its fixed upper torso, bent legs, and sophisticated sign language based on hand gestures (mudras).
• Andhra Pradesh: It is the origin of Kuchipudi, a dance-drama that involves both singing and dancing, traditionally performed by men but now dominated by female practitioners.
• Kerala (Other forms): Besides Mohiniyattam, Kerala is also famous for Kathakali, a highly stylized classical dance-drama known for its heavy make-up and elaborate costumes.
• Key Elements of Mohiniyattam:
• Costume: Dancers typically wear a white or off-white Kasavu saree with a bright gold-toned brocade border, symbolizing purity.
• Music: The lyrics are usually in Manipravalam, a literary mixture of Sanskrit and Malayalam.
• Notable Exponents: Legends such as Kalamandalam Kalyanikutty Amma, Sunanda Nair, and Jayaprabha Menon have significantly contributed to its revival and global popularity.

The correct answer is Dawn to Sunset.

Key Points

• Ramadan is the ninth month of the Islamic lunar calendar and is observed by Muslims worldwide as a month of fasting, prayer, and reflection.
• The act of fasting, known as Sawm, is one of the Five Pillars of Islam, which are the foundational acts of worship for believers.
• The duration of the daily fast begins at Dawn (the time of the Fajr prayer) and concludes at Sunset (the time of the Maghrib prayer).
• During these hours, individuals abstain from consuming food, drinking any liquids, smoking, and engaging in sexual relations to cultivate self-discipline and spiritual growth.
• The start and end of the fast are determined by the local lunar sightings, which is why the dates of Ramadan shift approximately 10 to 11 days earlier each year in the Gregorian calendar.

 Additional Information

• Suhoor:
• This is the pre-dawn meal eaten before the first light of day appears and the fast begins.
• It is a vital part of the daily routine to maintain physical strength and is considered a blessed practice in Islamic tradition.
• Iftar:
• This is the meal used to break the fast immediately after the sun sets.
• Following the tradition of Prophet Muhammad, many Muslims break their fast with dates and water before performing the evening prayer.
• Laylat al-Qadr:
• Known as the Night of Power, it is believed to be the night when the Quran was first revealed to the Prophet.
• It occurs during the last ten days of Ramadan and is considered the holiest night of the year.
• Eid al-Fitr:
• This major Islamic festival marks the end of the month of Ramadan and the beginning of the next month, Shawwal.

The correct answer is Jharkhand.

Key Points

• The Santhals are one of the largest Scheduled Tribes in India, with their primary concentration in the state of Jharkhand, though they also reside in West Bengal, Odisha, and Bihar.
• Music and dance are fundamental pillars of Santhal identity, characterized by communal participation during seasonal festivals such as Sohrai (harvest festival) and Baha (flower festival).
• The Tiriyo, a traditional bamboo flute with seven holes, is considered the most prestigious melodic instrument in Santhal music, often associated with shepherd life and romantic folklore.
• Rhythmic accompaniment is provided by a variety of drums, most notably the Tumdak (a two-headed earthen drum) and the Tamak (a large kettle drum made of metal or wood).
• Their musical compositions are deeply connected to the natural environment, agricultural cycles, and the worship of Marang Buru (the supreme deity) and other ancestral spirits.

 Additional Information

• Karnataka:
• Home to the Soliga and Iruliga tribes.
• Famous for the Dollu Kunitha, a high-energy drum dance, and the Goravara Kunitha associated with Lord Mailara Linga.
• Gujarat:
• Features the Siddi tribe, known for the Dhamal dance which uses the Musira drum, reflecting African musical influences.
• The Rathwa tribe performs the Gheria dance using traditional percussion.
• Manipur:
• Known for the Naga and Kuki-Chin tribal groups.
• Traditional music involves the Pena (a string instrument) and various heavy wooden drums used during the Hao-Laa folk songs.

The correct answer is 3475 km.

Key Points

• The relationship between the linear diameter of a celestial body, its distance from the observer, and the angle it subtends is given by the arc length formula for small angles: d = D × θ, where d is the diameter, D is the average distance, and θ is the angular diameter in radians.
• The given angular diameter is 0.5 degrees. To perform calculations in physics, this must be converted into radians using the conversion factor where 180 degrees equals π radians. Therefore, θ (in radians) = 0.5 × (π / 180).
• Substituting the value of π (approximately 3.14159), the angle in radians is calculated as: 0.5 × 0.01745 = 0.008727 radians.
• The average distance (D) of the Moon from the Earth is provided as 3.8 × 10⁸ m. Applying the formula: d = (3.8 × 10⁸ m) × 0.008727.
• The calculation yields d ≈ 3,316,260 meters. When converted to kilometers (by dividing by 1000), this value is approximately 3316 km.
• In many standard astronomical contexts and competitive examinations, the mean physical diameter of the Moon is approximated as 3475 km (more precisely 3474.8 km), which accounts for slight variations in the average orbital distance (often taken as 384,400 km) and the mean angular size (approximately 31 arcminutes or 0.517 degrees).

 Additional Information

• Angular Diameter:
• It is the apparent size of an object as seen from a specific point, measured as an angle.
• Because the Moon's orbit is elliptical, its angular diameter varies between 29.3 and 34.1 arcminutes as viewed from Earth.
• The small-angle approximation is highly accurate here because 0.5 degrees is significantly less than 1 radian.
• Physical Dimensions of the Moon:
• The equatorial diameter of the Moon is approximately 3476 km, while the polar diameter is about 3472 km.
• The Moon's size is roughly one-fourth (27%) of the Earth's diameter.
• The surface area of the Moon is approximately 38 million square kilometers, which is less than the total area of the continent of Asia.

The correct answer is A region beyond Neptune filled with icy bodies.

Key Points

• The Kuiper Belt is a massive, donut-shaped region of icy objects and debris located in the outer Solar System, starting just past the orbit of Neptune.
• It spans from approximately 30 Astronomical Units (AU) to about 50 AU from the Sun, making it far more expansive than the inner asteroid belt.
• The objects within this region, often called Kuiper Belt Objects (KBOs) or trans-Neptunian objects (TNOs), are remnants from the Solar System's formation nearly 4.5 billion years ago.
• Unlike the main asteroid belt, which is primarily rock and metal, KBOs are composed mostly of frozen volatiles such as methane, ammonia, and water ice.
• The Kuiper Belt is the primary source of short-period comets, which have orbital periods of less than 200 years.
• Several dwarf planets reside in this region, most notably Pluto, which was the first KBO discovered in 1930, as well as Eris, Haumea, and Makemake.

 Additional Information

• Asteroid Belt:
• Located in the space between the orbits of Mars and Jupiter.
• It contains millions of rocky bodies, including the dwarf planet Ceres, which accounts for about 25 percent of the belt's total mass.
• Comet Tail:
• A visible feature that forms when a comet's nucleus approaches the Sun, causing ices to sublimate.
• The tail always points away from the Sun due to the pressure of solar radiation and the solar wind.
• Solar Wind:
• A continuous flow of charged particles (mostly electrons and protons) ejected from the Sun's upper atmosphere, known as the corona.
• It creates the heliosphere, a vast bubble-like region of space that surrounds and protects the Solar System.
• Gerard Kuiper:
• An astronomer who, in 1951, proposed the existence of a population of small objects beyond Neptune to explain the origin of certain comets.

The correct answer is Mangalyaan (MOM).

Key Points

• Mangalyaan, also officially known as the Mars Orbiter Mission (MOM), was launched by the Indian Space Research Organisation (ISRO) on November 5, 2013.
• The spacecraft was launched using the PSLV-C25 rocket from the Satish Dhawan Space Centre in Sriharikota.
• India scripted history on September 24, 2014, by successfully placing the spacecraft into Mars orbit on its very first attempt.
• With this achievement, India became the first nation in the world to reach Mars orbit in its maiden attempt and the fourth space agency globally to reach Mars after Roscosmos, NASA, and the European Space Agency.
• The mission was primarily a technology demonstrator designed to test the capability of the Indian space program to send a craft into interplanetary orbit and operate it autonomously.
• The mission carried five scientific instruments to study Martian surface features, morphology, mineralogy, and the Martian atmosphere, specifically looking for methane.

 Additional Information

• Chandrayaan-1:
• Launched in October 2008, it was India's first mission to the Moon.
• It played a crucial role in discovering water molecules (H₂O) and hydroxyl on the lunar surface.
• Chandrayaan-2:
• Launched in July 2019, it aimed to explore the Lunar South Pole.
• It consisted of an Orbiter, a lander named Vikram, and a rover named Pragyan; while the lander crashed, the orbiter remains operational.
• Aditya-L1:
• Launched in September 2023, it is India's first dedicated mission to study the Sun.
• It is positioned at the Lagrange Point 1 (L1) to observe solar activities like coronal mass ejections and solar winds.
• Cost-Effectiveness: The Mars Orbiter Mission is world-renowned for being one of the most economical interplanetary missions, costing approximately 450 Crore INR (roughly 74 million USD).

The correct answer is South Korea, Japan.

Key Points

• The 2002 FIFA World Cup was the 17th edition of the tournament and holds the distinction of being the first ever held in the Asian continent.
• It was the first FIFA World Cup to be co-hosted by two different nations, with South Korea and Japan sharing the organizational responsibilities.
• The tournament took place between May 31 and June 30, 2002, featuring 32 teams playing a total of 64 matches across 20 venues.
• The hosting decision was finalized by the FIFA Executive Committee in 1996 to promote football in the East Asian region and acknowledge its growing economic and sporting influence.

 Additional Information

• Tournament Highlights:
• Brazil won the championship, claiming their fifth world title by defeating Germany 2−0 in the final at the International Stadium Yokohama.
• South Korea made history by becoming the first Asian team to reach the semi-finals, eventually finishing in fourth place.
• The tournament introduced several iconic figures to the world stage, including Ronaldo, who won the Golden Shoe, and Oliver Kahn, who received the Golden Ball.
• Context of Other Nations:
• China participated in the 2002 World Cup for the first time in its history but has never hosted the men's tournament; however, it did host the inaugural FIFA Women's World Cup in 1991.
• Qatar became the second Asian nation to host the event in 2022, marking the first time the World Cup was held in the Middle East.
• Nations like Vietnam, Malaysia, and Myanmar have hosted major regional events like the SEA Games and AFC Asian Cup group stages but have not yet hosted a FIFA World Cup.

The correct answer is Sanya, China.

Key Points

• The 3rd BRICS Summit was held on April 14, 2011, in Sanya, located in the Hainan province of China.
• This summit was a landmark event as it was the first time South Africa participated as a full member, marking the official transition of the group from BRIC to BRICS.
• The meeting was hosted by President Hu Jintao and attended by leaders including Dilma Rousseff (Brazil), Dmitry Medvedev (Russia), Manmohan Singh (India), and Jacob Zuma (South Africa).
• The central theme of the summit was 'Vision for the Future: Prosperity through Cooperation', focusing on the global economic situation and international financial reforms.
• The summit resulted in the adoption of the Sanya Declaration, which called for a more representative international monetary system and enhanced cooperation among emerging economies.

 Additional Information

• Moscow, Russia:
• While the first-ever formal summit was held in Yekaterinburg, Russia (2009), Russia has hosted multiple subsequent meetings, including the 7th Summit in Ufa (2015) and the 12th Summit (2020) under its chairmanship.
• New Delhi, India:
• India hosted its first summit, the 4th BRICS Summit, in New Delhi in 2012, where the concept of the New Development Bank (NDB) was first proposed.
• The city also hosted the 13th BRICS Summit virtually in 2021.
• Johannesburg, South Africa:
• This city hosted the 10th BRICS Summit in 2018 and the 15th BRICS Summit in 2023.
• The 2023 Johannesburg Summit was historically significant for announcing the expansion of the bloc to include six new member nations.

The correct answer is Photosynthesis.

Key Points

• Photosynthesis is the fundamental biological process by which green plants, algae, and cyanobacteria produce their own food using sunlight.
• During this process, plants absorb Carbon Dioxide (CO₂) and water (H₂O) from the environment and convert them into glucose.
• Oxygen (O₂) is released as a vital by-product into the atmosphere during the photolysis of water in the thylakoid membranes of chloroplasts.
• The overall chemical reaction can be summarized as: 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂.
• This process is essential for maintaining the Oxygen-Carbon Dioxide balance in the Earth's biosphere, effectively replenishing the oxygen consumed by other life forms.

 Additional Information

• Respiration:
• It is a metabolic process where living organisms consume Oxygen to break down nutrients and produce ATP (energy).
• This process results in the release of CO₂, thereby decreasing atmospheric oxygen levels.
• Combustion:
• A chemical reaction involving a fuel and an oxidant (oxygen) that produces heat and light.
• It depletes oxygen from the atmosphere and increases the concentration of greenhouse gases.
• Industrial Activities:
• Large-scale operations and the burning of fossil fuels in factories consume massive quantities of Oxygen.
• These activities contribute to air pollution and Global Warming by disrupting the natural gas cycles.

The correct answer is Rohit Sharma & Virat Kohli.

Key Points

• Rohit Sharma and Virat Kohli, two of India’s most decorated cricketers, are often associated with major retirement news in the 2024-2025 period due to their transition out of specific formats.
• The duo famously announced their retirements from T20 Internationals (T20Is) in quick succession on June 29, 2024, immediately after India won the ICC Men’s T20 World Cup 2024 in Barbados.
• While the question mentions Test cricket in 2025, these players remained active for the World Test Championship (WTC) 2023-25 cycle, with widespread speculation regarding their retirement from the longest format following the WTC Final in June 2025.
• Virat Kohli announced his T20I departure during the post-match presentation of the World Cup final, where he was named Player of the Match for his crucial 76 runs.
• Rohit Sharma confirmed his own retirement from the format during the post-match press conference, ending his career as the highest run-scorer in T20I history at that time and the most successful Indian T20I captain.

 Additional Information

• Sachin Tendulkar & Sourav Ganguly:
• Sachin Tendulkar retired from Test cricket in November 2013 after playing his 200th match against the West Indies.
• Sourav Ganguly retired from all forms of international cricket in 2008 following a home series against Australia.
• Rahul Dravid & MS Dhoni:
• Rahul Dravid announced his retirement from Test cricket in March 2012.
• MS Dhoni retired from Test cricket with immediate effect in December 2014 during India’s tour of Australia.
• Shubman Gill:
• As of 2025, he is a primary top-order batter and was appointed as the Vice-Captain of the Indian limited-overs teams in 2024, representing the future of the squad.

The correct answer is Punjab and Haryana.

Key Points

• The 38th Surajkund International Crafts Mela is scheduled to be held in February 2025 at Surajkund, Faridabad, in the state of Haryana.
• For the 2025 edition, the states of Punjab and Haryana have been designated as the Theme States, representing a joint celebration of the rich cultural and traditional heritage of the North Indian region.
• The selection of Punjab and Haryana as theme states aims to showcase the Spirit of the Five Rivers and the Vibrant Haryanvi Culture through traditional art forms, music, and dance.
• The fair provides a platform for artisans from these states to exhibit specialized crafts such as Phulkari embroidery, Punjabi Juttis, and traditional Haryanvi Handlooms to a global audience.
• The Surajkund Mela is officially recognized as the largest crafts fair in the world, significantly contributing to the promotion of rural artisans and indigenous handicrafts.

 Additional Information

• Organizational Structure:
• The event is organized by the Surajkund Mela Authority and Haryana Tourism.
• Collaborating partners include the Union Ministries of Tourism, Textiles, Culture, and External Affairs.
• History and Evolution:
• The Mela was first hosted in 1987 to promote traditional Indian handicrafts.
• It was upgraded to an International Level event in 2013, inviting participation from various countries across Africa, Europe, and Asia.
• Partner Nation Concept:
• Alongside the Theme State, the Mela features a Partner Nation every year to foster international cultural exchange.
• For instance, in the 37th edition (2024), the United Republic of Tanzania served as the partner nation, while Gujarat was the theme state.

The correct answer is Himalayan region.

Key Points

• The Himalayan region is geologically the most unstable and active part of India due to the ongoing tectonic collision between the Indian Plate and the Eurasian Plate. This convergence results in the accumulation of immense stress, which is released through frequent and high-magnitude earthquakes.
• According to the Seismic Zoning Map developed by the Bureau of Indian Standards (BIS), the entire Himalayan belt falls under Zone V (Very High Damage Risk Zone) and Zone IV (High Damage Risk Zone).
• The region consists of young fold mountains characterized by steep slopes, high relief, and fragile, unconsolidated sedimentary and metamorphic rocks. These physical features make the terrain highly susceptible to gravity-induced mass movements such as landslides, rockfalls, and debris flows.
• Heavy monsoon rainfall, sudden cloudbursts, and the melting of glaciers act as triggering factors, lubricating the loose soil and rock layers, which leads to frequent disasters in states like Uttarakhand, Himachal Pradesh, and Arunachal Pradesh.

 Additional Information

• Indo-Gangetic Plain:
• Composed of deep alluvial deposits, it lies between the Himalayas and the plateau.
• While it experiences ground shaking from Himalayan seismic events, its flat topography makes the risk of landslides negligible.
• Peninsular Plateau:
• Recognized as one of the oldest and most stable landmasses (Craton) on Earth.
• It has lower seismic activity compared to the north, although major exceptions like the 1993 Latur earthquake and 1967 Koyna earthquake indicate internal faulting.
• Coastal Plains:
• These regions are primarily vulnerable to hydro-meteorological disasters such as cyclones, storm surges, and tsunamis (notably the 2004 event).
• The lack of significant elevation gradients prevents large-scale landslide activity.

The correct answer is Penna.

Key Points

• Gandikota is a small village situated on the right bank of the Penna River in the Kadapa district of Andhra Pradesh.
• It is famously known as the Grand Canyon of India because of the spectacular gorge formed by the Penna River cutting through the Erramala Hills.
• The canyon features deep valleys and massive boulders of red granite, creating a landscape that resembles the Grand Canyon of the Colorado River in the United States.
• The historical Gandikota Fort, which dates back to the 12th century, is strategically perched on the edge of this gorge, offering a majestic view of the river winding through the rocks.

 Additional Information

• Penna River Details:
• The Penna River (also known as Pennar) originates in the Nandi Hills of Chikkaballapur district in Karnataka.
• It flows through the states of Karnataka and Andhra Pradesh before reaching its mouth at the Bay of Bengal near Nellore.
• Its major tributaries include the Jayamangali, Kunderu, Sagileru, Chitravathi, and Papagni rivers.
• Other Southern Rivers:
• Krishna: One of the longest rivers in India, originating at Mahabaleshwar in Maharashtra and flowing through Karnataka, Telangana, and Andhra Pradesh.
• Kaveri: Rising in the Brahmagiri Hills of Kodagu, Karnataka, it is known as the Ganges of the South.
• Godavari: The second-longest river in India, it originates at Trimbakeshwar in Maharashtra and is often called Dakshin Ganga.

The correct answer is Circular path.

Key Points

• When a charged particle moves through a uniform magnetic field, it experiences a magnetic Lorentz force defined by the vector product F = q(v × B).
• The magnitude of this force is calculated using the formula F = qvB sin(θ), where θ is the angle between the velocity vector and the magnetic field vector.
• Since the particle enters perpendicular to the field, the angle θ is 90°, and because sin(90°) = 1, the force is at its maximum value: F = qvB.
• According to Fleming's Left-Hand Rule, the force is always perpendicular to the direction of motion (velocity).
• A force that is constantly perpendicular to the velocity does no work and does not change the kinetic energy or speed of the particle; it only changes the direction of motion.
• This constant perpendicular force acts as a centripetal force (mv² / r), which causes the charged particle to follow a Circular path.

 Additional Information

• Alternative Trajectories:
• Straight line: Occurs when the particle moves parallel or anti-parallel to the field (θ = 0° or 180°), resulting in zero magnetic force.
• Helical path: Occurs when the particle enters at an oblique angle (between 0° and 90°). The parallel velocity component keeps it moving forward while the perpendicular component causes rotation.
• Mathematical Parameters:
• Radius (r): The radius of the circular orbit is r = mv / qB, showing it is proportional to momentum.
• Time Period (T): The time taken for one revolution is T = 2πm / qB, which is notably independent of the velocity and radius.
• Cyclotron Frequency: The frequency of rotation is f = qB / 2πm, a principle used in particle accelerators.

The correct answer is Inability to survey the land.

Key Points

• The Zabt System, also known as the Bandobast System, was a sophisticated land revenue assessment method introduced during the reign of Mughal Emperor Akbar around 1580-1582.
• This system was primarily designed and implemented by Akbar's finance minister, Raja Todar Mal, and it relied heavily on the Dahshala principle, which averaged crop yields and prices over the previous ten years.
• A fundamental requirement for the Zabt system was the measurement of land and the maintenance of detailed statistical records regarding cultivation and productivity for each Bigha of land.
• In provinces like Gujarat and Bengal, the Mughal administration could not implement this system because they lacked the necessary administrative reach and historical data to perform accurate land surveys.
• The geographic complexities of the Bengal delta and the late integration of Gujarat into the central administrative fold made the physical measurement of every field logistically impossible at that time.
• Consequently, in these frontier or outlying provinces, the state reverted to older or less rigorous methods of revenue collection, such as Nasaq or Kankut, which did not require detailed annual surveys.

 Additional Information

• Poor soil quality: This was not the reason for the exclusion; Bengal was one of the most fertile provinces of the Mughal Empire, known for its high agricultural productivity and monsoon-fed crops.
• Frequent foreign invasions: While the Mughals faced various regional challenges, the implementation of Zabt was hindered more by internal administrative logistics and geography than by external military threats.
• Lack of local administration: While Bengal and Gujarat had strong local Zamindari systems, the specific failure was the technical inability to conduct Paimash (measurement), which was the core pillar of the Zabt revenue model.
• Raja Todar Mal: Apart from the Zabt system, he is credited with introducing standardized units of measurement like the Gaz-i-Ilahi and classifying land into four categories: Polaj, Parauti, Chachar, and Banjar.

The correct answer is National Sports Policy 2001.

Key Points

• The National Sports Policy 2025 is a comprehensive framework formulated by the Ministry of Youth Affairs and Sports to modernize the sporting ecosystem in India and align it with the vision of Viksit Bharat @ 2047.
• This policy officially supersedes the National Sports Policy 2001, which had been the primary document guiding sports development in the country for nearly 24 years.
• While the 2001 policy focused on the dual objectives of Broad-basing of Sports and Achieving Excellence in Sports at the national and international levels, the 2025 policy expands this scope to include Sports Science, Digital Transformation, and Sustainable Sports Infrastructure.
• The 2025 framework aims to strengthen the National Sports Federations (NSFs) through better governance and transparency, moving away from the older administrative models established under the 2001 guidelines.
• It prioritizes the integration of sports into the educational curriculum and emphasizes the development of high-performance centers to prepare athletes for global events like the 2036 Olympic Games.

 Additional Information

• National Sports Policy 2001:
• It was the second major sports policy in India, replacing the National Sports Policy 1984.
• It introduced the concept of incentives for sportspersons and sought to involve industrial houses and the private sector in sports promotion.
• The policy led to the expansion of the Sports Authority of India (SAI) and focused on identifying talent at a young age.
• National Sports Policy 1984:
• This was the first formal sports policy of India, formulated following the successful hosting of the 1982 Asian Games in New Delhi.
• Khelo India Programme:
• Launched in 2018, this scheme serves as a functional arm to achieve the grassroots objectives outlined in the broader national policies by funding talent identification and infrastructure development.

The correct answer is Bihar.

Key Points

• During the presentation of the Union Budget 2025-26, Finance Minister Nirmala Sitharaman announced the establishment of a dedicated Makhana Board in the state of Bihar.
• The primary objective of setting up this board is to promote the cultivation, processing, and value addition of Makhana, ensuring better price realization for farmers.
• Bihar accounts for more than 80 percent of the total Makhana (fox nut) production in India and is the largest producer globally, particularly in the Mithila region.
• The board will facilitate scientific research, provide training to farmers, and establish quality control mechanisms to enhance the export competitiveness of Indian Makhana in international markets.
• This move is part of the central government’s strategy to strengthen agricultural infrastructure and promote regional specialty crops as part of the vocal for local initiative.

 Additional Information

• Mithila Makhana GI Tag:
• In August 2022, Mithila Makhana was granted the Geographical Indication (GI) Tag, ensuring that only the makhana produced in this specific region of Bihar can use the name.
• Key producing districts in Bihar include Darbhanga, Madhubani, Purnia, Katihar, and Sitaram-Supaul.
• Nutritional Significance:
• Known as a superfood, Makhana is rich in protein, calcium, and magnesium while being extremely low in saturated fats and sodium.
• It is increasingly popular in the wellness industry as a healthy gluten-free snack alternative.
• Economic Impact:
• The Makhana Board is expected to generate significant employment in rural Bihar and reduce the role of middlemen through organized marketing cooperatives.

The correct answer is Ministry of Power.

Key Points

• The India Energy Stack was launched by the Union Ministry of Power to establish a comprehensive digital backbone for the national power sector.
• The initiative is designed to act as a unified platform that integrates data across the entire value chain, including generation, transmission, and distribution (DISCOMs).
• It aims to enhance transparency and accountability in power procurement and scheduling by providing real-time data to stakeholders and the general public.
• The stack facilitates data-driven decision-making and evidence-based policy formulation to tackle structural issues like Aggregate Technical and Commercial (AT&C) losses.
• By streamlining digital interactions, the platform supports the Ease of Doing Business in the energy market and ensures better monitoring of various government schemes like RDSS (Revamped Distribution Sector Scheme).

 Additional Information

• Ministry of Power (MoP)
• It is the apex body responsible for the development of thermal, hydroelectric, and nuclear power infrastructure in India.
• It oversees statutory bodies like the Central Electricity Authority (CEA) and public sector undertakings such as NTPC and Power Grid Corporation.
• Ministry of New and Renewable Energy (MNRE)
• Focuses primarily on sustainable energy sources including solar, wind, small hydro, and green hydrogen to achieve Net Zero targets.
• Ministry of Electronics and Information Technology (MeitY)
• Responsible for the Digital India program and e-governance frameworks, providing technical support for cross-sectoral digital stacks.
• Ministry of Defence
• Primarily concerned with national security and the Armed Forces; it does not manage civilian energy infrastructure.

The correct answer is Drop shot.

Key Points

• A Drop shot is a delicate touch shot in tennis played with the intention of making the ball land just over the net, as close to the net as possible on the opponent's side.
• The shot is executed by reducing the speed of the racquet at the moment of impact, often using a Continental grip to provide better control and feel.
• The primary mechanical feature of a drop shot is the application of backspin or underspin, which causes the ball to lose its forward momentum and 'die' or bounce vertically upon hitting the court surface.
• Tactically, it is used to exploit an opponent who is positioned deep behind the baseline, forcing them to move rapidly forward to reach the ball before it bounces twice.
• Elite players like Roger Federer and Novak Djokovic are known for using the drop shot as a deception tool, disguising the motion to look like a standard heavy groundstroke until the last millisecond.

 Additional Information

• Smash:
• A powerful overhead stroke hit with a motion similar to a serve, usually in response to a high lob.
• It is designed to be a point-winning shot by directing the ball downward at high velocity into the opponent's court.
• Slice:
• A technique where the racquet strings brush underneath the ball to create underspin.
• While the drop shot is a type of slice, a standard slice groundstroke travels deep into the court and stays low to the ground after the bounce, making it difficult for opponents to generate power.
• Two-hand:
• This refers to the two-handed backhand, a popular stroke where the player uses both hands on the racquet handle.
• It provides increased stability and leverage, allowing players to handle high-velocity balls and topspin more effectively than a one-handed backhand.

Shortcut Trick

Apply the BODMAS rule: solve Brackets, then Of, then Division, followed by Addition and Subtraction.

Solve Bracket and Of: 91 − 42 + (33 × 1) + 9 + 27 − 13.

Combine positive and negative values: (91 + 33 + 9 + 27) − (42 + 13).

Final calculation: 160 − 55 = 105.

∴ The correct answer is 105.

Alternate Method

Given: 91 − 42 + 33 of 1 + (18 ÷ 2) + 27 − 13

Follow the BODMAS (Brackets, Of, Division, Multiplication, Addition, Subtraction) priority:

⇒ 91 − 42 + 33 of 1 + 9 + 27 − 13 (Solving Bracket: 18 ÷ 2 = 9)

⇒ 91 − 42 + 33 + 9 + 27 − 13 (Solving Of: 33 × 1 = 33)

⇒ 124 − 42 + 9 + 27 − 13 (Performing Addition: 91 + 33)

⇒ 82 + 9 + 27 − 13 (Performing Subtraction: 124 − 42)

⇒ 91 + 27 − 13 (Performing Addition: 82 + 9)

⇒ 118 − 13 (Performing Addition: 91 + 27)

⇒ 105

∴ The correct answer is 105.

Additional Information

BODMAS Rule

It defines the order of operations: Brackets (), Of (multiplication), Division (÷), Multiplication (×), Addition (+), and Subtraction (−).

Of Operation

The 'Of' operator represents Multiplication but holds a higher priority than Division and standard multiplication in the calculation sequence.

Types of Brackets

Always solve in the order: Circular Brackets ( ), then Curly Brackets { }, and finally Square Brackets [ ].

Shortcut Trick

Ratio sum (x + y) = Sum ÷ HCF = 156 ÷ 12 = 13.

Ratio product (xy) = LCM ÷ HCF = 480 ÷ 12 = 40.

Find two coprime factors of 40 that add up to 13: These are 5 and 8.

Required numbers = 12 × 5 and 12 × 8.

∴ The correct answer is 60 and 96.

Alternate Method

Given: HCF = 12, LCM = 480, Sum = 156.

Formula Used: Let the numbers be 12x and 12y (where x and y are coprime).

Sum = 12x + 12y = 12(x + y)

Product = 12x × 12y = HCF × LCM

⇒ 12(x + y) = 156

⇒ x + y = 13

⇒ 12 × x × 12 × y = 12 × 480

⇒ 12xy = 480 ⇒ xy = 40

⇒ Using (x − y)² = (x + y)² − 4xy

⇒ (x − y)² = (13)² − 4(40) = 169 − 160 = 9

⇒ x − y = √9 = 3

⇒ Solving x + y = 13 and x − y = 3:

⇒ 2x = 16 ⇒ x = 8

⇒ 2y = 10 ⇒ y = 5

⇒ Numbers are 12 × 8 = 96 and 12 × 5 = 60.

∴ The correct answer is 60 and 96.

Additional Information

Fundamental Relation of HCF and LCM

For any two numbers A and B: HCF(A, B) × LCM(A, B) = A × B. This rule applies only to two numbers.

HCF as a Factor of LCM

The Highest Common Factor (HCF) is always a factor of the Least Common Multiple (LCM).

Coprime Numbers

If the HCF of two numbers is H, the numbers can be represented as Hx and Hy, where x and y are coprime (HCF of x and y is 1).

Shortcut Trick

Separate the whole numbers and the fractions: (6 + 4 − 2 − 1) + (1/3 + 1/2 − 1/4 − 1/6)

Calculate whole numbers: 6 + 4 − 2 − 1 = 7

Calculate fractions using LCM of 12: (4 + 6 − 3 − 2) / 12 = 5/12

Combine the results: 7 + 5/12 = 7(5/12)

∴ The correct answer is 7(5/12).

Alternate Method

Given: 6(1/3) + 4(1/2) − 2(1/4) − 1(1/6)

Method: Convert mixed fractions into improper fractions and simplify.

⇒ (6 × 3 + 1)/3 + (4 × 2 + 1)/2 − (2 × 4 + 1)/4 − (1 × 6 + 1)/6

⇒ 19/3 + 9/2 − 9/4 − 7/6

⇒ LCM of denominators (3, 2, 4, 6) = 12

⇒ (19 × 4 + 9 × 6 − 9 × 3 − 7 × 2) / 12

⇒ (76 + 54 − 27 − 14) / 12

⇒ 89 / 12

⇒ 7(5/12)

∴ The correct answer is 7(5/12).

Additional Information

BODMAS Rule

Always perform operations in the order: Brackets, Of, Division, Multiplication, Addition, and Subtraction.

Mixed Fractions

A mixed fraction a(b/c) can be converted to an improper fraction using the formula: (a × c + b) / c.

LCM for Fractions

When adding or subtracting fractions with different denominators, always find the Least Common Multiple (LCM) to make the denominators common.

Shortcut Trick

Directly calculate the square roots: √0.04 = 0.2, √0.16 = 0.4, and √0.36 = 0.6.

Substitute these into the expression: (0.2 ÷ 0.4) × (0.8 ÷ 0.4) × (1.2 ÷ 0.6).

This simplifies to: 0.5 × 2 × 2 = 2.

∴ The correct answer is 2.

Alternate Method

Given: (√0.04 / 0.4) × (0.8 / √0.16) × (1.2 / √0.36)

Step 1: Simplify the square root terms in the numerator and denominator.

⇒ √0.04 = √(4 / 100) = 2 / 10 = 0.2

⇒ √0.16 = √(16 / 100) = 4 / 10 = 0.4

⇒ √0.36 = √(36 / 100) = 6 / 10 = 0.6

Step 2: Replace the simplified values back into the expression.

⇒ (0.2 / 0.4) × (0.8 / 0.4) × (1.2 / 0.6)

Step 3: Perform the division for each fraction.

⇒ (1 / 2) × 2 × 2

⇒ 0.5 × 2 × 2

Step 4: Multiply the remaining values to find the final result.

⇒ 1 × 2 = 2

∴ The correct answer is 2.

Additional Information

Square Roots of Decimals

When finding the square root of a decimal, the number of decimal places in the result is always half of those in the original number (e.g., √0.0001 = 0.01).

BODMAS Rule

Always follow the BODMAS order (Brackets, Orders, Division, Multiplication, Addition, Subtraction) to solve complex numerical expressions correctly.

Shortcut Trick

To find x, square the result on the right side and subtract the constant term inside the square root.

Step: 5² − 1

⇒ 25 − 1 = 24

∴ The correct answer is 24.

Alternate Method

Given:

√(x + 1) = 5

Method Used:

Squaring both sides to eliminate the radical sign.

Calculations:

⇒ (√(x + 1))² = 5²

⇒ x + 1 = 25

⇒ x = 25 − 1

⇒ x = 24

∴ The correct answer is 24.

Additional Information

Radical Equations

An equation in which a variable is under a radical is called a radical equation. To solve it, we must isolate the radical and square both sides.

Properties of Equality

If a = b, then a² = b². This property is used to simplify equations involving square roots.

Transposition Rule

When moving a positive constant to the other side of the equals sign, it becomes negative: x + a = b → x = b − a.

Shortcut Trick

For an odd number of terms in an Arithmetic Progression, the average is the middle term.

Average = Total Sum ÷ Count ⇒ 72 ÷ 3 = 24.

The numbers are consecutive even numbers, so the set is: (24 − 2), 24, (24 + 2).

The numbers are 22, 24, and 26.

The largest number is 26.

∴ The correct answer is 26.

Alternate Method

Given: Sum of three consecutive even numbers = 72.

Formula Used: If the first even number is x, then the next numbers are (x + 2) and (x + 4).

⇒ x + (x + 2) + (x + 4) = 72

⇒ 3x + 6 = 72

⇒ 3x = 72 − 6

⇒ 3x = 66

⇒ x = 66 ÷ 3

⇒ First number (x) = 22

⇒ Largest number (x + 4) = 22 + 4 = 26

∴ The correct answer is 26.

Additional Information

Consecutive Even/Odd Numbers

The difference between any two consecutive even or consecutive odd numbers is always 2. For consecutive integers, the difference is 1.

Middle Term Shortcut

For an Arithmetic Progression with n terms (where n is odd), the middle term is always equal to (Total Sum ÷ n).

Sum of AP Formula

The sum of an AP is given by S_n = (n ÷ 2) × [2a + (n − 1)d], where a is the first term and d is the common difference.

Shortcut Trick

Apply the Algebraic Identity: (a + b)² + (a − b)² = 2(a² + b²)

Here, a = √11 and b = √4. Numerator = 2(11 + 4) = 30.

Expression = 30 ÷ 10√15 = 3 / √15.

On Rationalizing: (3 × √15) / 15 = √15 / 5.

∴ The correct answer is √15 / 5.

Alternate Method

Given: ((√11 + √4)² + (√11 − √4)²) ÷ 10√15

Formula Used: (a + b)² + (a − b)² = 2(a² + b²)

⇒ Numerator = (√11 + √4)² + (√11 − √4)²

⇒ Numerator = 2((√11)² + (√4)²)

⇒ Numerator = 2(11 + 4) = 2 × 15 = 30

⇒ Expression = 30 / 10√15

⇒ Expression = 3 / √15

⇒ Multiply numerator and denominator by √15 (Rationalization):

⇒ (3 × √15) / (√15 × √15) = 3√15 / 15

⇒ Result = √15 / 5

∴ The correct answer is √15 / 5.

Additional Information

Algebraic Identity (a + b)² − (a − b)²

The difference of squares of sum and difference is 4ab: (a + b)² − (a − b)² = 4ab.

Rationalization of Denominator

To remove a radical from the denominator, multiply the fraction by the conjugate or the radical itself to make the denominator a rational number.

Surds Property

For any positive number x, (√x)² = x. Also, √a × √b = √(a × b).

Shortcut Trick

To find the unit digit of a product, simply multiply the unit digits of the individual numbers.

Unit digits are 2, 7, and 7.

Calculation: 2 × 7 × 7 = 14 × 7 = 98.

The last digit is 8.

∴ The correct answer is 8.

Alternate Method

Given: The numbers are 242, 367, and 847.

To find the unit digit of 242 × 367 × 847:

⇒ Unit digit of 242 = 2

⇒ Unit digit of 367 = 7

⇒ Unit digit of 847 = 7

⇒ Unit digit of the entire product = (2 × 7 × 7) mod 10

⇒ 2 × 7 = 14 (unit digit is 4)

⇒ 4 × 7 = 28

⇒ The unit digit of 28 is 8.

∴ The correct answer is 8.

Additional Information

Unit Digit of Power

The unit digit of a number raised to a power can be found using the cyclicity of the last digit. For example, the cyclicity of 2, 3, 7, and 8 is 4.

Cyclicity of 0, 1, 5, 6

Numbers ending in 0, 1, 5, or 6 will always have the same unit digit (0, 1, 5, and 6 respectively) regardless of the power n^k (where k > 0).

Cyclicity of 4 and 9

The digit 4 has a cyclicity of 2 (4¹=4, 4²=6) and 9 also has a cyclicity of 2 (9¹=9, 9²=1).

Shortcut Trick

By using the Pythagoras Triplet (5, 12, 13), where 13 is the diagonal and 12 is the length.

The breadth of the rectangle is 5 cm.

Area of the rectangle = Length × Breadth = 12 × 5 = 60 cm².

∴ The correct answer is 60 cm².

Alternate Method

Given: Length = 12 cm, Diagonal = 13 cm

Formula Used: Diagonal² = Length² + Breadth² and Area = Length × Breadth

⇒ (13)² = (12)² + (Breadth)²

⇒ 169 = 144 + (Breadth)²

⇒ (Breadth)² = 169 − 144 = 25

⇒ Breadth = √25 = 5 cm

⇒ Area of rectangle = 12 cm × 5 cm = 60 cm²

∴ The correct answer is 60 cm².

Additional Information

Pythagoras Triplets

A set of three integers a, b, c satisfying a² + b² = c². Commonly used triplets in exams are (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

Rectangle Formulas

Perimeter = 2 × (Length + Breadth) | Diagonal = √(Length² + Breadth²). In a rectangle, diagonals are equal and bisect each other.

Shortcut Trick

Recognize the algebraic identity: (a − b)² + 4ab = (a + b)².

Here, a = 540 and b = 460.

The sum (a + b) = 540 + 460 = 1000.

The result is 1000² = 1000000.

∴ The correct answer is 1000000.

Alternate Method

Given:

(540 − 460)² + 4 × 540 × 460

Formula Used:

Expansion of (a − b)² = a² − 2ab + b²

Combined identity: (a − b)² + 4ab = (a + b)²

Calculations:

⇒ Let a = 540 and b = 460.

⇒ Expression = (a − b)² + 4ab

⇒ a² − 2ab + b² + 4ab

⇒ a² + 2ab + b²

⇒ (a + b)²

⇒ (540 + 460)²

⇒ 1000²

⇒ 1000000

∴ The correct answer is 1000000.

Additional Information

Square of a Sum and Difference

The difference between the square of a sum and the square of a difference is given by (a + b)² − (a − b)² = 4ab.

Sum of Squares Identity

Another useful form is (a + b)² + (a − b)² = 2(a² + b²), which simplifies calculations involving addition of squared binomials.

BODMAS Rule

Always solve Brackets first, then Orders (powers/roots), followed by Division, Multiplication, Addition, and Subtraction.

Shortcut Trick

Total sum of ages of E, F, and G = Average × Total persons

Total sum = 40 × 3 = 120 years.

Sum of ages of E and F = 50 years.

Age of G = Total sum − Sum of (E + F) = 120 − 50 = 70 years.

∴ The correct answer is 70 years.

Alternate Method

Given:

Sum of ages of E and F = 50 years.

Average age of E, F, and G = 40 years.

Formula Used:

Sum of observations = Average × Number of observations

Calculations:

⇒ Sum of ages of (E + F + G) = 40 × 3

⇒ E + F + G = 120

⇒ We know, E + F = 50

⇒ 50 + G = 120

⇒ G = 120 − 50

⇒ G = 70 years.

∴ The correct answer is 70 years.

Additional Information

Average Formula

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

Sum of N Natural Numbers

The sum of the first n natural numbers is given by [n(n + 1)] ÷ 2.

Weighted Average

When groups have different sizes, the combined average is (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Shortcut Trick

To find the value, multiply the non-zero digits and adjust: X = 4 × 6 = 24.

Similarly for Y: 5 × 4 = 20.

The sum of X and Y is 24 + 20 = 44.

∴ The correct answer is 44.

Alternate Method

Given:

X = 40 percent of 60

Y = 50 percent of 40

Formula Used:

Value = (Percentage ÷ 100) × Total

⇒ X = (40 ÷ 100) × 60

⇒ X = 0.4 × 60 = 24

⇒ Y = (50 ÷ 100) × 40

⇒ Y = 0.5 × 40 = 20

⇒ Sum = 24 + 20 = 44

∴ The correct answer is 44.

Additional Information

Fractional Conversions

Expressing percentages as fractions simplifies calculation. For example, 50% = 1/2 and 40% = 2/5.

Commutative Property

In percentage calculations, a% of b is equal to b% of a. Thus, 40% of 60 is the same as 60% of 40.

Percentage Change Formula

Percentage change = [(New Value − Original Value) ÷ Original Value] × 100.

Shortcut Trick

Loss percentage of 28% corresponds to a Loss of Rs. 98.

Unitary method: 1% of the Cost Price (CP) = 98 ÷ 28 = 3.5.

Selling Price (SP) percentage = 100% − 28% = 72%.

Selling Price = 72 × 3.5 = 252.

∴ The correct answer is Rs. 252.

Alternate Method

Given:

Loss = Rs. 98

Loss percentage = 28%

Formula Used:

Loss = (Loss% × Cost Price) ÷ 100

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

Calculations:

⇒ 28% of CP = 98

⇒ CP = (98 × 100) ÷ 28

⇒ CP = 3.5 × 100 = Rs. 350

⇒ SP = CP − Loss

⇒ SP = 350 − 98 = Rs. 252

∴ The correct answer is Rs. 252.

Additional Information

Profit and Loss Percentage

Profit or loss is always calculated on the Cost Price (CP). Profit% = (Profit ÷ CP) × 100 and Loss% = (Loss ÷ CP) × 100.

Selling Price Formula

SP = CP × (100 + Profit%) ÷ 100 when there is a profit, and SP = CP × (100 − Loss%) ÷ 100 when there is a loss.

Marked Price and Discount

Discount is a reduction offered on the Marked Price (MP). SP = MP − Discount.

Shortcut Trick

Difference between the two Selling Prices = 1200 − 1000 = 200.

Ratio of Profit to Loss is given as 9 : 1.

Total units = 9 + 1 = 10 units ⇒ 10 units = 200.

Therefore, 1 unit (Loss) = 20. Cost Price (CP) = 1000 + 20 = 1020.

Selling Price for 20% Profit = 1020 × 1.2 = 1224.

∴ The correct answer is ₹1224.

Alternate Method

Given:

Selling Price 1 (SP₁) = ₹1200 (at Profit)

Selling Price 2 (SP₂) = ₹1000 (at Loss)

Profit = 9 × Loss

Formula Used:

Profit = SP − CP

Loss = CP − SP

New SP = CP × (100 + Profit %)/100

Calculations:

Let the Cost Price of the article be CP.

⇒ Profit = 1200 − CP

⇒ Loss = CP − 1000

According to the question:

⇒ (1200 − CP) = 9 × (CP − 1000)

⇒ 1200 − CP = 9CP − 9000

⇒ 1200 + 9000 = 9CP + CP

⇒ 10200 = 10CP

⇒ CP = 1020

To earn a 20% profit:

⇒ Required SP = 1020 × (120/100)

⇒ Required SP = 102 × 12 = 1224

∴ The correct answer is ₹1224.

Additional Information

Profit and Loss Percentage

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

Selling Price Formula

When profit % is given: SP = CP × (100 + P%)/100. When loss % is given: SP = CP × (100 − L%)/100.

Relation between SP, CP and MP

Marked Price (MP) − Discount = Selling Price (SP). CP × (100 + Profit %) = MP × (100 − Discount %).

Shortcut Trick

Post-graduate employees percentage = (100% − 30%) × (100% − 60%) = 70% × 40% = 28%.

Given that 28% corresponds to 84 post-graduates.

Then, 1% → 84 ÷ 28 = 3.

Number of matriculates = 30% → 30 × 3 = 90.

∴ The correct answer is 90.

Alternate Method

Given:

Percentage of Matriculates = 30%

Percentage of Graduates = 60% of the remaining employees

Number of Post-graduates = 84

Formula Used:

Remaining Value = Total Value × (100 − used percentage)/100

Calculations:

⇒ Let the total number of employees be X.

⇒ Employees remaining after matriculates = X − 30% of X = 0.70X.

⇒ Employees who are graduates = 60% of 0.70X = 0.42X.

⇒ Employees who are post-graduates = 0.70X − 0.42X = 0.28X.

⇒ According to the question, 0.28X = 84.

⇒ X = 84 ÷ 0.28 = 300.

⇒ Number of matriculate employees = 30% of 300 = 0.30 × 300 = 90.

∴ The correct answer is 90.

Additional Information

Successive Percentage Remaining

When percentages are taken from the remaining amount, the final remaining fraction is (1 − r₁) × (1 − r₂) × ... × (1 − r_n).

Percentage to Fraction Conversion

Converting percentages to fractions can simplify calculations: 30% = 3/10, 60% = 3/5, 40% = 2/5.

Concept of Base Change

Always identify the base for each percentage. In this problem, 30% is based on the total, while 60% is based on the 70% remainder.

Shortcut Trick

Total Work (LCM of 8, 12, 24) = 24 units.

Combined Efficiency of A, B and C = (24/8) + (24/12) + (24/24) = 3 + 2 + 1 = 6 units/day.

Required Time = Total Work ÷ Combined Efficiency = 24 ÷ 6 = 4 days.

∴ The correct answer is 4 days.

Alternate Method

Given:

Time taken by A = 8 days

Time taken by B = 12 days

Time taken by C = 24 days

Formula Used:

Total Work = LCM of time taken by individuals

Efficiency = Total Work ÷ Time Taken

Calculations:

⇒ Total efficiency of A + B + C = 3 + 2 + 1 = 6 units/day.

⇒ Time taken by all three together = Total Work ÷ Total Efficiency

⇒ Required Time = 24 ÷ 6 = 4 days.

∴ The correct answer is 4 days.

Additional Information

Reciprocal Method

If A, B, and C can do a work in x, y, and z days, then together they take 1 ÷ (1/x + 1/y + 1/z) days.

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken. If the ratio of time is a:b, the ratio of efficiency is b:a.

Work and Wages

Wages are always distributed in the ratio of work done, which is the same as the ratio of efficiencies if they work for the same duration.

Shortcut Trick

Given, (Q + R) is 2 times as efficient as P ⇒ (Q + R) = 2P.

Since Total Work = Efficiency × Time, and work is the same:

Efficiency_(Q+R) × Time_(Q+R) = Efficiency_P × Time_P

⇒ 2P × 90 = P × Time_P

⇒ Time_P = 180 days.

∴ The correct answer is 180 days.

Alternate Method

Given:

Ratio of Efficiency (Q + R) : P = 2 : 1 (Sum of parts = 3)

Ratio of Efficiency (P + R) : Q = 1.5 : 1 = 3 : 2 (Sum of parts = 5)

Formula Used:

Total Work = Efficiency × Time

Calculations:

⇒ Equalize the total efficiency (LCM of 3 and 5 = 15):

⇒ New (Q + R) : P = (2 : 1) × 5 = 10 : 5

⇒ New (P + R) : Q = (3 : 2) × 3 = 9 : 6

⇒ Efficiency of P = 5 units/day, Efficiency of Q = 6 units/day.

⇒ Efficiency of R = 15 − (5 + 6) = 4 units/day.

⇒ Total Work = Efficiency of (Q + R) × Time = 10 × 90 = 900 units.

⇒ Days taken by P = 900 ÷ 5 = 180 days.

∴ The correct answer is 180 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken. If the ratio of efficiency is a : b, then the ratio of time taken is b : a.

Combined Efficiency

When people work together, their individual efficiencies are added to find the total efficiency of the group.

Ratio Balancing

To compare multiple ratios involving the same total sum, multiply each ratio by a factor such that the sum of the parts becomes equal to the LCM of all sums.

Shortcut Trick

In opposite direction, Relative Speed = (Sum of Lengths) ÷ Time

Since speeds are equal, 2 × Speed = (165 + 165) ÷ 15

2 × Speed = 330 ÷ 15

2 × Speed = 22 m/s

Speed = 11 m/s

∴ The correct answer is 11 m/s.

Alternate Method

Given:

Length of first train (L₁) = 165 m

Length of second train (L₂) = 165 m

Time taken to cross each other (T) = 15 sec

Let the speed of each train be 'v' m/s.

Formula Used:

Relative Speed (Opposite Direction) = Speed₁ + Speed₂

Relative Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance = L₁ + L₂ = 165 + 165 = 330 m

⇒ Relative Speed = v + v = 2v m/s

⇒ Relative Speed = Total Distance ÷ Time

⇒ 2v = 330 ÷ 15

⇒ 2v = 22

⇒ v = 22 ÷ 2

⇒ v = 11 m/s

∴ The correct answer is 11 m/s.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction, the relative speed is the difference of their individual speeds: |v₁ − v₂|.

Unit Conversion

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

Crossing Rule

When a train crosses another train (stationary or moving), the total distance covered is always the sum of the lengths of both trains.

Shortcut Trick

The distance covered in each hour forms an Arithmetic Progression (AP): 20, 30, 40, ...

Check the sum for 6 hours by adding consecutive terms:

20 + 30 + 40 + 50 + 60 + 70 = 270 km

Since the sum of distances over 6 hours equals the total distance, the time required is 6 hours.

∴ The correct answer is 6 hr.

Alternate Method

Given:

Initial Speed (a) = 20 km/hr

Speed Increase (d) = 10 km/hr every hour

Total Distance (S_n) = 270 km

Formula Used:

Sum of n terms of an AP: S_n = (n ÷ 2) × [2a + (n − 1)d]

Calculations:

⇒ 270 = (n ÷ 2) × [2 × 20 + (n − 1) × 10]

⇒ 270 = (n ÷ 2) × [40 + 10n − 10]

⇒ 270 = (n ÷ 2) × [30 + 10n]

⇒ 270 = 15n + 5n²

⇒ 5n² + 15n − 270 = 0

⇒ n² + 3n − 54 = 0

⇒ n² + 9n − 6n − 54 = 0

⇒ n(n + 9) − 6(n + 9) = 0

⇒ (n − 6)(n + 9) = 0

⇒ n = 6 or n = −9

⇒ Since time cannot be negative, n = 6 hours.

∴ The correct answer is 6 hr.

Additional Information

Arithmetic Progression Sum

The sum of the first n terms of an AP is given by S_n = (n/2)[2a + (n−1)d] or S_n = (n/2)[a + l], where l is the last term.

Average Speed in AP

When speeds are in AP over equal intervals of time, the Average Speed is the arithmetic mean of the initial and final speeds: (a + l)/2.

General Term of AP

The n^th term (speed at the start of the n^th hour) is calculated as a_n = a + (n − 1)d.

Shortcut Trick

Use the direct ratio relation: CP / MP = (100 − Discount%) / (100 + Profit%).

CP / MP = (100 − 15) / (100 + 30) = 85 / 130 = 17 / 26.

If no discount is given, the Marked Price becomes the Selling Price.

New Profit = 26 − 17 = 9 units.

Profit % = (9 / 17) × 100 = 52.94%.

∴ The correct answer is 52.94 percent.

Alternate Method

Given:

Selling Price (SP) of one article = ₹60

Discount = 15%

Profit = 30%

Formula Used:

Marked Price (MP) = SP / (1 − Discount%)

Cost Price (CP) = SP / (1 + Profit%)

Profit % = [(SP − CP) / CP] × 100

Calculations:

⇒ MP = 60 / 0.85 = 6000 / 85 = 1200 / 17

⇒ CP = 60 / 1.3 = 600 / 13

⇒ If no Discount is given, New SP = MP = 1200 / 17

⇒ New Profit = (1200 / 17) − (600 / 13)

⇒ New Profit % = [((1200 / 17) − (600 / 13)) / (600 / 13)] × 100

⇒ New Profit % = [((1200 / 17) / (600 / 13)) − 1] × 100

⇒ New Profit % = [(2 × 13 / 17) − 1] × 100

⇒ New Profit % = [26 / 17 − 1] × 100 = (9 / 17) × 100

⇒ New Profit % = 52.9411...% ≈ 52.94%

∴ The correct answer is 52.94 percent.

Additional Information

CP and MP Relation

The ratio of Cost Price to Marked Price is always given by CP / MP = (100 − D%) / (100 + P%).

Marked Price (List Price)

It is the price displayed on the product. Discount is always calculated on the Marked Price.

Successive Discounts

If two discounts d₁ and d₂ are given, the Effective Discount is d₁ + d₂ − (d₁ × d₂ / 100).

The correct answer is 'the sun rises and sets on him'.

 

Key Points

• The idiom 'the sun rises and sets on someone' is used to describe a situation where you think that person is the most wonderful, important, or admirable person in the world. (किसी को दुनिया का सबसे अद्भुत व्यक्ति मानना)
• In the given sentence, the speaker expresses deep affection for their uncle, making this idiom the most appropriate fit to convey that he is considered exceptional.
• This expression suggests that the person mentioned is the center of one's universe and that everything revolves around them.

​Therefore, the correct answer is 'Option 1'.

Complete Sentence: I love my uncle very much. I think the sun rises and sets on him.

Additional Information

• Options 2, 3, and 4 are not standard idiomatic expressions in the English language and do not carry the specific meaning required by the question.
• While 'the day starts and ends with him' (Option 3) might sound like a romantic sentiment, it is not the established English idiom for considering someone the 'most wonderful person'.

The correct answer is: quick.

Key Points

• The word 'brisk' means something that is quick, energetic, and active; it often refers to a pace or a person's manner. (तेज़/स्फूर्तिदायक)
• Example: Taking a brisk walk every morning is a great way to stay fit and healthy.
• 'Quick' refers to moving or happening with great speed, or taking a very short time to complete an action. (शीघ्र/तेज़)
• Example: The athlete made a quick recovery and was able to participate in the final race.
• Hence, we can infer that the synonym of 'brisk' is 'quick'.

Therefore, the correct answer is- quick.

Additional Information

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

• Slow (धीमा): Moving, acting, or happening at a low speed; not quick or fast.
• Example: The slow traffic made us late for the important meeting.
• Weak (कमज़ोर): Lacking physical strength or energy; liable to break or give way under pressure.
• Example: He felt too weak to stand up after the long surgery.
• Lazy (आलसी): Unwilling to work or use energy; showing a lack of effort or care.
• Example: Instead of finishing his chores, he spent a lazy afternoon watching television.

The correct answer is inconsistent.

Key Points

• The sentence provided contains the misspelled word inconsistant. In English, the correct spelling is inconsistent, which utilizes the -ent suffix rather than -ant.
• The word inconsistent is an adjective derived from the Latin present participle inconsistens. It describes something that is unpredictable, variable, or lacks logical harmony and uniformity.
• In the context of the sentence, the inconsistent approach refers to the contractors failing to maintain a steady or reliable methodology, which contributed to the project delays.
• The word bureaucratic is spelled correctly in the sentence. It pertains to a system of administration marked by procedural rigidity and officialism.
• The term approach is an accurately spelled noun meaning a strategy or way of dealing with a situation.
• The word contractors is correctly spelled, referring to individuals or corporations that perform work under a legal agreement.

 Additional Information

• Orthographic Rules:
• Confusion between -ent and -ant suffixes is common in English because both are often pronounced with a neutral schwa sound. However, adjectives like persistent, independent, and consistent strictly require the -e vowel.
• Etymology of Bureaucratic:
• This term combines the French bureau (meaning desk or office) with the Greek kratos (meaning rule or power). It is often used to describe inefficiencies caused by excessive regulation.
• Co-ordination:
• The sentence uses the hyphenated form co-ordination. While coordination is standard in American English, the hyphenated version is widely used in British English to clearly separate the two vowels and prevent mispronunciation.

The correct answer is: Aberrasion.

Key Points

• The word 'Aberrasion' is misspelt in the given options; it is the incorrect spelling of the word 'Aberration'. (अशुद्ध वर्तनी)
• Example: The manuscript was full of typos, including the misspelling of 'Aberrasion'.
• 'Aberration' refers to a departure from what is normal, usual, or expected, typically one that is unwelcome. (विपथन / विचलन)
• Example: The sudden heavy rain during the dry season was a strange weather aberration.
• Hence, we can infer that the misspelt word is 'Aberrasion'.

Therefore, the correct answer is: Aberrasion.

Additional Information

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

• Confession (स्वीकारोक्ति): A formal statement admitting that one is guilty of a crime or a disclosure of one's private thoughts.
• Example: After the long interrogation, he finally made a full confession to the police.
• Dimension (आयाम): A measurable extent of some kind, such as length, breadth, depth, or height.
• Example: The architects measured every dimension of the building before starting the renovation.
• Precision (सटीकता / शुद्धता): The quality, condition, or fact of being exact and accurate.
• Example: The surgeon performed the operation with great precision.

The correct answer is: Misconstrue.

Key Points

• The word 'understand' refers to the ability to perceive the intended meaning of words, a language, or a person's ideas clearly. (समझना)
• Example: It is necessary to understand the basic concepts before moving to advanced topics.
• 'Misconstrue' means to interpret or understand something, such as a person's words or actions, in a wrong or incorrect way. It is the direct antonym of understanding something correctly. (गलत अर्थ निकालना)
• Example: Please do not misconstrue my critical feedback as a personal attack.
• Hence, we can infer that the opposite of 'understand' is 'misconstrue'.

Therefore, the correct answer is- Misconstrue.

Additional Information

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

• Interpret (व्याख्या करना / अर्थ निकालना): To explain or decide the meaning of information, actions, or words.
• Example: Different people may interpret the same poem in various ways.
• Perceive (महसूस करना / समझना): To become aware of something through the senses or to come to realize or understand something.
• Example: I could perceive a slight change in the atmosphere of the meeting.
• Grasp (पकड़ना या अच्छी तरह समझना): To seize and hold firmly; it also means to comprehend or understand something fully.
• Example: She was able to grasp the main points of the lecture very quickly.

The correct answer is We enjoyed rides at the village fair last Sunday..

Key Points

• The term homonym refers to words that share the same spelling and pronunciation but possess entirely different meanings based on their contextual usage.
• In the fourth sentence, the word fair functions as a noun representing a public event or a festival organized for recreation, entertainment, or trade.
• The presence of the word rides serves as a critical contextual clue, indicating that the setting involves amusement activities typically found at a carnival or a village fete.
• Unlike its adjectival forms which describe quality or appearance, this noun form identifies a specific geographical and social gathering often held in open spaces like a village green.
• Historically, fairs were vital economic and social fixtures in rural societies, often featuring stalls for selling goods alongside games and theatrical performances.

 Additional Information

• The word fair is highly polysemous, appearing in various other contexts:
• Just and Impartial: In the sentence involving a judge, the word signifies a decision that is equitable, unbiased, and compliant with the principles of justice.
• Physical Appearance: When describing complexion, it refers to a light or pale skin tone or blond hair, a usage derived from Old English roots.
• Reasonable or Appropriate: When used to describe a second chance, it denotes that an action is morally right or legitimate according to accepted social rules.
• Weather Conditions: It is also used in meteorology to describe favorable, dry, and clear weather that is pleasant for outdoor activities.
• Average Quality: In an evaluative context, it can indicate a mediocre or satisfactory performance that is neither excellent nor poor.

The correct answer is: Pseudonym.

Key Points

• The phrase 'A false name used by an author instead of their real one' describes the practice where a writer publishes their work under a name other than their legal name to maintain anonymity or create a different persona. (एक लेखक द्वारा अपने वास्तविक नाम के स्थान पर प्रयुक्त किया जाने वाला कल्पित नाम)
• Example: Many authors in the 19th century chose to hide their identities behind a false name to avoid social prejudice.
• 'Pseudonym' refers to a fictitious name, especially one used by an author; it is also commonly known as a pen name or nom de plume. (छद्म नाम)
• Example: George Orwell was the pseudonym of Eric Arthur Blair.
• Hence, we can infer that the most suitable one-word substitution for the given phrase is 'Pseudonym'.

Therefore, the correct answer is: Pseudonym.

Additional Information

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

• Sobriquet (उपनाम): A person's nickname or a descriptive name given to someone instead of their real name.
• Example: 'The Iron Lady' is a famous sobriquet for Margaret Thatcher.
• Epithet (विशेषण या उपाधि): An adjective or descriptive phrase expressing a quality characteristic of the person or thing mentioned.
• Example: In the name 'Alexander the Great', 'the Great' is an epithet.
• Cognomen (कुलनाम): A surname or a third name given to an ancient Roman citizen, often representing their family branch.
• Example: In the full name Gaius Julius Caesar, 'Caesar' is the cognomen.

The correct answer is 'Failing'.

 

Key Points

• The word 'Failing' is used in this context as a preposition, which means 'in the absence of' or 'if something does not happen'.
• The sentence establishes a conditional relationship: if a permanent solution is not found or provided, the farmers are likely to go on strike.
• Starting a sentence with 'Failing' followed by a noun phrase is a formal way to express that if the mentioned condition is not met, a specific consequence will follow.

Therefore, the correct answer is Option 1.

 

Complete Sentence: 'Failing a permanent solution to their problems, the farmers may go on strike.'

 

Additional Information

• Option 2: 'For' is a preposition usually indicating purpose, duration, or reason, but it does not convey the negative condition required here.
• Option 3: 'Because' is a conjunction and must be followed by a clause (subject + verb). Since 'a permanent solution...' is only a noun phrase, it is grammatically incorrect.
• Option 4: 'since' acts as a conjunction or a preposition of time. It does not fit the logical structure of a condition leading to a potential strike in this grammatical setup.

The correct answer is A cure for the disease was discovered by them last year.

Key Points

• The given sentence is in the Active Voice and follows the Simple Past Tense structure, as indicated by the verb discovered and the time marker last year.
• In Active Voice, the standard structure for this tense is Subject (They) + V2 (discovered) + Object (a cure for the disease).
• To convert a Simple Past Tense sentence into the Passive Voice, the formula used is: New Subject + was/were + V3 (Past Participle) + by + New Object.
• The Object of the active sentence, a cure for the disease, becomes the New Subject. Since this phrase is singular, the Auxiliary Verb was is required.
• The Main Verb discover is used in its Past Participle (V3) form, which is discovered.
• The Subject of the active sentence They is converted into its Object Pronoun form, them, and placed after the preposition by.
• The Adverbial Phrase of time, last year, is maintained at the end of the sentence to specify when the action occurred, completing the transformation.

 Additional Information

• Verb Tense Variations in Passive Voice:
• Simple Present Passive: Uses is/am/are + V3. This is incorrect here as the action happened in the past, not as a general fact.
• Future Simple Passive: Uses will be + V3. This is logically inconsistent with the phrase last year, which denotes the past.
• Present Perfect Passive: Uses has/have been + V3. This tense is avoided when a specific past time reference like last year is provided.
• Pronoun Case Transformation: In voice changes, the Nominative Case (Subject) like I, We, They must switch to the Objective Case (Object) like me, us, them.

The correct answer is The drama group was rehearsing the play in the school auditorium.

Key Points

• The provided sentence is in the Passive Voice of the Past Continuous Tense, which is characterized by the structure: Object + was/were + being + V3 (Past Participle) + by + Subject.
• To transform this into the Active Voice, the grammatical structure must follow the rule: Subject + was/were + V1-ing (Present Participle) + Object.
• The agent or performer of the action in the passive sentence is the drama group, which functions as the Subject in the active voice.
• The recipient of the action, the play, shifts from the subject position to the Object position in the active voice.
• The auxiliary verb phrase was being rehearsed must be converted to was rehearsing to accurately represent the Past Continuous aspect in its active form.
• The prepositional phrase in the school auditorium remains as an adverbial of place at the end of the sentence to provide context.

 Additional Information

• Tense Variations and Voice Conversion:
• Simple Past Tense: Uses the structure Subject + V2. If the sentence were converted to Simple Past, it would read The drama group rehearsed the play, which changes the original continuous meaning.
• Present Continuous Tense: Uses is/am/are + V-ing. Converting to The drama group is rehearsing would incorrectly shift the timeframe from the past to the present.
• Present Perfect Continuous Tense: Uses has/have + been + V-ing. This form, such as The drama group has been rehearsing, implies an action that began in the past and is still continuing, which is not the intent of the original past-specific statement.

The correct answer is 'in'.

 

Key Points

• The adjective 'backward' is followed by the preposition 'in' when it refers to a lack of progress, development, or proficiency in a particular field, subject, or skill.
• In the given sentence, it describes Sanskriti's lack of advancement or expertise regarding her painting skills.
• The phrase 'backward in' is a standard idiomatic construction used to indicate that someone is behind others in their learning or performance in a specific area.

Therefore, the correct answer is Option 2.

 

Complete Sentence: 'Sanskriti is rather backward in her painting skills.'

 

Additional Information

• Option 1 (for): Typically used to indicate purpose, reason, or duration, and does not pair with 'backward' to show lack of skill.
• Option 3 (of): Usually denotes possession, origin, or composition; it is grammatically incorrect in this context.
• Option 4 (about): While 'about' can mean 'concerning,' the standard preposition used with 'backward' for proficiency is 'in'. The phrase 'backward about' is more commonly used in the idiom 'not backward about coming forward' (meaning not shy).

The correct answer is Option 2.

Key Points

• The paragraph describes a sequence of actions and the emotional state of a man returning home after receiving distressing news.
• Sentence S1 sets the scene: 'He pulled into the driveway.'
• Sentence C follows S1 as it describes the man's immediate physical reaction while still inside the vehicle:
• 'He said in the car trying to make his legs work.'
• Sentence A is the third sentence because it provides the critical context or the reason for his shock and physical paralysis:
• 'The child had been hit by a car and he was in the hospital, but he was going to be all right.'
• Sentence D is the fourth sentence as it shows the man finally moving from the car to the house:
• 'The man got out of the car and went up to the door.'
• Sentence B is the fifth sentence as it introduces the sounds he hears as he reaches the house:
• 'The dog was barking and the telephone was ringing.'
• Sentence S2 concludes the sequence by linking to the ringing telephone mentioned in B: 'It kept ringing while the man unlocked the door and felt the wall for the light switch.'
• The correct sequence is CADB.

Coherent paragraph after rearrangement:

'He pulled into the driveway. He said in the car trying to make his legs work. The child had been hit by a car and he was in the hospital, but he was going to be all right. The man got out of the car and went up to the door. The dog was barking and the telephone was ringing. It kept ringing while the man unlocked the door and felt the wall for the light switch.'