Shortcut Trick

Total ratio = 4 + 3 + 7 + 6 = 20

Each part = 360 ÷ 20 = 18

⇒ Angles: 72, 54, 126, 108

Check adjacent sum:

⇒ 54 + 126 = 180 ✔

∴ Answer = Trapezium

Alternate Method

Given: Ratio = 4 : 3 : 7 : 6

Formula: Sum of angles = 360

⇒ Let angles be 4x, 3x, 7x, 6x

⇒ 20x = 360 ⇒ x = 18

⇒ Angles = 72, 54, 126, 108

⇒ Check trapezium condition: consecutive interior angles on same leg = 180

⇒ 54 + 126 = 180 ⇒ one pair of opposite sides parallel

P(72°) Q(54°) R(126°) S(108°)

∴ Quadrilateral is Trapezium

Additional Information

Trapezium: One pair of opposite sides parallel; consecutive angles between them sum = 180

Cyclic Quadrilateral: Opposite angles sum = 180

Parallelogram: Opposite angles equal and parallel sides in pairs

Angle Sum Property: Any quadrilateral total = 360

The correct answer is Led by hereditary militia with local administrative roles.

Key Points

• The Paika Rebellion of 1817 was an armed uprising against the British East India Company's rule in Odisha, primarily led by the Paikas, who were the traditional landed militia of the state.
• The Paikas were distinct because they held hereditary rent-free lands (known as Paikan Jagirs) in exchange for their military and police services to the Gajapati rulers of Khurda.
• During times of peace, these individuals performed administrative functions, such as maintaining law and order and policing within their localities, while during war, they served as the standing army.
• The rebellion was sparked when the British, after conquering Odisha in 1803, began resuming (taking back) these rent-free lands, imposing heavy land revenues, and abolishing the cowrie currency system in favor of silver.
• The uprising was led by Bakshi Jagabandhu Bidyadhar, the former Military Chief (Commander-in-Chief) of the King of Khurda, who had been dispossessed of his ancestral Killa Rorang estate by the British.
• Statement A is incorrect because the movement was entirely indigenous and did not depend on foreign mercenary forces; it was a grassroots resistance involving local tribals and peasants.
• Statement B is incorrect because while some dispossessed zamindars joined, the Paika Rebellion was a much broader socio-militaristic uprising rooted in the loss of hereditary rights rather than simple revenue concessions.
• Statement C is incorrect because the rebellion was rural and agrarian-military in nature, centered in Khurda, Banapur, and Puri, rather than being driven by urban craft guilds or traders.
• Statement D is correct because the Paikas represented a unique social class that combined peasantry with military and administrative responsibilities. Hence, the correct answer is option D.

Additional Information

• Historical Context: The British East India Company defeated the Marathas in 1803 to take control of Odisha. The Raja of Khurda, Mukunda Deva II, was eventually deposed, leading to the collapse of the traditional Paika system.
• Economic Grievances: Apart from land issues, the British established a monopoly over salt, which caused the price of this essential commodity to skyrocket, further fueling anger among the common populace and tribals like the Khonds.
• Timeline: The rebellion began in March 1817 when a group of 400 Khonds from Ganjam entered Khurda and joined forces with the Paikas. They attacked the Police Station and Government Treasury at Banapur.
• Suppression: The British declared Martial Law in Khurda. By 1818, the active rebellion was mostly suppressed, though guerrilla warfare continued for a few years. Bakshi Jagabandhu finally surrendered in 1825 and lived as a pensioner in Cuttack until his death in 1829.
• Recognition: Many historians and the Government of Odisha have advocated for the Paika Rebellion to be formally recognized as the First War of Indian Independence, predating the Revolt of 1857.

Important Points

• Social Structure: The Paikas were divided into three ranks: the Paharis (shield-bearers), the Banua (matchlockmen), and the Dhenkiyas (archers).
• Geographical Spread: While it started in Khurda, the insurrection spread rapidly to Puri, Pipli, Cuttack, and Kanika, showing the widespread discontent against colonial administrative policies.
• Administrative Impact: Following the rebellion, the British were forced to make concessions in revenue collection and land settlements in Odisha to prevent further unrest.
• Commemoration: In 2017, the Government of India celebrated the 200th anniversary of the Paika Rebellion with various national-level events and monuments dedicated to the martyrs of the uprising.

The correct answer is 1971.

Key Points

• The Intel 4004 was the world's first commercially available microprocessor, introduced by Intel Corporation on 15 November 1971.
• It was developed by a team led by Federico Faggin, with significant contributions from Ted Hoff and Stanley Mazor.
• The Intel 4004 was a 4-bit microprocessor containing approximately 2,300 transistors and operated at a clock speed of about 740 kHz.
• Originally designed for calculators manufactured by the Japanese company Busicom, it later became a revolutionary innovation in the field of computing.
• The launch of the Intel 4004 marked the beginning of the microprocessor era, paving the way for modern computers, smartphones, and embedded systems.
• Hence, the correct answer is 1971.

Additional Information

• Microprocessor:
• A microprocessor is the Central Processing Unit (CPU) integrated onto a single semiconductor chip.
• It performs arithmetic, logical, and control operations of a computer.
• Intel Corporation:
• Founded in 1968 by Robert Noyce and Gordon Moore.
• Headquartered in California, USA.
• Intel 4004 Specifications:
• Word Length: 4-bit.
• Transistors: Approximately 2,300.
• Clock Speed: Around 740 kHz.
• Evolution of Intel Processors:
• Intel 8008 (1972) – 8-bit microprocessor.
• Intel 8080 (1974) – Used in early personal computers.
• Intel 8086 (1978) – Introduced the x86 architecture.
• Importance of the Intel 4004:
• It transformed computing by replacing multiple integrated circuits with a single programmable chip.
• It laid the foundation for the development of modern computing devices.

Important Points

• World's First Commercial Microprocessor: Intel 4004.
• Launch Year: 1971.
• Bit Size: 4-bit.
• Developer: Intel Corporation.
• Application: Initially designed for Busicom calculators.

The correct answer is Ghiyasuddin Tughlaq.

Key Points

• Ghiyasuddin Tughlaq, also known as Ghazi Malik, was the founder of the Tughlaq dynasty in India and he ordered the construction of the Tughlaqabad Fort in 1321. Hence, statement A is correct.
• The fort was built to serve as the capital of the Delhi Sultanate and is considered the third city of Delhi, designed with massive stone fortifications to protect against Mongol invasions.
• The construction of this gigantic stone structure was completed in a remarkably short span of four years (between 1321 and 1325), featuring high walls and circular bastions.
• Ghiyasuddin Tughlaq ruled from 1320 to 1325, and his reign marked the beginning of a period characterized by significant administrative and military reforms in the Delhi Sultanate.
• The fort's architecture is a prime example of the Tughlaq style, which favored heavy, sloping walls (batter) and functional strength over the ornate decorations of previous dynasties.

Additional Information

• Alauddin Khalji:
• He was the most powerful ruler of the Khalji Dynasty (reign: 1296–1316) and is famous for building the Siri Fort (the second city of Delhi) and the Alai Darwaza. Hence, statement B is incorrect.
• He introduced significant market reforms and maintained a large standing army to repel Mongol attacks long before the Tughlaqs came to power.
• Muhammad bin Tughlaq:
• He was the son of Ghiyasuddin Tughlaq and ruled from 1325 to 1351; while he built the city of Jahanpanah, he did not build Tughlaqabad Fort. Hence, statement C is incorrect.
• He is known for his controversial decisions, such as shifting the capital from Delhi to Daulatabad in 1327 and introducing token currency.
• Firoz Shah Tughlaq:
• Reigning from 1351 to 1388, he was a prolific builder who established the city of Firozabad (Firoz Shah Kotla) and founded towns like Hissar, Fatehabad, and Jaunpur. Hence, statement D is incorrect.
• He is credited with developing extensive irrigation canals and hospital systems (Dar-ul-Shifa) across the empire.
• Location and Status:
• The Tughlaqabad Fort is located in South Delhi, India. Today, it stands mostly in ruins but remains a significant archaeological site under the Archaeological Survey of India (ASI).

Important Points

• Legend of the Curse: A famous historical legend mentions a conflict between Ghiyasuddin Tughlaq and the Sufi saint Nizamuddin Auliya. The saint reportedly cursed the fort, saying, "Ya rahe usar, ya base Gujar" (May it remain barren or be inhabited by herdsmen), which is often cited as the reason for its early abandonment.
• Tomb of Ghiyasuddin Tughlaq: Located across the fort and connected by a stone causeway, the tomb is a masterpiece of Indo-Islamic architecture. It features a white marble dome and sloping red sandstone walls, which became a signature of the Tughlaq era.
• Military Architecture: The fort was equipped with underground passages, granaries, and deep wells to sustain the population during long sieges, reflecting the constant threat of foreign invasions during the 14th century.

The correct answer is Because they are dangerous to wildlife.

Key Points

• The Supreme Court of India, in its order dated November 13, 2025, reiterated that mining activities in the vicinity of National Parks and Wildlife Sanctuaries are inherently hazardous to the ecological balance.
• Mining operations involve blasting, excavation, and the use of heavy machinery, which result in significant noise pollution and ground vibrations that distress and displace wild animals. Hence, option C is correct.
• Such activities lead to the destruction of natural habitats and the fragmentation of wildlife corridors, which are vital for the migration and survival of species.
• Mining does not create sustainable water sources; instead, it often leads to the depletion of groundwater and the contamination of streams with toxic minerals and silt. Hence, option A is incorrect.
• While some argue that mining can boost the local economy, the Supreme Court held that economic gains cannot override the "Precautionary Principle" regarding the environment. Hence, option D is incorrect.
• The court noted that mining activities generally deter tourism in the long run by destroying the pristine nature and biodiversity of the region. Hence, option B is incorrect.

Additional Information

• Eco-Sensitive Zones (ESZ):
• These are areas within 10 kilometers around Protected Areas, National Parks, and Wildlife Sanctuaries notified by the Ministry of Environment, Forest and Climate Change (MoEFCC).
• The Supreme Court has previously mandated a minimum 1 km ESZ for all protected areas to act as a "shock absorber" for the ecosystem.
• In these zones, activities are classified into Prohibited (like commercial mining), Regulated, and Permitted categories.
• Wildlife Protection Act, 1972:
• This Act provides the legal framework for the protection of various species of wild animals and plants and the management of their habitats across India.
• It prohibits the entry into or destruction of wildlife sanctuaries without proper authorization from the Chief Wildlife Warden.
• Environment Protection Act, 1986:
• This Act authorizes the Central Government to take measures to protect and improve the environment and set standards for pollution emissions.
• It is the umbrella legislation under which ESZ notifications are issued to prevent industrial hazards near sensitive zones.

Important Points

• Constitutional Mandate:
• Article 48A of the Directive Principles of State Policy mandates that the State shall endeavor to protect and improve the environment.
• Article 51A(g) establishes the fundamental duty of every citizen to protect and improve the natural environment, including forests, lakes, rivers, and wildlife.
• Public Trust Doctrine:
• The Supreme Court frequently applies this doctrine, which states that resources like air, water, and forests are held by the Government in trust for the free and unimpeded use of the public and for the protection of nature.
• Impact of Dust:
• Mining produces particulate matter (PM 2.5 and PM 10), which settles on leaves, hindering photosynthesis in forests and causing respiratory issues for wildlife.

Shortcut Trick

For A < 0, parabola opens downward ⇒ maximum at vertex

Direct formula:

Maximum value = (4AC − B²) ÷ 4A

∴ Answer = (4AC − B²) ÷ 4A

Alternate Method

Given: y = Ax² + Bx + C, A < 0

Formula: Vertex x-coordinate = −B ÷ 2A

⇒ Put x = −B ÷ 2A

⇒ y = A(−B ÷ 2A)² + B(−B ÷ 2A) + C

⇒ y = A(B² ÷ 4A²) − B² ÷ 2A + C

⇒ y = B² ÷ 4A − B² ÷ 2A + C

⇒ y = (B² − 2B²) ÷ 4A + C

⇒ y = (−B²) ÷ 4A + C

⇒ y = (4AC − B²) ÷ 4A

∴ Maximum value = (4AC − B²) ÷ 4A

Additional Information

Nature of Parabola: A > 0 ⇒ minimum, A < 0 ⇒ maximum

Vertex Formula: x = −B ÷ 2A gives extreme value point

Discriminant: D = B² − 4AC decides roots nature

Axis of Symmetry: x = −B ÷ 2A

The correct answer is Ernest Rutherford.

Key Points

• In 1911, the British physicist Ernest Rutherford conducted the famous alpha-particle scattering experiment, also known as the Gold Foil Experiment, which fundamentally changed the understanding of atomic structure.
• The experiment involved bombarding a very thin gold foil (approximately 1000 atoms thick) with fast-moving alpha particles, which are doubly-charged helium ions possessing a mass of 4u and high energy.
• Rutherford observed that most alpha particles passed straight through the foil, some were deflected by small angles, and a very small fraction (about 1 in 12,000) rebounded almost 180 degrees.
• From these observations, he concluded that the atom contains a very small, dense, and positively charged center called the nucleus, where nearly all the mass of the atom is concentrated.
• He proposed the Nuclear Model of the Atom, stating that electrons revolve around the nucleus in well-defined circular paths, much like planets around the sun.

Additional Information

• J.J. Thomson:
• In 1897, he discovered the electron using cathode ray tube experiments.
• In 1904, he proposed the Plum Pudding Model, which suggested that an atom is a sphere of positive charge with negatively charged electrons embedded in it like raisins in a pudding.
• John Dalton:
• In 1808, he presented Dalton’s Atomic Theory, which stated that all matter is made of indivisible particles called atoms.
• He theorized that atoms of the same element are identical in mass and chemical properties, forming the basis of modern chemistry.
• Niels Bohr:
• In 1913, he modified Rutherford's model to overcome the problem of atomic stability.
• He proposed the Bohr Model, stating that electrons revolve in discrete orbits (fixed energy levels) called shells (K, L, M, N), and they do not radiate energy while in these orbits.
• Gold Foil Selection:
• Gold was chosen for the experiment because of its high malleability, allowing it to be hammered into an extremely thin sheet, which was necessary to observe the scattering of individual alpha particles.

Important Points

• Rutherford is widely regarded as the "Father of Nuclear Physics" for his discovery of the atomic nucleus.
• A major drawback of the Rutherford model was that it could not explain the stability of the atom; according to classical electrodynamics, an accelerating electron should continuously lose energy and eventually spiral into the nucleus.
• The discovery of the nucleus led to the later discovery of the proton, a term coined by Rutherford in 1920 to describe the hydrogen nucleus as a fundamental particle.

The logic followed here is:

Logic: The second number is obtained by multiplying the first number by 2 and then subtracting the third number.

For, (21, 52, 5)

⇒ 21 × 2 = 42

⇒ 42 + 10 = 52

For, (45, 138, 24)

⇒ 45 × 2 = 90

⇒ 90 + 48 = 138

Now, checking the options using the same pattern:

Option 1) (41, 117, 18)

⇒ 41 × 2 = 82

⇒ 82 + 36 = 118 ≠ 117

Option 2) (11, 39, 9)

⇒ 11 × 2 = 22

⇒ 22 + 18 = 40 ≠ 39

Option 3) (17, 55, 11)

⇒ 17 × 2 = 34

⇒ 34 + 22 = 56 ≠ 55

Option 4) (36, 74, 1)

⇒ 36 × 2 = 72

⇒ 72 + 2 = 74 

Hence, the correct answer is Option 4.

The correct answer is Ins.

Key Points

• The Ins key, short for Insert, is a toggle key found on most computer keyboards that is primarily used to switch between Insert mode and Overwrite mode (also known as Overtype mode) during text entry.
• In Insert mode, which is the default setting in most modern word processors like Microsoft Word and Google Docs, any new character typed is placed at the current cursor position, and the existing text to the right is shifted forward.
• In Overwrite mode, the newly typed character replaces or "overwrites" the character currently situated to the right of the cursor, effectively deleting the old text as you type. Hence, the Ins key is the correct option for toggling these modes.
• The Ins key is typically located in the control keys or navigation block of a standard QWERTY keyboard, usually situated above the Delete key and to the right of the Backslash key.
• On many keyboards, the Insert function is also shared with the 0 (zero) key on the numeric keypad, which is activated when Num Lock is turned off.

Additional Information

• Tab Key (Option A):
• The Tab key (short for Tabulator) is primarily used to advance the cursor to the next tab stop in a document or to move focus between fields in a User Interface (UI).
• In word processing, it creates a specific indentation, usually 0.5 inches by default.
• It does not toggle between text entry modes. Hence, statement A is incorrect.
• Del Key (Option B):
• The Del or Delete key is used to remove the character immediately following the cursor or to delete a selected object or file.
• Unlike Backspace, which deletes to the left, Delete performs forward deletion.
• While it removes text, it does not change the behavior of how new text is entered. Hence, statement B is incorrect.
• F5 Key (Option D):
• The F5 key is a function key that serves different purposes depending on the operating system or software being used.
• In web browsers like Chrome or Edge, it is used to refresh or reload the current page.
• In Microsoft PowerPoint, it starts a slideshow from the first slide, and in Excel, it opens the "Go To" dialog box. Hence, statement D is incorrect.

Important Points

• Visual Indicator: In many terminal-based systems or older applications, the cursor changes shape when Overwrite mode is active, often switching from a vertical line to a solid block or an underscore.
• Modern Software Behavior: Many modern applications have disabled the Insert key toggle by default to prevent users from accidentally overwriting their work. For instance, in Microsoft Word, you may need to enable this feature via the Options menu before the key will function as a toggle.
• Combination Shortcuts: The Insert key is also used in various shortcuts, such as Shift + Insert, which acts as the Paste command in many Windows environments, serving as an alternative to Ctrl + V.
• Legacy Use: The concept of Overwrite mode dates back to mainframes and early MS-DOS editors, where overtyping was often the primary method of editing existing text strings due to limited processing power and simple interface designs.

The logic followed here is:

For, GLOW → KQRY

Similarly, OVUA → SAXC

Now, apply the same rule to WFAE:

Here, WFAE → AKDG

Hence, the correct answer is Option 2.

The logic followed here is:

Logic: The pattern is based on a fixed sequence of operations: Multiply by 2, Add 1, Multiply by 2.

For, 3 – 6 – 7 – 14

⇒ 3 × 2 = 6

⇒ 6 + 1 = 7

⇒ 7 × 2 = 14

For, 12 – 24 – 25 – 50

⇒ 12 × 2 = 24

⇒ 24 + 1 = 25

⇒ 25 × 2 = 50

Now, checking the options using the same pattern:

Option 1) 11 – 22 – 21 – 42

⇒ 11 × 2 = 22 

⇒ 22 + 1 = 23 ≠ 21

Option 2) 25 – 50 – 25 – 35

⇒ 25 × 2 = 50 

⇒ 50 + 1 = 51 ≠ 25

Option 3) 15 – 30 – 60 – 62

⇒ 15 × 2 = 30 

⇒ 30 + 1 = 31 ≠ 60

Option 4) 20 – 40 – 41 – 82

⇒ 20 × 2 = 40 

⇒ 40 + 1 = 41 

⇒ 41 × 2 = 82 

Hence, the correct answer is Option 4.

Shortcut Trick

Given a = 7 + 4√3

⇒ 1/a = 7 − 4√3 (since (7 + 4√3)(7 − 4√3) = 1)

⇒ a + 1/a = 14

Use identity: a³ + 1/a³ = (a + 1/a)³ − 3(a + 1/a)

⇒ = 14³ − 3×14 = 2744 − 42 = 2702

∴ Answer = 2702

Alternate Method

Given: a = 7 + 4√3

Formula: (x + y)³ = x³ + y³ + 3xy(x + y)

⇒ a³ = (7 + 4√3)³

⇒ 1/a = 7 − 4√3 ⇒ 1/a³ = (7 − 4√3)³

⇒ Add both:

⇒ a³ + 1/a³ = (7 + 4√3)³ + (7 − 4√3)³

⇒ = 2[7³ + 3×7×(4√3)²]

⇒ = 2[343 + 3×7×48]

⇒ = 2[343 + 1008] = 2×1351 = 2702

∴ Answer = 2702

Additional Information

Conjugate Property: (a + b)(a − b) = a² − b²

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

Shortcut Form: If ab = 1 ⇒ a³ + 1/a³ = (a + 1/a)³ − 3(a + 1/a)

Square Identity: (a + b)² = a² + b² + 2ab

Given Statements:

All spoons are forks.

All forks are cups.

Some spoons are plates.

The least possible Venn diagram for the given statements is:

Conclusions:

I. Some forks are plates - True (Since some spoons are plates and all spoons are forks, those plates that overlap with spoons must also overlap with forks. So some forks are plates.)

II. Some cups are plates - True (All forks are cups, and some forks are plates, so those plates are also inside cups. Hence, some cups are plates.)

So, both conclusions I and II follow.

Hence, the correct answer is "Option 1".

Shortcut Trick

7 : 63 ⇒ multiplier = 9 ⇒ x = 6.5 × 9 = 58.5

7 : 42 ⇒ multiplier = 6 ⇒ y = 4 × 6 = 24

⇒ x : y = 58.5 : 24

⇒ Multiply by 2 ⇒ 117 : 48

⇒ Simplify ⇒ 39 : 16

∴ Answer = 39 : 16

Alternate Method

Given: 7 : 63 :: 6.5 : x and 7 : 42 :: 4 : y

Formula: a : b :: c : d ⇒ d = (b × c) ÷ a

⇒ x = (63 × 6.5) ÷ 7 = 9 × 6.5 = 58.5

⇒ y = (42 × 4) ÷ 7 = 6 × 4 = 24

⇒ x : y = 58.5 : 24

⇒ Multiply by 2 ⇒ 117 : 48

⇒ Divide by 3 ⇒ 39 : 16

∴ Answer = 39 : 16

Additional Information

Proportion Rule: a : b :: c : d ⇒ ad = bc

Cross Multiplication: d = (b × c) ÷ a

Ratio Simplification: Divide by common factor

Decimal Handling: Multiply both terms to remove decimal

The logic followed here is:

So, 'LJR 14' will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

The logic followed here is:

63 → 159

⇒ 63 × 3 − 30 = 159

44 → 102

⇒ 44 × 3 − 30 = 102

So, the pattern is:

Result = (Number × 3) − 30

Now, applying the same pattern for 57:

⇒ 57 × 3 − 30 = 171 − 30 = 141

Hence, the correct answer is Option 2.

The correct answer is Kudankulam Nuclear Power Station.

Key Points

• Kudankulam Nuclear Power Station (KKNPP) is located in the Tirunelveli district of Tamil Nadu, making it the southernmost nuclear power plant in India. Hence, the correct answer is option D.
• It is a civil nuclear power plant built in collaboration with Russia (specifically Atomstroyexport, a subsidiary of Rosatom).
• The plant utilizes VVER-1000 reactors (Pressurized Water Reactors) and has a planned capacity of 6,000 MW once all six units are completed.
• Kakrapar Atomic Power Station is situated in the Tapi district (near Surat) of Gujarat, which is in Western India. Hence, statement A is incorrect.
• Narora Atomic Power Station is located in the Bulandshahr district of Uttar Pradesh, serving the Northern Grid of India. Hence, statement B is incorrect.
• Madras Atomic Power Station (MAPS), also known as Kalpakkam, is located in the Chengalpattu district of Tamil Nadu. While it is in the south, it is located north of Kudankulam along the coast. Hence, statement C is incorrect.

Additional Information

• Tarapur Atomic Power Station (TAPS): It was the first commercial nuclear power station built in India, commissioned in 1969. It is located in Palghar, Maharashtra, and was built with technical assistance from the United States of America.
• Rajasthan Atomic Power Station (RAPS): Located at Rawatbhata in the Chittorgarh district of Rajasthan. It was developed in collaboration with Canada and uses CANDU reactor technology.
• Kaiga Generating Station: Located in the Uttara Kannada district of Karnataka. It features Pressurized Heavy Water Reactors (PHWR) and is a key energy provider for the Southern Grid.
• Department of Atomic Energy (DAE): Established in 1954, it operates under the direct charge of the Prime Minister of India. It oversees the development of nuclear power technology and applications of radiation in agriculture, medicine, and industry.
• Homi J. Bhabha: Known as the "Father of the Indian Nuclear Programme," he envisioned India's three-stage nuclear power programme to achieve energy independence by utilizing the country's vast Thorium reserves.

Important Points

• NPCIL: The Nuclear Power Corporation of India Limited is a Public Sector Undertaking (PSU) headquartered in Mumbai. It is responsible for the design, construction, commissioning, and operation of nuclear power reactors.
• Operational Status: As of the current date, India has 20+ nuclear reactors in operation across 7 major sites, with a total installed capacity of over 7,480 MW.
• Uranium and Thorium: India imports Uranium from countries like Kazakhstan, Canada, and Uzbekistan to fuel its reactors, while simultaneously researching Thorium-based systems (Stage 3) found in monazite sands of Kerala and Tamil Nadu.
• Safety Features: The Kudankulam plant is equipped with "Generation 3+" safety features, including a Passive Heat Removal System (PHRS) and a Core Catcher, which are designed to prevent radiation leaks even during total power loss.

Shortcut Trick

Let total voters = N

Valid votes = 80% × 80% = 64% of N

Winning margin = (55% − 45%) of valid = 10% of valid

⇒ Margin = 10% of 64% of N = 6.4% of N

⇒ 6.4% of N = 368 ⇒ N = 368 ÷ 0.064 = 5750

∴ Answer = 5750

Alternate Method

Given:

80% voted, 20% invalid, winner gets 55%, margin = 368

Formula:

Margin = Difference% × Valid votes

Calculation:

⇒ Let total voters = N

⇒ Votes polled = 0.8N

⇒ Valid votes = 80% of 0.8N = 0.64N

⇒ Winner votes = 55% of 0.64N = 0.352N

⇒ Loser votes = 45% of 0.64N = 0.288N

⇒ Margin = 0.352N − 0.288N = 0.064N

⇒ 0.064N = 368

⇒ N = 368 ÷ 0.064 = 5750

∴ Total voters = 5750

Additional Information

Valid Votes: = Total votes polled − Invalid votes

Winning Margin: = Difference of % × Total valid votes

Percentage Conversion: x% = x ÷ 100

Shortcut Tip: Combine percentages stepwise to reduce calculation

The logic followed here is:

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

Only one person sits between D and B when counted from the left of B.

F sits third to the right of E.

C sits third to the left of G.

F sits to the immediate right of C.

A is not an immediate neighbour of C.

So, there is 1 person between A and C.

Hence, the correct answer is "Option 3".

Shortcut Trick

Sum of known digits = 7 + 1 + 3 + 8 + 8 + 4 + 5 = 36

For divisibility by 3 ⇒ (36 + A) must be multiple of 3

36 is already divisible by 3 ⇒ A must be divisible by 3

Possible digits: 0, 3, 6, 9

Maximum = 9

∴ Answer = 9

Alternate Method

Given: Number = 713A8845

Rule: A number is divisible by 3 if sum of digits is divisible by 3

⇒ Sum = 7 + 1 + 3 + A + 8 + 8 + 4 + 5

⇒ Sum = 36 + A

⇒ For divisibility: (36 + A) ÷ 3 should be integer

⇒ 36 is divisible by 3 ⇒ A must be multiple of 3

⇒ A ∈ {0, 3, 6, 9}

⇒ Maximum value = 9

∴ Required digit A = 9

Additional Information

Divisibility by 3: Sum of digits must be multiple of 3

Divisibility by 9: Sum of digits must be multiple of 9

Digit Range: A digit can take values from 0 to 9

Shortcut Tip: First check base sum, then adjust missing digit

The correct answer is Israel.

Key Points

• On November 20, 2024, India and Israel officially signed the Terms of Reference (ToR) to begin negotiations for a Comprehensive Free Trade Agreement (FTA). This significant milestone was achieved during a meeting in New Delhi, marking a new chapter in the economic relationship between the two nations.
• The Terms of Reference were signed by India’s Union Minister of Commerce and Industry, Piyush Goyal, and the Israeli Minister of Economy and Industry, Nir Barkat. The ToR serves as the framework that defines the scope, coverage, and timeline for the FTA negotiations.
• The primary objective of the proposed FTA is to substantially increase bilateral trade in goods and services, foster investment flows, and strengthen economic cooperation in high-tech sectors such as semiconductors, cybersecurity, and artificial intelligence.
• India and Israel have seen a consistent rise in trade volumes; for the financial year 2022-23, bilateral trade (excluding defense) stood at approximately $10.7 billion. The FTA is expected to address tariff and non-tariff barriers, potentially doubling trade figures in the near future.
• The negotiations will also focus on integrating supply chains and promoting innovation-led partnerships. This move aligns with India's broader strategy to sign FTAs with developed economies to boost its manufacturing and service exports.

Additional Information

• Diplomatic History: Although India recognized Israel in 1950, full diplomatic relations were established only in January 1992. The relationship was elevated to a Strategic Partnership during the historic visit of Prime Minister Narendra Modi to Israel in July 2017.
• Key Export-Import Commodities: Major Indian exports to Israel include pearls, precious stones, chemical products, and textiles. Conversely, India imports fertilizers, machinery, electrical equipment, and defense technologies from Israel. Diamonds constitute a major portion of the trade, accounting for nearly 50% of the bilateral commerce.
• Defense and Technology Cooperation: Israel is one of India's top four defense suppliers. Beyond defense, the two countries collaborate extensively under the India-Israel Industrial R&D and Technological Innovation Fund (I4F) to promote joint research in sectors like Water Management, Agriculture, and Healthcare.
• The I2U2 Grouping: Both nations are founding members of the I2U2 group (India, Israel, United Arab Emirates, and the United States). This platform, often called the 'West Asian Quad,' focuses on joint investments in six areas: water, energy, transportation, space, health, and food security.
• India's Recent FTAs: India has recently fast-tracked its trade diplomacy, signing the Comprehensive Economic Partnership Agreement (CEPA) with the United Arab Emirates in February 2022 and the Economic Cooperation and Trade Agreement (ECTA) with Australia in April 2022.

Important Points

• Center of Excellence (CoE): Israel has established 30 Centers of Excellence across 12 Indian states to share advanced agricultural technology and water harvesting techniques, benefiting thousands of Indian farmers.
• Water Cooperation: In 2020, India and Israel signed a cultural agreement and a cooperation agreement on water utility reform, focusing on desalination and wastewater treatment, which are critical for India's Jal Jeevan Mission.
• Startup Ecosystem: The India-Israel Innovation Bridge was launched to facilitate collaboration between startups from both countries, focusing on finding solutions for global challenges in agritech and medtech.

The correct answer is PT Usha.

Key Points

• Pilavullakandi Thekkeparambil Usha, popularly known as PT Usha, is a retired Indian track and field athlete who is often called the "Queen of Indian Track and Field". She was born on June 27, 1964, in the village of Payyoli, Kozhikode district, Kerala. Due to her lightning speed on the track and her place of birth, she earned the iconic nickname "Payyoli Express".
• She rose to national fame at the 1979 National School Games and made her Olympic debut at the age of 16 in the 1980 Moscow Olympics. She became a household name across India during the 1980s for her dominance in sprint events.
• PT Usha is most famously remembered for her performance at the 1984 Los Angeles Olympics. She became the first Indian woman to reach the final of an Olympic event, where she missed the bronze medal in the 400m hurdles by just 1/100th of a second.
• Throughout her career, she won four gold medals and one silver medal at the 1986 Seoul Asian Games. Overall, she has won 101 international medals and was awarded the Arjuna Award in 1983 and the Padma Shri (India's fourth-highest civilian award) in 1985.

Additional Information

• Leander Paes: He is a legendary Indian tennis player who is widely considered one of the greatest doubles and mixed doubles players in history. He holds the record for the most doubles wins in Davis Cup history. Paes won a bronze medal for India in the singles category at the 1996 Atlanta Olympics, becoming the first Indian to win an individual Olympic medal since 1952.
• Sania Mirza: She is a retired professional tennis player from India who achieved a former world No. 1 ranking in doubles. She has won six Grand Slam titles (three in women's doubles and three in mixed doubles). She was the first Indian woman to win a WTA title and is a recipient of the Major Dhyan Chand Khel Ratna award (2015).
• Shoaib Akhtar: He is a former Pakistani cricketer and fast bowler, famously nicknamed the "Rawalpindi Express" because of his birthplace (Rawalpindi) and his extreme bowling speed. He holds the world record for the fastest delivery ever bowled in international cricket, clocking 161.3 km/h (100.2 mph) during the 2003 Cricket World Cup.
• Milkha Singh: Another legendary Indian athlete known as "The Flying Sikh". He was a field sprinter who won gold medals at the 1958 and 1962 Asian Games. He famously finished fourth in the 400m final at the 1960 Rome Olympics, missing the podium by a fraction of a second.

Important Points

• Administrative Roles: In December 2022, PT Usha was elected unopposed as the President of the Indian Olympic Association (IOA). She is the first woman to head the organization in its 95-year history and the first Olympian to hold the post.
• Parliamentary Nomination: In July 2022, she was nominated to the Rajya Sabha (the Upper House of the Indian Parliament) by the President of India for her contribution to Indian sports.
• Usha School of Athletics: To give back to the sport, she founded the Usha School of Athletics in Koyilandy, Kerala. The academy focuses on identifying and training young talent to win medals for India at the Olympics.
• Records: During the 1985 Asian Track and Field Championships in Jakarta, she won five gold medals (100m, 200m, 400m, 400m hurdles, and 4x400m relay) and one bronze medal, a feat rarely matched in athletics history.

The correct answer is 340 m/s.

Key Points

• The speed of sound in air is approximately 343 meters per second (m/s) when the temperature is 20 degrees Celsius (68 degrees Fahrenheit).
• Sound is a longitudinal mechanical wave that propagates through a medium by the vibration of particles. In dry air at 0 degrees Celsius, the speed is 331 m/s.
• Option A (340 m/s) is the closest value to the standard speed of sound in air at normal atmospheric conditions. Hence, this statement is correct.
• Option B (12000 m/s) is far beyond the speed of sound in air; such high speeds are only observed in extremely stiff materials like diamond, where sound travels at approximately 12,000 m/s. Hence, this statement is incorrect.
• Option C (3 x 10^8 m/s) represents the speed of light in a vacuum (approximately 299,792,458 m/s), which is about a million times faster than sound. Hence, this statement is incorrect.
• Option D (3400 km/s) converts to 3,400,000 m/s, which is an unrealistic value for sound propagation in any common earthly medium. Hence, this statement is incorrect.

Additional Information

• Factors Affecting Speed: The speed of sound in air depends primarily on the temperature. For every 1 degree Celsius increase in temperature, the speed of sound increases by about 0.6 m/s.
• Medium Density: Sound travels fastest in solids, slower in liquids, and slowest in gases. For example, the speed of sound in steel is about 5,960 m/s and in water is about 1,480 m/s.
• Humidity: Increased humidity (water vapor in the air) slightly increases the speed of sound because water molecules are less dense than nitrogen and oxygen molecules, making the air lighter and easier for sound to move through.
• Pressure: At a constant temperature, changes in atmospheric pressure do not affect the speed of sound because the density changes proportionally, cancelling out the effect.
• Mach Number: The ratio of the speed of an object to the speed of sound in the surrounding medium is called the Mach Number. Mach 1 represents traveling at the speed of sound.

Important Points

• Newton-Laplace Formula: Sir Isaac Newton originally calculated the speed of sound assuming isothermal conditions, but Pierre-Simon Laplace corrected it in 1816 by accounting for adiabatic compression and expansion.
• Frequency and Wavelength: The speed (v) is related to frequency (f) and wavelength (λ) by the formula v = f × λ. However, the speed itself is a property of the medium, not the sound source.
• Audible Range: Humans can hear sound frequencies between 20 Hz and 20,000 Hz. Frequencies below this are infrasonic and above are ultrasonic.
• Thunder and Lightning: During a storm, we see lightning before we hear thunder because light travels at 3,00,000 km/s, while sound travels at only 0.34 km/s.

The logic followed here is:

thus, "85" will replace the question mark in the given series.

Hence, the correct option is "Option 4".

Family Chart:

Given:

A is the sister of B,

B is the mother of C,

C is the brother of D,

E is the husband of D.

Since,  A is wife’s mother’s sister.

Hence, the correct answer is Option 4.

Shortcut Trick

Use weighted average:

Overall avg = (53×424 + 86×337 + 57×122) ÷ (53+86+57)

⇒ = (22472 + 28982 + 6954) ÷ 196

⇒ = 58408 ÷ 196

⇒ = 298

∴ Answer = 298

Alternate Method

Given: A(53,424), B(86,337), C(57,122)

Formula: Overall average = Total expenditure ÷ Total members

⇒ Total A = 53 × 424 = 22472

⇒ Total B = 86 × 337 = 28982

⇒ Total C = 57 × 122 = 6954

⇒ Total expenditure = 22472 + 28982 + 6954 = 58408

⇒ Total members = 53 + 86 + 57 = 196

⇒ Average = 58408 ÷ 196 = 298

∴ Overall average = 298

Additional Information

Weighted Average: = (Σ (value × frequency)) ÷ total frequency

Shortcut Tip: Always multiply before adding

Common Mistake: Don’t take simple average of averages

Application: Used in marks, mixture, population problems

The correct answer is December 18.

Key Points

• International Migrants Day is an international day observed on December 18 every year to recognize the efforts, contributions, and rights of migrants worldwide.
• For the year 2025, the theme is “My Great Story: Cultures and Development”, which emphasizes the narrative of migrants as agents of cultural exchange and drivers of economic and social development.
• The United Nations General Assembly (UNGA) officially proclaimed December 18 as International Migrants Day on 4 December 2000 under resolution 55/93.
• The date was chosen because on 18 December 1990, the UNGA adopted the International Convention on the Protection of the Rights of All Migrant Workers and Members of Their Families.
• The day highlights the need for safe, orderly, and regular migration, addressing the challenges faced by over 280 million migrants globally. Hence, the option specifying December 18 is correct.

Additional Information

• International Organization for Migration (IOM):
• Established in 1951, the IOM is the leading intergovernmental organization in the field of migration and is part of the United Nations system.
• Headquartered in Geneva, Switzerland, it works closely with governmental, intergovernmental, and non-governmental partners to manage migration for the benefit of all.
• Global Compact for Migration (GCM):
• The Global Compact for Safe, Orderly and Regular Migration was adopted in December 2018.
• It is the first inter-governmentally negotiated agreement, prepared under the auspices of the United Nations, covering all dimensions of international migration in a holistic and comprehensive manner.
• Sustainable Development Goals (SDGs):
• Migration is integrated into the 2030 Agenda for Sustainable Development, particularly under SDG Target 10.7.
• This target aims to facilitate orderly, safe, regular, and responsible migration and mobility of people, including through the implementation of planned and well-managed migration policies.
• World Migration Report:
• The IOM publishes the World Migration Report every two years (e.g., 2022, 2024).
• According to the World Migration Report 2024, there are approximately 281 million international migrants, which represents about 3.6% of the global population.

Important Points

• Indian Context and Migration:
• India has the world's largest diaspora, with over 18 million people living outside their country of birth as of 2020 reports.
• The Ministry of External Affairs (MEA) handles the welfare of Non-Resident Indians (NRIs) and Overseas Citizens of India (OCI).
• Pravasi Bharatiya Divas (PBD) is celebrated in India on 9 January to mark the contribution of the overseas Indian community. It commemorates the return of Mahatma Gandhi from South Africa to Mumbai on 9 January 1915.
• Constitutional Provisions in India:
• Article 19(1)(e) of the Constitution of India grants citizens the fundamental right to reside and settle in any part of the territory of India.
• Articles 5 to 11 of the Indian Constitution deal with the citizenship of individuals at the commencement of the Constitution.
• Remittances:
• According to World Bank data, India is consistently one of the largest recipients of remittances globally, receiving over $100 billion in recent years (e.g., 2023).

Shortcut Trick

LCM of 4, 28 = 28 (Total work)

⇒ Tap A = 28 ÷ 4 = 7 units/hr

⇒ Tap B = 28 ÷ 28 = 1 unit/hr

⇒ Tap C (empty) = −1 unit/hr

⇒ Net work = 7 + 1 − 1 = 7 units/hr

⇒ Work required = 1/4 of 28 = 7 units

⇒ Time = 7 ÷ 7 = 1 hour

∴ Answer = 1 hour

Alternate Method

Given: Filling = 4 hr, 28 hr; Emptying = 28 hr

Table Method:

⇒ Net rate = 1/4 + 1/28 − 1/28 = 1/4

⇒ Work required = 1/4

⇒ Time = (1/4) ÷ (1/4) = 1 hour

∴ Time required = 1 hour

Additional Information

LCM Method: Assume total work = LCM of times

Efficiency: Work per hour = Total work ÷ Time

Net Work: Add filling, subtract emptying

Time Formula: Time = Work ÷ Net rate

The logic followed here is:

Given series: (Left) S # % 2 S 4 P # Z 4 B 8 5 R € * 8 © J & € N (Right)

Now, Remove all symbols: #, %, €, *, ©, &, €

Remaining series (letters and numbers only): S 2 S 4 P Z 4 B 8 5 R 8 J N

Now, Count from the left: S 2 S 4 P Z 4 B 8 5 R 8 J N

Fourth from the left = 4

Hence, the correct answer is Option 3.

Given: C, D, N, O, P and Q live on six different floors of the same building. The lowermost floor is numbered 1 and the topmost floor is numbered 6.

D lives on floor number 1.

Only two people live between Q and P.

Q lives below C.

Only two people live between O and C.

Only one person lives between D and C.

Now, people above N (floor 4) are O and P → 2 people

Hence, the correct answer is Option 3.

The correct answer is Warli.

Key Points

• Warli Painting is a world-renowned tribal art form that originated in the Sahyadri Range of Maharashtra, particularly within the Palghar and Thane districts. It is distinguished by its monochromatic style, where a white pigment made from rice paste, water, and gum is applied onto reddish-brown mud walls. Hence, option D is correct.
• Gond Painting is a traditional art form practiced by the Gond tribe, predominantly in Madhya Pradesh. This style is famous for its use of vibrant colors and intricate patterns consisting of dots and lines to depict flora, fauna, and local folklore. It does not follow a monochromatic scheme on mud walls. Hence, option A is incorrect.
• Madhubani Painting, also known as Mithila Art, hails from the Mithila region of Bihar and parts of Nepal. It is characterized by bold, geometric patterns and vibrant natural dyes derived from turmeric, indigo, and sandalwood, often featuring double outlines for figures. Hence, option B is incorrect.
• Pahari Painting refers to an umbrella term for miniature painting styles that developed in the Himalayan hill states of India (such as Himachal Pradesh and Jammu) during the 17th to 19th centuries. These are highly detailed courtly paintings known for their expressive colors and spiritual themes. Hence, option C is incorrect.

Additional Information

• Materials and Techniques: The Warli artists use a bamboo stick chewed at the end to serve as a brush. The background of the mud walls is prepared using cow dung and red mud, which provides the distinctive terracotta color that contrasts with the white rice-paste figures.
• Geographical Identity: Warli painting from Maharashtra has been granted the Geographical Indication (GI) tag, which protects the intellectual property of the tribal artisans and ensures the authenticity of the art form produced in the Palghar region.
• Themes of Art: Unlike many other Indian folk arts that focus on religious deities, Warli art primarily depicts social life, nature, and tribal rituals. Common scenes include harvesting, hunting, fishing, and communal dancing (specifically the Tarpa dance).
• Cultural Significance: Historically, Warli paintings were created by women (known as Suhasinis) on the walls of their huts during wedding ceremonies or harvest festivals to seek blessings and prosperity for the household.

Important Points

• Geometric Symbolism: Warli art is built upon three basic geometric shapes: the circle (representing the sun and moon), the triangle (representing mountains and conical trees), and the square (representing a sacred enclosure or a piece of land).
• Human Figures: In Warli paintings, human and animal bodies are represented by two triangles joined at the tip. The upper triangle represents the torso, while the lower triangle represents the pelvis. This symmetry symbolizes the balance of the universe.
• Historical Context: Although it gained global recognition in the 1970s due to artists like Jivya Soma Mashe, the roots of Warli art are believed to date back as far as the 10th century AD, showing similarities to Neolithic rock paintings found at Bhimbetka.
• Modern Evolution: Today, the art form has transitioned from mud walls to paper, canvas, and fabrics. It is widely used in fashion, home decor, and advertising, making it one of India's most recognizable cultural exports.

The correct answer is Kathak Kendra.

Key Points

• The National Institute of Kathak Dance, popularly known as Kathak Kendra, is the premier institution for training in Kathak, one of the eight classical dance forms of India.
• It is a constituent unit of the Sangeet Natak Akademi, which is India's National Academy of Music, Dance and Drama under the Ministry of Culture.
• The institute is located in New Delhi and was formally established in its current form in the year 1964.
• It was initially established as a wing of the Sriram Bharatiya Kala Kendra in 1955, primarily to provide a platform for the legendary Pandit Shambhu Maharaj to teach the nuances of the Lucknow Gharana.
• The Kathak Kendra focuses on preserving and promoting the diverse traditions of Kathak, specifically the Lucknow, Jaipur, and Banaras styles, while fostering innovation within the classical framework.

Additional Information

• Kathak Dance Overview:
• The word Kathak is derived from the Sanskrit word Katha, which means "story," and Kathakar, which means "storyteller."
• It originated in North India and was traditionally performed by wandering bards in temples and later in the Mughal courts.
• Key features include intricate footwork (Tatkar), lightning-fast pirouettes (Chakkars), and expressive facial movements (Abhinaya).
• Major Gharanas (Schools):
• Lucknow Gharana: Known for grace, elegance, and Bhava (expression). It was greatly patronized by Wajid Ali Shah, the last Nawab of Awadh.
• Jaipur Gharana: Emphasizes powerful footwork and complex rhythmic patterns.
• Banaras Gharana: Known for its sobriety and use of the Natwari style of dancing.
• Prominent Personalities:
• Pandit Birju Maharaj was perhaps the most famous face associated with Kathak Kendra, serving as its Head of Faculty and Director for several years.
• Other notable figures include Lachhu Maharaj, Shambhu Maharaj, and Sitara Devi, who have significantly contributed to the global recognition of this dance form.

Important Points

• Institutional Role: The Kathak Kendra offers specialized courses, including a five-year Diploma and post-graduate studies, making it a central hub for professional dancers and researchers.
• Cultural Impact: By functioning under the Sangeet Natak Akademi, which was established in 1953, the institute ensures that the Guru-Shishya Parampara (teacher-disciple tradition) continues in a modern academic setting.
• Sriram Bharatiya Kala Kendra: While Kathak Kendra is now an independent unit of the government, the Sriram Bharatiya Kala Kendra (founded in 1952) remains a private cultural organization in New Delhi that also promotes Kathak and other performing arts.
• National Importance: As a national institute, it represents the cultural heritage of India on international platforms and facilitates exchange programs with other countries to promote Indian classical arts.

The logic followed here is:

Given: Seven people B, C, D, O, P, Q and R are sitting around a circular table facing the centre.

Only one person sits between P and B when counted from the left of B.

Only one person sits between B and R.

Only one person sits between P and D.

Only two people sit between O and R.

Only one person sits between Q and D.

Now finding immediate neighbours of C:

Immediate right of C = P

Immediate left of C = D

Hence, the correct answer is "Option 1".

Given: # : KUC :: XHP : %

Option 1) # = FOW , % = DNV

For # (FOW) to KUC

For % (DNV) from XHP

Since, the pattern is not consistent for both transformations, Option 1 is incorrect.

Option 2) # = EOW , % = DNV

For # (EOW) to KUC

For % (DNV) from XHP

Since, both transformations follow a uniform +6 shift pattern, Option 2 is correct.

Option 3) # = EOW , % = DNO

For # (EOW) to KUC

For % (DNO) from XHP

Since, the pattern is not consistent, Option 3 is incorrect.

Option 4) # = EOX , % = DNV

For # (EOX) to KUC

For % (DNV) from XHP

Since, # does not follow a uniform shift, Option 4 is incorrect.

Hence, the correct answer is "Option 2".

The correct answer is Banabhatta.

Key Points

• Banabhatta was the celebrated Asthana Kavi (court poet) of King Harshavardhana, who ruled Northern India in the 7th century. Hence, option D is correct.
• He is most famous for writing the Harshacharita, which is the first historical biography in Sanskrit, detailing the life and rise to power of Harsha.
• Apart from the biography, Banabhatta authored Kadambari, which is considered one of the world's earliest novels.
• Harshavardhana, also known as Harsha, belonged to the Pushyabhuti or Vardhana dynasty and reigned from 606 AD to 647 AD.
• Under Harsha's patronage, Kannauj became a major political and cultural center in Northern India, shifting the capital from Thanesar.

Additional Information

• Harishena:
• Harishena was a 4th-century Sanskrit poet and a high-ranking official in the court of the Gupta Emperor Samudragupta.
• He is best known for composing the Prayag Prashasti (also known as the Allahabad Pillar Inscription), which describes the military achievements and character of Samudragupta. Hence, statement A is incorrect.
• Kalashoka:
• Kalashoka was a ruler of the Shishunaga dynasty of Magadha in ancient India.
• His reign is historically significant for the Second Buddhist Council, which was held at Vaishali in 383 BC. Hence, statement B is incorrect.
• Vasumitra:
• Vasumitra was a distinguished Buddhist monk and scholar who lived during the reign of the Kushan Emperor Kanishka.
• He presided over the Fourth Buddhist Council held in Kashmir (at Kundalvana) during the 1st or 2nd century AD. Hence, statement C is incorrect.

Important Points

• Harsha's Literary Contributions: King Harsha was not only a patron of arts but also an accomplished author himself. He wrote three famous Sanskrit plays: Ratnavali, Priyadarsika, and Nagananda.
• Xuanzang (Hiuen Tsang): The famous Chinese traveler visited India during Harsha's reign in 630 AD and stayed for about 15 years. His writings provide a detailed account of the socio-economic and religious conditions of that era.
• Military Conflict: While Harsha conquered much of Northern India, his southward expansion was halted by the Chalukya King Pulakeshin II on the banks of the Narmada River in 618-619 AD.
• Religious Tolerance: Harsha was known for his Mahayana Buddhist leanings but maintained tolerance toward other faiths. He organized a grand assembly at Kannauj and the Prayag Assembly (held every five years) for charitable distributions.

Shortcut Trick

Relative speed (same direction) = 72 − 54 = 18 km/hr

⇒ Convert: 18 × 5/18 = 5 m/s

Total distance = 150 + 120 = 270 m

⇒ Time = 270 ÷ 5 = 54 sec

∴ Answer = 54 seconds

Alternate Method

Given:

Formula: Time = Total length ÷ Relative speed

⇒ Relative speed = (72 − 54) = 18 km/hr

⇒ Convert to m/s: 18 × 5/18 = 5 m/s

⇒ Total length = 150 + 120 = 270 m

⇒ Time = 270 ÷ 5 = 54 sec

∴ Time required = 54 seconds

Additional Information

Relative Speed: Same direction ⇒ difference of speeds

Opposite Direction: Speeds are added

Conversion: km/hr to m/s ⇒ multiply by 5/18

Train Crossing: Distance = sum of lengths

The correct answer is Outsourcing.

Key Points

• Outsourcing is considered one of the most important outcomes of the Globalization process. In this practice, a company hires regular service from external sources, often located in other countries, which was previously performed internally. Hence, statement D is correct.
• Privatisation refers to the process of involving the private sector in the ownership or operation of a state-owned enterprise. While it was a part of the 1991 reforms, it is categorized as a policy measure rather than a direct outcome of globalization. Hence, statement A is incorrect.
• Nationalisation is the process of transforming private assets into public assets by bringing them under the public ownership of a national government. This was a prominent feature of the Indian economy in the 1960s and 1970s, which is the opposite of the current globalization trend. Hence, statement B is incorrect.
• Liberalisation refers to the relaxation of government restrictions in the areas of social, political, and economic policies. In the economic context, it means opening up the economy by removing barriers to entry and growth for the private sector. It acts as a prerequisite for globalization rather than its outcome. Hence, statement C is incorrect.
• India has emerged as a major hub for Outsourcing, particularly in Business Process Outsourcing (BPO) and Information Technology (IT) services, due to the availability of skilled manpower and lower wage rates.

Additional Information

• New Economic Policy (NEP) 1991: The NEP was launched in July 1991 under the leadership of Prime Minister P.V. Narasimha Rao and Finance Minister Dr. Manmohan Singh to address the Balance of Payments (BoP) crisis.
• LPG Model: The reforms are famously known as the LPG model, standing for Liberalisation, Privatisation, and Globalisation. The primary objective was to plunge the Indian economy into the arena of Globalization and to give it a new thrust on market orientation.
• Globalisation: It is the process of integrating the national economy with the world economy through the removal of barriers on international trade and capital movements. It involves the free flow of goods, services, capital, and labor across borders.
• Role of WTO: The World Trade Organization (WTO), established in 1995 as the successor to GATT, played a crucial role in facilitating globalization by encouraging member countries (including India) to reduce tariffs and non-tariff barriers.
• Impact on Service Sector: Globalization significantly boosted India's Service Sector. The export of services like software, banking, and technical consultancy grew exponentially, contributing heavily to India’s Gross Domestic Product (GDP).

Important Points

• Knowledge Process Outsourcing (KPO): Beyond simple data entry, India has moved into high-end KPO, which includes services like R&D, e-learning, business and market research, and legal services.
• FDI and FII: Globalization led to an increase in Foreign Direct Investment (FDI) and Foreign Institutional Investment (FII). The government has gradually increased FDI limits in various sectors like Insurance, Defense, and Retail.
• BPO Industry Growth: The Business Process Outsourcing industry in India provides employment to millions of youth and has turned India into the "back office of the world." Common services include customer care, record keeping, and accountancy.
• Challenges: While globalization has brought growth, it has also led to challenges such as increased competition for Micro, Small, and Medium Enterprises (MSMEs) and concerns regarding economic inequality.

The logic followed here is:

Given number: 3975684

Logic: Subtract 2 from each digit, then arrange the new digits in ascending order.

Original number: 3 9 7 5 6 8 4

After subtracting 2: 1 7 5 3 4 6 2

Ascending order: 1 2 3 4 5 6 7

Fifth digit from the left = 5

Hence, the correct answer is Option 1.

Given Statements:

I. M is taller than V but shorter than N. M is shorter than only one tree.

II. V is taller than T.

Analysis:

I. From Statement I → M is shorter than only one tree, so M is the second tallest.

Since, M is shorter than N, N must be taller than M.

Therefore, N is the tallest tree → Statement I alone is sufficient.

II. From Statement II → V is only compared with T, so no information about L, M, or N;

tallest cannot be determined → Not sufficient.

Using both I and II together → Statement I already identifies N as the tallest, so additional data is not required.

Hence, the correct answer is Option 2.

The logic followed here is:

Given series: (Left) K { J % I + H = G * F / D : - ! B C ? A # (Right)

Now, We need symbols which are immediately preceded by a letter and immediately followed by another letter.

So, needed pattern is: Letter - Symbol - Letter

(Left) K { J % I + H = G * F / D : - ! B C ? A # (Right)

Total valid symbols = 7

Hence, the correct answer is Option 2.

Shortcut Trick

In SI, doubling ⇒ Interest = Principal

⇒ Rate = 100 ÷ Time

⇒ Rate = 100 ÷ 18 = 5.555...

⇒ ≈ 5.56%

∴ Answer = 5.56%

Alternate Method

Given: Time = 18 years, Amount = 2P

Formula: SI = (P × R × T) ÷ 100

⇒ P = (P × R × 18) ÷ 100

⇒ 1 = (R × 18) ÷ 100

⇒ R = 100 ÷ 18 = 5.555...

⇒ R ≈ 5.56%

∴ Rate = 5.56% per annum

Additional Information

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

Doubling Rule (SI): Rate = 100 ÷ Time

Amount Formula: A = P + SI

Approximation: 100/18 ≈ 5.56

Family Chart:

Given:

Kc is the daughter of Cw,

Ef is the mother of Kc,

Qk is the brother of Ef,

Lu is the father of Qk.

Hence, Lu is related to Cw as Wife’s father.

Hence, the correct answer is Option 4.

Shortcut Trick

cosecA = 5/3 ⇒ sinA = 3/5 ⇒ cosA = 4/5

⇒ secA = 5/4

Use identities: 1 + cot²A = cosec²A

⇒ Numerator = 9 × (25/9) = 25

⇒ Denominator = 80(1 − secA)(1 + secA) = 80(1 − sec²A)

⇒ = 80(1 − 25/16) = 80(−9/16) = −45

⇒ Value = 25 ÷ (−45) = −5/9

∴ Answer = −5/9

Alternate Method

Given: cosecA = 5/3

Formula: sinA = 1/cosecA

⇒ sinA = 3/5

⇒ cosA = √(1 − sin²A) = √(1 − 9/25) = √(16/25) = 4/5

⇒ secA = 1/cosA = 5/4

⇒ 1 + cot²A = cosec²A = (5/3)² = 25/9

⇒ Numerator = 9 × 25/9 = 25

⇒ Denominator = 80(1 − secA)(1 + secA)

⇒ = 80(1 − sec²A)

⇒ = 80(1 − 25/16)

⇒ = 80 × (−9/16) = −45

⇒ Required value = 25 ÷ (−45) = −5/9

∴ Final Answer = −5/9

Additional Information

Pythagorean Identity: sin²A + cos²A = 1

Important Identity: 1 + cot²A = cosec²A

Sec Identity: 1 − sec²A = −tan²A

Conjugate Use: (1 − secA)(1 + secA) = 1 − sec²A

Shortcut Trick

Use: Product of numbers = HCF × LCM

⇒ Other number = (6 × 72) ÷ 18

⇒ = 432 ÷ 18 = 24

∴ Answer = 24

Alternate Method

Given:

HCF = 6, LCM = 72, One number = 18

Formula:

Product of two numbers = HCF × LCM

Calculation:

⇒ Product = 6 × 72 = 432

⇒ Other number = 432 ÷ 18 = 24

∴ Required number = 24

Additional Information

Key Relation: HCF × LCM = Product of numbers

HCF: Highest common factor (greatest divisor)

LCM: Least common multiple

Application: Used to find unknown numbers quickly

The correct answer is The law of inertia causes our body to resist the change in direction.

Key Points

• The phenomenon of being thrown to one side when a motorcar makes a sharp turn at high speed is a direct application of Newton's First Law of Motion, also known as the Law of Inertia.
• Inertia is the inherent property of an object to resist any change in its state of rest or uniform motion in a straight line. In this case, it is specifically Inertia of Direction, which is the tendency of a body to maintain its direction of motion. Hence, statement A is correct.
• When the car takes a sharp turn, the friction between the tires and the road provides the necessary centripetal force to change the car's direction. However, the passenger's body, due to inertia, tries to continue moving in its original straight-line path.
• As the car moves towards the center of the curve, the passenger feels an outward pull (often perceived as centrifugal force), which is actually just the body resisting the change in velocity (direction).
• Air pressure changes inside the car are negligible during a turn and do not possess the magnitude required to push a human body. Hence, statement B is incorrect.
• The force of gravity acts vertically downwards towards the center of the Earth and does not change its primary direction based on the horizontal turn of a vehicle. Hence, statement C is incorrect.
• While friction is required for the turn, the sensation of being thrown is caused by the body's mass and velocity, not by a decrease in friction itself. In fact, if friction were to decrease significantly, the car would skid rather than make a sharp turn. Hence, statement D is incorrect.

Additional Information

• Newton's First Law (1687): Formulated by Sir Isaac Newton in his work 'Philosophiæ Naturalis Principia Mathematica', it states that an object will remain at rest or in uniform motion unless acted upon by an external unbalanced force.
• Types of Inertia:
• Inertia of Rest: The inability of a body to change its state of rest by itself. Example: When a bus starts suddenly, passengers fall backwards.
• Inertia of Motion: The inability of a body to change its state of uniform motion. Example: An athlete runs some distance before taking a long jump to gain momentum.
• Inertia of Direction: The inability of a body to change its direction of motion. Example: The sparks produced during grinding of a stone fly off tangentially.
• Mass as a Measure: The quantitative measure of inertia is mass. An object with a higher numerical value of mass (measured in kilograms) possesses greater inertia and requires more force to change its state.
• Safety Applications: Seatbelts in cars are designed based on the principles of inertia. During a sudden brake or a sharp turn, the seatbelt provides the necessary external force to stop the body from moving forward or sideways, preventing accidents.

Important Points

• Centripetal vs. Centrifugal Force: Centripetal force is a real force that acts towards the center of the circular path. Centrifugal force is a pseudo-force (apparent force) that appears to act outward when observed from a non-inertial frame of reference (the accelerating car).
• Galileo's Contribution: Before Newton, Galileo Galilei was the first to suggest the concept of inertia through his experiments with inclined planes in the early 17th century.
• Banking of Roads: To prevent vehicles from skidding due to high inertia and lack of friction during turns at high speed, roads are often "banked" (tilted upwards towards the outer edge). This allows a component of the Normal Force to contribute to the centripetal force.

The logic followed here is:

For, RILA → SKOE

Similarly, KEPO → LGSS

Now, apply the same rule to MJRT:

Here, MJRT → NLUX

Hence, the correct answer is Option 4.

The correct answer is Gulf Cooperation Council (GCC).

Key Points

• The Gulf Cooperation Council (GCC) concluded its 46th Summit in Manama, Bahrain, where the participating leaders adopted the Sakhir Declaration.
• The GCC summit brought together the leaders of the six member states to discuss matters concerning political coordination, regional security, economic cooperation, and integration.
• The Sakhir Declaration reaffirmed the GCC countries' commitment to strengthening collective action, political unity, security cooperation, and economic integration.
• The GCC consists of six Arab Gulf countries: Saudi Arabia, Kuwait, the United Arab Emirates, Qatar, Bahrain, and Oman.
• Hence, the correct answer is Gulf Cooperation Council (GCC).

Additional Information

• Gulf Cooperation Council (GCC):
• The GCC was established on 25 May 1981 through the Charter of the Gulf Cooperation Council.
• Its headquarters is located in Riyadh, Saudi Arabia.
• The organisation promotes coordination, integration, and interconnection among its member states in areas including politics, economy, security, defence, and social affairs.
• GCC Member States:
• Bahrain
• Kuwait
• Oman
• Qatar
• Saudi Arabia
• United Arab Emirates (UAE)
• Sakhir Declaration:
• The declaration takes its name from Sakhir, an area in Bahrain associated with the summit.
• It emphasised the importance of GCC unity and collective cooperation in addressing regional challenges.
• The declaration also reaffirmed the objective of advancing deeper political, security, and economic integration among GCC members.
• GCC Summit:
• The GCC holds regular meetings of its highest-level leadership through the Supreme Council, comprising the heads of the member states.
• These summits provide a platform for discussing regional security, economic relations, international developments, and intra-GCC cooperation.

Important Points

• Organisation: Gulf Cooperation Council (GCC)
• 46th Summit: Held in Manama, Bahrain
• Declaration adopted: Sakhir Declaration
• Established: 25 May 1981
• Headquarters: Riyadh, Saudi Arabia
• Number of members: 6
• Core focus: Political, security, economic, and regional cooperation

The correct answer is DHRUV64 microprocessor.

Key Points

• DHRUV64 was launched on 15 December 2025 as India's first indigenously designed 1.0 GHz, 64-bit dual-core microprocessor.
• Developer: It was developed by the Centre for Development of Advanced Computing (C-DAC) under the Microprocessor Development Programme (MDP) initiated by the Ministry of Electronics and IT (MeitY).
• Architecture: The processor is based on the open-source RISC-V instruction set architecture, which helps eliminate dependence on foreign intellectual property (IP) and licensing fees.
• Significance: It marks a major step in the Digital India RISC-V (DIR-V) initiative, following the earlier THEJAS32 and THEJAS64 prototypes, and is intended for use in strategic sectors like 5G infrastructure, automotive electronics, and industrial automation.

Additional Information

• SHAKTI Microprocessor:
• Developed by IIT Madras, SHAKTI was India’s first indigenous microprocessor family launched earlier than VEGA.
• While SHAKTI proved the viability of Indian silicon, the VEGA-64 represents an evolution into higher clock speeds of 1.0 GHz and 64-bit dual-core capabilities for more intensive computing tasks.
• Digital India RISC-V (DIR-V) Program:
• Launched by the Government of India, the DIR-V program is tasked with making India a global hub for RISC-V talent and design.
• It envisions the development of various classes of processors, including E-class for IoT, A-class for high-performance applications, and H-class for high-performance computing.
• Role of C-DAC:
• C-DAC (Centre for Development of Advanced Computing) is the premier R&D organization of the Ministry of Electronics and Information Technology (MeitY) for carrying out R&D in IT, Electronics, and associated areas.
• It has been instrumental in the Microprocessor Development Programme (MDP), which led to the creation of the VEGA family of processors including 32-bit and 64-bit variants.
• Global Context and RISC-V:
• By adopting RISC-V, India joins a global movement towards open-source hardware, reducing dependency on proprietary architectures like ARM or x86.
• This move ensures security and sovereignty over the hardware level, preventing backdoors and ensuring long-term maintenance of critical infrastructure.

Important Points

• Specifications of VEGA-64: The processor operates at a frequency of 1.0 GHz, utilizes a 64-bit data width, and incorporates a Super-scalar execution pipeline to enhance performance-per-watt.
• Manufacturing and Fabrication: The VEGA series processors are typically fabricated at advanced semiconductor foundries, often utilizing nodes like 28nm or 180nm (for older variants at SCL Mohali), with 2025 milestones focusing on more compact and efficient process nodes.
• Applications: The VEGA-64 is targeted at General Purpose Computing, Secure Storage, Smart Mobility, and Automotive systems, providing a local alternative for critical data handling.
• Atmanirbhar Bharat: The development of indigenous microprocessors is a cornerstone of the Atmanirbhar Bharat (Self-Reliant India) initiative, aiming to reduce the import bill of electronic components which is currently one of the highest for the Indian economy.

The logic followed here is:

Given:

BUST → 3519

LIDS → 6894

Hence, the code for S is 9.

Hence, the correct answer is Option 1.

× 

Shortcut Trick

Backward method:

Q → R at 32% loss ⇒ 68% = 5406

⇒ 100% = 5406 ÷ 68 × 100 = 7950

P → Q at 50% profit ⇒ 150% = 7950

⇒ 100% = 7950 ÷ 1.5 = 5300

∴ Answer = 5300

Alternate Method

Given:

P→Q profit = 50%, Q→R loss = 32%, Final price = 5406

Formula:

SP = CP × (1 ± profit/loss%)

Calculation:

⇒ Let CP of Q = x

⇒ R paid = 68% of x

⇒ 0.68x = 5406

⇒ x = 5406 ÷ 0.68 = 7950

⇒ Let CP of P = y

⇒ Q bought at 150% of y

⇒ 1.5y = 7950

⇒ y = 7950 ÷ 1.5 = 5300

∴ Required price = 5300

Additional Information

Profit Formula: SP = CP × (1 + profit%)

Loss Formula: SP = CP × (1 − loss%)

Backward Method: Use reverse percentage from final value

Shortcut Tip: Convert % into multiplier (e.g., 68% = 0.68)

The correct answer is Foundation on Raga and Tala.

Key Points

• The primary similarity between Hindustani and Carnatic music systems is their common foundation on Raga (the melodic framework) and Tala (the rhythmic cycle). Both systems utilize these elements as the basic building blocks of musical expression.
• Both traditions trace their historical origins to ancient Indian texts, specifically the Samaveda and Bharata's Natya Shastra (written between 200 BCE and 200 CE). They shared a unified system until approximately the 13th or 14th century AD, when they began to diverge.
• They both utilize the Sapta Swara (seven notes) system—Sa, Re, Ga, Ma, Pa, Dha, and Ni—and place immense importance on Shruti (microtones or the smallest audible pitch).
• Both systems are essentially monophonic, focusing on a single melodic line accompanied by a drone, typically provided by the Tanpura. This distinguishes them from Western classical music, which is polyphonic or harmonic.
• The concept of Laya (tempo or rhythm) is central to both, where the performance progresses through different speeds to create a structured musical experience. Hence, the statement regarding the foundation on Raga and Tala is correct.

Additional Information

• Hindustani Music System:
• Prevalent in North India, it was significantly influenced by Persian, Arabic, and Afghan musical traditions during the Delhi Sultanate and Mughal eras.
• It places a heavy emphasis on improvisation (Manodharma) and the emotional nuances of the Gharana (musical lineage or school) system.
• Major vocal styles include Dhrupad, Khyal, Thumri, and Tappa. Prominent instruments used are the Sitar, Sarod, Tabla, and Shehnai.
• It classifies ragas into 10 Thaats (parent scales), a system formalised by Vishnu Narayan Bhatkhande in the early 20th century.
• Carnatic Music System:
• Rooted in South India (covering Tamil Nadu, Karnataka, Andhra Pradesh, and Kerala), it remained relatively untouched by external Persian influences and preserved indigenous characteristics.
• It is highly structured and focuses on Kritis or Keertanas (fixed compositions). The Trinity of Carnatic Music—Tyagaraja, Muthuswami Dikshitar, and Syama Sastri (active during the 18th and 19th centuries)—composed the bulk of the standard repertoire.
• It follows the 72 Melakarta system (scheme of parent scales) codified by Venkatamakhin in his 17th-century work, Chaturdandi Prakashika.
• Common instruments include the Veena, Violin, Mridangam, Ghatam, and Flute.

Important Points

• Terminology Differences: While the concepts are similar, the names often differ. For example, the unmetered melodic improvisation is called Alap in the North and Alapana in the South. Similarly, a rhythmic cycle is Tala in both, but the specific patterns like Teental (North) and Adi Tala (South) vary.
• Evolutionary Split: The divergence of the two systems is often attributed to the work of Sarangadeva in the 13th century (Sangeeta Ratnakara), which is considered the last text to be authoritative for both traditions before the distinct Persian influence began in the North.
• Modern Context: Today, both systems coexist and frequently interact through Jugalbandis (duets between Hindustani and Carnatic performers), showcasing their underlying structural similarities despite stylistic differences.

Given:

⇒ 3a - 4b + 2c = -9   ...(1)

⇒ -4a + 4b + 10c = 32   ...(2)

⇒ -a + 2b - 7c = -7   ...(3)

Formula Used:

Elimination method to solve system of linear equations

Calculation:

⇒ Adding (1) and 2×(3):   3a - 4b + 2c + (-2a + 4b - 14c) = -9 + (-14)  →  a - 12c = -23   ...(4)

⇒ From (2) and 2×(3):   -4a + 4b + 10c - (-2a + 4b - 14c) = 32 - (-14)  →  -2a + 24c = 46  →  -a + 12c = 23   ...(5)

⇒ Adding (4) and (5):   (a - 12c) + (-a + 12c) = -23 + 23  →  0 = 0  (dependent system, one free variable)

⇒ From (4):   a = 12c - 23

⇒ From (3):   2b = a + 7c - 7 = (12c - 23) + 7c - 7 = 19c - 30  →  b = (19c - 30) ÷ 2

⇒ For integer solution, put c = 2:   a = 12 × 2 - 23 = 24 - 23 = 1

⇒ b = (19 × 2 - 30) ÷ 2 = (38 - 30) ÷ 2 = 8 ÷ 2 = 4

⇒ Verify (1): 3 × 1 - 4 × 4 + 2 × 2 = 3 - 16 + 4 = -9 ✓

⇒ Verify (2): -4 × 1 + 4 × 4 + 10 × 2 = -4 + 16 + 20 = 32 ✓

⇒ Verify (3): -1 + 2 × 4 - 7 × 2 = -1 + 8 - 14 = -7 ✓

∴ The correct answer is a = 1, b = 4, c = 2.

The correct answer is ₹11.21 lakh crore.

Key Points

• In the Union Budget 2025–26 presented on 1 February 2025, Union Finance Minister Nirmala Sitharaman announced a capital expenditure (capex) outlay of ₹11,21,089.77 crore, commonly referred to as ₹11.21 lakh crore.
• Significance: This allocation represents approximately 3.1% of India's GDP.
• Comparison: It marked an increase from the previous year's original budget estimate (BE) of ₹11.11 lakh crore for FY 2024–25.
• Infrastructure Support: As part of this capex push, the government also proposed an outlay of ₹1.5 lakh crore for 50-year interest-free loans to states for their own capital expenditure.
• Impact: The increase in public investment was intended to continue the momentum of infrastructure development and crowd in private investment across the economy.

Additional Information

• Definition of Capital Expenditure:
• Capex refers to the funds used by the government to acquire, upgrade, and maintain physical assets such as property, plants, buildings, technology, or equipment.
• Unlike Revenue Expenditure, which is used for operational costs like salaries and pensions, Capex creates assets and helps in the long-term growth of the country's economy.
• Fiscal Deficit Targets:
• The government aims to reduce the Fiscal Deficit to 4.9% of GDP in FY 2024-25, moving toward a target of below 4.5% by FY 2025-26.
• Maintaining a high capex while reducing the deficit is a strategic move to ensure fiscal consolidation without hampering development.
• Historical Context:
• In the last three years, the capital expenditure has seen a tripling effect, rising from ₹4.39 lakh crore in 2020-21 to the current levels, reflecting a strong post-pandemic recovery strategy.
• The Interim Budget presented in February 2024 first proposed the ₹11.11 lakh crore figure, which was maintained in the Full Budget presented in July 2024.

Important Points

• Sector-Specific Allocations:
• Railways: A significant portion of the capex is directed towards the Indian Railways for the implementation of three major economic railway corridor programs identified under PM Gati Shakti.
• Road Transport: Continued funding for the National Highways Authority of India (NHAI) to expand the road network across the country.
• States' Support: The central government has also extended the scheme of fifty-year interest-free loans to State Governments for capital expenditure with an outlay of ₹1.3 lakh crore to spur regional development.
• Economic Impact:
• According to Reserve Bank of India (RBI) and Finance Ministry studies, every 1 rupee spent on Capital Expenditure has a multiplier effect of approximately 2.45 on the GDP, whereas revenue expenditure has a multiplier of less than 1.
• This high investment is designed to generate employment and increase private sector investment through crowding-in effects.

The correct answer is 23.5°N and 23.5°S.

Key Points

• The Tropical Climatic Region, also known as the Torrid Zone, is the area of the Earth located between the Tropic of Cancer at 23.5°N and the Tropic of Capricorn at 23.5°S.
• This region is centered around the Equator (0° latitude) and covers approximately 40% of the Earth's total surface area.
• It is characterized by being the only part of the globe where the Sun reaches a zenith point, meaning it appears directly overhead at least once during the solar year.
• The climate in this latitudinal extent is generally hot and humid throughout the year, with very little variation in temperature between different months, leading to a lack of distinct thermal seasons as seen in higher latitudes.
• The boundaries of 23.5°N and 23.5°S are determined by the axial tilt of the Earth, which is approximately 23.5 degrees relative to its orbital plane.

Additional Information

• Climate Sub-types: According to the Köppen climate classification, the tropics are divided into Tropical Rainforest (Af), Tropical Monsoon (Am), and Tropical Wet and Dry/Savanna (Aw).
• Tropical Rainforests receive high precipitation exceeding 2,000 mm annually.
• Tropical Savannas have a distinct dry season and are found further from the Equator toward the 23.5° limits.
• Pressure Belts: This region is the home of the Intertropical Convergence Zone (ITCZ), a low-pressure belt where trade winds from the Northern and Southern Hemispheres converge, causing heavy convective rainfall.
• Biodiversity: Although the tropical region covers a limited part of the Earth, it hosts over 50% of the world's plant and animal species, particularly within the Amazon Basin in South America and the Congo Basin in Africa.
• Global Location: Major countries situated within this latitudinal extent include Brazil, India (southern half), Indonesia, Nigeria, and Thailand.
• Solar Energy: The tropics receive the highest amount of insolation (incoming solar radiation) on Earth, making them crucial for global atmospheric circulation and the water cycle.

Important Points

• Solstices and Equinoxes: On June 21 (Summer Solstice), the sun is directly over the Tropic of Cancer (23.5°N). On December 22 (Winter Solstice), it is directly over the Tropic of Capricorn (23.5°S).
• Atmospheric Circulation: The heating in the tropics drives the Hadley Cell, where warm air rises at the Equator and sinks at approximately 30°N and 30°S, creating the subtropical high-pressure zones.
• Agriculture: The year-round warmth allows for the cultivation of specific crops such as coffee, cocoa, rubber, sugar cane, and bananas, which are primary exports for many tropical countries.
• Daylight Hours: Near the Equator, day and night are almost equal in length (12 hours each) throughout the year, whereas, near the 23.5° marks, there is a slight seasonal variation in daylight duration.

Given Statements:

All spoons are forks.

All forks are cups.

Some spoons are plates.

The least possible Venn diagram for the given statements is:

Conclusions:

I. Some forks are plates - True (Since some spoons are plates and all spoons are forks, those plates that overlap with spoons must also overlap with forks. So some forks are plates.)

II. Some cups are plates - True (All forks are cups, and some forks are plates, so those plates are also inside cups. Hence, some cups are plates.)

So, both conclusions I and II follow.

Hence, the correct answer is "Option 1".

Shortcut Trick

Total distance = 360 km

Break smartly:

⇒ 180 km @ 60 km/h → time = 3 hr

⇒ 120 km @ 40 km/h → time = 3 hr

⇒ Remaining = 60 km @ 60 km/h → time = 1 hr

Total time = 3 + 3 + 1 = 7 hr

Average speed = 360 ÷ 7 = 51.43 km/h

∴ Answer = 51.43 km/h

Alternate Method

Given:

Total distance = 360 km

First 180 km @ 60 km/h

Next 120 km @ 40 km/h

Remaining 60 km @ 60 km/h

Formula:

Average speed = Total distance ÷ Total time

Calculation:

⇒ Time₁ = 180 ÷ 60 = 3 hr

⇒ Time₂ = 120 ÷ 40 = 3 hr

⇒ Time₃ = 60 ÷ 60 = 1 hr

⇒ Total time = 3 + 3 + 1 = 7 hr

⇒ Average speed = 360 ÷ 7 = 51.43 km/h

∴ Final Answer = 51.43 km/h

Additional Information

Average Speed: Total distance ÷ Total time

Key Insight: Break journey into segments

Common Mistake: Do NOT average speeds directly

Shortcut Tip: Equal speeds simplify calculations

The correct answer is 1, 2, 3, and 4 only.

Key Points

• Article 249 of the Constitution of India empowers the Parliament to legislate on a matter in the State List if the Rajya Sabha passes a resolution supported by two-thirds of the members present and voting. This resolution must state that such legislation is necessary or expedient in the national interest. Hence, statement 1 is correct.
• Under Article 250, the Parliament acquires the power to make laws for the whole or any part of India with respect to any of the matters enumerated in the State List while a Proclamation of National Emergency is in operation. These laws cease to have effect six months after the emergency has ended. Hence, statement 2 is correct.
• Article 252 provides that if the legislatures of two or more states pass resolutions requesting the Parliament to enact laws on a specific matter in the State List, the Parliament can pass an act for regulating that matter. Such an act applies only to those states that made the request, though other states may adopt it later through their own legislatures. Hence, statement 3 is correct.
• Article 253 enables the Parliament to make any law for the whole or any part of the territory of India for implementing any treaty, agreement, or convention with any other country or international body. This remains true even if the subject matter falls under the State List. Hence, statement 4 is correct.
• The Indian Constitution follows a federal structure where powers are divided. There is no provision that allows the Parliament to legislate on state subjects at the sole discretion of the Prime Minister. Legislative competence is governed by constitutional articles and not by executive discretion. Hence, statement 5 is incorrect.

Additional Information

• Seventh Schedule: The Constitution provides a three-fold distribution of legislative subjects between the Union and the States, viz., List-I (Union List), List-II (State List), and List-III (Concurrent List).
• Residuary Powers: Under Article 248, the Parliament has exclusive power to make any law with respect to any matter not enumerated in the Concurrent List or State List. These are known as residuary powers.
• Article 254 (Repugnancy): If any provision of a law made by the Legislature of a State is repugnant to any provision of a law made by Parliament on a Concurrent List subject, the law made by Parliament shall prevail, and the state law shall be void to the extent of the repugnancy.
• President's Rule: Under Article 356 and Article 357, when President's Rule is imposed in a state, the Parliament is empowered to exercise the legislative powers of that State Legislature.

Important Points

• Specific Examples: Several important laws have been enacted by the Parliament under Article 252 after state requests, such as the Wildlife (Protection) Act, 1972 and the Water (Prevention and Control of Pollution) Act, 1974.
• Role of the Rajya Sabha: The power under Article 249 highlights the federal character of the Rajya Sabha as the representative of the states, ensuring that Parliament only intervenes in the State List when the states' representatives agree it is in the national interest.
• Time Limits: A resolution passed under Article 249 remains in force for a period not exceeding one year, though it can be renewed for further periods of one year at a time by the Rajya Sabha.

The logic followed here is:

Given:

BITE → 4568

TIME → 4826

Hence, the code for M is 2.

Hence, the correct answer is Option 2.

The correct answer is The central law overrides the state law unless the state law has Presidential assent.

Key Points

• Article 254 of the Constitution of India specifically deals with the inconsistency between laws made by Parliament and laws made by the Legislatures of States. It provides the mechanism to resolve conflicts when both bodies legislate on subjects listed in the Concurrent List (List III).
• According to Article 254(1), if any provision of a law made by the State Legislature is repugnant to any provision of a law made by Parliament, the Parliamentary law shall prevail, and the state law shall, to the extent of the repugnancy, be void. Hence, the general rule is that central law overrides state law.
• An important exception is provided under Article 254(2). If a state law on a Concurrent List subject contains provisions repugnant to an earlier Parliamentary law, it can still prevail in that particular state if it has been reserved for the consideration of the President and has received Presidential assent. Hence, the option stating the central law overrides unless there is Presidential assent is correct.
• The Concurrent List includes subjects where both the Union and the States have the power to legislate. However, the Constitution ensures uniformity across the country by giving Parliament overriding powers in case of conflict, ensuring national integration.
• The Supreme Court of India has interpreted this "repugnancy" in various judgments, stating that it arises when two enactments are so inconsistent that they cannot stand together, or when Parliament intended to occupy the entire field of legislation.

Additional Information

• The Seventh Schedule:
• The Seventh Schedule of the Indian Constitution distributes legislative powers between the Union and the States through three lists: the Union List (List I), the State List (List II), and the Concurrent List (List III).
• The Union List currently contains 100 subjects (originally 97) such as Defense, Foreign Affairs, and Banking, where only Parliament can legislate.
• The State List contains 61 subjects (originally 66) like Public Order, Police, and Agriculture, where State Legislatures usually have exclusive power.
• The Concurrent List contains 52 subjects (originally 47) including Education, Forests, Marriage, Adoption, and Succession.
• 42nd Amendment Act, 1976:
• This significant amendment moved five subjects from the State List to the Concurrent List: Education, Forests, Weights and Measures, Protection of Wild Animals and Birds, and Administration of Justice.
• Residuary Powers:
• Under Article 248, the power to legislate on any matter not mentioned in any of the three lists (known as Residuary Powers) is vested solely in the Parliament. This includes modern subjects like Cyber Law.

Important Points

• Doctrine of Pith and Substance: This legal doctrine is used by courts to determine which legislature has the authority to enact a law when there is an overlap between subjects. It looks at the "true nature and character" of the legislation.
• Article 249: It empowers Parliament to legislate on a subject in the State List if the Rajya Sabha passes a resolution by a two-thirds majority declaring it necessary in the national interest.
• Article 250: Parliament gains the power to legislate on any State List subject while a Proclamation of Emergency is in operation.
• Article 251: Clarifies that even when Parliament legislates under Articles 249 and 250, the State Legislature is not barred from making laws, but the Parliamentary law prevails in case of repugnancy.

The correct answer is Pandita Ramabai.

Key Points

• Pandita Ramabai Sarasvati founded the Arya Mahila Samaj on 30th November 1882 in Pune (then Poona) to serve the cause of women's rights and education. Hence, the correct option is Pandita Ramabai.
• The primary objective of the Arya Mahila Samaj was to provide education to women and to liberate them from the oppression of child marriage and the harsh social conditions faced by widows.
• The society worked towards creating awareness about the importance of female literacy and social empowerment, urging the Hunter Commission in 1882 to provide medical education for women in India.
• Pandita Ramabai aimed to create a network of women who could support each other, and the Arya Mahila Samaj established various branches across the Bombay Presidency to expand its reach.
• Through this organization, she advocated for the appointment of women doctors and school inspectors, which eventually led to the Dufferin Fund for providing medical aid to women.

Additional Information

• Mehribai Tata:
• She was a prominent social reformer and the wife of Sir Dorabji Tata.
• She played a significant role in the National Council of Women in India (NCWI), which was founded in 1925 to coordinate women's activities at a national level.
• Mehribai Tata was a staunch advocate for the Sarda Act (Child Marriage Restraint Act) and campaigned against the purdah system and untouchability.
• Sarla Devi Chaudhurani:
• She founded the Bharat Stree Mahamandal in 1910 in Allahabad.
• This was considered the first major all-India women's organization created by a woman for women.
• Its main goal was to promote female education across India, regardless of caste or creed, and to improve the status of women in society.
• Tarabai Premchand:
• She was a dedicated social worker associated with the Jain community and worked for the upliftment of women through education and vocational training.
• She was involved with several charitable trusts and played a role in the All India Women's Conference (AIWC).

Important Points

• Titles and Recognition: In 1878, the University of Calcutta conferred the titles of Pandita and Sarasvati upon Ramabai for her profound knowledge of Sanskrit and Vedic texts.
• Sharada Sadan: Apart from Arya Mahila Samaj, she founded the Sharada Sadan (Home for Learning) in 1889 in Mumbai to provide shelter and education to young widows.
• Mukti Mission: She also established the Mukti Mission at Kedgaon, which became a sanctuary for thousands of destitute women and orphans during the famine of 1896.
• Literary Work: Her famous book, 'The High-Caste Hindu Woman' (published in 1887), highlighted the darkest aspects of the lives of Hindu women, including child brides and widows, and helped gain international support for her cause.

The correct answer is North-Eastern Plateau Region.

Key Points

• The North-Eastern Plateau Region is the most mineral-rich belt in India, encompassing the Chota Nagpur Plateau, Odisha Plateau, and parts of West Bengal and Chhattisgarh.
• This region is uniquely characterized by its high concentration of both Iron ore and Coal, which are the fundamental pillars of the industrial sector. It holds nearly 90% of the country's Coal reserves.
• The belt is often referred to as the "Ruhr of India", comparing it to the mineral-rich Ruhr valley in Germany, due to its massive deposits of metallurgical coal and ferrous minerals.
• Major Coalfields such as Jharia, Raniganj, Bokaro, Giridih, and Karanpura are located within this specific geographical region.
• It also hosts world-class Iron ore deposits, particularly in the Singhbhum district of Jharkhand and the Keonjhar and Mayurbhanj districts of Odisha.

Additional Information

• South-Western Plateau Region: This belt extends over the Karnataka Plateau and adjacent Tamil Nadu. While it is rich in Iron ore (specifically in the Bababudan hills and Kudremukh), Manganese, and Bauxite, it significantly lacks Coal deposits, with the exception of Neyveli Lignite.
• North-Western Plateau Region: Spanning across the Aravalli range in Rajasthan and parts of Gujarat, this region is famous for non-ferrous minerals like Copper, Zinc, and Lead. It also contains significant Petroleum and Natural Gas reserves in the Cambay basin.
• Geological Age: Most of the Coal found in the North-Eastern belt belongs to the Gondwana period, dating back approximately 250 million years, whereas the Iron ore is typically found in the Dharwar and Cuddapah rock systems.
• Industrial Hubs: The proximity of raw materials led to the establishment of major Steel Plants in Jamshedpur (TISCO), Durgapur, Bhilai, and Rourkela, making this belt the backbone of India's manufacturing and infrastructure.
• Mineral Diversity: Besides coal and iron, the North-Eastern region is a primary source for Manganese, Bauxite, Mica, and Copper, contributing heavily to the national mining output and GDP.

Important Points

• Jharia Coalfield: Located in Jharkhand, it is the largest source of Coking Coal in India and is essential for the Iron and Steel industry.
• Raniganj Coalfield: Located in West Bengal, it is the oldest coal mine in India, where mining first commenced in the year 1774.
• Iron Ore Quality: The iron ore found in the Bailadila mines of Chhattisgarh is of very high Hematite grade, which is exported to countries like Japan and South Korea via the Visakhapatnam port.
• Administrative Oversight: The extraction and management of these resources are governed by the Mines and Minerals (Development and Regulation) Act, 1957, and monitored by the Ministry of Mines and Ministry of Coal of the Government of India.

Shortcut Trick

Use direct formula: Mean = Σfx ÷ Σf

⇒ 41 = (5295 + 40X) ÷ (98 + X)

⇒ 41(98 + X) = 5295 + 40X

⇒ 4018 + 41X = 5295 + 40X

⇒ X = 1277

∴ Answer = 1277

Alternate Method

Given: :contentReference[oaicite:0]{index=0}

Mean = 41

x_i = 30, 40, 55, 95

f_i = 31, X, 50, 17

Formula: Mean = (Σf_ix_i) ÷ (Σf_i)

Calculation:

⇒ Σf_ix_i = 30×31 + 40×X + 55×50 + 95×17

⇒ = 930 + 40X + 2750 + 1615 = 5295 + 40X

⇒ Σf_i = 31 + X + 50 + 17 = 98 + X

⇒ 41 = (5295 + 40X) ÷ (98 + X)

⇒ 41(98 + X) = 5295 + 40X

⇒ 4018 + 41X = 5295 + 40X

⇒ X = 1277

∴ Final Answer = 1277

Additional Information

Mean: Σfx ÷ Σf

Linear Equation: Cross-multiply to solve unknown

Tip: Keep Σfx and Σf separate

Check: Substitute back to verify

Shortcut Trick

Convert all to (10/13):

(13/10)⁴ = (10/13)⁻⁴, (13/10)¹⁷ = (10/13)⁻¹⁷

Total power = −4 + 16 − 17 = −5

⇒ (10/13)⁻⁵ = (10/13)^{3m + 18}

⇒ 3m + 18 = −5 ⇒ m = −23/3

∴ Answer = −23/3

Alternate Method

Given:

(13/10)⁴ × (10/13)¹⁶ × (13/10)¹⁷ = (10/13)^{3m + 18}

Formula:

a^m × aⁿ = a^m+n, and (a/b)⁻ⁿ = (b/a)ⁿ

Calculation:

⇒ Convert (13/10) = (10/13)⁻¹

⇒ (13/10)⁴ = (10/13)⁻⁴

⇒ (13/10)¹⁷ = (10/13)⁻¹⁷

⇒ LHS = (10/13)⁻⁴ × (10/13)¹⁶ × (10/13)⁻¹⁷

⇒ = (10/13)^{(−4 + 16 − 17)}

⇒ = (10/13)⁻⁵

⇒ RHS = (10/13)^{3m + 18}

⇒ Equate powers:

⇒ 3m + 18 = −5

⇒ 3m = −23

⇒ m = −23/3

∴ Final Answer = −23/3

Additional Information

Laws of Exponents: a^m × aⁿ = a^m+n

Negative Power: a⁻ⁿ = 1/aⁿ

Base Conversion: (a/b)⁻ⁿ = (b/a)ⁿ

Key Idea: Make bases same, then equate powers