SSC GD Constable 2026 Official Paper (Held On 05 May, 2026 Shift 3) (Previous Year Paper)

Logic followed here is,

46 × 2 + 5 = 92 + 5 = 97

97 × 2 + 5 = 194 + 5 = 199

199 × 2 + 5 = 398 + 5 = 403

403 × 2 + 5 = 806 + 5 = 811

811 × 2 + 5 = 1622 + 5 = 1627

1627 × 2 + 5 = 3254 + 5 = 3259

3259 × 2 + 5 = 6518 + 5 = 6523

The missing term that completes the series is 46.

The correct answer is "Option 1"

Pattern followed here is,

Hence, the correct answer is “Option 4”.

The logic followed in this pattern is a series of alphabetical shifts for each letter in the cluster.

For 'RF' related to 'TI':

For 'XA' related to 'ZD':

Applying the same logic to 'QC':

Thus, QC is related to SF.

Hence, the correct answer is 'Option 3'.

Pattern followed here is,

Hence, the correct answer is “Option 3”.

The logic followed in this pattern is a combination of alphabetical shifts and opposite letter pairs.

For 'CH' related to 'AS':

For 'TK' related to 'RP':

Applying the same logic to 'NS' to find the cluster related to 'LH':

The opposite letter is determined by the sum of their positional values being 27 (e.g., H(8) + S(19) = 27).

Thus, NS is the letter cluster related to LH.

Hence, the correct answer is 'Option 4'.

The logic followed in this pattern is based on alphabetical shifts between the consecutive letter clusters in each set.

For the set (LW, JQ, HK):

For the set (QE, OY, MS):

Applying the same logic to (VT, TN, RH):

Thus, the letter cluster group (VT, TN, RH) follows the same logic.

Therefore, the correct answer is 'Option 1'.

Given date: 21 September 2024 is a Thursday.

Target date: 27 April 2025.

We calculate the number of days month-wise from 21 September 2024 to 27 April 2025:

September 2024 (remaining days) = 30 − 21 = 9 days

October 2024 = 31 days

November 2024 = 30 days

December 2024 = 31 days

January 2025 = 31 days

February 2025 = 28 days (Since 2025 is a non-leap year)

March 2025 = 31 days

April 2025 (up to the target date) = 27 days

Total days = 9 + 31 + 30 + 31 + 31 + 28 + 31 + 27 = 218 days

Now, calculate the odd days by dividing the total days by 7:

218 ÷ 7 = 31 weeks and 1 day remainder.

Number of odd days = 1

Day on 27 April 2025 = Thursday + 1 day = Friday

Hence, the day on 27 April 2025 will be Friday.

Hence, the correct answer is “Option 2”.

The given date is 25 November 2020, which was a Wednesday.

We need to find the day on 25 March 2021. We calculate the number of days month by month:

November 2020: 30 − 25 = 5 days

December 2020: 31 days

January 2021: 31 days

February 2021: 28 days (as 2021 is a non-leap year)

March 2021: 25 days (up to the target date)

Total number of days = 5 + 31 + 31 + 28 + 25 = 120 days

To find the number of odd days, divide the total days by 7:

120 ÷ 7 = 17 weeks and 1 remainder.

The number of odd days is 1.

Now, add the odd days to the given day:

Day on 25 March 2021 = Wednesday + 1 odd day = Thursday

Hence, the correct answer is “Option 3”.

5 girls A, B, C, D and E are sitting in a row facing north (not necessarily in the same order).

1. Only E is to the left of D.
2. Only C is to the right of A.

B is third from the left end of the row.

Hence, the correct answer is “Option 2”.

Given that there are 6 boys with different ages.

From the clues, we can deduce the following relationships:

1. No one is elder than A.

→ A is the oldest boy.

2. C is elder than D but younger than B.

→ B > C > D

3. D is elder than E.

→ D > E

4. F is younger than E.

→ E > F

Combining all these facts gives the final order from oldest to youngest:

→ A > B > C > D > E > F

Only A is older than B.

Thus, the number of boys whose age is more than B is 1.

Hence, the correct answer is "Option 1".

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 4”.

ZA300 : YZ154

WY500 : VX354

Similarly,

TQ700 : ? 

Hence, the correct answer is 'Option 3'.

KPL22 : JOK441

IRO28 : HQN729

Similarly,

? : TKQ625

Hence, the correct answer is 'Option 1'.

The logic followed here is:

Logic: First Number = (Second Number × 2) + 6

For the second pair 282 : 138

⇒ (138 × 2) + 6

⇒ 276 + 6 = 282.

For the third pair 1166 : 580

⇒ (580 × 2) + 6

⇒ 1160 + 6 = 1166.

Applying the same logic to the first pair

? : 991

⇒ (991 × 2) + 6

⇒ 1982 + 6 = 1988.

Hence, the correct answer is 'Option 1'.

ACAI is coded as DCWD →

CHAP is coded as FLWK →

Similarly,

let's find the code for PIER:

Hence, the correct answer is “Option 1”.

The watch is 8 minutes slow at 8:00 AM.

The watch gains 8 seconds every hour.

First, we convert the total lag from minutes into seconds:

Total lag = 8 minutes

Total lag in seconds = 8 × 60 = 480 seconds

Now, we calculate the number of hours required to gain this lag:

Time taken = Total lag in seconds ÷ Gain per hour

Time taken = 480 ÷ 8 = 60 hours

Next, we add 60 hours to the initial time of 8:00 AM:

60 hours = 48 hours + 12 hours

Since 48 hours is exactly 2 days, the time after 48 hours will be 8:00 AM.

Now, add the remaining 12 hours:

8:00 AM + 12 hours = 8:00 PM

Therefore, the watch will show the correct time at 8:00 PM.

Hence, the correct answer is “Option 1”.

Logic followed here is,

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 2”.

The ratio of the present ages of the two students is 5 : 7.

Let their ages be 5x and 7x.

The difference between their ages is given as 8 years.

Sum of difference units = 7x - 5x = 2x = 8

x = 8 ÷ 2 = 4

Present age of the first student = 5 × 4 = 20 years

Present age of the second student = 7 × 4 = 28 years

Similarly, let us find the ages and ratio 7 years ago:

The ratio of their ages 7 years ago = 13 : 21

Hence, the correct answer is “Option 2”.

The correct answer is Antarctica.

Key Points

• The ozone hole was first discovered in 1985 by a team of scientists from the British Antarctic Survey (BAS), comprising Joseph Farman, Brian Gardiner, and Jonathan Shanklin.
• Their groundbreaking research was published in the scientific journal Nature, showing a dramatic seasonal decline in ozone levels over the Antarctic continent.
• The discovery was based on long-term data collected at the Halley Research Station and the Faraday Research Station using Dobson spectrophotometers.
• The thinning of the ozone layer was found to be most severe during the Southern Hemisphere spring (September to November) due to the presence of the Polar Vortex.
• The researchers observed that total ozone values had dropped by nearly 40 percent compared to measurements taken in the late 1950s and 1960s.

 Additional Information

• Ozone Layer and Mechanism:
• The ozone layer (O₃) is situated in the Stratosphere, roughly 15 to 35 kilometers above Earth, and absorbs harmful Ultraviolet (UV-B) radiation.
• The destruction of ozone is catalyzed by Chlorine and Bromine atoms released from Chlorofluorocarbons (CFCs) and Halons.
• In Antarctica, extreme cold leads to Polar Stratospheric Clouds (PSCs), which provide the chemical surface for CFCs to convert into active chlorine that destroys ozone.
• Comparison with Arctic:
• While ozone depletion also occurs in the Arctic, it is typically less severe because Arctic temperatures are warmer and the polar vortex is less stable than in Antarctica.
• Montreal Protocol:
• Following the discovery in Antarctica, the international community signed the Montreal Protocol in 1987 to phase out Ozone-Depleting Substances (ODS) globally.

The correct answer is Punjab.

Key Points

• Giddha is a popular and energetic folk dance that originated in the Punjab region, encompassing parts of modern-day India and Pakistan.
• It is traditionally performed by women and is often referred to as the feminine counterpart to the Bhangra dance, which is traditionally performed by men.
• The dance is characterized by its high-spirited rhythm, where performers stand in a circle and take turns performing in the center while others provide a rhythmic accompaniment through clapping.
• A defining feature of Giddha is the singing of Boliyan, which are traditional folk couplets or short songs that narrate stories of household life, social issues, family relationships, and female emotions.
• It is most vibrantly performed during the Teeyan festival to welcome the monsoon, as well as during the Baisakhi harvest festival and weddings.
• The attire for Giddha typically involves bright-colored Salwar Kameez or Lehenga paired with traditional Punjabi jewelry like the Saggi Phul and heavy embroidery work.

 Additional Information

• Rajasthan:
• Famous for the Ghoomar dance, traditionally performed by women of the Bhil tribe to worship Goddess Saraswati.
• The Kalbelia dance, associated with the snake-charmer community, is recognized on the UNESCO Representative List of the Intangible Cultural Heritage of Humanity.
• Maharashtra:
• The state is well-known for Lavani, a traditional dance performed to the rhythmic beats of the Dholki, often dealing with themes of society, religion, and politics.
• Lezim is another rhythmic folk form involving a musical instrument with jingling cymbals, commonly seen during Ganesh Chaturthi.
• Gujarat:
• Garba is the most iconic dance form, performed in circular formations around a Garbha Deep (lamp) during the Navratri festival.
• Dandiya Raas is another major folk dance where participants use decorated sticks to strike a rhythm while dancing.

The correct answer is Sun God (Surya).

Key Points

• Chhath Puja is a major Hindu festival primarily dedicated to the Sun God (Surya) and his sister Chhathi Maiya (Goddess Shashthi), thanking them for sustaining life on Earth and seeking their blessings.
• It is predominantly celebrated in the Indian states of Bihar, Jharkhand, and Uttar Pradesh, as well as in the Madhesh region of Nepal.
• The festival is unique as it is one of the few Hindu celebrations that involves the worship of a visible deity (Pratyaksh Devta) rather than idol worship in temples.
• It takes place on the sixth day (Shashthi) of the lunar month of Kartika in the Hindu calendar, which typically falls in October or November.

 Additional Information

• Ritual Sequence:
• Nahay Khay: The first day involves cleaning the house and consuming a Satvik meal after a holy bath in a river.
• Kharna: On the second day, devotees observe a day-long fast, breaking it after sunset with Kheer (rice pudding) and chapati.
• Sandhya Arghya: The third day is marked by a rigorous 36-hour fast without water, culminating in offering prayers to the setting sun at a water body.
• Usha Arghya: The final day involves offering Arghya to the rising sun, after which devotees break their fast with Thekua (a traditional dry sweet).
• Mythological Origins:
• Legends link the festival to the Mahabharata, where Karna (the son of Surya) performed these rituals, and Draupadi performed them to regain her kingdom.
• In the Ramayana, it is believed that Lord Rama and Goddess Sita offered prayers to the Sun God upon returning to Ayodhya.

The correct answer is They conducted yajnas and chanted mantras in low tones.

Key Points

• The Adhvaryu (or Adhvarya) was one of the four primary types of priests essential for the performance of Vedic rituals and sacrifices during the Vedic Period.
• According to the Yajurveda, which is the 'Veda of Prose Mantras' or 'Book of Rituals', the Adhvaryu was responsible for the physical and manual execution of the Yajna (sacrifice).
• The specific duties of the Adhvaryu included measuring the sacrificial ground, constructing the Vedi (altar), preparing the sacrificial vessels, lighting the sacred fire, and offering the Havis (oblation).
• During the ritual process, the Adhvaryu recited the Yajus (sacrificial formulas) in a specific rhythmic, low-toned chant, which is a characteristic feature that distinguished them from the high-pitched recitation of the Hotri.
• The role of the Adhvaryu ensured the precision of the ritual's technical steps, acting as the 'chief executive' of the sacrificial ceremony to maintain the sanctity and efficacy of the Vedic sacrifice.

 Additional Information

• The Vedic Priesthood consisted of four main categories, each associated with one of the four Vedas:
• Hotri:
• Associated with the Rigveda.
• Responsible for invoking the deities and reciting the Rig (hymns) during the sacrifice.
• Udgatri:
• Associated with the Samaveda.
• Specialized in singing the Saman (melodies), often compared to the musical aspect of the rituals.
• Brahman:
• Associated with the Atharvaveda.
• Served as the silent observer and supervisor of the entire Yajna to ensure no mistakes were made and to provide Prayaschitta (expiation) if errors occurred.
• The Yajurveda itself is divided into two major versions: the Shukla Yajurveda (White) and the Krishna Yajurveda (Black), containing the collections of prayers and sacrificial formulas used by the Adhvaryu.

The correct answer is 0.009 rad.

Key Points

• Angular diameter (or angular size) is the angle subtended by a circular object as seen by an observer from a specific distance.
• For celestial objects where the distance is significantly larger than the actual diameter, we utilize the small-angle approximation formula: θ ≈ D / d.
• In this formula, D represents the Moon's diameter, which is 3,474 km, and d represents the average distance from Earth, which is 384,000 km.
• The calculation is set up as θ = 3,474 ÷ 384,000, which yields the result in radians.
• Performing the division gives θ = 0.009046875 radians.
• Rounding to three decimal places, the angular diameter of the Moon as seen from Earth is 0.009 rad.

 Additional Information

• Small-Angle Approximation:
• This principle is used in astronomy and physics when the angle is small enough that the angle itself (in radians) is approximately equal to its sine and tangent.
• Radian Measure:
• A radian is the standard unit of angular measure. To convert radians to degrees, multiply by 180/π. An angle of 0.009 rad is roughly 0.51 degrees.
• Orbital Variations:
• The Moon follows an elliptical orbit. At perigee (closest point), its angular diameter appears slightly larger, while at apogee (farthest point), it appears smaller.
• Visual Appearance:
• The Sun has an angular diameter also measuring about 0.5 degrees. Because the Sun and Moon have similar angular sizes, total solar eclipses are possible when their paths align.

The correct answer is It increases.

Key Points

• According to Kepler's Third Law of Planetary Motion (the Law of Harmonies), the square of the orbital period (T) of a satellite is directly proportional to the cube of its orbital radius (r), expressed as T² ∝ r³.
• The orbital radius (r) is defined as the distance from the center of the Earth to the satellite, which is the sum of the Earth's radius (R) and the satellite's altitude (h), mathematically shown as r = R + h.
• When the altitude of the satellite increases from 300 km to 500 km (an increase of 200 km), the total orbital radius (r) also increases.
• The relationship for the orbital period is derived from the formula $T = 2\pi \sqrt{\frac{r^{3}}{GM}}$; since the radius (r) is in the numerator, an increase in altitude directly results in a longer orbital period.

 Additional Information

• Orbital Velocity and Altitude:
• The orbital speed (v) of a satellite is inversely proportional to the square root of the orbital radius, given by $v = \sqrt{\frac{GM}{r}}$.
• As the satellite's altitude increases, its orbital speed decreases; at an altitude of 300 km, the speed is approximately 7.8 km/s, but this speed will drop as it moves to 500 km.
• A slower speed combined with a longer orbital path (greater circumference) results in a significantly higher time period for one complete revolution.
• Low Earth Orbit (LEO) Characteristics:
• Satellites at altitudes between 160 km and 2,000 km are considered to be in Low Earth Orbit.
• The average Earth radius used in these orbital calculations is approximately 6,371 km.
• The Universal Gravitational Constant (G) is 6.674 × 10⁻¹¹ Nm²/kg² and the Mass of Earth (M) is roughly 5.97 × 10²⁴ kg.

The correct answer is 1.1 times.

Key Points

• The concept of efficiency (η) in propulsion and mechanical systems defines the ratio of the useful energy output (ideal energy) to the total energy input (actual energy).
• The mathematical relationship is expressed as η = Ideal Energy ÷ Actual Energy. To find the actual energy used relative to the ideal energy, the formula is rearranged as Actual Energy = Ideal Energy ÷ η.
• The problem specifies an efficiency of 90%, which corresponds to a decimal value of 0.9.
• To determine the factor of actual energy used, we calculate the ratio 1 ÷ 0.9, which equals approximately 1.111.... Hence, the actual energy used is 1.1 times the ideal energy when rounded to one decimal place.
• The payload capacity of 4000 kg and the specific satellite mass of 3600 kg indicate that the rocket is operating within its structural limits, but the energy ratio remains dependent on the system efficiency.

 Additional Information

• GSLV Mk III (LVM3):
• Commonly known as the Launch Vehicle Mark 3 (LVM3), it is the most powerful rocket developed by the Indian Space Research Organisation (ISRO).
• It is designed to deliver heavy communication satellites into Geosynchronous Transfer Orbit (GTO) using a complex cryogenic upper stage (C25).
• The vehicle utilizes two S200 solid strap-on boosters and an L110 liquid-propellant core stage to achieve the necessary thrust-to-weight ratio for heavy lifting.
• The specific impulse (Isp) and combustion efficiency of its engines determine the overall propellant mass required to reach a specific orbital velocity, where lower efficiency necessitates a higher mass fraction of fuel.

The correct answer is DY Patil Stadium, Navi Mumbai.

Key Points

• The inaugural final of the Indian Premier League (IPL) took place on June 1, 2008, at the DY Patil Stadium in Navi Mumbai, Maharashtra.
• The stadium, located in the Nerul area, was selected as the neutral venue for the historic first final, offering a then-modern capacity of approximately 55,000 spectators.
• The final match featured the Rajasthan Royals, led by the legendary Australian spinner Shane Warne, against the Chennai Super Kings, captained by MS Dhoni.
• The match ended in a thrilling finish where the Rajasthan Royals chased down a target of 164 runs, winning by 3 wickets on the final delivery of the innings.
• This victory established the Rajasthan Royals as the first-ever champions of the IPL, a tournament that would eventually become the world's premier domestic T20 cricket league.

 Additional Information

• IPL 2008 Awards and Statistics:
• Yusuf Pathan was named the Player of the Match in the final for his vital contribution of 56 runs and 3 wickets.
• Shane Watson, also from Rajasthan Royals, was declared the Player of the Tournament for his consistent all-round brilliance.
• The first Orange Cap was won by Shaun Marsh (Kings XI Punjab) for scoring 616 runs, and the first Purple Cap went to Sohail Tanvir (Rajasthan Royals) for 22 wickets.
• Context of Other Stadiums:
• M. Chinnaswamy Stadium: Located in Bengaluru, it hosted the first-ever match of the IPL between RCB and KKR on April 18, 2008.
• Eden Gardens: Based in Kolkata, it is the home ground of the Kolkata Knight Riders and one of the most iconic cricketing venues globally.
• Wankhede Stadium: Situated in Mumbai, it serves as the home ground for Mumbai Indians and hosted the second semi-final of the 2008 season.

The correct answer is GSAT-7.

Key Points

• GSAT-7, popularly known as Rukmini, is India's first dedicated multi-band military communication satellite developed by the Indian Space Research Organisation (ISRO).
• Launched on August 29, 2013, via the Ariane 5 launch vehicle from Kourou, French Guiana, it was specifically designed to modernize the Indian Navy's communication infrastructure.
• The satellite operates in a Geostationary Orbit at 74 degrees East longitude, providing a massive footprint over the Indian Ocean Region (IOR).
• It facilitates real-time networking of maritime assets, allowing warships, submarines, aircraft, and shore-based facilities to communicate securely without relying on foreign satellites.
• The payload includes UHF, S-band, C-band, and Ku-band transponders, which enable high-speed data transfer and beyond-the-horizon connectivity.

 Additional Information

• GSAT-12
• It is a communication satellite launched in 2011 to replace the aging INSAT-3B.
• Its primary functions include Disaster Management Support, tele-education, and tele-medicine services.
• GSAT-29
• A high-throughput communication satellite launched in 2018 by the GSLV Mk III rocket.
• It is designed to provide high-speed internet connectivity to remote areas, specifically Jammu & Kashmir and the North-Eastern states.
• Cartosat-2
• Part of the Indian Remote Sensing (IRS) satellite series used for Earth observation.
• It provides high-resolution panchromatic imagery used for urban planning, land information systems, and coastal land use monitoring.
• GSAT-7A
• Known as the Angry Bird, it was launched in 2018 to support the Indian Air Force (IAF) by interlinking different ground stations and airbases.

The correct answer is New Delhi, India.

Key Points

• The 13th BRICS Summit was held on September 9, 2021, under the chairmanship of the Prime Minister of India, Narendra Modi.
• The summit was hosted by India in a virtual format due to the restrictions imposed by the global COVID-19 pandemic.
• The specific theme for the 2021 summit was 'BRICS @ 15: Intra-BRICS Cooperation for Continuity, Consolidation and Consensus', marking the 15th anniversary of the group.
• This was the third time that India hosted the BRICS Summit, having previously organized the 4th Summit in 2012 and the 8th Summit in 2016.
• Key outcomes included the adoption of the 'New Delhi Declaration' and the BRICS Counter-Terrorism Action Plan, emphasizing cooperation in public health and digital technology.

 Additional Information

• BRICS is a grouping of five major emerging economies: Brazil, Russia, India, China, and South Africa, representing about 42% of the world population and 24% of the global GDP.
• China (Beijing):
• China hosted the 14th BRICS Summit in 2022, which was also held in a virtual format.
• Russia (Moscow):
• Russia chaired the 12th BRICS Summit in 2020. This meeting was originally scheduled to be held in Saint Petersburg but shifted online due to the pandemic.
• South Africa (Johannesburg):
• South Africa hosted the 15th BRICS Summit in 2023, which was the first in-person summit held after the pandemic and saw the historic announcement of the group's expansion.
• The New Development Bank (NDB), headquartered in Shanghai, is a significant institutional outcome of the BRICS partnership, focused on mobilizing resources for infrastructure and sustainable development.

The correct answer is Vasudevan Baskaran.

Key Points

• Vasudevan Baskaran was the distinguished captain of the Indian men's field hockey team that clinched the gold medal at the 1980 Summer Olympics held in Moscow, Soviet Union.
• This victory marked India's eighth Olympic gold medal in field hockey, a record that remains the highest for any nation in the history of the sport at the Olympics.
• In the high-stakes final match, the Indian team defeated Spain with a narrow 4−3 scoreline to stand atop the podium.
• Baskaran, who played the pivotal role of a halfback, was instrumental in leading a relatively young team to success after the disappointment of the 1976 Montreal Games.
• For his exemplary contribution and leadership, he was conferred with the Arjuna Award in 1979−1980 and the prestigious Padma Shri in 1981.

 Additional Information

• Ajit Pal Singh
• He was a legendary center-half who famously captained the Indian team to its first and only Hockey World Cup title in 1975 at Kuala Lumpur.
• Mohammed Shahid
• Known as one of the greatest dribblers in hockey history, he was a key forward in the 1980 gold-winning squad and was awarded the Padma Shri in 1986.
• Zafar Iqbal
• A prolific left-winger who was part of the 1980 Olympic team, he later served as the captain of the Indian national team during the 1984 Los Angeles Olympics.

The correct answer is It does not react easily..

Key Points

• Nitrogen exists as a diatomic molecule (N₂) and is characterized by its high chemical stability and lack of reactivity under standard atmospheric conditions.
• The primary reason for its inertness is the presence of a very strong triple covalent bond between the two nitrogen atoms, which requires a significant amount of energy to break.
• The bond dissociation energy of the nitrogen-nitrogen triple bond is approximately 941.4 kJ/mol, which is considerably higher than the bond energies of oxygen or hydrogen.
• Because of this extreme bond strength, nitrogen does not readily participate in chemical reactions at room temperature, acting as a diluent that slows down the combustion process of oxygen in the atmosphere.

 Additional Information

• Atmospheric Composition:
• Nitrogen is the most abundant gas in the Earth's atmosphere, comprising roughly 78% of the total volume.
• Despite being inert, it is a vital component of amino acids, proteins, and DNA in all living organisms.
• Nitrogen Fixation:
• The strong triple bond can only be broken by high-energy processes such as lightning strikes or through biological nitrogen fixation by specific bacteria like Rhizobium.
• Industrially, the Haber-Bosch process uses high pressure and temperature with a catalyst to overcome this inertness to produce ammonia.
• Industrial Applications:
• Nitrogen is used to provide an inert atmosphere in food packaging to prevent oxidation and spoilage.
• It is utilized in cryogenics as liquid nitrogen for the preservation of biological samples due to its low boiling point of −195.8°C.

The correct answer is Maharashtra State Road Development Corporation (MSRDC).

Key Points

• The SKOCH Award was conferred upon the Maharashtra State Road Development Corporation (MSRDC) in 2025 in recognition of its excellence in infrastructure development and project management.
• The specific project honored is the Maharashtra Samruddhi Mahamarg, also known as the Hindu Hrudaysamrat Balasaheb Thackeray Maharashtra Samruddhi Mahamarg, which is a flagship greenfield expressway.
• MSRDC was recognized for successfully executing one of India’s longest access-controlled expressways, spanning 701 kilometers and connecting the cities of Nagpur and Mumbai.
• The project was lauded by the SKOCH Group for its impact on regional connectivity, economic stimulation across 10 districts, and the implementation of state-of-the-art Intelligent Highway Management Systems.
• The award highlights the corporation’s commitment to fast-track construction, having completed major stretches in record time while adhering to global standards of safety and sustainability.

 Additional Information

• Maharashtra Samruddhi Mahamarg:
• This expressway is designed for a top speed of 150 km/h, effectively reducing the travel time between Nagpur and Mumbai from 16 hours to approximately 8 hours.
• It features over 50 flyovers, 24 interchanges, and specialized wildlife overpasses, ensuring that the ecological balance is maintained alongside industrial progress.
• The project facilitates the creation of Krushi Samruddhi Nagars (New Towns) to promote local employment and value addition to agricultural produce.
• Maharashtra State Road Development Corporation (MSRDC):
• Established by the Government of Maharashtra in 1996, it is a premier body responsible for the development of high-speed corridors and sea links.
• Notable previous projects include the Mumbai-Pune Expressway, which was India’s first access-controlled toll road, and the iconic Bandra-Worli Sea Link.

The correct answer is Operation Brahma.

Key Points

• Operation Brahma was initiated by the Government of India as a rapid Humanitarian Assistance and Disaster Relief (HADR) mission to support neighboring Myanmar after a severe earthquake.
• Under this operation, India mobilized critical relief supplies, including essential medicines, dry rations, temporary shelters, and specialized search-and-rescue tools.
• The operation was executed through coordinated efforts involving the Indian Air Force (IAF) and the National Disaster Response Force (NDRF) to ensure timely logistics and rescue support.
• This mission reflects India's proactive role as a first responder in the region and aligns with its strategic 'Neighborhood First' policy of assisting neighboring nations during natural crises.

 Additional Information

• Operation Samudra Setu:
• Launched by the Indian Navy in May 2020 as part of the national effort to repatriate Indian citizens stranded overseas during the COVID-19 pandemic.
• Naval vessels such as INS Jalashwa and INS Shardul were deployed to evacuate thousands of citizens back to India.
• Operation Maitri:
• A major joint relief and rescue operation conducted by the Indian Armed Forces following the catastrophic Nepal earthquake in April 2015.
• It stands as one of India's largest emergency bilateral rescue operations, offering medical aid, engineering assistance, and food supplies.
• Operation Sahayata:
• Launched by the Indian Navy in 2019 to provide immediate relief to Mozambique following the devastation caused by Cyclone Idai.
• Indian naval ships provided medical care, clean drinking water, and helicopter-based rescue operations in affected areas.

The correct answer is Buffer zones around protected areas.

Key Points

• Eco-Sensitive Zones (ESZs), also known as Ecologically Fragile Areas (EFAs), are designated areas surrounding National Parks and Wildlife Sanctuaries meant to act as a transition from high-protection zones to zones of lower protection.
• The primary objective of notifying these zones is to regulate human activities in the periphery of Protected Areas so that they serve as shock absorbers to the fragile ecosystem within.
• These zones are notified by the Ministry of Environment, Forest and Climate Change (MoEFCC) under the Environment (Protection) Act, 1986.
• As per the National Wildlife Action Plan (2002−2016), the central government usually prescribes a distance of up to 10 kilometers from the boundary of a protected area as an ESZ.
• However, the width of the ESZ can exceed 10 kilometers if it includes sensitive ecological corridors or specific geographical features essential for biodiversity conservation.
• The management of ESZs is crucial for maintaining ecological integrity and preventing habitat fragmentation caused by rapid urbanization or industrialization.

 Additional Information

• Classification of Activities:
• Prohibited Activities: These include commercial mining, setting up of sawmills, polluting industries, and major hydroelectric projects that cause significant environmental damage.
• Regulated Activities: These include the felling of trees, establishment of hotels and resorts, and the drastic change of agricultural land use, all of which require specific clearances.
• Permitted Activities: Activities that are eco-friendly, such as rainwater harvesting, organic farming, and the use of renewable energy sources, are encouraged within these zones.
• Distinction from other terms:
• Wildlife Corridors: These are specific geographical strips that connect two larger habitats to allow animal migration, whereas ESZs are peripheral buffers.
• Mining Zones: These are areas specifically earmarked for the extraction of minerals and are generally prohibited within the core of an ESZ.
• Pollution-affected areas: These are regions identified by Pollution Control Boards based on the Comprehensive Environmental Pollution Index (CEPI) and are not synonymous with ESZs.

The correct answer is To promote self-reliance across all sectors.

Key Points

• Atmanirbhar Bharat Abhiyan, which translates to Self-Reliant India, was launched by Prime Minister Narendra Modi in May 2020.
• The initiative was introduced as a strategic response to the economic disruptions caused by the COVID-19 pandemic, aiming to revive the national economy through structural reforms.
• The central goal is to make India self-sufficient by reducing its dependence on foreign imports and enhancing the capacities of domestic industries and local manufacturing.
• The government announced a comprehensive economic package worth 20 lakh crore rupees, equivalent to nearly 10% of India's GDP, to support this mission.
• The mission is built on five essential pillars: Economy (aiming for quantum leaps), Infrastructure (representing modern India), System (driven by 21st-century technology), Vibrant Demography (utilizing human capital), and Demand (harnessing the power of the supply chain).

 Additional Information

• Vocal for Local: A key component of the campaign that encourages citizens to promote and use indigenous products to help them achieve global standards and scale.
• MSME Sector Reforms: Under this initiative, the definition of Micro, Small, and Medium Enterprises was revised, and collateral-free automatic loans were provided to boost local productivity.
• Sector-Specific Focus: The abhiyan covers various sectors including Agriculture, Defense production, Civil Aviation, Power distribution, and Space research to ensure comprehensive national development.
• Global Integration: While the focus is on self-reliance, it does not advocate for isolationism; instead, it seeks to integrate India more deeply into global supply chains as a reliable manufacturing hub.

The correct answer is Narmada.

Key Points

• The Dhuandhar Falls is a spectacular waterfall located in the Bhedaghat area of the Jabalpur district in Madhya Pradesh.
• It is formed by the Narmada River, which is the fifth-longest river in the Indian subcontinent and is often referred to as the Lifeline of Madhya Pradesh and Gujarat.
• The name Dhuandhar is derived from two Hindi words: Dhuan (smoke) and Dhar (flow), describing the smoke-like mist created by the water falling from a height of approximately 30 meters.
• The river carves through the world-famous Marble Rocks before plunging down, creating a narrow canyon and a powerful cascade.
• The Narmada River flows through a rift valley between the Vindhya and Satpura ranges, moving in a westward direction towards the Arabian Sea.

 Additional Information

• Tapti River
• It originates in the Multai reserve forest of Betul district, Madhya Pradesh.
• Like the Narmada, it is a west-flowing river that drains into the Gulf of Khambhat.
• Kaveri River
• Rising in the Brahmagiri Hills of the Western Ghats in Karnataka, it is a major east-flowing river.
• It forms the famous Shivanasamudra Falls, which is utilized for one of India's first hydroelectric power stations.
• Godavari River
• It is the longest river of Peninsular India, originating at Trimbakeshwar near Nashik, Maharashtra.
• Often called the Dakshin Ganga, it flows across the Deccan Plateau and empties into the Bay of Bengal.

The correct answer is ₹25,000 crore.

Key Points

• During the presentation of the Union Budget 2025-26, the Finance Minister announced the establishment of a dedicated Maritime Development Fund (MDF) with an allocated corpus of ₹25,000 crore.
• The primary objective of this fund is to provide low-cost and long-term financing to the Indian maritime sector, which has traditionally faced challenges in accessing affordable credit for high-capital assets.
• The fund is specifically designed to incentivize indigenous shipbuilding, ship repair, and the modernization of the domestic fleet to enhance India's self-reliance in the shipping industry.
• By providing competitive credit, the government aims to increase the share of Indian-flagged vessels in global trade, thereby reducing the massive foreign exchange outflow currently paid as freight to international shipping lines.
• The ₹25,000 crore allocation is a strategic move to support the Maritime Amrit Kaal Vision 2047, which targets making India one of the top five global shipbuilding nations.

 Additional Information

• Maritime Amrit Kaal Vision 2047:
• This initiative by the Ministry of Ports, Shipping, and Waterways aims to quadruple port capacity and promote green shipping over the next two decades.
• It focuses on the development of Major Ports into world-class smart ports using AI and IoT technologies.
• Strategic Impact:
• The Maritime Development Fund is expected to complement the Shipbuilding Financial Assistance Policy (SBFAP), providing a holistic ecosystem for the maritime manufacturing sector.
• It addresses the Blue Economy goals by fostering sustainable growth in coastal shipping and Inland Waterways transport.
• The fund will also play a key role in the decarbonization of the shipping sector by supporting the construction of vessels powered by green hydrogen and ammonia.

The correct answer is Akbar.

Key Points

• Akbar (reigned 1556−1605) is recognized as the actual architect of the Mughal Empire, having successfully integrated various regional powers into a centralized administrative system.
• He introduced the Mansabdari System, which was a hierarchical administrative framework that determined the rank (Zat) and military obligations (Sawar) of the nobility and army officers.
• His land revenue policy, known as the Zabt System or Dahshala System, was developed by Raja Todar Mal and utilized detailed statistical data of crops and prices over a ten-year period.
• He is celebrated for his religious tolerance and the philosophy of Sulh-i-kul (universal peace), which aimed to treat all citizens equally regardless of their faith.
• In 1564, he abolished the Jizya tax, a discriminatory poll tax previously levied on non-Muslim subjects, and established the Ibadat Khana (House of Worship) in 1575 to facilitate interfaith dialogue.

 Additional Information

• Humayun:
• The second Mughal emperor and father of Akbar, he faced significant instability and lost the empire to Sher Shah Suri of the Suri Dynasty.
• He spent many years in exile in Persia before successfully reclaiming the throne in 1555 shortly before his accidental death.
• Jahangir:
• The son of Akbar, he is best known for his interest in Mughal art and naturalism, and for establishing the Zanjir-i-Adl (Chain of Justice) for direct appeals from his subjects.
• Aurangzeb:
• A grandson of Jahangir, he expanded the empire to its maximum territorial extent but is often contrasted with Akbar due to his orthodox policies and the reintroduction of the Jizya tax in 1679.

The correct answer is Perpendicular to field lines.

Key Points

• A rectangular loop carrying a current behaves as a magnetic dipole. It possesses a magnetic dipole moment (m), which is a vector quantity defined by the product of the current (I) and the area (A) of the loop (m = I × A).
• The direction of the magnetic moment is always perpendicular to the plane of the loop, as determined by the right-hand thumb rule.
• When suspended in a magnetic field (B), the loop experiences a torque (τ) that tends to rotate it. This torque is expressed by the formula: Torque = m × B sin(θ), where θ is the angle between the magnetic moment and the field lines.
• A system is in stable equilibrium when its potential energy (U) is at a minimum. The potential energy for a magnetic dipole is given by U = −mB cos(θ).
• Minimum potential energy occurs when cos(θ) = 1, which means θ = 0°. In this state, the magnetic moment vector is parallel to the external magnetic field lines.
• Since the magnetic moment vector is perpendicular to the plane of the loop, for the moment to align parallel to the field lines, the plane of the loop must naturally settle into a position perpendicular to the field lines.

 Additional Information

• Parallel to field lines:
• In this orientation, the plane of the loop is parallel to the field lines, meaning the magnetic moment is perpendicular to the field (θ = 90°).
• At this position, the torque is maximum (Torque = m × B), causing the loop to rotate away from this state immediately.
• This configuration is utilized in moving coil galvanometers with radial magnetic fields to ensure constant maximum sensitivity, but it is not the natural resting position in a uniform field.
• Magnetic Flux:
• The loop naturally attains a position that maximizes the magnetic flux passing through it.
• Magnetic Flux (Φ) = BA cos(θ) is maximized when the plane is perpendicular to the field lines (θ = 0° for the area vector).

Shortcut Trick

Solve Division and Multiplication first: 27 ÷ 3 = 9 and 19 × 1 = 19.

The expression simplifies to: 94 + 36 − 9 + 33 + 19 − 29.

Combine all positive and negative terms separately: (94 + 36 + 33 + 19) − (9 + 29).

Result: 182 − 38 = 144.

∴ The correct answer is 144.

Alternate Method

Follow the BODMAS rule to solve the expression: 94 + 36 − (27 ÷ 3) + 33 + 19 × 1 − 29.

Step 1: Solve the operation inside the bracket (Division).

⇒ 94 + 36 − 9 + 33 + 19 × 1 − 29

Step 2: Solve the Multiplication.

⇒ 94 + 36 − 9 + 33 + 19 − 29

Step 3: Perform Addition from left to right.

⇒ 130 − 9 + 33 + 19 − 29

⇒ 121 + 33 + 19 − 29

⇒ 154 + 19 − 29

⇒ 173 − 29

Step 4: Perform Subtraction.

⇒ 144

∴ The correct answer is 144.

Additional Information

BODMAS Rule

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

Precedence of Operations

Operations like Division and Multiplication have the same precedence and are solved from left to right, as are Addition and Subtraction.

VBODMAS Rule

This is an extension where V stands for Vinculum or bar bracket, which is solved before all other brackets.

Shortcut Trick

The time when all bells ring together again is the LCM of their ringing intervals.

Intervals: 18, 24, and 30 seconds.

LCM(18, 24, 30) = 360 seconds.

Time in minutes = 360 ÷ 60 = 6 min.

∴ The correct answer is 6 min.

Alternate Method

Given:

Interval of Bell 1 = 18 seconds

Interval of Bell 2 = 24 seconds

Interval of Bell 3 = 30 seconds

Starting time = 10:00:00 AM

Calculations:

⇒ To find the time when they ring together again, calculate the Least Common Multiple (LCM).

⇒ Prime factorization of 18 = 2 × 3 × 3 = 2¹ × 3²

⇒ Prime factorization of 24 = 2 × 2 × 2 × 3 = 2³ × 1¹

⇒ Prime factorization of 30 = 2 × 3 × 5 = 2¹ × 3¹ × 5¹

⇒ LCM = (Highest power of each prime factor) = 2³ × 3² × 5¹

⇒ LCM = 8 × 9 × 5 = 360 seconds

⇒ Convert seconds to minutes: Time = 360 ÷ 60

⇒ Time = 6 minutes

∴ The correct answer is 6 min.

Additional Information

LCM and Periodic Events

For any events occurring at regular intervals (like bells, traffic lights, or runners), the first time they coincide after starting together is the LCM of their individual time periods.

Relationship between HCF and LCM

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

Time Conversion Rules

To convert seconds to minutes, divide by 60. To convert minutes to hours, divide by 60. To convert hours to seconds, multiply by 3600 (60 × 60).

Shortcut Trick

Identify the pattern of denominators: 3 = 1 × 3, 15 = 3 × 5, 35 = 5 × 7, 63 = 7 × 9.

The difference between factors in each term is constant (d = 2).

Shortcut formula: Sum = (Number of terms) ÷ (First factor × Last factor)

Here, Number of terms = 4, First factor = 1, Last factor = 9.

Sum = 4 ÷ (1 × 9) = 4/9.

∴ The correct answer is 4/9.

Alternate Method

Given Expression: 1/3 + 1/15 + 1/35 + 1/63

Formula Used: 1/[n × (n+d)] = (1/d) × [1/n − 1/(n+d)]

⇒ 1/(1 × 3) + 1/(3 × 5) + 1/(5 × 7) + 1/(7 × 9)

⇒ (1/2) × [1/1 − 1/3] + (1/2) × [1/3 − 1/5] + (1/2) × [1/5 − 1/7] + (1/2) × [1/7 − 1/9]

⇒ (1/2) × [1/1 − 1/3 + 1/3 − 1/5 + 1/5 − 1/7 + 1/7 − 1/9]

⇒ (1/2) × [1 − 1/9]

⇒ (1/2) × [8/9]

⇒ 4/9

∴ The correct answer is 4/9.

Additional Information

Telescoping Series

A telescoping series is a series where the partial sums eventually only have a fixed number of terms after most terms cancel out.

General Sum Formula

For any series 1/(a₁×a₂) + 1/(a₂×a₃) + ... + 1/(a_n−1×a_n) where a_i forms an AP with common difference d: Sum = (1/d) × [1/First − 1/Last].

Partial Fraction Decomposition

It is the process of breaking down a complex fraction into a sum of simpler fractions, which is the foundational logic behind solving rational series.

Shortcut Trick

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

Here, a = 2.85 and b = 1.15.

⇒ Result = (2.85 + 1.15)²

⇒ Result = (4.00)² = 16

∴ The correct answer is 16.

Alternate Method

Given: (2.85 − 1.15)² + 4 × 2.85 × 1.15

Simplification Steps:

⇒ First, solve the subtraction inside the bracket: (1.70)² + 4 × 2.85 × 1.15

⇒ Calculate the square: 1.70 × 1.70 = 2.89

⇒ Calculate the multiplication part: 4 × 2.85 × 1.15 = 11.4 × 1.15 = 13.11

⇒ Add the two results: 2.89 + 13.11

⇒ Sum = 16.00

∴ The correct answer is 16.

Additional Information

Relation between Square Identities

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

Identity for Sum of Squares

Adding the identities (a + b)² and (a − b)² results in: (a + b)² + (a − b)² = 2(a² + b²).

BODMAS Rule

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

Shortcut Trick

Directly calculate square roots: √196 = 14, √49 = 7, and √81 = 9.

Solve for x using BODMAS: 14 ÷ 7 + 9 = 2 + 9 = 11.

Calculate the required value 2x: 2 × 11 = 22.

∴ The correct answer is 22.

Alternate Method

Given:

x = √196 ÷ √49 + √81

Calculation:

⇒ x = 14 ÷ 7 + 9 (Since 14² = 196, 7² = 49, and 9² = 81)

⇒ x = 2 + 9

⇒ x = 11

Now, find the value of 2x:

⇒ 2x = 2 × 11

⇒ 2x = 22

∴ The correct answer is 22.

Additional Information

BODMAS Rule

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

Perfect Squares

Numbers that are the result of multiplying an integer by itself. For example, 14 × 14 = 196 and 9 × 9 = 81.

Square Root Property

For non-negative numbers, √(a ÷ b) = √a ÷ √b. This allows for simplifying divisions involving radicals separately.

Shortcut Trick

Approximate the cube root of the product to find the middle number: √³315 ≈ 6.8.

The middle odd number near 6.8 is 7.

Consecutive odd numbers are 5, 7, and 9.

Sum = 5 + 7 + 9 = 21.

∴ The correct answer is 21.

Alternate Method

Given: The product of three consecutive odd numbers is 315.

Formula Used: Product of numbers = n₁ × n₂ × n₃

⇒ Factorize 315 into its prime factors: 315 = 5 × 63

⇒ 315 = 5 × 7 × 9

⇒ The numbers are identified as 5, 7, and 9 which are consecutive odd integers.

⇒ Required Sum = 5 + 7 + 9

⇒ Required Sum = 21

∴ The correct answer is 21.

Additional Information

Consecutive Odd/Even Numbers

Any sequence of consecutive odd or even numbers has a common difference of 2. If the first number is x, the next numbers are x + 2, x + 4, etc.

Average of Consecutive Numbers

For an odd count of consecutive numbers, the middle term is always the arithmetic mean (average) of the series.

Sum of Odd Numbers

The sum of the first n odd natural numbers starting from 1 is always n².

Shortcut Trick

The expression is in the form of a² + b² + 2ab, which equals (a + b)².

Here, a = 150 and b = 250.

⇒ (150 + 250)² = 400².

⇒ 400 × 400 = 160000.

∴ The correct answer is 160000.

Alternate Method

Given Expression: (150 × 150 + 250 × 250 + 2 × 150 × 250)

This is a simplification problem involving the expansion of a binomial square.

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

⇒ a² = 150 × 150 = 22500

⇒ b² = 250 × 250 = 62500

⇒ 2ab = 2 × 150 × 250 = 75000

⇒ Result = 22500 + 62500 + 75000

⇒ Result = 85000 + 75000

⇒ Result = 160000

∴ The correct answer is 160000.

Additional Information

Square of Sum Identity

The identity (a + b)² = a² + 2ab + b² is used to simplify the sum of squares and their product quickly.

Square of Difference Identity

Similarly, (a − b)² = a² − 2ab + b² is used when the middle term is subtracted.

Difference of Two Squares

The formula a² − b² = (a − b)(a + b) is vital for factoring expressions and simplifying divisions.

Calculation Shortcut for Squares

When squaring a number ending in 0, square the non-zero part and append double the number of zeros (e.g., 40² = 1600).

Shortcut Trick

Observe that each number in the numerator is exactly 10 times the corresponding number in the denominator (e.g., 4.1 = 0.41 × 10).

Since every term is squared, the numerator becomes 10² = 100 times the denominator.

The entire fraction inside the root simplifies to 100.

The value of the expression is √100 = 10.

∴ The correct answer is 10.

Alternate Method

Given: √(((4.1)² + (41.1)² + (411.1)²) / ((0.41)² + (4.11)² + (41.11)²))

Method: Factor out the common multiple from the numerator terms to match the denominator.

⇒ √(((10 × 0.41)² + (10 × 4.11)² + (10 × 41.11)²) / ((0.41)² + (4.11)² + (41.11)²))

⇒ √((10² × (0.41)² + 10² × (4.11)² + 10² × (41.11)²) / ((0.41)² + (4.11)² + (41.11)²))

⇒ √((100 × [(0.41)² + (4.11)² + (41.11)²]) / ((0.41)² + (4.11)² + (41.11)²))

⇒ √100

⇒ 10

∴ The correct answer is 10.

Additional Information

Power of a Product Rule

For any numbers a and b, (a × b)ⁿ = aⁿ × bⁿ. In this problem, (10 × x)² = 100x² was used to factor out the constant.

Decimal Point Shift

Multiplying a decimal number by 10 shifts the decimal point one place to the right, while dividing by 10 shifts it one place to the left.

Square Root of a Fraction

The square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator: √(a/b) = √a / √b.

Shortcut Trick

Recognize the standard Pythagorean triplet: (8, 15, 17).

Since the diagonal (hypotenuse) is 17 cm and the length is 15 cm, the breadth must be 8 cm.

Perimeter = 2 × (Length + Breadth) = 2 × (15 + 8).

Perimeter = 2 × 23 = 46 cm.

∴ The correct answer is 46 cm.

Alternate Method

Given:

Length (L) = 15 cm

Diagonal (D) = 17 cm

Formula Used:

In a rectangle, Breadth (B) = √(Diagonal² − Length²)

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

⇒ B² = D² − L²

⇒ B² = 17² − 15²

⇒ B² = 289 − 225

⇒ B² = 64

⇒ B = √64 = 8 cm

⇒ Perimeter = 2 × (15 + 8)

⇒ Perimeter = 2 × 23 = 46 cm

∴ The correct answer is 46 cm.

Additional Information

Pythagorean Triplets

Sets of three positive integers a, b, and c such that a² + b² = c². Common examples include (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Area of a Rectangle

The total space occupied by the rectangle is calculated as Length × Breadth.

Properties of Rectangle Diagonals

The diagonals of a rectangle are equal in length and bisect each other at the point of intersection.

Shortcut Trick

Identify the algebraic identity: 2(a² + b²) − (a − b)² = (a + b)².

Let a = 530 and b = 270.

The expression simplifies to: (530 + 270)².

⇒ 800² = 640000.

∴ The correct answer is 640000.

Alternate Method

Given: a = 530, b = 270

Formula Used: Expansion of squares and basic arithmetic.

⇒ 2[(530)² + (270)²] − (530 − 270)²

⇒ 2[280900 + 72900] − (260)²

⇒ 2[353800] − 67600

⇒ 707600 − 67600

⇒ 640000

∴ The correct answer is 640000.

Additional Information

Algebraic Identities

The identity 2(a² + b²) = (a + b)² + (a − b)² is derived from adding the expansions of (a + b)² and (a − b)².

Square of Binomial

(a + b)² = a² + b² + 2ab and (a − b)² = a² + b² − 2ab are fundamental tools for simplifying numerical expressions.

BODMAS Rule

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

Shortcut Trick

Average of 5 days = ₹120

Net deviation from average must be 0.

Deviations: (50−120), (105−120), (95−120), (160−120) ⇒ −70, −15, −25, +40

Sum of deviations = −70 − 15 − 25 + 40 = −70

5th day expenditure = 120 + 70 = 190

∴ The correct answer is ₹190.

Alternate Method

Given:

Average expenditure for 5 days = ₹120

Expenditure for first 4 days = ₹50, ₹105, ₹95, ₹160

Formula Used:

Total = Average × Number of observations

Calculations:

⇒ Total expenditure for 5 days = 120 × 5 = 600

⇒ Sum of expenditure for first 4 days = 50 + 105 + 95 + 160

⇒ Sum of 4 days = 410

⇒ 5th day expenditure = Total expenditure − Sum of 4 days

⇒ 5th day expenditure = 600 − 410 = 190

∴ The correct answer is ₹190.

Additional Information

Arithmetic Mean

The average or mean is calculated by dividing the sum of all values by the total number of values: Mean = (Σx_i) ÷ n.

Deviation Concept

The sum of deviations of all observations from their arithmetic mean is always zero: Σ(x_i − Mean) = 0.

Impact of Constant on Average

If every observation is increased or decreased by a constant 'k', the new average also increases or decreases by 'k'.

Shortcut Trick

The difference between Cost Price (CP) and Selling Price (SP) represents the Profit amount.

Given Profit% = 9% and the difference is ₹252.

Equating percentage to value: 9% → ₹252.

Calculating 100% (Cost Price): (252 ÷ 9) × 100 = 28 × 100 = ₹2800.

∴ The correct answer is ₹2800.

Alternate Method

Given:

Difference (SP − CP) = ₹252

Profit % = 9%

Formula Used:

Profit = (Profit % ÷ 100) × Cost Price (CP)

Calculations:

⇒ Profit = SP − CP = 252

⇒ 9% of CP = 252

⇒ (9 ÷ 100) × CP = 252

⇒ CP = (252 × 100) ÷ 9

⇒ CP = 28 × 100

⇒ CP = ₹2800

∴ The correct answer is ₹2800.

Additional Information

Profit and Loss Relationship

Profit occurs when Selling Price (SP) > Cost Price (CP). Profit = SP − CP. Loss occurs when CP > SP. Loss = CP − SP.

Percentage Calculation Base

Profit % and Loss % are always calculated on the Cost Price unless mentioned otherwise in the question. Formula: Profit % = (Profit ÷ CP) × 100.

Selling Price Formula

To find SP directly: SP = CP × (100 + Profit %) ÷ 100 or SP = CP × (100 − Loss %) ÷ 100.

Shortcut Trick

Find the effective percentage: (40 × 60) ÷ 100 = 24%.

Calculate 24% of the total value 6800.

⇒ 24 × 68 = 1632.

∴ The correct answer is 1632.

Alternate Method

Given:

Initial Value = 6800

First Percentage = 60%

Second Percentage = 40%

Calculations:

⇒ First, determine 60% of 6800:

⇒ (60 ÷ 100) × 6800 = 60 × 68 = 4080

⇒ Now, find 40% of the resultant 4080:

⇒ (40 ÷ 100) × 4080 = 40 × 40.8 = 1632

∴ The correct answer is 1632.

Additional Information

Compound Percentage Application

Finding a% of b% of a quantity is equivalent to finding (a × b / 100)% of that quantity. For example, 40% of 60% is 24%.

Fractional Equivalents

Simplifying percentages into fractions can speed up calculations: 40% = 2/5 and 60% = 3/5. Thus, (2/5) × (3/5) × 6800 = (6/25) × 6800 = 1632.

Percentage Change vs. Value

Always distinguish between a percentage of a percentage (multiplicative) and a percentage increase/decrease (additive/subtractive).

Shortcut Trick

Ratio of CP : SP = 3 : 5

Consider CP = 3 units and SP = 5 units.

Profit = SP − CP = 5 − 3 = 2 units.

Ratio of Profit : CP = 2 : 3.

∴ The correct answer is 2 : 3.

Alternate Method

Given:

Ratio of Cost Price (CP) to Selling Price (SP) = 3 : 5

Formula Used:

Profit = Selling Price − Cost Price

Calculations:

⇒ Let the Cost Price of the article be 3x.

⇒ Then the Selling Price of the article is 5x.

⇒ Profit = Selling Price − Cost Price

⇒ Profit = 5x − 3x = 2x

⇒ We need to find the ratio of Value of Profit to Cost Price.

⇒ Required Ratio = 2x : 3x

⇒ Required Ratio = 2 : 3

∴ The correct answer is 2 : 3.

Additional Information

Profit Percentage

Profit % = (Profit ÷ Cost Price) × 100. In this case, Profit % = (2 ÷ 3) × 100 = 66.66%.

Loss Percentage

Loss occurs when CP > SP. Loss % = (Loss ÷ Cost Price) × 100, where Loss = CP − SP.

Marked Price and Discount

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

Shortcut Trick

Let the total number of employees be 100%.

Matriculates = 20%, so Remaining = 80%.

Graduates = 40% of 80% = 32%.

Post-graduates = 80% − 32% = 48%.

Given 48% = 144 ⇒ 1% = 3 employees.

∴ The correct answer is 60 employees.

Alternate Method

Given:

Matriculates = 20% of Total

Graduates = 40% of (Total − Matriculates)

Post-graduates = 144

Calculations:

⇒ Let Total Employees = x

⇒ Employees after matriculates = x − 0.20x = 0.80x

⇒ Post-graduates = (100% − 40%) of 0.80x

⇒ 144 = 0.60 × 0.80x

⇒ 144 = 0.48x

⇒ x = 144 ÷ 0.48

⇒ x = 300

⇒ Number of Matriculates = 20% of 300

⇒ Matriculates = 0.20 × 300 = 60

∴ The correct answer is 60 employees.

Additional Information

Successive Percentage Reduction

When values are reduced step-by-step from the remainder, the final percentage is the product of the remaining multipliers: Final % = (1 − r₁) × (1 − r₂) × 100.

Base Value Concept

Always identify the base for each percentage. Here, 40% is calculated on the 80% remaining, not on the original 100% total.

Fraction Conversion

20% = 1/5 and 40% = 2/5. Total × (4/5) × (3/5) = 144 can also be used for faster calculation.

Shortcut Trick

Work completed in 6 days = 30%

Work completed in 1 day = 30% ÷ 6 = 5%

Work completed in 10 days = 5% × 10 = 50%

∴ The correct answer is 50%.

Alternate Method

Given:

Work done by A in 6 days (W₁) = 30%

Time period 1 (T₁) = 6 days

Time period 2 (T₂) = 10 days

Formula Used:

Work (W) = Efficiency (E) × Time (T)

Calculations:

⇒ Efficiency of A = W₁ ÷ T₁

⇒ Efficiency of A = 30% ÷ 6 = 5% per day

⇒ Work completed in 10 days (W₂) = Efficiency × T₂

⇒ W₂ = 5% × 10

⇒ W₂ = 50%

∴ The correct answer is 50%.

Additional Information

Rate of Work

Efficiency or rate of work is the amount of work completed in a unit of time (e.g., 1 day or 1 hour). Formula: Efficiency = Total Work ÷ Total Time.

Direct Proportionality

When efficiency is constant, work done is directly proportional to the time taken. If time increases, work done increases in the same ratio: W₁/T₁ = W₂/T₂.

Total Work Completion Time

To find the time taken for 100% work, use the unitary method: Total Time = (Current Time ÷ Current Work %) × 100. In this case: (6 ÷ 30) × 100 = 20 days.

Shortcut Trick

Efficiency of (Q + R) is 5 times that of P.

Since Work = Efficiency × Time, for the same work, Time is inversely proportional to Efficiency.

Ratio of Efficiency [(Q + R) : P] = 5 : 1.

Ratio of Time [(Q + R) : P] = 1 : 5.

Given, Time for (Q + R) = 45 days.

Time for P = 5 × 45 = 225 days.

∴ The correct answer is 225 days.

Alternate Method

Given:

(Q + R) = 5P ⇒ (P + Q + R) = 6P

(P + R) = 3Q ⇒ (P + Q + R) = 4Q

Time taken by (Q + R) = 45 days

Formula Used:

Total Work = Efficiency × Time

Calculations:

⇒ Let the efficiency of P be 1 unit/day.

⇒ Then, efficiency of (Q + R) = 5 × 1 = 5 units/day.

⇒ Total Work = Efficiency of (Q + R) × Time taken by (Q + R)

⇒ Total Work = 5 × 45 = 225 units.

⇒ Time taken by P alone = Total Work ÷ Efficiency of P

⇒ Time taken by P alone = 225 ÷ 1 = 225 days.

∴ The correct answer is 225 days.

Additional Information

Efficiency and Time Relationship

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

Total Work Formula

Total Work = Number of days × Efficiency. This remains constant for different individuals or groups performing the same task.

Combined Efficiency

When individuals work together, their individual efficiencies are added to find the combined rate of work per unit time.

Shortcut Trick

Convert Speed directly to m/s: 18 × (5/18) = 5 m/s.

Convert Time to seconds: 8 min × 60 = 480 seconds.

Bridge Length = Speed × Time = 5 × 480 = 2400 metres.

∴ The correct answer is 2400 m.

Alternate Method

Given:

Speed of the boy = 18 km/hr

Time taken to cross = 8 min

Formula Used:

Distance (Length) = Speed × Time

Calculations:

⇒ Step 1: Convert Speed from km/hr to m/s

⇒ Speed = 18 × (5/18) = 5 m/s

⇒ Step 2: Convert Time from minutes to seconds

⇒ Time = 8 × 60 = 480 seconds

⇒ Step 3: Calculate the Length of the bridge

⇒ Length = 5 × 480 = 2400 metres

∴ The correct answer is 2400 m.

Additional Information

Unit Conversion Rules

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

Basic Speed Formula

Distance = Speed × Time. Ensure all units are consistent (e.g., if distance is in metres, time must be in seconds and speed in m/s).

Average Speed

Average Speed = Total Distance ÷ Total Time. For two equal distances with speeds x and y, Average Speed = 2xy ÷ (x + y).

Shortcut Trick

Distance of bus = 80 × 10 = 800 km

Distance of train = 800 + 100 = 900 km

Time taken by train = 10 + 5 = 15 hr

Speed of train = 900 ÷ 15 = 60 km/hr

∴ The correct answer is 60 km/hr.

Alternate Method

Given:

Speed of bus = 80 km/hr

Time taken by bus = 10 hr

Extra distance by train = 100 km

Extra time taken by train = 5 hr

Formula Used:

Distance = Speed × Time

Speed = Distance ÷ Time

⇒ Distance covered by the bus = 80 × 10 = 800 km

⇒ Distance covered by the train = 800 + 100 = 900 km

⇒ Time taken by the train = 10 + 5 = 15 hr

⇒ Speed of the train = 900 ÷ 15 = 60 km/hr

∴ The correct answer is 60 km/hr.

Additional Information

Average Speed

It is the total distance traveled divided by the total time taken. Average Speed = (Total Distance) ÷ (Total Time).

Relative Speed

When two objects move in the same direction, relative speed = S₁ − S₂. When they move in opposite directions, relative speed = S₁ + S₂.

Speed 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

A 20% discount means the Selling Price (SP) is 80% of the Marked Price (MP).

Ratio of SP : MP = 80 : 100 = 4 : 5.

Check ratios: 2000 : 2500 = 20 : 25 = 4 : 5.

∴ The correct answer is Selling price = ₹2000 and Marked price = ₹2500.

Alternate Method

Given: Selling Price (SP) = ₹2000 and Marked Price (MP) = ₹2500.

Formula Used: Discount % = [(MP − SP) ÷ MP] × 100

⇒ Discount = MP − SP

⇒ Discount = 2500 − 2000 = ₹500

⇒ Discount % = (500 ÷ 2500) × 100

⇒ Discount % = (1 ÷ 5) × 100 = 20%

∴ The correct answer is Selling price = ₹2000 and Marked price = ₹2500.

Additional Information

Successive Discounts

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

Marked Price and Markup Percentage

Markup percentage is the percentage by which the Cost Price (CP) is increased to reach the MP. Markup % = [(MP − CP) ÷ CP] × 100.

Relation between CP and MP

The relationship between CP, MP, Profit%, and Discount% is given by MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

The correct answer is 'toot her own horn'.

Key Points

• The idiom 'toot one's own horn' means to boast or brag about one's own achievements, talents, or abilities, especially to draw attention to oneself.
• In the context of the sentence, Radhika is described as someone who focuses on working and achieving success quietly without seeking public praise or showing off.
• Therefore, the idiom 'toot her own horn' fits perfectly to describe what she avoids doing.

Therefore, the correct answer is 'Option 2'.

Complete Sentence: Radhika does not like to toot her own horn. She simply goes on working and achieving success in her life.

Additional Information

• A synonymous idiom for 'toot one's own horn' is 'blow one's own trumpet', which is more common in British English.
• The other phrases like 'sharpen her own horn', 'colour her own horn', and 'anoint her own horn' are not standard English idioms and carry no specific meaning in this context.

The correct answer is Option(1) i.e. 'Trustworthy'.

Key Points

• The word 'reliable' means someone or something that can be trusted to do what is expected or has been promised; it refers to consistency in quality or performance. (विश्वसनीय/भरोसेमंद)
• Example: Having a reliable car is essential for someone who has to commute a long distance every day.
• 'Trustworthy' refers to a person or thing that is able to be relied on as honest or truthful; it is synonymous with being dependable. (भरोसेमंद)
• Example: The manager needed a trustworthy employee to handle the company's financial accounts.
• Hence, we can infer that the most appropriate synonym of 'reliable' is 'trustworthy'.

Therefore, the correct answer is- Trustworthy.

Additional Information

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

• Uncertain (अनिश्चित): Something that is not known or definite; a state of doubt.
• Example: The weather forecast remains uncertain, so we might have to cancel the outdoor picnic.
• Untrue (असत्य): Something that is not in accordance with fact or reality.
• Example: She claimed that the accusations made against her were completely untrue.
• False (गलत/असत्य): Something that is not correct or true; often used for a statement or information.
• Example: Providing false information on a legal document can lead to serious consequences.

The correct answer is melodies.

Key Points

• In the given sentence, the word meloudies is misspelt. The correct spelling is melodies, which is the plural form of the noun melody.
• The word melodies refers to a sequence of musical notes that are musically satisfying or a primary part of a musical composition.
• The spelling error in meloudies involves the incorrect addition of the letter u. In English orthography, the long o sound in this specific word is represented by a single o, not the ou digraph found in words like cloud or loud.
• According to standard pluralization rules, when a word ends in a consonant followed by the letter y (such as melody), the y is dropped and replaced with ies to form the plural. Therefore, melody correctly becomes melodies.

 Additional Information

• Musician
• This term refers to a person who is talented in making music, especially as a profession.
• It is derived from the Old French word musicien and the Latin root musica.
• Profound
• An adjective used to describe a state, quality, or emotion that is very great or intense, or a person showing great knowledge or insight.
• The word originates from the Latin term profundus, meaning deep or bottomless.
• Symbolism
• This is a literary and artistic device where symbols are used to represent ideas or qualities.
• It stems from the Greek word symbolon, which refers to a mark, token, or sign used for identification.

The correct answer is: silhouette.

Key Points

• The word 'silhouette' refers to the dark shape and outline of someone or something visible against a lighter background, especially in dim light. (छायाचित्र)
• Example: The silhouette of the dome stood out against the evening sky.
• The correct spelling of the word is 'silhouette', which is sometimes misspelt as 'silhouete' or 'silhoute' by omitting the double 't' or the letter 'e'. (छायाचित्र)
• Example: He recognized his brother's silhouette in the dark corridor.
• Hence, we can infer that the misspelt word is 'silhouette'.

Therefore, the correct answer is: silhouette.

Additional Information

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

• Etiquette (शिष्टाचार): The customary code of polite behavior in society or among members of a particular profession or group.
• Example: He was deeply schooled in the etiquette of the royal court.
• Corvette (एक छोटा युद्धपोत): A small warship designed for convoy escort duty.
• Example: The naval fleet included a highly advanced corvette.
• Cassette (कैसेट): A sealed plastic unit containing a length of magnetic tape, used for recording and playing back sound or video.
• Example: She found an old cassette player in the attic.

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

Key Points

• The word 'filled' means to make a container, space, or area full, or to occupy all the available space in something. (भरा हुआ)
• Example: The room was filled with the pleasant aroma of freshly baked bread.
• 'Emptied' refers to the action of removing all the contents from a container or place; it is the direct opposite of filling. (खाली किया)
• Example: After the party, she emptied all the trash cans into the large bin outside.
• Hence, we can infer that the opposite of 'filled' is 'emptied'.

Therefore, the correct answer is- Emptied.

Additional Information

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

• Packed (खचाखच भरा हुआ): This means something is completely full of people or things, often to its limit.
• Example: The stadium was packed with thousands of fans for the championship game.
• Crowded (भीड़भाड़ वाला): This refers to a space that is full of people, sometimes making it difficult to move.
• Example: The crowded street market was full of tourists and local shoppers.
• Loaded (लदा हुआ): This means carrying or having a large or heavy amount of something inside or on top.
• Example: The delivery truck was loaded with heavy boxes for the new department store.

The correct answer is 'sew'.

Key Points

• The word 'sew' means to join, fasten, or repair something by making stitches with a needle and thread. (सिलाई करना)
• Since the sentence mentions a tailor and the process of stitching, 'sew' is the only contextually appropriate word among the given options.
• The words 'sow', 'sew', and 'so' are homophones—words that sound similar but have different meanings and spellings.

Therefore, the correct answer is 'Option 2'.

Complete Sentence: The tailor had to sew the cloth before stitching it.

Additional Information

• Sow (बोना): To plant seeds by scattering them on or in the earth.
• So (इसलिए/इतना): Used as an adverb to mean 'to such a great extent' or as a conjunction meaning 'and for this reason'.
• Saw (आरी/देखा): A hand tool for cutting wood or other hard materials, or the past tense of the verb 'see'.

The correct answer is: Homonym.

Key Points

• The phrase 'A word that has the same spelling or sound as another but a different meaning' refers to words that look or sound identical but represent entirely different concepts. (समान वर्तनी या ध्वनि वाले शब्द जिनका अर्थ भिन्न हो)
• Example: The word 'bark' can refer to the sound a dog makes or the outer covering of a tree trunk.
• 'Homonym' is the specific term used for a word that is spelled or pronounced like another word but has a different meaning. (अनेकार्थक शब्द)
• Example: 'Fair' can mean equitable, or it can refer to a traveling exhibition or circus.
• Therefore, the correct answer is- Homonym.

Additional Information

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

• Synonym (पर्यायवाची): A word or phrase that means exactly or nearly the same as another word or phrase in the same language.
• Example: 'Happy' and 'Joyful' are synonyms because they convey similar emotions.
• Antonym (विलोम): A word that is opposite in meaning to another word.
• Example: 'Hot' is the antonym of 'Cold'.
• Acronym (संक्षिप्तीक्षर): An abbreviation formed from the initial letters of other words and pronounced as a word.
• Example: 'NASA' is an acronym for the National Aeronautics and Space Administration.

The correct answer is 'in lieu of'.

Key Points

• The prepositional phrase 'in lieu of' is used to mean 'instead of' or 'in place of'.
• In employment and professional contexts, it is frequently used to indicate that one benefit (like leave) is being provided as a substitute for something else (like working on a holiday).
• The sentence indicates that the two days' leave is a compensatory substitute for the effort of working during a holiday, making 'in lieu of' the most appropriate choice.

Therefore, the correct answer is Option 3.

Complete Sentence: 'The school allowed teachers to take two days' leave in lieu of working on the holiday.'

Additional Information

• Option 1: 'in addition to' means 'as well as' or 'besides'. This would imply the leave was added to something else rather than replacing the holiday work.
• Option 2: 'because of' means 'due to' or 'by reason of'. While working is the reason for the leave, it doesn't capture the sense of compensatory substitution that 'in lieu of' does.
• Option 4: 'regarding' means 'about' or 'with reference to', which does not fit the grammatical or logical structure of the sentence.

The correct answer is The treaty was signed by the two kings just before the battle began..

Key Points

• Analyze the sentence structure in Active Voice: The two kings (Subject) + signed (Verb in Simple Past) + the treaty (Object) + just before the battle began (Adverbial Clause).
• Identify the tense of the main verb: The word signed is the V2 (Simple Past) form of the verb sign.
• Apply the Passive Voice conversion rule for the Simple Past Tense: The structure changes to New Subject (Original Object) + was/were + V3 (Past Participle) + by + New Object (Original Subject).
• Determine the auxiliary verb: Since the new subject, The treaty, is singular, the auxiliary verb was is used instead of were.
• Convert the main verb to its Past Participle (V3) form: The third form of sign remains signed.
• Retain the Adverbial Clause: The phrase just before the battle began describes the timing of the action and remains unchanged at the end of the sentence.
• Final Construction: The treaty (Subject) + was signed (Passive Verb) + by the two kings (Agent) + just before the battle began.

 Additional Information

• Understanding Voice conversion across different tenses:
• Past Perfect Tense: If the active voice is had signed, the passive becomes had been signed. This is used for actions completed before another point in the past.
• Simple Present Tense: If the active voice is signs, the passive becomes is/am/are signed. This is used for habitual actions or general truths.
• Simple Future Tense: If the active voice is will sign, the passive becomes will be signed.
• Transitive Verbs: Only verbs that take an object can be transformed into passive voice because the object must become the new subject.
• The use of the preposition by is essential to introduce the agent or the doer of the action in a passive construction.

The correct answer is Thousands of enthusiastic supporters attended the victory celebrations.

Key Points

• The original sentence is written in the Passive Voice within the Simple Past Tense (also known as Past Indefinite).
• The Passive Voice structure for the Simple Past is: Object + was/were + V3 (Past Participle) + by + Subject (Agent). In this case, 'The victory celebrations' is the object, 'were attended' is the verb, and 'thousands of enthusiastic supporters' is the agent.
• To transform a sentence into the Active Voice, the Agent (the one performing the action) must become the Subject of the sentence.
• The Active Voice structure for the Simple Past Tense is: Subject + V2 (Past Tense Verb) + Object.
• The V2 (second form) of the verb 'attend' is attended. The auxiliary verb 'were' is removed during the conversion to active voice.
• By following these rules, 'Thousands of enthusiastic supporters' moves to the front, followed by the verb 'attended', and finally the original subject 'the victory celebrations' becomes the Object.

 Additional Information

• Voice and Tense Consistency: One of the fundamental rules of voice conversion is that the Tense of the sentence must never change. If the passive sentence is in the past, the active sentence must remain in the past.
• Tense Identification in Distractors:
• Simple Present Tense: Using the base verb 'attend' indicates a routine or general truth, which incorrectly shifts the timeline from the past to the present.
• Present Continuous Tense: The construction 'are attending' represents an action happening at the current moment, which does not match the completed past action 'were attended'.
• Past Perfect Tense: The form 'had attended' is used to describe an action completed before another past event. Since there is no such secondary past reference in the original sentence, this tense is inappropriate.
• Grammar Breakdown:
• Subject: The doer of the action (Thousands of enthusiastic supporters).
• Verb (V2): The action performed in the past (attended).
• Direct Object: The entity receiving the action (The victory celebrations).

The correct answer is 'under'.

Key Points

• The correct preposition to fill in the blank is 'under'.
• The phrase 'go under the knife' is a common idiomatic expression meaning to have a medical operation or surgical procedure.
• In the given sentence, the words 'patient' and 'ICU' (Intensive Care Unit) confirm that the context is medical, making the idiom appropriate.
• The other options like 'below' or 'after' do not form a standard idiom with 'knife' in a medical context.

Therefore, the correct answer is Option 2.

Complete Sentence: 'The patient went under the knife yesterday and is in the ICU now.'

Additional Information

• Option 1: 'ower' appears to be a misspelling and is not a valid preposition in this context.
• Option 3: 'below' generally means at a lower level or position, but it is not used in the specific idiom for undergoing surgery.
• Option 4: 'after' refers to time or following behind someone, which does not fit the meaning of undergoing an operation.

The correct answer is Option 2.

Key Points

• The paragraph follows a narrative structure, starting with a crisis, followed by a moment of despair, and concluding with a successful resolution.
• S1 is the fixed first sentence as it establishes the setting and the primary conflict:
• 'The dove Chitrani passed by the same place with her family, but being off their guard, they all flew into the net and were captured.'
• Sentence C follows S1 as it introduces a rhetorical question reflecting the immediate concern of the captured birds:
• 'What was to be done?'
• Sentence A follows C as it continues the sequence of rhetorical questions, intensifying the gravity of the situation:
• 'How could they escape from certain death?'
• Sentence D is the third in the sequence because it answers the previous questions by expressing the initial sense of hopelessness and despair:
• 'There was in fact no escape, no hope of obtaining their liberty.'
• Sentence B follows D as the turning point of the story, where the birds take collective action just as the danger (the fowler) approaches:
• 'Already the fowler was running up to seize his prey when all at once under the impulse of danger they took to flight together, carrying with them the net that enclosed them.'
• S2 is the fixed last sentence, confirming the outcome of the action described in B:
• 'So they succeeded in escaping, and the fowler... was not a little surprised when he saw them fly away with his nets.'
• The correct logical sequence is CADB.

Coherent paragraph after rearrangement:

'The dove Chitrani passed by the same place with her family, but being off their guard, they all flew into the net and were captured. What was to be done? How could they escape from certain death? There was in fact no escape, no hope of obtaining their liberty. Already the fowler was running up to seize his prey when all at once under the impulse of danger they took to flight together, carrying with them the net that enclosed them. So they succeeded in escaping, and the fowler, who had reckoned upon his capture, was not a little surprised when he saw them fly away with his nets.'

The correct answer is Option 4.

Key Points

• The paragraph follows a narrative structure, beginning with the introduction of a character and his routine, followed by a specific incident and its climax.
• Sentence S1 introduces the main subjects: a hawker and his ass, setting the scene for their travels.
• Sentence D follows S1 as it explains the hawker's general practice: whenever they stopped, he would take the pack off the ass, dress it in a lion's skin, and let it graze in fields where watchmen were too afraid to approach.
• Sentence A is the third sentence because it transitions from the general routine to a specific day ('So one day') when the hawker stopped in a village and left the disguised ass in a barley-field.
• Sentence C follows A as it describes the immediate reaction of the watchmen in that specific village; seeing the 'lion', they were terrified and went home to spread the news.
• Sentence B is the fifth sentence as it details the villagers' response to the news: they gathered with weapons and drums and approached the field making noise.
• Sentence S2 concludes the sequence: the noise and presence of the villagers terrified the ass, causing it to bray and reveal its true identity.
• The correct sequence is DACB.

Coherent paragraph after rearrangement:

'At that time a hawker used to go from place to place, trafficking in goods carried by an ass. Now at each place he came to, when he took the pack down from the ass's back, he used to clothe him in a lion's skin and turn him loose in the rice and barley fields, and when the watchmen in the fields saw the ass, they dared not go near him, taking him for a lion. So one day the hawker stopped in a village; and while he was getting his own breakfast cooked, he dressed the ass in a lion's skin and turned him loose in a barley-field. The watchmen in the field dared not go up to him, but going home, they published the news. Then all the villagers came out with weapons in their hands; and blowing chanks and beating drums, they went near the field and shouted. Terrified with the fear of death, the ass uttered a cry - the cry of an ass!'

The correct answer is take the bull by the horns.

Key Points

• The phrase take the bull by the horns is a standard idiomatic expression in English that means to deal with a difficult situation or a challenge in a very direct and confident way.
• The idiom implies courage and decisiveness, suggesting that one should confront a problem head-on rather than avoiding it or being tentative.
• In the context of the sentence, resolving pending issues for the sake of progress requires a proactive approach, which is perfectly captured by this metaphor.
• The original phrase in the question, take the bull by the head, is an incorrect variation and does not carry any established linguistic meaning.
• Using the correct idiom ensures that the sentence maintains semantic clarity and adheres to the rules of standard English usage.

 Additional Information

• Idiomatic Analysis:
• Take the bull by the horns: Often used in business or leadership contexts to describe taking initiative during a crisis. It originated from the physical act of ranching or bullfighting, where grabbing the horns is the only way to gain control.
• Take the bull by the tail: This is not a recognized idiom. Figuratively, trying to control a bull from the rear would be considered counterproductive or cowardly, which contradicts the intended meaning of the sentence.
• Pull the bull by its ears: This phrase is nonsensical in an idiomatic sense and has no historical or literary background in the English language.
• Sentence Improvement:
• This category of verbal ability questions tests a candidate's knowledge of phrasal verbs, collocations, and idioms to ensure the sentence is grammatically and stylistically sound.

The correct answer is Option 3.

Key Points

• The error lies in the third part of the sentence: might drive on for hr.
• The term hr is an abbreviation for hour, which is a singular countable noun.
• Singular countable nouns must be preceded by an article (a/an) or a determiner. Since hour begins with a vowel sound (the 'h' is silent), it requires the article an.
• The grammatically correct phrase should be for an hour or for hours.
• Thus, the error is located in Option 3.

Therefore, the correct answer is might drive on for hr.

Correct Sentence: 'If you are looking for a free parking space, you might drive on for an hour until you find one.'

Additional Information

• Option 1: 'If you are looking for' is the subordinate clause starting with a conditional conjunction, which is grammatically correct.
• Option 2: 'a free parking space, you' uses the article a correctly before the singular countable noun phrase free parking space.
• Option 4: 'until you find one.' uses the pronoun one to refer back to the parking space, which is correct usage.
• The article an is used before words that start with a vowel sound, such as honest, honor, and hour, regardless of the starting consonant letter.