RRB NTPC (Graduate) CBT-I Official Paper (Held On: 17 Mar, 2026 Shift 3) (Previous Year Paper)

Shortcut Trick

Removed part = 45° out of 360° ⇒ removed = 1/8

Remaining volume = 7/8 of cylinder

Total volume = πr²h = π × 12² × 25 = 3600π

Required = 7/8 × 3600π = 3150π

∴ Answer = 3150π

Alternate Method

45° r = 12 cm

Given:

r = 12 cm, h = 25 cm, angle = 45°

Formula:

Volume of cylinder = πr²h

Sector volume = (θ/360) × πr²h

Calculations:

⇒ Total volume = π × 12² × 25 = 3600π

⇒ Removed volume = (45/360) × 3600π = 1/8 × 3600π = 450π

⇒ Remaining = 3600π − 450π = 3150π

Final Answer: 3150π cm³

Additional Information

Volume of Cylinder: πr²h → depends on base area and height.

Sector of Cylinder: Fraction = θ/360 → same fraction applies to volume.

Mensuration Shortcut: Always find fraction removed first to save time.

Angle Conversion: 45° = 1/8 of full circle (360°).

The correct answer is Mental health in humanitarian emergencies.

Key Points

• The World Mental Health Day theme for 10 October 2025 is "Access to Services - Mental Health in Catastrophes and Emergencies".
• This theme emphasizes protecting mental well-being during crises (natural disasters, conflicts, pandemics) and the urgent need to provide psychological support to affected populations

Additional Information

• India's Mental Health Initiatives:
• National Mental Health Programme (NMHP): Launched in 1982 to ensure the availability of mental health services.
• Mental Healthcare Act, 2017: This act provides a legal framework to protect the rights of persons with mental illness and decriminalizes suicide attempts.
• Tele-MANAS: Launched during the Union Budget 2022-23, the Tele-Mental Health Assistance and Networking Across States initiative provides 24/7 free counseling services across the country.

Important Points

• Global Statistics: According to the World Health Organization (WHO), nearly 1 in 7 adolescents (aged 10-19 years) globally experience a mental disorder, yet these remain largely unrecognized and untreated.
• The Green Ribbon: The Green Ribbon is the international symbol for mental health awareness. People wear it on 10 October to show support for the millions of people living with mental health challenges.
• SDG Target 3.4: Under the Sustainable Development Goals (SDGs), the United Nations aims to reduce premature mortality from non-communicable diseases by one-third through prevention and treatment and promote mental health and well-being by 2030.
• Kiran Helpline: The Ministry of Social Justice and Empowerment in India launched the Kiran helpline (1800-599-0019) in September 2020 to provide mental health rehabilitation services.

The correct answer is Uses minimum power.

Key Points

• Hibernation is a specific power management mode in computer operating systems that saves the current state of the system to the Hard Disk or Solid State Drive (SSD) before completely powering off.
• Unlike Sleep Mode, which keeps the system state in the Random Access Memory (RAM) and requires a continuous supply of electricity, Hibernation allows the computer to be fully turned off, meaning it uses minimum power (essentially zero) while preserving open documents and running applications. Hence, the statement regarding minimum power is correct.
• When a computer enters Hibernation, it writes the contents of its RAM into a file on the storage drive, often named hiberfil.sys in Windows environments.
• This mode is particularly useful for laptop users who need to save their battery life for an extended period without losing their active workspace or closing their programs.
• The primary function of Hibernation is to provide a middle ground between Sleep Mode (fast wake-up but uses battery) and Shut Down (no power use but loses all open work).

Additional Information

• Sleep Mode vs. Hibernation:
• In Sleep Mode, the computer enters a low-power state, but the RAM remains powered to keep the data "volatile." This allows for a near-instant wake-up time, usually within 2 to 5 seconds.
• In Hibernation, the wake-up time is longer (typically 20 to 40 seconds) because the system must read the saved data back from the Hard Drive into the RAM.
• Hybrid Sleep:
• This is a combination of Sleep and Hibernation designed primarily for desktop computers. It saves the state to both the RAM and the Hard Disk, ensuring that if a power failure occurs, the data is still safe on the disk.
• Storage Requirements:
• To enable Hibernation, the computer must have enough free disk space to accommodate a file equal to the size of the installed RAM (e.g., if you have 8GB of RAM, you need at least 8GB of disk space).
• Historical Context:
• The Hibernate feature became widely popular with the release of Windows 95 (OSR2) and Windows 98, significantly improving mobile computing efficiency for early notebook users.

Important Points

• Power Outages: One of the greatest features of Hibernation is that it protects your data against unexpected power loss. Since the state is stored on a non-volatile storage medium, even if the battery dies or the plug is pulled, your data remains intact.
• Hardware Wear: On older Hard Disk Drives (HDDs), frequent hibernating might involve significant mechanical read/write actions, but on modern SSDs, this process is highly efficient, though it does contribute to the Total Bytes Written (TBW) metric over a number of years.
• Modern Standby: In newer Windows 10 and Windows 11 devices, a feature called Modern Standby (S0 Low Power Idling) is replacing traditional sleep/hibernate to allow the PC to stay connected to the internet and receive notifications while in a low-power state.
• When to use: It is recommended to use Hibernation if you will not be using your laptop for more than 2 or 3 hours, or if you want to keep your current state but have no access to a charging port.

The correct answer is British and French.

Key Points

• The Battle of Wandiwash was a decisive battle in Indian history, fought on January 22, 1760.
• It was a major confrontation between the British East India Company and the French East India Company.
• The British forces were led by Sir Eyre Coote, while the French forces were commanded by the Comte de Lally.
• This battle was the turning point of the Third Carnatic War (1758–1763), which was the Indian theater of the global Seven Years' War fought between Britain and France.
• The British emerged victorious, effectively ending French colonial ambitions in India and paving the way for British supremacy over the Indian subcontinent.

Additional Information

• The Carnatic Wars:
• These were a series of three military conflicts in the middle of the 18^th century on the Indian subcontinent.
• The conflicts involved numerous nominally independent rulers and their vassals, struggles for succession and territory, and included a diplomatic and military struggle between the French East India Company and the British East India Company.
• The wars were mainly fought in the territories of the Nizam of Hyderabad and the Carnatic region (modern-day Tamil Nadu and Andhra Pradesh).
• Treaty of Paris (1763):
• The Seven Years' War ended with the signing of the Treaty of Paris in 1763.
• According to the treaty, the French factories (trading posts) in India, such as Pondicherry and Chandernagore, were restored to France.
• However, the French were prohibited from fortifying these settlements or maintaining large armies in India, which ensured British dominance.
• Key Figures:
• Sir Eyre Coote: A British soldier who gained fame for his role in the Battle of Wandiwash and later became the Commander-in-Chief of the British forces in India.
• Comte de Lally: A French general of Irish descent who was later executed in France for his failure in the Indian campaign.

Important Points

• Location: The battle took place at Wandiwash, which is now known as Vandavasi, located in the Tiruvannamalai district of Tamil Nadu, India.
• Military Strength: The British army consisted of approximately 1,900 European troops and 2,100 Indian sepoys, while the French army had around 2,250 European troops and 1,300 Indian allies.
• Consequences for Other Powers:
• Portuguese: By the 18^th century, Portuguese influence in India was largely confined to Goa, Daman, and Diu. They were not major participants in the Carnatic Wars.
• Dutch: The Dutch power in India had already been significantly weakened following their defeat by the British in the Battle of Chinsurah (also known as the Battle of Biderra) in 1759.
• Impact on French Settlements: Following the defeat at Wandiwash, the French capital of Pondicherry was besieged and fell to the British in January 1761, marking the complete collapse of French political power in India.

The correct answer is The Occupational Safety, Health and Working Conditions Code, 2020.

Key Points

• The Occupational Safety, Health and Working Conditions Code, 2020 is the specific legislation that provides for the employment of women in all establishments for all types of work. This includes permitting women to work during night shifts, which is defined as the period between 7 PM and 6 AM. Hence, the statement regarding women working in night shifts falls under this code.
• Under this code, the Government mandates that if a woman is required to work at night, the employer must ensure adequate safety, health, and welfare facilities. Furthermore, the prior consent of the woman worker is a mandatory requirement before assigning her to a night shift.
• This code is a massive reform that consolidates and replaces 13 central labour laws, including the Factories Act, 1948, the Mines Act, 1952, and the Contract Labour (Regulation and Abolition) Act, 1970.
• The primary objective of this code is to regulate the health and safety conditions of workers in establishments with 10 or more workers and in all mines and docks, ensuring a standardized environment across India.

Additional Information

• The Code on Wages, 2019:
• This was the first code to be passed by Parliament in August 2019. It replaced four existing laws: the Payment of Wages Act, 1936, the Minimum Wages Act, 1948, the Payment of Bonus Act, 1965, and the Equal Remuneration Act, 1976.
• It ensures that there is no discrimination on the ground of gender in matters relating to wages and recruitment for the same work or work of a similar nature.
• The Industrial Relations Code, 2020:
• This code consolidates three functional central labour laws: the Trade Unions Act, 1926, the Industrial Employment (Standing Orders) Act, 1946, and the Industrial Disputes Act, 1947.
• It aims to improve business efficiency by increasing the threshold for retrenchment and closure in industrial establishments from 100 to 300 workers without requiring prior government permission.
• The Code on Social Security, 2020:
• This code replaces nine laws, including the Employees’ Provident Fund Act, 1952, and the Maternity Benefit Act, 1961.
• A significant feature of this code is the universalization of social security benefits, extending coverage to unorganized workers, gig workers, and platform workers for the first time in India.
• Broad Labour Reform Context:
• The Government of India decided to amalgamate 29 central labour laws into four Labour Codes based on the recommendations of the Second National Commission on Labour (2002).
• The goal of these reforms is to provide ease of doing business while ensuring worker protection and transparency through digitalization and simplified compliance.

Important Points

• Empowerment of Women: By allowing women to work in all sectors (including hazardous processes with safeguards), the OSH Code 2020 removes traditional barriers that limited female labor force participation.
• Annual Health Check-up: The OSH Code introduces a provision for a free annual health check-up for workers above a certain age (usually 45 years) in specific establishments, enhancing the preventive healthcare framework for the workforce.
• Inter-State Migrant Workers: The code provides specific benefits for migrant workers, including a journey allowance and the "One Nation, One Ration Card" facility to ensure food security when they move across state boundaries for employment.

The logic followed here is:

Given:

WEAR → 8246

CAST → 3851

Hence, the code for A is 8.

Hence, the correct answer is Option 3.

The correct answer is Taj Mahal, Agra.

Key Points

• Ustad Ahmad Lahori is celebrated as the chief architect of the Taj Mahal, one of the most iconic structures of Mughal architecture. He was a master builder in the court of Emperor Shah Jahan and is often credited with the creative vision behind this UNESCO World Heritage Site.
• The Taj Mahal was commissioned by Emperor Shah Jahan in the year 1631 to house the tomb of his favorite wife, Mumtaz Mahal. It also serves as the final resting place for the Emperor himself.
• Construction of the Taj Mahal complex is believed to have begun in 1632. The main mausoleum was completed in 1648, while the surrounding buildings and gardens were finished by 1653.
• Ahmad Lahori is also traditionally credited as the architect of the Red Fort (Lal Qila) in Delhi, showing his significant influence on the Golden Age of Mughal building projects.
• The monument was designated as a UNESCO World Heritage Site in 1983 for being "the jewel of Muslim art in India and one of the universally admired masterpieces of the world's heritage."

Additional Information

• Fatehpur Sikri, Agra:
• Founded in 1571 by Emperor Akbar, it served as the capital of the Mughal Empire until 1585.
• It is famous for the Buland Darwaza (Gate of Magnificence), which was built to commemorate Akbar's victory over Gujarat.
• The architectural style is a blend of Hindu and Muslim traditions. Hence, this option is incorrect regarding Ustad Ahmad Lahori.
• Humayun's Tomb, Delhi:
• Commissioned by Humayun's first wife, Empress Bega Begum (also known as Haji Begum), in 1558.
• The chief architect was Mirak Mirza Ghiyas, a Persian designer.
• It was the first garden-tomb on the Indian subcontinent and inspired the design of the Taj Mahal. Hence, this option is incorrect.
• Jaisalmer Fort, Rajasthan:
• Built in 1156 AD by the Bhati Rajput ruler Rawal Jaisal.
• It is known as the Sonar Quila or Golden Fort because of its yellow sandstone walls that shimmer like gold in the sunlight.
• It is one of the few "living forts" in the world, as a portion of the city's population still resides inside. Hence, this option is incorrect.

Important Points

• Architectural Features: The Taj Mahal is renowned for its perfect symmetry, the use of white Makrana marble, and the Pietra Dura (parchin kari) inlay work using semi-precious stones.
• The Charbagh: The complex features a 300-meter square Charbagh (Mughal garden), which uses raised pathways that divide each of the four quarters of the garden into 16 sunken flowerbeds.
• Global Recognition: In 2007, the Taj Mahal was declared a winner of the New 7 Wonders of the World (2000–2007) initiative.
• Material Sourcing: While the marble came from Rajasthan, Jasper was sourced from Punjab, Jade and Crystal from China, Turquoise from Tibet, and Lapis Lazuli from Afghanistan.

The correct answer is virtual and upright.

Key Points

• When an object is placed between the pole (P) and the principal focus (F) of a concave mirror, the light rays originating from the object diverge after reflection from the mirror surface.
• Since the reflected rays are diverging, they do not intersect in front of the mirror to form a real image. Instead, when these rays are produced backwards, they appear to meet at a point behind the mirror.
• The nature of the image formed in this specific case is virtual, meaning it cannot be projected onto a screen.
• The orientation of the image is upright (also known as erect), which means it is in the same vertical direction as the object.
• Regarding the size, the image is magnified or enlarged, being significantly larger than the actual object.
• This is the unique position for a concave mirror where it acts as a magnifying glass, producing a virtual and upright image instead of the usual real and inverted images produced at other positions.

Additional Information

• Concave Mirror (Converging Mirror):
• A concave mirror is a spherical mirror with an inward-curving reflecting surface. It is often called a converging mirror because it tends to collect light that falls on it, refocusing parallel incoming rays to a focus.
• The focal length (f) of a concave mirror is considered negative according to the Cartesian sign convention.
• The relationship between the radius of curvature (R) and focal length (f) is given by the formula R = 2f.
• Applications/Uses of this Property:
• Shaving Mirrors: Men use concave mirrors to see a magnified and upright image of the face for a better shave.
• Dentists' Mirrors: Dentists use these mirrors to see enlarged images of the teeth of patients while keeping the mirror very close (within the focal length).
• Makeup Mirrors: Used to provide a clear, upright, and enlarged view of facial features.
• Image Characteristics at Different Positions:
• At Infinity: The image is formed at the Focus (F); it is real, inverted, and highly diminished.
• Beyond C (Center of Curvature): The image is formed between F and C; it is real, inverted, and diminished.
• At C: The image is formed at C; it is real, inverted, and of the same size as the object.
• Between C and F: The image is formed beyond C; it is real, inverted, and enlarged.
• At F: The image is formed at infinity; it is real, inverted, and highly enlarged.

Important Points

• Real vs Virtual Image: A real image is formed when light rays actually meet at a point after reflection, whereas a virtual image is formed when light rays only appear to diverge from a point. Real images are always inverted in mirrors, while virtual images are always upright.
• Mirror Formula: The position of the image can be calculated using the mirror formula: 1/f = 1/v + 1/u, where v is the image distance, u is the object distance, and f is the focal length.
• Magnification (m): It is the ratio of the height of the image to the height of the object. For virtual images in a mirror, the magnification value is positive.

Given Statements:

I. N is taller than L.

II. V is taller than N. M is only shorter than one tree.

Analysis:

Statement I alone → Not sufficient

(Only tells N > L, no full order of all 5 trees, so shortest cannot be identified)

Statement II alone → Not sufficient

(V > N is given and M is second tallest, but relation between L, N, T is unknown, so shortest cannot be identified)

Now, combining I and II:

From II:

V is taller than N

M is only shorter than one tree → M is second tallest

So, M cannot be shortest.

From I:

N > L → L is below N

So, even after combining both statements, we cannot determine the shortest tree.

Hence, the correct answer is "Option 2".

Given: F, G, H, L, M, N and O have exams on different days from Monday to Sunday.

G has exam on Friday.

Only two people have exams between M and G.

Only four people have exams between F and M.

N has exam immediately after O.

L doesn’t have exam on Monday.

Now, There are four people between L and H.

Hence, the correct answer is Option 1.

Shortcut Trick

Use a² − b² = (a − b)(a + b)

⇒ (0.7 − 0.4)(0.7 + 0.4) = 0.3 × 1.1 = 0.33

⇒ 0.33 ÷ 0.33 = 1

∴ Answer = 1

Alternate Method

Given:

Expression = (0.7² − 0.4²) ÷ 0.33

Formula:

a² − b² = (a − b)(a + b)

Calculations:

⇒ 0.7² = 0.49

⇒ 0.4² = 0.16

⇒ 0.49 − 0.16 = 0.33

⇒ 0.33 ÷ 0.33 = 1

Final Answer: 1

Additional Information

Identity: a² − b² = (a − b)(a + b)

Decimal Tip: Convert into fractions if calculation becomes complex.

Speed Trick: Always check identities before squaring numbers.

Approximation Check: Numerator ≈ denominator ⇒ answer near 1.

The correct answer is Jabalpur.

Key Points

• The Bundela Uprising of 1842 was a significant armed rebellion against the British East India Company in Central India.
• The uprising was primarily centered in the Sagar-Narmada territories, which encompasses regions like Jabalpur, Sagar, Damoh, Narsinghpur, and Hoshangabad. Hence, the region of Jabalpur saw the uprising in 1842.
• The rebellion was led by prominent local landlords and chieftains, most notably Madhukar Shah of Narhut and Jawahar Singh Bundela of Chandrapur.
• The primary cause of the revolt was the oppressive land revenue policy and the high tax assessments (the Malguari system) imposed by the British after they annexed the Saugor and Nerbudda territories from the Marathas in 1818.
• Other leaders like Delan Shah, a Gond chief from Narsinghpur, also joined the movement, making it a combined effort of Bundela and Gond tribes against British exploitation.

Additional Information

• Vizianagram:
• This region is located in the modern-day state of Andhra Pradesh.
• It was the site of a revolt in 1794 when the Raja of Vizianagram, Vizieram Rauze, rose against the British East India Company after they attempted to disband his troops and demanded a huge tribute.
• This event is historically distinct from the Bundela uprising and occurred nearly 50 years earlier.
• Saurashtra:
• Located in Gujarat, this region saw various resistances against the British, such as the Vheras uprising between 1818 and 1820.
• The Bundelas were not geographically associated with Saurashtra, as their influence was concentrated in Central India (modern Madhya Pradesh and Uttar Pradesh).
• Ganjam:
• Located in Odisha, Ganjam was the center of multiple uprisings, including the Ganjam Rebellion led by Dhananjaya Bhanja, the Raja of Gumsur, in 1835-37.
• Another notable movement in this region was the Savara Rebellion (1853-1856). These events were unrelated to the Bundela ethnic group or the 1842 timeline of the Sagar-Narmada territories.

Important Points

• Consequences: The British authorities, under Lord Ellenborough, used military force to suppress the Bundela Uprising. By 1843, the main leaders were captured or surrendered. Madhukar Shah was executed by the British, becoming a local martyr.
• Geopolitical Impact: Although the 1842 rebellion was localized, it reflected the deep-seated resentment against British interference in traditional land-holding systems. It is often seen by historians as a precursor to the Great Revolt of 1857 in Central India.
• Administrative Changes: Following the unrest, the British were forced to make some administrative adjustments to the revenue collection system in the Sagar-Narmada territories to prevent further mass dissatisfaction.
• Role of Forest Tribes: The 1842 movement was unique because it bridged the gap between the Bundela ruling class and the tribal Gonds, demonstrating a unified front against colonial rule in the Vindhyan and Satpura ranges.

The correct answer is Significant reduction.

Key Points

• The share of agriculture and allied sectors in India’s Gross Domestic Product (GDP) has witnessed a Significant reduction over the decades, dropping from approximately 51.8% in 1950-51 to about 15.4% to 17.4% by 2016-17. This reflects the structural transformation of the Indian economy from agrarian to service-oriented.
• In the early years of independence (1950s), agriculture was the backbone of the economy, providing the majority of national income and employment. However, as the Industrial (Secondary) and Service (Tertiary) sectors grew at much higher rates, the relative contribution of agriculture naturally declined.
• The trend of Significant reduction does not imply a decrease in total agricultural production; in fact, India’s food grain production increased from about 50 million tonnes in 1950 to over 275 million tonnes by 2016-17. The decline is strictly in terms of its percentage share in the overall GDP.
• During the Planning Era, especially after the Second Five-Year Plan, the focus shifted toward heavy industries, and later, after the 1991 Liberalization, toward the Service Sector, which accelerated the shrinking share of the primary sector.

Additional Information

• Sectoral Composition of GDP:
• The Primary Sector (Agriculture, Mining, Fishing) share has decreased consistently.
• The Secondary Sector (Manufacturing, Electricity, Construction) saw moderate growth but has remained relatively stagnant compared to services.
• The Tertiary Sector (Services, Trade, Transport, Communication) has seen an explosive rise, contributing more than 53% of the GDP in 2016-17.
• Employment vs. GDP Contribution:
• There is a major disparity in India where agriculture contributes only about 15-17% to GDP but still employs nearly 43-49% of the total workforce as of 2016.
• This phenomenon is often termed "disguised unemployment," where more people are engaged in agriculture than are actually required for the current level of production.
• The Green Revolution (1960s):
• The introduction of High Yielding Variety (HYV) seeds, better irrigation, and fertilizers under the leadership of M.S. Swaminathan significantly boosted productivity but did not stop the declining trend of agriculture’s share in GDP relative to other booming sectors.
• Economic Liberalization 1991:
• The LPG (Liberalization, Privatization, and Globalization) reforms opened the economy, leading to a surge in Information Technology (IT) and Banking, which further overshadowed the agricultural contribution.

Important Points

• Gross Value Added (GVA): Recent economic data uses GVA at basic prices to measure sectoral performance. In 2016-17, the GVA growth for agriculture was around 6.3%, though its total share remained low.
• Data Collection: The Central Statistics Office (CSO), under the Ministry of Statistics and Programme Implementation (MoSPI), is the nodal agency responsible for calculating these GDP figures and sectoral shares.
• Engel’s Law: This economic principle suggests that as family income rises, the proportion of income spent on food declines, even if absolute expenditure on food rises. This contributes to the long-term decline of the agricultural sector’s share in a developing economy’s GDP.

Given: K, L, M, N, P, Q and R are sitting around a circular table facing the centre.

Q sits third to the left of N.

M sits second to the left of R.

N is the immediate neighbour of both L and M.

K is not an immediate neighbour of Q.

Now, counting from the right of P (counter-clockwise), the people between P and M are: L and N → 2 people.

Hence, the correct answer is "Option 4".

Given: (Left) L U & P % F A & D $ # K Q * M Ω Y @ E T * £ R (Right)

Now,

Symbols, which are immediately preceded by a letter and also immediately followed by another symbol.

So, Needed pattern is: Letter - Symbol - Symbol.

(Left) L U & P % F A & D $ # K Q * M Ω Y @ E T * £ R (Right)

Only two symbols satisfy the condition.

Hence, the correct answer is 'Option 1'.

The correct answer is Panaji Port.

Key Points

• The Maritime Amrit Kaal Vision 2047 (MAKV 2047) is a comprehensive roadmap launched by Prime Minister Narendra Modi in October 2023 during the Global Maritime India Summit to transform India's maritime sector over the next 25 years.
• The vision identifies several Major Port Authorities for massive modernization and infrastructure expansion to create "Mega Ports" with a capacity exceeding 300 to 500 MTPA. Deendayal Port Authority (Kandla) in Gujarat is a primary site identified for such expansion due to its strategic location and existing high cargo throughput. Hence, the statement regarding Deendayal Port is correct as it is identified for expansion.
• V.O. Chidambaranar Port Authority (Tuticorin) in Tamil Nadu has been specifically identified for development as a Green Hydrogen Hub and for significant capacity expansion under the 2047 vision. Hence, the statement regarding V.O. Chidambaranar Port is correct.
• Paradip Port Authority in Odisha is another critical major port identified for modernization to become a world-class mega port, aiming to handle vast volumes of coal and iron ore to support the industrial growth of Eastern India. Hence, the statement regarding Paradip Port is correct.
• Panaji Port, located in Goa, is classified as a minor/non-major port and is under the jurisdiction of the State Government (Goa Maritime Board). While the MAKV 2047 covers the entire maritime ecosystem, the primary infrastructure expansion and port modernization targets for "Mega Port" status focus on the 12 Major Port Authorities under the Union Government. Panaji Port is not among the primary Major Port Authorities identified for the 10,000 MTPA capacity goal. Hence, Panaji Port is the correct option as it is NOT a Major Port Authority identified for this specific expansion.

Additional Information

• Maritime Amrit Kaal Vision 2047 Goals: The initiative aims to increase the total port capacity of India from the current levels to approximately 10,000 Million Tonnes Per Annum (MTPA) by the year 2047. It focuses on port-led development, reducing logistics costs, and enhancing the Ease of Doing Business in the maritime sector.
• Development of Mega Ports: Under this vision, India aims to develop at least two ports with a capacity of 1,000 MTPA and several others with 500 MTPA capacity. Vizhinjam Port in Kerala and Vadhavan Port in Maharashtra are also pivotal to this transshipment and mega-port strategy.
• Green Port Initiative (Harit Sagar): A significant pillar of the MAKV 2047 is the "Harit Sagar" guidelines, which aim to achieve Zero Carbon Emission at Indian ports. The vision includes the installation of renewable energy sources, green hydrogen production, and the adoption of LNG/Electric-powered vessels at Major Ports.
• Logistics and Technology: The vision integrates the National Logistics Portal (Marine) and the Sagar-Setu mobile app to digitize maritime trade. It aims to reduce the "turnaround time" of ships to match global standards of less than 24 hours.
• Investment and Employment: The roadmap envisions an investment of over Rs. 80 lakh crore in the maritime sector, which is expected to create millions of jobs and significantly boost India's GDP through increased maritime trade.

Important Points

• Major Ports vs. Minor Ports: In India, there are 12 Major Ports governed by the Major Port Authorities Act, 2021, and over 200 Minor/Intermediate Ports governed by state maritime boards. The Ministry of Ports, Shipping and Waterways directly oversees the Major Ports, which are the primary focus of the Amrit Kaal Vision for infrastructure scaling.
• Maritime India Summit 2023: This event served as the launchpad for the vision, attracting global investors and resulting in hundreds of Memorandums of Understanding (MoUs) worth billions of dollars to enhance connectivity and maritime infrastructure.

The correct answer is Article 15(3).

Key Points

• Article 15(3) of the Constitution of India specifically empowers the State to make any special provisions for the welfare and protection of women and children.
• This clause acts as a vital exception to the general rule of non-discrimination established in Article 15(1) and Article 15(2), which prohibits the State from discriminating against any citizen on grounds only of religion, race, caste, sex, place of birth, or any of them.
• The logic behind Article 15(3) is the concept of protective discrimination or affirmative action; it recognizes that women and children have unique social and physical positions that may require special legal safeguards.
• This constitutional provision has enabled the government to implement various welfare measures, such as the reservation of seats for women in local self-government bodies (Panchayats and Municipalities) and the enactment of specialized laws like the Maternity Benefit Act.
• It also provides the legal foundation for the free education of children and other social security schemes directed toward their growth and safety.

Additional Information

• Article 19(5):
• This article pertains to the Right to Freedom and allows the State to impose reasonable restrictions on the exercise of the rights to move freely and reside in any part of India.
• Such restrictions can be imposed in the interest of the general public or for the protection of the interests of any Scheduled Tribe.
• Article 23(2):
• While Article 23(1) prohibits traffic in human beings and begar (forced labor), Article 23(2) provides an exception.
• It permits the State to impose compulsory service for public purposes, such as military training or social service, provided the State does not discriminate on grounds of religion, race, caste, or class.
• Article 16(2):
• This article is a component of the Right to Equality regarding public employment.
• It mandates that no citizen shall, on grounds only of religion, race, caste, sex, descent, place of birth, residence, or any of them, be ineligible for, or discriminated against in respect of, any employment or office under the State.

Important Points

• The Fundamental Rights are enshrined in Part III of the Indian Constitution, ranging from Article 12 to 35.
• The Right to Equality encompasses Articles 14 to 18, which aim to establish social and legal equality in India.
• Article 15(3) was heavily cited during the formulation of the Right of Children to Free and Compulsory Education (RTE) Act, 2009, which ensures that every child aged 6 to 14 years has a right to formal schooling.
• The Supreme Court of India has consistently upheld that laws favoring women, such as those related to sexual harassment at the workplace or domestic violence protection, are constitutionally valid under the umbrella of Article 15(3).
• The 73^rd and 74^th Constitutional Amendment Acts of 1992, which mandated one-third reservation for women in local bodies, draw their functional authority from the spirit of this article.

The correct answer is Gold foil experiment.

Key Points

• The discovery of the atomic nucleus was the result of the alpha-particle scattering experiment, famously known as the Gold foil experiment, conducted by Ernest Rutherford and his team in 1911.
• In this experiment, high-energy alpha particles (doubly charged helium ions) were bombarded onto a very thin sheet of gold foil, which was approximately 1000 atoms thick.
• Rutherford observed that most of the alpha particles passed straight through the foil without any deflection, leading to the conclusion that most of the space inside an atom is empty.
• He noticed that a small fraction of the particles were deflected by small angles, and a very tiny number (about 1 in 12,000) rebounded back, suggesting a 180-degree deflection.
• Based on these observations, Rutherford concluded that the positive charge and nearly all the mass of the atom are concentrated in a very small, dense region at the center, which he named the nucleus. Hence, the statement regarding the discovery via the Gold foil experiment is correct.

Additional Information

• Cathode Ray Experiment:
• This experiment was conducted by J.J. Thomson in 1897 using a vacuum tube.
• It led to the discovery of electrons, the first subatomic particles to be identified.
• Thomson proved that cathode rays consisted of negatively charged particles, which he originally called "corpuscles."
• Canal Ray Experiment:
• Performed by Eugen Goldstein in 1886, this experiment involved the use of a perforated cathode in a discharge tube.
• He discovered positive rays (canal rays) moving in the opposite direction to cathode rays.
• This discovery eventually led to the identification of the proton, which carries a positive charge.
• Oil Drop Experiment:
• Conducted by Robert Millikan and Harvey Fletcher in 1909 at the University of Chicago.
• The primary purpose was to measure the elementary electronic charge.
• They determined the charge of a single electron to be approximately 1.602 x 10^-19 Coulombs.
• Malleability of Gold:
• Gold was specifically chosen for Rutherford's experiment because it is the most malleable metal.
• This property allowed the researchers to create a foil so thin that it was only a few hundred nanometers thick, ensuring that the alpha particles interacted with only a few layers of atoms.

Important Points

• Rutherford’s Atomic Model:
• Following the discovery, Rutherford proposed a nuclear model of the atom, where electrons revolve around the nucleus in circular paths called orbits, similar to planets revolving around the sun.
• He stated that the nucleus is extremely small; the radius of the nucleus is about 10^-15 meters, while the radius of the atom is about 10^-10 meters.
• Limitations:
• A major drawback of Rutherford's model was its inability to explain atomic stability. According to classical electromagnetic theory, an accelerating charged particle (the electron) should radiate energy and eventually collapse into the nucleus.
• This limitation was later addressed by Niels Bohr in 1913 with the introduction of discrete energy levels or shells.

The logic followed here is:

Option 1) ECH

Option 2) KFN

Option 3) MKP

Option 4) WUZ

Now, KFN  follows a different pattern.

Hence, the correct answer is Option 2.

The logic followed here is:

For, MUNI → OSPG

For, SDIK → UBKI

Now, apply to BZMP:

So, BZMP → DXON

Hence, the correct answer is Option 1.

The correct answer is Kailasa Temple at Ellora.

Key Points

• The Rashtrakutas were a powerful dynasty that ruled large parts of the Indian subcontinent between the 8^th and 10^th centuries.
• The Kailasa Temple, located in Cave 16 of the Ellora Caves in Sambhaji Nagar (formerly Aurangabad), Maharashtra, is considered their greatest architectural achievement.
• It was commissioned by the Rashtrakuta King Krishna I (reigned 756–774 AD) during the 8^th century.
• The temple is a monolithic structure, which means it was carved out of a single massive basalt cliff. Unlike traditional buildings that are constructed from the ground up, this temple was carved using a top-down excavation method.
• The architecture of the temple follows the Dravidian style, characterized by its Gopuram (monumental entrance tower) and complex Vimana (temple tower).

Additional Information

• Rashtrakuta Dynasty:
• The dynasty was founded by Dantidurga in 753 AD after he overthrew the Chalukyas of Badami.
• Their capital was established at Manyakheta (modern-day Malkhed in Karnataka).
• Famous rulers include Amoghavarsha I, who was a great patron of literature and wrote the Kavirajamarga, the earliest available work on rhetoric, poetics, and grammar in the Kannada language.
• Brihadeeswara Temple:
• Located in Thanjavur, Tamil Nadu, this temple was built by the Chola emperor Rajaraja I in 1010 AD.
• It is an outstanding example of Chola architecture and is dedicated to Lord Shiva.
• Konark Sun Temple:
• Situated in Puri, Odisha, this 13^th-century marvel was built by King Narasimhadeva I of the Eastern Ganga Dynasty.
• It is designed in the shape of a colossal chariot with 24 wheels pulled by seven horses, dedicated to the Sun God (Surya).
• Sanchi Stupa:
• Located in Madhya Pradesh, it is one of the oldest stone structures in India, originally commissioned by the Mauryan Emperor Ashoka in the 3^rd century BC.
• It serves as a major center for Buddhist pilgrimage and architecture.

Important Points

• The Ellora Caves consist of 34 monasteries and temples extending over a distance of more than 2 kilometers. These include 17 Hindu, 12 Buddhist, and 5 Jain caves, demonstrating the religious harmony of ancient India.
• The Kailasa Temple was designed to represent Mount Kailash, the celestial abode of Lord Shiva.
• The temple complex includes massive stone sculptures depicting scenes from the Ramayana and the Mahabharata, as well as a famous relief showing the demon king Ravana attempting to lift Mount Kailash.
• The Ellora Caves were designated as a UNESCO World Heritage Site in 1983 due to their cultural and historical significance.
• It is estimated that over 200,000 tonnes of rock were excavated to create the Kailasa Temple, a feat that showcases the advanced engineering skills of the Rashtrakuta era artisans.

The logic followed here is:

Logic: Each step increases by a fixed alternating pattern of +15, +25, +35.

Now verify the given sets:

For, 25 – 40 – 65 – 100

⇒ 25 + 15 = 40

⇒ 40 + 25 = 65

⇒ 65 + 35 = 100

For, 70 – 85 – 110 – 145

⇒ 70 + 15 = 85

⇒ 85 + 25 = 110

⇒ 110 + 35 = 145

Now, checking the options:

Option 1) 50 – 65 – 90 – 125

⇒ 50 + 15 = 65

⇒ 65 + 25 = 90

⇒ 90 + 35 = 125 

Option 2) 15 – 30 – 65 – 90

⇒ 15 + 15 = 30

⇒ 30 + 25 = 55 ≠ 65 

Option 3) 95 – 110 – 130 – 170

⇒ 95 + 15 = 110

⇒ 110 + 25 = 135 ≠ 130 

Option 4) 65 – 80 – 105 – 150

⇒ 65 + 15 = 80

⇒ 80 + 25 = 105

⇒ 105 + 35 = 140 ≠ 150 

Hence, the correct answer is Option 1.

The logic followed here is:

So, 'BPH 30' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

Shortcut Trick

Net work = 1/4 + 1/31 − 1/31 = 1/4

⇒ Only first tap remains effective

⇒ Time for full tank = 4 hr

⇒ Time for 1/4 tank = 1 hr

∴ Answer = 1

Alternate Method

Given:

Tap A = 4 hr, Tap B = 31 hr, Tap C (empty) = 31 hr

Formula:

Net rate = 1/4 + 1/31 − 1/31

Calculations:

⇒ Net rate = 1/4

⇒ Time for full tank = 4 hr

⇒ Time for 1/4 tank = 4 × 1/4 = 1 hr

Final Answer: 1 hour

Additional Information

Work Rate: Rate = Work ÷ Time

Pipe Concept: Filling = positive, Emptying = negative

Shortcut Tip: Same time pipes cancel each other

Unit Work: Assume total work = 1 for easy calculation

The correct answer is United Nations.

Key Points

• The United Nations (UN) is the primary international organization responsible for facilitating the creation of a global Treaty on Cybersecurity and Cybercrime. In August 2024, the United Nations Ad Hoc Committee finalized the first-ever global treaty to combat cybercrime, which is expected to be formally adopted by the General Assembly in the 2024-2025 session.
• The treaty aims to strengthen international cooperation in the investigation and prosecution of crimes involving computer systems, including data theft, hacking, and online exploitation. This oversight by the United Nations ensures that the framework respects international law and the sovereignty of member nations.
• The United Nations Office on Drugs and Crime (UNODC) serves as the secretariat for the treaty negotiations. This body provides the necessary technical assistance and platform for all 193 member states to negotiate terms that balance security with human rights and privacy.
• The process for this treaty was initiated by the General Assembly Resolution 74/247, which established an open-ended Ad Hoc Committee to elaborate a comprehensive international convention on countering the use of information and communications technologies (ICTs) for criminal purposes.
• By October 2025, the implementation phase and the formalization of global standards under the United Nations umbrella provide a unified legal basis for countries that previously lacked specific cybersecurity legislation.

Additional Information

• World Bank:
• Established in 1944 at the Bretton Woods Conference, the World Bank is an international financial institution.
• While it provides financial support and technical assistance for digital infrastructure and cyber resilience in developing nations, it does not have the mandate to oversee or draft international legal treaties on security.
• UNESCO:
• The United Nations Educational, Scientific and Cultural Organization was founded in 1945.
• It focuses on promoting peace through education and ethics in artificial intelligence. While it advocates for digital literacy and internet universality, it is not the governing body for cybersecurity treaties.
• NATO:
• The North Atlantic Treaty Organization is a political and military alliance established in 1949.
• Although NATO considers cyber defense a part of its collective defense (Article 5), its jurisdiction is limited to its 32 member states and does not oversee global treaties for the entire international community.
• United Nations (UN) Structure:
• The UN consists of six principal organs, including the General Assembly and the Secretariat.
• It is the only body with the global legitimacy to host negotiations that involve both the Global North and the Global South, ensuring that developing countries have a voice in the digital governance framework.

Important Points

• The Budapest Convention (2001): Before the UN treaty, the Council of Europe's Budapest Convention was the primary instrument for international cybercrime cooperation. However, many nations, including India and Russia, did not sign it due to concerns over data sovereignty.
• Cyber Diplomacy: The role of the United Nations in 2025 reflects the shift toward cyber diplomacy, where digital security is treated with the same diplomatic weight as nuclear non-proliferation or climate change.
• Data Privacy: A key challenge during the UN negotiations was ensuring that the treaty would not be used by authoritarian regimes to suppress dissent or violate human rights under the guise of cybersecurity.
• Technical Assistance: The UN framework emphasizes providing technical expertise to lower-income countries to help them build robust CERTs (Computer Emergency Response Teams) and National Cybersecurity Strategies.

Shortcut Trick

Total of 5 numbers = 5 × 20 = 100

Total of remaining 4 numbers = 4 × 18 = 72

⇒ Excluded number = 100 − 72 = 28

∴ Answer = 28

Alternate Method

Given:

Average of 5 numbers = 20

Average of 4 numbers = 18

Formula:

Sum = Average × Number of terms

Calculations:

⇒ Sum of 5 numbers = 20 × 5 = 100

⇒ Sum of 4 numbers = 18 × 4 = 72

⇒ Excluded number = 100 − 72 = 28

Final Answer: 28

Additional Information

Average Formula: Average = Sum ÷ Number of terms

Sum Concept: Sum = Average × Count

Shortcut Tip: Difference of sums gives missing value directly

Exam Hack: Avoid listing numbers, directly use totals

The correct answer is .csv.

Key Points

• The .csv (Comma Separated Values) file format is a plain text file that uses a specific delimiter (typically a comma) to separate values, making it the most suitable format for storing structured data.
• Each line of the file corresponds to a data record, and each record consists of one or more fields, which allows it to be easily interpreted as tabular data by applications like Microsoft Excel, Google Sheets, and LibreOffice Calc.
• One of its primary functions is to facilitate the exchange of data between different platforms or software that might otherwise be incompatible, as it does not contain complex formatting or macros.
• Because it is human-readable and lightweight, it is widely used in Data Science and software development for exporting and importing large databases or datasets.
• In a spreadsheet application, importing a .csv file automatically populates the rows and columns based on the line breaks and commas present in the text file.

Additional Information

• .mp4 (MPEG-4 Part 14):
• This is a digital multimedia container format most commonly used to store video and audio data.
• It can also store other data such as subtitles and still images, utilizing lossy compression to maintain high quality while keeping the file size relatively small.
• It is based on the QuickTime File Format and is widely supported across smartphones, computers, and streaming services.
• .exe (Executable File):
• An .exe file is a common file extension for a program that can be executed or run by the Microsoft Windows operating system.
• It contains binary machine code that the CPU interprets to perform specific functions or launch software applications.
• Unlike data files, executable files are not meant to be read by humans but are essential for installing and running programs on a PC.
• .png (Portable Network Graphics):
• This is a raster-graphics file format that supports lossless data compression.
• It was created as an improved, non-patented replacement for Graphics Interchange Format (GIF) and is the most used lossless image compression format on the Internet.
• Key features include support for transparency (alpha channels) and 24-bit RGB color palettes, making it ideal for web design and logos.

Important Points

• Data Delimiters: While the "C" in CSV stands for Comma, some regions or organisations use different delimiters such as semicolons (;) or tabs (\t) to avoid confusion with numerical values that use commas as decimal separators.
• Structure vs. Formatting: A CSV file only stores the raw data; it cannot save cell colors, font styles, formulas, or merged cells. For these features, users must save the file in proprietary formats like .xlsx.
• Historical Context: The CSV format has existed since the early days of business computing in the 1970s, long before the standardisation of modern spreadsheet software, proving its longevity and reliability.
• Applications in Web: Many government agencies and open data portals provide reports and indices in CSV format to ensure the transparency and accessibility of public data for researchers.

Given: (Left) @ © € E 8 9 X © 7 6 9 4 S N % $ 2 © 1 # O N (Right)

Now,

We need to remove all the numbers and then find the 8^th element from the left.

After removing numbers (8, 9, 7, 6, 9, 4, 2, 1), the series becomes:  @ © € E X © S N % $ © # O N

Now, count from the left:  @ © € E X © S N % $ © # O N

So, the 8^th element is N.

Hence, the correct answer is 'Option 1'.$

Shortcut Trick

Speed ratio = 4 : 7 ⇒ Time ratio = 7 : 4

Extra time = 3 parts = 15 min

⇒ 1 part = 5 min

⇒ Normal time = 4 parts = 20 min

∴ Answer = 20 minutes

Alternate Method

Given:

Reduced speed = 4/7 of normal

Delay = 15 min

Formula:

Time ∝ 1/Speed

Calculations:

⇒ Let normal speed = 7, reduced speed = 4

⇒ Time ratio = 7/4

⇒ Difference = 7T/4 − T = 3T/4 = 15

⇒ T = 20 min

Final Answer: 20 minutes

Additional Information

Speed-Time Relation: Speed × Time = Distance

Inverse Relation: Time ∝ 1/Speed

Ratio Trick: Convert speed ratio to time ratio by inverse

Exam Shortcut: Use parts method for quick solving

The correct answer is Nagar Panchayat.

Key Points

• Article 243Q of the Constitution of India mandates the constitution of three types of municipalities in every State.
• A Nagar Panchayat (by whatever name called) is constituted for a transitional area, which is an area in transition from a rural area to an urban area.
• A Municipal Council is constituted for a smaller urban area.
• A Municipal Corporation is constituted for a larger urban area.
• The Governor of a State, by public notification, specifies whether an area is a transitional area, a smaller urban area, or a larger urban area based on factors such as population, density of population, revenue generated for local administration, percentage of employment in non-agricultural activities, and economic importance.
• The 74^th Amendment Act of 1992 added Part IX-A to the Constitution, which deals with the administration of Municipalities.

Additional Information

• 74^th Constitutional Amendment Act, 1992:
• This Act came into force on June 1, 1993.
• It aimed at revitalizing and strengthening urban local bodies (ULBs) so that they function effectively as units of self-government.
• It inserted the Twelfth Schedule into the Constitution, which contains 18 functional items placed under the purview of municipalities.
• Composition of Municipalities (Article 243R):
• All seats in a municipality are filled by persons chosen by direct election from the territorial constituencies in the municipal area.
• Each municipal area is divided into territorial constituencies known as wards.
• Reservation of Seats (Article 243T):
• Seats are reserved for Scheduled Castes (SC) and Scheduled Tribes (ST) in every municipality in proportion to their population.
• Not less than one-third (1/3) of the total number of seats are reserved for women (including the number of seats reserved for SC/ST women).
• Duration of Municipalities (Article 243U):
• The municipality has a fixed term of 5 years from the date appointed for its first meeting.
• In case of dissolution, elections to constitute a new municipality must be completed within a period of 6 months.

Important Points

• State Election Commission (Article 243ZA):
• The superintendence, direction, and control of the preparation of electoral rolls and the conduct of all elections to the municipalities are vested in the State Election Commission.
• State Finance Commission (Article 243Y):
• The Finance Commission constituted under Article 243-I (for Panchayats) also reviews the financial position of the municipalities and makes recommendations to the Governor regarding the distribution of taxes, duties, tolls, and fees between the State and the Municipalities.
• District Planning Committee (Article 243ZD):
• Every State must constitute a District Planning Committee at the district level to consolidate the plans prepared by the Panchayats and the Municipalities in the district.
• Metropolitan Planning Committee (Article 243ZE):
• In every metropolitan area (an area having a population of 10 lakh or more), a Metropolitan Planning Committee must be constituted to prepare a draft development plan for the metropolitan area as a whole.

Shortcut Trick

Apply BODMAS: do ÷ and × first

18 ÷ 6 = 3 and 2 × 4 = 8

Expression becomes: 16 + 3 − 8

Now solve left to right: 19 − 8 = 11

∴ Answer = 11

Alternate Method

Given:

Expression: 16 + 18 ÷ 6 − 2 × 4

Formula used:

BODMAS rule: Brackets → Orders → Division → Multiplication → Addition → Subtraction

Calculations:

⇒ 16 + 18 ÷ 6 − 2 × 4

⇒ 16 + 3 − 8

⇒ 19 − 8 = 11

∴ The correct answer is 11.

Additional Information

BODMAS Rule

Order of operations: Brackets → Orders → Division → Multiplication → Addition → Subtraction.

Division and Multiplication Priority

Division and multiplication have equal priority and are solved left to right.

Addition and Subtraction Rule

After ÷ and ×, perform + and − from left to right.

Common Mistake

Solving left to right directly without applying BODMAS leads to wrong answers.

Family Chart:

Decoding the Symbols:

Given: P + Q − R × S ÷ T

It means: P is the husband of Q, Q is the mother of R, R is the brother of S, S is the father of T.

 

⇒ Therefore P is T’s father’s father.

Hence, the correct answer is "Option 3".

The logic followed here is:

Given:

LIME → 4839

TIME → 9324

So, T → 2

Hence, the correct answer is Option 3.

The logic followed here is:

Now, checking all options:

Option 1) TU → WX

Option 2) JL → NP

Option 3) EG → IK

Option 4) CE → GI

Now, Only TU → WX follows different pattern.

Hence, the correct answer is Option 1.

Shortcut Trick

Let son = x, then father = 3x and daughter = x − 3

3 years ago total: (3x − 3) + (x − 3) + (x − 6)

Total = 5x − 12 = 58

5x = 70 ⇒ x = 14

∴ Answer = 42

Alternate Method

Given:

Vanraj = 3 × son

Daughter = son − 3

Sum of ages 3 years ago = 58

Formula used:

Total age = sum of individual ages

Father = 3x Son = x Daughter = x−3 3 years ago total = 58

Calculations:

⇒ Let son = x

⇒ Father = 3x, Daughter = x − 3

⇒ 3 years ago: (3x − 3) + (x − 3) + (x − 6) = 58

⇒ 5x − 12 = 58

⇒ 5x = 70 ⇒ x = 14

⇒ Vanraj = 3x = 42

∴ The correct answer is 42.

Additional Information

Age Reduction Concept

If age decreases by n years, subtract n from each person's present age.

Linear Equation Method

Form one equation using given conditions and solve for unknown variable.

Family Age Problems

Use relations like father = multiple of son to simplify quickly.

Shortcut Insight

Total reduction after 3 years = 3 persons × 3 = 9 years.

The logic followed here is:

For, LUB → OSE

For,  RQH → UOK

Now, checking all options:

Option 1) GOQ → LMV

Option 2) XMN → AKQ

Option 3) KMT → MHV

Option 4) KGY → OBC

Hence, the correct answer is Option 2.

The correct answer is Ujjain.

Key Points

• Ashoka, one of the greatest emperors of ancient India, served as the Viceroy (Governor) of Ujjain (the capital of the Avanti province) during the reign of his father, Bindusara.
• As a prince, he was also sent to Taxila (Takshashila) to suppress a major revolt against the central Mauryan administration, where he demonstrated exceptional military and diplomatic skills. Hence, the statement regarding his viceroyship in Ujjain is correct.
• Ujjain was a highly strategic and commercial hub in central India, connecting the trade routes between the Gangetic Valley and the western coast, making it a crucial administrative post for a royal prince.
• His tenure in Ujjain is historically significant because it was there that he reportedly met Devi, the daughter of a trader from Vidisha, who later became his wife and gave birth to his children, Mahinda and Sanghamitta.
• The experience gained by Ashoka while governing provinces like Ujjain and Taxila prepared him for the complex administrative challenges he would face after ascending the throne in 268 BCE.

Additional Information

• Bindusara (r. 297 – 273 BCE):
• He was the son of Chandragupta Maurya and the second ruler of the Mauryan Dynasty.
• Known by the title Amitraghata (Slayer of Foes), he maintained the vast empire inherited from his father and kept friendly relations with Hellenic kingdoms.
• Patliputra:
• Located near modern-day Patna, it served as the imperial capital of the Mauryan Empire.
• While Bindusara ruled the empire from this central seat of power, his sons were appointed as Kumaramatyas (Princely Viceroys) in distant provinces.
• Tosali:
• It was the provincial capital of the Kalinga region.
• This region only became a formal part of the Mauryan Empire after Ashoka conquered it in the Kalinga War around 261 BCE, which took place years after his father's death.
• Saurashtra:
• This western region (modern Gujarat) was managed by local governors such as Pushyagupta under Chandragupta Maurya and Tushaspa (a Yavana/Greek) under Ashoka.
• It was famous for the construction of the Sudarsana Lake, an important irrigation project of that era.

Important Points

• Succession Struggle: After the death of Bindusara in 273 BCE, a war of succession broke out between Ashoka and his brothers (notably Susima). According to Buddhist traditions like the Mahavamsa, Ashoka emerged victorious and was formally crowned in 268 BCE.
• Mauryan Administrative Divisions: The empire was divided into four main provinces: Uttarapatha (Taxila), Avantiratha (Ujjain), Dakshinapatha (Suvarnagiri), and Prachyapatha (Tosali, after the Kalinga conquest).
• Inscriptions and Sources: Much of what we know about Ashoka's early life and administration comes from the Edits of Ashoka, the Ashokavadana, and Dipavamsa. These texts highlight his transition from Chanda Ashoka (Fierce Ashoka) to Dharma Ashoka (Pious Ashoka).
• Geographical Extent: Under Bindusara, the empire spanned almost the entire Indian subcontinent, excluding the far south (Tamil regions) and Kalinga on the eastern coast.

Shortcut Trick

Total Work = LCM(40, 72) = 360 units.

Efficiency (A+B+C) = 9, Efficiency (B+C) = 5.

Efficiency A = 9 − 5 = 4; Efficiency B = 1.5 × 4 = 6.

Remaining work after 16 days = 360 − (16 × 9) = 360 − 144 = 216 units.

Time taken by B = 216 ÷ 6 = 36 days.

∴ Answer = 36 days

Alternate Method

Given:

Days taken by (A+B+C) = 40 days

Days taken by (B+C) = 72 days

Efficiency of B = 50% more than A

Formula used:

Total Work = LCM of all given days

Efficiency = Total Work ÷ Number of Days

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

Efficiency of A = 9 − 5 = 4

Calculations:

Efficiency of B = 150% of A = (150/100) × 4 = 6

⇒ Work done by (A+B+C) in 16 days = 16 × 9 = 144 units

⇒ Remaining work = 360 − 144 = 216 units

⇒ Days taken by B alone = 216 ÷ 6 = 36 days

∴ The correct answer is 36 days.

Additional Information

Efficiency and Time Relationship

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

Work and Wages

Wages are always distributed in the ratio of the work done by individuals. If they work for the same duration, wages are distributed in the ratio of their efficiencies.

Combined Work Formula

If A can do a work in 'a' days and B in 'b' days, then together they can do it in (a × b) ÷ (a + b) days.

The logic followed here is:

So, '67' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

Shortcut Trick

Use reverse multiplying factors

Q to R: 52% loss ⇒ multiply by 48/100

P to Q: 30% profit ⇒ multiply by 130/100

3900 = CP × 130/100 × 48/100

CP = 3900 × 100 × 100 ÷ (130 × 48) = 6250

∴ Answer = 6250

Alternate Method

Given:

P → Q : 30% profit

Q → R : 52% loss

R paid = 3900

Formula used:

Selling Price = Cost Price × (1 ± percentage/100)

P (CP = x) Q R (3900) +30% −52%

Calculations:

⇒ Let CP of P = x

⇒ SP to Q = x × 130/100

⇒ SP to R = x × 130/100 × 48/100

⇒ x × 130 × 48 / 10000 = 3900

⇒ x = 3900 × 10000 / (130 × 48)

⇒ x = 6250

∴ The correct answer is 6250.

Additional Information

Multiplying Factor Method

Profit: multiply by (100 + profit)% ÷ 100, Loss: multiply by (100 − loss)% ÷ 100.

Successive Change

Net change = a + b + (a × b)/100 where a and b are % changes.

Reverse Calculation

To find original CP, divide final value by all multiplying factors.

Common Shortcut

Combine factors directly instead of stepwise calculation to save time.

Shortcut Trick

For 2 years: CI − SI = P × (r/100)²

Here r = 4%

Difference = P × (4/100)² = P × 16/10000

47 = P × 16/10000

P = 47 × 10000 ÷ 16 = 29375

∴ Answer = 29375

Alternate Method

Given:

Rate = 4% per annum

Time = 2 years

CI − SI = 47

Formula used:

CI − SI (2 years) = P × (r/100)²

 Start (P) Year 1 Year 2 4% 4%

Calculations:

⇒ 47 = P × (4/100)²

⇒ 47 = P × 16/10000

⇒ P = 47 × 10000 ÷ 16

⇒ P = 29375

∴ The correct answer is 29375.

Additional Information

CI Formula

Amount = P × (1 + r/100)^t

SI Formula

SI = P × r × t ÷ 100

Shortcut (2 Years)

CI − SI = P × (r/100)²

Key Insight

Difference arises due to interest on interest in second year.

The correct answer is 124.3 points.

Key Points

• The FAO Food Price Index (FFPI) is a measure of the monthly change in international prices of a basket of food commodities. It reached an average of 124.3 points in December 2025, reflecting the global supply and demand dynamics of that period.
• The index is calculated as the average of five commodity group price indices, which are weighted based on the average export shares of each group for the 2014-2016 period.
• The base period for the FFPI is currently 2014-2016, where the index value is set to 100. Any value above 100 indicates an increase in prices relative to that base period. Hence, the mention of 124.3 points represents a 24.3% increase over the base.
• The FFPI serves as a crucial indicator for global food security and inflationary trends. It helps the United Nations and various governments monitor food price volatility, which can impact low-income countries and vulnerable populations.
• Monthly fluctuations in the index are often driven by factors such as weather patterns, geopolitical conflicts, changes in energy costs (which affect production and transport), and currency exchange rates.

Additional Information

• Composition of the Index:
• Cereal Price Index: This index tracks the prices of major grains including wheat, maize (corn), and rice. It is a significant component of the overall FFPI as cereals are staple foods globally.
• Vegetable Oil Price Index: It monitors the international prices of palm oil, soy oil, sunflower oil, and rapeseed oil.
• Dairy Price Index: This includes the prices of butter, whole milk powder (WMP), skim milk powder (SMP), and cheese.
• Meat Price Index: It covers the prices of poultry, bovine (beef), pig, and ovine (lamb) meat.
• Sugar Price Index: This tracks the International Sugar Agreement prices and reflects global sugar trade dynamics.
• Organization Profile:
• The Food and Agriculture Organization (FAO) is a specialized agency of the United Nations that leads international efforts to defeat hunger.
• It was founded on 16 October 1945, a date now celebrated annually as World Food Day.
• The headquarters of the FAO is located in Rome, Italy.
• As of 2024, the organization has 194 Member Nations, two associate members, and one member organization, the European Union.

Important Points

• Historical Context: The FFPI was first introduced by the FAO in 1996 as a public good to help monitor developments in the global agricultural commodity markets.
• Economic Impact: High food prices or extreme volatility can lead to social unrest and economic instability, particularly in import-dependent nations. For instance, the spikes in 2008 and 2011 led to significant global food crises.
• Data Collection: The FAO collects price data from various international markets and trading hubs to ensure the index remains a reliable and unbiased representation of the global market.
• Reports: The FAO releases the Food Outlook report twice a year (usually in June and November), providing a detailed analysis of market trends and forecasts for major food groups.

The correct answer is 2004.

Key Points

• Tamil was the first language in India to be officially accorded the status of a Classical Language.
• The announcement was made by the Government of India in October 2004 following a long-standing demand from scholars and the state government.
• To be categorized as a Classical Language, the language must possess high antiquity of its early texts/recorded history over a period of 1500–2000 years.
• The criteria also specify that the literary tradition must be original and not borrowed from another speech community, which Tamil fulfills through its Sangam literature.
• The recognition was formalized through a notification by the Ministry of Home Affairs on October 12, 2004, marking a significant milestone for Dravidian languages.

Additional Information

• Following Tamil, several other languages have been granted Classical status based on their historical and literary significance:
• Sanskrit was declared a classical language in 2005.
• Both Telugu and Kannada were granted the status in 2008.
• Malayalam was added to the list in 2013.
• Odia became the sixth language to receive the honor in 2014.
• In a historic decision in October 2024, the Union Cabinet, chaired by Prime Minister Narendra Modi, approved the inclusion of five more languages: Marathi, Pali, Prakrit, Assamese, and Bengali.
• The Ministry of Education provides various benefits for these languages, including two major International Awards for eminent scholars and the establishment of a Centre of Excellence for Studies in Classical Languages.
• The University Grants Commission (UGC) also creates a certain number of Professional Chairs in Central Universities for these recognized languages to promote research and teaching.

Important Points

• The Expert Advisory Committee of the Sahitya Akademi plays a crucial role in examining proposals for Classical Language status before they are recommended to the Cabinet.
• Tamil is part of the Dravidian language family and is one of the longest-surviving classical languages in the world, with recorded history spanning over 2,000 years.
• Apart from India, Tamil holds official status in Sri Lanka and Singapore, and it is widely spoken in the Indian State of Tamil Nadu and the Union Territory of Puducherry.
• The Sangam period (approximately 300 BCE to 300 CE) produced a vast body of Tamil literature, including the famous Tolkappiyam (grammar) and Eight Anthologies (Ettuthokai), which served as a primary basis for its classical claim.

Given: L, M, N, D, E and F live on six different floors of the same building.

The lowermost floor is numbered 1 and the topmost floor is numbered 6.

L lives on an even numbered floor, but not on floor number 4.

Only two people live between L and E.

D lives on an odd numbered floor, but not on the lowermost floor.

Only two people live between D and N.

F lives immediately below D.

Now, the person immediately above M is N.

Hence, the correct answer is Option 3.

The correct answer is Memories of Lord Krishna.

Key Points

• Raut Nacha is a traditional folk dance performed by the Yadav/Yadu (also known as Raut) community in the state of Chhattisgarh, India.
• This dance form is deeply rooted in the devotion to Lord Krishna and reflects the warrior spirit and cultural heritage of the cowherd community, who consider themselves descendants of the Yaduvanshi lineage.
• The performance is a symbolic representation of the victory of good over evil, specifically commemorating the battle between Lord Krishna and the demon king Kansa. Hence, the option "Memories of Lord Krishna" is correct.
• The dance is traditionally performed during the period following Diwali, specifically on the auspicious day of Dev Uthani Ekadashi (the 11^th day of the Shukla Paksha in the month of Kartik), which is believed to be the time when the gods awaken from their sleep.
• Performers wear colorful, vibrant costumes and carry decorated sticks or shields, performing synchronized steps and rhythmic movements to the beat of traditional instruments like the Mandhar (drum).

Additional Information

• Location and Popularity: While performed across rural Chhattisgarh, the city of Bilaspur is famous for hosting the Raut Nacha Mahotsav annually since 1978. This festival draws thousands of participants and spectators, showcasing the cultural richness of the region.
• Significance of Dohas: A unique feature of the dance is the recitation of Dohas (rhyming couplets). These couplets often contain philosophical meanings, moral lessons, or praises of Lord Krishna and the ancestors.
• Other Options Context:
• Stories of Goddess Parvati: These are typically central to dances like Gaur Maria or regional Teej celebrations, but not the primary focus of Raut Nacha. Hence, this statement is incorrect.
• Epics of Lord Rama: The life of Lord Rama is celebrated through Ramleela and Sua Nacha (partially) but Raut Nacha specifically honors Krishna. Hence, this statement is incorrect.
• Legends of Lord Shiva: While Chhattisgarh has many Shaivite traditions, Raut Nacha is strictly a Vaishnavite (Krishna-centric) folk form. Hence, this statement is incorrect.
• Traditional Instruments: The dance is accompanied by the Dhol, Nagada, Singi (trumpet), and flutes, creating a high-energy atmosphere.

Important Points

• Cultural Identity: The dance serves as a social gathering tool for the Raut community to strengthen communal bonds and pass down ancestral stories to the younger generation.
• Attire Details: The dancers often wear waistcoats, ghungroos (bells) on their ankles, and headgears decorated with peacock feathers, which is a direct symbolism of Lord Krishna.
• Evolution: Over the years, the dance has evolved from a purely religious ritual to a performing art that represents the identity of the state of Chhattisgarh at national level events like the Republic Day Parade in New Delhi.

Shortcut Trick

Amount becomes 5P ⇒ Interest = 4P

SI = (P × R × T) ÷ 100 = 4P

⇒ (R × 24) ÷ 100 = 4

⇒ R = (4 × 100) ÷ 24 = 16.67%

∴ Answer = 16.67%

Alternate Method

Given:

Amount = 5P

Time = 24 years

Formula:

SI = (P × R × T) ÷ 100

Calculations:

⇒ Interest = 5P − P = 4P

⇒ 4P = (P × R × 24) ÷ 100

⇒ 4 = (R × 24) ÷ 100

⇒ R = (4 × 100) ÷ 24 = 16.67%

Final Answer: 16.67%

Additional Information

Simple Interest: SI = (P × R × T) ÷ 100

Amount Relation: A = P + SI

Growth Concept: 5 times means 4P interest

Exam Trick: Cancel P early to simplify calculation

The correct answer is Copper.

Key Points

• The districts of Jhunjhunu and Alwar in the state of Rajasthan are premier regions for the mining and production of Copper in India.
• Jhunjhunu is home to the world-famous Khetri Copper Complex, which is one of the most significant copper-producing belts in the country.
• In Alwar, the Kho-Dariba area is well-known for its rich deposits of copper ore, contributing significantly to the state's mineral wealth.
• Bauxite is the primary ore for Aluminum. In India, it is largely found in Odisha, Gujarat, and Jharkhand. It is not the major mineral associated with the Jhunjhunu or Alwar districts. Hence, the statement regarding Bauxite is incorrect.
• Gold deposits in Rajasthan are primarily located in the Anandpur Bhukia and Jagpura areas of the Banswara district. While small traces might exist elsewhere, it is not the defining mineral for Jhunjhunu or Alwar. Hence, the statement regarding Gold is incorrect.
• Mica is largely produced in Bhilwara, Ajmer, and Tonk districts of Rajasthan. Bhilwara is often referred to as the Mica City of Rajasthan. It is not the primary mineral found in the specified districts of the question. Hence, the statement regarding Mica is incorrect.
• Copper is a non-ferrous base metal that is highly ductile and has excellent electrical conductivity. The Khetri-Singhana belt in Jhunjhunu and Kho-Dariba in Alwar are the centers of its extraction. Hence, the statement regarding Copper is correct.

Additional Information

• Mineral Wealth of Rajasthan: Rajasthan is known as the "Museum of Minerals" because it produces about 81 different varieties of minerals. It has a monopoly in the production of Zinc, Lead, Wollastonite, and Selenite.
• Characteristics of Copper:
• Uses: It is extensively used in the electrical industry for making wires, transformers, and generators due to its high conductivity. It is also used in plumbing, industrial machinery, and for creating alloys like Brass (Copper + Zinc) and Bronze (Copper + Tin).
• Location: Major copper reserves in India are located in Madhya Pradesh (Balaghat), Rajasthan (Jhunjhunu and Alwar), and Jharkhand (Singhbhum).
• Age: Copper mining in the Khetri region has historical roots dating back to the Mauryan period and has been active for over 2000 years.
• Hindustan Copper Limited (HCL): This is a Public Sector Undertaking (PSU) under the Ministry of Mines, Government of India. It was incorporated in the year 1967. It manages the Khetri Copper Complex (KCC) in Rajasthan.

Important Points

• Khetri Copper Complex: Located in Jhunjhunu, it includes the Khetri, Kolihan, Banwas, and Chandmari mines. It is a major hub for integrated copper production, including smelting and refining.
• Global Context: Chile is the world's largest producer of copper. While India has significant reserves, it still imports a portion of its copper requirements to meet the high demand in the electronics and infrastructure sectors.
• Geological Feature: The copper deposits in Rajasthan are mostly found in the Aravalli Range, which is one of the oldest fold mountain systems in the world, formed during the Proterozoic Eon.

The correct answer is Ctrl + C and Ctrl + V.

Key Points

• Ctrl + C and Ctrl + V: This pair represents the standard keyboard shortcuts in almost all Graphical User Interfaces (GUIs) for performing the copy and paste operations. Ctrl + C is used to duplicate the selected data to the Clipboard, while Ctrl + V is used to insert that data into a specific location. Hence, this option is correct.
• Function of Copy (Ctrl + C): When a user selects a piece of text, image, or file and presses Ctrl + C, the computer stores a reference or the actual data in a temporary storage area known as the Clipboard. This allows the original content to remain in its place while creating a replica.
• Function of Paste (Ctrl + V): The paste command retrieves whatever is currently stored in the system clipboard and places it at the cursor's location. This function can be used multiple times to create several copies of the same item until a new item is copied.
• Origin: These commands were popularized by Larry Tesler while working at Xerox PARC in the 1970s. They became industry standards with the rise of Apple Macintosh and Microsoft Windows operating systems.
• Efficiency: Using these keyboard shortcuts significantly increases productivity compared to using a mouse to navigate through "Edit" menus or right-click context menus.

Additional Information

• Ctrl + F and Ctrl + C: In this pair, Ctrl + F is the shortcut for Find, which opens a search box to locate specific text within a document or webpage. Ctrl + C is for Copy. While both are useful, they do not function together as a "copy-paste" pair. Hence, this option is incorrect.
• Ctrl + Tab and Ctrl + S: Ctrl + Tab is a navigation shortcut used to switch between open tabs in web browsers like Google Chrome or Mozilla Firefox. Ctrl + S is the Save command, used to commit changes to a file on the hard drive. Hence, this option is incorrect.
• Ctrl + F and Ctrl + S: This combination links the Find utility and the Save command. It is often used during editing but does not involve duplicating or moving text. Hence, this option is incorrect.
• Clipboard Management: Modern versions of Windows 10 and Windows 11 have introduced Windows + V, which allows users to view their Clipboard History, enabling them to choose from several previously copied items rather than just the most recent one.
• Cut Command (Ctrl + X): Often confused with copy, Ctrl + X removes the selected text from its original position and places it on the Clipboard. This is used for "moving" text rather than "duplicating" it.

Important Points

• Universal Compatibility: These shortcuts work across various platforms, including Microsoft Word, Excel, PowerPoint, and most web browsers.
• macOS Variants: On Apple computers, the Command (⌘) key is used instead of Control. Therefore, Copy is Command + C and Paste is Command + V.
• Undo and Redo: To complement copy-paste, users frequently use Ctrl + Z for Undo (reversing an action) and Ctrl + Y (or Ctrl + Shift + Z) for Redo.
• Select All: Before copying large amounts of text, users often use Ctrl + A to Select All content within a window or text box.

Shortcut Trick

Given x + 1/(18x) = 3

Cube both sides:

⇒ (x + 1/(18x))³ = 27

⇒ x³ + 1/(5832x³) + 3(x × 1/(18x))(x + 1/(18x)) = 27

⇒ x³ + 1/(5832x³) + 3(1/18)(3) = 27

⇒ x³ + 1/(5832x³) + 1/2 = 27

⇒ x³ + 1/(5832x³) = 26.5

⇒ Multiply by 18:

⇒ 18x³ + 1/(324x³) = 18 × 26.5 = 477

∴ Answer = 477

Alternate Method

Given:

x + 1/(18x) = 3

Formula:

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculations:

⇒ Let a = x, b = 1/(18x)

⇒ ab = 1/18

⇒ (x + 1/(18x))³ = x³ + 1/(5832x³) + 3 × (1/18) × 3

⇒ 27 = x³ + 1/(5832x³) + 1/2

⇒ x³ + 1/(5832x³) = 53/2

⇒ Multiply by 18:

⇒ 18x³ + 1/(324x³) = 18 × 53/2 = 477

Final Answer: 477

Additional Information

Identity: (a + b)³ = a³ + b³ + 3ab(a + b)

Key Step: Find ab before applying identity

Exam Trick: Multiply at the end to match required form

Power Handling: Carefully cube denominator values

The correct answer is Composite volcano.

Key Points

• A Composite volcano, also known as a stratovolcano, is a tall, conical volcano built up by many layers (strata) of hardened lava, tephra, pumice, and volcanic ash.
• These volcanoes are characterized by a steep profile and periodic explosive eruptions and effusive eruptions, although some have exhibited collapsed craters called calderas.
• The magma forming this type of volcano is typically intermediate to high in silica content (andesitic, dacitic, or rhyolitic), which makes it more viscous (thick) than the basaltic magma found in shield volcanoes.
• Due to high viscosity, the lava travels short distances from the vent before cooling and hardening, which contributes to the conical shape and steep slopes of the stratovolcano.
• Famous examples of composite volcanoes include Mount Fuji in Japan, Mount Rainier and Mount St. Helens in the United States, and Mount Vesuvius in Italy.
• These volcanoes are most commonly found along subduction zones, where one tectonic plate is being pushed beneath another, such as along the Pacific Ring of Fire.

Additional Information

• Shield Volcano:
• A Shield volcano is a type of volcano usually built almost entirely of fluid basaltic lava flows.
• They are named for their large size and low profile, resembling a warrior's shield lying on the ground.
• The low viscosity of the lava allows it to flow over great distances, creating broad, gentle slopes.
• The Hawaiian Islands are composed of a chain of shield volcanoes, including Mauna Loa and Kilauea.
• Cinder Cone Volcano:
• Cinder cones are the simplest type of volcano, built from particles and blobs of congealed lava ejected from a single vent.
• As the gas-charged lava is blown violently into the air, it breaks into small fragments that solidify and fall as cinders (tephra) around the vent to form a circular or oval cone.
• Most cinder cones have a bowl-shaped crater at the summit and rarely rise more than a thousand feet above their surroundings.
• An example is Parícutin in Mexico, which grew out of a cornfield in 1943.
• Fissure Volcano:
• A Fissure volcano or vent is a linear volcanic vent through which lava erupts, usually without any explosive activity.
• The vent is usually a few meters wide but may be many kilometers long.
• Fissure vents can cause large flood basalts and are common in Iceland and along mid-ocean ridges.

Important Points

• Ring of Fire: A 40,000 km horseshoe-shaped basin in the Pacific Ocean where a large number of earthquakes and volcanic eruptions occur. It contains approximately 75% of the world's active volcanoes.
• Pyroclastic Flow: A fast-moving current of hot gas and volcanic matter (collectively known as tephra) that moves away from a volcano reaching speeds of up to 700 km/h. This is a common and deadly feature of composite volcano eruptions.
• Magma vs. Lava: Magma is the molten rock stored underground, while Lava is the term for magma once it reaches the surface through a volcanic vent.
• Volcanic Explosivity Index (VEI): A relative measure of the explosiveness of volcanic eruptions, ranging from 0 to 8. Stratovolcanoes typically score higher on this index compared to shield volcanoes.

Shortcut Trick

Take minimum structure using primes:

12 = 2² × 3, 18 = 2 × 3², 6 = 2 × 3

Assign: a = 2²×3, b = 2²×3², c = 2×3²

⇒ a = 12, b = 36, c = 18

⇒ Sum = 66 = 6k ⇒ k = 11

∴ Answer = 11

Alternate Method

Given:

gcd(a, b) = 12, gcd(b, c) = 18, gcd(c, a) = 6

Prime Factorization:

12 = 2² × 3

18 = 2 × 3²

6 = 2 × 3

Construction:

⇒ a must contain 2² and 3

⇒ b must contain 2² and 3²

⇒ c must contain 2 and 3²

Minimum values:

⇒ a = 12, b = 36, c = 18

Calculations:

⇒ Sum = 12 + 36 + 18 = 66

⇒ 66 = 6k ⇒ k = 11

Final Answer: 11

Additional Information

GCD Rule: gcd takes minimum powers of primes

LCM Insight: LCM takes maximum powers

Construction Trick: Assign minimum values satisfying all gcd conditions

Exam Tip: Always use prime factorization in gcd problems

Given number: 5267341

Logic:

Add 1 to each odd digit

Subtract 2 from each even digit

Original number: 5 2 6 7 3 4 1

New number: 6 0 4 8 4 2 2

Now, second from the left = 0

Hence, the correct answer is Option 2.

The correct answer is 2014.

Key Points

• The Padhe Bharat Badhe Bharat (PBBB) scheme was officially launched in 2014 as a nationwide sub-programme of the Sarva Shiksha Abhiyan (SSA).
• The primary objective of the scheme is to improve the reading, writing, and mathematical skills of children in Class I and Class II.
• It was introduced by the Ministry of Human Resource Development (now known as the Ministry of Education) to ensure that every child attains foundational literacy and numeracy.
• The program recognizes that the first few years of primary education are critical for a child's future learning outcomes and focuses on building a strong foundation in language and arithmetic.
• The scheme provides a framework for States and Union Territories to implement effective classroom practices and teacher training modules specifically designed for early graders.

Additional Information

• Twin Tracks of PBBB:
• The scheme operates on two main tracks: Early Reading and Writing with Comprehension (ERWC) and Early Mathematics (EM).
• ERWC focuses on enabling children to read with understanding and express themselves in writing.
• EM is designed to help children understand reasoning, numbers, shapes, and measurement through activity-based learning.
• Integration with Samagra Shiksha:
• Following the reorganization of educational schemes, Padhe Bharat Badhe Bharat has been subsumed under the Samagra Shiksha Abhiyan, which is an integrated scheme for school education from Pre-school to Class XII.
• This integration ensures a seamless transition and continuous monitoring of learning levels across all stages of school education in India.
• Related Initiatives:
• In 2021, the government launched the NIPUN Bharat Mission (National Initiative for Proficiency in Reading with Understanding and Numeracy).
• NIPUN Bharat aims to achieve the goal of universal foundational literacy and numeracy for every child by the end of Grade 3 by the year 2026-27.
• These missions align with the goals of the National Education Policy (NEP) 2020, which prioritizes foundational learning.
• Target Beneficiaries and Impact:
• The scheme targets children in the age group of 6 to 8 years studying in government and government-aided schools across the country.
• It emphasizes the use of pedagogical tools and print-rich environments in schools to make learning more engaging and effective for young learners.

Important Points

• The scheme encourages the use of Mother Tongue or Home Language as the medium of instruction in early years to bridge the gap between home and school environments.
• Monitoring of the scheme is done through the Project Approval Board (PAB) of the Ministry of Education, which reviews the progress made by different States annually.
• Special focus is given to District-level implementation and the creation of Teacher Resource Material to help educators handle multi-grade and multi-level classrooms efficiently.

The logic followed here is:

Logic: 2^nd number = (1^st number + 3^rd number) ÷ 3

(9,11,24)

(9 + 24) ÷ 3 = 33 ÷ 3 = 11 (2^nd number)

(15,14,27)

(15 + 27) ÷ 3 = 42 ÷ 3 = 14 (2^nd number)

Option (1): (2,11,31)

(2 + 31) ÷ 3 = 33 ÷ 3 = 11 ⇒ 2^nd number (True)

Hence, the correct answer is option (1).

Shortcut Trick

Mean proportional of two numbers a and b = √(a × b)

Given speeds: a = 20 and b = 45

Mean proportional = √(20 × 45)

Mean proportional = √900 = 30 km/h

∴ Answer = 30 km/h

Alternate Method 

Given:

Speed of first vehicle (a) = 20 km/h

Speed of second vehicle (b) = 45 km/h

Formula used:

If x is the mean proportional between a and b, then a : x :: x : b

⇒ x² = a × b

 20 km/h (a) Mean Proportional (x) 30 km/h 45 km/h (b) Ratio: 20 : x = x : 45

Calculations:

Let the mean proportional be x.

⇒ x = √(20 × 45)

⇒ x = √(4 × 5 × 5 × 9)

⇒ x = 2 × 5 × 3

⇒ x = 30 km/h

∴ The correct answer is 30 km/h (Option 4).

Additional Information

Third Proportional

If a, b, and c are in continued proportion, then c is the third proportional to a and b, where c = b² ÷ a.

Fourth Proportional

If four numbers a, b, c, and d are in proportion (a:b = c:d), then d is the fourth proportional, where d = (b × c) ÷ a.

Duplicate Ratio

The duplicate ratio of two numbers a and b is the ratio of their squares, expressed as a² : b².

Compound Ratio

For two ratios a:b and c:d, the compound ratio is calculated by multiplying the antecedents and the consequents, given by (a × c) : (b × d).

Given: (Left) ^ 5 % 5 \ 6 # + # + 1 6 ? # 6 & 7 & 9 < % (Right)

Now,

Numbers, which are immediately preceded by a symbol and also immediately followed by a symbol.

So, Needed pattern is: Symbol - Number - Symbol.

(Left) ^ 5 % 5 \ 6 # + # + 1 6 ? # 6 & 7 & 9 < % (Right)

Total such numbers = 6

Hence, the correct answer is 'Option 3'.

The correct answer is Godrej Aerospace.

Key Points

• Godrej Aerospace, a unit of Godrej & Boyce, successfully delivered the first human-rated Vikas engine to the Indian Space Research Organisation (ISRO) in November 2025 for the Gaganyaan mission.
• The Vikas engine is a high-thrust liquid-fueled rocket engine that powers the second stage (L110) of the Launch Vehicle Mark-3 (LVM3), which is India's heaviest satellite launch vehicle.
• The human-rated version of the engine is specifically modified to meet the safety standards required for carrying astronauts into space, involving enhanced reliability and redundancy systems.
• Godrej Aerospace has been a trusted industrial partner of ISRO since 1985, contributing to major programs such as Chandrayaan, Mangalyaan, and the Polar Satellite Launch Vehicle (PSLV).
• The engine was manufactured at the company's advanced facility in Vikhroli, Mumbai, Maharashtra, highlighting the role of the private sector in India's growing space economy.

Additional Information

• Gaganyaan Mission:
• This is India's first crewed orbital spacecraft mission, intended to send a three-member crew to an altitude of 400 km for a period of 3 days.
• The mission aims to demonstrate human spaceflight capability and ensure the safe return of the astronauts to Earth, specifically landing in Indian sea waters.
• Vikas Engine Technical Details:
• The engine was originally developed by the Liquid Propulsion Systems Centre (LPSC) in the 1970s, based on the French Viking engine technology.
• It generates a nominal thrust of approximately 800 kN (kilo-Newtons) and uses Unsymmetrical Dimethylhydrazine (UDMH) as fuel and Nitrogen Tetroxide (N2O4) as the oxidizer.
• Role of Other Organisations:
• Hindustan Aeronautics Limited (HAL): This public sector undertaking (PSU) is responsible for manufacturing the Crew Module and the structural hardware of the LVM3 rocket.
• Bharat Electronics (BEL): This organization provides critical avionics, cockpit display systems, and communication equipment for the mission.
• ISRO (Indian Space Research Organisation): Established in 1969, it serves as the lead national space agency overseeing the design, testing, and execution of the Gaganyaan project.

Important Points

• Human-Rating Process: For a rocket engine to be human-rated, it must undergo static fire tests for a duration longer than the actual flight time to ensure it can withstand vibrations and thermal stresses without failure.
• Safety Margins: The human-rated Vikas engine features a margin of safety that is significantly higher than standard satellite launch engines to minimize the risk to human life.
• Strategic Impact: The successful delivery by a private company like Godrej Aerospace aligns with the Government of India's vision of Atmanirbhar Bharat and the opening of the space sector to private industries through IN-SPACe.
• Launch Vehicle Structure: The LVM3 rocket consists of two S200 solid rocket boosters, a core liquid L110 stage (using two Vikas engines), and a C25 cryogenic upper stage.

Given Statements:

All rabbits are yaks.

All yaks are whales.

No whale is a shark.

The least possible Venn diagram for the given statement is: 

Conclusions:

I. No rabbit is a shark → True (Rabbits are inside Yaks and Yaks are inside Whales, and no whale is a shark, so rabbits also cannot be sharks).

II. Some whales are rabbits → True (Since all rabbits are yaks and all yaks are whales, rabbits exist inside whales, so some whales are rabbits).

So, both conclusion I and II follow.

Hence, the correct answer is "Option 1".

Shortcut Trick

Total circumference of the circle (r = 7 cm) = 2 × 22/7 × 7 = 44 cm.

Arc angle ratio = 240° ÷ 360° = 2/3.

Arc length = 2/3 × 44 = 88/3 = 29.33 cm.

∴ Answer = 29.33 cm

Alternate Method

 

Given:

Radius (r) = 7 cm

Central Angle (θ) = 240°

Use π = 22/7

Formula used:

Length of Arc = (θ ÷ 360°) × 2πr

 r = 7 cm 240° Arc Length (L) ≈ 29.33 cm

Calculations:

Length of Arc = (240° ÷ 360°) × 2 × (22/7) × 7

⇒ Length of Arc = (2/3) × 44

⇒ Length of Arc = 88/3

⇒ Length of Arc ≈ 29.333...

∴ The correct answer is 29.33 cm.

Additional Information

Area of a Sector

The area of a sector with central angle θ is given by Area = (θ ÷ 360°) × πr².

Perimeter of a Sector

The total boundary of a sector includes the arc and the two radii. Perimeter = Arc Length + 2r.

Arc Length in Radians

If the central angle θ is measured in radians, the arc length s is simply calculated as s = r × θ.

Circumference and Diameter

The full circumference of a circle is 2πr or πd, where d is the diameter (2r).

Shortcut Trick

Income = 4x, 5x and Expenditure = 3y, 4y

Savings: 4x − 3y = 10000 and 5x − 4y = 12000

Multiply: (1)×4 ⇒ 16x − 12y = 40000, (2)×3 ⇒ 15x − 12y = 36000

Subtract ⇒ x = 4000

Income of A = 4x = 16000

∴ Answer = 16000

Alternate Method

Given:

Income ratio A:B = 4 : 5

Expenditure ratio A:B = 3 : 4

Savings of A = 10000, B = 12000

Formula used:

Savings = Income − Expenditure

A: 4x − 3y B: 5x − 4y = 10000 = 12000

Calculations:

⇒ 4x − 3y = 10000 ...(1)

⇒ 5x − 4y = 12000 ...(2)

⇒ Multiply (1) by 4: 16x − 12y = 40000

⇒ Multiply (2) by 3: 15x − 12y = 36000

⇒ Subtract ⇒ x = 4000

⇒ Income of A = 4x = 16000

∴ The correct answer is 16000.

Additional Information

Savings Formula

Savings = Income − Expenditure

Ratio Assumption

Assume variables (x, y) based on given ratios to simplify equations.

Elimination Technique

Multiply equations to equalize coefficients and subtract.

Exam Tip

Use cross multiplication for faster solving in ratio-based problems.

Shortcut Trick

831 is 72 less than 35% of total

⇒ 35% of total = 831 + 72 = 903

⇒ Total = 903 × 100 ÷ 35 = 2580

Friend % = 774 × 100 ÷ 2580

= 30%

∴ Answer = 30%

Alternate Method

Given:

Girish marks = 831

Short by 72 from 35% of total

Friend marks = 774

Formula used:

Percentage = (Marks obtained × 100) ÷ Total marks

Total Marks = 2580 35% = 903 Girish = 831

Calculations:

⇒ 35% of total = 831 + 72 = 903

⇒ Total marks = 903 × 100 ÷ 35 = 2580

⇒ Friend percentage = 774 × 100 ÷ 2580

⇒ = 30%

∴ The correct answer is 30%.

Additional Information

Percentage Formula

Percentage = (Part ÷ Whole) × 100

Reverse Percentage

If x is y% of total, then total = x × 100 ÷ y

Shortcut Insight

Always first convert given condition into exact percentage value.

Exam Tip

Avoid decimals by keeping fraction form till final step.

The correct answer is Atlantic Ocean.

Key Points

• The Canary Current is a prominent wind-driven surface current that is part of the North Atlantic Ocean circulation system.
• It is categorized as a cold ocean current because it carries cooler water from higher latitudes toward the equator.
• The current flows in a southward direction along the western coast of Africa, stretching from approximately 30°N to 10°N. Its flow path passes the Canary Islands, from which it derives its name.
• It represents the eastern boundary current of the North Atlantic Subtropical Gyre. It originates where the North Atlantic Drift (an extension of the Gulf Stream) turns south as it nears the European coast.
• This current is vital for global climate regulation as it helps in the heat exchange between the polar regions and the tropics.

Additional Information

• Pacific Ocean Currents: This ocean features major currents such as the Kuroshio Current (warm) near Japan, the California Current (cold) along the North American coast, and the Humboldt Current (cold) along the South American coast.
• Atlantic Ocean Currents: Besides the Canary Current, this ocean includes the Gulf Stream (warm), which influences the climate of Western Europe, the Benguela Current (cold) off the coast of South Africa, and the Brazil Current (warm).
• Indian Ocean Currents: These are unique because they change direction based on the seasonal monsoon winds. Notable currents include the Agulhas Current (warm) and the West Australian Current (cold).
• Southern Ocean: The primary feature here is the Antarctic Circumpolar Current (ACC). It is the only current that flows completely around the globe without being blocked by landmasses, moving from west to east.

Important Points

• Ecological Importance: The Canary Current is associated with major coastal upwelling. Upwelling brings nutrient-rich, cold deep waters to the surface, supporting one of the most productive fisheries in the world near Morocco, Mauritania, and Senegal.
• Climatic Impact: Because it is a cold current, it cools the air above it, leading to high atmospheric stability. This inhibits rainfall, contributing significantly to the aridity of the Sahara Desert along the West African coastline.
• Navigation and History: Historically, the Canary Current and the associated Trade Winds were crucial for maritime exploration, including the voyages of Christopher Columbus toward the Americas in 1492.
• Temperature Characteristics: The surface temperatures of the current typically range between 18°C and 22°C, which is notably cooler than the tropical waters further out in the Atlantic.

Given: A, B, C, D, E, F and G are sitting around a circular table facing the centre.

D sits to the immediate right of C.

Only three people sit between E and C when counted from the right of C.

Only two people sit between B and D when counted from the right of B.

F sits to the immediate right of A.

Now, immediate left neighbour (clockwise direction):

i. G → B → (Z)

ii. E → F → (Y)

iii. A → D → (X)

iv. C → G → (W)

So, i-Z, ii-Y, iii-X, iv-W

Hence, the correct answer is "Option 1".