SSC GD Constable 2026 Official Paper (Held On 18 May, 2026 Shift 2) (Previous Year Paper)

Logic followed here is, 

388 − 3 = 385 (385 is wrong term)

385 − 5 = 380

380 − 7 = 373

373 − 9 = 364

364 − 11 = 353

353 − 13 = 340

340 − 15 = 325

Hence, the correct answer is “Option 3”.

Pattern followed here is,

Hence, the correct answer is “Option 2”.

For 'JH' related to 'OS':

For 'RC' related to 'WX':

Applying the same logic to find the missing cluster related to 'RZ':

Thus, MA is the cluster related to RZ.

Hence, the correct answer is 'Option 2'.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

For 'BV' related to 'UE':

For 'XA' related to 'QZ':

Applying the same logic to 'CJ':

Thus, CJ is related to VQ.

Hence, the correct answer is 'Option 4'.

For the set '(HS, JU, MX)':

For the set '(WO, YQ, BT)':

Applying the same logic to '(LZ, NB, QE)':

Thus, the letter clusters in the set '(LZ, NB, QE)' follow the same logic.

Hence, the correct answer is 'Option 3'.

Given that the 8th of the current month is Thursday.

The total number of days in the current month is 30.

Remaining days in the current month = 30 − 8 = 22 days

Number of days in the next month up to the 15th = 15 days

Total days from the 8th of the current month to the 15th of the next month = 22 + 15 = 37 days

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

37 ÷ 7 = 5 weeks and 2 odd days

Now, add the odd days to the given day:

Thursday + 2 days = Saturday

Hence, the 15th of the next month will be Saturday.

Hence, the correct answer is “Option 2”.

We need to find the day for 1st January 1755.

First, we calculate the odd days up to 31st December 1754.

Total years = 1754 years = 1600 years + 100 years + 54 years

1. Odd days in 1600 years = 0
2. Odd days in 100 years = 5
3. Odd days in 54 years:

Number of leap years = 54 ÷ 4 = 13 leap years

Number of ordinary years = 54 − 13 = 41 ordinary years

Odd days = (13 × 2) + (41 × 1) = 26 + 41 = 67 odd days

67 odd days = 67 ÷ 7 = 4 odd days (Remainder)

Total odd days until 31st December 1754 = 0 + 5 + 4 = 9 odd days

9 odd days = 9 ÷ 7 = 2 odd days

Now, we add the day for 1st January 1755:

Total odd days = 2 (from previous years) + 1 (for 1st Jan) = 3 odd days

According to the day code:

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

Therefore, the first day of the year 1755 was Wednesday.

Hence, the correct answer is “Option 3”.

Important Points To find the day of the week for any date, we calculate the number of odd days.

Number of odd days in 400 years = 0

Number of odd days in 100 years = 5

An ordinary year (365 days) has (365 ÷ 7) = 1 odd day.

A leap year (366 days) has (366 ÷ 7) = 2 odd days.

5 persons J, K, L, P and Q are sitting in a row facing north (not necessarily in the same order).

1. L is second to the left of J.
2. L is second to the right of P.
3. K is second to the left of Q.

J is sitting at the right end of the row.

Hence, the correct answer is “Option 1”.

7 children P, Q, R, S, T, U and V are sitting in a row facing north (not necessarily in the same order).

1. P is to the immediate right of R.
2. There are two children between T and Q.
3. V is to the immediate right of S.
4. V is to the immediate left of Q.
5. There is one children between P and S.
6. There are two children between S and U.

T is sitting between P and S.

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 3”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 1”.

CP10 : ER38

VS40 : XU68

Similarly,

For, ? : KO56

Hence, the correct answer is 'Option 2'.

AK120 : FD250 →

LL210 : QE340 →

Similarly,

KM250 : ? → 

Hence, the correct answer is 'Option 4'.

The logic followed here is:

Logic: Second Number = (First Number ÷ 2) + 2

For the first pair 540 : 272

⇒ (540 ÷ 2) + 2

⇒ 270 + 2 = 272.

For the second pair 210 : 107

⇒ (210 ÷ 2) + 2

⇒ 105 + 2 = 107.

Applying the same logic to the third pair

134 : ?

⇒ (134 ÷ 2) + 2

⇒ 67 + 2 = 69.

Hence, the correct answer is 'Option 3'.

GUFF is coded as HWIJ →

MONK is coded as NQQO →

Similarly,

let's find the code for HINT:

Hence, the correct answer is “Option 3”.

The clock shows the correct time at 9 AM. We need to find the time it shows at 9 PM on the same day.

Total time elapsed from 9 AM to 9 PM = 12 hours

Convert the total hours into minutes:

1 hour = 60 minutes

12 hours = 12 × 60 = 720 minutes

The clock gains 1 second every 3 minutes.

Total gain in 720 minutes = 720 ÷ 3 = 240 seconds

Now, convert the total gain from seconds into minutes:

60 seconds = 1 minute

240 seconds = 240 ÷ 60 = 4 minutes

The clock is 4 minutes faster than the actual time at 9 PM.

Time shown by the clock = 9:00:00 PM + 4 minutes = 9:04:00 PM

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 3”.

Ratio of present ages = 11 : 5

Difference between their ages = 18 years

Let the present ages of the two students be 11x and 5x.

Difference in terms of x = 11x − 5x = 6x

According to the question:

6x = 18

x = 18 ÷ 6 = 3

Student 1 age after 5 years = 33 + 5 = 38 years

Student 2 age after 5 years = 15 + 5 = 20 years

Ratio after 5 years = 38 : 20

Ratio = 19 : 10

Hence, the correct answer is “Option 3”.

The correct answer is 4°C.

Key Points

• Water exhibits a unique physical phenomenon known as the Anomalous Expansion of Water. While most substances expand when heated and contract when cooled, water behaves differently between the temperatures of 0°C and 4°C.
• Density is defined as the mass per unit volume of a substance. For a constant mass, density is inversely proportional to the volume it occupies.
• When ice at 0°C is heated, it melts into water, and the volume actually decreases as the temperature rises toward 4°C. This is due to the collapse of the open hexagonal crystal lattice structure of ice.
• At exactly 4°C (more precisely 3.98°C), water reaches its minimum volume. Because the volume is at its lowest, the density reaches its maximum value of approximately 1000 kg/m³ or 1 g/cm³.
• Once the temperature rises above 4°C, the increased kinetic energy of the water molecules causes them to move further apart, resulting in standard thermal expansion and a decrease in density.

 Additional Information

• 0°C (Freezing Point):
• At this temperature, water molecules form stable hydrogen bonds that create a cage-like structure in ice.
• This structure makes ice less dense (approx 917 kg/m³) than liquid water, which is why ice floats.
• 100°C (Boiling Point):
• This is the temperature at which the vapor pressure of the liquid equals the external atmospheric pressure.
• At this stage, water undergoes a phase change to steam, and its density drops drastically as molecules become widely separated.
• Ecological Importance:
• In cold climates, as lake water cools to 4°C, it becomes heavy and sinks to the bottom.
• This process ensures that the bottom of deep lakes remains at 4°C, allowing aquatic life to survive even when the surface is covered in insulating ice.

The correct answer is Nidhi Tewari.

Key Points

• In March 2025, the Appointments Committee of the Cabinet (ACC) officially approved the appointment of Nidhi Tewari as the Private Secretary (PS) to Prime Minister Narendra Modi.
• Nidhi Tewari is a high-ranking diplomat belonging to the 2014 batch of the Indian Foreign Service (IFS).
• Prior to this prestigious elevation, she served as a Deputy Secretary within the Prime Minister's Office (PMO), demonstrating extensive experience in executive administration and strategic coordination.
• The role of a Private Secretary to the Prime Minister is a critical bureaucratic position responsible for managing the Prime Minister’s official engagements, processing sensitive files, and maintaining liaison with various Union Ministries and foreign dignitaries.
• The appointment is typically made on a co-terminus basis, meaning the tenure is linked with the term of the Prime Minister or until further government orders.

 Additional Information

• Prime Minister's Office (PMO):
• The PMO consists of the immediate staff of the Prime Minister and provides secretarial assistance to the head of the government.
• It is headed by the Principal Secretary to the Prime Minister, who oversees the overall functioning of the office.
• Sunita Williams:
• She is a world-renowned Indian-origin American astronaut and a retired United States Navy officer.
• She holds several records for spacewalks and is not associated with the administrative appointments of the Government of India.
• Indian Foreign Service (IFS):
• Established in 1946, it is the premier diplomatic civil service under Group A of the Central Civil Services.
• Officers are recruited through the Civil Services Examination conducted by the UPSC and are responsible for representing India's interests in international relations.

The correct answer is Anju Rathi Rana.

Key Points

• Anju Rathi Rana, a senior officer of the Indian Legal Service (ILS), was formally appointed as the Union Law Secretary in March 2025.
• She assumed the role of Secretary in the Department of Legal Affairs, which operates under the Ministry of Law and Justice, Government of India.
• The Appointments Committee of the Cabinet (ACC), chaired by the Prime Minister, approved her elevation to this prestigious position from her previous role as Additional Secretary.
• As the Law Secretary, her primary responsibilities include rendering legal advice to various Union Ministries, managing Government Litigation in the Supreme Court and High Courts, and overseeing the Indian Legal Service cadre.
• She is instrumental in the administration of the Legal Services Authorities Act, 1987, ensuring the provision of free legal aid to the weaker sections of society.

 Additional Information

• Shubhanshu Shukla:
• He is a Wing Commander in the Indian Air Force (IAF) and was selected as the prime astronaut for the Axiom-4 mission to the International Space Station (ISS), a collaborative effort between ISRO and NASA.
• K. Vinod Chandran:
• He is a distinguished jurist currently serving as the Chief Justice of the Patna High Court. He has previously served as a judge in the Kerala High Court.
• Department of Legal Affairs:
• This department is responsible for the Attorney General of India, the Solicitor General of India, and the Central Agency Section which conducts litigation on behalf of the Union.
• It also handles matters related to Arbitration and the Notaries Act, 1952.

The correct answer is 985.

Key Points

• Rajaraja I, born as Arulmozhi Varman, ascended the Chola throne in 985 CE after the reign of Uttama Chola.
• His coronation marked the beginning of a new era of Chola imperialism, where the dynasty expanded its influence across South India and the Indian Ocean.
• He ruled for approximately 29 years, until 1014 CE, establishing the Cholas as the most formidable power in the region.
• He is celebrated for his military genius, having defeated the Pandyan, Chera, and Chalukya dynasties to consolidate his authority.

 Additional Information

• Architectural Marvels:
• He commissioned the construction of the Brihadisvara Temple (also known as Rajarajeshwaram) at Thanjavur, which was completed in 1010 CE and is a UNESCO World Heritage Site.
• The temple is famous for its Vimana (tower) and the massive monolithic Nandi.
• Naval Supremacy and Expansion:
• Under his leadership, the Chola Navy became a dominant force, leading to the conquest of the Maldives and the northern parts of Sri Lanka.
• He captured the Malabar Coast (Kandalur Salai) to control the lucrative trade routes with the Arabs.
• Administrative Reforms:
• He introduced a highly organized system of local self-government through village assemblies known as Sabhas and Ur.
• In 1000 CE, he conducted a comprehensive land survey to streamline revenue administration and taxation.
• He was succeeded by his equally illustrious son, Rajendra Chola I, in 1014 CE.

The correct answer is UPSC.

Key Points

• The Union Public Service Commission (UPSC) launched the Pratibha Setu initiative in August 2025 to bridge the gap between high-caliber candidates and diverse employment opportunities.
• The portal is designed to provide a platform for candidates who have performed exceptionally well in major competitive exams, such as the Civil Services Examination (CSE) and Engineering Services Examination (ESE), but did not make the final selection list due to the limited number of vacancies.
• It allows the private sector and Public Sector Undertakings (PSUs) to access a database of pre-vetted and disciplined talent who have already cleared rigorous screening processes and reached the Interview/Personality Test stage.
• This move aims to optimize human resource utilization in India by ensuring that the country's most intellectually capable youth find productive roles in the economy, even outside traditional administrative services.

 Additional Information

• UPSC:
• It is a Constitutional Body established under Article 315 to 323 of the Constitution of India.
• Its primary mandate is to conduct examinations for appointments to the All India Services and Central Services of the Union.
• AICTE (All India Council for Technical Education):
• A statutory body responsible for the proper planning and coordinated development of technical education and management education systems in India.
• UGC (University Grants Commission):
• A statutory body set up by the Department of Higher Education to maintain standards of university education and provide recognition to universities in India.
• CBSE (Central Board of Secondary Education):
• A national-level board of education for public and private schools, focused on the standardization of secondary education and conducting All India Senior School Certificate Examinations.

The correct answer is Startups, Women and Youth Advantage Through e-Transactions.

Key Points

• SWAYATT is a flagship initiative launched by the Ministry of Commerce and Industry through the Government e-Marketplace (GeM) portal.
• The acronym SWAYATT stands for Startups, Women and Youth Advantage Through e-Transactions, representing a concerted effort to promote digital inclusion.
• Launched originally in February 2019, the initiative celebrated its 6th anniversary in February 2025, marking significant milestones in bringing diverse seller groups into the mainstream Public Procurement fold.
• The primary objective of the program is to provide Startups, Women Entrepreneurs, and Youth with easier access to the government market, thereby fostering the Ease of Doing Business.
• By leveraging e-Transactions, the initiative ensures transparency, reduces manual intervention, and facilitates Direct Benefit Transfers to small-scale and marginalized entrepreneurs.
• The initiative aligns with the broader vision of Atmanirbhar Bharat (Self-reliant India) by encouraging local manufacturing and indigenous service providers to compete at a national level.

 Additional Information

• Government e-Marketplace (GeM):
• An online platform established in 2016 for the procurement of common-use goods and services by various Government Departments and Public Sector Undertakings (PSUs).
• It aims to enhance Efficiency, Speed, and Transparency in government buying processes.
• Startups and DPIIT:
• Entities recognized by the Department for Promotion of Industry and Internal Trade (DPIIT) are eligible for specific relaxations under SWAYATT, such as exemptions from Prior Turnover and Prior Experience criteria in government tenders.
• Womaniya on GeM:
• A related initiative that specifically targets Women Entrepreneurs and Self-Help Groups (SHGs) to sell handicrafts, organic products, and other goods directly to the government.

The correct answer is Mayil Aattam.

Key Points

• Mayil Aattam, also known as the Peacock Dance, is a traditional religious and artistic folk dance native to the states of Tamil Nadu and Kerala.
• The dance is specifically performed in temples dedicated to Lord Murugan, the Hindu deity of war, as the peacock is recognized as his divine vehicle (Vahana).
• Performers wear elaborate costumes that include a peacock beak and a structural dress adorned with actual peacock feathers that can be opened and closed like a fan using a specialized thread mechanism.
• A unique characteristic of this dance is that the performers attach wooden tall pegs to their feet, requiring significant balance to mimic the graceful movements, strutting, and rhythmic hopping of a peacock.
• This ritualistic performance is carried out to seek divine blessings and is usually accompanied by traditional musical instruments like the Nadaswaram and Thavil.

 Additional Information

• Gambhira:
• A vibrant mask dance originating from the Malda district of West Bengal.
• It is performed during the Gajan festival in honor of Lord Shiva and often features solo or group performances highlighting social issues.
• Pung Cholom:
• A unique Manipuri classical dance form known as the Drum Dance.
• It involves dancers playing the Pung (a traditional drum) while executing acrobatic stunts, high leaps, and rapid spins.
• Theru Koothu:
• An ancient street theatre form of Tamil Nadu, literally meaning 'street play'.
• Performances are usually held during the Aadi festival and focus on mythological stories, particularly the life of Draupadi from the Mahabharata.

The correct answer is Chhattisgarh.

Key Points

• The Hareli festival is considered the first festival of the year in the Indian state of Chhattisgarh, marking the beginning of the agricultural cycle.
• It is celebrated on the Amavasya (new moon day) of the Hindu month of Shravan, which typically falls during the peak of the monsoon season in July or August.
• The term Hareli is derived from the Hindi word Haryali, signifying the lush greenery that covers the landscape during this time.
• During the festival, farmers offer prayers to their agricultural implements such as ploughs, shovels, and axes, as well as to their livestock, expressing gratitude for a successful sowing season.
• A primary ritual involves the preparation of Cheela, a traditional salted pancake made from rice flour, which is offered to the deities.
• Young men and children participate in the Gedi tradition, where they walk on tall bamboo stilts to celebrate the festival and navigate through the muddy monsoon terrain.

 Additional Information

• Assam
• Famous for the Bihu festivals, specifically Bohag Bihu, which marks the Assamese New Year, and Magh Bihu, the harvest festival.
• Himachal Pradesh
• Known for the Kullu Dussehra, a week-long international festival, and the Minjar Mela held in Chamba to celebrate the blossoming of maize.
• Gujarat
• Recognized for the nine-day Navratri festival featuring Garba dance and the International Kite Festival (Uttarayan) held in January.
• Ritualistic Significance
• In Chhattisgarh, people place Neem leaves at the entrances of their homes during Hareli to protect their families from seasonal diseases and ward off negative energy.

The correct answer is Haryana.

Key Points

• The Haryana government has announced the development of the world's largest curated jungle safari park, which will be spread across an area of 10,000 acres in the Aravalli mountain range.
• The project is designed to span across the Gurugram and Nuh districts, significantly boosting the state's tourism potential and contributing to wildlife conservation.
• At 10,000 acres, this safari park will be five times the size of the Sharjah Safari Park in the UAE, which currently holds the record for the largest curated safari park outside Africa with an area of about 2,000 acres.
• The project is a collaborative effort between the Union Ministry of Environment, Forest and Climate Change and the Government of Haryana, aimed at protecting the ecologically sensitive Aravalli hills.
• A Global Design Competition was initiated by the state to select an international agency for the park's design, focusing on creating a world-class facility for eco-tourism.

 Additional Information

• Aravalli Range Significance:
• The Aravalli Range is one of the world's oldest fold mountain systems, running through Gujarat, Rajasthan, Haryana, and Delhi.
• It acts as a natural barrier against the eastward expansion of the Thar Desert and is a vital recharge zone for groundwater in the NCR region.
• The hills are home to diverse flora and fauna, including leopards, striped hyenas, nilgai, and over 180 species of birds.
• Proposed Safari Features:
• The park is planned to include ten specific zones, including a large herpetarium, an exotic bird aviary, and specialized zones for big cats (lions, tigers, and leopards).
• It will also feature a botanical garden, nature trails, and an underwater aquarium to enhance the educational and recreational experience for visitors.
• The initiative aims to prevent illegal mining and encroachment in the Aravallis by establishing a protected, managed sanctuary.

The correct answer is Bihar.

Key Points

• The Kosi-Mechi Intra-state Link Project is a significant water management initiative in the state of Bihar designed to divert surplus water from the Kosi river to the Mechi river.
• It is India's second major river interlinking project to receive central approval, following the Ken-Betwa project.
• The project aims to provide irrigation to approximately 2.14 lakh hectares of agricultural land in the Seemanchal region, specifically benefitting the districts of Purnia, Kishanganj, Araria, and Katihar.
• The Mechi river is a tributary of the Mahananda river, and this link facilitates the transfer of water from the Kosi basin to the Mahananda basin without the need for large dam construction.
• The project is estimated to cost around 4,900 crore and involves the construction of a 76.20 km long canal to channel the water.

 Additional Information

• Kosi River:
• Commonly referred to as the Sorrow of Bihar, it is known for its unpredictable nature and frequent course changes that lead to catastrophic flooding in North Bihar.
• It originates in the Himalayas and is an antecedent river that eventually joins the Ganges.
• Interlinking of Rivers (ILR):
• The national perspective plan for ILR was formulated by the Ministry of Jal Shakti to transfer water from surplus basins to water-deficit basins.
• The National Water Development Agency (NWDA) is the nodal agency responsible for the feasibility studies and implementation of these links.
• Madhya Pradesh:
• Associated with the Ken-Betwa link project, which was the first major initiative under the National Perspective Plan for river interlinking.

The correct answer is 320 tonnes.

Key Points

• The Polar Satellite Launch Vehicle (PSLV) is an expendable medium-lift launch vehicle designed and operated by the Indian Space Research Organisation (ISRO) to carry payloads to Sun-Synchronous Polar Orbits (SSPO) and Geosynchronous Transfer Orbits (GTO).
• The PSLV-XL configuration is the most powerful variant of the PSLV family, featuring a gross lift-off weight (GLOW) of approximately 320 tonnes.
• This weight is largely attributed to the use of six extended strap-on motors (PSOM-XL), which are significantly larger than the boosters used in the standard PSLV-G variant.
• Each of the six PSOM-XL strap-on boosters carries 12.2 tonnes of solid propellant, providing the necessary additional thrust to lift heavier satellites or reach higher orbits.
• The vehicle stands at a total height of 44.4 meters and utilizes a four-stage propulsion system that alternates between solid and liquid fuels to achieve high efficiency and precision.

 Additional Information

• Systematic Stage Breakdown:
• First Stage (PS1): Uses an S138 solid motor containing 138 tonnes of HTPB-based propellant, generating a massive peak thrust for lift-off.
• Second Stage (PS2): Powered by the liquid-fueled Vikas Engine, which uses UDMH (Unsymmetrical Dimethylhydrazine) as fuel and N₂O₄ as an oxidizer.
• Third Stage (PS3): A high-performance solid rocket motor (S7) that provides thrust during the upper atmospheric phase.
• Fourth Stage (PS4): A liquid stage equipped with two engines using MMH (Monomethylhydrazine) and MON-3 (Mixed Oxides of Nitrogen), allowing for multiple restarts and high-precision orbit injection.
• Major Mission Successes:
• The PSLV-XL was famously used for India's first lunar mission, Chandrayaan-1, in 2008.
• It successfully launched the Mars Orbiter Mission (Mangalyaan) in 2013, marking India as the first nation to reach Mars on its maiden attempt.
• The variant is also the workhorse for the NavIC (Indian Regional Navigation Satellite System) constellation and the solar mission Aditya-L1.

The correct answer is Both I and II.

Key Points

• AstroSat is India's first dedicated multi-wavelength space observatory, launched by the Indian Space Research Organisation (ISRO) on September 28, 2015. It is designed to observe the universe simultaneously in optical, ultraviolet, and X-ray wavebands.
• Statement I pertains to the discovery made using the Ultra Violet Imaging Telescope (UVIT). AstroSat detected extreme ultraviolet (EUV) light from a galaxy called AUDFs01, which is located 9.3 billion light-years away from Earth. This landmark discovery helped scientists understand how the cosmic dark ages ended and how the first stars ionized the universe. Hence, statement I is correct.
• Statement II refers to the capabilities of the Cadmium Zinc Telluride Imager (CZTI) payload. This instrument successfully measured the polarisation of X-rays from the Crab Pulsar, a supernova remnant in the Milky Way. This was a significant technical milestone, as measuring X-ray polarisation is extremely challenging and provides deep insights into the magnetic field geometry of celestial objects. Hence, statement II is correct.

 Additional Information

• The AstroSat mission carries five distinct scientific payloads:
• Ultra Violet Imaging Telescope (UVIT): Capable of observing in Far-UV, Near-UV, and Visible bands.
• Soft X-ray Telescope (SXT): Employs Wolter-I grazing incidence optics to study X-ray spectra between 0.3 to 8 keV.
• Large Area X-ray Proportional Counter (LAXPC): Designed for high time-resolution studies of X-ray binaries and active galactic nuclei.
• Cadmium Zinc Telluride Imager (CZTI): Functions as a hard X-ray detector with imaging and polarimetry features.
• Scanning Sky Monitor (SSM): Specifically monitors the sky for transient X-ray events.
• The satellite was launched into a 650 km near-equatorial orbit by the PSLV-C30 launch vehicle from Sriharikota.

The correct answer is IIT Madras.

Key Points

• The Shakti microprocessor project is a significant initiative led by the Reconfigurable Intelligent Systems Engineering (RISE) laboratory at IIT Madras.
• It is recognized as India's first indigenous industrial-grade microprocessor, designed to reduce dependency on foreign hardware and enhance national security in the computing domain.
• The processor is based on the RISC-V (Reduced Instruction Set Computer) open-source Instruction Set Architecture (ISA), which allows for customization without the heavy licensing fees associated with proprietary architectures like ARM or Intel.
• Development was funded by the Ministry of Electronics and Information Technology (MeitY) under the Microprocessor Development Programme to foster the Digital India mission.
• The project encompasses a family of processors tailored for diverse applications, including Internet of Things (IoT) devices, mobile phones, and high-performance computing systems.
• In 2018, the first batch of Shakti chips, specifically the C-Class, was successfully fabricated at the Semi-Conductor Laboratory (SCL) in Mohali, marking a milestone in domestic semiconductor manufacturing.

 Additional Information

• AJIT Microprocessor:
• Developed by IIT Bombay, this is another indigenous processor focusing on low-power, medium-performance applications.
• It was designed using the SPARC V8 architecture and is often utilized in satellite and navigation systems.
• Shakti Processor Variants:
• E-Class: A tiny, low-power processor designed for embedded systems and smart cards.
• C-Class: A 64-bit core aimed at mid-range controllers, typically used in networking and storage devices.
• I-Class: Designed for mobile, laptop, and high-end computing requirements with multi-core support.
• Atmanirbhar Bharat in Electronics:
• The Shakti project is a cornerstone of the Self-Reliant India vision, aiming to create a robust ecosystem for fabless chip design within the country.

The correct answer is IIT Ropar.

Key Points

• In December 2024, researchers at the Indian Institute of Technology (IIT) Ropar unveiled an innovative, cost-effective Bluetooth Low Energy (BLE) Gateway.
• The gateway is specifically engineered to bridge the gap between IoT sensors and cloud-based platforms, facilitating seamless data transmission for various Internet of Things applications.
• A standout feature of this development is the integration of advanced data security protocols, which ensure that the data collected from peripheral devices remains protected from cyber-attacks and unauthorized access during transit.
• The device is designed for low power consumption, making it ideal for remote monitoring in sectors like agriculture, smart cities, and industrial automation where energy efficiency is a priority.
• This innovation aims to provide an affordable alternative to expensive proprietary gateways, supporting the Make in India initiative by empowering local startups and MSMEs with indigenous technology.

 Additional Information

• Bluetooth Low Energy (BLE) Technology
• It is a wireless communication protocol designed for short-range data exchange with minimal energy use.
• Commonly used in wearable devices, beacons, and smart home systems.
• Unlike Classic Bluetooth, BLE remains in sleep mode unless a connection is initiated, which significantly extends battery life.
• IoT Ecosystem Security
• Gateways serve as the central hub or aggregator for multiple sensors; hence, securing this node is vital for the integrity of the entire IoT network.
• The IIT Ropar solution focuses on encryption and secure authentication to prevent data breaches in sensitive environments like healthcare.
• IIT Ropar
• Located in Rupnagar, Punjab, it was established in 2008 as one of the second-generation Indian Institutes of Technology.
• The institute is known for its research in Artificial Intelligence, Renewable Energy, and Biomedical Engineering.

The correct answer is Gandhinagar.

Key Points

• The BIMSTEC Youth Summit-2025 was successfully hosted in Gandhinagar, the capital city of Gujarat, India, from 7-11 February 2025.
• The summit brought together youth leaders and delegates from the seven member states of the Bay of Bengal Initiative for Multi-Sectoral Technical and Economic Cooperation (BIMSTEC).
• The core objective of the summit was to promote regional integration, foster bilateral and multilateral relations, and provide a platform for youth to share ideas on leadership, sustainable development, and technological innovation.

 Additional Information

• BIMSTEC Overview:
• It is an international organization comprising seven South Asian and Southeast Asian nations: Bangladesh, Bhutan, India, Myanmar, Nepal, Sri Lanka, and Thailand.
• Established on 6 June 1997 through the landmark Bangkok Declaration, its primary goal is to foster rapid economic development and cooperation across diverse sectors.
• The permanent secretariat of BIMSTEC is located in Dhaka, Bangladesh.
• Other Cities in Context:
• Dhaka: Serves as the capital of Bangladesh and houses the permanent BIMSTEC Secretariat, coordinating regional activities.
• Colombo: The commercial capital of Sri Lanka, which historically chaired BIMSTEC and spearheaded its science, technology, and innovation sectors.
• Chennai: A major Indian port city that serves as a key gateway for maritime trade and connectivity projects linking India with Southeast Asian BIMSTEC partners.

The correct answer is 2025.

Key Points

• Dev Kumar Meena, a phenomenal athlete hailing from Madhya Pradesh, established a new national record in the men's pole vault event.
• He successfully cleared a towering height of 5.40 metres to claim the prestigious national record, achieving this milestone in the year 2025.
• This extraordinary feat solidifies his position as one of India's most promising track and field talents, surpassing previous junior and senior benchmarks in the vertical jump discipline.

 Additional Information

• Pole Vaulting:
• It is a highly technical track and field discipline requiring an exceptional combination of speed, agility, gymnastic ability, and upper-body strength.
• Athletes utilize a highly flexible pole made of carbon fiber or fiberglass to vault over a high crossbar without dislodging it.
• Career Milestones of Dev Meena:
• In 2023, Dev Meena secured a gold medal at the National U-20 Athletics Championships by clearing a height of 5.16 metres, which earned him a direct qualification for the World Under-20 Athletics Championships.
• The years 2014 and 2019 represent periods of older national marks set by previous generations of Indian athletes, before Dev Meena reached his peak performance of 5.40 metres in 2025.

The correct answer is Only I.

Key Points

• Track events encompass all running competitions that take place on the specialized 400-meter oval track, including sprints, middle-distance, and long-distance races. Hence, statement I is correct.
• In the official taxonomy of Athletics (Track and Field), there is no technical classification referred to as Ground events; competitions are strictly categorized into track, field, road, and combined events. Hence, statement II is incorrect.
• The standard running track consists of two parallel straights and two bends, typically made of synthetic rubber or polyurethane to provide optimal traction for spiked shoes.
• Events such as the 110m hurdles, 400m hurdles, and the 3000m steeplechase are also categorized under track events because they are contested on the running circuit.

 Additional Information

• Classification of Athletics:
• Field Events: These take place in the central area (infield) and are divided into Jumping events (High Jump, Pole Vault, Long Jump, Triple Jump) and Throwing events (Shot Put, Discus, Hammer, Javelin).
• Sprints: Short races requiring maximum velocity, typically the 100m, 200m, and 400m.
• Relays: Team events where four runners carry a baton, most commonly the 4 × 100m and 4 × 400m.
• Road Events: Competitions conducted on paved courses, including the Marathon (42.195 km) and Race Walking (20km and 50km).
• Combined Events: Multi-discipline contests such as the Decathlon (ten events for men) and Heptathlon (seven events for women) that test overall versatility.

The correct answer is Parallel straight lines inside the solenoid and concentric circles outside..

Key Points

• A solenoid is defined as a long, thin loop of wire, often wrapped around a metallic core, which produces a magnetic field when an electric current is passed through it. It effectively converts electrical energy into magnetic energy.
• Inside the solenoid, the magnetic field lines are parallel straight lines. This specific geometry indicates that the magnetic field is uniform in both magnitude and direction at all points within the central volume of the coil.
• Outside the solenoid, the magnetic field is non-uniform. Near the individual turns of the conducting wire, the field lines form concentric circles. These individual circular fields interact and combine to form a pattern that resembles the field of a bar magnet.
• The strength of the magnetic field inside the solenoid is constant, while the field strength decreases significantly as one moves further away from the solenoid exterior.
• The direction of the magnetic field is determined by the Right-Hand Thumb Rule, where the fingers wrap in the direction of the current and the thumb points towards the North Pole.

 Additional Information

• Factors Affecting Magnetic Field Strength (B):
• Number of Turns (n): The magnetic field is directly proportional to the number of turns per unit length. More turns result in a stronger magnetic field.
• Current (I): The field intensity is directly proportional to the amount of current flowing through the coil. Increasing the current increases the flux density.
• Nature of Core Material: Using a soft iron core inside the solenoid increases the magnetic field strength by thousands of times, creating an electromagnet due to high magnetic permeability.
• Electromagnet Applications:
• Solenoids are widely used in electric bells, magnetic locks, and medical imaging devices like MRI scanners.
• They are also essential components in relays and valves where controlled linear motion is required.

The correct answer is Jantar.

Key Points

• The Jantar is an ancient and unique stringed musical instrument belonging to the Veena family, primarily used in the folk music traditions of Rajasthan.
• It is distinguished by its construction, featuring two large resonators made of dried gourds (tumbas) connected by a central bamboo or wooden neck known as the Dandi.
• The instrument typically consists of two strings made of steel and roughly 14 frets which are often adhered to the neck using wax or resin.
• The Jantar is played almost exclusively by the Bhopas, the priest-singers of Rajasthan, while performing the Phad (narrative scroll painting) of the folk deity Lord Devnarayan.
• Unlike many other stringed instruments, the Jantar is played while hanging around the neck of the performer with a strap, allowing the musician to dance or move during the ritualistic narration.

 Additional Information

• Trumpet:
• A high-pitched brass instrument used in orchestral and jazz music, producing sound through the vibration of the musician's lips on a metal mouthpiece and regulated by piston valves.
• Nadaswaram:
• A traditional double-reed wind instrument from South India, considered a Mangala Vadya (auspicious instrument) used in temples and weddings.
• It is crafted from a dark, hard wood known as Aacha and features a conical bore ending in a large metal or wooden bell.
• Mridangam:
• The primary percussion instrument of Carnatic music, it is a double-sided drum carved from a single piece of jackfruit wood.
• Its two heads are made of layered animal hide and are tuned to the tonic note of the main performer.

The correct answer is Fuel for home and industry.

Key Points

• Liquefied Petroleum Gas (LPG) is a flammable mixture of hydrocarbon gases, primarily propane and butane, which are separated from crude oil during the fractional distillation process at petroleum refineries.
• It is described as petroleum gas in liquid form because these hydrocarbons are gaseous at standard temperature and pressure but are easily liquefied under moderate pressure for efficient storage and transport in cylinders.
• LPG is a preferred clean-burning fuel for domestic purposes, such as cooking on gas stoves and water heating, because it leaves no residue and has a very high calorific value of approximately 50,000 kJ/kg.
• In the industrial sector, it is utilized for metal cutting, steam generation, food processing, and as a feedstock for various chemical synthesis processes.
• Because it is naturally odorless, a pungent-smelling substance called Ethyl Mercaptan is added to LPG to allow for the easy detection of gas leaks, ensuring safety in homes and factories.

 Additional Information

• Paraffin Wax:
• A byproduct of the lubricating oil fraction of petroleum.
• Used in the manufacture of ointments, cosmetic vaseline, candles, wax paper, and polishes.
• Diesel:
• A heavier petroleum fraction used in compression-ignition engines.
• Mainly used as fuel for heavy motor vehicles like trucks and buses, as well as electric generators and railway engines.
• Bitumen:
• The heaviest residual component of crude oil distillation.
• Crucial for road surfacing and the production of moisture-resistant paints and waterproofing materials.

Shortcut Trick

Solve the expression using BODMAS order: Brackets → Division → Multiplication → Addition → Subtraction.

Step 1: 66 + 38 − (27) + 7 + 33 − 14

Step 2: Combine positive terms (66 + 38 + 7 + 33) = 144

Step 3: Combine negative terms (27 + 14) = 41

Step 4: Final calculation 144 − 41 = 103.

∴ The correct answer is 103.

Alternate Method

Given Expression: 66 + 38 − (27 × 1) + 42 ÷ 6 + 33 − 14

Following the BODMAS rule:

⇒ Solve Bracket: (27 × 1) = 27

⇒ Expression: 66 + 38 − 27 + 42 ÷ 6 + 33 − 14

⇒ Perform Division: 42 ÷ 6 = 7

⇒ Expression: 66 + 38 − 27 + 7 + 33 − 14

⇒ Perform Addition: 66 + 38 + 7 + 33 = 144

⇒ Perform Subtraction: 144 − 27 − 14

⇒ 117 − 14 = 103

∴ The correct answer is 103.

Additional Information

BODMAS Rule

The rule determines the priority of operations: Brackets ((), {}, []), Of/Orders (powers/roots), Division (÷), Multiplication (×), Addition (+), and Subtraction (−).

Left-to-Right Rule

When operators of the same priority (like Multiplication and Division, or Addition and Subtraction) appear together, solve them sequentially from left to right.

Shortcut Trick

Break the square root into individual parts using the product property: √(a × b) = √a × √b.

Calculate: √0.81 = 0.9 and √0.04 = 0.2.

Multiply the results: 0.9 × 0.2 = 0.18.

∴ The correct answer is 0.18.

Alternate Method

Given: √(0.81 × 0.04)

Formula Used: The square root of a decimal number and standard multiplication rules.

⇒ √(0.81 × 0.04)

⇒ √(0.0324)

⇒ √(324 / 10000)

⇒ 18 / 100

⇒ 0.18

∴ The correct answer is 0.18.

Additional Information

Square Root 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., 4 places in 0.0324 → 2 places in 0.18).

Product Property of Radicals

For any non-negative numbers a and b, √(a × b) = √a × √b. This helps in simplifying complex radicals by splitting them into perfect squares.

Perfect Squares to Remember

Memorizing perfect squares up to 30 (like 18² = 324) is essential for fast simplification in banking and quantitative aptitude exams.

Shortcut Trick

Recognize perfect powers: 3375 is 15³ and 81 is 9².

For cube roots, 3 decimal places become 1: √³(3.375) = 1.5.

For square roots, 2 decimal places become 1: √(0.81) = 0.9.

Final calculation: 1.5 × 0.9 = 1.35.

∴ The correct answer is 1.35.

Alternate Method

Given: √³(3.375) × √(0.81)

Convert the decimal numbers into fractions for easier calculation:

⇒ √³(3375/1000) × √(81/100)

Applying the root properties √ⁿ(a/b) = √ⁿ(a)/√ⁿ(b):

⇒ (√³(3375) / √³(1000)) × (√(81) / √(100))

⇒ (15 / 10) × (9 / 10)

⇒ 1.5 × 0.9

⇒ 1.35

∴ The correct answer is 1.35.

Additional Information

Cube Root of Decimals

If a decimal number has 3n decimal places, its cube root will have n decimal places.

Square Root of Decimals

If a decimal number has 2n decimal places, its square root will have n decimal places.

Multiplication of Decimals

The number of decimal places in the product is the sum of the decimal places in the multipliers (1.5 × 0.9 → 1+1 = 2 places).

Shortcut Trick

Multiply the numerator and denominator by the conjugate of the denominator, which is (√3 + √2).

The denominator simplifies to (√3)² − (√2)² = 3 − 2 = 1.

The expression becomes (√3 + √2)² × (√3 + √2) = (√3 + √2)³.

Using the identity (a + b)³ = a³ + 3a²b + 3ab² + b³, we get:

3√3 + 3(3)(√2) + 3(√3)(2) + 2√2 = 3√3 + 9√2 + 6√3 + 2√2 = 9√3 + 11√2.

∴ The correct answer is 9√3 + 11√2.

Alternate Method

Given: The expression is [(√3 + √2)²] / (√3 − √2).

Formula Used: (a + b)² = a² + b² + 2ab and Rationalization by multiplying the conjugate pair.

⇒ Expand the numerator: (√3 + √2)² = (√3)² + (√2)² + 2 × √3 × √2

⇒ Numerator = 3 + 2 + 2√6 = 5 + 2√6

⇒ Rationalize: [ (5 + 2√6) / (√3 − √2) ] × [ (√3 + √2) / (√3 + √2) ]

⇒ [ (5 + 2√6)(√3 + √2) ] / [ (√3)² − (√2)² ]

⇒ [ 5√3 + 5√2 + 2√6√3 + 2√6√2 ] / (3 − 2)

⇒ 5√3 + 5√2 + 2√18 + 2√12

⇒ 5√3 + 5√2 + 2(3√2) + 2(2√3)

⇒ 5√3 + 5√2 + 6√2 + 4√3

⇒ (5 + 4)√3 + (5 + 6)√2

⇒ 9√3 + 11√2

∴ The correct answer is 9√3 + 11√2.

Additional Information

Rationalization of Surds

To simplify a fraction with a surd in the denominator, multiply the numerator and denominator by the conjugate (changing the sign between the terms).

Conjugate Pairs

For a surd expression (x − y), the conjugate is (x + y). Multiplying them results in a rational number (x² − y²) via the difference of squares property.

Addition of Surds

Only like surds (surds with the same radicand) can be added or subtracted, similar to like terms in algebra (e.g., 5√3 + 4√3 = 9√3).

Shortcut Trick

Find the approximate cube root of the product 3315 to identify the middle number.

Since 15³ = 3375, the middle number must be close to 15.

The product ends in 5, so one of the consecutive odd numbers must be 15.

Check the set {13, 15, 17}: 13 × 15 × 17 = 195 × 17 = 3315.

The largest of these numbers is 17.

∴ The correct answer is 17.

Alternate Method

Given: Product of three consecutive odd numbers is 3315.

Formula: Let the three numbers be (x − 2), x, and (x + 2).

⇒ (x − 2) × x × (x + 2) = 3315

⇒ x × (x² − 4) = 3315

⇒ x³ − 4x = 3315

⇒ Since x³ ≈ 3315, we know 15³ = 3375 and 14³ = 2744.

⇒ x must be 15 (as it is the middle odd number).

⇒ Verification: 15 × (15² − 4) = 15 × (225 − 4) = 15 × 221 = 3315.

⇒ The numbers are 13, 15, and 17.

⇒ Largest number = 17.

∴ The correct answer is 17.

Additional Information

Consecutive Odd Numbers

Numbers that follow each other in order with a common difference of 2, such as 2n+1, 2n+3, 2n+5.

Unit Digit Rule

If the product of numbers ends in 5, at least one of the factors must have a unit digit of 5 (and no factor can be even).

Estimation by Cubes

For three consecutive numbers, the product (n−1)n(n+1) = n³ − n, which is very close to n³.

Shortcut Trick

Count decimal places: Numerator has 6 (3+3), Denominator has 5 (3+2).

Shift decimal points to simplify: (64 × 256) ÷ (4 × 160) = 16384 ÷ 640 = 25.6.

Calculate the square root: √25.6 ≈ 5.0596.

Rounding to the nearest provided option, we get 5.05.

∴ The correct answer is 5.05.

Alternate Method

Given Expression: √[(0.064 × 0.256) ÷ (0.004 × 0.16)]

Method: Simplifying the fraction inside the square root by adjusting decimal powers.

⇒ √[ (64 × 10⁻³ × 256 × 10⁻³) ÷ (4 × 10⁻³ × 16 × 10⁻²) ]

⇒ √[ (16384 × 10⁻⁶) ÷ (64 × 10⁻⁵) ]

⇒ √[ (16384 ÷ 64) × 10^{−6 − (−5)} ]

⇒ √[ 256 × 10⁻¹ ]

⇒ √25.6

⇒ 5.0596... ≈ 5.05

∴ The correct answer is 5.05.

Additional Information

Square Root of Decimals

When finding the square root of a decimal, the number of decimal places in the result is half the number of places in the original number (e.g., √0.0016 = 0.04).

Decimal Point Shift

A fraction a/b remains unchanged if the decimal point is shifted the same number of places to the right in both the numerator and denominator.

Approximation Technique

Since 5² = 25 and 5.1² = 26.01, the value of √25.6 must lie between 5 and 5.1.

Shortcut Trick

The series 3 + 6 + 9 + ... + 300 is 3 × (1 + 2 + 3 + ... + 100).

Use the sum of first n natural numbers formula: [n(n + 1)] ÷ 2.

Here n = 100, so Sum = 3 × [100 × 101 ÷ 2].

Sum = 3 × 5050 = 15150.

∴ The correct answer is 15150.

Alternate Method

The given series is an Arithmetic Progression (AP).

Given:

First term (a) = 3

Common difference (d) = 6 − 3 = 3

Last term (l) = 300

Formula Used:

n = [(l − a) ÷ d] + 1

S_n = (n ÷ 2) × (a + l)

Calculations:

⇒ n = [(300 − 3) ÷ 3] + 1

⇒ n = [297 ÷ 3] + 1 = 99 + 1 = 100

⇒ S₁₀₀ = (100 ÷ 2) × (3 + 300)

⇒ S₁₀₀ = 50 × 303

⇒ S₁₀₀ = 15150

∴ The correct answer is 15150.

Additional Information

Arithmetic Progression (AP)

A sequence where each term is obtained by adding a constant common difference (d) to the preceding term. The sum is S_n = n/2 [2a + (n − 1)d].

Sum of First n Natural Numbers

The sum of the series 1 + 2 + 3 + ... + n is given by the formula S = [n(n + 1)] ÷ 2.

n-th term of an AP

The general term of an AP is calculated as a_n = a + (n − 1)d, where 'a' is the first term and 'd' is the common difference.

Shortcut Trick

Numbers 4950, 7425, and 7623 all have a digit sum of 18, making them divisible by 9.

For these numbers, the alternating digit sum (odd − even positions) is 0, making them divisible by 11.

For 7841: Sum = 7 + 8 + 4 + 1 = 20 (Not divisible by 9).

Difference = (7 + 4) − (8 + 1) = 2 (Not divisible by 11).

∴ The correct answer is 7841.

Alternate Method

Given: Numbers are 4950, 7425, 7623, 7841.

Method: Apply Divisibility Rules for 9 and 11.

Rule for 9: Sum of digits must be divisible by 9.

Rule for 11: |(Sum of digits at odd places) − (Sum of digits at even places)| must be 0 or 11.

⇒ Checking 4950: Sum = 4 + 9 + 5 + 0 = 18 (Divisible by 9); Diff = (4 + 5) − (9 + 0) = 0 (Divisible by 11).

⇒ Checking 7425: Sum = 7 + 4 + 2 + 5 = 18 (Divisible by 9); Diff = (7 + 2) − (4 + 5) = 0 (Divisible by 11).

⇒ Checking 7623: Sum = 7 + 6 + 2 + 3 = 18 (Divisible by 9); Diff = (7 + 2) − (6 + 3) = 0 (Divisible by 11).

⇒ Checking 7841: Sum = 7 + 8 + 4 + 1 = 20 (Not divisible by 9); Diff = (7 + 4) − (8 + 1) = 2 (Not divisible by 11).

∴ The correct answer is 7841.

Additional Information

Divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

Divisibility by 9

Every number divisible by 9 is also divisible by 3, but the reverse is not always true.

Divisibility by 11 shortcut

For a 4-digit number abcd, the rule is (a + c) − (b + d) must be 0 or a multiple of 11.

Shortcut Trick

To calculate the area of a path built outside a rectangle, use the formula:

Area of path = 2w(L + B + 2w)

Where L = 90, B = 50, and w = 1.5.

Area = 2 × 1.5 × (90 + 50 + 2 × 1.5) = 3 × (140 + 3) = 3 × 143 = 429 m².

∴ The correct answer is 429 m².

Alternate Method

Given:

Length of the rectangular garden (L) = 90 m

Breadth of the rectangular garden (B) = 50 m

Width of the path (w) = 1.5 m

Formula Used:

Area of Path = (Area of outer rectangle) − (Area of inner garden)

Calculations:

⇒ Outer Length = 90 + 1.5 + 1.5 = 93 m

⇒ Outer Breadth = 50 + 1.5 + 1.5 = 53 m

⇒ Outer Area = 93 × 53 = 4929 m²

⇒ Inner Area = 90 × 50 = 4500 m²

⇒ Area of the path = 4929 − 4500 = 429 m²

∴ The correct answer is 429 m².

Additional Information

Path Inside a Rectangle

If a path of width w is built inside a rectangle of length L and breadth B, its area is given by Area = 2w(L + B − 2w).

Crossroads in the Middle

If two paths of width w cross each other at right angles in the middle of the garden, Area = w(L + B − w).

Perimeter and Fencing

The cost of fencing is always calculated on the perimeter. Outer perimeter for this garden = 2(93 + 53) = 292 m.

Shortcut Trick

According to the Property of Averages, if every observation in a dataset is multiplied or divided by a constant k, the Average of the dataset is also multiplied or divided by the same constant k.

Original Average = N

Operation: Each of the 30 numbers is divided by 6.

New Average = Original Average ÷ 6 = N/6.

∴ The correct answer is N/6.

Alternate Method

Given:

Total numbers = 30

Initial Average = N

Divisor for each number = 6

Formula Used:

Average = Sum of all observations ÷ Total number of observations

Calculations:

⇒ Sum of 30 numbers = Average × Count = 30 × N = 30N

⇒ Since each number is divided by 6, the new sum will be:

⇒ New Sum = (30N) ÷ 6 = 5N

⇒ New Average = New Sum ÷ Count

⇒ New Average = 5N ÷ 30

⇒ New Average = N/6

∴ The correct answer is N/6.

Additional Information

Addition and Subtraction Rule

If a constant k is added to or subtracted from each observation, the new average is the original average ± k.

Multiplication Rule

If each observation is multiplied by a constant k, the new average becomes k × (original average).

Weighted Average

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

Shortcut Trick

To find the longest rod length that can cut all pieces without waste, calculate the HCF (Highest Common Factor) of the given lengths.

Given lengths: 90 cm, 75 cm, and 105 cm.

Shortcut: Find the difference between the numbers: 90 − 75 = 15 and 105 − 90 = 15.

Since 15 divides all three numbers (90 = 15 × 6, 75 = 15 × 5, 105 = 15 × 7), the HCF is 15.

∴ The correct answer is 15 cm.

Alternate Method

Given:

Length of Iron Piece 1 = 90 cm

Length of Iron Piece 2 = 75 cm

Length of Iron Piece 3 = 105 cm

Formula Used:

Maximum possible length = HCF(Length₁, Length₂, Length₃)

Calculations:

Prime factorization of the numbers:

⇒ 90 = 2 × 3 × 3 × 5 = 2 × 3² × 5

⇒ 75 = 3 × 5 × 5 = 3 × 5²

⇒ 105 = 3 × 5 × 7

⇒ Common prime factors = 3¹ × 5¹

⇒ HCF = 3 × 5 = 15

The maximum length of each rod must be 15 cm.

∴ The correct answer is 15 cm.

Additional Information

HCF (Highest Common Factor)

It is the greatest number that divides two or more numbers without leaving a remainder. It is also known as GCD (Greatest Common Divisor).

LCM (Least Common Multiple)

The smallest number that is a multiple of two or more numbers. Relationship: Product of two numbers = HCF × LCM.

Total Number of Rods

If the question asks for the minimum number of rods, divide each piece by HCF: (90÷15) + (75÷15) + (105÷15) = 6 + 5 + 7 = 18 rods.

Shortcut Trick

Let the total number be 100%.

The problem states: 25% + 90 = 100%.

⇒ 100% − 25% = 90

⇒ 75% = 90

⇒ 100% = (90 ÷ 75) × 100 = 1.2 × 100 = 120.

∴ The correct answer is 120.

Alternate Method

Given:

Percentage of the number = 25%

Value added to the percentage = 90

Formula Used:

Let the number be x. The equation is: (Percentage ÷ 100) × x + Value = x

Calculations:

⇒ (25 ÷ 100) × x + 90 = x

⇒ 0.25x + 90 = x

⇒ x − 0.25x = 90

⇒ 0.75x = 90

⇒ x = 90 ÷ 0.75

⇒ x = (90 × 100) ÷ 75

⇒ x = 120

∴ The correct answer is 120.

Additional Information

Percentage to Fraction Conversion

To simplify calculations, convert common percentages to fractions: 25% = 1/4, 50% = 1/2, 75% = 3/4, and 100% = 1.

Base Value Rule

In percentage problems, the original number or quantity is always considered as the base, which represents 100%.

Finding Total from Part

If P% of a number is V, then the number is calculated as (V ÷ P) × 100.

Shortcut Trick

Ratio of CP : SP = 2 : 5

Profit = 5 − 2 = 3 units

Given, 3 units = Rs. 900 → 1 unit = Rs. 300

Cost Price (CP) = 2 units = 2 × Rs. 300 = Rs. 600

∴ The correct answer is Rs. 600.

Alternate Method

Given:

Ratio of Cost Price (CP) to Selling Price (SP) = 2 : 5

Profit = Rs. 900

Formula Used:

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

Calculations:

⇒ Let the Cost Price be 2x and the Selling Price be 5x.

⇒ Profit = 5x − 2x

⇒ 3x = 900

⇒ x = 900 ÷ 3 = 300

⇒ Cost Price (CP) = 2x = 2 × 300 = 600

∴ The correct answer is Rs. 600.

Additional Information

Profit Percentage

Profit % = (Profit ÷ CP) × 100. It measures the gain relative to the cost.

Loss Percentage

Loss % = (Loss ÷ CP) × 100. It measures the deficit relative to the cost.

Relationship between CP and SP

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

Shortcut Trick

Convert everything to grams: 6600 g (Original) and 7590 g (Measured).

Absolute Error = 7590 − 6600 = 990 g.

Error % = (990 ÷ 6600) × 100 = 99 ÷ 6.6 = 15%.

∴ The correct answer is 15%.

Alternate Method

Given:

Original Weight = 6 kg 600 g

Measured Weight = 7 kg 590 g

Formula Used:

Error Percentage = (Measured Value − Original Value) ÷ Original Value × 100

Calculations:

⇒ Original Weight = (6 × 1000) + 600 = 6600 g

⇒ Measured Weight = (7 × 1000) + 590 = 7590 g

⇒ Error = 7590 − 6600 = 990 g

⇒ Error % = (990 ÷ 6600) × 100

⇒ Error % = 99000 ÷ 6600

⇒ Error % = 990 ÷ 66

⇒ Error % = 15%

∴ The correct answer is 15%.

Additional Information

Percentage Error Formula

It is the difference between the measured value and the true value, expressed as a percentage of the true value: |Approx − Exact| ÷ |Exact| × 100.

Unit Conversion

Always convert different units to a single base unit before performing percentage calculations. For mass, 1 kg = 1000 g.

Percentage Change

Percentage increase or decrease is always calculated on the original (base) value, never on the final or measured value.

Shortcut Trick

Profit = 20% of Selling Price (SP) = 1/5 of SP.

Let SP = 5 units, then Profit = 1 unit.

Cost Price (CP) = SP − Profit = 5 − 1 = 4 units.

Required Ratio of Profit : CP = 1 : 4.

∴ The correct answer is 1 : 4.

Alternate Method

Given:

Profit = 20% of Selling Price (SP).

Formula Used:

1. Profit = Selling Price − Cost Price (CP)
2. Ratio = Profit / Cost Price

Calculations:

⇒ Let the Selling Price (SP) of the article be ₹100.

⇒ Profit = 20% of SP = 20/100 × 100 = ₹20.

⇒ Cost Price (CP) = SP − Profit = 100 − 20 = ₹80.

⇒ Ratio of Profit to Cost Price = 20 : 80.

⇒ Ratio = 1 : 4.

∴ The correct answer is 1 : 4.

Additional Information

Profit Percentage on Cost Price

Profit % = (Profit / CP) × 100. In this case, Profit % on CP = (20/80) × 100 = 25%.

Relationship between Profit % on SP and CP

If profit % on SP is x%, then Profit % on CP = [x / (100 − x)] × 100.

Loss on Selling Price

If a person incurs a loss on SP, then CP = SP + Loss. The ratio would be calculated as Loss : (SP + Loss).

Shortcut Trick

Part of tank emptied = (Given time) ÷ (Total time to empty)

Part emptied = 6 ÷ 36

Part emptied = 1/6

∴ The correct answer is 1/6.

Alternate Method

Given:

Total time to empty the tank = 36 hr

Time for which the pipe is open = 6 hr

⇒ Total work to empty the tank = 1 unit ⇒ Work done by pipe in 36 hr = 1 unit ⇒ Work done by pipe in 1 hr = 1/36 unit ⇒ Work done by pipe in 6 hr = (1/36) × 6 ⇒ Simplified fraction = 1/6

∴ The correct answer is 1/6.

Additional Information

Pipes and Cisterns

Work done by an outlet pipe (emptying) is always taken as negative, while work by an inlet pipe (filling) is taken as positive.

Efficiency and Time

Efficiency of a pipe is the part of the tank it can fill or empty in 1 unit of time. Efficiency = 1 ÷ Total Time.

Combined Work Formula

If pipe A fills in x hr and pipe B empties in y hr, net work in 1 hr = (1/x) − (1/y).

Shortcut Trick

Ratio of efficiency A : B = 1 : 4 (since time A : B = 4 : 1).

Total work = A's time × A's efficiency = 80 × 1 = 80 units.

Efficiency of C = Efficiency of (A + B) = 1 + 4 = 5 units/day.

Total efficiency of A + B + C = 1 + 4 + 5 = 10 units/day.

Required time = 80 ÷ 10 = 8 days.

∴ The correct answer is 8 days.

Alternate Method

Given:

Time taken by A = 80 days.

Time taken by A is 4 times that of B.

⇒ Time taken by B = 80 ÷ 4 = 20 days.

Time taken by C = Time taken by A and B together.

⇒ 1/C = 1/A + 1/B = 1/80 + 1/20 = (1 + 4) ÷ 80 = 5/80 = 1/16.

⇒ Time taken by C = 16 days.

Calculations:

⇒ Total efficiency of (A + B + C) = 1 + 4 + 5 = 10 units/day.

⇒ Time taken by A, B and C together = Total Work ÷ Total Efficiency

⇒ Time = 80 ÷ 10 = 8 days.

∴ The correct answer is 8 days.

Additional Information

Efficiency and Time Relationship

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

Work and Wages

Wages are distributed in the ratio of the work done by each person, which is the product of their efficiency and the time they worked.

Combined Work Formula

If two people finish a work in 'x' and 'y' days respectively, they together finish it in (x × y) ÷ (x + y) days.

Shortcut Trick

When distance is constant, the ratio of time taken is inversely proportional to the ratio of speeds.

Ratio of speeds (A : B) = 8 : 36 = 2 : 9

Ratio of time (A : B) = 1/2 : 1/9 = 9 : 2

∴ The correct answer is 9 : 2.

Alternate Method

Given:

Speed of A (S_A) = 8 km/hr

Speed of B (S_B) = 36 km/hr

Formula Used:

Speed × Time = Distance

Calculations:

⇒ Let the distance be D km.

⇒ Time taken by A (T_A) = D ÷ 8

⇒ Time taken by B (T_B) = D ÷ 36

⇒ Ratio of time taken (T_A : T_B) = (D / 8) : (D / 36)

⇒ T_A : T_B = 36 : 8

⇒ Dividing both by 4: T_A : T_B = 9 : 2

∴ The correct answer is 9 : 2.

Additional Information

Average Speed Formula

If a person covers the same distance at two different speeds x and y, the Average Speed = (2xy) ÷ (x + y).

Relative Speed

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

Speed-Time Relationship

Speed is inversely proportional to time for a constant distance (S ∝ 1/T). If speed increases by a factor of x/y, time decreases by a factor of y/x.

Shortcut Trick

When two objects start simultaneously and meet at a point, the time (t) spent traveling is constant for both.

Since Distance = Speed × Time, if time is constant, then Distance ∝ Speed.

Ratio of distances (D_A : D_B) = Ratio of speeds (S_A : S_B).

Ratio = 54 : 27 = 2 : 1.

∴ The correct answer is 2 : 1.

Alternate Method

Given:

Speed of A (S_A) = 54 km/hr

Speed of B (S_B) = 27 km/hr

Starting point of A = P, Starting point of B = Q, Meeting point = S.

Formula: Distance = Speed × Time

Let the time taken by A and B to meet at point S be t hours.

⇒ Distance covered by A to reach S (PS) = S_A × t = 54 × t

⇒ Distance covered by B to reach S (QS) = S_B × t = 27 × t

⇒ Ratio of distances = Distance PS : Distance QS

⇒ Ratio = (54 × t) : (27 × t)

⇒ Ratio = 54 : 27

⇒ Ratio = 2 : 1

∴ The correct answer is 2 : 1.

Additional Information

Relative Speed Concept

When two objects move towards each other, their relative speed is the sum of their individual speeds: S_rel = S₁ + S₂.

Constant Distance Relation

If distance is constant, Speed is inversely proportional to Time: S₁/S₂ = T₂/T₁.

Meeting Time Formula

Meeting Time = Initial Distance ÷ Relative Speed = (Distance PQ) ÷ (S_A + S_B).

Direct Proportionality

When time is constant, the ratio of distances is always equal to the ratio of their respective speeds: D₁/D₂ = S₁/S₂.

Shortcut Trick

Use the Ratio Method for successive discounts:

10% discount → 1/10 (MP = 10, SP = 9)

20% discount → 1/5 (MP = 5, SP = 4)

Combined Ratio (MP : SP) = (10 × 5) : (9 × 4) = 50 : 36

Dividing by the common factor 2, we get 25 : 18.

∴ The correct answer is 25 : 18.

Alternate Method

Given: First discount = 10%, Second discount = 20%.

Formula Used: Selling Price (SP) = Marked Price (MP) × (1 − d₁/100) × (1 − d₂/100)

⇒ Let the Marked Price (MP) be 100.

⇒ Selling Price after first discount = 100 − (10% of 100) = 100 − 10 = 90.

⇒ Final Selling Price (SP) after second discount = 90 − (20% of 90) = 90 − 18 = 72.

⇒ Ratio of Marked Price to Selling Price = 100 : 72.

⇒ Divide both sides by 4: 100 ÷ 4 : 72 ÷ 4 = 25 : 18.

∴ The correct answer is 25 : 18.

Additional Information

Successive Discount Formula

The single equivalent discount for two successive discounts of x% and y% is calculated using the formula: Total Discount = [x + y − (x × y)/100]%.

Relationship between MP and SP

The Marked Price (MP) is the price printed on the label, and Selling Price (SP) is the final price paid after all discounts are subtracted: SP = MP × (100 − d%)/100.

Percentage Change Logic

Discounts are effectively negative percentage changes applied sequentially to the base value (MP).

The correct answer is 'under the auspices of'.

Key Points

• The idiom 'under the auspices of' means with the backing, support, or patronage of a particular person or organization.
• In the given sentence, the construction of the bridge is being carried out with the patronage or support of the Chief Minister, making this the most appropriate fit.
• The other options provide meanings related to oversight or instruction rather than official support or patronage.

Therefore, the correct answer is 'Option 3'.

Complete Sentence: The bridge is being built here under the auspices of the chief minister of the state.

Additional Information

• Under the supervision of: Refers to a situation where someone is monitoring or overseeing the work to ensure it is done correctly.
• Under the guidance of: Refers to following the advice, leadership, or mentorship of an experienced person.
• Under the direction of: Refers to being managed, ordered, or controlled by someone in a position of authority.

The correct answer is: Defenseless.

Key Points

• The word 'vulnerable' means someone or something that is exposed to the possibility of being attacked or harmed, either physically or emotionally. (असुरक्षित)
• Example: Older people are often more vulnerable to certain diseases.
• 'Defenseless' refers to someone or something that lacks protection or is unable to defend itself against attack or harm. (रक्षाहीन)
• Example: The defenseless animals were unable to escape the approaching forest fire.
• Hence, we can infer that the synonym of 'vulnerable' is 'Defenseless'.

Therefore, the correct answer is: Defenseless.

Additional Information

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

• strong (मजबूत): Having the power to move heavy weights or perform other physically demanding tasks; not easily broken or damaged.
• Example: The bridge was built with strong steel cables to withstand high winds.
• secure (सुरक्षित): Fixed or fastened so as not to give way, become loose, or be lost; certain to remain safe.
• Example: Please ensure that all the windows are secure before you leave the house.
• Protected (संरक्षित): Kept safe from harm, injury, or attack through various measures or guards.
• Example: National parks are protected areas where wildlife can live without human interference.

The correct answer is governance.

Key Points

• In the provided sentence, the word governence is misspelled. The correct spelling is governance, which concludes with the suffix -ance rather than -ence.
• Linguistically, governance is derived from the Old French word governance, which itself stems from the Latin verb gubernare, meaning to steer or rule.
• The term refers to the action or manner of governing an organization, state, or specific sector. In this context, it pertains to the regulatory frameworks and oversight mechanisms required for data centres to operate sustainably.
• A common orthographic rule for nouns ending in the /əns/ sound involves checking the source verb; verbs like govern, maintain, and guide lead to nouns ending in -ance (governance, maintenance, guidance).

 Additional Information

• emissions:
• This refers to the discharge of substances, particularly carbon dioxide and other greenhouse gases, into the atmosphere.
• Monitoring carbon emissions is a critical component of environmental reporting for high-energy industries like AI computing.
• accountable:
• This adjective defines the obligation of an individual or organization to account for its activities and accept responsibility for them.
• Accountability in AI deployments is essential for ensuring transparency and preventing algorithmic bias or unethical data usage.
• deployments:
• In a technical context, this refers to the implementation and integration of software or hardware systems into a live environment.
• The phrase accountable AI deployments emphasizes the need for continuous ethical monitoring after Artificial Intelligence models are released to the public.

The correct answer is: Inevitable.

Key Points

• The word 'Inevitible' is a misspelt word; the correct spelling of this word is 'Inevitable', which means certain to happen and unable to be avoided. (अपरिहार्य)
• Example: It was inevitible that they would meet again.
• 'Inevitable' refers to something that is certain to happen and unavoidable. (अपरिहार्य/अनिवार्य)
• Example: The accident was the inevitable consequence of carelessness.
• Hence, we can infer that the misspelt word is 'Inevitable'.

Therefore, the correct answer is: Inevitable.

Additional Information

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

• Credible (विश्वसनीय): Able to be believed; convincing.
• Example: We need to find a credible witness for the trial.
• Invisible (अदृश्य): Unable to be seen.
• Example: Wind is invisible, but we can feel its effects.
• Plausible (प्रशंसनीय/सत्य प्रतीत होने वाला): Seeming reasonable or probable.
• Example: She gave a plausible explanation for her absence.

The correct answer is 'Option (3)' i.e. Decrease.

Key Points

• The word 'increase' means to become or make greater in size, amount, intensity, or degree. (बढ़ना)
• Example: The company aims to increase its annual sales by twenty percent this year.
• 'Decrease' refers to the act of making or becoming smaller or fewer in size, amount, intensity, or degree. (घटाना/कमी करना)
• Example: There has been a significant decrease in the number of smokers over the last decade.
• Hence, we can infer that the opposite of 'increase' is 'decrease'.

Therefore, the correct answer is- Decrease.

Additional Information

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

• Grow (बढ़ना/विकास करना): To undergo natural development by increasing in size and changing physically; to become larger or greater over time.
• Example: Children grow out of their clothes very quickly during their early years.
• Expand (विस्तार करना): To become larger or more extensive in scope, volume, or area.
• Example: The balloon began to expand as more air was pumped into it.
• Raise (बढ़ाना/उठाना): To lift or move something to a higher position; to increase the amount, level, or strength of something.
• Example: The charity event managed to raise a lot of money for the local hospital.

The correct answer is 'drought'.

Key Points

• The word 'drought' refers to a prolonged period of abnormally low rainfall, leading to a shortage of water. (सूखा)
• In the context of the sentence, villagers praying for rain indicates that they are experiencing a lack of water or a dry spell, which is accurately described by the term 'drought'.
• The other words 'draught', 'draft', and 'drift' do not relate to weather conditions or a lack of rain.

Therefore, the correct answer is 'Option 4'.

Complete Sentence: The villagers prayed for rain during the long summer drought.

Additional Information

• Draught (हवा का झोंका / घूँट): In British English, this refers to a current of cool air in a room or a single act of drinking.
• Draft (प्रारूप): A preliminary version of a piece of writing or a document.
• Drift (बहाव): A continuous slow movement from one place to another, often caused by water or air currents.

The correct answer is Option (2) i.e. kleptomania.

Key Points

• The phrase 'a mental condition where a person feels an uncontrollable urge to steal' refers to an impulse control disorder where the individual cannot resist stealing items, regardless of their value or need. (चोरी करने की तीव्र इच्छा)
• Example: Doctors identified that her habit of taking small items from the office was actually driven by an uncontrollable urge to steal.
• 'Kleptomania' is a recognized psychiatric condition characterized by the recurrent failure to resist impulses to steal objects that are not needed for personal use or for their monetary value. (चोरी करने की बीमारी)
• Example: Despite having a successful career and plenty of money, he was arrested for shoplifting due to his kleptomania.
• Hence, we can infer that the one-word substitution for the given condition is 'kleptomania'.

Therefore, the correct answer is- kleptomania.

Additional Information

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

• Pyromania (चीजों को आग लगाने की तीव्र इच्छा): An obsessive desire to set fire to things, often to relieve tension or for gratification.
• Example: The psychologist noted that the patient exhibited signs of pyromania, often feeling a rush of relief after seeing flames.
• Bibliomania (पुस्तकों के प्रति अत्यधिक लगाव): A passionate or obsessive enthusiasm for collecting and possessing books.
• Example: His bibliomania was evident when he bought three different editions of the same novel just for their unique covers.
• Anglomania (अंग्रेजी रीति-रिवाजों के प्रति अत्यधिक लगाव): An excessive admiration or obsession with English customs, manners, or products.
• Example: Her anglomania led her to adopt a British accent and spend all her vacations in London.

The correct answer is 'from'.

Key Points

• The preposition 'from' is used with 'made' when the original material undergoes a chemical or physical transformation to create the final product.
• In this sentence, bamboo is processed into pulp and then into paper; the original form of the bamboo is completely changed.
• Therefore, 'made from' is the grammatically correct choice for describing this manufacturing process.

Therefore, the correct answer is Option 2.

Complete Sentence: 'Good quality paper is made from bamboo.'

Additional Information

• Made of: This is used when the material stays the same and is still recognizable in the final product (e.g., 'The chair is made of wood').
• Made by: This is used to refer to the person, company, or method that produced the item (e.g., 'This cake was made by my mother').
• Made out of: Often used when an object has been repurposed or changed from one thing into another (e.g., 'He made a candle holder out of a wine bottle').

The correct answer is Will the new park be inaugurated by the mayor next week?.

Key Points

• The given sentence is an interrogative sentence in the Simple Future Tense. In the Active Voice, the structure follows: Will + Subject + V1 (Base Form) + Object + ...?
• In this specific sentence, the mayor acts as the subject, inaugurate is the main verb, and the new park is the direct object.
• To convert a Simple Future interrogative sentence into Passive Voice, the structure must be: Will + Object (as new subject) + be + V3 (Past Participle) + by + Subject (as new object)?
• Following this rule, the object the new park moves to the position immediately after the auxiliary verb will.
• The verb inaugurate is transformed into its passive form, which is be inaugurated (using the past participle).
• The original subject the mayor is introduced by the preposition by at the end of the clause.
• The time expression next week remains unchanged as it functions as an adverbial adjunct.

 Additional Information

• The incorrect options fail primarily due to tense inconsistency:
• Is the new park...: This represents the Simple Present Tense passive voice, which is used for habitual actions or general truths, not future events.
• Has the new park been...: This represents the Present Perfect Tense passive voice, which indicates an action that has already been completed in the recent past.
• Was the new park...: This represents the Simple Past Tense passive voice, used for actions that occurred and were completed at a specific time in the past.
• In voice transformation, the temporal meaning and aspect of the original sentence must be strictly preserved to maintain grammatical accuracy.

The correct answer is The secretary will have finalised the report before the chairman arrives for the meeting.

Key Points

• The original sentence is in the Passive Voice of the Future Perfect Tense. This is identified by the structure will have been + past participle (V3).
• In Passive Voice, the focus is on the Object (the report), while in Active Voice, the focus shifts to the Subject or doer of the action (the secretary).
• The standard formula for Future Perfect Tense in Active Voice is: Subject + will + have + past participle (V3) + Object.
• To convert, the agent the secretary moves to the subject position, the verb will have been finalised changes to will have finalised, and the patient the report moves to the object position.
• The subordinate time clause (before the chairman arrives for the meeting) remains unchanged as it provides the temporal context for the completion of the main action.

 Additional Information

• Understanding Tense Mismatch in other options:
• Simple Present Tense: Used in option 2 (finalises). It denotes regularity or habitual actions, which contradicts the specific future completion indicated in the original sentence.
• Past Perfect Tense: Used in option 3 (had finalised). This tense is used to describe an action that was completed before another past action, which changes the timeline from future to past.
• Past Continuous Tense: Used in option 4 (was finalising). This indicates an ongoing action in the past, failing to convey the sense of completion inherent in the perfect tense.
• General Rule for Active to Passive in Future Perfect:
• Active: Sub + will + have + V3 + Obj.
• Passive: Obj + will + have + been + V3 + by + Sub.

The correct answer is Option 3.

Key Points

• The error lies in the use of the preposition among in the third part of the sentence.
• While among is generally used for more than two items in a vague or collective sense, between is used when referring to distinct, individual entities, regardless of the number.
• In the given sentence, the relationship is being established between three specific, individual components: an organism, its habitat, and the predators.
• When expressing a relationship between distinct items, the preposition between is grammatically appropriate.
• Therefore, the phrase among an organism, its habitat, should be corrected to between an organism, its habitat,.

Therefore, the correct answer is among an organism, its habitat,.

Correct Sentence: 'In their study, they tried to find out the relationship between an organism, its habitat, and the predators present there.'

Additional Information

• Option 1: In their study, they tried to – This part correctly introduces the subject and the action in the past tense.
• Option 2: find out the relationship – This part correctly uses the phrasal verb find out to mean discover or investigate.
• Option 4: and the predators present there. – This part correctly lists the final entity in the relationship and uses there to refer back to the habitat.

The correct answer is 'in'.

Key Points

• In English grammar, certain adjectives and verbs are followed by fixed prepositions.
• The adjective absorbed is followed by the preposition in when it signifies being very interested, deeply involved, or engrossed in an activity or subject.
• The sentence indicates that Mahasweta is giving her full attention to the reading of scriptures, which requires the use of in.

Therefore, the correct answer is Option 3.

Complete Sentence: 'Mahasweta is completely absorbed in reading scriptures.'

Additional Information

• Option 1 (at): This is typically used for precise locations, times, or specific targets (e.g., 'at the station', 'at 5 o'clock') and does not pair with 'absorbed'.
• Option 2 (with): While we use with for tools or associations (e.g., 'occupied with'), it is grammatically incorrect when used with 'absorbed' in the context of mental focus.
• Option 4 (01): This is a numerical value and is irrelevant to the grammatical structure of the sentence.

The correct answer is Option 2.

Key Points

• The paragraph describes a nostalgic reflection on childhood and the blending of memories during the holiday season.
• S1 sets the scene by mentioning the narrator was eleven and living on a farm in Cape Breton.
• Sentence D is the first sentence to follow S1 because it provides immediate context to the location mentioned:
• 'My family had been there for a long, long time and so it seemed had I.' (The word 'there' refers back to the farm in Cape Breton).
• Sentence C follows as it continues the reflection on time:
• 'And much of that time seems like the proverbial yesterday.'
• Sentence A is the third sentence as it introduces a transition from the past to the present moment of the narration:
• 'Yet when I speak on this Christmas 1977, I am not sure how much I speak with the voice of that time or how much in the voice of what I have since become.'
• Sentence B follows A because it expands on the narrator's uncertainty regarding their memory:
• 'And I am not sure how many liberties I may be taking with the boy I think I was.'
• S2 provides the concluding thought, explaining that Christmas is a time where past and present are often imperfectly blended.
• The correct sequence is DCAB.

Coherent paragraph after rearrangement:

'I am speaking here of a time when I was eleven and lived with my family on our small farm on the west coast of Cape Breton. My family had been there for a long, long time and so it seemed had I. And much of that time seems like the proverbial yesterday. Yet when I speak on this Christmas 1977, I am not sure how much I speak with the voice of that time or how much in the voice of what I have since become. And I am not sure how many liberties I may be taking with the boy I think I was. For Christmas is a time of both past and present and often the two are imperfectly blended.'

The correct answer is Option 1.

Key Points

• The paragraph describes a method to listen to one's heartbeat more clearly than by just lying on a pillow.
• Sentence D follows S1: Sentence S1 mentions hearing 'it' (the heartbeat) through a pillow. Sentence D provides a contrast, stating there is a place where it can be heard 'even better than that', making it the logical transition from the opening statement.
• 'But I know that there is a place where you can hear it even better than that.'
• Sentence A follows D: After claiming there is a better way to hear the heartbeat, the author introduces the procedure. Sentence A acts as the instructional bridge.
• 'Here is what you do.'
• Sentence C is the third sentence: It describes the first physical step of the process introduced in Sentence A.
• 'You ease yourself into a tub of water, you ease yourself down.'
• Sentence B is the fourth sentence: After getting into the tub, the next logical action is to settle down and let the water become still.
• 'You lie back and wait for the ripples to smooth away.'
• Sentence S2 concludes the sequence: The final fixed sentence completes the action by describing the moment of submergence to finally 'listen' as promised in D.
• The correct sequence is DACB.

Coherent paragraph after rearrangement:

'Sometimes you hear it through the pillow at night. But I know that there is a place where you can hear it even better than that. Here is what you do. You ease yourself into a tub of water, you ease yourself down. You lie back and wait for the ripples to smooth away. Then you take a deep breath, and slide your head under, and listen for the playfulness of your heart.'

The correct answer is Option 1.

Key Points

• The original sentence contains an error in the idiomatic expression 'in a view to providing.'
• The correct idiom is 'with a view to,' which means with the intention or hope of doing something.
• In English grammar, the phrase 'with a view to' is always followed by a gerund (the -ing form of the verb) rather than the base form of the verb.
• Therefore, the phrase 'with a view to providing' is the grammatically accurate replacement for the underlined part.

Therefore, the correct answer is Option 1.

Correct Sentence: 'They moved to a quieter neighbourhood with a view to providing their children with a better environment.'

Additional Information

• Option 2: 'for the purpose of providing' – While this is grammatically correct and conveys a similar meaning, 'with a view to' is the specific idiomatic correction intended for the error 'in a view to.'
• Option 3: 'in order to provide' – This is also grammatically correct, but it uses the infinitive form (to provide) instead of the gerund form (providing) used in the original sentence.
• Option 4: 'No improvement required' – This is incorrect because the original phrase 'in a view to' is not a standard English idiom.