SSC GD Constable 2026 Official Paper (Held On 25 May, 2026 Shift 3) (Previous Year Paper)

Logic followed here is:

Logic: Every number in the series is obtained by multiplying the previous number by 2.

Hence, the correct answer is "Option 4".

The logic followed here is:

The letters in each term follow a specific positional value pattern. Each term is divided into its first letter and second letter.

The missing term is JA.

Hence, the correct answer is "Option 2".

Logic followed here is.

Logic: The series follows a pattern where the positional values of the first and second letters in each term increment by constant values to form the next term.

The observed pattern correctly identifies the next term in the series as JL.

Hence, the correct answer is "Option 2".

Logic followed here is:

The series follows a pattern of successive subtraction of even numbers starting from 2.

The missing term is 846.

Hence, the correct answer is "Option 2".

Logic followed here is.

Logic: The difference between consecutive terms follows a pattern of subtracting successive even numbers (8, 10, 12, 14, 16, 18, 20) from the previous term.

As observed, the pattern of differences should be −8, −10, −12, −14, −16, −18, −20. The term −120 breaks this pattern as the difference between −105 and −120 is −15, and the difference between −120 and −139 is −19.

Therefore, the wrong term in the series is −120.

Hence, the correct answer is "Option 1".

According to the given information, five boys L, M, N, P, and A are sitting in a row facing north.

Step 1: A is fourth to the right of L.

Since there are only 5 seats in the row, L must be sitting at the extreme left end (Position 1) and A must be sitting at the extreme right end (Position 5).

Step 2: N is second to the right of L.

Counting two places from L towards the right, N is placed at Position 3.

Step 3: P is not the immediate neighbour of L.

The empty positions left are Position 2 and Position 4. The immediate neighbour of L is at Position 2. Since P cannot sit at Position 2, P must be placed at Position 4.

Step 4: Place the remaining person M in the only vacant spot, which is Position 2.

Final Sitting Arrangement:

Now, we need to find how many boys are sitting to the right of M.

From the arrangement, the boys to the right of M (Position 2) are N (Position 3), P (Position 4), and A (Position 5).

Number of boys to the right of M = 3.

Hence, the correct answer is "Option 2".

1. Since all persons face the centre: right = counterclockwise, left = clockwise. Fix L at pos(1). M sits third to the right of L (counterclockwise): L(1) → pos(7) → pos(6) → M(5).

2. G sits second to the right of K (counterclockwise) and second to the left of J (clockwise). This implies the counterclockwise sequence K - x - G - y - J. We place K(6), G(4), and J(2) as they fit the remaining positions relative to M(5).

3. I is not the immediate neighbour of J(2). Since the neighbours of pos(2) are pos(1) and pos(3), I cannot sit at pos(3). Thus, I must sit at pos(7).

4. M is not the immediate neighbour of H. The remaining person H is placed at pos(3). The neighbours of M(5) are pos(4) and pos(6), which are G and K. This satisfies all conditions.

The immediate neighbours of M (pos 5) are the persons sitting at pos(4) and pos(6), who are G and K.

Hence, the correct answer is 'Option 4'.

Logic followed here is based on the linear arrangement of 7 persons (A, B, C, D, E, F, and G) facing North.

Step 1: F is third to the left of A.

If we place A at a position, F will be three places to its left.

F _ _ A

Step 2: G is third to the left of F.

G _ _ F _ _ A

This occupies all 7 positions in the row.

Step 3: C is second to the right of F.

Counting from F towards the right, C will be at the 6th position from the left.

G _ _ F _ C A

Step 4: E is to the immediate left of D.

This requires two adjacent empty spots. The only such spots are the 2nd and 3rd positions.

Therefore, E is at position 2 and D is at position 3.

G E D F _ C A

Step 5: Place the remaining person.

The only person left is B, who will occupy the 5th position.

Final Arrangement:

From the table, the immediate neighbours are:

• G and E
• E and D
• D and F
• F and B
• B and C
• C and A

Comparing these pairs with the given options, D and F are immediate neighbours.

The correct answer is option 1

Given:

Ravi's salary = ₹24,000

He spends:

• 1/3 of his salary on rent.
• 1/4 of his salary on groceries.

Calculation:

Amount spent on rent = (1/3) × 24,000 = ₹8,000

Amount spent on groceries = (1/4) × 24,000 = ₹6,000

Total amount spent = 8,000 + 6,000 = ₹14,000

Amount left = 24,000 − 14,000 = ₹10,000

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: Second Number = First Number + 55

For the first pair 7109 : 7164

⇒ 7109 + 55 = 7164.

Similarly, for the third pair 2735 : 2790

⇒ 2735 + 55 = 2790.

Applying the same logic to the second pair

6293 : ?

⇒ 6293 + 55 = 6348.

Hence, the correct answer is 'Option 1'.

The logic followed here is:

Logic: Second Number = First Number − 43

For the pair 3388 : 3345

⇒ 3388 − 43 = 3345.

For the pair 724 : 681

⇒ 724 − 43 = 681.

Applying the same logic to the pair

1244 : ?

⇒ 1244 − 43 = 1201.

Hence, the correct answer is 'Option 4'.

Logic followed here is.

Logic: Each letter of the word is shifted forward by 3 positions in the English alphabetical series to obtain its code.

LUSH is coded as OXVK →

FERN is coded as IHUQ →

Similarly, let us find the code for SLUM:

Therefore, SLUM is coded as VOXP.

Hence, the correct answer is "Option 2".

The logic followed here is that each term in the series consists of two letters followed by a number, and each element follows a specific pattern.

The missing term is NU100.

Hence, the correct answer is "Option 3".

Logic followed here is:

Logic: Each term in the series follows a specific pattern of addition or subtraction for the letters and a constant addition for the numbers.

The term JQI502 follows the first two letters and the number pattern but deviates in the third letter. However, HUG369 is significantly wrong as its first letter, second letter, and number all fail to follow the +3, −3, and +134 pattern.

Hence, the correct answer is "Option 3".

The logic followed for the given series is based on the positional values of the letters and a constant addition for the numbers.

Logic: Each term in the series is derived by applying a specific mathematical operation to the previous term.

As per the pattern +3 for the third letter, the last term should have H (8) and the number should be 1430.

Therefore, ENI1400 is the wrong term in the series.

Hence, the correct answer is "Option 1".

Concept:

Hour hand covers 360° in 12 hours

Angular distance covered in 1 hour = 360⁄12 = 30°

Angular distance covered in 60 minutes = 30°

Angular distance covered in 1 minute = 1⁄2°

Calculation:

Minute hand covers 360° in 60 minutes

60 minutes = 360°

1 minute = 360⁄60 ⇒ 1 minute = 6°

Here Given Time is 6:30 PM

Minute = 30

Angle covered by minute hand = 30 × 6 = 180°

Angle covered by hour hand = 6 × 30 + 30 × ½ = 180 + 15 = 195°

Angle between hour and minute hands = 195 − 180 = 15°

Hence, the angle between hour and minute hands is 15°

Alternate Method

The angle between the hour hand and minute hand = $|60H - 11M|\over2$

Here, H = hours and M = minutes.

Given H = 6 and M = 30.

So, Angle = $(60 \times 6 - 11 \times 30)\over2$

Angle = $(360 - 330)\over2$

Angle = 30⁄2 = 15°

Hence, the correct answer is 15°

Concept:

To find the time shown by a clock that gains or loses time, first determine the total duration elapsed from the starting point to the final point, and then calculate the total gain or loss based on the given rate during that interval.

Calculation:

The time interval from 3 AM to 3 PM on the same day is exactly 12 hours.

First, convert the total hours into minutes:

1 hour = 60 minutes

12 hours = 12 × 60 = 720 minutes

The clock gains 1 second every 2 minutes.

Total gain in 720 minutes = 720 ÷ 2 = 360 seconds

Now, convert the total gain from seconds into minutes:

60 seconds = 1 minute

360 seconds = 360 ÷ 60 = 6 minutes

The actual time is 3:00 PM. Since the clock has gained 6 minutes, it will show a time that is 6 minutes ahead of the actual time:

Clock Time = 3:00 PM + 6 minutes = 3:06:00 PM

Hence, the correct answer is 3:06:00.

The logic followed in this series is:

Hence, the correct image is "Option 1".

The logic followed in this series is:

Hence, the correct image is "Option 1".

The logic followed here is:

Hence, the correct image is "Option 1".

The correct answer is Birsa Munda.

Key Points

• Birsa Munda was a charismatic tribal leader and folk hero from the Munda tribe who spearheaded a 19th-century religious and political movement in the Chotanagpur Plateau region (modern-day Jharkhand).
• He is revered by the tribal community as Dharti Aba or Dharati Baba, which translates to Father of the Earth, due to his struggle for tribal land rights and cultural identity.
• He led the Munda Rebellion, also known as Ulgulan (The Great Tumult), between 1899 and 1900 against the British Raj and the Dikus (outsiders/landlords) who exploited the tribal population.
• The movement specifically targeted the destruction of the traditional Khuntkatti land system by Thikadars and Zamindars, seeking to establish a Munda Raj.
• In recognition of his contribution to the Indian independence movement, his portrait was unveiled in the Central Hall of the Indian Parliament in 1989, making him the only tribal leader to receive such an honor.
• The Government of India celebrates his birth anniversary, November 15, as Janjatiya Gaurav Divas.

 Additional Information

• Alluri Sitarama Raju:
• A revolutionary from Andhra Pradesh who led the Rampa Rebellion (1922−24).
• He fought against the 1882 Madras Forest Act and is famously called Manyam Veerudu (Hero of the Jungle).
• Komaram Bheem:
• A Gond tribal leader from Telangana who fought against the Asaf Jahi dynasty and the British.
• He is credited with the powerful slogan Jal, Jangal, Jameen (Water, Forest, Land).
• Peer Ali Khan:
• An Indian revolutionary and rebel who participated in the Revolt of 1857 in Patna, Bihar.
• A bookbinder by profession, he was executed by the British for his role in the uprising.

The correct answer is Alok Ranjan.

Key Points

• The Appointments Committee of the Cabinet (ACC), headed by the Prime Minister, officially approved the appointment of Alok Ranjan as the Director of the National Crime Records Bureau (NCRB) in September 2024. Hence, the statement is correct.
• Alok Ranjan is a distinguished officer of the 1991 batch of the Indian Police Service (IPS) from the Madhya Pradesh cadre. Hence, the statement is correct.
• Prior to this prestigious appointment, he served as the Additional Director General (ADG) in the Central Reserve Police Force (CRPF), demonstrating extensive experience in internal security and law enforcement. Hence, the statement is correct.
• His tenure as the Chief of NCRB is set to continue until his superannuation on June 30, 2026, or until further orders from the government. Hence, the statement is correct.
• As the head of the NCRB, he is responsible for overseeing the collection, analysis, and dissemination of crime statistics across India and managing critical IT-enabled policing systems. Hence, the statement is correct.

 Additional Information

• National Crime Records Bureau (NCRB):
• Established in 1986, it functions as a specialized wing under the Ministry of Home Affairs (MHA), headquartered in New Delhi.
• The bureau was formed based on the recommendations of the Tandon Committee and the National Police Commission (1977-1981) to empower Indian Police with Information Technology.
• It publishes the highly influential annual report titled Crime in India, which serves as a primary statistical tool for policy-makers and law enforcement agencies.
• It is the nodal agency for implementing the Crime and Criminal Tracking Network & Systems (CCTNS) and maintaining the National Fingerprint Bureau.
• Gyanesh Kumar:
• He is a retired IAS officer who was appointed as an Election Commissioner of India in March 2024.

The correct answer is Dr. M.R. Srinivasan.

Key Points

• Dr. Muthanna Ramaswamy Srinivasan (born 1930) was a legendary Indian nuclear scientist who served as the Chairman of the Atomic Energy Commission (AEC) and Secretary of the Department of Atomic Energy (DAE).
• He is celebrated as the architect of India's nuclear power program, specifically for his pioneering work on the Pressurized Heavy Water Reactor (PHWR) technology, which utilized indigenous natural uranium and heavy water.
• He was the founding Chairman and Managing Director of the Nuclear Power Corporation of India Limited (NPCIL), an organization he helped establish in 1987 to streamline the commercial operation of nuclear power plants.
• Under his technical leadership, India successfully commissioned major nuclear projects including the Madras Atomic Power Station (MAPS) at Kalpakkam and the Narora Atomic Power Station (NAPS) in Uttar Pradesh.
• His strategic vision helped India achieve self-reliance in the nuclear fuel cycle, including heavy water production and reactor design, during periods of severe international technology denial.
• He was a member of the National Security Advisory Board and played a vital role in representing India at the International Atomic Energy Agency (IAEA) in Vienna.

 Additional Information

• Honors and Awards:
• Padma Vibhushan: Conferred in 2015 for his exceptional contribution to science and engineering.
• Padma Bhushan (1990) and Padma Shri (1984): Awarded for his administrative and scientific excellence in nuclear development.
• Notable Nuclear Figures:
• Dr. Homi Bhabha: Known as the Father of the Indian Nuclear Program, he established the Tata Institute of Fundamental Research (TIFR) and passed away in 1966.
• Dr. A.P.J. Abdul Kalam: Known as the Missile Man of India, he was a key figure in the Pokhran-II tests and served as the 11th President of India; he passed away in 2015.
• Dr. Raja Ramanna: A renowned physicist who directed the Smiling Buddha (Pokhran-I) test in 1974 and served as the Director of BARC; he passed away in 2004.

The correct answer is Kidney.

Key Points

• The Kidney is the primary organ of the urinary system, responsible for osmoregulation, blood pressure regulation, and the excretion of nitrogenous wastes like urea. While it possesses secondary endocrine functions, it is not classified as a primary part of the endocrine system. Hence, statement 1 is correct.
• The Hypothalamus is a critical part of the endocrine system located in the forebrain. It produces releasing and inhibiting hormones that control the pituitary gland, acting as the master regulator of the entire system. Hence, statement 2 is incorrect.
• The Pancreas is a heterocrine gland, meaning it has both exocrine and endocrine functions. Its endocrine part, the Islets of Langerhans, secretes vital hormones such as insulin and glucagon directly into the blood to manage glucose levels. Hence, statement 3 is incorrect.
• The Ovaries are the female gonads and are fundamental endocrine organs that secrete steroid hormones, specifically estrogen and progesterone, which regulate the reproductive cycle and secondary sexual characteristics. Hence, statement 4 is incorrect.

 Additional Information

• Endocrine System Characteristics:
• It consists of ductless glands that secrete chemical messengers called hormones directly into the circulatory system.
• Major primary glands include the Pituitary, Thyroid, Parathyroid, Adrenal, and Pineal glands.
• The system helps maintain homeostasis and coordinates long-term processes like growth, metabolism, and reproduction.
• Hormonal role of Kidneys:
• Despite being an excretory organ, the kidney secretes Erythropoietin (EPO), which stimulates red blood cell production in the bone marrow.
• It also produces Renin, an enzyme that initiates the RAAS pathway to regulate blood pressure and fluid volume.

The correct answer is Vomiting.

Key Points

• Involuntary actions are physiological activities that occur automatically without any conscious thought or the will of the individual. These actions are primarily controlled by the autonomous nervous system and the hindbrain.
• Vomiting is a complex reflex action that involves the forceful expulsion of stomach contents through the mouth. This action is coordinated by the vomiting center located in the medulla oblongata of the brain.
• The process of vomiting involves the simultaneous contraction of the diaphragm and abdominal muscles, coupled with the relaxation of the cardiac sphincter. Since these muscle movements are triggered by the brain without conscious intent, vomiting is an involuntary action.
• In contrast, activities such as Writing, Talking, and Moving a chair are categorized as voluntary actions. These are initiated by the cerebrum in the forebrain and require deliberate effort, decision-making, and conscious motor control.

 Additional Information

• Medulla Oblongata:
• It is a vital part of the hindbrain that regulates several autonomic functions essential for survival.
• Besides vomiting, it controls blood pressure, heartbeat, respiration, and reflexes like sneezing, swallowing, and coughing.
• Voluntary Nervous System:
• Also known as the Somatic Nervous System, it handles the movements of skeletal muscles.
• The Cerebral Cortex is responsible for processing the information required to perform complex tasks like speech and fine motor skills like writing.
• Reflex Arc:
• While vomiting is a reflex, some other involuntary responses occur via the spinal cord to allow for extremely rapid reactions to external stimuli, such as pulling a hand away from a hot object.

The correct answer is A system with AI-enabled cameras.

Key Points

• TrailGuard AI is a sophisticated AI-powered surveillance system designed specifically to enhance wildlife security and combat illegal poaching in protected areas.
• The technology was deployed in the Similipal Tiger Reserve (STR) in Odisha during February 2025 to create a digital perimeter around the core tiger habitat.
• The system consists of AI-enabled cameras that utilize edge computing to process images instantly on the device rather than sending all raw footage to a central server.
• The primary function of these cameras is to detect human intruders, poachers, or unauthorized vehicles in real-time, filtering out images of wind-blown vegetation or non-target animals.
• Once a threat is identified, the system transmits real-time alerts and photographic evidence to forest rangers and quick response teams via satellite or cellular networks.

 Additional Information

• Similipal Tiger Reserve:
• Located in the Mayurbhanj district of Odisha, it is famous for being the only natural habitat in the world for melanistic tigers (black tigers).
• It was declared a Tiger Reserve in 1973 and became part of the UNESCO World Network of Biosphere Reserves in 2009.
• The reserve is home to a rich variety of flora and fauna, including the Asian Elephant and the Chousingha.
• Technological Features:
• The TrailGuard AI technology was developed by the conservation organization Resolve in partnership with Intel and Hugging Face.
• It employs the Intel Movidius Vision Processing Unit (VPU), which allows the camera to operate for years on a small battery by using very low power.
• The device is compact and easily camouflaged, making it nearly invisible to intruders attempting to bypass traditional security measures.

The correct answer is Venus.

Key Points

• Venus is categorized as a Terrestrial Planet, which means it possesses a solid, rocky surface unlike the massive planets composed mainly of fluids and gases.
• The internal structure of Venus consists of a metallic iron core, a rocky silicate mantle, and a solid crust, similar to the geological composition of Earth.
• In contrast, Jupiter and Saturn are known as Gas Giants, composed almost entirely of hydrogen and helium with no well-defined solid surface to land on.
• Uranus (along with Neptune) is classified as an Ice Giant, made up of a hot, dense fluid of icy materials such as water, methane, and ammonia surrounding a small rocky core.
• While Venus has an extremely thick atmosphere, the planet itself is a rocky body, making it the only option among the four that is not primarily made of gases and liquids.

 Additional Information

• Classification of Planets:
• Inner Planets (Terrestrial):
• Includes Mercury, Venus, Earth, and Mars.
• These planets have high densities, are composed of heavy metals and rocks, and have few or no moons.
• They are located inside the Asteroid Belt.
• Outer Planets (Jovian):
• Includes Jupiter, Saturn, Uranus, and Neptune.
• They are characterized by large radii, low densities, and complex ring systems.
• Their atmospheres are incredibly deep, transitioning into liquid layers under extreme pressure and temperature.
• Specifics of Venus:
• Venus is the hottest planet in the Solar System due to a runaway greenhouse effect caused by an atmosphere that is 96% carbon dioxide.
• Its surface pressure is roughly 92 times that of Earth, equivalent to being 1 kilometer underwater.
• It rotates in a retrograde direction (clockwise), meaning the Sun rises in the west and sets in the east.

The correct answer is Uttarakhand.

Key Points

• Khuded folk songs are deeply rooted in the cultural fabric of the Garhwal region of Uttarakhand.
• These songs primarily depict the melancholy and suffering of a married woman who is longing for her maternal home (referred to locally as Maait).
• The word Khuded originates from the local dialect word Khuda, which translates to the feeling of homesickness or the pain of separation from loved ones.
• Traditionally, these songs are performed by women while they are engaged in daily chores such as gathering fodder in the forests or working in the agricultural fields of the Himalayan slopes.
• The lyrics often describe the geographical barriers, such as high mountains and dense forests, that intensify the sense of isolation felt by the woman in her husband’s village.
• Khuded songs serve as a powerful medium for emotional release, reflecting the socio-cultural reality of historical Garhwali society where women were often married into distant villages.

 Additional Information

• Other Folk Traditions of Uttarakhand:
• Chhopati: These are popular love songs from the Tehri Garhwal district, typically sung in a dialogue format between men and women during cultural gatherings.
• Bajuband: A traditional folk song of the shepherd community in the Garhwal hills, often themed around themes of love and sacrifice.
• Basanti: These songs are composed to celebrate the arrival of the spring season and are usually sung individually or in groups during Basant Panchami.
• Jhumelo: A rhythmic dance-song performed during festivals, which highlights the natural beauty of the Himalayas and community bonding.
• Jagars: A unique form of ritualistic vocal music used to invoke local deities and spirits, common in both Kumaon and Garhwal regions.
• Folk Music of Other States:
• Rajasthan: Characterized by diverse styles like Maand, Manganiyar, and Langa traditions.
• Assam: Famous for Bihu Geets and the devotional Borgeet composed by Srimanta Sankardev.
• Karnataka: Known for Bhavageete (expressionist poetry) and the rhythmic Dollu Kunitha.

The correct answer is Mizoram.

Key Points

• Lemlawi is a traditional Jew’s harp (or mouth harp) that is deeply rooted in the cultural heritage of the Mizo people in Mizoram.
• It is categorized as a lamellophone, consisting of a flexible bamboo or metal tongue attached to a frame. The traditional version is usually carved from a single piece of Sairil bamboo.
• The instrument is played by placing it between the teeth or lips; the musician plucks the projecting tongue of the instrument with their finger while using their mouth cavity as a natural resonator to amplify the sound.
• Players can manipulate the timbre and pitch of the Lemlawi by changing the shape of their mouth and controlling their breath, creating a distinctive rhythmic and droning melody.
• Historically, the Lemlawi was used for personal relaxation and was a popular instrument for young men and women during courtship to communicate subtle feelings.

 Additional Information

• Mizoram:
• Khuang: The most significant Mizo musical instrument, a drum made of hollowed wood and wrapped with animal skin, essential for all traditional dances.
• Tuium: A percussion instrument made of a bamboo tube with strings pulled out from the bamboo outer skin itself.
• Seki: A rhythmic instrument made from the horns of a Mithun (a local bovine), played by striking two horns together.
• Telangana:
• Features the Oggu Dolu, a hand-held drum used in Oggu Katha storytelling, and the Kommulu, a brass wind instrument.
• Gujarat:
• Home to the Jodia Pava (double flute) and the Ravanahatha, an ancient bowed string instrument often used by folk musicians.
• Karnataka:
• Known for the Saraswati Veena in classical music and folk instruments like the Dollu and Tamate.

The correct answer is They were excellent engineers.

Key Points

• The Indus Valley Civilization (also known as the Harappan Civilization), existing roughly between 2500 BCE and 1700 BCE, provides extensive archaeological evidence of highly advanced urban planning and architectural mastery.
• Their cities, such as Harappa and Mohenjo-daro, were laid out on a meticulous grid system (gridiron pattern) where streets intersected at right angles, a feat that required sophisticated mathematical and surveying skills.
• The people developed a complex drainage system that was unparalleled in the ancient world; every house was connected to street drains made of mortared brick and covered with stone slabs or terracotta lids for easy maintenance.
• Structures like the Great Bath at Mohenjo-daro demonstrate their expertise in civil engineering through the use of bitumen (natural tar) for waterproofing, ensuring the massive tank remained leak-proof for centuries.
• The discovery of the dockyard at Lothal highlights their understanding of hydrography and maritime engineering, as it featured a lock system to regulate water flow during high and low tides.

 Additional Information

• Standardization and Materials:
• Harappans used standardized burnt bricks with a consistent ratio of 1:2:4 (thickness to width to length), which is a hallmark of an organized industrial society.
• In Dholavira, archaeologists found a sophisticated water management system consisting of giant stone-cut reservoirs and channels to harvest every drop of water in an arid environment.
• The Citadel or upper town was often built on raised platforms of mud-bricks to protect administrative buildings from frequent flooding of the Indus River and its tributaries.

The correct answer is Both I and II.

Key Points

• Plantation and vegetation cover play a crucial role in maintaining the physical properties of the soil, such as its texture, structure, and water-holding capacity. Roots of trees and plants bind the soil particles together, preventing soil erosion and maintaining nutrient levels like nitrogen and phosphorus. Hence, statement I is correct.
• Deforestation leads to the exposure of the soil surface to agents of erosion like wind and water. When the fertile topsoil layer, which is rich in humus, is washed away, the lower, hard and rocky layers are revealed. These layers possess significantly less organic matter and are far less fertile than the surface soil. Hence, statement II is correct.

 Additional Information

• Deforestation:
• It refers to the large-scale clearing of forests for agriculture, urbanization, or industrial purposes.
• It significantly disrupts the water cycle and increases carbon dioxide (CO₂) levels in the atmosphere, contributing to global warming.
• Desertification:
• The continuous removal of the topsoil layer through erosion gradually converts fertile land into deserts.
• This process reduces the infiltration rate of water into the ground, often leading to floods in nearby areas during heavy rainfall.
• Soil Fertility:
• The loss of vegetative cover prevents the replenishment of nutrients through the decomposition of leaves and organic matter, rendering the land unsuitable for cultivation.

The correct answer is South Africa.

Key Points

• The 2022 Commonwealth Games, officially known as the XXII Commonwealth Games and commonly known as Birmingham 2022, was an international multi-sport event for members of the Commonwealth.
• India delivered a strong performance, finishing in the 4th position in the final medals tally with a total of 61 medals, comprising 22 Gold, 16 Silver, and 23 Bronze.
• Australia secured the 1st rank by winning a total of 178 medals (67 Gold, 57 Silver, 54 Bronze). Hence, statement 3 is incorrect.
• England finished in the 2nd rank with a total of 176 medals (57 Gold, 66 Silver, 53 Bronze). Hence, statement 2 is incorrect.
• Canada occupied the 3rd rank, finishing just above India with 92 medals (26 Gold, 32 Silver, 34 Bronze). Hence, statement 1 is incorrect.
• South Africa finished in the 9th rank in the overall medals tally, securing only 27 medals (7 Gold, 9 Silver, 11 Bronze). Since the 9th rank is numerically lower than India's 4th rank, it ranked below India. Hence, statement 4 is correct.

 Additional Information

• Indian Performance Overview:
• Wrestling was India's most successful sport, contributing 12 medals, including 6 Gold.
• Sharath Kamal (Table Tennis) was the most successful Indian athlete at the event, winning 4 medals.
• India won its first-ever medal in Lawn Bowls, with the women's fours team clinching the Gold.
• Event Details:
• Motto: 'Sport is just the beginning'.
• Mascot: Perry the Bull.
• The games featured 72 Commonwealth nations and territories.

The correct answer is Jammu and Kashmir.

Key Points

• The 38th National Games of India, hosted by Uttarakhand in early 2025, featured intense competition among various states and Union Territories.
• Among the Union Territories specified in the options, Jammu and Kashmir emerged at the top by securing the maximum number of medals.
• Athletes from Jammu and Kashmir showcased exceptional talent and dominated in specialized disciplines, particularly in wushu, pencak silat, fencing, gymnastics, and kayaking.
• The sustained focus on sports infrastructure development under the Prime Minister's Development Package (PMDP) has significantly enhanced the competitive standards of athletes from the region.

 Additional Information

• Other Union Territories' Performance:
• Chandigarh: Despite having a robust sports framework, Chandigarh's medal contribution was concentrated in specific events like athletics, resulting in a lower overall count than Jammu and Kashmir.
• Andaman and Nicobar Islands: Participated with a smaller contingent, winning limited medals primarily in water-based adventure sports such as canoeing and rowing.
• Puducherry: Registered minimal medal representation, trailing behind the other competing Union Territories.
• About the National Games:
• The National Games are organized under the aegis of the Indian Olympic Association (IOA) to identify grassroots athletic talent capable of representing India in global forums.

The correct answer is Both I and II.

Key Points

• Poultry fowl are highly susceptible to a variety of viral infections that can cause mass mortality and significant economic losses in the farming industry. Major viral diseases include Ranikhet disease (Newcastle Disease), Fowl Pox, and Infectious Bursal Disease (Gumboro). These viruses often target the respiratory, nervous, or immune systems of the birds. Hence, statement I is correct.
• Bacterial pathogens are equally responsible for numerous poultry ailments that affect growth and egg-laying capacity. Common examples include Fowl Cholera (caused by Pasteurella multocida), Salmonellosis, and Chronic Respiratory Disease (caused by Mycoplasma). These infections typically spread through contaminated feed, water, or poor sanitation practices. Hence, statement II is correct.

 Additional Information

• Viral Disease Characteristics:
• Ranikhet Disease is one of the most lethal viral diseases in India, characterized by gasping, nasal discharge, and neurological symptoms like paralysis.
• Avian Influenza (Bird Flu) is a highly contagious viral infection that can occasionally cross the species barrier to infect humans.
• Bacterial Disease Characteristics:
• Fowl Cholera usually presents as an acute septicaemia with high morbidity and sudden death in the flock.
• Pullorum Disease, caused by Salmonella pullorum, primarily affects young chicks and is transmitted through the egg from the mother bird.
• Other Pathogens:
• In addition to viruses and bacteria, poultry suffer from fungal infections like Aspergillosis (Brooder Pneumonia) and parasitic diseases such as Coccidiosis caused by protozoa.
• Prevention strategies involve regular vaccination, administration of antibiotics for bacterial issues, and maintaining strict biosecurity and hygiene in poultry sheds.

The correct answer is Orangutan.

Key Points

• The term Orangutan is derived from the Malay and Indonesian words orang, which means person or man, and hutan, which means forest.
• When combined, the name literally translates to man of the forest, a reference to their high intelligence and predominantly arboreal lifestyle in dense tropical jungles.
• These great apes are geographically restricted to the rainforests of Southeast Asia, specifically inhabiting the islands of Borneo and Sumatra.
• They are recognized for their distinctive reddish-brown hair and extreme manual dexterity, sharing approximately 97 percent of their DNA with humans.

 Additional Information

• Orangutans (Genus Pongo):
• There are three distinct species: the Bornean (Pongo pygmaeus), the Sumatran (Pongo abelii), and the recently identified Tapanuli orangutan (Pongo tapanuliensis).
• They are the largest tree-dwelling mammals and are known for their unique method of movement called brachiation.
• Sumatran Tiger:
• Scientifically known as Panthera tigris sumatrae, it is a critically endangered subspecies found only on the Indonesian island of Sumatra.
• Komodo Dragon:
• Recognized as Varanus komodoensis, it is the heaviest and largest lizard species on Earth, endemic to the Lesser Sunda Islands of Indonesia.
• Irrawaddy Dolphins:
• Known as Orcaella brevirostris, these are euryhaline dolphins found in coastal areas, estuaries, and rivers like the Mekong and the Irrawaddy in South and Southeast Asia.

The correct answer is Apis florae.

Key Points

• Apis florae, commonly referred to as the Little Bee or Dwarf Honey Bee, is the smallest species among the genus Apis in terms of body size.
• These bees are native to South and Southeast Asia, including countries like India, and are typically found in tropical and subtropical regions.
• They build a single vertical comb that is usually no larger than the size of a human palm, often suspended from twigs, bushes, or shrubbery in open-air environments.
• Due to their small size and specific nesting habits, they produce a relatively small amount of honey, generally ranging from 200 to 900 grams per colony annually.
• The Apis florae is known for being docile and less aggressive compared to larger species, although they exhibit a high tendency for absconding (leaving the nest) if disturbed.

 Additional Information

• Apis dorsata:
• Commonly known as the Rock Bee or Giant Honey Bee.
• It is the largest honeybee species and is highly aggressive, making it difficult to domesticate.
• A single colony can yield 35 to 40 kg of honey.
• Apis cerana indica:
• Popularly known as the Indian Honey Bee or Eastern Honey Bee.
• It is a medium-sized bee that is widely used for apiculture in India because it is relatively easy to domesticate in moveable frames.
• The average honey yield is approximately 2 to 5 kg per colony.
• Apis mellifera:
• Known as the European Honey Bee or Western Honey Bee.
• It was introduced to India for commercial beekeeping due to its high honey production capacity and low swarming tendency.
• It can yield between 25 to 40 kg of honey per colony.

The correct answer is Both I and II.

Key Points

• Nitrogen is an indispensable constituent of proteins, which are complex macromolecules formed by long chains of amino acids. Every amino acid contains a central carbon atom bonded to an amino group (-NH₂), a carboxyl group, and a side chain; the presence of nitrogen in the amino group makes it a fundamental building block for all cellular structures, enzymes, and hormones. Hence, statement I is correct.
• Chlorophyll, the green pigment located in the chloroplasts of plants, algae, and cyanobacteria, is essential for photosynthesis. The molecular structure of chlorophyll (such as Chlorophyll a, C₅₅H₇₂O₅N₄Mg) contains a porphyrin ring composed of four pyrrole rings, each of which contains a nitrogen atom coordinated to a central magnesium atom. Hence, statement II is correct.

 Additional Information

• Nitrogen is a major macronutrient required by plants in the greatest amount, typically absorbed from the soil as nitrate (NO₃−) or ammonium (NH₄⁺).
• Nucleic Acids: Nitrogen is a key component of DNA and RNA, forming the nitrogenous bases (Adenine, Guanine, Cytosine, Thymine, and Uracil) that carry genetic information.
• ATP (Adenosine Triphosphate): This primary energy-transfer molecule in cells contains nitrogen within its adenine moiety.
• Vitamins and Alkaloids: Many metabolic regulators and secondary metabolites also incorporate nitrogen into their chemical frameworks.
• Nitrogen Cycle: Since atmospheric nitrogen (N₂) cannot be used directly by most organisms, it must be converted into organic forms through nitrogen fixation by bacteria like Rhizobium.

The correct answer is Oxfam India.

Key Points

• The India Discrimination Report is a flagship publication by Oxfam India that highlights the extent of inequality and prejudice in the Indian labor market.
• The report utilizes unit-level data from the Periodic Labour Force Survey (PLFS) and the National Sample Survey (NSS) to analyze how identity-based factors affect employment and earnings.
• One of the primary findings is that gender discrimination is a structural issue, where a massive portion of the wage gap between men and women is attributed to discrimination rather than differences in education or work experience.
• The study quantifies discrimination against Scheduled Castes (SC), Scheduled Tribes (ST), and Muslims, noting that these groups face significant hurdles in accessing regular salaried jobs compared to the general category.
• It points out that social identity often outweighs human capital (skills and qualifications) in determining economic outcomes in both urban and rural India.

 Additional Information

• Oxfam India:
• It is a non-profit organization and a member of the global Oxfam confederation, working towards eliminating poverty and social injustice.
• Apart from discrimination, it frequently publishes the Survival of the Richest report and other studies on wealth inequality.
• Centre for Equity Studies (CES):
• This autonomous research institution is known for publishing the India Exclusion Report, which tracks the exclusion of marginalized groups from public goods and services.
• Tata Trusts:
• A philanthropic giant in India that supports the India Justice Report, which assesses the capacity of various states to deliver justice through the police, judiciary, and prisons.
• Praja Foundation:
• This organization focuses on accountability in urban governance and publishes reports concerning the performance of elected representatives and the state of civic amenities in cities like Mumbai and Delhi.

The correct answer is Dayanand Saraswati.

Key Points

• Dayanand Saraswati was a profound scholar and social reformer who founded the Arya Samaj on April 7, 1875, in Bombay (now Mumbai).
• Born in 1824 as Mool Shankar in Gujarat, he emphasized the supreme authority of the Vedas, which he considered the infallible source of all knowledge and truth.
• He gave the famous call 'Back to the Vedas' to advocate for a return to the purity of ancient Vedic traditions and to discard later distortions in Hinduism.
• His seminal work, Satyarth Prakash (The Light of Truth), published in 1875, outlined his philosophy of monotheism and his opposition to idol worship, polytheism, and caste discrimination.
• The Arya Samaj played a critical role in promoting women's education, widow remarriage, and social equality through a network of Gurukuls and Dayanand Anglo-Vedic (DAV) institutions.
• He also initiated the Shuddhi movement, which aimed at reconverting individuals who had previously converted to other religions back into the Hindu fold.

 Additional Information

• Swami Vivekananda:
• He was the primary disciple of Ramakrishna Paramahansa and established the Ramakrishna Mission in 1897.
• He is internationally recognized for his powerful speech at the Parliament of the World's Religions in Chicago in 1893, where he introduced Vedanta and Yoga to the Western world.
• Raja Ram Mohan Roy:
• Known as the 'Father of Modern India', he founded the Brahmo Samaj in 1828 to promote monotheism and human dignity.
• His persistent efforts were instrumental in the legal abolition of Sati in 1829 under Lord William Bentinck.
• Ishwar Chandra Vidyasagar:
• A key figure of the Bengal Renaissance, he was a scholar and educator who fought tirelessly for women's rights.
• His advocacy was central to the enactment of the Hindu Widows' Remarriage Act, 1856, and he revolutionized Bengali typography.

The correct answer is World Trade Organization.

Key Points

• The Global Trade Outlook and Statistics is a flagship annual report published by the World Trade Organization (WTO) that provides a comprehensive analysis of the latest developments in world trade.
• The 2025 edition of the report offers detailed projections for global merchandise trade growth, analyzing how factors like geopolitical tensions, inflation, and monetary policies influence trade volumes across different regions.
• It serves as a critical analytical tool for evaluating trade-to-GDP ratios and understanding the shifts in commercial services, including digitally delivered services which have seen significant growth in recent years.
• The report highlights the resilience of supply chains and the impact of regional trade agreements on the overall stability of the multilateral trading system.
• By utilizing historical data and econometric modeling, the WTO provides policymakers with insights into trade costs, commodity prices, and the potential risks facing the global economy in the short to medium term.

 Additional Information

• World Trade Organization (WTO):
• Established: 1 January 1995, following the Marrakesh Agreement.
• Headquarters: Geneva, Switzerland.
• Role: It is the only international organization dealing with the global rules of trade between nations, aiming to ensure that trade flows as smoothly and freely as possible.
• International Monetary Fund (IMF):
• Primary Publication: Known for the World Economic Outlook (WEO) and the Global Financial Stability Report.
• Focus: Monitors the international monetary system and provides loans to member countries facing balance of payments problems.
• World Bank:
• Primary Publication: Publishes the World Development Report and Global Economic Prospects.
• Focus: Provides financial and technical assistance to developing countries for development projects to reduce poverty.
• UNESCO:
• Focus: Specializes in education, science, and culture; it publishes the Global Education Monitoring Report.

Shortcut Trick

Apply BODMAS: Solve Bracket (34 + 21) = 55.

Perform Multiplication: 55 × 2 = 110.

Expression becomes: 86 + 57 − 110 + 63 − 19.

Combine positive terms: 86 + 57 + 63 = 206.

Final calculation: 206 − 110 − 19 = 77.

∴ The correct answer is 77.

Alternate Method

Given: 86 + 57 − (34 + 21) × 2 + 63 − 19

Method: Apply the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction).

⇒ 86 + 57 − (55) × 2 + 63 − 19

⇒ 86 + 57 − 110 + 63 − 19

⇒ (86 + 57 + 63) − (110 + 19)

⇒ 206 − 129

⇒ 77

∴ The correct answer is 77.

Additional Information

BODMAS Rule

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

Types of Brackets

Brackets are solved in the order: Round brackets ( ), then Curly brackets { }, and finally Square brackets [ ].

Addition and Subtraction

While addition and subtraction have the same priority, it is usually safer to group all positive numbers and negative numbers separately before subtracting.

Shortcut Trick

Solve using BODMAS: First divide 33 ÷ 3 = 11 and multiply 22 × 2 = 44.

The expression becomes: 89 − 47 + 44 + 11 + 28 − 14.

Sum of positive terms: 89 + 44 + 11 + 28 = 172.

Sum of negative terms: 47 + 14 = 61.

Final result: 172 − 61 = 111.

∴ The correct answer is 111.

Alternate Method

Given Expression: 89 − 47 + 22 × 2 + 33 ÷ 3 + 28 − 14

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

⇒ 89 − 47 + 22 × 2 + 11 + 28 − 14 (Performing Division: 33 ÷ 3 = 11)

⇒ 89 − 47 + 44 + 11 + 28 − 14 (Performing Multiplication: 22 × 2 = 44)

⇒ 42 + 44 + 11 + 28 − 14 (Performing Subtraction: 89 − 47 = 42)

⇒ 86 + 11 + 28 − 14 (Performing Addition: 42 + 44 = 86)

⇒ 97 + 28 − 14 (Performing Addition: 86 + 11 = 97)

⇒ 125 − 14 (Performing Addition: 97 + 28 = 125)

⇒ 111 (Performing Subtraction)

∴ The correct answer is 111.

Additional Information

VBODMAS Rule

V stands for Vinculum (bar bracket), which is solved first. The remaining sequence follows B (Brackets), O (Of/Orders), D (Division), M (Multiplication), A (Addition), and S (Subtraction).

Arithmetic Priority

Division and Multiplication have higher priority than Addition and Subtraction. If multiple operations of the same priority exist, solve from left to right.

Grouping Method

To simplify large expressions, group all positive numbers and negative numbers separately before the final subtraction to minimize calculation errors.

Shortcut Trick

Area of Wall 1 = 20 × 15 = 300 m²

Area of Wall 2 = 30 × 20 = 600 m²

Since Time ∝ Area, the area doubles (300 to 600), so time also doubles.

Required Time = 6 × 2 = 12 hr.

∴ The correct answer is 12 hr.

Alternate Method

Given:

Dimensions of Wall 1 = 20 m × 15 m, Time₁ = 6 hr

Dimensions of Wall 2 = 30 m × 20 m

Formula Used:

Area = Length × Breadth

Direct Proportion: Time₁ / Area₁ = Time₂ / Area₂

Calculations:

⇒ Area of Wall 1 (A₁) = 20 × 15 = 300 m²

⇒ Area of Wall 2 (A₂) = 30 × 20 = 600 m²

⇒ According to Direct Proportion:

⇒ 6 / 300 = Time₂ / 600

⇒ Time₂ = (6 × 600) / 300

⇒ Time₂ = 6 × 2

⇒ Time₂ = 12 hr

∴ The correct answer is 12 hr.

Additional Information

Direct Variation

When two quantities are related such that an increase in one results in a proportional increase in the other, it is direct variation (y = kx).

Work-Time Relation

For constant efficiency, work done is directly proportional to time. Formula: W₁/T₁ = W₂/T₂.

Chain Rule

General formula for work: (M₁ × D₁ × H₁) / W₁ = (M₂ × D₂ × H₂) / W₂, where W represents the amount of work (area here).

Shortcut Trick

Ratio of Speed = 40 : (40 + 10) = 40 : 50 = 4 : 5.

Since distance is constant, the ratio of Time = 5 : 4.

Difference in time units = 5 − 4 = 1 unit.

Given that 1 unit = 1 hour, so original time = 5 units = 5 hours.

Total distance = Original Speed × Original Time = 40 × 5 = 200 km.

∴ The correct answer is 200 km.

Alternate Method

Given:

Original speed (s₁) = 40 km/h

Increased speed (s₂) = 40 + 10 = 50 km/h

Time difference (Δt) = 1 hour

Formula Used:

Distance = [ (s₁ × s₂) / (s₂ − s₁) ] × Δt

Calculations:

⇒ Distance = [ (40 × 50) / (50 − 40) ] × 1

⇒ Distance = [ 2000 / 10 ] × 1

⇒ Distance = 200 × 1

⇒ Distance = 200 km

∴ The correct answer is 200 km.

Additional Information

Speed-Distance Relationship

Speed is inversely proportional to time when distance is constant (S ∝ 1/T). If speed increases, time decreases by the same factor.

Unit Conversion

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

Average Speed

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

Shortcut Trick

Remaining fraction of saline = (1 − 12/60) × (1 − 15/60)

Remaining fraction = (4/5) × (3/4) = 3/5

Final concentration = Initial concentration × Remaining fraction

Final concentration = 70% × 3/5 = 14% × 3 = 42%

∴ The correct answer is 42%.

Alternate Method

Given:

Initial volume (V) = 60 ml

Initial concentration = 70%

First replacement volume (x₁) = 12 ml

Second replacement volume (x₂) = 15 ml

Formula:

Final Concentration = Initial Concentration × (1 − x₁/V) × (1 − x₂/V)

Calculations:

⇒ Final Saline % = 70 × (1 − 12/60) × (1 − 15/60)

⇒ Final Saline % = 70 × (1 − 1/5) × (1 − 1/4)

⇒ Final Saline % = 70 × (4/5) × (3/4)

⇒ Final Saline % = 70 × (3/5)

⇒ Final Saline % = 14 × 3 = 42

∴ The correct answer is 42%.

Additional Information

Removal and Replacement Formula

If a container contains V units of liquid from which x units are taken out and replaced by water, after n operations, the quantity of pure liquid = V × (1 − x/V)ⁿ.

Concentration Ratio

Concentration of a solution is the ratio of solute to the total volume of the solution, often expressed as (Solute Volume ÷ Total Volume) × 100.

Successive Changes

When different volumes are withdrawn, the net reduction factor is the product of individual remaining fractions: (1 − x₁/V) × (1 − x₂/V) × ... × (1 − x_n/V).

Shortcut Trick

Convert the target fraction 7/12 to have the common denominator of 24 (the largest denominator in the options).

7/12 = (7 × 2) / (12 × 2) = 14/24.

Now, compare the numerators: 13/24 has a smaller numerator (13) than 14/24 (14).

All other options (2/3 = 16/24, 5/8 = 15/24, 11/8 > 1) are greater than 14/24.

∴ The correct answer is 13/24.

Alternate Method

Given: Target fraction = 7/12.

Formula Used: To compare fractions, convert them to decimals or a common denominator.

Step 1: Convert the target fraction to a decimal.

⇒ 7/12 = 7 ÷ 12 ≈ 0.5833

Step 2: Convert the options to decimals for comparison.

⇒ Option 1: 2/3 = 0.6666 (Larger than 0.5833)

⇒ Option 2: 5/8 = 0.625 (Larger than 0.5833)

⇒ Option 3: 11/8 = 1.375 (Much larger than 1)

⇒ Option 4: 13/24 = 13 ÷ 24 ≈ 0.5416 (Smaller than 0.5833)

⇒ Comparing 0.5416 and 0.5833, we find 0.5416 < 0.5833.

∴ The correct answer is 13/24.

Additional Information

Cross-Multiplication Method

To compare two fractions a/b and c/d, check the product ad and bc. If ad < bc, then a/b < c/d.

Common Denominator Rule

When denominators are equal, the fraction with the smaller numerator is the smaller fraction.

Proper vs. Improper Fractions

A proper fraction (numerator < denominator) is always smaller than an improper fraction (numerator ≥ denominator).

Shortcut Trick

Estimate the middle term by finding the cube root of the product: √³4845.

Since 16³ = 4096 and 17³ = 4913, the middle odd number must be 17.

The three consecutive odd numbers are (17 − 2), 17, and (17 + 2), which are 15, 17, and 19.

Verify the product: 15 × 17 × 19 = 255 × 19 = 4845.

The smallest number among them is 15.

∴ The correct answer is 15.

Alternate Method

Given: Product of three consecutive odd numbers = 4845.

Perform prime factorization of 4845 to identify the odd factors:

⇒ 4845 ÷ 5 = 969

⇒ 969 ÷ 3 = 323

⇒ 323 is not divisible by 3, 5, 7, 11, or 13. Testing 17:

⇒ 323 ÷ 17 = 19

⇒ Prime factors are 5, 3, 17, and 19.

⇒ Grouping them into three consecutive numbers: (5 × 3), 17, 19

⇒ Numbers = 15, 17, 19

⇒ Smallest number = 15

∴ The correct answer is 15.

Additional Information

Consecutive Odd Numbers

Consecutive odd numbers always have a common difference of 2 and can be represented as n, n+2, n+4...

Factorization Rule

When the product of consecutive integers is given, the middle term is always close to the n^th root of the product.

Sum of Consecutive Odd Numbers

The sum of n consecutive odd numbers starting from 1 is always a perfect square, given by n².

Shortcut Trick

Identify the nearest perfect cube to 350.

We know that 7³ = 343 and 8³ = 512.

Testing x = 7: Sum = 7³ + 7 = 343 + 7 = 350.

Since the sum matches 350, the required number is 7.

∴ The correct answer is 7.

Alternate Method

Given: The sum of a positive number and its cube is 350.

Let the number be x.

Formula Used: x³ + x = 350

⇒ x³ + x − 350 = 0

⇒ By Trial and Error method, we test the value x = 7.

⇒ 7³ + 7 = 343 + 7

⇒ 350 = 350

⇒ The Left Hand Side (LHS) equals the Right Hand Side (RHS).

∴ The correct answer is 7.

Additional Information

Cubic Equation Properties

A cubic equation x³ + ax + b = 0 has at least one real root. For positive x, the function f(x) = x³ + x is strictly increasing, meaning it has only one positive solution.

Perfect Cubes

Memorizing cubes up to 10 is essential: 5³ = 125, 6³ = 216, 7³ = 343, 8³ = 512, 9³ = 729.

Rational Root Theorem

Potential integer roots of a polynomial are always factors of the constant term (in this case, factors of 350 like 1, 2, 5, 7, 10, etc.).

Shortcut Trick

Use the Difference of Squares identity a² − b² = (a − b)(a + b) by pairing terms: (38² − 36²) + (41² − 29²).

(38 − 36)(38 + 36) + (41 − 29)(41 + 29)

⇒ 2 × 74 + 12 × 70

⇒ 148 + 840 = 988

∴ The correct answer is 988.

Alternate Method

Given Expression: 38² + 41² − 29² − 36²

Calculate the Squares of the numbers individually:

⇒ 38² = 1444

⇒ 41² = 1681

⇒ 29² = 841

⇒ 36² = 1296

Substitute the squared values back into the expression:

⇒ 1444 + 1681 − 841 − 1296

Group the Addition and Subtraction terms:

⇒ (1444 + 1681) − (841 + 1296)

⇒ 3125 − 2137

⇒ 988

∴ The correct answer is 988.

Additional Information

Algebraic Identities for Squares

Standard identities like (a + b)² = a² + 2ab + b² and a² − b² = (a − b)(a + b) are essential for solving complex arithmetic quickly.

BODMAS Rule

Always solve expressions in the order of Brackets, Orders (Powers/Roots), Division, Multiplication, Addition, and Subtraction.

Fast Calculation Tips

Memorizing Squares up to 50 and Cubes up to 20 helps in reducing the time spent on basic calculations during competitive exams.

Shortcut Trick

Side of the square = √Area = √36 = 6 cm.

Perimeter of the square = 4 × Side = 4 × 6 = 24 cm.

∴ The correct answer is 24 cm.

Alternate Method

Given:

Area of the square = 36 cm²

Formula Used:

Area of a square = (Side)²

Perimeter of a square = 4 × Side

Calculations:

⇒ Area = Side²

⇒ 36 = Side²

⇒ Side = √36

⇒ Side = 6 cm

⇒ Perimeter = 4 × Side

⇒ Perimeter = 4 × 6

⇒ Perimeter = 24 cm

∴ The correct answer is 24 cm.

Additional Information

Diagonal of a Square

The diagonal (d) of a square with side (s) is given by d = s√2.

Area using Diagonal

The area of a square can also be calculated using its diagonal as Area = d² ÷ 2.

Properties of a Square

All sides are equal, all interior angles are 90°, and diagonals bisect each other at 90°.

Shortcut Trick

The relationship between the Area and the Diagonal (d) of a square is: Area = d² ÷ 2.

⇒ 144 = d² ÷ 2

⇒ d² = 144 × 2 = 288

⇒ d = √288 = 12√2 cm.

∴ The correct answer is 12√2 cm.

Alternate Method

Given: Area of the square = 144 cm²

Formula used: Area = (side)² and Diagonal = side × √2

⇒ Side² = 144

⇒ Side = √144

⇒ Side = 12 cm

⇒ Diagonal of a square = side × √2

⇒ Diagonal = 12 × √2 = 12√2 cm

∴ The correct answer is 12√2 cm.

Additional Information

Perimeter of a Square

The total boundary length of a square is calculated as 4 × side.

Area in terms of Diagonal

The Area of a square can be expressed as 1/2 × (Diagonal)².

Properties of Diagonals

In a square, both diagonals are equal in length and bisect each other at right angles (90°).

Shortcut Trick

In a Rectangle, the sum of Length and Breadth is always half of the Perimeter.

L + B = Perimeter ÷ 2

12 + B = 40 ÷ 2 = 20

B = 20 − 12 = 8 cm

∴ The correct answer is 8 cm.

Alternate Method

Given:

Perimeter of the rectangle = 40 cm

Length (L) of the rectangle = 12 cm

Formula Used:

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

Calculations:

⇒ 40 = 2 × (12 + B)

⇒ 40 ÷ 2 = 12 + B

⇒ 20 = 12 + B

⇒ B = 20 − 12

⇒ B = 8 cm

∴ The correct answer is 8 cm.

Additional Information

Area of a Rectangle

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

Diagonal of a Rectangle

The distance between opposite corners is found using Pythagoras theorem: d = √(L² + B²).

Perimeter of a Square

For a Square, all sides (a) are equal, so the Perimeter = 4 × a.

Shortcut Trick

Required sum = (Sum of squares of first 25 natural numbers) − (Sum of squares of first 10).

Using formula Σn² = [n(n + 1)(2n + 1)] ÷ 6.

Sum(1 to 25) = [25 × 26 × 51] ÷ 6 = 5525.

Sum(1 to 10) = [10 × 11 × 21] ÷ 6 = 385.

Result = 5525 − 385 = 5140.

∴ The correct answer is 5140.

Alternate Method

Given: 11² + 12² + 13² + ... + 25²

Formula Used: The sum of squares of first n natural numbers is S_n = [n(n + 1)(2n + 1)] ÷ 6.

⇒ Required value = (1² + 2² + ... + 25²) − (1² + 2² + ... + 10²)

⇒ S₂₅ = [25 × (25 + 1) × (2 × 25 + 1)] ÷ 6

⇒ S₂₅ = (25 × 26 × 51) ÷ 6 = 5525

⇒ S₁₀ = [10 × (10 + 1) × (2 × 10 + 1)] ÷ 6

⇒ S₁₀ = (10 × 11 × 21) ÷ 6 = 385

⇒ Final Sum = 5525 − 385 = 5140

∴ The correct answer is 5140.

Additional Information

Sum of first n natural numbers

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

Sum of cubes of first n natural numbers

The sum of cubes Σn³ is equal to the square of the sum of the first n numbers: [[n(n + 1)] ÷ 2]².

Sum of first n odd numbers

The sum of the first n odd natural numbers (1 + 3 + 5 + ... up to n terms) is simply n².

Sum of squares of first n even numbers

The sum of squares of the first n even numbers (2² + 4² + ... + (2n)²) is [2n(n + 1)(2n + 1)] ÷ 3.

Shortcut Trick

Assume the average expenditure of 220 as the base value.

Calculate net deviation for the first 4 days: (220−220) + (175−220) + (185−220) + (190−220) = 0 − 45 − 35 − 30 = −110.

To keep the average constant at 220, the 5th day must compensate for this negative deviation.

Expenditure on 5th day = 220 + 110 = 330.

∴ The correct answer is ₹330.

Alternate Method

Given:

Average expenditure for 5 days = ₹220

Expenditures for first 4 days = ₹220, ₹175, ₹185, and ₹190

Formula Used:

Total Sum = Average × Number of observations

Value of nth item = Total Sum − Sum of (n−1) items

Calculations:

⇒ Total expenditure for 5 days = 220 × 5 = ₹1100

⇒ Sum of expenditure for first 4 days = 220 + 175 + 185 + 190

⇒ Sum of 4 days = ₹770

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

⇒ 5th day = 1100 − 770

⇒ 5th day = ₹330

∴ The correct answer is ₹330.

Additional Information

Concept of Average

The average (Arithmetic Mean) is the sum of all observations divided by the total number of observations. Formula: Average = Σx ÷ n.

Net Deviation Method

In any set of numbers, the algebraic sum of deviations from the mean is always zero. This property is used to find a missing value quickly without calculating the total sum.

Change in Average

If a new observation is added, New Sum = (Old Average × Old n) + New Observation. The new average then becomes (New Sum) ÷ (n + 1).

Shortcut Trick

For any set of numbers, if every number in the set is increased by a constant k, the new average will also increase by k.

The first sequence starts at a and the second sequence starts at a + 7, meaning each of the 13 consecutive numbers has increased by exactly 7.

Since the initial average is x and the increase per term is 7, the new average is x + 7.

∴ The correct answer is x + 7.

Alternate Method

Given:

Number of terms (n) = 13

First sequence starts with a. Average = x

Second sequence starts with a + 7.

Formula Used:

Average of consecutive numbers = (First term + Last term) ÷ 2

Calculations:

⇒ For the first sequence: a, a+1, a+2, ..., a+12

⇒ Average x = (a + a + 12) ÷ 2

⇒ x = (2a + 12) ÷ 2 = a + 6

⇒ For the second sequence: (a + 7), (a + 8), ..., (a + 7 + 12)

⇒ Last term of second sequence = a + 19

⇒ New Average = ((a + 7) + (a + 19)) ÷ 2

⇒ New Average = (2a + 26) ÷ 2 = a + 13

⇒ Comparing with x: New Average = (a + 6) + 7 = x + 7

∴ The correct answer is x + 7.

Additional Information

Average of Arithmetic Progression

For any sequence in AP, the average is exactly the middle term if the number of terms is odd, or the mean of the two middle terms if even.

Linear Property of Mean

If every observation in a data set is multiplied by k and then increased by c, the new mean becomes (Original Mean × k) + c.

Sum of Natural Numbers

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

Shortcut Trick

If A percent of A is given as a value K, then the relationship is A² / 100 = K.

Here, K = 729.

⇒ A² = 729 × 100 = 72900.

∴ The correct answer is 72900.

Alternate Method

Given:

The percentage of a number itself is given: A% of A = 729.

Formula Used:

x% of y = (x ÷ 100) × y

Calculations:

⇒ (A / 100) × A = 729

⇒ A² / 100 = 729

⇒ A² = 729 × 100

⇒ A² = 72900

∴ The correct answer is 72900.

Additional Information

Percentage Concept

The term percent means per hundred. Any value x% is equivalent to the fraction x/100.

Squares of Numbers

The square of a number is the result of multiplying the number by itself. For example, if A = 270, then A² = 72900.

Direct Proportion in Percentages

When the base and the percentage rate are the same (A% of A), the result is always proportional to the square of that base divided by 100.

Shortcut Trick

Ratio of Selling Price (SP) to Cost Price (CP) = 13 : 10

Let CP = 10 units and SP = 13 units.

Profit = SP − CP = 13 − 10 = 3 units.

Profit percentage = (Profit / CP) × 100 = (3 / 10) × 100 = 30%.

∴ The correct answer is 30%.

Alternate Method

Given:

The ratio of Selling Price (SP) to Cost Price (CP) = 13 : 10

Formula Used:

Profit % = [(SP − CP) / CP] × 100

Calculations:

⇒ Let CP = 10k and SP = 13k (where k is a constant)

⇒ Profit = 13k − 10k = 3k

⇒ Profit % = (3k / 10k) × 100

⇒ Profit % = 0.3 × 100

⇒ Profit % = 30%

∴ The correct answer is 30%.

Additional Information

Loss Percentage

If the Cost Price is greater than the Selling Price, it is a loss. Loss % = [(CP − SP) / CP] × 100.

Relationship with Marked Price

Profit % can also be related to Mark-up % and Discount % using the formula: (100 + Profit %) / (100 − Discount %) = MP / CP.

Fractional Conversions

A profit of 30% implies the multiplier for CP to reach SP is 1.3 (or 13/10).

Shortcut Trick

Apply the MDH Formula: (M₁ × D₁) / W₁ = (M₂ × D₂) / W₂

(12 × 10) / (1/2) = (M₂ × 20) / (1/3)

120 × 2 = M₂ × 60

240 = 60 × M₂ ⇒ M₂ = 4 men

∴ The correct answer is 4 men.

Alternate Method

Given:

Initial men (M₁) = 12 men, Days (D₁) = 10 days, Work (W₁) = 1/2 part

Final men (M₂) = ?, Days (D₂) = 20 days, Work (W₂) = 1/3 part

Formula Used:

(M₁ × D₁ × E₁) / W₁ = (M₂ × D₂ × E₂) / W₂

Calculations:

⇒ (12 × 10) / (1/2) = (M₂ × 20) / (1/3)

⇒ 120 × 2 = M₂ × 20 × 3

⇒ 240 = M₂ × 60

⇒ M₂ = 240 ÷ 60

⇒ M₂ = 4 men

∴ The correct answer is 4 men.

Additional Information

Chain Rule Formula

The general relationship is M₁D₁H₁/W₁ = M₂D₂H₂/W₂, where M is men, D is days, H is hours, and W is work.

Direct and Inverse Proportionality

Number of men is directly proportional to work (W ∝ M) and inversely proportional to time (M ∝ 1/D).

Work-Rate Logic

Total man-days required for 1 unit of work = (M × D) ÷ Part of work. Here, (12 × 10) ÷ (1/2) = 240 man-days.

Shortcut Trick

Efficiency ratio A : B = 1 : 5 (since time ratio is 5 : 1).

Let efficiency of A = 1, then efficiency of B = 5 and Total Work = 100 units.

Efficiency of C = Efficiency (A + B) = 1 + 5 = 6.

Total efficiency (A + B + C) = 1 + 5 + 6 = 12 units/day.

Time taken = Total Work ÷ Total Efficiency = 100 ÷ 12 = 25/3 days.

∴ The correct answer is 25/3 days.

Alternate Method

Given:

Time taken by A = 100 days.

Time taken by A = 5 × Time taken by B.

Time taken by C = Time taken by (A + B) together.

Calculations:

⇒ Time taken by B = 100 ÷ 5 = 20 days.

⇒ Let Total Work = LCM(100, 20) = 100 units.

⇒ Efficiency of A = 1 unit/day.

⇒ Efficiency of B = 5 units/day.

⇒ Combined efficiency of A + B = 1 + 5 = 6 units/day.

⇒ Since C takes the same time as A + B, Efficiency of C = Efficiency of (A + B) = 6 units/day.

⇒ Total efficiency of A + B + C = 1 + 5 + 6 = 12 units/day.

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

⇒ Time = 100 ÷ 12 = 25/3 days.

∴ The correct answer is 25/3 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete the work. Efficiency = Work ÷ Time.

Combined Efficiency Rule

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

Work and Wages

Wages are generally distributed in the ratio of work done or the ratio of efficiencies if they work for the same duration.

Shortcut Trick

Total units = 3 + 2 = 5 units

5 units = 300 students ⇒ 1 unit = 60 students

Initial Boys = 3 × 60 = 180

Total Boys now = 180 + 30 = 210

∴ The correct answer is 210 boys.

Alternate Method

Given:

Total number of students = 300

Ratio of boys to girls = 3 : 2

Additional boys admitted = 30

⇒ Sum of ratio parts = 3 + 2 = 5

⇒ Number of boys = (3 ÷ 5) × 300

⇒ Number of boys = 3 × 60 = 180

⇒ Number of girls = (2 ÷ 5) × 300 = 120

⇒ After admitting 30 more boys, new count = 180 + 30

⇒ Total boys now = 210

∴ The correct answer is 210 boys.

Additional Information

Ratio and Proportion

A ratio compares two quantities by division. If a total S is divided in the ratio a:b, the parts are a × S / (a+b) and b × S / (a+b).

New Ratio Calculation

To find the new ratio after an addition, add the extra amount to the specific part. Here, new ratio of Boys:Girls = 210:120 = 7:4.

Percentage of Boys

Initial % of boys = (3/5) × 100 = 60%. After addition, total students = 330, % of boys ≈ 63.63%.

The correct answer is: To accomplish a large goal by doing smaller, cumulative tasks.

Key Points

• The idiom 'eat an elephant one bite at a time' refers to the practice of tackling a daunting or enormous task by breaking it down into smaller, manageable parts. (किसी बड़े काम को छोटे-छोटे टुकड़ों में बांटकर पूरा करना)
• Example: Don't be overwhelmed by the entire syllabus; just eat an elephant one bite at a time and study one chapter each day.
• 'To accomplish a large goal by doing smaller, cumulative tasks' means to reach a significant objective through a series of minor, sequential steps that add up over time. (छोटे, संचयी कार्यों को करके एक बड़े लक्ष्य को प्राप्त करना)
• Example: The developer completed the complex software project by eating an elephant one bite at a time, focusing on individual modules.
• Hence, we can infer that the meaning of the idiom is to handle a large responsibility through incremental progress.

Therefore, the correct answer is: To accomplish a large goal by doing smaller, cumulative tasks.

Additional Information

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

• To have seen or experienced as much as one can endure (जितना सहन किया जा सके उतना देख लिया या अनुभव कर लिया होना): This describes a person who has reached the limit of their patience or endurance.
• Example: After weeks of heavy rain and flooding, the residents had seen as much as they could endure.
• An extremely obvious circumstance that can hardly be overlooked (एक अत्यंत स्पष्ट परिस्थिति जिसे शायद ही अनदेखा किया जा सके): This refers to a conspicuous problem or fact that everyone is aware of but may be ignoring.
• Example: The decline in quality was an obvious circumstance that the management failed to address.
• To recover from a drinking bout (शराब के नशे से उबरना): This refers to the recovery process following a period of excessive alcohol consumption.
• Example: He spent the entire morning trying to recover from a drinking bout at the wedding reception.

The correct answer is: Variety.

Key Points

• The word 'diversity' refers to the state of being diverse; it indicates a range of different things or the inclusion of many different elements. (विविधता)
• Example: The biological diversity of the rainforest is truly breathtaking.
• 'Variety' refers to the quality or state of being different or diverse, and it is used to describe a collection of different things of the same general type. It is the closest synonym to diversity. (विभिन्नता)
• Example: The menu offers a wide variety of seafood dishes.
• Hence, we can infer that the closest synonym of 'diversity' is 'variety'.

Therefore, the correct answer is- Variety.

Additional Information

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

• Sameness (समानता): The quality of being the same; a lack of variety or change.
• Example: The sameness of the daily routine started to become tiring.
• Uniformity (एकरूपता): The quality or state of being uniform; consistency or staying the same in all cases and at all times.
• Example: The factory maintains a high level of uniformity in its production process.
• Simplicity (सादगी): The quality or condition of being easy to understand or do; the state of being plain or uncomplicated.
• Example: I admire the simplicity and elegance of her writing style.

The correct answer is: deforestation.

Key Points

• The word 'deforestration' is a common misspelling of the term used for cutting down trees on a large scale. (वनों की कटाई)
• Example: The effects of deforestration can be devastating for the global climate.
• 'deforestation' is the correct spelling, which means the clearing or thinning of forests by humans. (वनों की कटाई)
• Example: Global efforts are being made to reduce deforestation and protect natural habitats.
• Hence, we can infer that the misspelt word is 'deforestation'.

Therefore, the correct answer is: deforestation.

Additional Information

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

• accelerate (तेजी लाना): To cause to happen sooner or more quickly.
• Example: The new technology will help to accelerate the production process.
• biodiversity (जैव विविधता): The variety of plant and animal life in a particular habitat.
• Example: Preserving biodiversity is crucial for the health of our ecosystem.
• degradation (ह्रास): The process of something becoming worse or being destroyed.
• Example: Environmental degradation poses a threat to many species.

The correct answer is: Quicksilver.

Key Points

• The term 'misspelt word' refers to a word that has been spelled incorrectly according to standard English spelling rules. (अशुद्ध वर्तनी वाला शब्द)
• Example: Finding the misspelt word in a text is a common exercise to improve vocabulary and spelling skills.
• 'Quicksilver' refers to the liquid metal mercury, or a highly changeable and unpredictable temperament. It is sometimes misspelt as 'Quicksilvar' or 'Quicksiler' in tests. (पारा / अत्यंत चंचल)
• Example: The temperature was so high that the quicksilver in the thermometer rose rapidly.
• Hence, we can infer that the misspelt word is 'Quicksilver'.

Therefore, the correct answer is: Quicksilver.

Additional Information

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

• Quantitative (मात्रात्मक): Relating to, measuring, or measured by the quantity of something rather than its quality.
• Example: The researchers conducted a quantitative analysis of the data to find the exact percentages.
• Quarantine (संगरोध): A state, period, or place of isolation in which people or animals that have arrived from elsewhere or been exposed to infectious or contagious disease are placed.
• Example: The passengers were kept in quarantine for fourteen days to prevent the spread of the virus.
• Questionable (संदेहास्पद): Doubtful as regards truth, quality, or honesty; open to question.
• Example: The authenticity of the painting is highly questionable.

The correct answer is: Foolish.

Key Points

• The word 'Sensible' means having, using, or showing good sense or sound judgment; it describes someone who is practical and reasonable. (समझदार)
• Example: It was sensible of her to check the weather forecast before planning the outdoor picnic.
• 'Foolish' refers to someone or something that lacks good sense or judgment; it describes actions that are unwise or senseless. (मूर्खतापूर्ण)
• Example: It would be foolish to ignore the warning signs posted near the cliff edge.
• Hence, we can infer that the antonym or opposite of 'Sensible' is 'Foolish'.

Therefore, the correct answer is- Foolish.

Additional Information

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

• Rational (तर्कसंगत): Based on or in accordance with reason or logic.
• Example: During a crisis, it is important to remain rational and not let emotions take over.
• Wise (बुद्धिमान): Having or showing experience, knowledge, and good judgment.
• Example: The king was known for being a wise ruler who cared for his people.
• Judicious (विवेकपूर्ण): Having, showing, or done with good judgment or sense; being careful in making decisions.
• Example: The judicious use of electricity can help significantly reduce your monthly bills.

The correct answer is 'ruined'.

Key Points

• The word 'ruined' means reduced to a state of decay, collapse, or disintegration; it describes something that has been damaged so badly that it is no longer useful or beautiful. (नष्ट या बर्बाद)
• The sentence states the painting was 'nearly destroyed', which implies that while it was close to being lost, it was fortunately not completely 'ruined'.
• The word 'luckily' acts as a transition to show that despite the fire, the final outcome was not as bad as it could have been.

Therefore, the correct answer is 'Option 2'.

Complete Sentence: The old painting was nearly destroyed by fire, but luckily it was not ruined.

Additional Information

• Reined (past tense of rein): To check or guide a horse by pulling on its reins. (लगाम लगाना)
• Reined in: A phrasal verb meaning to limit or control something or someone. (नियंत्रित करना)
• Rained (past tense of rain): Water falling from the sky in drops. (बारिश होना)

The correct answer is: Gazebo.

Key Points

• The phrase 'a freestanding roofed structure usually open on the sides' refers to a small building, often found in gardens or parks, designed to provide shade and a place to rest while enjoying the surroundings. (एक स्वतंत्र छत वाली संरचना जो आमतौर पर किनारों से खुली होती है)
• Example: We sat in the gazebo to protect ourselves from the afternoon sun while watching the children play.
• 'Gazebo' is a pavilion-like structure, sometimes octagonal or turret-shaped, built as a summerhouse or a decorative feature in a landscape. (बारहदरी / छतरीनुमा मंडप)
• Example: The local park has a beautiful white gazebo where the band plays music on Sunday evenings.
• Hence, we can conclude that the one-word substitute for the given phrase is 'Gazebo'.

Therefore, the correct answer is: Gazebo.

Additional Information

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

• Gizmo (कल-पुर्जा / यंत्र): A small mechanical or electronic device or gadget, especially one whose name is not known.
• Example: He showed me a clever little gizmo for opening stubborn jar lids.
• Glabella (भौंहों के बीच का भाग): The smooth part of the forehead located between the eyebrows and above the nose.
• Example: The doctor noticed a slight swelling on the patient's glabella during the examination.
• Gossamer (महीन जाल / बहुत पतला): A very light, thin, and delicate substance, often referring to cobwebs or fine fabric.
• Example: The morning grass was covered in gossamer webs that sparkled with dew.

The correct answer is The Earth is still thought to be flat by some people!.

Key Points

• The original sentence is in the Active Voice following the structure: Subject (Some people) + Verb (think) + Noun Clause (that the Earth is flat).
• When converting sentences with Reporting Verbs (like think, believe, say, or claim) into the Passive Voice, two structures are commonly used: the Impersonal Passive (starting with 'It is...') or the Personal Passive (starting with the subject of the clause).
• In the Personal Passive construction, the subject of the subordinate clause (The Earth) becomes the subject of the passive sentence. The main verb (think), which is in the Present Indefinite Tense, is changed to is thought. Hence, the structure becomes Subject + is/am/are + Past Participle + to-infinitive.
• The verb in the subordinate clause (is) is replaced by its Infinitive form (to be) to maintain grammatical continuity. The adverb still is placed before the past participle to retain the original meaning and emphasis.
• Finally, the original subject (Some people) is introduced using the preposition by. Therefore, the transformation yields: The Earth is still thought to be flat by some people!

 Additional Information

• The Impersonal Passive version of this sentence would be: It is still thought by some people that the Earth is flat! However, this was not provided among the correct options.
• Verbs of Perception and Cognition:
• Verbs like consider, know, report, and understand follow this same rule of Passive Transformation.
• If the action in the subordinate clause happened before the thinking, a Perfect Infinitive (to have been) would be used instead of a Simple Infinitive (to be).
• Tense Consistency: In option 2, the use of was thought is incorrect because the original sentence is in the Present Tense. Passive voice must always preserve the Tense of the active verb.

The correct answer is It is alleged that the man is a cheat..

Key Points

• The given sentence They allege that the man is a cheat follows a structure where the subject is the indefinite pronoun They, followed by a reporting verb (allege), and a noun clause (that the man is a cheat) acting as the direct object.
• To convert sentences with a that-clause into the passive voice, the impersonal passive construction is commonly used, which begins with the formal introductory subject It.
• The reporting verb in the active sentence, allege, is in the Simple Present Tense. In the passive voice, this tense is formed using is/am/are + past participle (V3). Since It is a third-person singular subject, the auxiliary verb is is used followed by alleged.
• The subordinate noun clause (that the man is a cheat) remains in its original form and is placed after the passive reporting verb.
• This transformation shifts the emphasis from the anonymous subject (They) to the statement of allegation itself, making the tone more formal and objective.

 Additional Information

• Reporting Verbs and Passive Structures:
• Verbs such as say, believe, think, claim, and report follow this same pattern when the active subject is general or unknown.
• Tense Mismatch: The options The man was alleged to be a cheat and The man was a cheat they alleged are incorrect because they use the Past Tense (was), whereas the original sentence is in the Present Tense.
• Infinitive Conversion: While a personal passive like The man is alleged to be a cheat is a valid alternative, the impersonal passive starting with It is the most direct conversion for the provided options.
• Meaning Shift: The option The man is alleged to have cheated uses a perfect infinitive, which suggests a completed past action rather than the current stative identity of being a cheat mentioned in the original text.

The correct answer is 'in'.

Key Points

• The preposition 'in' is used to describe something located within the area or volume of a three-dimensional space, such as the canopy, branches, and leaves of a tree.
• Since fruits like oranges grow and hang nestled inside the branches and foliage of a tree, the phrase 'in the tree' is grammatically correct and suitable in this context.

Therefore, the correct answer is Option 3.

Complete Sentence: 'There had been a large number of oranges in the tree last year.'

Additional Information

• Option 1: 'at' is incorrect because it is used to indicate a specific point or location, not containment.
• Option 2: 'on' usually refers to being on the surface of something, but 'in the tree' is the correct choice here to refer to the oranges within the tree's branches.
• Option 4: 'with' is incorrect as it indicates accompaniment or using an instrument.

The correct answer is Option 3.

Key Points

• The sentence includes the specific time marker yesterday, which indicates a completed action in the past.
• When a sentence contains a definite point of time in the past (such as yesterday, last night, or two days ago), the Simple Past Tense must be used instead of the Present Perfect Tense.
• The phrase has arrested is in the Present Perfect Tense, which is grammatically incorrect when paired with a specific past time reference.
• The correct verb form to replace it is arrested, which is the Simple Past form.

Therefore, the correct answer is arrested the thief along with.

Correct Sentence: 'The police arrested the thief along with his accomplices yesterday.'

Additional Information

• Option 1 ('have arrested the thief along with'): This uses the Present Perfect Tense (plural), which is still incorrect because of the specific time reference yesterday.
• Option 2 ('had arrested the thief along with'): This uses the Past Perfect Tense. The Past Perfect is generally used to describe an action that happened before another action in the past, rather than a single event with a specific time stamp like yesterday.
• Option 4 ('No improvement required'): This is incorrect because the original sentence uses the Present Perfect Tense with a past time marker, violating standard grammar rules.
• Note: While 'police' is a collective noun usually treated as plural (taking 'have' or 'are'), the primary grammatical error here is the tense mismatch with the word yesterday.

The correct answer is Option 3.

Key Points

• The paragraph describes a supernatural or eerie experience involving a cloud and mysterious voices heard at night.
• Sentence A follows S1: S1 introduces a cloud hurrying across the zenith. Sentence A continues this visual description by identifying the cloud as a black mass sweeping northward while noting that the rest of the blue sky was still visible.
• Sentence D follows A: After establishing the cloud's position directly overhead, Sentence D introduces a new sensory element—a confused and doubtful sound of voices coming from the depths of that very cloud.
• Sentence C follows D: This sentence provides more detail about the voices mentioned in D. The listener begins to recognize the accents of townspeople, including both pious individuals and those seen at the tavern.
• Sentence B follows C: After the specific identification in C, the listener experiences a moment of doubt. Sentence B explains that the sounds became so indistinct that he wondered if it was just the murmur of the old forest.
• S2 completes the sequence: The doubt in B is resolved in S2, where a stronger swell of those familiar tones from Salem village is heard, confirming that the voices were real.
• The correct logical sequence is ADCB.

Coherent paragraph after rearrangement:

'While he still gazed upward into the deep arch of the firmament and had lifted his hands to pray, a cloud, though no wind was stirring, hurried across the zenith and hid the brightening stars. The blue sky was still visible, except directly overhead, where this black mass of cloud was sweeping swiftly northward. Aloft in the air, as if from the depths of the cloud, came a confused and doubtful sound of voices. Once the listener fancied that he could distinguish the accents of townspeople of his own, men and women, both pious and ungodly, many of whom he had met at the communion table and had seen others rioting at the tavern. The next moment, so indistinct were the sounds, he doubted whether he had heard aught but the murmur of the old forest, whispering without a wind. Then came a stronger swell of those familiar tones, heard daily in the sunshine at Salem village, but never until now from a cloud of night.'

Therefore, the correct sequence is ADCB.

The correct answer is Option 2.

Key Points

• The paragraph begins with S1, which sets the scene of confusion in a waiting room after a bell sounds.
• Sentence C follows as it provides specific details of the confusion mentioned in S1:
• 'People seized their luggage and trampled on each other's toes; the porter who stood at the entrance door was stormed with questions.'
• Sentence A follows as it summarizes the atmosphere created by the actions in Sentence C:
• 'There was bustle and noise everywhere.'
• Sentence D is the third sentence as it shifts the focus from the general station noise to the narrator's specific action of boarding:
• 'I entered the third-class carriage in which the fair-haired student was sitting.'
• Sentence B follows because the pronoun 'it' refers back to the 'third-class carriage' mentioned in Sentence D, and it describes the student's situation:
• 'His friend had put him into it, settling him in the corner seat beside the window, as if he were an invalid, and urging him to take comfort.'
• The sequence concludes with S2, which describes the student's difficulty in responding or speaking.
• The correct sequence is CADB.

Coherent paragraph after rearrangement:

The bell sounded, and the waiting room became a scene of confusion. People seized their luggage and trampled on each other's toes; the porter who stood at the entrance door was stormed with questions. There was bustle and noise everywhere. I entered the third-class carriage in which the fair-haired student was sitting. His friend had put him into it, settling him in the corner seat beside the window, as if he were an invalid, and urging him to take comfort. It did not come easy to him; the words seemed to stick in his throat.

The correct answer is No improvement required.

Key Points

• The original sentence follows the grammatical rule of Parallelism, which dictates that items in a series or list must share the same grammatical structure to ensure clarity and balance.
• In this sentence, the phrase needs to functions as the lead-in to a series of three infinitive actions. The to-infinitive marker (to) applies to all subsequent verbs in the list: address, provide, and increase.
• The first verb, address, is in its base form. To maintain consistency, every subsequent verb in the list must also remain in the base form.
• The second verb, provide, correctly maintains this base form, ensuring it is parallel with 'address'.
• The third verb, increase, similarly follows the base form structure, effectively completing the parallel sequence connected by the coordinating conjunction and.
• Since all three components—address, provide, and increase—are in the same grammatical form, the sentence is technically and stylistically correct as written.

 Additional Information

• Parallel Structure:
• This concept is essential in formal writing and competitive exams to avoid faulty parallelism, which occurs when items in a series have different grammatical forms.
• When using the infinitive ('to' + verb) in a list, you can either repeat the 'to' before every verb (e.g., to address, to provide, and to increase) or use it only once before the first verb, provided all subsequent verbs are in the base form.
• Incorrect Option Analysis:
• Option 1: Uses the present participle (providing), which breaks the flow established by the base verbs 'address' and 'increase'.
• Option 2: Starts with the gerund/participle (addressing), which does not logically follow the infinitive marker 'to' in this context.
• Option 3: Concludes with increasing, creating an asymmetrical list because the first two verbs are in the base form while the third is not.

The correct answer is is no small feat.

Key Points

• The expression no small feat is a widely used idiomatic phrase in the English language which signifies that an achievement is significant, difficult, or requires extraordinary effort.
• In the given sentence, the original phrase is not small feat is grammatically incorrect because the singular countable noun feat requires an article (like a) or a determiner (like no) to function correctly within the predicate.
• The word no acts as a determiner that modifies the noun phrase small feat, providing a more emphatic tone than simply saying not a small feat.
• Contextually, climbing Mount Everest is a monumental task, and the idiom no small feat perfectly captures the gravity and magnitude of such an accomplishment.
• Therefore, replacing the underlined part with is no small feat ensures both grammatical precision and idiomatic naturalness.