The correct answer is Gurjara-Pratiharas.

Key Points

• The Tripartite Struggle was a significant historical conflict that took place in North India between the 8^th century and the 10^th century.
• The struggle was centered around the control of the city of Kannauj, which was considered a symbol of prestige and sovereign power after the death of Harshavardhana.
• Three major dynasties were involved in this long-standing conflict: the Gurjara-Pratiharas of Western India, the Palas of Bengal, and the Rashtrakutas of the Deccan.
• The Gurjara-Pratiharas ultimately managed to establish long-term control over Kannauj. During the reign of Nagabhata II (around 816 AD), the dynasty successfully conquered Kannauj and made it their capital city. Hence, the Gurjara-Pratiharas are the correct answer as they ruled over Kannauj as their primary seat of power during this era.
• The conflict initially began when the Pratihara king Vatsaraja defeated the Pala ruler Dharmapala and the Rashtrakuta king Dhruva Dharavarsha intervened, defeating both.

Additional Information

• Significance of Kannauj:
• Located in the Ganga valley in present-day Uttar Pradesh, Kannauj was strategically important for trade and agriculture.
• Possession of Kannauj signified lordship over the Indo-Gangetic plains, leading to its nickname as the "Mahodaya Nagar".
• The Palas:
• Founded by Gopala in 750 AD, this dynasty ruled over Bengal and Bihar.
• Dharmapala and Devapala were the most powerful rulers who briefly installed their nominees on the throne of Kannauj during the struggle.
• The Rashtrakutas:
• Founded by Dantidurga in 753 AD with their capital at Manyakheta in the Deccan region (modern-day Karnataka).
• Rulers like Dhruva, Govinda III, and Indra III frequently invaded North India and defeated the Pratiharas and Palas, but they often returned south, allowing the Pratiharas to regain control.
• The Chalukyas and Cholas:
• The Chalukyas of Badami had declined by the mid-8^th century, and the Chalukyas of Kalyani rose later; they were not primary participants in the Tripartite Struggle.
• The Cholas were a powerful maritime empire in South India that reached its peak under Rajaraja I and Rajendra I in the 11^th century, well after the core period of the Tripartite Struggle.

Important Points

• Consequences of the Struggle:
• The constant warfare for over two centuries exhausted the resources of all three dynasties, leading to their eventual fragmentation and decline.
• The weakness of these empires paved the way for the rise of small Rajput principalities and later facilitated the Ghaznavid and Ghurid invasions of India.
• Mihira Bhoja:
• The Gurjara-Pratihara ruler Mihira Bhoja (836–885 AD) was one of the most formidable monarchs of this period. He consolidated Kannauj and successfully defended his territory against both the Palas and the Rashtrakutas.
• The Arab traveler Al-Masudi referred to the Gurjara-Pratihara kingdom as Al-Juzr and praised their powerful cavalry.

Family Chart:

Given:

A is the wife of B,

B is the father of C,

D is the brother of C,

E is the son of D.

 

Here, A is related to E as Father’s mother

Hence, the correct answer is Option 3.

Given Statements:

Some ants are lizards.

All lizards are spiders.

No spider is a rat.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some rats are lizards - False (Because no spider is a rat and all lizards are spiders, so lizards cannot be rats).

II. Some spiders are ants - True (Since some ants are lizards and all lizards are spiders, those ants are also spiders).

So, only conclusion II follows.

Hence, the correct answer is Option 3.

Given Statements:

All oranges are apples.

No apple is a banana.

No banana is a kiwi.

The least possible Venn diagram for the given statement is:

Conclusions:

I. No orange is a banana - True (Since all oranges are apples and no apple is a banana, oranges cannot be bananas).

II. No apple is a kiwi - False (There is no direct relation given between apples and kiwi; both can overlap).

So, only conclusion I follows.

Hence, the correct answer is Option 1.

Shortcut Trick

⇒ X = 13a, Y = 13b and HCF(a,b) = 1

⇒ XY = 6760 ⇒ 169ab = 6760 ⇒ ab = 40

⇒ Prime factor: 40 = 2³ × 5

⇒ Coprime pairs ⇒ assign full powers: (1,40), (5,8)

⇒ With X > Y ⇒ (40,1), (8,5) ⇒ total 2 pairs

∴ Answer = 2

Alternate Method

Given: XY = 6760, HCF = 13

Formula: X = 13a, Y = 13b, where HCF(a,b) = 1

⇒ XY = 169ab = 6760

⇒ ab = 6760 / 169 = 40

⇒ Factors of 40: (1,40), (2,20), (4,10), (5,8)

⇒ Coprime pairs:

⇒ (1,40), (5,8)

⇒ Since X > Y:

⇒ (a,b) = (40,1), (8,5)

⇒ Total possible pairs = 2

∴ Final Answer = 2

Additional Information

HCF Form: X = HCF × a, Y = HCF × b

Product Rule: XY = HCF² × ab

Coprime Condition: HCF(a,b) = 1

Counting Trick: Distribute prime powers fully to keep coprime

The correct answer is 239AA.

Key Points

• Article 239AA of the Indian Constitution was inserted by the Constitution (Sixty-ninth Amendment) Act, 1991. It conferred a special status on the Union Territory of Delhi, designating it as the National Capital Territory (NCT) of Delhi.
• As per this article, the Administrator of the National Capital Territory of Delhi, appointed under Article 239, shall be designated as the Lieutenant Governor.
• The article provided for the creation of a Legislative Assembly for the NCT of Delhi, the members of which are chosen by direct election from territorial constituencies in the Union Territory.
• The Legislative Assembly has the power to make laws for the whole or any part of the NCT of Delhi with respect to any of the matters enumerated in the State List or Concurrent List, except for three specific subjects: Public Order, Police, and Land.
• These provisions officially came into force on February 1, 1992, marking a significant shift in the administrative and political structure of the capital city of India.

Additional Information

• Article 239AB: This article deals with the failure of constitutional machinery in the NCT of Delhi. It allows the President, on receiving a report from the Lieutenant Governor, to suspend the operation of any provision of Article 239AA if the administration of the territory cannot be carried on in accordance with the law.
• Article 239: This is the general provision for the administration of Union Territories. It states that every Union Territory shall be administered by the President acting, to such extent as he thinks fit, through an administrator appointed by him with such designation as he may specify.
• Article 239A: This article was inserted by the Constitution (Fourteenth Amendment) Act, 1962, to create local Legislatures or Council of Ministers or both for certain Union Territories like Puducherry.
• Article 239B: Grants the Administrator of certain Union Territories the power to promulgate ordinances during the recess of the Legislature.
• The 69^th Amendment Act was based on the recommendations of the S. Balakrishnan Committee, which was set up in 1987 to look into the demands for statehood for Delhi and suggested a compromise of a Legislative Assembly with limited powers.

Important Points

• Composition of the Assembly: The Legislative Assembly of Delhi consists of 70 members. The total number of seats is determined by Parliament by law.
• Council of Ministers: Article 239AA(4) provides for a Council of Ministers consisting of not more than 10% of the total number of members in the Legislative Assembly (which equals 7 ministers, including the Chief Minister), to aid and advise the Lieutenant Governor in the exercise of his functions.
• Difference of Opinion: In case of a difference of opinion between the Lieutenant Governor and his Ministers on any matter, the Lieutenant Governor shall refer it to the President for decision and act according to the decision given by the President.
• Government of NCT of Delhi (Amendment) Act, 2021: This recent amendment further clarified that the expression "Government" referred to in any law to be made by the Legislative Assembly shall mean the Lieutenant Governor, thereby increasing the discretionary powers of the LG.
• The NCT of Delhi is unique because, unlike other Union Territories (except Puducherry and Jammu and Kashmir), it has its own elected Government while remaining under the ultimate control of the Union Government through the Ministry of Home Affairs.

Shortcut Trick

⇒ Relative speed initially = 225 − 180 = 45 m/min

⇒ Time for 1^st overtake = 900 / 45 = 20 min

⇒ Speeds reduce by 5% each time ⇒ relative speed also × 0.95

⇒ Times form GP: 20, 20/0.95, 20/(0.95)²

⇒ Total time = 20 + 21.05 + 22.16 = 63.21 min

∴ Answer = 63.21

Alternate Method

Given: Track = 900 m

⇒ Speeds: A = 225, B = 180

Formula: Time = Distance / Relative Speed

⇒ 1^st overtake:

⇒ Relative speed = 225 − 180 = 45

⇒ t₁ = 900 / 45 = 20 min

⇒ After 1^st overtake speeds reduce:

⇒ A = 225 × 0.95 = 213.75

⇒ B = 180 × 0.95 = 171

⇒ Relative speed = 42.75

⇒ t₂ = 900 / 42.75 = 21.05 min

⇒ After 2^nd overtake speeds reduce again:

⇒ A = 213.75 × 0.95 = 203.06

⇒ B = 171 × 0.95 = 162.45

⇒ Relative speed = 40.61

⇒ t₃ = 900 / 40.61 = 22.16 min

⇒ Total time = 20 + 21.05 + 22.16 = 63.21 min

∴ Final Answer = 63.21

Additional Information

Relative Speed: Difference of speeds for same direction

Circular Track: Overtake when relative distance = track length

Successive Reduction: New speed = old speed × factor

GP Insight: Time increases as speed decreases proportionally

The correct answer is Section 7.

Key Points

• Section 7 of the Citizenship Act, 1955, specifically addresses the "Incorporation of Territory." It stipulates that if any foreign territory becomes a part of India, the Central Government has the authority to specify which persons from that territory shall be recognized as citizens of India.
• Under this provision, the notification of citizenship is issued by the government through an order published in the Official Gazette. This ensures a legal transition for the inhabitants of the newly annexed or merged land.
• A primary historical example of the application of Section 7 occurred when Pondicherry (now Puducherry) became part of the Indian Union. The Government issued the Citizenship (Pondicherry) Order, 1962, to grant Indian citizenship to the residents of that territory.
• The power granted under this section is absolute for the Central Government, allowing it to determine the date from which such persons shall become citizens based on their connection with the incorporated territory.
• This section is distinct from other modes of acquisition because it does not require individual applications or specific residency periods like naturalization or registration; it is a collective grant of citizenship based on sovereign territorial change.

Additional Information

• Section 5 (Citizenship by Registration): This section allows the Central Government to register any person (not being an illegal migrant) as a citizen of India if they belong to certain categories. For instance, a person of Indian origin who is ordinarily resident in India for 7 years before making an application can apply under this section.
• Section 6 (Citizenship by Naturalization): This pertains to foreigners who have resided in India for a specific duration. The applicant must have resided in India or been in Government Service for at least 12 months immediately preceding the date of application, and for 11 years out of the preceding 14 years.
• Section 9 (Termination of Citizenship): This section mandates the automatic termination of Indian citizenship if a citizen of India voluntarily acquires the citizenship of another country. India does not permit dual citizenship, except for the Overseas Citizen of India (OCI) scheme which provides limited rights.
• The Citizenship Act, 1955: This is the comprehensive Act passed by the Parliament to provide for the acquisition and determination of Indian citizenship. It has been amended several times, most notably in 1986, 1992, 2003, 2005, 2015, and 2019.
• Constitutional Framework: While Articles 5 to 11 of the Constitution of India deal with citizenship at the commencement of the Constitution (26 January 1950), Article 11 specifically empowers Parliament to make any provision regarding the acquisition and termination of citizenship.

Important Points

• Modes of Acquisition: The 1955 Act prescribes five ways to acquire citizenship: Birth (Section 3), Descent (Section 4), Registration (Section 5), Naturalization (Section 6), and Incorporation of Territory (Section 7).
• Loss of Citizenship: The Act mentions three ways an individual can lose their citizenship: Renunciation (voluntary giving up), Termination (by operation of law upon acquiring another nationality), and Deprivation (compulsory termination by the Central Government on grounds of fraud, disloyalty to the Constitution, or illegal conduct).
• Citizenship Amendment Act (CAA) 2019: This amendment sought to provide a faster path to citizenship for persecuted minorities (Hindus, Sikhs, Buddhists, Jains, Parsis, and Christians) from Afghanistan, Bangladesh, and Pakistan who entered India on or before 31 December 2014.
• Nodal Ministry: The Ministry of Home Affairs is the primary organisation responsible for matters related to citizenship and the implementation of the Citizenship Act in India.

The correct answer is Hydrated Iron (III) Oxide (Fe2O3·xH2O).

Key Points

• Rusting is a specific type of corrosion that occurs when iron or iron-based alloys are exposed to oxygen and moisture (water) for a prolonged period.
• The reddish-brown coating formed during this process is chemically known as Hydrated Iron (III) Oxide, represented by the chemical formula Fe2O3·xH2O.
• The process of rusting is an oxidation reaction where iron metal loses electrons to oxygen in the presence of water. The overall chemical equation can be simplified as: 4Fe + 3O2 + 6H2O → 4Fe(OH)3, which then dehydrates to form Fe2O3·nH2O.
• Unlike the protective oxide layers formed on metals like aluminum, rust is porous and flaky. It does not stick firmly to the surface, allowing the oxidation process to continue deep into the metal until the object is completely eaten away.
• For rusting to occur, both air (oxygen) and moisture (water) are essential requirements. If either is absent, the reddish-brown coating will not form on the iron article.

Additional Information

• Methods of Prevention:
• Galvanization: This is the process of applying a protective zinc coating to iron or steel to prevent rusting. Zinc is more reactive than iron and acts as a sacrificial anode.
• Alloying: Mixing iron with other elements like chromium, nickel, and manganese produces stainless steel, which is highly resistant to corrosion.
• Painting and Greasing: Applying a layer of paint, oil, or grease creates a physical barrier that prevents oxygen and moisture from coming into contact with the metal surface.
• Other Iron Oxides:
• Iron (II) Oxide (FeO): Also known as ferrous oxide, it is a black-colored powder that is not the primary component of common rust.
• Iron (II, III) Oxide (Fe3O4): Naturally occurring as the mineral magnetite, it is often found as a black scale on iron heated to high temperatures.
• Factors Accelerating Rusting:
• Saltwater: The presence of electrolytes (salts) in water increases the speed of the electrochemical reaction involved in rusting, which is why ships and coastal structures corrode faster.
• Acidity: Lower pH levels (acidic environments) increase the rate of corrosion by providing more hydrogen ions for the reaction.

Important Points

• Rusting is considered a chemical change because it results in the formation of a new substance, Hydrated Iron (III) Oxide, which has different properties than the original iron.
• In the Periodic Table, iron (Fe) is a transition metal with the atomic number 26. It is one of the most widely used metals in construction, machinery, and infrastructure due to its strength.
• The economic impact of corrosion is significant; it is estimated that countries spend approximately 3% to 4% of their Gross Domestic Product (GDP) annually on replacing corroded parts and prevention measures.
• Hydrated Iron (III) Oxide is also used as a pigment in various industries, known as Pigment Brown 6 or Pigment Red 101, due to its distinct color and stability.

Family Chart:

Decoding the Symbols:

Given: E % R # D + N @ B

It means: E is the father of R, R is the sister of D, D is the wife of N, N is the son of B.

 

So, E is related to B as Son’s wife’s father.

Hence, the correct answer is Option 1.

Shortcut Trick

⇒ Use identity: a³ + b³ = (a + b)(a² − ab + b²)

⇒ Numerator / denominator cancels ⇒ = (525 + 321)

⇒ = 846

⇒ Expression = 846 × 1/(96 − 36) = 846/60

⇒ = 14.1

∴ Answer = 14.1

Alternate Method

Given: Expression with cubes and squares

Formula: a³ + b³ = (a + b)(a² − ab + b²)

⇒ Let a = 525, b = 321

⇒ Numerator = a³ + b³ = (a + b)(a² − ab + b²)

⇒ Denominator = (a² − ab + b²)

⇒ Cancel common term:

⇒ = a + b = 525 + 321 = 846

⇒ Remaining expression:

⇒ 846 × 1/(96 − 36)

⇒ = 846/60 = 14.1

∴ Final Answer = 14.1

Additional Information

Cube Identity: a³ + b³ = (a + b)(a² − ab + b²)

Cancellation: Common terms simplify large expressions

Difference: 96 − 36 = 60

Speed Trick: Always check identities before expanding

The correct answer is Longitudinal Waves.

Key Points

• Longitudinal Waves: These are mechanical waves in which the displacement of the medium is in the same direction as, or the opposite direction to, the direction of propagation of the wave. In gases, waves propagate through compressions (high pressure) and rarefactions (low pressure). Because gases possess volume elasticity (or Bulk Modulus), they can support the transmission of these pressure variations. Hence, statement 3 is correct.
• Transverse Waves: In these waves, the particles of the medium move perpendicular to the direction of the wave's propagation. These waves require a medium with shear strength or rigidity to propagate. Since gases (and liquids) do not have shear modulus and cannot sustain a shearing force, transverse mechanical waves cannot propagate through the bulk of a gas. Hence, statement 1 is incorrect.
• Stationary Waves: Also known as standing waves, these are formed by the superposition of two waves of the same frequency and amplitude traveling in opposite directions. While they can be observed in gas-filled cavities (like organ pipes), they do not "propagate" energy from one location to another in the traditional sense, as the wave profile remains stationary in space. Hence, statement 2 is incorrect.
• Gravity Waves: These are waves generated in a fluid medium or at the interface between two media (like the atmosphere and ocean) when the force of gravity or buoyancy tries to restore equilibrium. While they exist in the atmosphere, they are distinct from the standard acoustic waves that propagate through the bulk of the gas via molecular collisions. Hence, statement 4 is incorrect.

Additional Information

• Properties of Sound in Gases: Sound is the most common example of a longitudinal wave. The speed of sound in a gas depends on the temperature, density, and molecular structure of the gas. At 20 degrees Celsius, the speed of sound in dry air is approximately 343 meters per second.
• Elasticity and Density: The speed of a longitudinal wave in a medium is determined by the formula v = √(B/ρ), where B is the Bulk Modulus and ρ is the density. Gases have a lower Bulk Modulus compared to solids and liquids, which is why sound generally travels slower in gases than in water or steel.
• Newton's Formula and Laplace Correction: In 1687, Sir Isaac Newton assumed sound propagation in gases was an isothermal process. However, this led to inaccurate results. In 1816, Pierre-Simon Laplace corrected this by treating the process as adiabatic, as heat does not have enough time to flow between compressions and rarefactions.
• Electromagnetic Waves vs. Mechanical Waves: It is important to note that light (an electromagnetic wave) is transverse in nature and can travel through a vacuum or gases. However, the question pertains to mechanical waves that require the gas molecules as a medium for propagation.

Important Points

• Fluid Dynamics: Since both liquids and gases are classified as fluids, they share the characteristic of being unable to support transverse mechanical waves in their interior. Only longitudinal waves can travel through the interior of any fluid.
• Seismic Waves: In Geophysics, P-waves (Primary waves) are longitudinal and can travel through the Earth's liquid outer core, whereas S-waves (Secondary waves) are transverse and cannot, which provides evidence for the liquid nature of the core.
• Molecular Collisions: In a gas, the mean free path (the average distance a molecule travels before colliding) affects the propagation of high-frequency ultrasonic waves. If the wavelength becomes comparable to the mean free path, the wave can no longer propagate effectively.

Given: P, Q, R, S, T, U and V have exams from Monday to Sunday.

Only two people have exams before Q.

Only three people have exams after V.

Only three people have exams between S and Q.

P has the exam immediately before T but not on Monday.

R does not have the exam on Tuesday.

People between R and T → U, Q, V, P → 4

Hence, the correct answer is Option 3.

The correct answer is 51.5%.

Key Points

• By November 2025, non-fossil fuels accounted for 51.5% of India’s total installed electricity capacity.
• India achieved the milestone of 50% non-fossil installed capacity in June 2025, five years ahead of its 2030 NDC target.
• The total installed power capacity stood at 509.64 GW.
• Non-fossil fuel capacity reached 262.74 GW, including 253.96 GW from renewable energy (including large hydro) and 8.78 GW from nuclear power.
• Fossil fuel capacity accounted for 246.90 GW, making up 48.45% of the total capacity.
• Solar energy emerged as the largest contributor, with installed capacity reaching 132.85 GW.
• Wind energy capacity stood at 53.99 GW.
• Large hydropower capacity was approximately 50.35 GW.
• India added a record 44.51 GW of renewable energy capacity between January and November 2025.

Additional Information

• Sources of Non-Fossil Power:
• Solar Power: This is the largest contributor to the renewable energy basket, with an installed capacity exceeding 73 GW as of late 2023.
• Wind Power: India ranks fourth globally in wind power capacity, with installations totaling over 44 GW located primarily in states like Tamil Nadu, Gujarat, and Karnataka.
• Large Hydro: Since 2019, Large Hydropower projects (above 25 MW) have been officially classified as renewable energy, significantly boosting the percentage of non-fossil fuel in the total mix.
• Nuclear Power: India currently operates 23 nuclear reactors with a total capacity of 7.48 GW, and aims to increase this to 22.48 GW by 2031.
• Commitments and Policies:
• Nationally Determined Contributions (NDCs): Under the updated NDC, India is committed to reducing the emissions intensity of its GDP by 45% by 2030 from 2005 levels.
• Energy Conservation (Amendment) Act, 2022: This Act empowers the government to mandate the use of non-fossil sources for energy and establishes a Carbon Credit Trading market in India.
• Green Hydrogen Mission: Launched in 2023 with an outlay of ₹19,744 crore, this mission aims to make India a global hub for the production and export of Green Hydrogen, further reducing dependence on fossil fuels.

Important Points

• Total Capacity Context: As of the financial year 2023-24, Coal remains the single largest source of electricity generation, but its share in "installed capacity" is gradually declining as Renewable Energy (RE) additions outpace thermal additions.
• Global Ranking: India currently stands 4^th globally in Renewable Energy installed capacity, 4^th in Wind Power, and 5^th in Solar Power capacity.
• Institutional Support: Organizations like the Solar Energy Corporation of India (SECI) and the Indian Renewable Energy Development Agency (IREDA) play a pivotal role in financing and implementing these large-scale transitions.
• Data Fact: In the year 2023, Renewable Energy sources (including large hydro) accounted for about 30% of the actual electricity generation, while the installed capacity percentage is higher (around 45.8%) because fossil fuel plants usually operate at a higher Plant Load Factor (PLF).

Shortcut Trick

⇒ Average of 1 to n = (first + last) / 2

⇒ = (1 + 63) / 2 = 64 / 2

⇒ = 32

∴ Answer = 32

Alternate Method

Given: Natural numbers from 1 to 63

Formula: Average = Sum / Number of terms

⇒ Sum = n(n+1)/2 = 63×64/2 = 2016

⇒ Number of terms = 63

⇒ Average = 2016 / 63 = 32

∴ Final Answer = 32

Additional Information

AP Average: (first + last)/2

Sum Formula: n(n+1)/2

Natural Numbers: Start from 1

Symmetry Trick: Pairs give constant sum

The logic followed here is:

So, 'ACA 105' will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic:

First − Second = 120

Second − Third = 60

Now, checking all options:

Option 1: (412, 292, 232)

⇒ 412 − 292 = 120 

⇒ 292 − 232 = 60 

Option 2: (394, 264, 204)

⇒ 394 − 264 = 130 

⇒ 264 − 204 = 60 

Option 3: (432, 332, 252)

⇒ 432 − 332 = 100 

⇒ 332 − 252 = 80 

Option 4: (449, 329, 249)

⇒ 449 − 329 = 120 

⇒ 329 − 249 = 80 

Only (412, 292, 232) satisfies both conditions.

Hence, the correct answer is Option 1.

The correct answer is 42^nd Amendment, 1976.

Key Points

• The 42^nd Amendment Act, passed in 1976, is one of the most significant amendments in the history of the Constitution of India.
• It amended the Preamble of the Constitution to include three new terms: Socialist, Secular, and Integrity. Prior to this, India was described as a "Sovereign Democratic Republic." After the amendment, it became a "Sovereign Socialist Secular Democratic Republic."
• The addition of the word Socialist was intended to reflect the state's commitment to social and economic justice, aiming to reduce inequalities in income and status.
• This amendment was enacted during the National Emergency (1975–1977) under the government led by Prime Minister Indira Gandhi.
• The 42^nd Amendment is frequently referred to as the "Mini-Constitution" because of the massive number of changes it introduced to various parts of the Indian Constitution.

Additional Information

• 44^th Amendment Act, 1978:
• Enacted by the Janata Party government led by Morarji Desai to nullify several controversial changes brought by the 42^nd Amendment.
• It removed the Right to Property from the list of Fundamental Rights and made it a Legal Right under Article 300A.
• It also ensured that the Right to Life and Liberty (Article 21) cannot be suspended even during an Emergency.
• 1^st Amendment Act, 1951:
• This was the first ever change to the Constitution, moved by Jawaharlal Nehru.
• It introduced the Ninth Schedule to protect land reform laws from being challenged in courts on the grounds of violating Fundamental Rights.
• It also placed "reasonable restrictions" on the Freedom of Speech and Expression.
• 26^th Amendment Act, 1971:
• This amendment was crucial in the history of post-independence India as it abolished the Privy Purses.
• It ended the recognition of the titles and special privileges previously enjoyed by the rulers of former Princely States.
• Preamble of India:
• The Preamble is based on the "Objectives Resolution" drafted and moved by Pandit Jawaharlal Nehru on 13 December 1946 and adopted by the Constituent Assembly.
• It serves as an introduction to the Constitution and outlines its basic philosophy and objectives.

Important Points

• Legal Status of the Preamble: In the landmark Kesavananda Bharati case of 1973, the Supreme Court ruled that the Preamble is a part of the Constitution and can be amended under Article 368, provided the Basic Structure of the Constitution remains intact.
• Frequency of Amendments: To date, the Preamble of the Indian Constitution has been amended only once, which was through the 42^nd Amendment Act of 1976.
• Swaran Singh Committee: Most of the provisions of the 42^nd Amendment were based on the recommendations of the Swaran Singh Committee, which was appointed by the government to suggest changes to the Constitution.
• Fundamental Duties: Apart from changing the Preamble, the 42^nd Amendment also added Part IV-A containing Article 51A, which listed 10 Fundamental Duties for Indian citizens.
• Directive Principles: It gave precedence to Directive Principles of State Policy over Fundamental Rights in certain cases and added new directives like Equal Justice and Free Legal Aid (Article 39A).

Shortcut Trick

⇒ Midpoints: 15, 25, 35, 45, 55

⇒ Take A = 35 ⇒ deviations: -20, -10, 0, 10, 20

⇒ Mean = A ⇒ Σfd = 0

⇒ (-20×42) + (-10×26) + (0×45) + (10×46) + (20×X) = 0

⇒ -840 - 260 + 0 + 460 + 20X = 0

⇒ -640 + 20X = 0 ⇒ X = 32

∴ Answer = 32

Alternate Method

Given: Mean = 35

Formula: Mean = Σ(fx) / Σf

⇒ Midpoints (x): 15, 25, 35, 45, 55

⇒ Σfx = 42×15 + 26×25 + 45×35 + 46×45 + X×55

⇒ = 630 + 650 + 1575 + 2070 + 55X = 4925 + 55X

⇒ Σf = 42 + 26 + 45 + 46 + X = 159 + X

⇒ Mean = (4925 + 55X) / (159 + X) = 35

⇒ 4925 + 55X = 35(159 + X)

⇒ 4925 + 55X = 5565 + 35X

⇒ 20X = 640

⇒ X = 32

∴ Final Answer = 32

Additional Information

Mean Formula: Mean = Σ(fx) / Σf

Assumed Mean: If mean = A ⇒ Σfd = 0

Midpoint: x = (lower + upper)/2

Shortcut Insight: Use deviations when mean equals midpoint

Shortcut Trick

⇒ Cube LSA = 4a² = 324 ⇒ a² = 81 ⇒ a = 9 cm

⇒ Volume of cube = 9³ = 729

⇒ Container: 4bh = 864, h = 18 ⇒ b = 12 cm

⇒ Base area = 12² = 144

⇒ Rise = Volume ÷ Base area = 729 ÷ 144 ≈ 5.06

∴ Answer = 5 cm

Alternate Method

Given:

Cube LSA = 324 cm²

Container height = 18 cm

Container LSA = 864 cm²

Formula:

Cube LSA = 4a²

Container LSA = 4 × side × height

Volume = side³

Rise in water = Volume displaced ÷ Base area

Container Cube

Calculations:

⇒ Cube: 4a² = 324 ⇒ a² = 81 ⇒ a = 9 cm

⇒ Volume of cube = 9³ = 729 cm³

⇒ Container: 4 × side × 18 = 864

⇒ 72 × side = 864 ⇒ side = 12 cm

⇒ Base area = 12² = 144 cm²

⇒ Rise = 729 ÷ 144 ≈ 5.06 cm

Final Answer: 5 cm

Additional Information

1. Displacement Principle: Submerged object displaces equal volume of water

2. Cube LSA: 4a² (excluding top and bottom)

3. Container LSA: 4 × base side × height

4. Height Rise: Volume ÷ Base area

The correct answer is Through mechanisms like the Finance Commission that allocate resources.

Key Points

• Article 280 of the Constitution of India mandates the establishment of a Finance Commission every five years by the President to define the financial relations between the central government and the state governments.
• The primary function of the Finance Commission is to recommend the distribution of net proceeds of taxes between the Union and the States (vertical devolution) and the allocation between the states themselves (horizontal devolution). For the 15^th Finance Commission, the vertical devolution was set at 41% for the states.
• Centre-State financial relations are governed by the Seventh Schedule of the Constitution, which divides taxing powers. While the Centre collects major taxes like Income Tax and Corporation Tax, the States have the power to levy taxes on land revenue, state excise, and sales tax on petroleum and liquor.
• Governance is impacted by these relations because states rely on Central transfers to fund social sector schemes. This fiscal federalism ensures that states with lower revenue-generating capacity receive higher Grants-in-aid to maintain administrative standards.
• Statement 1 is incorrect because financial resources are limited by the FRBM Act, 2003, and the overall fiscal deficit targets. Statement 2 is incorrect as states retain independent taxing powers under the State List. Statement 4 is incorrect because Article 202 mandates every state to present its own Annual Financial Statement or Budget. Hence, the third option is the only correct mechanism described.

Additional Information

• Goods and Services Tax (GST): Introduced on July 1, 2017, through the 101^st Constitutional Amendment Act, it revolutionized financial relations by subsuming various central and state indirect taxes. The GST Council, chaired by the Union Finance Minister, serves as a joint forum for the Centre and States to decide on tax rates and exemptions.
• Grants-in-Aid: Under Article 275, the Parliament can provide financial assistance to specific states in need of help, particularly for the welfare of Scheduled Tribes or to improve administration in Scheduled Areas.
• NITI Aayog: Replacing the Planning Commission in January 2015, it acts as a premier policy think tank providing directional and policy inputs. It fosters Cooperative Federalism through structured support initiatives with the states on a continuous basis.
• Borrowing Powers: Under Article 293, the State Executive has the power to borrow money within the territory of India upon the security of the Consolidated Fund of the State, subject to limits set by the State Legislature and consent from the Centre if previous loans are outstanding.

Important Points

• 15^th Finance Commission: Chaired by Shri N.K. Singh, it used 2011 Census data for the first time, moving away from 1971 data, which significantly influenced the resource allocation based on demographic performance and tax effort.
• Centrally Sponsored Schemes (CSS): These are schemes where the funding is shared between the Centre and States, usually in a 60:40 ratio for general states and 90:10 for North-Eastern and Himalayan States.
• Article 268 to 293: These articles in Part XII of the Constitution deal with the distribution of revenues between the Union and the States, ensuring a balance of fiscal powers.
• Fiscal Responsibility and Budget Management (FRBM) Act: This 2003 act sets targets for the government to reduce fiscal deficits. States are generally required to keep their fiscal deficit within 3% of their GSDP (Gross State Domestic Product).

The correct answer is 79.74%.

Key Points

• The Jal Jeevan Mission (JJM) is a flagship program of the Government of India, launched by Prime Minister Narendra Modi on August 15, 2019.
• As of February 1, 2025, the percentage of rural households in India provided with tap water connections reached 79.74%.
• This milestone signifies that over 15.42 crore rural households now have access to clean tap water, out of a total target of approximately 19.34 crore households.
• At the inception of the mission in August 2019, only about 3.23 crore households (representing 16.64%) had a Functional Household Tap Connection (FHTC).
• The mission aims to ensure the supply of 55 litres of water per person per day to every rural household through FHTCs by the target timeline.

Additional Information

• Ministry and Department: The mission is being implemented by the Department of Drinking Water and Sanitation under the Ministry of Jal Shakti.
• Funding Mechanism: The central government and states share the financial burden. The fund-sharing ratio is 90:10 for Himalayan and North-Eastern States, 50:50 for other States, and 100% for Union Territories.
• Implementation Strategy: The program follows a community-driven approach, involving Gram Panchayats and Village Water and Sanitation Committees (VWSC) to plan, implement, manage, operate, and maintain their own in-village water supply systems.
• Har Ghar Jal Certification: Goa became the first "Har Ghar Jal" certified State in India, followed by Dadra and Nagar Haveli and Daman and Diu as the first certified Union Territory. Other states like Haryana, Gujarat, and Telangana have also achieved 100% coverage.
• Technological Integration: A JJM Dashboard was developed to provide real-time data and transparency regarding the progress of the mission across every village and district in the country.

Important Points

• Water Quality: The mission focuses on water quality monitoring and surveillance. It empowers local communities by training at least 5 women in every village to use Field Test Kits (FTKs) for testing water samples.
• Sustainability Components: Beyond just providing taps, the mission includes source sustainability measures such as recharge and reuse through greywater management, water conservation, and rainwater harvesting.
• Empowerment and Health: The mission significantly reduces the drudgery of women and girls who previously traveled long distances to fetch water, while also reducing the incidence of water-borne diseases like cholera, typhoid, and dysentery.
• Scope: In addition to households, the mission prioritizes providing tap water to Schools, Anganwadi centres, and Public Institutions to ensure the health and hygiene of children.

Shortcut Trick

⇒ Let valid votes = V

⇒ Winner gets 58%, loser gets 42% ⇒ Difference = 16% of V

⇒ 16% of V = 336 ⇒ V = 336 × 100 ÷ 16 = 2100

⇒ Valid = 80% of polled ⇒ Polled = 2100 ÷ 0.8 = 2625

⇒ Polled = 84% of registered ⇒ Registered = 2625 ÷ 0.84 = 3125

∴ Answer = 3125

Alternate Method

Given:

84% voters cast votes

20% votes invalid ⇒ 80% valid

Winner = 58%, Loser = 42%

Margin = 336 votes

Formula:

Margin = Difference % × Valid votes

Calculations:

⇒ Difference = (58 − 42)% = 16%

⇒ 16% of valid votes = 336

⇒ Valid votes = 336 × 100 ÷ 16 = 2100

⇒ Valid = 80% of polled

⇒ Polled votes = 2100 × 100 ÷ 80 = 2625

⇒ Polled = 84% of registered

⇒ Registered voters = 2625 × 100 ÷ 84 = 3125

Final Answer: 3125

Additional Information

1. Election Margin: Margin = (Winner% − Loser%) × Valid votes

2. Valid Votes: Valid = Total polled × (1 − invalid%)

3. Reverse Percentage: Total = Part × 100 ÷ %

4. Step Flow: Margin → Valid → Polled → Registered

The logic followed here is:

Given:

Manan starts from Point A and drives 42 km South.

He turns left → 40 km East.

He turns left → 54 km North.

He turns left → 48 km West.

He takes a final left → 12 km South.

 

So, Manan must travel 8 km East to reach Point A.

Hence, the correct answer is Option 4.

The logic followed here is:

For, VUP → %

So, % = QPK

Now, apply the same pattern to NMH → #

So, # = SRM

Hence, the correct answer is Option 3.

The correct answer is Windows Kernel.

Key Points

• The Windows Kernel is the central core of the Windows Operating System, serving as the bridge between software applications and the physical hardware of the computer. It is responsible for critical low-level operations like memory management and process scheduling. Hence, statement 1 is correct.
• In terms of memory management, the kernel tracks every memory location, managing the transition between Physical RAM and Virtual Memory to ensure that each process has enough resources to execute without interfering with others.
• The process scheduling function of the kernel determines which thread or process receives CPU time and for how long. It uses complex algorithms to prioritize tasks, ensuring system stability and responsiveness for the user.
• The Windows Kernel operates in Kernel Mode (also known as Ring 0), which grants it unrestricted access to the system hardware and CPU instructions, protecting the system from crashes caused by faulty user-level applications.
• It also handles Interrupt Management, where it responds to signals from hardware devices like keyboards, mice, and hard drives, ensuring that the processor handles these events immediately and accurately.

Additional Information

• Architecture Type: The Windows OS utilizes a Hybrid Kernel architecture, which combines the speed of a Monolithic Kernel with the modularity of a Microkernel. This design started with Windows NT and continues through modern versions like Windows 10 and Windows 11.
• Hardware Abstraction Layer (HAL): A vital sub-component of the Windows executive, the HAL is a software layer that hides hardware differences from the rest of the kernel, allowing the OS to run on different motherboards and chipsets without major code changes.
• I/O Management: The kernel includes an I/O Manager that facilitates communication between applications and device drivers. It translates read/write requests into I/O Request Packets (IRPs) that the hardware can understand.
• Security Reference Monitor (SRM): This component within the kernel enforces access control and security policies on the local system, ensuring that users can only access files and objects they are authorized to use.
• Registry Management: While the Registry is a database, the kernel manages the Configuration Manager, which handles the reading and writing of system settings and configuration data during boot time and runtime.

Important Points

• Service Control Manager (SCM): The Service Control Manager is a user-mode process that manages the starting, stopping, and interaction of system services; it does not handle low-level memory or CPU scheduling directly. Hence, statement 2 is incorrect.
• Windows Explorer (File Explorer): Now officially called File Explorer, this is the graphical user interface (GUI) that allows users to navigate folders and manage files. It is a user-mode application, not a core kernel component. Hence, statement 3 is incorrect.
• Task Scheduler: The Task Scheduler is a service that allows users to automate scripts or programs to run at specific times or dates. While it schedules tasks, it does not perform low-level thread scheduling at the CPU level. Hence, statement 4 is incorrect.
• User Mode vs. Kernel Mode: In Windows, applications run in User Mode to prevent them from accessing critical memory areas. If an application crashes, it only affects itself, whereas a crash in Kernel Mode usually results in a Blue Screen of Death (BSOD).
• Object Manager: The Windows Kernel uses an Object Manager to manage system resources such as files, ports, and semaphores as standardized objects, providing a uniform way to track and secure these resources.

Shortcut Trick

⇒ a : b : c = 3 : 4 : 5 ⇒ take a = 3k, b = 4k, c = 5k

⇒ Put directly: 2(3k) − 3(4k) + 4(5k) = 56

⇒ 6k − 12k + 20k = 56 ⇒ 14k = 56 ⇒ k = 4

⇒ c = 5k = 20

∴ Answer = 20

Alternate Method

Given:

a : b : c = 3 : 4 : 5

2a − 3b + 4c = 56

Formula:

If a : b : c = x : y : z ⇒ a = xk, b = yk, c = zk

Calculations:

⇒ Let a = 3k, b = 4k, c = 5k

⇒ Substitute:

⇒ 2(3k) − 3(4k) + 4(5k) = 56

⇒ 6k − 12k + 20k = 56

⇒ 14k = 56

⇒ k = 4

⇒ c = 5k = 20

Final Answer: 20

Additional Information

1. Ratio Concept: Multiply ratio by common factor k

2. Substitution: Replace variables to simplify equation

3. Linear Equation: Solve for k using basic algebra

4. Final Step: Substitute k back to get required value

Shortcut Trick

⇒ (−60 ÷ −6) = 10 and (−2 × 8) = −16

⇒ Expression becomes: −9 − 10 − 16

⇒ −9 − 10 = −19

⇒ −19 − 16 = −35

∴ Answer = −35

Alternate Method

Given:

Expression = (−9) − (−60) ÷ (−6) + (−2) × 8

Formula:

BODMAS Rule → Division and Multiplication first

Calculations:

⇒ Step 1: (−60) ÷ (−6) = 10

⇒ Step 2: (−2) × 8 = −16

⇒ Expression becomes: −9 − 10 − 16

⇒ Step 3: −9 − 10 = −19

⇒ Step 4: −19 − 16 = −35

Final Answer: −35

Additional Information

1. Sign Rule: (− ÷ − = +), (− × + = −)

2. BODMAS: Division & Multiplication before addition/subtraction

3. Negative Addition: Adding negative means subtracting

4. Simplification: Convert stepwise into linear expression

Shortcut Trick

⇒ Successive increase: 10% and 20%

⇒ Net increase = 10 + 20 + (10×20)/100 = 32%

⇒ Final population = 2,90,000 × 1.32

⇒ = 3,82,800

∴ Answer = 3,82,800

Alternate Method

Given:

Initial population = 2,90,000

First year increase = 10%

Second year increase = 20%

Formula:

Final Value = Initial × (1 + r₁/100) × (1 + r₂/100)

Calculations:

⇒ After 1^st year = 2,90,000 × 1.10 = 3,19,000

⇒ After 2^nd year = 3,19,000 × 1.20 = 3,82,800

Final Answer: 3,82,800

Additional Information

1. Successive Percentage: a + b + (ab/100)

2. Growth Formula: Final = Initial × (1 + r/100)

3. Compound Growth: Applied year after year

4. Shortcut Tip: Use net % to avoid stepwise multiplication

Given:

: NQW :: LOU : %

Option 1) # = HKQ, % = RUO

For # (HKQ) to NQW

 

For LOU to % (RUO)

Since the pattern (+6, +6, +6) does not match (+6, +6, -6), Option 1 is incorrect.

Option 2) # = KKQ, % = RUA

For # (KKQ) to NQW

 

For LOU to % (RUA)

 

Since the pattern (+3, +6, +6) does not match (+6, +6, +6), Option 2 is incorrect.

Option 3) # = HKQ, % = RUA

For # (HKQ) to NQW

 

For LOU to % (RUA)

Since the pattern for HKQ to NQW (+6, +6, +6) is the same as the pattern for LOU to RUA (+6, +6, +6), Option 3 is correct.

Option 4) # = HKQ, % = RUL

For # (HKQ) to NQW

 

For LOU to % (RUL)

 

Since the pattern (+6, +6, +6) does not match (+6, +6, -9), Option 4 is incorrect.

Hence, the correct answer is "Option 3".

Shortcut Trick

⇒ Angle at B = 180 − 135 = 45°

⇒ AO ∥ DE ⇒ corresponding angle = 80°

⇒ Interior angle at O (triangle) = 180 − 80 = 100°

⇒ In △BOC: x + 45 + 100 = 180

⇒ x = 35°

∴ Answer = 35°

Alternate Method

Given: AO ∥ DE, angle at B = 135°, angle at D = 80°

Concept: Linear pair + corresponding angles + triangle sum

⇒ Angle at B in triangle = 180 − 135 = 45°

⇒ Corresponding angle at O = 80°

⇒ Interior angle at O in triangle = 180 − 80 = 100°

⇒ In △BOC:

⇒ x + 45 + 100 = 180

⇒ x = 35°

∴ Final Answer = 35°

Additional Information

Linear Pair: Adjacent angles sum = 180°

Corresponding Angles: Equal when lines are parallel

Interior Angle: Straight line gives supplement

Triangle Rule: Sum = 180°

Shortcut Trick

⇒ Given ∠A = 92°

⇒ t₁ ∥ t₂ ⇒ ∠A = ∠C = 92°

⇒ u ∥ v ⇒ C and B are co-interior ⇒ B = 180 − 92 = 88°

⇒ B and D are vertical opposite ⇒ ∠D = 88°

∴ Answer = 88°

Alternate Method

Given: u ∥ v, t₁ ∥ t₂, ∠A = 92°

Concepts Used: Corresponding angles, co-interior angles, vertical opposite

⇒ Since t₁ ∥ t₂:

⇒ ∠A = ∠C = 92°

⇒ Since u ∥ v:

⇒ ∠C + ∠B = 180° (co-interior)

⇒ 92 + B = 180

⇒ ∠B = 88°

⇒ Vertical opposite angles:

⇒ ∠D = ∠B = 88°

∴ Final Answer = 88°

Additional Information

Corresponding Angles: Equal for parallel lines

Co-interior Angles: Sum = 180°

Vertical Angles: Opposite angles equal

Key Tip: Identify correct angle relation carefully

The correct answer is Nagaland.

Key Points

• According to the Census 2011, Nagaland was the only state in India to record a negative decadal population growth rate. Between the years 2001 and 2011, its growth rate was approximately -0.58% (often rounded to -0.6%).
• This negative growth was a significant shift from the 1991-2001 census period, where Nagaland had reported an exceptionally high growth rate of 64.53%. Experts suggest this anomaly was likely due to the correction of previous over-estimations and inflated figures in the 2001 Census.
• The Census 2011 was the 15^th National Census of the country since 1872 and the 7^th after Independence. It was conducted under the guidance of C. Chandramouli, the then Registrar General and Census Commissioner of India.
• In contrast to Nagaland, the state of Meghalaya recorded the highest decadal growth rate among all states at 27.9%, followed by Arunachal Pradesh at 26%.
• While Nagaland showed a decline, the state of Kerala recorded the lowest positive decadal growth rate among the states at 4.9%.

Additional Information

• Population Growth in Other States (2001-2011):
• Gujarat: This western state recorded a decadal growth rate of 19.3%. Gujarat has consistently shown industrial and urban growth, contributing to its population dynamics.
• Kerala: Known for its high literacy and advanced social indicators, Kerala had a growth rate of 4.9%. This was the lowest among the states (excluding Nagaland) and significantly lower than the national average.
• Punjab: The state of Punjab recorded a decadal growth rate of 13.9%. It is one of the states where the growth rate remained lower than the overall Indian average.
• National Average: The overall decadal population growth rate of India during 2001-2011 was 17.7%, a decrease from 21.5% in the previous decade (1991-2001).
• Significant Census 2011 Facts:
• The slogan of the 2011 Census was "Our Census, Our Future".
• The total population of India as per the 2011 Census was 1.21 billion (approximately 121.08 crore), making it the second most populous country at that time.
• Uttar Pradesh was identified as the most populous state, while Sikkim was the least populous state in India.
• Thane district in Maharashtra was the most populated district in the country.

Important Points

• Decadal Growth Rate: It refers to the percentage of total population growth in a particular area (state/country) over a period of 10 years. It is a vital indicator used by the government for resource allocation and policy planning.
• Demographic Transition: The decline in growth rates in states like Kerala and the negative growth in Nagaland indicate different stages of demographic transition. Lower growth rates are typically associated with higher literacy rates, better healthcare, and increased urbanization.
• Gender Statistics: In the 2011 Census, the child sex ratio (0-6 years) saw a decline to 919, which remains a critical concern for policymakers. The overall sex ratio in India was 943 females per 1000 males.
• Literacy Rate: The national literacy rate was recorded at 73%. Kerala topped the list with a 94% literacy rate, while Bihar was at the bottom with 61.8%.
• Administrative Units: During the 2011 Census, there were 28 states and 7 Union Territories (before the reorganization of Jammu and Kashmir and the merger of Dadra and Nagar Haveli and Daman and Diu).

Given:

Seven boxes A, C, G, H, J, N and R are kept one over the other but not necessarily in the same order.

Only three boxes are kept below N.

Only two boxes are kept between N and J.

Only G is kept immediately above H.

C is kept at some place below R and at some place above A.

 

Boxes above C → N, R, H, G

i.e. There are 4 boxes kept above C

Hence, the correct answer is Option (2).

The correct answer is 2025 Treaty Event.

Key Points

• The 2025 Treaty Event is a high-level United Nations event held annually, typically during the opening of the General Debate of the General Assembly in September 2025 in New York. It serves as a dedicated platform for member states to demonstrate their commitment to the international legal framework.
• The primary objective of the event is to encourage the universal participation of member states in multilateral treaties deposited with the Secretary-General. These treaties span a wide range of global issues, including human rights, disarmament, environmental protection, penal law, and the law of the sea.
• The tradition of the Treaty Event was established in the year 2000 during the Millennium Summit to promote the rule of law at the international level. Since its inception, it has resulted in thousands of treaty actions, including signatures, ratifications, and accessions.
• For the 2025 cycle, the United Nations highlights specific multilateral treaties that address contemporary global challenges, such as the Agreement under the United Nations Convention on the Law of the Sea on the Conservation and Sustainable Use of Marine Biological Diversity of Areas Beyond National Jurisdiction (BBNJ Agreement).
• The event provides a unique opportunity for Heads of State and Heads of Government to deposit their instruments of ratification in a high-profile setting, signaling their country's adherence to international law and global standards.

Additional Information

• UN Ocean Conference 2025: This conference is scheduled to be held in Nice, France, in June 2025. It is co-hosted by France and Costa Rica and focuses specifically on Sustainable Development Goal 14 (Life Below Water) to support the conservation and sustainable use of the oceans, seas, and marine resources.
• Paris Climate Summit (COP30): The 30^th session of the Conference of the Parties (COP30) to the UNFCCC is expected to take place in Belém, Brazil, in November 2025. This event is critical for the Paris Agreement as it will involve the submission of new Nationally Determined Contributions (NDCs) by member states to tackle climate change.
• UN Biodiversity Summit: While COP16 of the Convention on Biological Diversity (CBD) occurs in 2024, the year 2025 remains significant for implementing the Kunming-Montreal Global Biodiversity Framework, which aims to protect 30% of the planet's land and oceans by 2030.
• Treaty Section of the OLA: The Office of Legal Affairs (OLA) of the United Nations, specifically the Treaty Section, is responsible for the technical and legal processing of all treaty actions during the event. They maintain the United Nations Treaty Series, which contains over 250,000 treaties and related actions.

Important Points

• Role of the Secretary-General: The United Nations Secretary-General acts as the depositary for more than 600 multilateral treaties. In this role, the Secretary-General ensures that all legal formalities regarding the entry into force and implementation of these treaties are strictly followed.
• Legal Terminologies: It is important to distinguish between Signature (a preliminary endorsement of a treaty), Ratification (the formal process by which a state confirms its consent to be bound, usually involving domestic legislative approval), and Accession (the act by which a state joins a treaty that has already been negotiated and signed by other states).
• Law of the Sea: The United Nations Convention on the Law of the Sea (UNCLOS), often described as the "constitution for the oceans," remains a central pillar of the Treaty Event, especially with the recent focus on the BBNJ Agreement, which was adopted in June 2023 and opened for signature in September 2023.

The correct answer is They head important ministries like Home, Defence, and Finance.

Key Points

• Cabinet Ministers are senior members of the Council of Ministers and hold independent charge of specific ministries or departments of the Government of India.
• They head the most crucial and strategically important portfolios such as Home, Defence, Finance, External Affairs, and Railways. Hence, the statement "They head important ministries like Home, Defence, and Finance" is correct.
• They are the core policy-making body of the central government, responsible for deliberating and deciding upon major national policies, legislations, and administrative matters. Therefore, the statement "They are not involved in policy decisions" is incorrect.
• Cabinet Ministers are the only category of ministers who have a legal right to attend Cabinet meetings, which are presided over by the Prime Minister. Consequently, the statement "They do not attend Cabinet meetings" is incorrect.
• The role of assisting senior ministers is typically performed by Ministers of State or Deputy Ministers, not by the Cabinet Ministers themselves. This makes the statement "They only assist other ministers in their duties" incorrect.

Additional Information

• Structure of the Council of Ministers: The Union Council of Ministers consists of three ranks: Cabinet Ministers, Ministers of State, and Deputy Ministers. The total number of ministers cannot exceed 15% of the total strength of the Lok Sabha, as per the 91^st Amendment Act, 2003.
• Constitutional Status: Article 74 of the Constitution of India provides for a Council of Ministers with the Prime Minister at the head to aid and advise the President. Article 75 deals with the appointment, tenure, responsibility, and salaries of the ministers.
• Collective Responsibility: Under Article 75(3), the Council of Ministers is collectively responsible to the Lok Sabha. This means that if a no-confidence motion is passed against one minister, the entire council must resign.
• Definition of Cabinet: While the word 'Cabinet' was not originally detailed in the Constitution, it was inserted into Article 352 via the 44^th Amendment Act, 1978. It defines the Cabinet as the council consisting of the Prime Minister and other ministers of Cabinet rank.
• Selection and Appointment: Ministers are appointed by the President on the advice of the Prime Minister. A person who is not a member of either House of Parliament can also be appointed as a minister, but they must become a member of either Lok Sabha or Rajya Sabha within 6 months.

Important Points

• Cabinet Committees: These are specialized units like the Appointments Committee of the Cabinet (ACC) and the Cabinet Committee on Economic Affairs (CCEA) that handle specific issues. They are usually chaired by the Prime Minister and consist mainly of Cabinet Ministers.
• Role of the Prime Minister: The Prime Minister is the "primus inter pares" (first among equals) and determines the size of the Cabinet and the portfolios allocated to each minister.
• Cabinet Secretariat: This office provides secretarial assistance to the Cabinet and its committees. It is headed by the Cabinet Secretary, who is the topmost civil servant in India and acts as the chairman of the Senior Selection Board.
• Advisory Function: The advice tendered by the Council of Ministers to the President is binding after the 42^nd Amendment Act, 1976 (subject to the President's power to ask for reconsideration once under the 44^th Amendment).

Shortcut Trick

⇒ 27 hr fill and 27 hr empty cancel each other

⇒ Only 4 hr tap works

⇒ 1/4 tank filled in 1 hr

∴ Answer = 1

Alternate Method

Given: Times = 4 hr, 27 hr, 27 hr

LCM Method:

⇒ LCM of 4 and 27 = 108 (total work)

⇒ Net work per hour = 27 + 4 − 4 = 27

⇒ Work needed = 1/4 of 108 = 27

⇒ Time = 27 / 27 = 1 hr

∴ Final Answer = 1

Additional Information

LCM Method: Convert total work into common units

Efficiency: Work per unit time

Net Work: Add filling, subtract emptying

Partial Work: Required fraction of total work

Given Statements:

I. D sits to the immediate left of F. C is the immediate neighbour of A and E.

II. B sits second to the left of F. C sits second to the right of F.

Analysis:

I. From Statement I → We know D–F relation and that C is between A and E, but full arrangement cannot be fixed → Not sufficient.

II. From Statement II → Positions of B, F and C are known, but A, D, E are unknown → Not sufficient.

Using both I and II together → Even after combining, we can form arrangement but cannot uniquely decide whether A or E sits to the immediate right of C → Not sufficient.

Hence, the correct answer is Option 4.

The correct answer is Output Device.

Key Points

• An Output Device is a piece of computer hardware equipment used to communicate the results of data processing carried out by an information processing system (such as a computer) to the outside world. Headphones fall strictly into this category as they receive electronic signals and convert them into audible sound waves. Hence, the statement that headphones are an output device is correct.
• The primary function of headphones is to provide a private audio experience for the user. They act as transducers, converting electrical energy from a device like a smartphone, laptop, or MP3 player into acoustic energy.
• Unlike speakers, which are also output devices designed for multiple listeners, headphones are localized output devices intended for a single user. They allow for the consumption of multimedia content without disturbing others in the vicinity.
• In the context of the Human-Computer Interaction (HCI), headphones represent the auditory output channel. They are essential for tasks involving sound monitoring, video editing, and gaming, where directional audio and clarity are required.

Additional Information

• History and Origin: The first modern headphones were developed in 1910 by Nathaniel Baldwin, who manufactured them in his kitchen and sold them to the United States Navy. They were initially used for radio communication before becoming a consumer electronic staple.
• Types of Headphones:
• Over-ear (Circumaural): These have large earcups that surround the entire ear, offering excellent sound isolation.
• On-ear (Supra-aural): These sit directly on the outer ear and are generally lighter and more portable.
• In-ear (Earbuds/IEMs): These are inserted into the ear canal, making them the most compact option, often used with mobile devices.
• Input vs. Output Devices: While an Output Device (like headphones or a monitor) displays or emits processed data, an Input Device (like a keyboard or mouse) sends data and control signals to the computer for processing.
• Hybrid Devices: Some devices, known as headsets, combine both output (headphones) and input (a microphone). These are widely used in telecommunications, customer service, and online gaming.
• Storage and Calculation Devices: A Storage Device (like a Hard Disk Drive or SSD) is used for permanent data retention, while a Calculator Device (like a microprocessor or ALU) is responsible for performing arithmetic and logic operations. Headphones perform neither of these functions.

Important Points

• Connectivity: Headphones can connect to devices via wired connections (using a 3.5mm jack, USB-C, or Lightning port) or wireless technologies such as Bluetooth (versions 5.0 and above are currently standard).
• Technical Specifications: Key metrics for headphones include Impedance (measured in Ohms), Frequency Response (typically 20Hz to 20kHz), and Sensitivity (measured in dB/mW). These factors determine the audio quality and the power required to drive the device.
• Applications: Beyond entertainment, headphones are used in specialized fields such as Aviation for pilot communication, in Medical Science for audiometry tests, and in Military operations for sonar monitoring.
• Features: Modern output devices in this category often feature Active Noise Cancellation (ANC), which uses microphones to pick up external noise and create anti-noise to cancel it out, providing a clearer output.

Shortcut Trick

⇒ Successive change ⇒ ×1.7 × 0.33

⇒ Net factor = 1.7 × 0.33 = 0.561

⇒ Final price = 0.561 × P's CP

⇒ 3927 = 0.561 × CP

⇒ CP = 3927 / 0.561 = 7000

∴ Answer = 7000

Alternate Method

Given: Profit = 70%, Loss = 67%, Final price = 3927

LCM Method:

⇒ Assume P's CP = 100

⇒ P sells to Q at 70% profit ⇒ SP = 170

⇒ Q sells at 67% loss ⇒ retains 33%

⇒ SP to R = 170 × 33/100 = 56.1

⇒ So 56.1 corresponds to 3927

⇒ 1 corresponds to 3927 / 56.1

⇒ 100 corresponds to (3927 / 56.1) × 100 = 7000

∴ Final Answer = 7000

Additional Information

Successive Change: Multiply factors

Profit: SP = CP × (1 + profit%)

Loss: SP = CP × (1 − loss%)

Shortcut: Combine percentage effects

Shortcut Trick

⇒ Assume CP of 1 kg = 100

⇒ SP at 25% loss = 75

⇒ Let actual weight = x ⇒ CP = 100x

⇒ Gain 70% ⇒ 75 = 1.7 × 100x

⇒ x = 75 / 170 = 0.4412 kg = 441.2 g

∴ Answer = 441.2 g

Alternate Method

Given:

Loss percent = 25%

Gain percent = 70%

Formula Used:

Selling price at loss = Cost price × (1 − loss%)

Gain% = (Actual gain ÷ Cost price) × 100

Calculation:

⇒ Let cost price of 1 kg = 100

⇒ Selling price at 25% loss = 100 × 0.75 = 75

⇒ Let actual weight given = x kg

⇒ Cost of x kg = 100x

⇒ Gain% = [(75 − 100x) ÷ (100x)] × 100

⇒ 70 = [(75 − 100x) ÷ (100x)] × 100

⇒ 0.7 = (75 − 100x) ÷ (100x)

⇒ 70x = 75 − 100x

⇒ 170x = 75

⇒ x = 75 ÷ 170

⇒ x ≈ 0.4412 kg

⇒ In grams = 441.2 g

∴ Final Answer = 441.2 g

Additional Information

False Weight Concept: Profit arises by giving less quantity

Loss Trick: SP reduced but quantity reduced more

Profit Formula: Based on actual cost (100x)

Conversion: 1 kg = 1000 g

The correct answer is Ladakh.

Key Points

• Ladakh is the only Union Territory of India that shares a land border with Afghanistan. This border is located in the Wakhan Corridor region. Hence, statement 2 is correct.
• The length of the border between India and Afghanistan is approximately 106 km, which is the shortest international border India shares with any neighbor. This border is technically known as the Durand Line.
• Rajasthan shares its international border exclusively with Pakistan to its west. It does not have any geographical contact with Afghanistan. Hence, statement 1 is incorrect.
• Prior to the Jammu and Kashmir Reorganization Act, 2019, the undivided state of Jammu and Kashmir shared this border. However, after the reorganization on October 31, 2019, the area bordering Afghanistan (Gilgit-Baltistan) falls under the Union Territory of Ladakh. Hence, statement 3 is incorrect.
• Punjab shares a 547 km long international border with Pakistan (the Radcliffe Line). It is separated from Afghanistan by the territory of Pakistan. Hence, statement 4 is incorrect.

Additional Information

• India's Land Borders: India shares a total land frontier of 15,106.7 km with seven countries. These include Bangladesh (4,096.7 km), China (3,488 km), Pakistan (3,323 km), Nepal (1,751 km), Myanmar (1,643 km), Bhutan (699 km), and Afghanistan (106 km).
• The Durand Line: This line was established in 1893 following an agreement between Sir Mortimer Durand of British India and Amir Abdur Rahman Khan of Afghanistan. It currently serves as the international border between Pakistan and Afghanistan, and a small portion serves as the border between India and Afghanistan.
• Union Territory of Ladakh: Created in 2019, it is the largest Union Territory of India in terms of area. It is a high-altitude cold desert bounded by the Karakoram range in the north and the Himalayas in the south. It shares borders with Pakistan (Line of Control) and China (Line of Actual Control).
• Strategic Significance: The Wakhan Corridor is a narrow strip of territory in northeastern Afghanistan that extends to China and separates Tajikistan from Pakistan and the Gilgit-Baltistan region.

Important Points

• Territorial Claims: Although the border with Afghanistan is currently in Pakistan Occupied Kashmir (POK), the Government of India maintains its sovereign claim over the entire region of Gilgit-Baltistan, which makes Afghanistan a direct neighbor of India in official Indian maps.
• Bordering States/UTs with Pakistan: The states of Gujarat, Rajasthan, and Punjab, along with the Union Territories of Jammu and Kashmir and Ladakh, share borders with Pakistan.
• Longest Border: Bangladesh shares the longest border with India, touching five states: West Bengal, Assam, Meghalaya, Tripura, and Mizoram.
• Establishment of UTs: The Jammu and Kashmir Reorganization Act was passed by the Parliament of India in August 2019, leading to the formation of two separate Union Territories on 31 October 2019.

The logic followed here is based on the alphabetical difference between corresponding letters in each pair:

Option 1: PR – SU

Option 2: MO – PR

Option 3: HJ – KM

Option 4: DF – GJ

Thus, DF – GJ does not follow the same pattern.

Hence, the odd one out is Option 4.

The correct answer is ₹10,000.

Key Points

• The Pradhan Mantri Jan-Dhan Yojana (PMJDY), launched by Prime Minister Narendra Modi on 28^th August 2014, is a National Mission on Financial Inclusion aimed at ensuring access to financial services in an affordable manner.
• One of the primary features of the scheme is the overdraft facility. Initially, the limit was set at ₹5,000, but the Government of India doubled this limit to ₹10,000 in September 2018 to provide better credit access to the underprivileged. Hence, the statement regarding the limit of ₹10,000 is correct.
• The upper age limit for availing of the overdraft facility was also revised from 60 years to 65 years, ensuring that more senior citizens could benefit from this short-term credit function.
• To facilitate ease of use, there are no conditions attached for overdraft amounts up to ₹2,000. For amounts above this, up to the numerical value of ₹10,000, certain eligibility criteria based on account conduct apply.
• The PMJDY accounts are Zero Balance accounts, meaning there is no requirement to maintain a minimum balance, which is a crucial application for low-income earners across the country.

Additional Information

• Insurance Benefits: Every PMJDY account holder is provided with a RuPay Debit Card. For accounts opened after 28^th August 2018, the Accidental Insurance Cover has been increased from ₹1 lakh to ₹2 lakh.
• Direct Benefit Transfer (DBT): The scheme serves as a platform for Direct Benefit Transfer, ensuring that subsidies from various government laws and guidelines reach the beneficiaries directly without any leakages.
• The Six Pillars: The PMJDY is based on six pillars: Universal access to banking services, basic savings accounts with overdraft, Financial Literacy Program, Credit Guarantee Fund, Insurance, and Pension schemes for the unorganized sector.
• Life Cover: A life insurance cover of ₹30,000 is available to eligible beneficiaries who opened their accounts for the first time between August 2014 and January 2015.
• Impact and Data: According to official reports, as of August 2024, the total number of Jan Dhan accounts has crossed the 53 crore mark, with a total deposit balance exceeding ₹2.3 lakh crore, signifying a massive shift in the financial landscape of India.

Important Points

• Eligibility: Any Indian citizen above the age of 10 years can open a PMJDY account. The overdraft facility is generally available after six months of satisfactory operation of the account.
• Micro-Pension: The scheme also links account holders to the Atal Pension Yojana (APY), providing social security through a pension system for the unorganized sector.
• Banking Correspondents: To increase reach in rural locations, the government utilizes Bank Mitras or Banking Correspondents who provide banking services at the doorstep of villagers.
• Digital Transactions: The RuPay card promotes digital payments, aligning with the Digital India initiative and reducing the country's dependency on cash.

Given: Seven boxes A, B, C, D, E, F and G are kept one over the other but not necessarily in the same order.

Only two boxes are kept below A.

Only two boxes are kept between E and A.

F is kept immediately above B.

D is kept above G but below A.

Boxes below C but above B → E, F → 2

Hence, the correct answer is Option 2.

The correct answer is Uniformly accelerated motion.

Key Points

• Uniformly accelerated motion occurs when an object's velocity changes by an equal amount in every equal time interval. In the case of free fall, an object is under the sole influence of gravity, which provides a constant acceleration. Hence, statement 1 is correct.
• Uniform motion refers to a type of motion where an object covers equal distances in equal intervals of time, implying a constant velocity and zero acceleration. Since a falling object speeds up due to gravity, its velocity is not constant. Hence, statement 2 is incorrect.
• Non-uniform motion is a broad category where the velocity of an object changes over time. While free fall involves changing velocity, it is more specifically classified as uniformly accelerated motion because the rate of change (acceleration) remains constant throughout the descent. Hence, statement 3 is incorrect.
• Periodic motion is a motion that repeats itself at regular intervals of time, such as a pendulum or the Earth's orbit around the Sun. Free fall is a unidirectional movement toward the center of a celestial body and does not repeat in cycles naturally. Hence, statement 4 is incorrect.
• The acceleration due to gravity on Earth is approximately 9.8 m/s². This means that for every second an object is in free fall, its downward velocity increases by exactly 9.8 meters per second, assuming air resistance is negligible.

Additional Information

• Concept of Free Fall:
• In Physics, free fall is defined as the motion of a body where gravity is the only force acting upon it. In a strict Newtonian sense, this only occurs in a vacuum where no air resistance or fluid friction exists to oppose the motion.
• Historical experiments by Galileo Galilei in the late 16^th century demonstrated that all objects, regardless of their mass, fall with the same acceleration in the absence of air resistance. This challenged the Aristotelian view that heavier objects fall faster.
• Mathematical Equations:
• The motion of a free-falling object can be described by the three equations of motion. If an object starts from rest (initial velocity u = 0), the final velocity (v) after time (t) is given by v = gt.
• The distance (h) covered during free fall is calculated using the formula h = ½gt². These numerical values help in engineering and ballistics to predict the impact and timing of falling bodies.
• Factors Influencing Motion:
• On Earth, the value of g varies slightly depending on location; it is higher at the poles (approx 9.83 m/s²) and lower at the equator (approx 9.78 m/s²) due to the Earth's rotation and oblate spheroid shape.
• In real-world applications, air resistance eventually balances the force of gravity, leading to terminal velocity, at which point the acceleration becomes zero and the motion becomes uniform.

Important Points

• Weightlessness: An object in free fall experiences a state of apparent weightlessness. This is the principle behind astronauts training in neutral buoyancy tanks or microgravity aircraft (often called the "Vomit Comet").
• Universal Gravitation: Sir Isaac Newton's Law of Universal Gravitation, published in 1687, explains that the force of gravity depends on the mass of the two objects and the distance between their centers. This law governs the free fall of planets in orbit just as it governs a falling apple.
• Vacuum Experiments: Modern NASA facilities, like the Space Power Facility in Ohio, have performed free fall tests using a feather and a bowling ball in a vacuum chamber, proving they fall at the exact same rate when air is removed.

Shortcut Trick

⇒ Let Vijay = V, Ajay = A

⇒ V(1.1)¹⁷ = A(1.1)¹⁸

⇒ V = A × 1.1

⇒ Ratio V : A = 11 : 10

⇒ Total = 21 parts = 1407 ⇒ 1 part = 67

⇒ Ajay = 10 × 67 = 670

∴ Answer = 670

Alternate Method

Given:

Total money = 1407

Rate = 10% p.a.

Vijay time = 17 years

Ajay time = 18 years

Formula:

Amount = P(1 + r/100)ⁿ

Calculations:

⇒ Vijay’s amount = V(1.1)¹⁷

⇒ Ajay’s amount = A(1.1)¹⁸

⇒ Given equal:

⇒ V(1.1)¹⁷ = A(1.1)¹⁸

⇒ V = A(1.1)

⇒ Ratio V : A = 1.1 : 1 = 11 : 10

⇒ Total ratio = 21 parts

⇒ 1 part = 1407 ÷ 21 = 67

⇒ Ajay’s share = 10 × 67 = 670

Final Answer: 670

Additional Information

1. Compound Interest: A = P(1 + r/100)ⁿ

2. Equal Amount Trick: Compare powers to form ratio

3. Ratio Conversion: Decimal ratio → integer ratio

4. Distribution Rule: Total ÷ sum of ratio parts

The correct answer is To promote equal pay for equal work for both men and women.

Key Points

• Article 39 of the Constitution of India contains certain principles of policy to be followed by the State. It is a part of the Directive Principles of State Policy (DPSP), which are mentioned in Part IV.
• Specifically, Article 39(d) mandates that the State shall direct its policy towards securing that there is equal pay for equal work for both men and women. Hence, the statement in the correct option is mentioned in Article 39.
• Other provisions under Article 39 include:
• Article 39(a): Citizens, men and women equally, have the right to an adequate means of livelihood.
• Article 39(b): Ownership and control of the material resources of the community are distributed to subserve the common good.
• Article 39(c): The operation of the economic system does not result in the concentration of wealth and means of production to the common detriment.
• Article 39(e): The health and strength of workers and the tender age of children are not abused.
• Article 39(f): Children are given opportunities and facilities to develop in a healthy manner. This clause was modified by the 42^nd Amendment Act of 1976.
• These principles are fundamental in the governance of the country, and it shall be the duty of the State to apply these principles in making laws.

Additional Information

• Directive Principles of State Policy (DPSP):
• The DPSP are enumerated in Articles 36 to 51 of the Indian Constitution.
• The concept was borrowed from the Irish Constitution of 1937, which had copied it from the Spanish Constitution.
• They are non-justiciable in nature, meaning they are not legally enforceable by the courts for their violation.
• Article 39A (Equal Justice and Free Legal Aid):
• The objective "To ensure equal justice and provide free legal aid" is mentioned in Article 39A, not Article 39. Hence, this statement is incorrect in the context of Article 39.
• This article was added by the 42^nd Constitutional Amendment Act in 1976 to promote justice on the basis of equal opportunity.
• Article 40 (Organisation of Village Panchayats):
• The objective "To organise village panchayats" is mentioned in Article 40. Hence, this statement is incorrect in the context of Article 39.
• It directs the State to endow them with such powers and authority as may be necessary to enable them to function as units of self-government.
• Article 48 (Organisation of Agriculture and Animal Husbandry):
• The objective "To organise agriculture and animal husbandry" is mentioned in Article 48. Hence, this statement is incorrect in the context of Article 39.
• It directs the State to organize these sectors on modern and scientific lines and take steps for preserving and improving the breeds of cattle.

Important Points

• The Supreme Court of India has often relied on Article 39(d) to interpret labor laws and ensure that gender discrimination in wages is eliminated.
• The Equal Remuneration Act, 1976 was enacted by the Parliament to give effect to the constitutional provision of equal pay for equal work.
• The DPSP are classified into three broad categories: Socialistic Principles, Gandhian Principles, and Liberal-Intellectual Principles. Article 39 falls under the Socialistic Principles.
• The Minerva Mills Case (1980) emphasized that the Constitution is founded on the bedrock of the balance between Fundamental Rights and Directive Principles.

The correct answer is 80,000.

Key Points

• According to the Mahāvagga, which is a significant part of the Vinaya Pitaka (one of the three baskets of early Buddhist literature), it is mentioned that the kingdom of Magadha comprised 80,000 villages (gāmas) during the reign of King Bimbisāra.
• King Bimbisāra is recorded to have summoned an assembly of the gāmanis (village headmen) from each of these 80,000 villages to address administrative matters and to encourage them to seek the guidance of the Buddha.
• This large numerical value of 80,000 highlights the vast extent, dense population, and organized administrative structure of the Magadha empire in the 6^th century BCE.
• The mention of such a specific number in Buddhist texts serves to emphasize Bimbisāra's status as a powerful monarch and his deep connection with the Buddhist sangha. Hence, the option stating 80,000 is correct.

Additional Information

• King Bimbisāra: He ruled Magadha from approximately 544 BCE to 492 BCE and was the founder of the Haryanka Dynasty. He was a contemporary of Gautama Buddha and was known for his policy of expansion through conquest and matrimonial alliances.
• Matrimonial Alliances: To strengthen Magadha, Bimbisāra married princesses from powerful neighboring states, including Kosala Devi (sister of King Prasenajit of Kosala), Chellana (a Lichchhavi princess from Vaishali), and Khema (princess of Madra in Punjab).
• The Title 'Seniya': He was the first Indian king to maintain a standing army, which earned him the title of Seniya (one who has an army). This military strength was crucial for his annexation of the kingdom of Anga.
• Capital City: His capital was Girivraja, later known as Rajagriha (modern-day Rajgir in Bihar). The city was strategically fortified by five hills, making it a secure center for the growing Magadhan power.
• Religious Patronage: While Bimbisāra was a great devotee of the Buddha and donated the Veluvana bamboo grove to the Sangha, historical accounts also suggest he showed respect toward Jainism and other contemporary sects.

Important Points

• Rise of Magadha: The kingdom of Magadha became the most powerful Mahajanapada due to its geographical location near iron ore mines and fertile land in the Gangetic plains, which provided agricultural surplus and advanced weaponry.
• Administrative Setup: The Magadhan administration under Bimbisāra was highly efficient. He appointed various officials known as Mahamattas to oversee different functions like executive, judicial, and military affairs.
• Succession: Bimbisāra was eventually succeeded by his son, Ajatashatru, who according to Buddhist and Jain traditions, imprisoned his father to seize the throne. Ajatashatru continued the expansionist policies of his father, further consolidating Magadha's dominance.
• Early Buddhist Texts: The Vinaya Pitaka, from which this data is derived, primarily deals with the rules of conduct for monks but provides invaluable historical data regarding the socio-political conditions of ancient India.

The logic followed here is:

 

thus, "244" will replace the question mark in the given series.

Hence, the correct option is "Option 4".

The logic followed here is based on the alphabetical difference between corresponding letters in each pair:

Option 1: BD – EH

Option 2: LN – OQ

Option 3: JL – MO

Option 4: NP – QS

Thus, BD – EH does not follow the same pattern.

Hence, the odd one out is Option 1.

The logic followed here is:

thus, "36" will replace the question mark in the given series.

Hence, the correct option is "Option 1".

The correct answer is Andaman & Nicobar Islands.

Key Points

• Barren Island is located in the Andaman Sea and is politically part of the Andaman and Nicobar Islands, a Union Territory of India.
• It is famously known as the only active volcano along a chain of volcanoes from Sumatra to Myanmar and is the only active one in the Indian subcontinent and South Asia.
• The island is situated approximately 138 kilometers (86 miles) northeast of the territory's capital, Port Blair.
• As mentioned in the question context, the volcano witnessed two eruptions in the year 2025, continuing its history of frequent activity since the 1991 eruption, which ended a 150-year period of dormancy.
• The island is currently uninhabited by humans, though it supports a small population of feral goats, birds, and crabs that have adapted to the harsh volcanic environment.

Additional Information

• Andaman & Nicobar Islands: This Union Territory consists of 572 islands, of which only about 38 are inhabited. It is divided into three districts: North and Middle Andaman, South Andaman, and Nicobar.
• Geological Setting: The Barren Island volcano is part of the Neogene-Quaternary volcanic arc. It lies near the boundary of the Indian Plate and the Burmese Microplate, a subduction zone that creates significant seismic and volcanic activity.
• Narcondam Island: Another volcanic island in the Andaman Sea, located about 150 km north of Barren Island. Unlike Barren Island, Narcondam is classified as a dormant volcano and is a UNESCO World Heritage site due to its unique biodiversity, including the Narcondam Hornbill.
• Lakshadweep: For contrast, this Union Territory on the western coast of India consists of coral atolls rather than volcanic islands. It is the smallest Union Territory of India by area.
• Other Options: Puducherry and Dadra & Nagar Haveli and Daman & Diu are coastal or land-locked territories on the mainland and do not contain any volcanic formations.

Important Points

• Eruption History: The first recorded eruption of Barren Island occurred in 1787. After several eruptions in the 18^th and 19^th centuries, it remained quiet until 1991. Major recent activities were also recorded in 2005, 2017, and notably in 2025.
• Topography: The volcano reaches an elevation of 354 meters above sea level, but it is actually the summit of a much larger submarine volcano rising from the ocean floor at a depth of nearly 2,250 meters.
• Tourism and Accessibility: Landing on Barren Island is strictly prohibited for security and safety reasons. However, tourists can view the island from chartered boats or seaplanes operated from Port Blair under specific government guidelines.
• Scientific Monitoring: The Geological Survey of India (GSI) and the National Institute of Oceanography (NIO) closely monitor the island's activities to study plate tectonics and volcanology in the Bay of Bengal region.

Given:

ROAD → 9416

DORM → 3691

⇒ M corresponds to 3

Hence, the correct answer is Option 3.

Shortcut Trick

⇒ Total frequency = 120 ⇒ Median position = 120 ÷ 2 = 60^th item

⇒ Cumulative check: till 4 = 45, till 5 = 65

⇒ 60^th item lies in x = 5

∴ Answer = 5

Alternate Method

Given:

Formula:

Median position = N ÷ 2

Calculations:

⇒ Total frequency N = 8 + 10 + 11 + 16 + 20 + 25 + 15 + 9 + 6 = 120

⇒ Median position = 120 ÷ 2 = 60

⇒ 60^th item lies where cf just exceeds 60 ⇒ at x = 5

Final Answer: 5

Additional Information

1. Median: Middle value of ordered data

2. Cumulative Frequency: Running total of frequencies

3. Odd vs Even: For even N, take N/2 position

4. Key Rule: First cf ≥ N/2 gives median value

Given: (Left) T O @ $J$ S € M L I * N G © Y & T P £ Y T (Right)

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

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

(Left) T O @ $ J $ S € M L I * N G © Y & T P £ Y T (Right)

So, Only one symbol satisfies the condition.

Hence, the correct answer is Option 4.

The correct answer is Law of Segregation.

Key Points

• The Law of Segregation, also known as Mendel's First Law, states that during the production of gametes, the two copies of each hereditary factor (alleles) segregate so that offspring acquire one factor from each parent.
• This law explains that in a diploid organism, the two alleles for a specific trait separate during the process of meiosis (specifically Anaphase I), ensuring that each gamete (egg or sperm) carries only one allele for each gene.
• Gregor Mendel formulated this principle after performing monohybrid cross experiments with Pisum sativum (garden pea) plants in the mid-19^th century, specifically around 1865.
• The law is based on the observation that recessive traits, which might be "hidden" in the F1 generation, reappear in the F2 generation in a specific 3:1 phenotypic ratio. Hence, the statement regarding the separation of alleles is explained by the Law of Segregation.
• This principle is fundamental to understanding how genetic diversity is maintained and how traits are passed from one generation to the next without blending.

Additional Information

• Law of Dominance:
• This law states that in a heterozygote, one allele will conceal the presence of another allele for the same characteristic. Rather than both alleles contributing to a phenotype, the dominant allele will be expressed exclusively.
• The recessive allele will remain "latent" but will be transmitted to offspring in the same manner as the dominant allele. The recessive trait will only be expressed by offspring that have two copies of this allele (homozygous recessive).
• Law of Independent Assortment:
• Known as Mendel's Second Law, it states that the alleles of two (or more) different genes get sorted into gametes independently of one another.
• In other words, the allele a gamete receives for one gene does not influence the allele received for another gene. This is typically observed in dihybrid crosses and applies to genes located on different chromosomes.
• This law results in a typical 9:3:3:1 phenotypic ratio in the F2 generation.
• Gregor Mendel:
• Known as the "Father of Genetics", he was an Austrian monk who conducted his famous experiments in the Brno monastery (now in the Czech Republic) between 1856 and 1863.
• He tracked 7 distinct characteristics of pea plants, including seed shape, seed color, flower color, and stem height.

Important Points

• Exceptions to Mendel's Laws:
• Incomplete Dominance: Where the phenotype of the offspring is a blend of the parents (e.g., pink flowers in Mirabilis jalapa from red and white parents).
• Codominance: Where both alleles are expressed equally in the phenotype, such as the ABO blood group system in humans.
• Linkage: Genes that are located very close to each other on the same chromosome tend to be inherited together, which violates the Law of Independent Assortment.
• Genotype vs. Phenotype:
• Genotype refers to the genetic makeup (e.g., Tt), while Phenotype refers to the physical appearance (e.g., Tall).
• A Punnett Square is a common tool used to predict the genotypes and phenotypes of offspring based on the Law of Segregation.

Shortcut Trick

⇒ A:B = 2:3, B:C = 4:5, C:D = 6:7

⇒ Equalize B: LCM(3,4) = 12 ⇒ A:B = 8:12, B:C = 12:15

⇒ Equalize C: LCM(15,6) = 30 ⇒ B:C = 24:30, C:D = 30:35

⇒ Final ratio A:B:C:D = 16:24:30:35

⇒ Total parts = 105 ⇒ 1 part = 7770 ÷ 105 = 74

⇒ A = 16 × 74 = 1184

∴ Answer = 1184

Alternate Method

Given:

A : B = 2 : 3

B : C = 4 : 5

C : D = 6 : 7

Total = 7770

Formula:

Convert chained ratios into a common ratio

Calculations:

⇒ A : B = 2 : 3 ⇒ multiply by 4 ⇒ 8 : 12

⇒ B : C = 4 : 5 ⇒ multiply by 3 ⇒ 12 : 15

⇒ Now A : B : C = 8 : 12 : 15

⇒ C : D = 6 : 7 ⇒ match C = 15 ⇒ multiply by 2 ⇒ 12 : 14

⇒ Adjust all:

⇒ A : B : C = 16 : 24 : 30

⇒ C : D = 30 : 35

⇒ Final ratio A : B : C : D = 16 : 24 : 30 : 35

⇒ Total parts = 16 + 24 + 30 + 35 = 105

⇒ 1 part = 7770 ÷ 105 = 74

⇒ A’s share = 16 × 74 = 1184

Final Answer: 1184

Additional Information

1. Chain Ratio: Match common terms stepwise

2. LCM Trick: Use LCM to equalize middle terms

3. Total Parts: Sum of final ratio

4. Share Formula: (Part ÷ Total parts) × Total amount

The correct answer is Constitutional reforms.

Key Points

• The Moderates (Early Nationalists) dominated the Indian National Congress from its inception in 1885 until 1905. Their primary method was Constitutional reforms, which involved working within the legal framework provided by the British Government to seek gradual changes. Hence, statement 1 is correct.
• The Swadeshi Movement was characteristically adopted by the Extremists (Radicals) following the Partition of Bengal in 1905. It involved the use of indigenous goods and was a shift toward more radical mass mobilization. Hence, statement 2 is incorrect.
• The Promotion of Vedic education was a feature of socio-religious reform movements, most notably the Arya Samaj founded by Dayanand Saraswati in 1875. While it influenced national pride, it was not the characteristic political method of the Moderates. Hence, statement 3 is incorrect.
• The Boycott of foreign goods and institutions became a major political tool during the Anti-Partition Agitation (1905-1908) and was championed by Extremist leaders like Lala Lajpat Rai and Bal Gangadhar Tilak. Hence, statement 4 is incorrect.
• Moderates believed in the British sense of justice and fair play. They utilized the policy of the Three Ps: Petition, Prayer, and Protest to convey their demands to the United Kingdom government.

Additional Information

• Prominent Moderate Leaders:
• Dadabhai Naoroji: Known as the Grand Old Man of India, he was a three-time president of the Indian National Congress and the first Indian to be elected to the British House of Commons in 1892.
• Gopal Krishna Gokhale: He founded the Servants of India Society in 1905 and was considered the political guru of Mahatma Gandhi.
• Womesh Chandra Bonnerjee: He served as the first president of the Indian National Congress during the Bombay session in 1885.
• Surendranath Banerjea: Often called the Indian Burke, he founded the Indian National Association in 1876.
• Economic Critique of Colonialism:
• One of the greatest contributions of the Moderates was the Drain of Wealth theory, primarily formulated by Dadabhai Naoroji in his book "Poverty and Un-British Rule in India".
• They argued that India's poverty was not natural but was a result of the British policy of exporting Indian resources to England without any equivalent return.
• Political Demands:
• They demanded the Indianization of higher grades of administrative services through simultaneous Civil Services Examinations in India and England.
• They sought the expansion and reform of Legislative Councils, leading to the enactment of the Indian Councils Act of 1892.

Important Points

• The Safety Valve Theory: It was suggested by some historians that the Indian National Congress was formed by A.O. Hume in 1885 under Lord Dufferin to provide a "safety valve" for the release of Indian discontent to prevent another revolt like 1857.
• The Shift in 1905: The Moderates' failure to achieve significant concessions from the British and the reactionary policies of Lord Curzon led to the rise of the Extremist faction within the Congress, eventually leading to the Surat Split in 1907.
• Methods of Agitation: While the Moderates used memorandums and resolutions, they avoided mass strikes or passive resistance, fearing that the British would suppress the nascent movement with force.
• Administrative Reforms: They campaigned for the separation of the Judiciary from the Executive and the repeal of the Arms Act of 1878 and the Vernacular Press Act.

Given:

WAND → 1846

GNAW → 4165

⇒ G corresponds to 5

Hence, the correct answer is Option 3.

The correct answer is The Great Bath.

Key Points

• The Harappan cities were generally divided into two or more parts. The part to the West was smaller but higher, known as the Citadel, while the part to the East was larger but lower, called the Lower Town.
• The Great Bath is one of the most remarkable structures found within the Citadel area of Mohenjo-daro, a major city of the Indus Valley Civilization located in present-day Pakistan.
• It was a large rectangular tank in a courtyard surrounded by a corridor on all four sides. The tank was made watertight by using a layer of natural tar (bitumen) and lined with burnt bricks and plaster.
• There were two flights of steps, one on the North and the other on the South, leading into the tank. There were rooms on three sides, in one of which was a large well used to supply water to the bath.
• Scholars suggest that The Great Bath was used for special ritual bathing or religious ceremonies, reflecting the administrative and spiritual importance of the Citadel. Hence, the correct answer is Option 4.

Additional Information

• Absence of Huge Temples: Unlike the contemporary civilizations of Mesopotamia or Egypt, the Harappans did not build huge temples or monumental religious structures. Their religious life is inferred from seals, terracotta figurines (such as the Mother Goddess), and amulets.
• Grand Palaces: While the Citadel likely housed the ruling elite or priest-kings, there is no definitive archaeological evidence of grand palaces similar to those found in later historical periods. The structures in the Citadel were primarily functional and administrative.
• Dwelling Houses: Most of the dwelling houses were located in the Lower Town. These houses were built of baked bricks and usually had a central courtyard with rooms around it. Most houses had a separate bathing area and were connected to the sophisticated drainage system.
• Geographic Extent: The Harappan Civilization flourished during the Bronze Age, roughly between 2600 BCE and 1900 BCE. It spanned across parts of modern-day India (Gujarat, Rajasthan, Haryana, Punjab), Pakistan, and Afghanistan.

Important Points

• Mohenjo-daro: Meaning "Mound of the Dead," it was discovered by R.D. Banerji in 1922. Apart from The Great Bath, it is famous for the Granary (the largest building), the Bronze Dancing Girl statue, and numerous steatite seals.
• Harappa: The first site to be discovered (in 1921 by Daya Ram Sahni), which gave the civilization its name. Notable finds include six granaries in a row and working floors.
• Urban Planning: The civilization is renowned for its grid system of street planning, where roads cut each other at right angles. The use of standardized burnt bricks (ratio 4:2:1) across all sites indicates a high level of centralized authority or cultural uniformity.
• Economic Features: The Harappans practiced advanced agriculture (wheat, barley, cotton) and engaged in overseas trade with Mesopotamia through the port city of Lothal in Gujarat, which featured a man-made brick dockyard.

Given numbers: 194, 582, 419, 149, 825

Here, Third digit of the highest number

Second digit of the lowest number

Original numbers: 194 582 419 149 825

Now,

Resultant: 5 + 4 = 9

Hence, the correct answer is Option 4.

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

D sits to the immediate right of A.

Only three people sit between D and G when counted from the left of D.

Only three people sit between A and F when counted from the right of F.

E sits to the immediate right of B.

So, the people between D and E when counted from the right of D are F, C, G and B = 4 people

Hence, the correct answer is "Option 1".

The correct answer is Ooty is situated at a higher altitude, leading to lower temperatures.

Key Points

• The primary reason for the temperature difference between Ooty and Coimbatore is the Altitude (elevation above sea level). In the troposphere, temperature generally decreases with increasing height, a phenomenon known as the Normal Lapse Rate.
• Ooty, also known as Udhagamandalam, is situated at a high altitude of approximately 2,240 meters (7,350 feet) above sea level in the Nilgiri Hills.
• Coimbatore is located on the plains at an elevation of about 411 meters (1,348 feet). Because it is at a much lower elevation, it experiences higher temperatures than the hill station.
• The Normal Lapse Rate states that for every 1,000 meters of ascent, the temperature drops by about 6.5 degrees Celsius (or 1 degree Celsius for every 165 meters). This vertical temperature gradient explains why Ooty remains cool even during summer. Hence, the statement regarding higher altitude is correct.

Additional Information

• Location and Geography: Both cities are located in the state of Tamil Nadu, India. They are situated at nearly the same latitude (around 11° North), which means they receive a similar amount of solar radiation. However, the mountainous terrain of the Western Ghats creates distinct microclimates.
• The Nilgiri Biosphere Reserve: Ooty is the headquarters of the Nilgiris district. It is a part of the Nilgiri Biosphere Reserve, which was the first biosphere reserve in India established in 1986. The high elevation attracts heavy rainfall during the Southwest Monsoon and Northeast Monsoon.
• Coimbatore's Climate: Coimbatore is often called the Manchester of South India. It is located on the leeward side of the Western Ghats near the Palghat Gap. While the gap allows cool winds to pass through, the low altitude prevents it from having a temperate climate like Ooty.
• Factors Affecting Climate: The climate of a place is determined by Latitude, Altitude, Pressure and Wind system, Distance from the sea (continentality), Ocean currents, and Relief features. In this specific case, Relief (Altitude) is the dominant factor.

Important Points

• Cold Desert Winds: The statement regarding cold desert winds from the north is incorrect. India is protected from the frigid Siberian winds by the Himalayan mountain range. Moreover, South India is too far south to be influenced by northern desert winds.
• Solar Radiation: Since both locations are at the same latitude, the difference in solar radiation is negligible. Therefore, lower solar radiation is not the cause of Ooty's coolness.
• Distance from the Sea: Both Ooty and Coimbatore are inland cities. Ooty is actually further into the mountain ranges than the coastal plains, but its "coolness" is not a result of being "closer to the sea." In fact, proximity to the sea usually moderates temperature (smaller range), whereas high altitude significantly lowers the absolute temperature.
• Environmental Data: During May (peak summer), the average high temperature in Coimbatore can reach 35 degrees Celsius, while in Ooty, it typically stays around 20 to 25 degrees Celsius.