SSC GD Constable 2026 Official Paper (Held On 31 May, 2026 Shift 3) (Previous Year Paper)

Pattern followed here is,

Hence, the correct answer is “Option 2”.

For 'CJ' related to 'YC':

For 'TH' related to 'PA':

Applying the same logic to 'PX':

Thus, PX is related to LQ.

Hence, the correct answer is 'Option 1'.

For the set '(BW, YQ, VK)':

For the set '(JZ, GT, DN)':

Applying the same logic to the set '(HI, EC, BW)':

Thus, the set (HI, EC, BW) follows the same logic as the given sets.

Hence, the correct answer is 'Option 4'.

The given year is 2000.

To determine if 2000 is a leap year, we divide it by 400:

2000 ÷ 400 = 5

Since 2000 is perfectly divisible by 400, it is a leap year. Therefore, February in the year 2000 had 29 days.

Now, let us list the number of days for the months mentioned in the question:

• Number of days in January = 31
• Number of days in April = 30
• Number of days in February (Leap Year) = 29
• Number of days in November = 30

Total sum of days = 31 + 30 + 29 + 30

Total sum = 120

Hence, the sum of the number of days in these months is 120.

Therefore, the correct answer is 120.

Given reference date is 19 April 2013, which was a Friday.

We need to find the day on 19 September 2013.

Number of days between 19 April and 19 September in the year 2013:

• April: 30 − 19 = 11 days
• May: 31 days
• June: 30 days
• July: 31 days
• August: 31 days
• September: 19 days (up to the target date)

Total days = 11 + 31 + 30 + 31 + 31 + 19 = 153 days

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

153 ÷ 7 = 21 weeks and 6 odd days (as 153 = 21 × 7 + 6)

Now, add the number of odd days to the given day:

Friday + 6 days = Thursday

Alternatively, adding 6 days is the same as subtracting 1 day (7 − 1 = 6):

Friday − 1 day = Thursday

Hence, the day on 19 September 2013 was Thursday.

Therefore, the correct answer is Thursday.

7 friends P, Q, R, S, T, U and V are sitting around a circular table facing towards the centre (not necessarily in the same order).

1. U is not the immediate neighbour of P.
2. T is second to the left of P.
3. R and T are immediate neighbours.
4. S is third to the left of R.
5. Q is the immediate neighbour of S and T.

U is sitting fourth to the left of R.

Hence, the correct answer is “Option 1”.

Formula:

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

Sum = 12 + 16 + 20 + 24 + 28 = 100

Total count = 5

Average = 100 ÷ 5 = 20

Hence, the correct answer is “Option 3”.

The given time is 2:45.

To find the mirror image, subtract the hours and minutes from 11:60:

Hours: 11 − 2 = 9

Minutes: 60 − 45 = 15

So, the mirror image of 2:45 is 9:15.

Hence, the mirror image of the clock at 2:45 is 9:15.

Alternate Method

The formula for finding the mirror image is:

Mirror Image = 11:60 − Actual Time

Mirror Image = 11:60 − 2:45 = 9:15

Hence, the correct answer is 9:15.

The logic followed here is:

Logic: Second Number = First Number × 2

For the first pair 168 : 336

⇒ 168 × 2 = 336.

For the second pair 145 : 290

⇒ 145 × 2 = 290.

Applying the same logic to the third pair

130 : ?

⇒ 130 × 2 = 260.

Hence, the correct answer is 'Option 2'.

The least possible Venn diagram for the given statements is:

(I) All roses are plants **→ Follow (**Since all roses are flowers and all flowers are plants, the roses circle is entirely contained within the plants circle.)

(II) Some plants are roses **→ Follow (**Because all roses are plants, the region belonging to roses is a subset of the plants region, confirming that at least some plants are roses.)

Both conclusions I and II follow.

Hence, the correct answer is “Option 2”.

The logic followed here is,

Hence, the correct answer is 'Option 3'.

The logic followed here is:

Logic: Second Number = (First Number)² + (First Number + 1)

For the first pair 12 : 157

⇒ (12)² + (12 + 1)

⇒ 144 + 13 = 157.

For the third pair 23 : 553

⇒ (23)² + (23 + 1)

⇒ 529 + 24 = 553.

Applying the same logic to the second pair 17 : ?

⇒ (17)² + (17 + 1)

⇒ 289 + 18 = 307.

Hence, the correct answer is 'Option 2'.

Given: _JV_IBJ_H_BJ___I

(1) B, H, V, I, V, H → 

BJVHI/ BJVHI/ BJVHI (Repeat the pattern BJVHI)

(2) Y, H, V, H, V, H → 

YJVHI/ BJVHH/ BJVHI

(3) B, H, V, V, I, H → 

BJVHI/ BJVHV/ BJIHI

(4) Y, H, V, V, H, I → 

YJVHI/ BJVHV/ BJHII

Hence, the correct answer is “Option 1”.

Seven persons, A, B, C, D, E, F and G, sit in a linear row and face towards the south.

1. Only four persons sit between A and F.
2. A doesn't sit at the extreme end.
3. B sits third to the left of D, who doesn't sit adjacent to F.
4. Only one person sits between D and G.
5. G doesn't sit adjacent to B and A.
6. E sits to the right of C.

F sits fourth to the right of C.

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 1”.

 First Pair: KM520 : MQ660

Third Pair: LO125 : NS265

Similarly,

For the Second Pair: ? : DT820 

Hence, the correct answer is 'Option 3'.

The logic followed here is:

Logic: Second Number = First Number + 45

For the third pair 1040 : 1085

⇒ 1040 + 45 = 1085.

For the second pair 1778 : 1823

⇒ 1778 + 45 = 1823.

Applying the same logic to the first pair

2191 : ?

⇒ 2191 + 45 = 2236.

Hence, the correct answer is 'Option 4'.

The logic followed here is:

Logic: Second Number = First Number + 230

For the first pair 611 : 841

⇒ 611 + 230 = 841.

For the second pair 869 : 1099

⇒ 869 + 230 = 1099.

Applying the same logic to the third pair

? : 740

⇒ ? + 230 = 740

⇒ ? = 740 − 230

⇒ 510.

Hence, the correct answer is 'Option 4'.

The pattern observed is: (Sum of positional values of letters) − 1.

RAID is coded as 31 →

Sum of positional values = 18 + 1 + 9 + 4 = 32

Code = 32 − 1 = 31

AIM is coded as 22 →

Sum of positional values = 1 + 9 + 13 = 23

Code = 23 − 1 = 22

Similarly, let's find the code for MATE:

Sum of positional values = 13 + 1 + 20 + 5 = 39

Code = 39 − 1 = 38

Hence, the correct answer is “Option 1”.

ELECT is coded as FMGFX →

COILS is coded as DPKOW →

Similarly,

Let's find the code for CREED:

Hence, the correct answer is “Option 1”.

The correct answer is Not fixed by the constitution.

Key Points

• Article 76 of the Indian Constitution establishes the office of the Attorney General of India (AGI), who serves as the highest law officer in the country.
• The Constitution of India does not provide a fixed tenure or term of office (such as 5 or 6 years) for the Attorney General.
• The AGI is appointed by the President of India and holds office during the pleasure of the President, which means they can be removed at any time without a specific process.
• There are no specific grounds for removal mentioned in the Constitution for the AGI, unlike the procedure for judges of the Supreme Court.
• Conventionally, the Attorney General resigns when the Council of Ministers (the Government) resigns or is replaced, as the appointment is made based on the advice of the Union Cabinet.

 Additional Information

• Qualifications and Appointment:
• To be appointed as AGI, a person must be qualified to be appointed as a Judge of the Supreme Court.
• This requires being a Citizen of India and having served as a High Court Judge for at least 5 years or as an Advocate of a High Court for 10 years.
• Functions and Rights:
• The AGI provides legal advice to the Government of India on matters referred by the President.
• Under Article 88, the AGI has the right to speak and participate in the proceedings of both Houses of Parliament (Lok Sabha and Rajya Sabha) but does not have the right to vote.
• They have the right of audience in all courts across the territory of India while performing official duties.
• Remuneration:
• The remuneration of the AGI is not fixed by the Constitution; it is determined by the President of India.

The correct answer is Kutum Bihu.

Key Points

• Rongali Bihu, also known as Bohag Bihu, is the most prominent festival celebrated in Assam, marking the beginning of the Assamese New Year and the arrival of the spring season.
• The festival spans seven days, known as Xaat Bihu, and is deeply rooted in the agrarian culture of the state, celebrating the onset of the seeding time.
• Kutum Bihu is traditionally observed as the third day of the festival sequence. The term Kutum in the Assamese language signifies relatives or kinfolk.
• On this day, people focus on maintaining social ties by visiting the homes of their extended families, in-laws, and close friends.
• The core tradition involves the exchange of gifts and hosting elaborate meals, where traditional delicacies like Jolpan, Pitha, and Laroo are served to guests.
• This phase of the festival serves to strengthen communal harmony and familial bonds after the personal and spiritual rituals of the preceding days.

 Additional Information

• Goru Bihu:
• Observed on the last day of the outgoing year (Sankranti), it is dedicated to the worship of cattle.
• Cows are washed with Maha-Haladhi (turmeric and black gram) and stroked with sprigs of Dighaloti and Makhioti plants for protection.
• Manuh Bihu:
• The first day of the New Year, where people take ceremonial baths and seek blessings from elders.
• It is characterized by the presentation of the Bihuwan (the traditional Gamosa) as a token of high esteem and affection.
• Bohagi Bihu:
• This is a general nomenclature for the entire spring festival, often used interchangeably with Rongali Bihu to denote the month-long festivities of dance and folk music.

The correct answer is Rajasthan.

Key Points

• Ghoomar is the most iconic folk dance of Rajasthan, traditionally performed by women wearing flowing Ghaghara (skirts) that create a graceful swirling effect during pirouettes.
• Historically, Ghoomar was developed by the Bhil tribe to perform rituals dedicated to the Goddess Saraswati, but it was subsequently embraced by the Rajput royalty and is now a staple of various festive occasions like Teej and Gangaur.
• Kalbelia is a high-energy dance form performed by the Kalbelia community, who were traditionally known as nomadic snake charmers; the dance movements are designed to replicate the lithe, serpentine motions of a cobra.
• The Kalbelia folk songs and dances of Rajasthan gained international recognition when they were inscribed on UNESCO’S Representative List of the Intangible Cultural Heritage of Humanity in 2010.
• Musical accompaniment for these dances involves traditional Rajasthani instruments like the Been (a woodwind instrument), Dholak, Manjira (cymbals), and Khanjari, which provide the fast-paced rhythmic backbone for the performances.
• While Ghoomar focuses on feminine grace and rhythmic circles, Kalbelia is known for its incredible physical flexibility and the use of black costumes embroidered with intricate silver patterns.

 Additional Information

• Gujarat:
• Famed for Garba, a circular dance performed during the nine nights of Navratri to honor Goddess Durga.
• Another prominent form is Dandiya Raas, where dancers use polished wooden sticks to create rhythmic percussion while moving in complex patterns.
• Himachal Pradesh:
• Well-known for the Nati dance, which holds a Guinness World Record for being one of the largest folk dances in terms of participants.
• Other regional forms include Dangi and Chhanak Chham, often performed during local fairs like the Kullu Dussehra.
• Sikkim:
• Home to the Singhi Chham or the Snow Lion Dance, where performers dress as the mythical snow lion, a cultural symbol of the Himalayas.
• The Yak Chham is another traditional dance that pays tribute to the yak, an animal vital to the livelihood of the people in the Eastern Himalayas.

The correct answer is Paulo Coelho.

Key Points

• Paulo Coelho is a highly influential Brazilian novelist and lyricist, born on August 24, 1947, in Rio de Janeiro. He is celebrated for his philosophical and symbolic narratives that explore spiritual journeys.
• The Alchemist (originally titled O Alquimista in Portuguese) was first published in 1988. It follows the story of an Andalusian shepherd named Santiago who travels from Spain to the Egyptian pyramids in search of a hidden treasure.
• The novel is built around the concept of a Personal Legend, a term Coelho uses to describe an individual's true destiny or life's purpose. The narrative posits that when a person wants something, the entire universe conspires in helping them to achieve it.
• The book has achieved unparalleled global success, having been translated into more than 80 languages. It holds the Guinness World Record for the most translated book by a living author and has sold over 65 million copies worldwide.
• The story was originally inspired by Jorge Luis Borges's short story titled The Tale of Two Dreamers and reflects themes of alchemy, omens, and the Soul of the World.

 Additional Information

• Dan Brown:
• An American author known for his Robert Langdon thriller series, including The Da Vinci Code and Angels & Demons.
• His work frequently involves symbology, secret societies like the Illuminati, and historical conspiracies.
• Gabriel García Márquez:
• A Colombian novelist and Nobel Prize in Literature winner (1982).
• He is a foundational figure in the magical realism genre, most famous for his 1967 novel One Hundred Years of Solitude.
• Khaled Hosseini:
• An Afghan-American novelist and physician.
• He is best known for his debut novel The Kite Runner (2003) and A Thousand Splendid Suns, which depict Afghan history and family dynamics.

The correct answer is Liver and pancreas.

Key Points

• The small intestine, specifically the duodenum, is the primary site for the chemical digestion of food. It receives vital digestive juices from two major accessory glands: the liver and the pancreas.
• The liver secretes bile juice, which reaches the duodenum through the common bile duct. Bile contains no enzymes but is essential for the emulsification of fats, breaking down large fat globules into smaller micelles to increase the surface area for enzyme action.
• The pancreas functions as a major secretory organ that produces pancreatic juice. This juice contains crucial enzymes such as trypsinogen, chymotrypsinogen, amylases, lipases, and nucleases, which are necessary for digesting proteins, carbohydrates, and fats.
• Both the bile duct and the pancreatic duct join together to form the common hepatopancreatic duct, which opens into the duodenum, guarded by the sphincter of Oddi.
• The secretions from these organs are highly alkaline, helping to neutralize the acidic chyme received from the stomach, creating an optimal pH (around 7.8) for intestinal enzymes to function.

 Additional Information

• Liver
• It is the largest gland in the human body, weighing approximately 1.2 to 1.5 kg in an adult.
• Beyond digestion, it performs functions like detoxification, protein synthesis, and the storage of glycogen, Vitamin A, and Vitamin D.
• Pancreas
• It is a heterocrine gland, meaning it has both exocrine functions (secreting digestive enzymes) and endocrine functions (secreting hormones like insulin and glucagon).
• The endocrine part consists of the Islets of Langerhans, which regulate blood sugar levels.
• Excluded Organs
• Kidneys: Part of the urinary system, responsible for filtering blood and removing nitrogenous wastes like urea.
• Spleen: A lymphatic organ that acts as a reservoir for erythrocytes (RBCs) and filters the blood for the immune system.
• Lungs: Central organs of the respiratory system designed for the exchange of oxygen and carbon dioxide.

The correct answer is Morarji Desai.

Key Points

• Morarji Desai served as the 4th Prime Minister of India from 1977 to 1979, leading the first non-Congress government under the Janata Party banner.
• He is the only Indian citizen to have been conferred with the highest civilian awards of both India and Pakistan: the Bharat Ratna and the Nishan-e-Pakistan.
• In 1990, the Government of Pakistan honored him with the Nishan-e-Pakistan for his significant efforts in fostering peace and improving diplomatic ties between the two South Asian nations.
• The Government of India awarded him the Bharat Ratna in 1991, recognizing his immense contribution to Indian politics and his role as a freedom fighter and administrator.
• His tenure as Prime Minister was marked by the dismantling of the restrictive structures imposed during the Emergency (1975−1977) and a commitment to Gandhian principles and fiscal discipline.

 Additional Information

• Atal Bihari Vajpayee:
• A founding member of the Bharatiya Janata Party (BJP), he served three terms as Prime Minister and received the Bharat Ratna in 2015.
• He is credited with making India a nuclear power through the Pokhran-II tests in 1998.
• Lal Bahadur Shastri:
• The 2nd Prime Minister of India who led the country during the 1965 Indo-Pakistani War and popularized the slogan Jai Jawan Jai Kisan.
• He was the first person to be posthumously awarded the Bharat Ratna in 1966.
• P. V. Narasimha Rao:
• Served as the 9th Prime Minister and is celebrated for implementing the 1991 Economic Reforms (LPG model) that transformed the Indian economy.
• Financial Milestone: Morarji Desai holds the record for presenting ten Union Budgets, the highest number by any Indian Finance Minister in history.

The correct answer is Bhagirathi.

Key Points

• The Tehri Dam is a multi-purpose rock and earth-fill embankment dam located on the Bhagirathi River near Tehri in the state of Uttarakhand.
• Standing at a height of 260.5 meters (855 feet), it is the highest dam in India and ranks among the tallest dams in the world.
• The dam serves as the primary component of the Tehri Hydropower Complex, which includes the Tehri Dam & Hydroelectric Project (1,000 MW) and the Koteshwar Hydroelectric Project.
• The reservoir created by the dam, known as Tehri Lake, has a surface area of approximately 52 square kilometers and provides water for irrigation to 270,000 hectares of land.
• The project also supplies significant amounts of drinking water to the urban populations of Delhi and Uttar Pradesh.
• Construction of the dam officially began in 1978 with financial and technical assistance from the USSR, and the first unit was commissioned in 2006.

 Additional Information

• Yamuna River:
• It is the longest tributary of the Ganga and originates from the Yamunotri Glacier in the Bandarpunch peaks.
• Significant structures include the Lakhwar Dam and the Dakpathar Barrage.
• Ganga River:
• The Bhagirathi is considered the source stream of the Ganga, which officially takes the name Ganga after meeting the Alaknanda at Devprayag.
• The Farakka Barrage is a major structure located on this river in West Bengal.
• Godavari River:
• Known as the Dakshin Ganga, it is the largest river system in Peninsular India.
• Key projects include the Jayakwadi Dam in Maharashtra and the Sriram Sagar Project in Telangana.

The correct answer is 1997.

Key Points

• Mahesh Bhupathi etched his name in history by becoming the first Indian to win a Grand Slam title in 1997.
• He achieved this historic feat in the Mixed Doubles category at the French Open (Roland Garros) held in Paris.
• Bhupathi partnered with Japanese player Rika Hiraki to clinch the title, defeating the top-seeded American pair of Patrick Galbraith and Lisa Raymond in the final with a score of 6-4, 6-1.
• This victory was a landmark moment for Indian Tennis, as it broke the barrier for Indian athletes on the global professional circuit.
• Following this success, he reached the World No. 1 ranking in doubles in 1999, further solidifying his status as a legendary sportsman.

 Additional Information

• Mahesh Bhupathi:
• Born on June 7, 1974, in Chennai, he is one of the most decorated doubles players with a total of 12 Grand Slam titles.
• He won 4 Men's Doubles titles and 8 Mixed Doubles titles throughout his career.
• He is famous for his partnership with Leander Paes, known as the 'Indian Express', together winning three Grand Slam titles and reaching the finals of all four majors in 1999.
• He was awarded the Padma Shri in 2001 and the Arjuna Award in 1995 for his contributions to sports.
• Grand Slam Context:
• The French Open is the only Grand Slam tournament played on clay courts, known for its slow surface and high bounce.
• The other three Grand Slam events are the Australian Open (Hard court), Wimbledon (Grass court), and the US Open (Hard court).
• Bhupathi's success paved the way for other Indian stars like Sania Mirza, who became the first Indian woman to win a Grand Slam title in 2009.

The correct answer is Companion cells.

Key Points

• Xylem is a complex permanent tissue in vascular plants primarily responsible for the conduction of water and minerals from the roots to the aerial parts of the plant.
• The xylem tissue is composed of four distinct types of cells: Tracheids, Vessels (or tracheae), Xylem parenchyma, and Xylem fibers.
• Tracheids and Vessels are the main water-conducting elements; they are dead at maturity and possess thick, lignified cell walls to withstand high internal pressure.
• Xylem parenchyma is the only living component of the xylem tissue, primarily functioning in the storage of food materials (starch) and the lateral conduction of water.
• Companion cells are specialized parenchymatous cells that are thin-walled and contain dense cytoplasm and a prominent nucleus.
• Unlike the components of the xylem, Companion cells are fundamentally associated with Sieve tube elements within the Phloem tissue, which is responsible for the translocation of organic nutrients.

 Additional Information

• Phloem Tissue Components:
• Sieve Tubes: Long, tube-like structures that lack a nucleus at maturity and transport photosynthates.
• Companion Cells: Regulate the metabolic activities of sieve tubes and help maintain the pressure gradient required for nutrient transport.
• Phloem Parenchyma: Living cells that store resins, latex, and mucilage.
• Phloem Fibers: Also known as bast fibers, these are dead sclerenchymatous cells providing mechanical strength.
• Functional Differences:
• Xylem transport is generally unidirectional (upward movement).
• Phloem transport is bidirectional, moving sugars from leaves (source) to storage organs or growing parts (sink).

The correct answer is Third Summit.

Key Points

• The Third BIMSTEC Summit was held in Nay Pyi Taw, Myanmar, on March 4, 2014, where the heads of state decided to provide a permanent physical structure to the organization.
• The leaders signed the Memorandum of Association (MoA) on the establishment of the BIMSTEC Secretariat during this summit to enhance institutional capacity and coordination.
• Following this decision, the BIMSTEC Secretariat was formally inaugurated in Dhaka, Bangladesh, on September 13, 2014.
• The establishment of the Secretariat marked a shift from a purely consultative mechanism to a more structured inter-governmental organization with a dedicated budget and staff.
• The Secretariat is responsible for facilitating the implementation of projects, managing the BIMSTEC calendar, and supporting various technical and ministerial meetings.

 Additional Information

• First Summit:
• Held in Bangkok, Thailand, in 2004, it was the inaugural summit that upgraded the grouping from ministerial to summit level.
• It focused on establishing the Framework Agreement on the BIMSTEC Free Trade Area (FTA).
• Second Summit:
• Conducted in New Delhi, India, in 2008, focusing on poverty alleviation and regional connectivity.
• It emphasized cooperation in the fields of energy security and counter-terrorism.
• Fourth Summit:
• Organized in Kathmandu, Nepal, in 2018, with the theme Towards a Peaceful, Prosperous and Sustainable Bay of Bengal Region.
• It resulted in the signing of the Memorandum of Understanding on the BIMSTEC Grid Interconnection.
• BIMSTEC Overview:
• Founded in 1997 through the Bangkok Declaration, it comprises seven members: Bangladesh, Bhutan, India, Myanmar, Nepal, Sri Lanka, and Thailand.
• Sumith Nakandala from Sri Lanka served as the first Secretary General of the permanent Secretariat.

The correct answer is 2010.

Key Points

• The Women's Kabaddi discipline was officially introduced as a competitive event for the first time in the Asian Games during the 16th edition held in Guangzhou, China, in 2010.
• The Indian Women's Team scripted history by clinching the first-ever gold medal in the sport, defeating Thailand in the final with a score of 28−14.
• This victory established India's absolute dominance in Kabaddi on the continental stage, as both the Men's and Women's teams secured Gold Medals in the same year.
• The team was spearheaded by prominent players like Mamtha Poojary, who played a significant role in India's gold-winning campaigns in both 2010 and the subsequent 2014 Incheon Games.
• Prior to the 2010 debut, Kabaddi was predominantly a male-dominated sport in international multi-sport events, making this gold medal a landmark moment for women's sports in India.

 Additional Information

• Chronology of Kabaddi in Asian Games:
• Men's Kabaddi: It was introduced much earlier as a medal sport at the 1990 Beijing Asian Games, where India won the inaugural gold.
• 2014 Edition: India successfully defended its title at Incheon, South Korea, by defeating Iran in a closely contested final.
• 2018 Edition: At the Jakarta-Palembang Games, the Indian women's team's winning streak ended as they settled for the Silver Medal after losing to Iran.
• 2022 Edition: Held in Hangzhou (in 2023), India regained the Gold Medal by defeating Chinese Taipei.
• Governing Bodies and Rules:
• The Amateur Kabaddi Federation of India (AKFI) is the national body that governs the sport, while the International Kabaddi Federation (IKF) manages it globally.
• For women's international matches, the court dimensions are 12 meters × 8 meters, and the match duration consists of two halves of 15 minutes each.

The correct answer is Calcium.

Key Points

• In 1866, the English scientist John Newlands arranged the then-known 56 elements in increasing order of their atomic masses.
• He observed that the chemical and physical properties of every eighth element were a repetition of the properties of the first element, similar to the notes in a musical octave.
• This classification, known as Newlands Law of Octaves, was found to be applicable and valid only up to Calcium (atomic number 20).
• For elements heavier than Calcium, the periodicity of properties broke down, as every eighth element no longer matched the properties of the first element in the vertical column.
• The law worked well only with lighter elements and failed to account for the transitional behavior of heavier elements.

 Additional Information

• Limitations of Newlands Law:
• Limited Scope: Newlands assumed only 56 elements existed in nature and that no more would be discovered, which was later proven wrong.
• Incorrect Grouping: In an attempt to fit elements into his table, he placed dissimilar elements like Cobalt and Nickel in the same column as halogens like Fluorine and Chlorine.
• Noble Gases: The discovery of Noble Gases (He, Ne, Ar) later made the law irrelevant because the eighth element was no longer the one with similar properties.
• Thorium:
• It was the 56th and final element in Newlands periodic table.
• Hydrogen:
• It was the first element in the arrangement due to its lowest atomic mass.
• Potassium:
• While Potassium is an alkali metal that follows the octave rule relative to Sodium, the overall systematic application of the law ceased immediately after Calcium.

The correct answer is M. S. Swaminathan.

Key Points

• M. S. Swaminathan (1925–2023) was a renowned agronomist and geneticist who is widely celebrated as the Father of the Green Revolution in India.
• He was posthumously conferred with the Bharat Ratna, India’s highest civilian honor, in 2024 for his transformative role in ensuring food security for the nation.
• During the 1960s, he spearheaded the introduction of High-Yielding Varieties (HYV) of wheat and rice, which dramatically increased agricultural productivity and helped India overcome the ship-to-mouth crisis.
• He served as the Director General of the Indian Council of Agricultural Research (ICAR) and later the International Rice Research Institute (IRRI), contributing extensively to agricultural research and policy.
• Swaminathan also headed the National Commission on Farmers (2004), where he proposed the Swaminathan Formula for determining the Minimum Support Price (MSP) at 50 percent above the cost of production (C2 + 50%).

 Additional Information

• Verghese Kurien:
• Known as the Father of the White Revolution in India.
• He was the brain behind Operation Flood, which transformed India from a milk-deficient nation into the world’s largest milk producer.
• He founded the National Dairy Development Board (NDDB) and the brand Amul.
• Norman Borlaug:
• Recognized as the Father of the Green Revolution globally.
• An American biologist who won the Nobel Peace Prize in 1970 for developing semi-dwarf, high-yield, disease-resistant wheat varieties.
• C. Subramaniam:
• Served as the Union Minister for Food and Agriculture during the mid-1960s.
• He provided the critical political leadership and administrative framework that allowed the scientific advancements of the Green Revolution to be implemented successfully.
• He was awarded the Bharat Ratna in 1998.

The correct answer is Financial aid to economically weaker women.

Key Points

• The Subhadra Yojana is a landmark social welfare initiative launched by the Government of Odisha to promote gender equality and the financial independence of women in the state.
• The primary objective of the scheme is to provide direct financial assistance to women belonging to economically weaker sections, enabling them to meet their personal and entrepreneurial needs.
• The scheme targets approximately 1 crore women across Odisha, focusing on those in the age group of 21 to 60 years who do not fall under high-income brackets or government employment.
• Each eligible beneficiary receives a total financial benefit of Rs. 50,000 over a period of five years, which is deposited directly into their Aadhaar-linked bank accounts.

 Additional Information

• Launch Details:
• The scheme was officially launched by Prime Minister Narendra Modi on September 17, 2024, in Bhubaneswar, marking his 74th birthday.
• The initiative is part of the state government's commitment to fulfill its election manifesto regarding women's welfare.
• Disbursement Mechanism:
• The annual assistance of Rs. 10,000 is paid in two equal installments of Rs. 5,000 each.
• The first installment is typically released on Rakhi Purnima and the second on International Women's Day (March 8).
• The use of Direct Benefit Transfer (DBT) and Subhadra Cards ensures transparency and prevents leakages in the system.
• Exclusion Criteria:
• To ensure the benefit reaches the most vulnerable populations, women from families paying income tax, or those receiving more than Rs. 1,500 per month from other government schemes, are generally excluded.

The correct answer is Agricultural diversification and higher surplus.

Key Points

• The introduction of the Persian Wheel (known as Saqiya or Araghatta) revolutionized the lifting of water from wells, which led to a massive increase in the efficiency of irrigation throughout the Delhi Sultanate.
• State-sponsored initiatives, particularly under Sultan Firoz Shah Tughlaq, involved the construction of extensive canal networks like the Western Yamuna Canal, bringing vast arid lands under stable cultivation.
• Agricultural productivity saw a significant rise as these irrigation facilities allowed for multiple cropping seasons, shifting the focus from simple subsistence farming to the production of a higher surplus.
• The Sultanate era witnessed the introduction and promotion of high-value cash crops such as sugarcane, indigo, and cotton, which contributed to agricultural diversification.
• The growth in agricultural surplus facilitated the expansion of trade and supported the rapid urbanization of the period, as rural produce could now sustain a large non-agricultural population.
• Investment in horticulture was significant, with historical records noting the establishment of over 1,200 fruit gardens around Delhi, enhancing the variety of available produce.

 Additional Information

• Economic and Administrative Framework:
• Subsistence Farming: This refers to a traditional system where farmers grow only enough food to meet their own family's needs; the innovations of the Sultanate helped move the economy beyond this stage toward commercialization.
• Diwan-i-Amir-Kohi: A dedicated Department of Agriculture created by Sultan Muhammad bin Tughlaq to bring more land under cultivation through state-funded loans known as Sondhar.
• Kharaj: The land revenue system became more structured, often collected in cash, which necessitated the sale of the agricultural surplus in the markets.
• Crop Rotation: The period saw early experiments with crop rotation and the use of better quality seeds to ensure the soil remained fertile while maximizing output.

The correct answer is 16 omega.

Key Points

• The resistance (R) of a conductor is mathematically expressed by the formula R = ρ × (L / A), where ρ represents the resistivity of the material, L is the length, and A is the cross-sectional area.
• When a wire is stretched, its total volume (V) remains constant. Since volume is the product of area and length (V = A × L), increasing the length results in a corresponding decrease in the cross-sectional area.
• In this scenario, the wire is stretched to double its length, making the new length L′ = 2L. To maintain a constant volume, the new cross-sectional area A′ must become A / 2.
• Substituting these new parameters into the resistance equation gives the new resistance R′ = ρ × (2L / (A / 2)), which simplifies to R′ = 4 × (ρL / A), or R′ = 4R.
• Given that the initial resistance of the wire is 4 Ω, the new resistance is calculated as 4 × 4 Ω = 16 Ω.

 Additional Information

• Resistivity (ρ):
• It is a specific property of the material that defines how strongly it opposes the flow of electric current.
• Unlike resistance, resistivity does not change with the dimensions (length or area) of the wire; it only changes with the material type and temperature.
• Relationship for Stretching:
• A useful shortcut for competitive exams: If a wire is stretched n times its original length, the new resistance becomes n² times the original resistance.
• For this problem, since n = 2, the resistance increases by a factor of 2² = 4.
• Factors Affecting Resistance:
• Nature of Material: Conductors like Copper and Silver have low resistance, while insulators have very high resistance.
• Temperature: In most metallic conductors, resistance increases linearly with an increase in temperature due to increased atomic vibrations.

The correct answer is Moho.

Key Points

• The Mohorovicic discontinuity, colloquially known as the Moho, is the boundary layer that separates the Earth's crust from the underlying mantle.
• It was identified in 1909 by Andrija Mohorovicic, a Croatian seismologist, who observed that seismic waves accelerated upon reaching this depth due to a change in rock density.
• The Moho lies at an average depth of 8 kilometers beneath the ocean floor and roughly 32 to 70 kilometers beneath continental landmasses, particularly under high mountain ranges.
• This transition represents a major chemical and rheological shift, moving from the silica-rich rocks of the crust to the peridotite-rich materials of the upper mantle.

 Additional Information

• Conrad Discontinuity:
• It acts as the transition zone between the upper continental crust (granitic layer) and the lower continental crust (basaltic layer).
• It is not as globally persistent as the Moho and is primarily detected in continental lithosphere.
• Repetti Discontinuity:
• This boundary separates the upper mantle from the lower mantle (mesosphere).
• It is typically located at a depth of approximately 660 kilometers and is characterized by phase changes in silicate minerals.
• Gutenberg Discontinuity:
• It defines the interface between the mantle and the outer core.
• Located at a depth of about 2,900 kilometers, it marks the point where S-waves disappear and P-waves slow down significantly due to the liquid nature of the outer core.
• Lehmann Discontinuity:
• This is the boundary between the liquid outer core and the solid inner core.
• It occurs at a depth of about 5,150 kilometers below the Earth's surface.

The correct answer is Badshah Khan.

Key Points

• Khan Abdul Ghaffar Khan was a towering figure in the Indian independence movement and a close associate of Mahatma Gandhi, known for his commitment to non-violence.
• He was affectionately called Badshah Khan (meaning 'King of Chiefs') by his followers in the North-West Frontier Province (NWFP), reflecting his immense spiritual and political authority.
• He founded the Khudai Khidmatgar (Servants of God) in 1929, a non-violent resistance group that played a pivotal role in the struggle against British imperialism.
• Due to his shared ideology and close friendship with Gandhi, he earned the title Frontier Gandhi (Sarhadi Gandhi) for leading the Civil Disobedience Movement in the frontier regions.
• In 1987, he became the first non-Indian to be honored with the Bharat Ratna, India's highest civilian award, recognizing his lifelong dedication to peace and human rights.
• He was a vocal opponent of the Partition of India, championing the cause of a united India and later advocating for the rights of the Pashtun people.

 Additional Information

• Baba-e-Qaum:
• This title signifies Father of the Nation. It is primarily used to refer to Muhammad Ali Jinnah in Pakistan, while in India, Mahatma Gandhi is addressed as Rashtrapita or Baba-e-Qaum.
• Raja ji:
• This was the popular moniker for Chakravarti Rajagopalachari, an influential statesman, freedom fighter, and the last Governor-General of India.
• Sardar:
• This title, meaning Chief or Leader, was famously conferred upon Vallabhbhai Patel by the women of Bardoli following his successful leadership during the Bardoli Satyagraha of 1928.

The correct answer is Water.

Key Points

• Irrigation is the process of supplying water to crops at regular intervals, which is vital for protecting them from extreme weather conditions like frost and hot air currents.
• Water has a high specific heat capacity, which allows it to absorb and store a large amount of thermal energy during the day and release it slowly at night, preventing the soil temperature from dropping to dangerous levels during frost.
• In the presence of hot air currents or Loo, water is absorbed by the roots and moves through the plant to the leaves, where it evaporates in a process called transpiration.
• The evaporation of water from the stomata creates a cooling effect on the plant surface, much like sweating in humans, which prevents the protoplasm from drying out and protects plant tissues from desiccation.
• Maintaining adequate soil moisture through irrigation ensures that the plant remains turgid, allowing it to withstand the physical stress caused by strong, dry winds.

 Additional Information

• Manure
• It is an organic substance obtained from the decomposition of plant or animal wastes by microbes.
• It improves soil texture and water-holding capacity but does not directly provide thermal insulation against frost.
• Fertilisers
• These are chemical substances produced in factories that are rich in specific nutrients like Nitrogen, Phosphorus, and Potassium.
• Common examples include Urea, Ammonium sulphate, Super phosphate, and NPK.
• Starch
• A carbohydrate and polysaccharide that serves as the primary energy storage molecule in plants.
• It is synthesized during photosynthesis and stored in various organs like roots, tubers, and seeds for future metabolic use.

The correct answer is 14.3%.

Key Points

• According to recent data from the World Bank and global remittance monitors, India maintained its position as the top recipient of remittances worldwide in 2024.
• India captured approximately 14.3% of the total global remittance inflows, which underscores the significant economic footprint of the Indian diaspora.
• The total remittance value for India reached an estimated $124 billion, showing a growth of over 7% compared to the previous year.
• This substantial share is attributed to the high concentration of Indian migrants in high-income countries like the United States, the United Kingdom, and the United Arab Emirates.
• Remittances into India currently represent nearly 3% of the nation's Gross Domestic Product (GDP), serving as a critical source of foreign exchange and external financing.

 Additional Information

• Global Remittance Trends:
• In 2024, total global remittance flows reached approximately $860 billion, with low- and middle-income countries receiving the bulk of these funds.
• Other leading recipients following India include Mexico, China, the Philippines, and Egypt.
• The South Asia region as a whole saw a growth in remittances, largely driven by the surge in inflows to India.
• Key Drivers of Inflows:
• High-Skilled Migration: There is an increasing shift toward high-skilled migration to OECD countries, which yields higher per-capita remittances.
• Digital Integration: The expansion of the Unified Payments Interface (UPI) for cross-border payments has reduced transaction costs and increased the speed of transfers.
• GCC Contribution: While the United States is the largest source, the Gulf Cooperation Council (GCC) countries continue to be a vital corridor for India.

Shortcut Trick

Solve bracket and multiplication terms independently: (44 + 18) = 62 and 32 × 2 = 64.

Simplify the core expression: 83 + 61 − 45 = 99.

Combine results: 99 + 64 − 62 = 99 + 2 = 101.

∴ The correct answer is 101.

Alternate Method

Given: 83 + 61 − 45 + 32 × 2 − (44 + 18)

According to the BODMAS rule, we must solve the expression in the order of Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

⇒ 83 + 61 − 45 + 32 × 2 − 62 (Solving Bracket)

⇒ 83 + 61 − 45 + 64 − 62 (Solving Multiplication)

⇒ 144 − 45 + 64 − 62 (Addition from left to right)

⇒ 99 + 64 − 62 (Subtraction from left to right)

⇒ 163 − 62

⇒ 101

∴ The correct answer is 101.

Additional Information

BODMAS Rule

It defines the order of operations: Brackets (), Of/Orders (x²), Division (÷), Multiplication (×), Addition (+), and Subtraction (−).

Priority of Addition and Subtraction

Both addition and subtraction have the same level of priority and should be calculated from left to right as they appear in the expression.

Types of Brackets

Solve in the following sequence: Parentheses (), then Braces {}, and finally Square Brackets [].

Shortcut Trick

Apply the BODMAS rule by grouping positive and negative values for faster calculation.

Sum of positive terms: 64 + 84 + (28 × 2) = 64 + 84 + 56 = 204

Sum of negative terms: (31 + 17) + 66 = 48 + 66 = 114

Net result: 204 − 114 = 90

∴ The correct answer is 90.

Alternate Method

Given Expression: 64 + 84 − (31 + 17) + 28 × 2 − 66

Formula Used: VBODMAS rule (Vinculum, Brackets, Of, Division, Multiplication, Addition, Subtraction)

⇒ 64 + 84 − (48) + 28 × 2 − 66 (Solving Brackets first)

⇒ 64 + 84 − 48 + 56 − 66 (Performing Multiplication: 28 × 2)

⇒ 148 − 48 + 56 − 66 (Performing Addition: 64 + 84)

⇒ 100 + 56 − 66 (Performing Subtraction: 148 − 48)

⇒ 156 − 66 (Performing Addition: 100 + 56)

⇒ 90

∴ The correct answer is 90.

Additional Information

BODMAS Hierarchy

It establishes the precedence: Brackets (), Orders (powers/roots), Division ÷, Multiplication ×, Addition +, and Subtraction −.

Types of Brackets

When multiple brackets are present, solve them in the order of Round brackets ( ), then Curly brackets { }, and finally Square brackets [ ].

Left-to-Right Rule

For operations with the same Priority (like addition and subtraction), solve the expression from left to right to ensure accuracy.

Shortcut Trick

Apply the BODMAS rule to simplify the expression efficiently.

Solve Brackets and Division first: (19 × 2) = 38 and 26 ÷ 2 = 13.

The expression becomes: 87 + 44 − 38 + 13 + 35 − 14 + 18.

Sum of positive terms: 87 + 44 + 13 + 35 + 18 = 197.

Sum of negative terms: 38 + 14 = 52.

Final subtraction: 197 − 52 = 145.

∴ The correct answer is 145.

Alternate Method

Given:

87 + 44 − (19 × 2) + 26 ÷ 2 + 35 − 14 + 18

Formula Used:

The BODMAS rule dictates the order of operations: Brackets, Of, Division, Multiplication, Addition, and Subtraction.

Calculation:

⇒ 87 + 44 − 38 + 26 ÷ 2 + 35 − 14 + 18

⇒ 87 + 44 − 38 + 13 + 35 − 14 + 18

⇒ 131 − 38 + 13 + 35 − 14 + 18

⇒ 93 + 13 + 35 − 14 + 18

⇒ 106 + 35 − 14 + 18

⇒ 141 − 14 + 18

⇒ 127 + 18

⇒ 145

∴ The correct answer is 145.

Additional Information

BODMAS Rule

It ensures a standard procedure for solving complex arithmetic expressions by prioritizing operations in the order: Brackets (), Orders (powers/roots), Division (÷), Multiplication (×), Addition (+), and Subtraction (−).

Grouping Method

To minimize calculation errors, group all terms with a plus sign and all terms with a minus sign separately before performing the final subtraction.

Left-to-Right Rule

When operations of the same priority (like Addition and Subtraction) remain, solve the expression strictly from left to right to maintain accuracy.

Shortcut Trick

Identify the number of terms (n): The denominators are 2, 6, 12, ..., 156, which follow the pattern n(n+1). Since 12 × 13 = 156, there are 12 terms.

Calculate Integer sum: 888 × 12 = 10656.

Calculate Fractional sum: Use the formula n/(n+1) for the series 1/(1×2) + 1/(2×3) + ... + 1/(n(n+1)).

⇒ Sum = 12/(12 + 1) = 12/13.

Combine both: 10656 + 12/13 = 10656 12/13.

∴ The correct answer is 10656 12/13.

Alternate Method

Given Expression: 888 1/2 + 888 1/6 + 888 1/12 + ... + 888 1/156

The given expression consists of mixed fractions. We can separate the integer parts and the fractional parts using the property: a b/c = a + b/c.

⇒ Total Sum = (888 + 888 + ... + 888) + (1/2 + 1/6 + 1/12 + ... + 1/156)

⇒ Since 156 = 12 × 13, the denominators are 1×2, 2×3, 3×4, ..., 12×13. This confirms there are 12 terms.

⇒ Integer sum = 888 × 12 = 10656.

⇒ Fractional part (Telescoping Series) = [1/1 − 1/2] + [1/2 − 1/3] + [1/3 − 1/4] + ... + [1/12 − 1/13].

⇒ Fraction sum = 1 − 1/13 = 12/13.

⇒ Final Answer = 10656 + 12/13 = 10656 12/13.

∴ The correct answer is 10656 12/13.

Additional Information

Mixed Fraction Decomposition

Any mixed fraction of the form A b/c can be written as A + b/c. In a series of such fractions, the whole numbers and fractions can be summed independently.

Telescoping Sum Formula

For a series of the form 1/[n × (n + k)], the general expansion is (1/k) × [1/n − 1/(n + k)]. When k = 1, it simplifies to 1/n − 1/(n + 1).

Sum of Consecutive Product Series

The sum of the first n terms of the series 1/(1×2) + 1/(2×3) + ... + 1/[n(n+1)] is always equal to n/(n+1).

Shortcut Trick

Solve each bracket individually by shifting decimal points.

(0.12 ÷ 0.3) = 0.4

(0.015 ÷ 0.5) = 0.03

Result = 0.4 × 0.03 = 0.012

∴ The correct answer is 0.012.

Alternate Method

Given:

((0.12) ÷ (0.3)) × ((0.015) ÷ (0.5))

Method:

Apply BODMAS rule and convert decimals into fractions for easier calculation.

Calculations:

⇒ (12 / 100 ÷ 3 / 10) × (15 / 1000 ÷ 5 / 10)

⇒ (12 / 100 × 10 / 3) × (15 / 1000 × 10 / 5)

⇒ (4 / 10) × (3 / 100)

⇒ 12 / 1000

⇒ 0.012

∴ The correct answer is 0.012.

Additional Information

Decimal Multiplication Rule

When multiplying decimals, multiply the numbers as whole numbers first. The total number of decimal places in the answer is the sum of the decimal places in the multipliers.

Decimal Division Shortcut

To divide decimals, move the decimal point in the divisor to the right until it is a whole number, and move the decimal point in the dividend the same number of places.

Shortcut Trick

Let a = 5.25 and b = 1.25, which gives (a − b) = 4.

Observe the denominator: a² + b² − 13.125. Since 2ab = 2 × 5.25 × 1.25 = 13.125, it simplifies to (a − b)² = 4² = 16.

Calculate the numerator: (a³ − b³) − 14.75. Since a³ − b³ = 142.75, the numerator is 142.75 − 14.75 = 128.

The final value is 128 ÷ 16 = 8.

∴ The correct answer is 8.

Alternate Method

Given variables: a = 5.25 and b = 1.25

Formulas used: a³ − b³ = (a − b)(a² + ab + b²) and (a − b)² = a² − 2ab + b²

⇒ a² = (5.25)² = 27.5625

⇒ b² = (1.25)² = 1.5625

⇒ ab = 5.25 × 1.25 = 6.5625

⇒ a³ − b³ = (5.25 − 1.25) × (27.5625 + 6.5625 + 1.5625) = 4 × 35.6875 = 142.75

⇒ Numerator = (a³ − b³) − 14.75 = 142.75 − 14.75 = 128

⇒ Denominator = a² + b² − 13.125 = 27.5625 + 1.5625 − 13.125 = 16

⇒ Result = 128 ÷ 16 = 8

∴ The correct answer is 8.

Additional Information

Algebraic Identity: Difference of Cubes

The expression a³ − b³ can be factored as (a − b)(a² + ab + b²), which is useful for simplifying higher-order decimal calculations.

Algebraic Identity: Square of Difference

The expression a² − 2ab + b² is equal to (a − b)². Recognizing the 2ab term (like 13.125 here) helps in quick simplification.

BODMAS Rule

Always resolve the numerator and denominator separately before performing the final division operation in complex fractions.

Shortcut Trick

To find the HCF of numbers in exponent form, identify the common prime bases.

Pick the lowest power for each common prime factor.

Common prime bases are 2 and 5.

The minimum power of 2 is 4 and the minimum power of 5 is 2.

∴ The correct answer is 2⁴ × 5².

Alternate Method

Given:

First number (N₁) = 2⁴ × 5³

Second number (N₂) = 2⁶ × 5²

Formula Used:

The Highest Common Factor (HCF) of given numbers is the product of the least powers of common prime factors.

Calculation:

⇒ Prime factors common to both N₁ and N₂ are 2 and 5.

⇒ Comparing the powers of base 2: min(4, 6) = 4.

⇒ Comparing the powers of base 5: min(3, 2) = 2.

⇒ HCF = 2⁴ × 5²

∴ The correct answer is 2⁴ × 5².

Additional Information

LCM of Exponential Forms

The Least Common Multiple (LCM) is found by taking the highest power of every prime factor present in any of the numbers: LCM = 2⁶ × 5³.

Product of Two Numbers

For any two numbers A and B, the relationship between their HCF and LCM is: A × B = HCF(A, B) × LCM(A, B).

HCF of Co-prime Numbers

The HCF of co-prime numbers (numbers with no common factors other than 1) is always 1.

Shortcut Trick

The length of the longest rod is the HCF (Highest Common Factor) of 56, 84, and 112.

Find the differences between the numbers: 84 − 56 = 28 and 112 − 84 = 28.

The HCF must be 28 or a factor of 28.

Check: 56 ÷ 28 = 2, 84 ÷ 28 = 3, 112 ÷ 28 = 4.

Since 28 divides all given lengths, the HCF is 28.

∴ The correct answer is 28 cm.

Alternate Method

Given:

Length of first piece = 56 cm

Length of second piece = 84 cm

Length of third piece = 112 cm

Formula Used:

Longest rod length = HCF (Piece₁, Piece₂, Piece₃)

Calculations:

Prime factorization of the lengths:

⇒ 56 = 2 × 2 × 2 × 7 = 2³ × 7

⇒ 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7

⇒ 112 = 2 × 2 × 2 × 2 × 7 = 2⁴ × 7

⇒ HCF = 2² × 7 (taking the lowest power of common factors)

⇒ HCF = 4 × 7 = 28 cm

∴ The correct answer is 28 cm.

Additional Information

Highest Common Factor (HCF)

It is the greatest number that divides two or more given numbers without leaving a remainder. For any set of numbers, HCF ≤ minimum number in the set.

HCF and LCM Relation

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

Number of Rods

To find the total number of rods made, divide the total length by the HCF: (56 + 84 + 112) ÷ 28 = 2 + 3 + 4 = 9 rods.

Shortcut Trick

A = Largest 2-digit multiple of LCM(2, 11) = 22 → 22 × 4 = 88.

B = Largest 3-digit multiple of LCM(6, 13) = 78 → 78 × 12 = 936.

Required value = B − A = 936 − 88 = 848.

∴ The correct answer is 848.

Alternate Method

Given:

A is the largest two-digit number divisible by 2 and 11.

B is the largest three-digit number divisible by 6 and 13.

Formula Used:

If a number is divisible by two coprime numbers x and y, it must be divisible by their product (LCM).

Calculations:

⇒ LCM of 2 and 11 = 2 × 11 = 22

⇒ Multiples of 22: 22, 44, 66, 88, 110...

⇒ Largest two-digit number A = 88

⇒ LCM of 6 and 13 = 6 × 13 = 78

⇒ To find largest 3-digit multiple, divide 999 by 78: 999 ÷ 78 ≈ 12.807

⇒ Largest three-digit number B = 78 × 12 = 936

⇒ Required value = B − A

⇒ 936 − 88 = 848

∴ The correct answer is 848.

Additional Information

Divisibility Rule of 6

A number is divisible by 6 if it is divisible by both 2 (even number) and 3 (sum of digits is divisible by 3).

Divisibility Rule of 11

A number is divisible by 11 if the difference between the sum of digits at odd positions and even positions is either 0 or a multiple of 11.

LCM for Largest Multiples

To find the largest n-digit number divisible by x and y, find the LCM(x, y) and divide the largest n-digit number (like 99 or 999) by this LCM to find the multiplier.

Shortcut Trick

LCM of 4 and 7 is 28. Largest two-digit multiple (A) = 28 × 3 = 84.

LCM of 7 and 11 is 77. Largest three-digit multiple (B) = 77 × 12 = 924.

Required value = B − A = 924 − 84 = 840.

∴ The correct answer is 840.

Alternate Method

Given:

Divisors for A: 4 and 7 | Divisors for B: 7 and 11

Formula Used:

Number must be a multiple of the Least Common Multiple (LCM) of its divisors.

Calculations:

⇒ For A: LCM(4, 7) = 28

⇒ Multiples of 28 are 28, 56, 84, 112... Largest 2-digit is 84.

⇒ For B: LCM(7, 11) = 77

⇒ 999 ÷ 77 = 12 with remainder 75.

⇒ Largest 3-digit multiple = 77 × 12 = 924.

⇒ Required Difference = 924 − 84 = 840.

∴ The correct answer is 840.

Additional Information

LCM for Coprime Numbers

If two numbers have no common factor other than 1, their LCM is simply their product (e.g., 7 × 11 = 77).

Finding Multiples within Limits

To find the largest multiple of n less than L, calculate the remainder of L ÷ n and subtract it from L.

Divisibility by 11

A number is divisible by 11 if the difference between the sum of digits at odd positions and even positions is 0 or a multiple of 11.

Shortcut Trick

In a zig-zag (M-shape) figure between parallel lines AB and CD, the sum of the interior-facing angles is equal to the middle vertex angle.

Angle at A + Angle at C = Angle at E

3x + 2x = 60°

5x = 60°

x = 12°

∴ The correct answer is 12.

Alternate Method

Given: AB || CD, ∠BAE = 3x, ∠DCE = 2x, and ∠AEC = 60°.

Formula Used: When two lines are parallel, the alternate interior angles formed by a transversal are equal.

Draw a line EF parallel to AB and CD passing through E.

⇒ ∠BAE = ∠AEF (Alternate Interior Angles)

⇒ ∠AEF = 3x

⇒ ∠DCE = ∠CEF (Alternate Interior Angles)

⇒ ∠CEF = 2x

⇒ ∠AEC = ∠AEF + ∠CEF

⇒ 60° = 3x + 2x

⇒ 60° = 5x

⇒ x = 60° ÷ 5

⇒ x = 12

∴ The correct answer is 12.

Additional Information

Alternate Interior Angles

When a transversal cuts two parallel lines, the angles on opposite sides of the transversal and inside the parallel lines are equal (∠1 = ∠2).

Consecutive Interior Angles

The sum of interior angles on the same side of a transversal cutting parallel lines is always 180° (Supplementary angles).

The Zig-Zag (M) Property

For any number of segments between two parallel lines, the sum of angles pointing to the left equals the sum of angles pointing to the right.

Shortcut Trick

Use the product-difference formula when the combined time and time for one group are given.

Time taken by C = (Time_A+B+C × Time_A+B) ÷ (Time_A+B − Time_A+B+C)

⇒ Time taken by C = (8 × 10) ÷ (10 − 8)

⇒ Time taken by C = 80 ÷ 2 = 40 days.

∴ The correct answer is 40 days.

Alternate Method

Given:

Time taken by A, B and C together = 8 days

Time taken by A and B together = 10 days

Calculations:

⇒ Total Work = LCM of 8 and 10 = 40 units

⇒ Efficiency of C = Efficiency of (A+B+C) − Efficiency of (A+B)

⇒ Efficiency of C = 5 − 4 = 1 unit/day

⇒ Time taken by C = Total Work ÷ Efficiency of C

⇒ Time = 40 ÷ 1 = 40 days

∴ The correct answer is 40 days.

Additional Information

Work and Efficiency Relationship

Total Work = Time × Efficiency. Efficiency is the amount of work done in a single day and is inversely proportional to the Time taken.

Combined Efficiency Rule

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

Pipes and Cisterns Analogy

The same logic applies to filling pipes (positive efficiency) and emptying pipes (negative efficiency) in tank-related problems.

Shortcut Trick

Ratio of Time taken by A and B = 15 : 20 = 3 : 4.

Since they work together, the ratio of Wages is the inverse of the time ratio = 4 : 3.

Total units = 4 + 3 = 7 units → ₹3500.

Difference in shares = 4 − 3 = 1 unit.

Value of 1 unit = 3500 ÷ 7 = ₹500.

∴ The correct answer is ₹500.

Alternate Method

Given:

Total wage for the work = ₹3500.

Time taken by A = 15 days.

Time taken by B = 20 days.

Formula Used:

Wage is distributed in the ratio of Efficiency when the time period of work is the same for all workers.

Efficiency = Total Work ÷ Time Taken.

Calculations:

⇒ Total Efficiency = 4 + 3 = 7 units.

⇒ 7 units corresponds to the total amount of ₹3500.

⇒ 1 unit = 3500 ÷ 7 = ₹500.

⇒ A's share = 4 × 500 = ₹2000.

⇒ B's share = 3 × 500 = ₹1500.

⇒ Difference in amounts = 2000 − 1500 = ₹500.

∴ The correct answer is ₹500.

Additional Information

Wage Distribution Rule

Wages are always distributed in proportion to the total work done by each person (Work = Efficiency × Time).

Constant Time Case

If all individuals work for the same number of days, the ratio of their wages is exactly equal to the ratio of their efficiencies.

Efficiency-Time Relationship

Efficiency is inversely proportional to the time taken to complete a task. If A takes x days and B takes y days, their efficiency ratio is y : x.

Shortcut Trick

Total work = 20 men × 80 days = 1600 units.

Required work = 40% of 1600 = 640 units.

Time taken by 32 men = 640 ÷ 32 = 20 days.

∴ The correct answer is 20 days.

Alternate Method

Given:

Initial men (M₁) = 20, Days (D₁) = 80

Final men (M₂) = 32, Work (W₂) = 40% of total work

Formula Used:

(M₁ × D₁) ÷ W₁ = (M₂ × D₂) ÷ W₂

⇒ Total work (W₁) = 20 × 80 = 1600 units (assuming 1 man does 1 unit/day).

⇒ Required work (W₂) = 40% of 1600 = (40 ÷ 100) × 1600 = 640 units.

⇒ Efficiency of 32 men = 32 × 1 = 32 units/day.

⇒ Time taken (D₂) = Required work ÷ Efficiency

⇒ D₂ = 640 ÷ 32 = 20 days.

∴ The correct answer is 20 days.

Additional Information

The MDH Rule

The relationship between Men (M), Days (D), Hours (H), and Work (W) is given by (M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂.

Efficiency and Time

For a constant amount of work, efficiency is inversely proportional to the time taken (E₁ × T₁ = E₂ × T₂).

Work-Man-Days

The total work is often measured in man-days, which is the product of the number of men and the number of days they work.

Shortcut Trick

Net change formula: Profit % = Mark-up % + Discount % + (Mark-up × Discount)/100

Mark-up = +50% (as MP is 150% of CP)

Discount = −20% (as SP is 80% of MP, discount = 100 − 80 = 20%)

Profit % = 50 − 20 + [50 × (−20)]/100 = 30 − 10 = 20%

∴ The correct answer is 20%.

Alternate Method

Given:

Marked Price (MP) = 150% of Cost Price (CP)

Selling Price (SP) = 80% of Marked Price (MP)

Calculations:

⇒ Let the Cost Price (CP) of the article be ₹100.

⇒ Marked Price (MP) = 150% of CP = (150 ÷ 100) × 100 = ₹150.

⇒ Selling Price (SP) = 80% of MP = (80 ÷ 100) × 150.

⇒ SP = 0.8 × 150 = ₹120.

⇒ Profit = SP − CP = 120 − 100 = ₹20.

⇒ Profit Percentage = (Profit ÷ CP) × 100.

⇒ Profit % = (20 ÷ 100) × 100 = 20%.

∴ The correct answer is 20%.

Additional Information

Mark-up Percentage

It is the percentage by which the cost price is increased to reach the marked price. Formula: [(MP − CP) ÷ CP] × 100.

Discount Percentage

Discount is always calculated on the Marked Price (MP). Formula: [(MP − SP) ÷ MP] × 100.

Profit and Loss

Profit occurs when SP > CP, and Loss occurs when CP > SP. Both are always calculated on the Cost Price (CP) unless stated otherwise.

Shortcut Trick

A 25% discount implies that the Selling Price (SP) is 75% of the Marked Price (MP).

The ratio of SP to MP must be 75 : 100, which simplifies to 3 : 4.

Checking Option 4: Ratio = 1350 : 1800 = 135 : 180 = 3 : 4 (by dividing both sides by 45).

∴ The correct answer is Selling price = Rs. 1350 and Marked price = Rs. 1800.

Alternate Method

Given: Check each option for a 25% discount rate.

Formula Used: Discount % = [(Marked Price − Selling Price) ÷ Marked Price] × 100

Testing Option 4:

⇒ Marked Price (MP) = Rs. 1800

⇒ Selling Price (SP) = Rs. 1350

⇒ Discount = 1800 − 1350 = 450

⇒ Discount % = (450 ÷ 1800) × 100

⇒ Discount % = (1 ÷ 4) × 100 = 25%

∴ The correct answer is Selling price = Rs. 1350 and Marked price = Rs. 1800.

Additional Information

Marked Price (MP)

The price at which an article is listed or printed on its label, also known as the list price.

Selling Price (SP)

The actual price paid by the customer after the discount is deducted from the Marked Price: SP = MP − Discount.

Successive Discounts

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

Shortcut Trick

Article ratio = 20000 ÷ 500 = 40 times.

Total Marked Price (MP) for 20000 articles = 250 × 40 = Rs. 10000.

Effective Selling Price (SP) factor = 100% − 20% = 80% (or 0.8).

Total Selling Price = 10000 × 0.8 = Rs. 8000.

∴ The correct answer is Rs. 8000.

Alternate Method

Given:

Total Marked Price of 500 articles = Rs. 250

Discount percentage = 20%

Total articles to be sold = 20000

Formula Used:

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

Calculations:

⇒ Marked Price of 1 article = 250 ÷ 500 = Rs. 0.50

⇒ Marked Price of 20000 articles = 20000 × 0.50 = Rs. 10000

⇒ Discount Amount = 20% of 10000 = (20 ÷ 100) × 10000 = Rs. 2000

⇒ Selling Price = Total MP − Discount Amount

⇒ Selling Price = 10000 − 2000 = Rs. 8000

∴ The correct answer is Rs. 8000.

Additional Information

Relationship between MP and SP

The Selling Price is always calculated on the Marked Price after deducting the discount: SP = MP × (1 − d/100).

Successive Discounts

If two successive discounts of a% and b% are given, the Equivalent Discount = [a + b − (a × b)/100]%.

Mark-up Percentage

The extra price added to the Cost Price to arrive at the Marked Price is the Mark-up. Mark-up % = [(MP − CP) ÷ CP] × 100.

Shortcut Trick

Simplify the first ratio by cross-multiplying denominators: (3/4) : (4/3) → 9 : 16.

In a proportion 9 : 16 :: 45y : A, identify the multiplier for the first term.

Since 9 × 5y = 45y, the same multiplier applies to the second term.

A = 16 × 5y = 80y.

∴ The correct answer is 80y.

Alternate Method

Given: (3/4) : (4/3) :: 45y : A

Formula: Product of Extremes = Product of Means

⇒ (3/4) × A = (4/3) × 45y

⇒ (3/4) × A = 4 × (45y ÷ 3)

⇒ (3/4) × A = 4 × 15y

⇒ (3/4) × A = 60y

⇒ A = 60y × (4/3)

⇒ A = (60y ÷ 3) × 4

⇒ A = 20y × 4

⇒ A = 80y

∴ The correct answer is 80y.

Additional Information

Fundamental Rule of Proportion

For any four numbers a, b, c, and d in proportion (a : b :: c : d), the relation a × d = b × c always holds true.

Fourth Proportional

If a, b, and c are three given quantities, the fourth proportional x is calculated as x = (b × c) ÷ a.

Mean Proportional

The mean proportional between two numbers a and b is given by √(a × b).

Shortcut Trick

Simplify the first ratio: (4/7) : (7/4) → 4×4 : 7×7 = 16 : 49.

Since the ratios are in proportion, 16 units = 112y.

Divide by 16 to find 1 unit: 1 unit = 112y ÷ 16 = 7y.

Therefore, A = 49 units = 49 × 7y = 343y.

∴ The correct answer is 343y.

Alternate Method

Given: First ratio = (4/7) : (7/4), Second ratio = 112y : A, and they are in proportion (::).

Formula Used: Product of Extremes = Product of Means

Calculations:

⇒ (4/7) × A = (7/4) × 112y

⇒ A = (7/4) × 112y × (7/4)

⇒ A = (7/4) × (112y ÷ 4) × 7

⇒ A = (7/4) × 28y × 7

⇒ A = 7 × (28y ÷ 4) × 7

⇒ A = 7 × 7y × 7

⇒ A = 49 × 7y

⇒ A = 343y

∴ The correct answer is 343y.

Additional Information

Properties of Proportion

If a : b :: c : d, then a × d = b × c. Here, a and d are called extremes, and b and c are called means.

Fourth Proportional

The value of the fourth term (d) in a proportion a : b :: c : d is calculated as d = (b × c) ÷ a.

Continued Proportion

Three numbers a, b, and c are in continued proportion if a : b :: b : c, which implies b² = a × c (Mean Proportional).

Shortcut Trick

In the proportion (x + 7) : 50 :: 14 : 25, compare the second terms.

Since 50 is twice of 25 (50 = 25 × 2), the first term must also be twice of 14.

⇒ (x + 7) = 14 × 2 = 28

⇒ x = 28 − 7 = 21

∴ The correct answer is 21.

Alternate Method

Given: (x + 7) : 50 :: 14 : 25

Formula Used: If a : b :: c : d, then a × d = b × c (Product of Extremes = Product of Means).

⇒ (x + 7) × 25 = 50 × 14

⇒ x + 7 = (50 × 14) ÷ 25

⇒ x + 7 = 2 × 14

⇒ x + 7 = 28

⇒ x = 28 − 7

⇒ x = 21

∴ The correct answer is 21.

Additional Information

Definition of Proportion

An equality of two ratios is called a proportion. If a, b, c, d are in proportion, then a : b = c : d.

Fourth Proportional

If a : b :: c : x, then x is the fourth proportional and is calculated as x = (b × c) ÷ a.

Mean Proportional

The mean proportional between two numbers a and b is given by √(a × b).

The correct answer is 'apple-pie order'.

Key Points

• The idiom 'apple-pie order' refers to a state of being perfectly arranged, neat, or in complete order. (बिल्कुल सही क्रम में)
• In the context of the sentence, the interior looks marvellous because the maid has kept everything extremely organized and tidy.
• The other options such as 'apple-orange order', 'apple-cake order', and 'apple-peanut order' are non-existent phrases and do not convey any idiomatic meaning in English.

​Therefore, the correct answer is 'Option 4'.

Complete Sentence: The maid has kept all the furniture and belongings in apple-pie order. Really, the interior looks marvellous.

Additional Information

• The origin of the phrase 'apple-pie order' is somewhat uncertain, but it has been used since the late 18th century to describe meticulous organization.
• Synonyms for this idiom include spick and span, shipshape, and orderly.
• Example: She spent the whole afternoon putting her books in apple-pie order.

The correct answer is: Inimical.

Key Points

• The word 'Inimical' means tending to obstruct or harm, or being unfriendly and hostile towards someone or something. (हानिकारक / विरोधी)
• Example: The harsh climate of the desert is inimical to many forms of plant life.
• 'Inimical' is correctly spelled and refers to conditions or actions that are unfavorable or detrimental. (शत्रुवत)
• Example: His inimical attitude towards the new policy made the transition difficult for the entire department.
• Hence, we can infer that 'Inimical' is the correctly spelt word among the given options.

Therefore, the correct answer is: Inimical.

Additional Information

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

• Infallible (अचूक): This is the correct spelling (not Infallable); it refers to someone or something that is incapable of making mistakes or being wrong.
• Example: Even the most advanced technology is not infallible and can occasionally fail.
• Ineffable (अकथनीय): This is the correct spelling (not Inefable); it refers to something that is too great or extreme to be expressed in words.
• Example: The mountain climber felt a sense of ineffable joy upon reaching the summit.
• Ignoramus (अज्ञानी): This is the correct spelling (not Ignoremus); it refers to an extremely ignorant or stupid person.
• Example: He is a brilliant scientist but a complete ignoramus when it comes to social etiquette.

The correct answer is: Careful.

Key Points

• The word 'Cautious' refers to someone who is avoiding potential danger or risks; it implies being wary and taking great care. (सावधान)
• Example: The driver was extremely cautious while navigating the narrow, foggy mountain roads.
• 'Careful' describes the act of giving a lot of attention and thought to what you are doing so that you do not have an accident or make a mistake. (सजग)
• Example: You need to be very careful when handling these fragile antique ornaments.
• Hence, we can infer that the closest synonym of 'Cautious' is 'Careful'.

Therefore, the correct answer is- Careful.

Additional Information

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

• Reckless (लापरवाह): Doing something dangerous and not worrying about the risks and the possible results.
• Example: He showed a reckless disregard for the safety of others by speeding through the residential area.
• Quick (तेज़): Doing something in a short time or moving at a high speed.
• Example: She gave a quick response to the emergency call.
• Confident (आत्मविश्वासी): Being certain of your own abilities or having trust in people, plans, or the future.
• Example: The candidate appeared confident and well-prepared during the entire interview process.

The correct answer is: Prepondrance.

Key Points

• The word 'Prepondrance' is the misspelt version of the word 'Preponderance', which describes a situation where there is a greater amount or importance of something. (अशुद्ध वर्तनी)
• Example: The student made a spelling error by writing 'prepondrance' instead of the correct term in his essay.
• 'Preponderance' refers to the quality or fact of being greater in number, quantity, or importance; a predominance. (अधिकता)
• Example: In this region, there is a preponderance of rainy days during the month of July.
• Hence, we can infer that 'prepondrance' is the misspelt word among the given options.

Therefore, the correct answer is- Prepondrance.

Additional Information

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

• Procrastinate (टालमटोल करना): To delay or postpone action; to put off doing something.
• Example: It is better to complete your tasks immediately rather than to procrastinate and face stress later.
• Perturbation (व्याकुलता): Anxiety or mental uneasiness; a state of being worried or upset.
• Example: The sudden news of the market crash caused a great deal of perturbation among the investors.
• Perpendicular (लंबवत): At an angle of 90 degrees to a given line, plane, or surface.
• Example: The carpenter ensured that the legs of the table were perfectly perpendicular to the top surface.

The correct answer is I bought a new wrist watch yesterday..

Key Points

• A homonym is a word that shares the same spelling and pronunciation as another word but has a completely different meaning. The word watch is a prominent example in English linguistics, functioning as both a noun and a verb.
• When used as a noun, specifically in the context of a timepiece, it refers to a small, portable instrument for measuring and showing time, typically worn on a strap around the wrist or carried in a pocket.
• In the sentence 'I bought a new wrist watch yesterday.', the word watch is preceded by the modifier wrist and the article 'a', identifying it as a countable noun representing a physical object.
• The word evolved from the Old English wæccan, which originally meant 'to be awake' or 'to remain alert'. Historically, the term shifted from the act of surveillance (a watchman) to the period of duty (a watch), and eventually to the mechanical device used to track those shifts in the 15th and 16th centuries.
• The presence of the word wrist in this sentence serves as a semantic marker, eliminating ambiguity and confirming the timepiece definition.

 Additional Information

• The term watch as a verb carries several distinct meanings based on contextual usage:
• Visual Observation: To look at or observe something with sustained attention over a duration, such as a football match or a television program.
• Surveillance and Guarding: To keep a person, group, or place under protective or restrictive supervision (e.g., a guard monitoring prisoners).
• Vigilance: To be cautious or alert to potential hazards, often used in imperative sentences like 'Watch your step'.
• Monitoring: To follow the progress or development of a situation closely to detect changes.

The correct answer is stage fear.

Key Points

• The passage explicitly mentions that Ananya had always been afraid of speaking in front of a crowd.
• This specific anxiety related to performing or speaking before an audience is widely known as stage fear (or glossophobia).
• Her hesitation to raise her hand in class and her trembling hands during the speech competition are classic symptoms of this struggle.
• By participating in the competition and delivering her speech, she directly confronted her stage fear to gain confidence.

Therefore, the correct answer is stage fear.

Correct Sentence: 'Ananya had always been afraid of speaking in front of a crowd, which indicates she struggled with stage fear.'

Additional Information

• Fear of animals: The story does not mention any interactions with or fears regarding animals.
• Fear of teachers: While she avoided raising her hand, the text attributes this to the crowd rather than a fear of her teacher.
• Fear of exams: The narrative focuses on a speech competition and public speaking, not academic exams or tests.

The correct answer is Option 2.

Key Points

• The passage highlights that Ananya had a deep-seated fear of speaking in front of crowds and usually avoided participation.
• When the speech competition was announced, she felt an internal urge to change her habits and overcome her limitations.
• Participating in the event was a deliberate choice to confront her anxiety and push herself toward personal growth.
• The story concludes by explaining that her success was measured by the confidence she gained, proving that courage is about trying even when scared.

Therefore, the correct answer is To face her fear and grow.

Context from the Passage: 'But when her teacher announced a speech competition, something inside her wanted to change.'

Additional Information

• To win a trophy – Although it was a competition, the text specifies she didn't win the first prize, and her primary motivation was the internal desire for change.
• Her friend forced her – The passage does not mention any friend or external pressure; the decision was entirely her own.
• She wanted to skip class – There is no reference in the story suggesting she used the competition as an excuse to avoid regular classes.

The correct answer is Option 2.

Key Points

• The passage tells the story of a girl named Ananya who struggled with stage fear and decided to face it by participating in a speech competition.
• According to the text, when she prepared for the event, 'She chose a topic close to her heart - The Power of Self-Belief.'
• This specific topic was chosen because it resonated with her personal struggle to find courage and confidence.
• The mention of the topic occurs early in the narrative to set the stage for her practice and final performance.

Therefore, the topic Ananya spoke on was The Power of Self-Belief.

Additional Information

• Clean India: This is a common theme for school speeches but is not mentioned in this particular story about Ananya.
• My Favorite Game: The passage focuses on self-improvement and public speaking rather than hobbies or sports.
• Saving Trees: While an important environmental topic, it has no relevance to the context of this passage.
• Ananya's primary goal was to gain confidence, which is why the topic of self-belief was appropriate for her journey.

The correct answer is Option 3.

Key Points

• The passage explicitly mentions that to prepare for the speech competition, Ananya practised daily in front of a mirror.
• She also sought support by asking her family to listen to her, which helped build her readiness.
• When she felt nervous on stage, it was the memory of all her practice at home that allowed her voice to grow stronger.
• Therefore, the combination of consistent practice and family support was the key factor in her performance.

Therefore, the correct answer is Option 3.

Supporting Evidence: 'She practised daily in front of a mirror and asked her family to listen... she took a deep breath and remembered all her practice.'

Additional Information

• Option 1: Reading a book – While reading is a good habit, the story specifically highlights active practice and verbal rehearsal as her preparation method.
• Option 2: Running away from stage – This would have resulted in a failure to participate; the story is about facing fear, not avoiding it.
• Option 4: Memorizing answers – This is a strategy for exams, whereas a speech competition requires practicing delivery and expression.

The correct answer is Option 3.

Key Points

• The story describes Ananya's struggle with stage fear and her journey to overcome it.
• Although she entered a speech competition, her primary goal was to change herself and build courage.
• The text explicitly states that while she did not win the first prize, she won something far more valuable: confidence.
• Her biggest achievement was the internal victory of facing her fear and completing her task despite being scared.
• This aligns with the central theme of the passage: courage isn't about being unafraid; it's about trying even when you're scared.

Therefore, the correct answer is Gaining confidence by facing fear.

Correct Sentence: 'Ananya's biggest achievement in the story was gaining confidence by facing fear.'

Additional Information

• Winning the competition: This is incorrect because the passage specifically mentions that she didn't win first prize.
• Scolding the audience: This is incorrect; the audience clapped loudly for her after she finished her speech.
• Getting a gift from her teacher: There is no mention in the passage of the teacher giving her a physical gift as an achievement.

The correct answer is Is a play being prepared by the children for the school annual day?.

Key Points

• The sentence provided is in the Present Continuous Tense and follows an Interrogative Structure. In Active Voice, this structure is: Is/Am/Are + Subject + Verb-ing + Object?
• To convert a Present Continuous sentence into Passive Voice, the structure must be: Is/Am/Are + New Subject (Object of the active voice) + being + Past Participle (V3) + by + New Object (Subject of the active voice)?
• The Object in the active sentence is 'a play'. Since 'a play' is a singular noun, the passive sentence begins with the auxiliary verb 'Is' to maintain grammatical agreement.
• The Subject of the active sentence, 'the children', becomes the Agent in the passive sentence and is preceded by the preposition 'by'.
• The verb 'preparing' is transformed into its Passive form by using the auxiliary 'being' (to indicate continuous action) followed by the Past Participle form 'prepared'.
• The phrase 'for the school annual day' acts as an Adverbial Complement and remains unchanged in its relative position within the sentence.

 Additional Information

• Rules for Voice Change in Interrogative Sentences:
• Tense Consistency: The Tense of the sentence must never change during the conversion from active to passive voice.
• Sentence Type: An Interrogative sentence in the active voice must remain Interrogative in the passive voice.
• Pronoun Changes: While not applicable here, subjects like 'I', 'He', or 'They' would change to 'me', 'him', or 'them' respectively when moved to the object position.
• Present Simple Passive: Uses Is/Am/Are + V3 (e.g., 'Is a play prepared...?').
• Past Continuous Passive: Uses Was/Were + being + V3 (e.g., 'Was a play being prepared...?').

The correct answer is The villagers had repaired the broken bridge before the storm struck..

Key Points

• To convert a sentence from Passive Voice to Active Voice, the agent of the action (the villagers) must be shifted to the subject position at the beginning of the sentence.
• The original sentence is in the Past Perfect Tense in the passive form, identified by the auxiliary structure had been + past participle (had been repaired).
• In the Active Voice, the Past Perfect Tense must maintain its temporal aspect by using the structure had + past participle (had repaired) without the word been.
• The passive subject (The broken bridge) becomes the direct object in the active sentence, following the main verb.
• The adverbial clause (before the storm struck) remains constant to indicate the sequence of events, where one past action was completed before another past action occurred.
• The resulting active construction follows the Subject + Verb + Object pattern: The villagers (Subject) + had repaired (Verb) + the broken bridge (Object).

 Additional Information

• Understanding Tense Consistency in Voice Conversion:
• Simple Past Tense: Option 1 uses repaired, which fails to capture the Past Perfect necessity of the original sentence indicating an action completed prior to the storm.
• Simple Present Tense: Option 2 uses repair, which is grammatically incorrect in a context describing a past event (the storm struck).
• Syntactic Reordering: Option 4 changes the focus and conjunction structure, which alters the original meaning and emphasis of the source sentence.
• Past Perfect Active Rule: This tense is specifically used to clarify that the repair work was finished before the storm arrived, maintaining the logical timeline.

The correct answer is 'from'.

Key Points

• The verb recovering refers to the process of returning to a normal state of health after an illness, injury, or setback.
• In English grammar, the verb recover is typically followed by the fixed preposition 'from'.
• The sentence describes a patient getting better after suffering from a chronic illness, making from the grammatically correct choice.
• Options 1, 2, and 4 do not fit the idiomatic usage of the verb recovering in this context.

Therefore, the correct answer is Option 3.

Complete Sentence: 'The patient was gradually recovering from his chronic illness.'

Additional Information

• Option 1 (with): With is generally used to indicate accompaniment or the instrument of an action, which is incorrect here.
• Option 2 (of): While we say someone is cured of a disease, we do not use of with recovering.
• Option 4 (Off): Off usually indicates separation or movement away from a position and is not used to describe health recovery.

The correct answer is Option 2.

Key Points

• The primary issue in the underlined part is the choice of preposition following the noun need.
• When the word need is used as a noun to indicate that something is required or necessary, it is most commonly followed by the preposition for.
• The standard collocation is need for something (e.g., the need for change, the need for speed).
• The expression need of is generally reserved for the idiom in need of, which describes a state of lacking something essential.
• Thus, the phrase need for stronger regulations is the grammatically correct improvement for the sentence.

Therefore, the correct answer is Option 2.

Correct Sentence: 'The chairman emphasized the need for stronger regulations to curb financial fraud.'

Additional Information

• Option 1: 'need in stronger regulations' – This uses an incorrect preposition. Need does not take in when expressing a requirement for an object.
• Option 3: 'need to stronger regulations' – The preposition to is used after need when followed by a verb (infinitive form, e.g., 'need to implement'), but not when followed directly by a noun phrase like 'stronger regulations'.
• Option 4: 'No improvement required' – This is incorrect because need of is less appropriate than need for in this context of expressing a formal requirement.

The correct answer is 'with'.

Key Points

• The preposition 'with' is used to indicate the instrument, tool, or object used to perform a specific action.
• In the given sentence, the 'key' is the instrument used to perform the action of opening the door.
• Therefore, 'with' is the grammatically correct preposition for this context.

Therefore, the correct answer is Option 2.