Given Statements:

I. Chirag is taller than Anuj and Bhavesh but shorter than Darshan.

II. Eklavya is taller than Chirag but shorter than Darshan.

Question: Who is the tallest?

Analysis:

From Statement I:

Darshan > Chirag > Anuj, Bhavesh

But Eklavya’s position is unknown, so tallest cannot be decided.

So, Statement I alone is not sufficient.

From Statement II:

Darshan > Eklavya > Chirag

But Anuj and Bhavesh’s positions are unknown, so tallest cannot be decided.

So, Statement II alone is not sufficient.

Combining I and II:

From I: Darshan > Chirag > Anuj, Bhavesh

From II: Darshan > Eklavya > Chirag

So, overall order becomes:

Darshan > Eklavya > Chirag > Anuj, Bhavesh

Now it is clear that Darshan is the tallest.

Hence, both statements I and II together are sufficient, but neither statement alone is sufficient.

Hence, the correct answer is "Option 2".

Shortcut Trick

Add (1) and (2): 3x − 2y = −4

Subtract (2) from (3): 3y + 2z = 3

Use (1): x = 2 + y − z

Solve quickly ⇒ y = −1, z = 3, x = −2

∴ Answer: (−2, −1, 3)

Alternate Method

Given:

x − y + z = 2

2x − y − z = −6

2x + 2y + z = −3

Formula used:

Elimination method

Calculation:

⇒ (1) + (2): x − y + z + 2x − y − z = 2 − 6

⇒ 3x − 2y = −4 ...(4)

⇒ (3) − (2): (2x + 2y + z) − (2x − y − z) = −3 − (−6)

⇒ 3y + 2z = 3 ...(5)

⇒ From (1): x = 2 + y − z

⇒ Substitute in (4): 3(2 + y − z) − 2y = −4

⇒ 6 + 3y − 3z − 2y = −4

⇒ y − 3z = −10 ...(6)

⇒ Solve (5) and (6):

⇒ 3y + 2z = 3

⇒ y − 3z = −10

⇒ From (6): y = 3z − 10

⇒ Substitute: 3(3z − 10) + 2z = 3

⇒ 9z − 30 + 2z = 3

⇒ 11z = 33 ⇒ z = 3

⇒ y = 3(3) − 10 = −1

⇒ x = 2 + (−1) − 3 = −2

∴ The solution is (−2, −1, 3).

Additional Information

Elimination Method

Add or subtract equations to eliminate variables step-by-step

Substitution Method

Express one variable and substitute into others

Consistency

System has a unique solution when equations intersect at one point

Check

Always verify by substituting values back

The correct answer is The combustion of the fuel is incomplete..

Key Points

• The blackening of the exterior of a cooking vessel is a physical indication that the combustion of the fuel is incomplete. When fuel does not burn completely, it produces unburnt carbon particles (soot) that deposit on the surface of the vessel.
• Fuel, such as LPG (Liquefied Petroleum Gas), kerosene, or wood, consists of hydrocarbons. If there is a sufficient supply of oxygen, these hydrocarbons burn completely to produce Carbon Dioxide (CO2) and Water (H2O), resulting in a clean blue flame. Hence, the statement regarding incomplete combustion is correct.
• If the air holes of a gas stove are blocked or restricted, the oxygen supply becomes limited. This leads to a yellow, sooty flame instead of a blue one. Hence, the statement that the fuel is fully burned is incorrect.
• While moisture in the fuel can cause sputtering or difficulty in lighting the stove, it is not the direct cause of the black coating on the vessel. Hence, the statement about fuel containing moisture is incorrect.
• The blackening of the pot is related to the chemical reaction of the fuel with oxygen at the burner and is entirely independent of the state of the food inside the vessel. Hence, the statement that the food is undercooked is incorrect.

Additional Information

• Saturated Hydrocarbons: Compounds like alkanes (e.g., methane, propane, butane) generally burn with a clean blue flame under complete combustion conditions. LPG, which is primarily a mixture of propane and butane, is designed to burn cleanly in household stoves.
• Unsaturated Hydrocarbons: Compounds like alkenes and alkynes (e.g., ethene, ethyne) have a higher carbon-to-hydrogen ratio. They often burn with a yellow sooty flame even in air because the atmospheric oxygen is often insufficient for their complete oxidation.
• Efficiency and Energy: Complete combustion is an exothermic reaction that releases the maximum possible thermal energy from the fuel. Incomplete combustion is less efficient, meaning more fuel is consumed to reach the same cooking temperature.
• Environmental and Health Impact: Incomplete combustion produces Carbon Monoxide (CO), which is a colorless, odorless, and highly toxic gas. It also releases particulate matter (PM), which contributes to indoor air pollution and respiratory issues.
• Maintenance: To fix the issue of a blackened vessel, one should clean the burner holes of the stove to ensure a proper air-fuel mixture. This restores the oxidizing flame (blue) and prevents fuel wastage.

Important Points

• Oxidizing vs. Reducing Flame: A blue flame is also known as an oxidizing flame because it has an excess of oxygen. A yellow flame is a reducing flame where carbon particles are heated to incandescence, giving the flame its characteristic color and producing soot.
• Chemical Equation: The general equation for complete combustion of methane is CH4 + 2O2 → CO2 + 2H2O + Energy. In contrast, incomplete combustion may follow 2CH4 + 3O2 → 2CO + 4H2O or even produce pure Carbon (C).
• Historical Context: Before the widespread use of LPG, cooking was done on chulhas using biomass or coal. These fuels almost always undergo incomplete combustion due to their complex molecular structure and poor aeration, which is why traditional cooking pots are almost always blackened.

The correct answer is Bal Gangadhar Tilak and Muhammad Ali Jinnah.

Key Points

• The Lucknow Pact was an agreement reached between the Indian National Congress (INC) and the All India Muslim League during their joint session held at Lucknow in December 1916.
• Bal Gangadhar Tilak, representing the Extremist faction of the Congress, and Muhammad Ali Jinnah, who was then a member of both the Congress and the Muslim League, were the primary architects of this historic rapprochement. Hence, the pair in Option B is correct.
• The pact was significant because it marked the reunion of the Moderate and Extremist wings of the Indian National Congress, which had split earlier during the Surat Session in 1907.
• Under the agreement, the Congress agreed to the Muslim League’s demand for separate electorates in the provincial councils, while both parties presented a joint set of constitutional demands to the British Government.
• Lala Lajpat Rai and Bipin Chandra Pal were prominent Extremist leaders (part of the Lal-Bal-Pal trio), but they were not the lead negotiators for this specific pact between the two organizations. Hence, Option A is incorrect.
• Gopal Krishna Gokhale, a tall Moderate leader, passed away in 1915, a year before the pact was signed, although Annie Besant played a major role in bringing the factions together through her Home Rule League efforts. Hence, Option C is incorrect.
• Dadabhai Naoroji and Surendranath Banerjee were veteran Moderate leaders of the Congress, but they were not the central figures driving the 1916 negotiations with the Muslim League. Hence, Option D is incorrect.

Additional Information

• President of the Session: The 1916 Lucknow Session of the Indian National Congress was presided over by Ambica Charan Mazumdar, who famously remarked that the split of 1907 had finally been healed.
• Joint Demands: The Congress-League Scheme demanded that the British should declare their intention to confer Self-Government or Dominion Status on India at an early date. They proposed that 80% of the members of Provincial Legislative Councils should be elected.
• Separate Electorates: One of the most debated features of the Lucknow Pact was the formal acceptance of Separate Electorates for Muslims, a system where only Muslim voters could elect Muslim representatives. While this brought temporary unity, many historians argue it sowed the seeds of communalism and the eventual Partition.
• Role of Muhammad Ali Jinnah: At this stage of his career, Jinnah was known as the “Ambassador of Hindu-Muslim Unity,” a title bestowed upon him by Sarojini Naidu for his efforts in bridging the gap between the two communities.
• External Factors: The First World War (1914–1918) and the Khilafat issue (discontent among Indian Muslims over the treatment of the Caliph of Turkey by the British) acted as catalysts in bringing the Muslim League closer to the nationalist movement.

Important Points

• Home Rule Leagues: During 1916, Annie Besant and Bal Gangadhar Tilak had launched their respective Home Rule Leagues. These organizations created a massive political awakening in India, pressuring the Congress leadership to unite and take a firm stand against British rule.
• Constitutional Reforms: The Lucknow Pact directly influenced the Montagu-Chelmsford Reforms of 1919 (also known as the Government of India Act 1919), although the British did not grant the degree of self-government demanded by the Indian leaders.
• Seat Sharing: The pact specified the proportion of Muslim representation in various provinces; for example, in Punjab, they were allotted 50% of the elected seats, and in Bengal, 40%. In the Imperial Legislative Council (Central), one-third of the Indian elected members were to be Muslims.

Given: J, K, L, R, S and T live on six different floors of a building numbered 1 to 6.

Only two people live between R and J.

Only two people live between T and K.

No one lives above T.

J lives below K but above S.

Now, people below L are 3 people.

Hence, the correct answer is "Option 2".

The correct answer is Limestone.

Key Points

• Limestone is a non-metallic mineral because it does not contain any metal elements in its chemical composition. It is primarily composed of calcium carbonate (CaCO3) or the double carbonate of calcium and magnesium.
• Copper is a metallic mineral that belongs to the non-ferrous category. It is a highly ductile and malleable metal used extensively in electrical wiring and electronics.
• Gold is a metallic natural resource classified as a precious metal. It is found in alluvial (placer) deposits or quartz veins and is highly valued for jewelry and investment.
• Iron ore is a metallic mineral and is the primary source of metallic iron. It is categorized as a ferrous mineral because it contains iron. It is the backbone of modern industrial development.

Additional Information

• Classification of Minerals:
• Metallic Minerals: These minerals contain metal in raw form. They are subdivided into Ferrous (containing iron, e.g., Iron Ore, Manganese) and Non-ferrous (not containing iron, e.g., Gold, Copper, Silver).
• Non-metallic Minerals: These do not contain metals. Examples include Limestone, Mica, Gypsum, Coal, and Petroleum.
• Characteristics of Limestone:
• Composition: It is a sedimentary rock composed mainly of skeletal fragments of marine organisms such as coral, forams, and molluscs.
• Uses: It is the essential raw material for the cement industry. It is also used as a flux in smelting iron ore in blast furnaces within the iron and steel industry.
• Global Production: China is the leading producer of limestone globally, followed by the United States and India.
• Metallic Resource Features:
• Copper: Major deposits in India are found in the Balaghat mines in Madhya Pradesh, Khetri mines in Rajasthan, and Singhbhum district of Jharkhand.
• Iron Ore: India is rich in high-grade iron ore. The main types are Magnetite (highest quality with 70% iron content) and Hematite (most important industrial ore).
• Gold: In India, Karnataka is the leading producer, specifically the Kolar Gold Fields (KGF) and Hutti Gold Mines.

Important Points

• Distribution in India: Rajasthan is the largest producer of Limestone in India, contributing approximately 21% of the national output, followed by Madhya Pradesh (11%) and Andhra Pradesh (11%).
• Environmental Impact: Mining of limestone and other minerals is often referred to as a "killer industry" due to the health hazards to miners and the environmental degradation, including deforestation and water pollution.
• Regulatory Framework: In India, the Mines and Minerals (Development and Regulation) Act, 1957 governs the mining sector. Minerals like limestone are classified as major minerals, though some applications are treated as minor minerals under state guidelines.
• Statistical Data: As per the Indian Bureau of Mines (IBM), the total resources of limestone in India are estimated at over 200 billion tonnes, widely distributed across sedimentary basins.

Shortcut Trick

Amount doubles in 6 years ⇒ factor = 2

16 = 2⁴

So 4 doubling periods needed

Total time = 4 × 6 = 24 years

∴ Answer = 24 years

Alternate Method

Given:

Amount doubles in 6 years, compounded annually

Formula used:

A = P(1 + r)^t

Calculation:

⇒ Let rate = r

⇒ After 6 years: 2P = P(1 + r)⁶

⇒ (1 + r)⁶ = 2

⇒ For 16 times:

⇒ 16P = P(1 + r)^t

⇒ (1 + r)^t = 16 = 2⁴

⇒ But (1 + r)⁶ = 2

⇒ ⇒ (1 + r)²⁴ = 2⁴ = 16

⇒ So t = 24 years

∴ The correct answer is 24 years.

Additional Information

Compound Growth

Amount grows exponentially: A = P(1 + r)^t

Doubling Concept

If amount doubles in T years, then 2ⁿ growth takes nT years

Exponential Relation

16 = 2⁴ helps convert problem into doubling cycles

Shortcut Tip

Convert final amount into powers of 2 when doubling is given

Shortcut Trick

l : r = 29 : 20 ⇒ take l = 29k, r = 20k

h = √(29² − 20²)k = 21k

Volume = 2800πk³ = (24192/5)π ⇒ k³ = 216/125 ⇒ k = 6/5

CSA = πrl = π(20k)(29k) = 580πk²

= 580π × (36/25) = (20880/25)π = 835.2π

∴ Answer = 835.2π cm²

Alternate Method

Given:

l : r = 29 : 20, Volume = (24192/5)π cm³

Formula used:

Volume = (1/3)πr²h, CSA = πrl

Calculation:

⇒ Let l = 29k, r = 20k

⇒ h = √(l² − r²) = √(29² − 20²)k = 21k

⇒ Volume = (1/3)π(20k)²(21k)

⇒ = 2800πk³

⇒ 2800πk³ = (24192/5)π

⇒ k³ = 216/125 ⇒ k = 6/5

⇒ CSA = πrl = π(20k)(29k)

⇒ = 580πk²

⇒ = 580π × (36/25)

⇒ = (20880/25)π = 835.2π

∴ The correct answer is 835.2π cm²**.**

Additional Information

Cone Identity

l² = r² + h²

CSA Formula

CSA = πrl

Volume Formula

Volume = (1/3)πr²h

Triplet Use

29, 20, 21 forms a Pythagorean triplet

Shortcut Trick

Total food = Men × Days = 100 × 27 = 2700

Remaining men = 100 − 40 = 60

Days = 2700 ÷ 60 = 45

∴ Answer = 45 days

Alternate Method

Given:

100 men → 27 days, 40 men leave

Formula used:

Total work (food) = Men × Days (constant)

Calculation:

⇒ Total food = 100 × 27 = 2700 man-days

⇒ Remaining men = 100 − 40 = 60

⇒ Required days = 2700 ÷ 60

⇒ = 45 days

∴ The correct answer is 45 days.

Additional Information

Man-Days Concept

Total consumption = men × days remains constant

Inverse Relation

Fewer men ⇒ more days

Formula

Men₁ × Days₁ = Men₂ × Days₂

Quick Tip

Always compute total man-days first

Given: (Left) € A © D R & I % B B V @ A J $ £ * S B £ N L (Right)

Now,

We need symbols which are immediately preceded by a letter AND immediately followed by a symbol.

So, Needed pattern is: Letter - Symbol - Symbol

 (Left) € A © D R & I % B B V @ A J $ £ * S B £ N L (Right)

So, total = 1

Hence, the correct answer is Option 3.

The correct answer is Fluorine.

Key Points

• Fluorine is a chemical element with the symbol F and atomic number 9. It belongs to Group 17 of the periodic table, which is also known as the Halogen group.
• At room temperature (standard condition of 25°C or 298 K), Fluorine exists as a pale yellow, highly toxic diatomic gas (F₂). It is the lightest of all halogens. Hence, the statement regarding Fluorine being a gas is correct.
• Iodine (atomic number 53) also belongs to Group 17, but it is a lustrous, purple-black solid at room temperature due to stronger intermolecular forces. Hence, the statement regarding Iodine being a gas at room temperature is incorrect.
• Bromine (atomic number 35) is the only non-metallic element that is a fuming reddish-brown liquid at room temperature. While it evaporates easily, its primary state is liquid. Hence, the statement regarding Bromine being a gas at room temperature is incorrect.
• Astatine (atomic number 85) is a radioactive member of the halogen group. It is naturally occurring in very small amounts and is a solid at room temperature. Hence, the statement regarding Astatine being a gas at room temperature is incorrect.

Additional Information

• Characteristics of Halogens (Group 17):
• The Halogens consist of five or six chemically related elements: Fluorine, Chlorine, Bromine, Iodine, Astatine, and possibly Tennessine.
• These elements are highly reactive non-metals because they have seven valence electrons and need only one more to achieve a stable noble gas configuration.
• The name "Halogen" comes from Greek words meaning "salt-producing," as they react with metals to form salts like Sodium Chloride (NaCl) and Calcium Fluoride (CaF₂).
• Physical State Trends:
• As we move down Group 17, the atomic radius increases and the melting and boiling points also increase.
• This trend results in different physical states at room temperature: Fluorine and Chlorine are gases, Bromine is a liquid, and Iodine and Astatine are solids.
• The increase in mass leads to stronger London dispersion forces (a type of van der Waals force), requiring more energy to change the state.
• Applications and Uses:
• Fluorine: Used in toothpaste (as sodium fluoride) to prevent dental cavities, in the manufacturing of Teflon (non-stick coating), and in uranium enrichment for nuclear power.
• Chlorine: Widely used as a disinfectant for drinking water and swimming pools, and in the production of PVC plastics.
• Bromine: Used in flame retardants, pesticides, and photography (as silver bromide).
• Iodine: Essential for thyroid gland function in humans; used as an antiseptic (Tincture of Iodine) and in iodized salt.

Important Points

• Electronegativity: Fluorine is the most electronegative element in the entire periodic table with a value of 4.0 on the Pauling scale. This means it has the strongest tendency to attract electrons.
• Reactivity: Due to its high electronegativity and small atomic size, Fluorine is so reactive that it can even react with some noble gases like Xenon and Krypton under specific conditions.
• Coloration: Halogens exhibit distinct colors: Fluorine is pale yellow, Chlorine is greenish-yellow, Bromine is reddish-brown, and Iodine vapor is violet.
• Oxidizing Agents: All halogens act as powerful oxidizing agents, with Fluorine being the strongest among them. Their oxidizing power decreases as you move down the group from Fluorine to Iodine.

Shortcut Trick

Let total voters = N

Votes polled = 90% ⇒ 0.9N

Valid votes = 80% ⇒ 0.72N

Winner margin = (51% − 49%) of valid = 2% of 0.72N

⇒ 0.02 × 0.72N = 3870 ⇒ N = 3870 / 0.0144

⇒ N = 268750

∴ Answer = 268750

Alternate Method

Given:

90% voted, 20% invalid, winner got 51% valid votes, margin = 3870

Formula used:

Margin = Difference% × Valid votes

Calculation:

⇒ Let total voters = N

⇒ Votes polled = 90% of N = 0.9N

⇒ Valid votes = 80% of 0.9N = 0.72N

⇒ Winner margin = (51% − 49%) of valid votes

⇒ = 2% of 0.72N

⇒ = 0.02 × 0.72N = 0.0144N

⇒ 0.0144N = 3870

⇒ N = 3870 ÷ 0.0144

⇒ N = 268750

∴ The correct answer is 268750.

Additional Information

Valid Votes

Valid = Polled − Invalid votes

Margin Concept

Margin = Difference in percentage × total valid votes

Shortcut Tip

Combine percentages stepwise: 90% × 80% = 72%

Key Insight

Use percentage difference (51 − 49) instead of separate calculations

The correct answer is Mumbai.

Key Points

• The 3^rd Council Meeting of the International Organization for Marine Aids to Navigation (IALA) was hosted in Mumbai, India, in February 2025.
• This significant international event was organized by the Directorate General of Lighthouses and Lightships (DGLL), which operates under the Ministry of Ports, Shipping and Waterways (MoPSW).
• The meeting followed the landmark transition of IALA into an Intergovernmental Organization (IGO), a move formalized after the 2020 Paris Convention to enhance global cooperation in maritime safety.
• India is an elected member of the IALA Council for the 2023-2027 period, reflecting the country's strategic importance in the Indian Ocean Region (IOR) and its commitment to international maritime standards.
• The primary focus of the 2025 meeting included digitalization of navigation, implementation of e-Navigation, and ensuring the safety of sea lanes through advanced Aids to Navigation (AtoN).

Additional Information

• IALA (International Association of Marine Aids to Navigation and Lighthouse Authorities):
• Established in 1957, it is headquartered in Saint-Germain-en-Laye, France.
• It brings together marine aids to navigation authorities, manufacturers, and consultants from across the world to harmonize standards for lighthouses, buoys, and Vessel Traffic Services (VTS).
• Directorate General of Lighthouses and Lightships (DGLL):
• It is a statutory body in India with its head office located in Noida, Uttar Pradesh.
• The DGLL manages over 190 lighthouses along the Indian coastline, providing vital visual and radio aids to mariners.
• Marine Aids to Navigation Act, 2021:
• This act replaced the colonial-era Lighthouse Act, 1927, to provide a modern framework for the development and management of vessel traffic services and aids to navigation in India.
• It empowers the Central Government to designate any aid to navigation as a "heritage lighthouse" to promote tourism.
• Maritime India Vision 2030:
• A decade-long blueprint released by the Government of India to overhaul the maritime sector, aiming to develop world-class ports and transform 75 lighthouses into tourism hubs.
• It focuses on the Blue Economy and increasing the cargo handling capacity of Indian ports.

Important Points

• The hosting of the IALA Council Meeting in Mumbai underscores the city's status as the Maritime Capital of India and its pivotal role in international shipping and logistics.
• During the 2025 summit, discussions emphasized the use of Renewable Energy for powering lighthouses, aligning with India's goals under the International Solar Alliance (ISA).
• The Union Minister for Ports, Shipping and Waterways, Shri Sarbananda Sonowal, highlighted that India is transitioning from a "Service Provider" to a "Global Leader" in maritime technology and safety protocols.
• Advancements in Automatic Identification Systems (AIS) and Differential Global Positioning Systems (DGPS) were key technical components discussed to prevent maritime accidents in congested waters.

Shortcut Trick

Let actual SP = 120 (LCM trick)

SP₁ = (5/12)×120 = 50

Loss 20% ⇒ SP₁ = 80% of CP ⇒ CP = 50/0.8 = 62.5

SP₂ = 80% of 120 = 96

Profit % = (96 − 62.5)/62.5 × 100 = 53.6%

∴ Answer = 53.6%

Alternate Method

Given:

Selling at (5/12) of actual SP gives 20% loss

Then selling at 80% of actual SP → find profit %

Formula used:

SP = CP × (1 − loss/100), Profit % = (SP − CP)/CP × 100

Calculation:

⇒ Let actual SP = 120

⇒ First SP = (5/12) × 120 = 50

⇒ 50 = 80% of CP ⇒ 50 = 0.8CP

⇒ CP = 50 / 0.8 = 62.5

⇒ Second SP = 80% of 120 = 96

⇒ Profit = 96 − 62.5 = 33.5

⇒ Profit % = (33.5 / 62.5) × 100

⇒ = 53.6%

∴ The correct answer is 53.6%.

Additional Information

Fraction Trick

Take LCM (12) to eliminate fraction easily

Loss Relation

SP = CP × 0.8 for 20% loss

Profit Formula

Profit % = (Profit / CP) × 100

Key Insight

Find CP first, then compute new profit

Shortcut Trick

SI = (P × R × T) / 100

1080 = (7200 × 6 × T) / 100

⇒ 1080 = 432T

⇒ T = 1080 / 432 = 2.5

∴ Answer = 2.5 years

Alternate Method

Given:

Principal = 7200, SI = 1080, Rate = 6%

Formula used:

SI = (P × R × T) / 100

Calculation:

⇒ 1080 = (7200 × 6 × T) / 100

⇒ 1080 = 432T

⇒ T = 1080 ÷ 432

⇒ T = 2.5 years

∴ The correct answer is 2.5 years.

Additional Information

Simple Interest Formula

SI = (P × R × T) / 100

Rearranged Formula

T = (SI × 100) / (P × R)

Units

Time is in years when rate is per annum

Shortcut Tip

Simplify numbers early to avoid large calculations

Shortcut Trick

sinA = 3/5 ⇒ cosecA = 5/3

Numerator = 11 + 3cosecA = 11 + 5 = 16

Denominator = 4 − 5sinA = 4 − 3 = 1

⇒ √(16/1) = 4

∴ Answer = 4

Alternate Method

Given:

sinA = 3/5

Formula used:

cosecA = 1 / sinA

Calculation:

⇒ cosecA = 5/3

⇒ Substitute in expression:

⇒ √[(11 + 3×5/3) / (4 − 5×3/5)]

⇒ = √[(11 + 5) / (4 − 3)]

⇒ = √(16/1)

⇒ = 4

∴ The correct answer is 4.

Additional Information

Reciprocal Identity

cosecA = 1 / sinA

Substitution Method

Replace trigonometric values directly to simplify

Simplification Tip

Convert fractions early to avoid complexity

Square Root

√16 = 4

Given: (Left) R # L ? V ! M S + N - $ O T * P / < Q U (Right)

Now,

We need symbols which are immediately preceded by a letter and also immediately followed by another symbol.

So, Needed pattern is: Letter - Symbol - Symbol

 (Left) R # L ? V ! M S + N - $ O T * P / < Q U (Right)

So, Total = 2

Hence, the correct answer is Option 3.

Shortcut Trick

Apply BODMAS

(-56) ÷ (-14) = 4

(-3) × 7 = -21

⇒ -9 - 4 - 21 = -34

∴ Answer = -34

Alternate Method

Given:

(-9) - (-56) ÷ (-14) + (-3) × 7

Formula used:

BODMAS rule

Calculation:

⇒ (-56) ÷ (-14) = 4

⇒ (-3) × 7 = -21

⇒ Substitute:

⇒ -9 - 4 + (-21)

⇒ = -9 - 4 - 21

⇒ = -34

∴ The correct answer is -34.

Additional Information

BODMAS Rule

Division and multiplication first, then addition/subtraction

Sign Rules

(− ÷ −) = +, (− × +) = −

Simplification

Always reduce expression step by step

Common Mistake

Ignoring order of operations leads to wrong answer

Family Chart:

Decoding the Symbols:

Given: G + R − W × D ÷ M

It means: G is the daughter of R, R is the mother of W, W is the wife of D, D is the father of M.

 

Here, G is Mother’s sister of M.

Hence, the correct answer is "Option 3".

The logic followed here is:

thus, "248" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

Shortcut Trick

Use weighted average

Total = (25×137 + 26×443 + 21×461)

= 3425 + 11518 + 9681 = 24624

Total members = 25 + 26 + 21 = 72

Average = 24624 ÷ 72 = 342

∴ Answer = 342

Alternate Method

Given:

Group A: 25 members, avg = 137

Group B: 26 members, avg = 443

Group C: 21 members, avg = 461

Formula used:

Overall average = (Σ (number × average)) ÷ total members

Calculation:

⇒ Total A = 25 × 137 = 3425

⇒ Total B = 26 × 443 = 11518

⇒ Total C = 21 × 461 = 9681

⇒ Total amount = 3425 + 11518 + 9681 = 24624

⇒ Total members = 25 + 26 + 21 = 72

⇒ Average = 24624 ÷ 72

⇒ = 342

∴ The correct answer is 342.

Additional Information

Weighted Average

Use when groups have different sizes

Formula

Average = (Σ wx) ÷ Σ w

Shortcut Tip

Multiply average with group size first, then divide by total

Application

Useful in combining multiple group averages

The correct answer is Supplementary wage employment.

Key Points

• The National Food for Work Programme (NFWP) was launched on 14^th November 2004 by the then Prime Minister of India. The primary objective of this scheme is to provide supplementary wage employment to the rural poor who are in need of wage labor and are willing to perform unskilled manual labor.
• This program was specifically targeted at the 150 most backward districts of the country to provide food security through the creation of need-based economic, social, and community assets.
• The scheme is a 100% Centrally Sponsored Scheme, meaning the Union Government provides all funds and resources, including food grains, while the State Governments are responsible for implementation and monitoring.
• Under the program, food grains are provided to the states free of cost. However, the transportation cost, handling charges, and taxes on food grains are the responsibility of the State Government.
• The District Collector is the nodal officer at the district level who has the overall responsibility for planning, implementation, coordination, monitoring, and supervision of the program.

Additional Information

• Transition to MGNREGA: In 2005, the National Food for Work Programme was subsumed into the National Rural Employment Guarantee Act (NREGA), which was later renamed the Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA). This act provides a legal guarantee for 100 days of employment in every financial year to adult members of any rural household.
• Payment Mechanism: Wages under the NFWP were paid partly in food grains and partly in cash. A minimum of 5 kg of food grains per person-day was generally provided, and at least 25% of the wages were to be paid in cash to meet other essential needs.
• Identification of Districts: The 150 districts were identified by the Planning Commission (now NITI Aayog) based on criteria such as agricultural productivity per worker, average wage rate for agricultural laborers, and the concentration of SC/ST populations.
• Focus Areas: The works undertaken under this scheme primarily focused on water conservation, drought proofing (including afforestation and tree plantation), land development, flood control, and rural connectivity (all-weather roads).

Important Points

• Asset Creation: The program aimed not just at temporary relief but at creating durable assets in rural areas to improve the socio-economic infrastructure of backward regions.
• Social Audit: To ensure transparency and prevent corruption, the concept of social audit was encouraged, where the Gram Sabha would monitor the execution of works and the distribution of food grains.
• Eligibility: The scheme was open to all rural poor who were prepared to do unskilled manual work at the minimum wage prescribed by the state. No gender discrimination was allowed, and equal wages were mandated for both men and women.
• Implementation Agency: While the Collector is the nodal head, the works could be executed by Panchayati Raj Institutions (PRIs), Line Departments, or other Government Agencies. No private contractors were allowed to be involved in the execution of the program.

Given Statements:

Some towns are districts.

No district is a state.

No state is a city.

The least possible Venn diagram shows:

Conclusions:

(I) No town is a state

We only know some towns are districts, and districts are not states.

But towns that are not districts may still overlap with states.

So, this conclusion does not necessarily follow.

(II) No district is a city

Districts are separate from states, and states are separate from cities, but there is no direct restriction between districts and cities.

So, districts may or may not overlap with cities.

Hence, this conclusion also does not necessarily follow.

Hence, neither conclusion (I) nor (II) follows.

Hence, the correct answer is "Option 3".

The logic followed here is:

So, 'AEL 27' will replace the question mark in the given series.

Hence, the correct answer is "Option 1".

Shortcut Trick

Apply BODMAS

20 ÷ 4 = 5

3 × 4 = 12

⇒ 16 + 5 − 12 = 9

∴ Answer = 9

Alternate Method

Given:

16 + 20 ÷ 4 − 3 × 4

Formula used:

BODMAS rule

Calculation:

⇒ 20 ÷ 4 = 5

⇒ 3 × 4 = 12

⇒ Substitute:

⇒ 16 + 5 − 12

⇒ = 21 − 12

⇒ = 9

∴ The correct answer is 9.

Additional Information

BODMAS Rule

Division and multiplication first, then addition/subtraction

Order Tip

Solve ÷ and × left to right

Simplification

Reduce step by step for accuracy

Common Error

Ignoring order leads to wrong result

Shortcut Trick

Q → R at 50% loss ⇒ SP = 0.5 × CP

So CP(Q) = 6895 ÷ 0.5 = 13790

P → Q at 40% profit ⇒ SP = 1.4 × CP

So CP(P) = 13790 ÷ 1.4 = 9850

∴ Answer = 9850

Alternate Method

Given:

P sells to Q at 40% profit, Q sells to R at 50% loss, R pays ₹6895

Formula used:

SP = CP × (1 ± percentage/100)

Calculation:

⇒ Let CP of Q = x

⇒ Q sells at 50% loss ⇒ SP = 0.5x

⇒ 0.5x = 6895 ⇒ x = 13790

⇒ This is SP of P

⇒ P sells at 40% profit ⇒ SP = 1.4 × CP

⇒ 1.4 × CP = 13790

⇒ CP = 13790 ÷ 1.4

⇒ CP = 9850

∴ The correct answer is ₹9850.

Additional Information

Loss Concept

50% loss ⇒ SP = 0.5 × CP

Profit Concept

40% profit ⇒ SP = 1.4 × CP

Reverse Calculation

Work backward from final price

Shortcut Tip

Convert percentages into multipliers for faster solving

Given number: 8634157

Logic: Add 1 to each odd digit and subtract 2 from each even digit

Original number: 8 6 3 4 1 5 7

New number: 6 4 4 2 2 6 8

Second from the left = 4

Hence, the correct answer is Option 1.

The correct answer is 7.5.

Key Points

• In MS-Excel, formulas follow a specific Order of Operations, often referred to as BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) or PEMDAS.
• According to the question, the values assigned to the cells are A1 = 2, A2 = 3, and A3 = 2. These are numerical constants entered into the Excel Worksheet.
• The formula provided is =A1*A2 + A2/A3. In this expression, MS-Excel identifies two primary arithmetic operations before the final addition: Multiplication (represented by the asterisk *) and Division (represented by the forward slash /).
• Step 1: The Multiplication operation A1*A2 is performed first. Substituting the values, we get 2 * 3, which equals 6.
• Step 2: The Division operation A2/A3 is performed simultaneously or subsequently based on its position. Substituting the values, we get 3 / 2, which equals 1.5.
• Step 3: Finally, the Addition operation is performed by summing the results of the previous steps. This results in 6 + 1.5, which equals 7.5. Hence, the result of the formula is 7.5 and the statement is correct.

Additional Information

• Arithmetic Operators in Excel: MS-Excel uses standard operators for calculations: + for addition, - for subtraction, * for multiplication, / for division, ^ for exponentiation, and % for percentage. All formulas must start with an Equal Sign (=) to be recognized by the software.
• Operator Precedence: If a formula contains multiple operators, Excel evaluates them in the following order:
• Parentheses (): Anything inside brackets is calculated first.
• Exponentials (^): Powers and roots.
• *Multiplication and Division ( and /)**: Evaluated from left to right.
• Addition and Subtraction (+ and -): Evaluated from left to right.
• Cell Referencing: The formula uses Relative Cell References (A1, A2, A3). If this formula were copied to another cell, the references would shift automatically unless Absolute References (using the $ sign, e.g., $A$1) were used.
• Function vs. Formula: While a Formula is an expression defined by the user (like the one in the question), a Function is a built-in predefined formula in Excel, such as SUM(), AVERAGE(), or PRODUCT().
• Data Types: In MS-Excel 365 or older versions like Excel 2019, the result of a division involving integers can result in a Decimal (Floating point) value, as seen in this example (1.5).

Important Points

• Evaluation Error Prevention: If a cell referenced in the formula (like A3) contained a 0, Excel would return a #DIV/0! error, as division by zero is undefined.
• Displaying Formulas: To view the formula instead of the result (7.5) in the cell, users can press Ctrl + ` (grave accent) or toggle the Show Formulas button in the Formula Auditing group under the Formulas tab.
• Precision: MS-Excel maintains a precision of up to 15 significant digits, ensuring that complex calculations involving multiple divisions and multiplications remain highly accurate for Financial and Scientific data analysis.
• Auto-Update: One of the core features of Excel is that if the value in cell A1 is changed from 2 to 5, the result of the formula will Automatically Recalculate from 7.5 to 16.5 instantly$.

Shortcut Trick

For circles between two common tangents ⇒ radii form a GP

r₁ : r₂ : r₃ : r₄ : r₅ in GP

Given r₁ = 4, r₅ = 9

⇒ r₅ = r₁ × k⁴ ⇒ 9 = 4k⁴

⇒ k⁴ = 9/4 ⇒ k² = 3/2

Middle circle r₃ = r₁ × k²

⇒ r₃ = 4 × (3/2) = 6

∴ Answer = 6

Alternate Method

Given:

5 circles between two common tangents

Smallest radius = 4, Largest radius = 9

Concept Used:

Radii form a geometric progression (GP)

Calculation:

⇒ Let radii = a, ar, ar², ar³, ar⁴

⇒ a = 4, ar⁴ = 9

⇒ 4r⁴ = 9 ⇒ r⁴ = 9/4

⇒ r² = √(9/4) = 3/2

⇒ Middle radius = ar²

⇒ = 4 × (3/2) = 6

∴ The correct answer is 6.

Additional Information

Key Concept

Circles between two common tangents form a geometric progression

GP Formula

Last term = First term × rⁿ⁻¹

Middle Term

For odd number of terms, middle = a × r²

Quick Tip

Find common ratio using first and last term directly

Shortcut Trick

Linear pair at C: 6x + (5x + y) = 180 ⇒ 11x + y = 180

Alternate angles: (5x + y) = (2x + 3y)

⇒ 3x = 2y ⇒ y = 3x/2

Substitute: 11x + 3x/2 = 180 ⇒ 25x/2 = 180 ⇒ x = 14.4

⇒ y = 21.6

∠QCD = 5x + y = 72 + 21.6 = 93.6°

∴ Answer = 93.6°

Alternate Method

Given:

PQ ∥ RS, transversal AB

∠ACQ = 6x, ∠QCD = (5x + y), ∠BDS = (2x + 3y)

Concept used:

Linear pair and alternate interior angles

Calculation:

⇒ At point C: ∠ACQ + ∠QCD = 180°

⇒ 6x + (5x + y) = 180

⇒ 11x + y = 180 ...(1)

⇒ Since lines are parallel:

⇒ ∠QCD = ∠BDS

⇒ 5x + y = 2x + 3y

⇒ 3x = 2y ⇒ y = 3x/2 ...(2)

⇒ Substitute (2) in (1):

⇒ 11x + 3x/2 = 180

⇒ 25x/2 = 180

⇒ x = 14.4

⇒ y = 3x/2 = 21.6

⇒ ∠QCD = 5x + y = 72 + 21.6 = 93.6°

∴ The correct answer is 93.6°.

Additional Information

Linear Pair

Sum of adjacent angles on a line = 180°

Parallel Lines

Alternate interior angles are equal

Strategy

Form equations using angle properties and solve simultaneously

Tip

Always identify angle relations before forming equations

The correct answer is birth.

Key Points

• According to the Citizenship Act, 1955, citizenship by birth is granted to individuals based on their date of birth and location. A person born in India on or after 26 January 1950 but before 1 July 1987 is a citizen of India by birth, irrespective of the nationality of his parents. Hence, the statement is correct.
• This provision reflects the principle of jus soli (right of the soil), where the location of birth is the primary factor for determining citizenship. During this specific period, there were no additional requirements regarding the citizenship status of the parents.
• The Citizenship Act was later amended because this liberal provision was perceived to be prone to misuse, particularly regarding illegal immigration. Consequently, for those born between 1 July 1987 and 3 December 2004, at least one parent must be a citizen of India at the time of the person's birth.
• For persons born in India on or after 3 December 2004, both parents must be citizens of India, or one parent must be a citizen and the other must not be an illegal migrant at the time of birth.
• The Ministry of Home Affairs is the nodal ministry in India responsible for matters related to citizenship and the implementation of the Citizenship Act, 1955.

Additional Information

• Citizenship by Descent:
• A person born outside India on or after 26 January 1950 but before 10 December 1992 is a citizen of India by descent if his father was a citizen of India at the time of his birth.
• From 10 December 1992 onwards, a person born outside India is considered a citizen if either of the parents is a citizen of India at the time of birth.
• Citizenship by Registration:
• The Central Government may, on an application, register any person (not being an illegal migrant) as a citizen of India if they belong to categories such as persons of Indian origin who are ordinarily resident in India for seven years.
• It also applies to persons who are married to citizens of India and are ordinarily resident in India for seven years before making an application.
• Citizenship by Naturalisation:
• A person can acquire Indian citizenship by naturalisation if they have resided in India for a certain period (generally 12 years) and meet specific qualifications mentioned in the Third Schedule of the Act.
• The applicant must have a good character and an adequate knowledge of a language specified in the Eighth Schedule of the Constitution of India.
• Citizenship by Incorporation of Territory:
• If any foreign territory becomes a part of India, the Government of India specifies the persons who among the people of the territory shall be the citizens of India.
• An example is when Pondicherry (now Puducherry) became part of India in 1962, the Government issued the Citizenship (Pondicherry) Order, 1962.

Important Points

• Constitutional Provisions: Articles 5 to 11 under Part II of the Constitution of India deal with citizenship. However, these articles only identified the persons who became citizens of India at the commencement of the Constitution on 26 January 1950.
• Single Citizenship: Unlike the USA, where there is dual citizenship (National and State), India provides for Single Citizenship. This concept was borrowed from the British Constitution to promote fraternity and unity among the citizens.
• Termination of Citizenship: The Citizenship Act, 1955 prescribes three ways of losing citizenship: Renunciation (voluntary giving up), Termination (when a citizen voluntarily acquires citizenship of another country), and Deprivation (compulsory termination by the Central Government based on fraud or disloyalty).
• OCI Scheme: The Overseas Citizenship of India (OCI) scheme was introduced by amending the Citizenship Act, 1955 in August 2005 to provide certain rights to the Indian Diaspora, though it does not amount to dual citizenship as OCI holders do not have voting rights.

The correct answer is 1934–35.

Key Points

• The Ranji Trophy is India's premier domestic first-class cricket championship, and it was first held in the year 1934–35.
• The first match of the tournament was played on 4 November 1934 between Madras and Mysore at the Chepauk ground in Madras (now Chennai).
• The competition is named after Kumar Shri Ranjitsinhji, the Jam Sahib of Nawanagar, who was the first Indian to play international cricket for England and Sussex.
• The trophy itself was donated by Maharaja Bhupinder Singh of Patiala in memory of Ranjitsinhji, who passed away in 1933.
• The first-ever winner of the Ranji Trophy was Bombay (now Mumbai), who defeated North India in the final match of the 1934–35 season.

Additional Information

• Governance and Format:
• The tournament is organized annually by the Board of Control for Cricket in India (BCCI).
• It follows a round-robin and knockout format, where various regional and state cricket associations compete for the title.
• Currently, the tournament features 38 teams representing different states of India and regional cricket bodies.
• Mumbai’s Dominance:
• The Mumbai cricket team is the most successful team in the history of the Ranji Trophy, having won a record 42 titles as of the 2023–24 season.
• They also hold the record for the most consecutive wins, securing 15 titles in a row from 1958–59 to 1972–73.
• Significance in Indian Cricket:
• The Ranji Trophy serves as the primary breeding ground for selecting players for the Indian National Cricket Team.
• Performances in this first-class format are highly valued by national selectors to gauge a player's temperament and skill for Test cricket.
• Recent Developments:
• In 2020, for the first time since its inception, the Ranji Trophy was cancelled for the 2020–21 season due to the COVID-19 pandemic.
• The 2023–24 edition was won by Mumbai, who defeated Vidarbha in the final to reclaim the championship.

Important Points

• Ranjitsinhji (The Namesake): Although the premier domestic tournament is named after him, Ranjitsinhji never actually played for an Indian team in India; he played his major cricket in England between 1896 and 1902.
• Individual Records:
• The record for the most runs in Ranji Trophy history is held by Wasim Jaffer, who scored over 12,000 runs.
• The record for the most wickets is held by Rajinder Goel, who took 637 wickets during his career, despite never playing for the Indian national team.
• Eligibility: Players are eligible to represent their respective states or associations based on their birthplace or through specific BCCI guidelines regarding residency and professional registration.

The correct answer is Paris Agreement.

Key Points

• The Paris Agreement is a legally binding international treaty on climate change. It was adopted by 196 Parties at the UN Climate Change Conference (COP21) in Paris, France, on 12 December 2015.
• Its primary goal is to limit global warming to well below 2 degrees Celsius, preferably to 1.5 degrees Celsius, compared to pre-industrial levels.
• India reaffirmed its commitment to the Paris Agreement during the 2025 climate summit, highlighting its progress toward Nationally Determined Contributions (NDCs).
• India has committed to achieving Net Zero emissions by the year 2070, a target first announced at COP26 in Glasgow.
• The agreement operates on a 5-year cycle of increasingly ambitious climate action carried out by countries. India updated its NDCs in 2022, aiming to reduce the emissions intensity of its GDP by 45 percent by 2030.

Additional Information

• Kyoto Protocol:
• Adopted in 1997 and entered into force in 2005, it was the first international agreement to set binding targets for greenhouse gas emissions.
• It primarily placed a heavier burden on developed nations under the principle of "common but differentiated responsibilities."
• Montreal Protocol:
• Signed in 1987, it is a landmark agreement designed to protect the Ozone Layer by phasing out the production of substances like Chlorofluorocarbons (CFCs).
• It is considered one of the most successful environmental treaties, with universal ratification by all 198 UN Member States.
• Basel Convention:
• Adopted in 1989, this treaty regulates the transboundary movements of hazardous wastes and their disposal.
• It aims to protect human health and the environment against the adverse effects resulting from the generation and management of hazardous and other wastes.
• International Solar Alliance (ISA):
• Launched by India and France in 2015, the ISA is an action-oriented platform to increase the deployment of solar energy technologies.
• It targets "Sunshine Countries" located between the Tropic of Cancer and the Tropic of Capricorn to reduce dependence on fossil fuels.

Important Points

• Panchamrit Targets: India’s five-fold strategy includes reaching 500 GW of non-fossil energy capacity and meeting 50 percent of its energy requirements from renewable energy by 2030.
• LiFE Movement: The Lifestyle for Environment initiative was introduced by the Indian Prime Minister to promote sustainable consumption and production.
• Global Stocktake: Under the Paris Agreement, the Global Stocktake happens every five years to assess the collective progress toward meeting the agreement's long-term goals.

The correct answer is Bharatiya Vayuyan Adhiniyam, 2024.

Key Points

• The Bharatiya Vayuyan Adhiniyam, 2024 was introduced in the Lok Sabha to replace the Aircraft Act of 1934, which was a 90-year-old colonial-era legislation. The primary objective is to provide a modern legal framework for the design, manufacture, possession, use, operation, sale, import, and export of aircraft in India.
• The Act aims to empower the Central Government to make rules for the regulation and control of all aviation-related activities, ensuring they align with international standards set by the International Civil Aviation Organization (ICAO).
• One of the most significant features of this legislation is the formal statutory status given to existing regulatory bodies, namely the Directorate General of Civil Aviation (DGCA), the Bureau of Civil Aviation Security (BCAS), and the Aircraft Accident Investigation Bureau (AAIB).
• It introduces provisions for Ease of Doing Business by simplifying the licensing and certification processes, which is expected to boost the Make in India initiative in the aviation manufacturing sector.
• The scope of the Act has been expanded to include unmanned aircraft systems (drones) and advanced air mobility, addressing the technological advancements that were not envisioned in the 1934 Act.

Additional Information

• The Carriage by Air (Amendment) Act, 2022: This legislation primarily deals with the liability of air carriers and the compensation paid to passengers in case of accidents, delays, or loss of baggage. It is based on the Montreal Convention and does not focus on the administrative re-enactment of the 1934 Act.
• Protection of Interests in Aircraft Objects Act, 2023: This Act was designed to implement the Cape Town Convention and Protocol, which provides a legal framework for financing and leasing of aircraft engines and airframes. It protects the rights of lessors and financiers but is specific to financial interests rather than general aviation regulation.
• Aircraft (Security) Rules, 2020 & Amendments (2022): These rules are secondary legislations (subordinate legislation) framed under the Aircraft Act, 1934. They focus specifically on anti-hijacking measures, ground security, and airport protection. While they modernize security protocols, they do not replace the parent Act.
• Regulatory Landscape in India: The Ministry of Civil Aviation (MoCA) is the nodal ministry responsible for the formulation of national policies and programs for the development and regulation of civil aviation. The Bharatiya Vayuyan Adhiniyam, 2024 is a major step in the National Civil Aviation Policy (NCAP) 2016 vision to make India the third-largest civil aviation market globally.

Important Points

• Decriminalization and Penalties: The Bharatiya Vayuyan Adhiniyam, 2024 seeks to rationalize penalties. It shifts several minor offenses from criminal imprisonment to monetary fines and administrative penalties, which reduces the burden on the judiciary and improves the operational environment for airlines.
• Radio-telegraphy and Licensing: Unlike the 1934 Act, the new law modernizes the requirements for radio-telegraphy apparatus on aircraft and simplifies the process for issuing pilot licenses and certificate of airworthiness.
• Sovereignty and Safety: The Act reaffirms India's sovereignty over its airspace and grants the government emergency powers to prohibit or regulate flight activities in the interest of national security or public safety.
• Historical Context: The Aircraft Act, 1934 was enacted during the British Raj. While it was amended several times (most recently in 2020), it was found inadequate to handle the complexities of a $170 billion aviation industry that India is projected to become$.

The correct answer is 1 and 3 only.

Key Points

• Article 167 of the Constitution of India defines the duties of the Chief Minister regarding the furnishing of information to the Governor. It states that the Chief Minister must communicate all decisions of the Council of Ministers relating to state administration and legislative proposals to the Governor. Hence, statement 1 is correct.
• Article 165 is specifically related to the appointment and duties of the Advocate-General for the State. The provision where the Governor administers the oaths of office and secrecy to the Ministers is actually contained in Article 164(3). Hence, statement 2 is incorrect.
• Article 163 provides for a Council of Ministers with the Chief Minister at the head to aid and advise the Governor in the exercise of his functions. This article also mentions that this advice is not required in matters where the Governor is mandated to act in his discretion. Hence, statement 3 is correct.
• The Chief Minister acts as the sole link of communication between the Governor and the State Council of Ministers, ensuring that the Constitutional Head is kept informed of all executive actions.

Additional Information

• Article 164 (Other Provisions as to Ministers):
• The Chief Minister is appointed by the Governor, and other Ministers are appointed by the Governor on the Chief Minister's advice.
• The Council of Ministers is collectively responsible to the Legislative Assembly of the State, reflecting the parliamentary form of government.
• The total number of Ministers, including the Chief Minister, in a State shall not exceed 15% of the total strength of the Legislative Assembly, as per the 91^st Constitutional Amendment Act, 2003.
• Article 166 (Conduct of Business):
• All executive actions of the Government of a State shall be expressed to be taken in the name of the Governor.
• The Governor makes rules for the more convenient transaction of the business of the Government of the State.
• The State Executive:
• The State Executive consists of the Governor, the Chief Minister, the Council of Ministers, and the Advocate-General of the State.
• While the Governor is the nominal executive authority (de jure head), the Chief Minister is the real executive authority (de facto head).

Important Points

• Advocate-General (Article 165): He is the highest law officer in the state. To be appointed, a person must be qualified to be a Judge of a High Court. He holds office during the pleasure of the Governor.
• Discretionary Power: If any question arises whether a matter falls within the Governor's discretion or not, the decision of the Governor is final, and the validity of anything done by him cannot be called into question.
• Oath and Secrecy: According to Article 164, the Governor administers the oath of office and oath of secrecy to every minister according to the forms set out in the Third Schedule of the Constitution.
• Membership Requirement: A Minister who is not a member of the State Legislature for any period of six consecutive months shall cease to be a Minister at the expiration of that period.

Shortcut Trick

Take base: Buy 10 get 2 free ⇒ 12 kits

Total MRP = 12 × 12000 = 144000

Pay only for 10 ⇒ 120000

Apply discounts:

⇒ 15% discount ⇒ 120000 × 0.85 = 102000

⇒ Additional 5% ⇒ 102000 × 0.95 = 96900

Effective discount:

⇒ Discount = 144000 − 96900 = 47100

⇒ % = (47100 / 144000) × 100 ≈ 32.71%

∴ Answer = 32.71%

Alternate Method

Given:

Price per kit = ₹12000

Offer: Buy 10 get 2 free

Volume discount = 15%

Institutional discount = 5%

Formula used:

Effective Discount % = (Total discount ÷ Total MRP) × 100

Calculation:

⇒ Total kits received = 12

⇒ Total MRP = 12 × 12000 = 144000

⇒ Cost for 10 kits = 120000

⇒ After 15% discount = 120000 × 85/100 = 102000

⇒ After 5% discount = 102000 × 95/100 = 96900

⇒ Total discount = 144000 − 96900 = 47100

⇒ Discount % = (47100 ÷ 144000) × 100

⇒ = 32.71%

∴ The correct answer is 32.71%.

Additional Information

Successive Discount

Net factor = (1 − d₁)(1 − d₂)

Free Item Concept

Buy X get Y free ⇒ effective price reduces

Quick Tip

Always compare final payment with total MRP

Shortcut Trick

Let A : B = 5x : 7x

C joins after 4 months with (7x/2)

A = 5x×8 + 3x×4 = 52x

B = 7x×12 = 84x

C = (7x/2)×8 = 28x

Ratio = 52 : 84 : 28 = 13 : 21 : 7

B’s share = (21/41) × 27675 = 14175

∴ Answer = ₹14175

Alternate Method

Given:

A : B = 5 : 7, C joins after 4 months

Profit Ratio:

52 : 84 : 28 = 13 : 21 : 7

Total Ratio = 41

B’s Share:

= (21/41) × 27675 = 14175

∴ The correct answer is ₹14175.

Given: # : MIN :: RNS : %

Option 1) # = OKP , % = PLQ

For # (OKP) to MIN

For % (PLQ) to RNS

Since, both transformations follow a consistent shift pattern, Option 1 is correct.

Option 2) # = OKP , % = PLR

For # (OKP) to MIN

For % (PLR) to RNS

Since, the patterns do not match, Option 2 is incorrect.

Option 3) # = OKO , % = PLQ

For # (OKO) to MIN

For % (PLQ) to RNS

Since, the patterns do not match, Option 3 is incorrect.

Option 4) # = OKP , % = PMQ

For # (OKP) to MIN

For % (PMQ) to RNS

Since, the patterns do not match, Option 4 is incorrect.

Hence, the correct answer is "Option 1".

The correct answer is Bakshi Jagabandhu.

Key Points

• Bakshi Jagabandhu, whose full name was Bakshi Jagabandhu Bidyadhar Mohapatra Bhramarbar Raya, was the legendary leader of the Paika Rebellion of 1817. He was the Buxi (military chief) of the Raja of Khurda. Hence, the option containing Bakshi Jagabandhu is the correct statement.
• The rebellion was an armed uprising against the British East India Company's rule in Odisha. It is often referred to as the "First War of Independence" by some historians and the Odisha government.
• The Paikas were the traditional landed militia of Odisha who enjoyed rent-free land (Paikan lands) in return for their military service to the Kingdom of Khurda.
• The rebellion was triggered in March 1817 when the British policies led to the takeover of Paikan lands, the introduction of a new currency system, and the heavy Salt Tax, which made life difficult for the local population.
• Under Bakshi Jagabandhu's leadership, the rebels attacked British symbols of authority, such as police stations and treasuries in Banapur and Khurda. The revolt quickly spread to other regions like Puri, Pipili, and Cuttack.
• Despite the bravery of the Paikas, the rebellion was eventually suppressed by the British forces by 1818. However, Bakshi Jagabandhu remained at large and continued guerrilla warfare until he surrendered in 1825. He died in 1829 while in custody at Cuttack.

Additional Information

• Chittu Singh: He was a prominent leader of the Ramosi Rebellion. The Ramosis, who served in the lower ranks of the Maratha army, revolted in 1822 in Satara, Maharashtra, against British rule and heavy land revenue assessments. Hence, statement A is incorrect.
• Alluri Sitarama Raju: He was a revolutionary who led the Rampa Rebellion of 1922 in the Godavari agency of Andhra Pradesh. He fought against the British Madras Forest Act of 1882, which restricted the free movement of tribal people in forests. He is celebrated as "Manyam Veerudu" (Hero of the Jungles). Hence, statement B is incorrect.
• Sidhu Murmu: Along with his brother Kanhu Murmu, he led the Santhal Rebellion (also known as the Santhal Hool) in 1855-56. This rebellion took place in the Rajmahal Hills (modern-day Jharkhand) against the oppressive Zamindari system and British colonial policies. Hence, statement D is incorrect.

Important Points

• The British East India Company conquered Odisha in 1803 after defeating the Marathas in the Second Anglo-Maratha War. This conquest led to the dethroning of the Raja of Khurda, which sowed the seeds of discontent.
• One of the major economic causes was the abolition of the Cowrie currency (shells) and the demand for taxes in Silver, which the peasants found nearly impossible to acquire.
• The Paika Rebellion is significant because it was a unified struggle involving tribal communities (like the Konds), the Paika militia, and local Zamindars against foreign rule.
• In 2017, the Government of India released a commemorative coin and a stamp to mark the 200^th anniversary of this historic uprising.

The correct answer is Goa and Tripura.

Key Points

• According to the Census 2011, the literacy rate of Goa is 88.70%, and the literacy rate of Tripura is 87.22%. Both these states have literacy levels significantly above the 80% mark. Hence, option D is correct.
• In Option A, while Himachal Pradesh recorded a literacy rate of 82.80%, Haryana stood at 75.55%. Since Haryana is below the threshold, this pair does not satisfy the condition. Hence, statement A is incorrect.
• In Option B, Tamil Nadu barely crossed the threshold with 80.09%, but Assam had a literacy rate of 72.19%. Hence, statement B is incorrect.
• In Option C, Sikkim recorded a literacy rate of 81.42%, which is above 80%, but Odisha recorded 72.87%. Hence, statement C is incorrect.
• The Census 2011 data revealed that several States and Union Territories (UTs) like Kerala, Lakshadweep, Mizoram, Goa, and Tripura maintained high literacy standards, contributing to the overall national average.

Additional Information

• Definition of Literacy Rate: As per the Census of India, a person aged 7 years and above who can both read and write with understanding in any language is considered literate. The formula used is (Number of Literate Persons / Population aged 7 and above) multiplied by 100.
• Top Performing States: Kerala retains the top position with a 94.00% literacy rate, followed by the Union Territory of Lakshadweep at 91.85%. Mizoram ranks third with 91.33%. These regions have consistently implemented educational reforms and social awareness campaigns.
• States at the Bottom: Bihar recorded the lowest literacy rate in the country at 61.80%, followed by Arunachal Pradesh at 65.38% and Rajasthan at 66.11% during the 2011 survey.
• Gender Disparity: The Census 2011 highlighted a gap between male and female literacy. The male literacy rate was 80.89%, while the female literacy rate was 64.64%. Reducing this numerical value gap has been a primary goal of government laws like the Right to Education Act (2009).
• National Average: The overall literacy rate in India according to the Census 2011 was 73.00%. This showed a significant increase from the 2001 Census, which was 64.83%.

Important Points

• Administrative Features: The Registrar General and Census Commissioner of India, under the Ministry of Home Affairs, is responsible for conducting the decennial Census. The 2011 Census was the 15^th National Census of the country since 1872.
• Literacy in Union Territories: Among UTs, Lakshadweep has the highest literacy (91.85%), while Dadra and Nagar Haveli had the lowest at 76.24% in 2011. High literacy in islands and small states is often attributed to smaller population sizes and localized government focus.
• Socio-Economic Impact: Higher literacy rates in states like Goa and Tripura correlate with better Human Development Index (HDI) rankings, improved healthcare functions, and higher employment applications in the service sector.
• Future Trends: While the official 2021 Census was delayed, reports from the National Statistical Office (NSO) suggest that India's literacy rate has improved further, reaching approximately 77.7% in 2017-18.

The correct answer is Up to three years.

Key Points

• Article 356 of the Constitution of India provides for the imposition of President’s Rule in a state if there is a failure of constitutional machinery. This is also popularly known as a State Emergency or Constitutional Emergency.
• A proclamation imposing President’s Rule must be approved by both Houses of Parliament (the Lok Sabha and the Rajya Sabha) within two months from the date of its issue. This approval is done through a simple majority.
• Once approved by the Parliament, the President’s Rule continues for six months. It can be extended for a maximum period of three years with the approval of the Parliament every six months.
• However, the 44^th Amendment Act of 1978 introduced a constraint: the President's Rule cannot be extended beyond one year unless a Proclamation of National Emergency is in operation in the whole of India or in the whole or any part of the state, or the Election Commission certifies that there are difficulties in holding general elections to the Legislative Assembly of the state concerned.
• The ultimate maximum limit for the President's Rule in a state remains three years, after which the constitutional machinery must be restored through fresh elections.

Additional Information

• Grounds of Imposition: President's Rule can be proclaimed under two circumstances. First, under Article 356, if the President is satisfied (based on a report from the Governor of the state or otherwise) that the state government cannot be carried on in accordance with the Constitution. Second, under Article 365, if a state fails to comply with or give effect to any direction from the Union.
• Consequences: Upon the imposition of President's Rule, the President dismisses the State Council of Ministers headed by the Chief Minister. The Governor, on behalf of the President, carries on the state administration with the help of the Chief Secretary or advisors appointed by the President.
• Legislative Powers: The Parliament exercises the power of the State Legislature. Any law made by the Parliament (or the President) during this period continues to be operative even after the President's Rule is revoked, until repealed or amended by the State Legislature.
• Judicial Review: In the landmark S.R. Bommai case (1994), the Supreme Court of India held that the President’s proclamation under Article 356 is subject to judicial review. The court can strike down the proclamation if it is found to be mala fide or based on irrelevant grounds.
• Historical Context: President's Rule was first imposed in the state of Punjab in the year 1951. Since then, it has been invoked more than 100 times across various states in India.

Important Points

• Revocation: A proclamation of President’s Rule can be revoked by the President at any time by a subsequent proclamation. Such a revocation does not require parliamentary approval.
• Status of State Assembly: During the President's Rule, the State Legislative Assembly is either suspended or dissolved by the President. If suspended, it can be reactivated once the rule is lifted; if dissolved, fresh elections must be held.
• Article 352 vs Article 356: While a National Emergency (Article 352) affects the relationship of the Union with all states and continues the state government and legislature, President's Rule (Article 356) specifically targets one state and results in the suspension/dissolution of the state's executive and legislative powers.
• Financial Impact: Unlike a Financial Emergency (Article 360), President’s Rule does not inherently allow the Union to reduce the salaries of state employees, though the Parliament takes over the passage of the State Budget.

The correct answer is 2000.

Key Points

• The Pradhan Mantri Gram Sadak Yojana (PMGSY) was launched on 25^th December 2000. This nationwide plan aims to provide good all-weather road connectivity to unconnected villages.
• It was initiated by the then Prime Minister of India, Atal Bihari Vajpayee, under the Ministry of Rural Development.
• The primary objective is to provide single all-weather road connectivity to eligible unconnected habitations in the rural areas with a population of 500 persons and above in plain areas.
• For Hill States (North-East, Sikkim, Himachal Pradesh, Jammu & Kashmir, Uttarakhand), the Desert Areas, and Tribal (Schedule V) areas, the objective is to connect habitations with a population of 250 persons and above.
• The scheme is a Centrally Sponsored Scheme. Initially, it was 100% funded by the Central Government, but since 2015-16, the funding is shared between the Centre and States.

Additional Information

• Phases of PMGSY:
• PMGSY-I: Launched in 2000 to provide basic connectivity to high-population habitations.
• PMGSY-II: Launched in May 2013, it focused on the consolidation of the existing 50,000 km Rural Road Network to improve its efficiency as a provider of transportation services.
• PMGSY-III: Approved by the Cabinet in July 2019, it involves the consolidation of 1,25,000 km through routes and Major Rural Links that connect habitations to Gramin Agricultural Markets (GrAMs), Higher Secondary Schools, and Hospitals.
• Funding Pattern:
• For most states, the fund sharing ratio is 60:40 between the Central Government and the State Government.
• For 8 North-Eastern states and 3 Himalayan states (Jammu & Kashmir, Himachal Pradesh, Uttarakhand), the ratio is 90:10.
• Digital Governance:
• The OMMAS (Online Management, Monitoring and Accounting System) geographic information system was developed to identify targets and monitor progress.
• The Meri Sadak mobile app was launched in 2015 to enable citizens to register complaints regarding the quality and pace of work of PMGSY roads.

Important Points

• RCPLWEA: The Road Connectivity Project for Left Wing Extremism Affected Areas was launched in 2016 as a separate vertical under PMGSY to provide all-weather road connectivity in 44 districts across 9 states affected by LWE.
• Green Technologies: PMGSY promotes the use of "Green Technologies" and non-conventional materials like Waste Plastic, Cold Mix Technology, Fly Ash, and Geo-textiles in road construction to reduce the carbon footprint.
• Quality Control: A three-tier quality control mechanism is in place to ensure the durability of the roads. Tier 1 is at the Program Implementation Unit level, Tier 2 involves independent State Quality Monitors (SQM), and Tier 3 involves independent National Quality Monitors (NQM).
• Impact: As of recent data, over 7,00,000 km of road length has been completed under various interventions of the scheme, significantly improving rural socio-economic development.

The correct answer is A program that manages memory, processes, and devices.

Key Points

• An Operating System (OS) is a system software that acts as an intermediary or interface between a computer user and the computer hardware.
• Its primary function is to manage hardware resources like the Central Processing Unit (CPU), Main Memory (RAM), Storage, and Input/Output (I/O) devices.
• Statement 1: A program used to access the internet refers to a Web Browser, such as Google Chrome or Mozilla Firefox. Hence, statement 1 is incorrect.
• Statement 2: A program used to watch videos is classified as Application Software or a Media Player, such as VLC Media Player. Hence, statement 2 is incorrect.
• Statement 3: An OS performs Memory Management, Processor Management, and Device Management to ensure the system runs smoothly. Hence, statement 3 is correct.
• Statement 4: A program used for data entry is typically a spreadsheet or database application like Microsoft Excel. Hence, statement 4 is incorrect.

Additional Information

• Functions of an Operating System:
• Process Management: It handles the creation, deletion, and scheduling of various processes or tasks.
• Memory Management: It allocates and de-allocates memory space (RAM) as needed by different applications.
• File Management: It manages directories and files for efficient storage and retrieval on Hard Disk Drives (HDD) or Solid State Drives (SSD).
• Security: It provides data security and prevents unauthorized access to the system through passwords and encryption.
• Types of Operating Systems:
• Batch OS: Users do not interact directly with the computer; jobs are processed in batches.
• Real-Time OS (RTOS): Used in environments where time constraints are very strict, such as missile systems or air traffic control.
• Distributed OS: Uses multiple central processors to serve multiple real-time applications and users.
• Mobile OS: Specifically designed for smartphones and tablets, such as Android (developed by Google) and iOS (developed by Apple).
• Common Examples:
• Microsoft Windows: Introduced in 1985, it is the most widely used GUI-based OS for personal computers.
• Linux: An open-source OS created by Linus Torvalds in 1991, known for its stability and security in servers.
• macOS: A proprietary OS developed by Apple Inc. for Macintosh computers.

Important Points

• The Kernel is the core component of an operating system that manages operations of the computer and hardware.
• Booting is the initial set of operations that a computer system performs when electrical power is switched on, loading the OS from secondary storage into the main memory.
• An OS can provide a Command Line Interface (CLI), where users type text commands, or a Graphical User Interface (GUI), which uses windows, icons, and menus.
• The first operating system, GM-NAA I/O, was produced in 1956 by General Motors for the IBM 704 mainframe computer.

Given: (Left) K Y C K & A A C P N P Y M R B # + J $ & ^ (Right)

Now,

We need symbols which are immediately preceded by a symbol and also immediately followed by a letter.

So, Needed pattern is: Symbol - Symbol - Letter

(Left) K Y C K & A A C P N P Y M R B # + J $ & ^ (Right)

Here, total = 1

Hence, the correct answer is Option 3.

Shortcut Trick

Relative speed = 130 + 70 = 200 km/hr

= 200 × (5/18) = 55.56 m/s

Total distance = speed × time = 55.56 × 14 = 777.78 m

Length of other train = 777.78 − 130 = 647.78 m

∴ Answer = 647.78 m

Alternate Method

Given:

Speeds = 130 km/hr and 70 km/hr

Length of first train = 130 m

Time = 14 sec

Formula used:

Distance = Relative speed × Time

Calculation:

⇒ Relative speed = 130 + 70 = 200 km/hr

⇒ Convert to m/s: 200 × (5/18) = 55.56 m/s

⇒ Total distance covered = 55.56 × 14 = 777.78 m

⇒ Total distance = sum of lengths

⇒ Length of second train = 777.78 − 130

⇒ = 647.78 m

∴ The correct answer is 647.78 m.

Additional Information

Relative Speed

Opposite direction ⇒ speeds add

Unit Conversion

km/hr to m/s ⇒ multiply by 5/18

Train Concept

Crossing ⇒ total length = sum of both trains

Given: Seven boxes A, B, C, D, E, F and G are kept one above another in a single stack (positions 1 bottom to 7 top).

Only two boxes are kept between B and G.

Only D is kept above E.

No box is kept below G.

A is kept below F but above C.

Now, boxes above C are 5 boxes.

Hence, the correct answer is "Option 2".

Given:

“food is delicious” → “ga dc vr”

“harry loves food” → “dc hu bw”

Now,

So, food → dc

Hence, the correct answer is Option 4.

The correct answer is A stretched rubber band.

Key Points

• Potential energy is defined as the energy stored in an object due to its position, arrangement, or state. Unlike kinetic energy, which is energy in motion, potential energy is "stored" and has the capacity to do work when released.
• A stretched rubber band is a clear example of Elastic Potential Energy. When work is performed to stretch the band, the energy is stored within the polymer chains of the material. This stored energy is released as kinetic energy once the band is let go. Hence, statement D is correct.
• A falling rock possesses Kinetic Energy because it is in a state of active motion. While the rock had high Gravitational Potential Energy while resting at a height, that energy is actively being converted into motion as it descends. Hence, statement A is incorrect.
• A burning candle is primarily an example of Chemical Energy being converted into Thermal (heat) and Luminous (light) energy. The energy is stored in the chemical bonds of the paraffin wax and is released through an exothermic reaction during combustion. Hence, statement B is incorrect.
• A moving car represents Kinetic Energy. Any object with mass that is traveling at a specific velocity possesses this form of energy, which is calculated based on its speed and weight. Hence, statement C is incorrect.

Additional Information

• Historical Context: The term potential energy was first proposed by the Scottish engineer and physicist William Rankine in the year 1853. It has since become a fundamental concept in classical mechanics.
• Gravitational Potential Energy: This is the most common form of potential energy, which depends on an object's height and mass. The standard formula used to calculate it is PE = mgh, where m is mass, g is the acceleration due to gravity (approximately 9.8 m/s² on Earth), and h is the elevation above a reference point.
• Chemical Potential Energy: This is energy stored in the atomic bonds of substances. Common examples include batteries, biomass, petroleum, and natural gas. In the context of India, the Ministry of New and Renewable Energy promotes biogas as a way to utilize chemical potential energy from organic waste.
• Elastic Potential Energy: This occurs when an object is compressed or stretched. It is governed by Hooke’s Law, which states that the force needed to extend or compress a spring by some distance is proportional to that distance. The energy stored is given by 1/2 kx², where k is the spring constant and x is the displacement.

Important Points

• Law of Conservation of Energy: This law states that energy cannot be created or destroyed, only transformed. In a pendulum, energy constantly shifts between potential (at the highest points) and kinetic (at the lowest point).
• SI Unit: The Standard International unit for measuring all forms of energy, including potential energy, is the Joule (J). This unit is named in honor of the English physicist James Prescott Joule for his work on the nature of heat and its relationship to mechanical work.
• Applications in Infrastructure: Huge amounts of potential energy are utilized in Hydroelectric Dams, such as the Tehri Dam in Uttarakhand. Water stored at a high altitude in the reservoir possesses massive gravitational potential energy, which is used to turn turbines to generate electricity.
• Nuclear Potential Energy: This is the potential energy of the nucleons (protons and neutrons) inside an atomic nucleus. This energy is harnessed in nuclear power plants, such as the Kudankulam Nuclear Power Plant in Tamil Nadu, through the process of nuclear fission.

The correct answer is Maharashtra.

Key Points

• The state government of Maharashtra issued a comprehensive notification in December 2025 to ensure the strict enforcement of the prohibition on all forms of physical and emotional punishment in schools.
• This enforcement is rooted in the statutory provisions of the Right of Children to Free and Compulsory Education (RTE) Act, 2009, which mandates a child-friendly and fear-free environment in educational institutions.
• Under the Maharashtra state directives, any instance of Corporal Punishment or Mental Harassment is treated as a major misconduct, leading to immediate disciplinary action against the erring staff or school management.
• The State Education Department of Maharashtra mandated the formation of School Management Committees (SMCs) and special monitoring cells to track and report violations of child rights within school premises.
• The move aims to improve the Learning Outcomes and psychological well-being of students by shifting from punitive measures to Positive Pedagogical approaches in classrooms across the state.

Additional Information

• Right to Education (RTE) Act, 2009:
• The Right of Children to Free and Compulsory Education Act was enacted by the Parliament of India on 4 August 2009.
• It came into legal force on 1 April 2010, making India one of the 135 countries to make education a fundamental right for every child.
• The act provides for the right of children to free and compulsory education in a neighborhood school till the completion of elementary education (classes 1 to 8).
• Constitutional Provision:
• The 86^th Amendment Act, 2002 inserted Article 21A into the Constitution of India.
• Article 21A declares that the State shall provide free and compulsory education to all children of the age of 6 to 14 years in such a manner as the State may determine.
• Prohibition of Corporal Punishment:
• Section 17(1) of the RTE Act states that no child shall be subjected to Physical Punishment or Mental Harassment.
• Section 17(2) mandates that any person who contravenes the provisions of sub-section (1) shall be liable to disciplinary action under the service rules applicable to such person.

Important Points

• Role of NCPCR: The National Commission for Protection of Child Rights (NCPCR) is the apex body that monitors the implementation of the RTE Act. It has issued detailed guidelines for the Elimination of Corporal Punishment (ECP) in schools.
• Definition of Corporal Punishment: It includes any physical force intended to cause some degree of pain or discomfort, however light, as well as non-physical forms of punishment that are cruel and degrading, such as verbal abuse, sarcasm, or humiliation.
• Legal Redressal: Apart from the RTE Act, victims of physical abuse in schools can seek protection under the Juvenile Justice (Care and Protection of Children) Act, 2015, specifically Section 75, which deals with punishment for cruelty to a child.
• Impact on Enrollment: Strict enforcement of these laws has historically led to a decrease in Dropout Rates and an increase in Gross Enrolment Ratio (GER) as schools become safer environments for children.

The correct answer is 1908.

Key Points

• Bal Gangadhar Tilak was arrested by the British authorities in the year 1908 on charges of sedition. This followed his articles published in his Marathi newspaper, Kesari, where he defended the actions of young revolutionaries.
• The primary reason for his arrest was an article published in May 1908 concerning the Muzaffarpur bomb incident involving Khudiram Bose and Prafulla Chaki. Tilak argued that the bomb was a response to the oppressive policies of the British Raj.
• The trial took place in Bombay (now Mumbai) in July 1908. Justice Davar presided over the case, and Tilak was represented by Mohammad Ali Jinnah, though the jury eventually found him guilty.
• Following the trial, Tilak was sentenced to six years of rigorous imprisonment. He was deported to the Mandalay prison in Burma (present-day Myanmar), where he remained from 1908 until 1914.
• During his incarceration in Mandalay, he wrote the famous book Gita Rahasya, which is an exposition of Karma Yoga based on the Bhagavad Gita.

Additional Information

• Kesari and Mahratta: Tilak founded two newspapers to spread the message of nationalism. Kesari was published in Marathi to reach the masses, while Mahratta was published in English for the educated class. These papers were instrumental in criticizing the British administration.
• Lokanmanya Title: Due to his immense popularity and dedication to the cause of Indian independence, the people of India conferred upon him the title Lokanmanya, which means "Accepted by the people as their leader."
• Educational Initiatives: In 1884, Tilak, along with Gopal Ganesh Agarkar and others, founded the Deccan Education Society in Pune to improve the quality of education for Indian youth and instill nationalist ideas. They also established Fergusson College in 1885.
• Home Rule League: After his release from prison in 1914, Tilak launched the Indian Home Rule League in April 1916 at Belgaum. He worked alongside Annie Besant to demand self-government for India within the British Empire.
• Lal-Bal-Pal: Tilak was part of the famous extremist trio of the Indian National Congress known as Lal-Bal-Pal, consisting of Lala Lajpat Rai from Punjab, Bal Gangadhar Tilak from Maharashtra, and Bipin Chandra Pal from Bengal.

Important Points

• Section 124A: Tilak was charged under Section 124A of the Indian Penal Code (IPC), which deals with sedition. This law was used extensively by the British to suppress the Indian National Movement.
• Slogan of Swaraj: Tilak is famously known for his slogan, "Swaraj is my birthright and I shall have it!" which became a battle cry for millions of Indians during the struggle for freedom.
• Social Festivals: To foster a sense of unity and national identity, Tilak transformed the Ganesh Chaturthi festival (starting in 1893) and Shivaji Jayanti (starting in 1895) into public events to organize the people against British rule.
• Personal Details: Born on July 23, 1856, in Ratnagiri, Maharashtra, Tilak was a scholar, mathematician, and philosopher. He passed away on August 1, 1920, the same day the Non-Cooperation Movement was launched by Mahatma Gandhi.
• Valentine Chirol: The British journalist Valentine Chirol described Tilak as the "Father of Indian Unrest" in his book "Indian Unrest," highlighting Tilak's role in instigating the first organized resistance against colonial rule.

The logic followed here is:

For, DUMB → FXOE

For, LGUN → NJWQ

Now, applying the same logic to RPAW:

So, RPAW → TSCZ

Hence, the correct answer is Option 2.

The logic followed here is based on the alphabetical position pattern:

Option 1: DFB

Option 2: NPL

Option 3: QSO

Option 4: SUR

Thus, SUR breaks this pattern.

Hence, the odd one out is Option 4.

The correct answer is Nauradehi Wildlife Sanctuary.

Key Points

• In October 2025, the Madhya Pradesh government officially announced that Nauradehi Wildlife Sanctuary (now part of the Veerangana Durgavati Tiger Reserve) would be developed as the third permanent home for cheetahs in the state.
• The inclusion of Nauradehi is a strategic move to create a metapopulation—a group of spatially separated populations of the same species that interact at some level. By dispersing the cheetahs across Kuno, Gandhi Sagar, and Nauradehi, the government aims to reduce ecological pressure on Kuno and minimise the risk of a single disease or localized event wiping out the entire Indian population.

Additional Information

• Project Cheetah:
• It is the world’s first intercontinental large wild carnivore translocation project, launched by the Government of India to restore the species after its extinction in the country in 1952.
• The first batch of 8 cheetahs was brought from Namibia on September 17, 2022, and released into Kuno National Park by PM Narendra Modi.
• A second batch of 12 cheetahs was translocated from South Africa in February 2023 to increase genetic diversity and population size.
• Geographical Significance:
• The Chambal River flows through the sanctuary, and the Gandhi Sagar Dam, one of the four major dams built on the river, is located within its vicinity.
• The presence of the Chambal River provides a perennial water source, supporting diverse flora and fauna including Chinkara, Nilgai, and Mugger Crocodiles.
• Administrative Bodies:
• The project is overseen by the National Tiger Conservation Authority (NTCA) in collaboration with the Wildlife Institute of India (WII) and the Madhya Pradesh Forest Department.

Important Points

• Other Potential Habitats:
• While Gandhi Sagar is the immediate priority, the Nauradehi Wildlife Sanctuary (now part of the Veerangana Durgavati Tiger Reserve) has also been identified as a highly suitable long-term habitat for cheetahs due to its massive landscape of over 1,000 square kilometers.
• Madhav National Park in the Shivpuri district is another site being evaluated for future phases of the reintroduction program.
• Conservation Goals:
• The primary goal of Project Cheetah is not just to reintroduce a species but to conserve India's grasslands and open scrub forests, which are critical for water security and rural livelihoods.
• The successful establishment of a metapopulation across multiple sites like Kuno and Gandhi Sagar reduces the risk of disease or localized disasters wiping out the entire population.

The correct answer is MS Excel.

Key Points

• MS Excel is a spreadsheet program developed by Microsoft as part of the Office productivity suite. It is designed to help users perform mathematical calculations, organize data in rows and columns, and create graphical representations of information. Since it is designed for a specific end-user task, it is a classic example of Application Software. Hence, statement B is correct.
• Windows is a graphical Operating System (OS) developed by Microsoft. It acts as the primary interface between the computer user and the hardware, managing resources and providing a platform for other programs to run. Because it manages the system itself, it is classified as System Software. Hence, statement A is incorrect.
• BIOS, which stands for Basic Input/Output System, is a type of firmware stored on a small memory chip on the motherboard. It is the first software that runs when a computer starts, responsible for the Power-On Self-Test (POST) and booting the operating system. It belongs to the category of System Software. Hence, statement C is incorrect.
• Linux is a family of open-source Unix-like operating systems based on the Linux kernel, first released by Linus Torvalds on September 17, 1991. Like Windows, it serves the fundamental purpose of managing hardware and software resources, making it System Software. Hence, statement D is incorrect.

Additional Information

• Application Software: This refers to software that performs specific functional tasks for the end-user. Examples include Word Processors (like MS Word), Web Browsers (like Google Chrome), Media Players (like VLC), and Database Management Systems (like Oracle). These are not essential for the computer's basic functioning but are vital for user productivity.
• System Software: These are programs designed to run a computer's hardware and application programs. If we think of the computer system as a layered architecture, the system software is the interface between the hardware and user applications. It includes the Operating System, Utility Software, and Device Drivers.
• Microsoft Excel Features: Launched initially for Macintosh in 1985 and Windows in 1987, Excel provides powerful features such as Pivot Tables, Macro programming via Visual Basic for Applications (VBA), and data analysis tools. It uses a grid of cells identified by column letters and row numbers.
• Utility Software: This is a sub-type of system software that helps configure, optimize, or maintain a computer. Examples include Antivirus software, disk defragmenters, and file compression tools like WinZip.
• Open Source vs Proprietary: Linux is a prime example of Open Source software where the source code is available for anyone to modify. In contrast, Windows and MS Excel are Proprietary Software owned by Microsoft Corporation, requiring a license for use.

Important Points

• Historical Context: The first spreadsheet program was VisiCalc, released in 1979, which significantly drove the adoption of personal computers in the business world. Later, Lotus 1-2-3 became the industry standard before Microsoft Excel took over the market in the early 1990s.
• Booting Process: The BIOS is gradually being replaced in modern computers by UEFI (Unified Extensible Firmware Interface), which offers faster boot times, secure boot features, and support for larger hard drives (greater than 2.2 Terabytes).
• Operating System Market: As of recent data, Windows remains the most widely used desktop OS globally, while Linux dominates the server and supercomputer markets due to its stability and security features.
• Functionality of Excel: Modern versions of Excel can handle up to 1,048,576 rows and 16,384 columns in a single worksheet, making it a critical tool for data scientists and accountants worldwide.

Shortcut Trick

Total surface area of cube = 6a²

⇒ 6 × 91²

⇒ 6 × 8281

⇒ 49686

∴ Answer = 49,686 cm²

Alternate Method

Given:

Side of cube = 91 cm

Formula used:

Total surface area of cube = 6a²

   91

All 6 faces are squares

Calculation:

⇒ TSA = 6 × a²

⇒ = 6 × 91²

⇒ = 6 × 8281

⇒ = 49686 cm²

∴ The correct answer is 49,686 cm².

Additional Information

Cube Formula

Total surface area = 6a²

Square Calculation

91² = (90 + 1)² = 8100 + 180 + 1 = 8281

Faces of Cube

A cube has 6 identical square faces

Quick Tip

Use (a + b)² identity for faster squaring

The correct answer is United Kingdom.

Key Points

• According to Stanford University’s Global AI Vibrancy Index 2024 (included in the 2025 AI Index Report), the top three countries in the rankings are:
• United States (Score: 78.6)
• China (Score: 36.95)
• India (Score: 21.59) ​
• The United Kingdom did not make the top three; it typically ranks in the top five or six depending on the specific pillar being measured, but trailed India, China, and the U.S. in the overall 2024 vibrancy score.
• India's Rise: India made a significant leap from 7^th place in 2023 to 3^rd place in 2024, primarily driven by its strong AI talent pool and research output.

Additional Information

• Dimensions of the Index: The vibrancy index evaluates countries based on three primary pillars: Research and Development (R&D), Economy, and Infrastructure. This includes 28 indicators such as conference publications, AI startups, and government strategy.
• Private Investment Trends: In 2023, global private investment in AI saw a decline for the second consecutive year, yet investment specifically in Generative AI surged nearly eightfold to US$ 25.2 billion.
• Model Origins: The United States produced 61 notable AI models in 2023, compared to 15 from China and 21 from the European Union.
• United Kingdom’s Role: The UK hosted the world's first AI Safety Summit at Bletchley Park in November 2023, reinforcing its position as a global hub for AI Governance and Regulation.
• China’s Strength: Despite regulatory challenges, China accounts for roughly 60% of the world's Industrial Robot installations, indicating a high level of AI Automation in its economy.

Important Points

• India’s Specific Achievements: While not in the top three overall, India ranks 1^st globally in the AI Skill Penetration Rate, which is 3.0 times the global average. This reflects the high density of AI-skilled Software Engineers and Data Scientists in the Indian workforce.
• GitHub Contributions: India also holds a significant share of GitHub AI Projects, indicating a strong developer community and growth in Open-Source AI development.
• Global Rankings: Following the United Kingdom, other high-ranking countries in the 2024 report include France, Germany, and Canada. These nations are part of the Global Partnership on Artificial Intelligence (GPAI).
• Responsible AI: The 2024 index highlighted a lack of standardized Safety Evaluations for Large Language Models (LLMs), which remains a critical challenge for all top-ranked countries including the USA and China$.

Shortcut Trick

Mean = Σ(fx) ÷ Σf

Σf = 24 + 38 + 26 + 32 + 13 = 133

Σ(fx) = (16×24) + (21×38) + (47×26) + (80×32) + (99×13)

= 384 + 798 + 1222 + 2560 + 1287 = 6251

Mean = 6251 ÷ 133 = 47

∴ Answer = 47

Alternate Method

Given:

Marks: 16, 21, 47, 80, 99

Frequencies: 24, 38, 26, 32, 13

Formula used:

Mean = Σ(fx) ÷ Σf

Calculation:

⇒ Σf = 24 + 38 + 26 + 32 + 13 = 133

⇒ Σ(fx) = (16×24) + (21×38) + (47×26) + (80×32) + (99×13)

⇒ = 384 + 798 + 1222 + 2560 + 1287

⇒ = 6251

⇒ Mean = 6251 ÷ 133

⇒ = 47

∴ The correct answer is 47.

Additional Information

Mean of Discrete Data

Mean = Σ(fx) ÷ Σf

Frequency (f)

Number of times a value occurs

Shortcut Tip

Multiply first, then add to avoid repeated calculations

Check

Mean must lie within the range of given values

The logic followed here is:

Logic: third number = first number − second number

For, (252, 80, 172)

⇒ 252 − 80 = 172

For, (170, 55, 115)

⇒ 170 − 55 = 115

Now, checking the options using the same pattern:

Option 1) (236, 105, 141)

⇒ 236 − 105 = 131 ≠ 141

Option 2) (212, 72, 130)

⇒ 212 − 72 = 140 ≠ 130

Option 3) (180, 53, 137)

⇒ 180 − 53 = 127 ≠ 137

Option 4) (195, 95, 100)

⇒ 195 − 95 = 100 = 100

Hence, only (195, 95, 100) follows the same pattern.

Hence, the correct answer is Option 4.

Shortcut Trick

Profit ratio = investments = 1570 : 1760 : 1620

Total = 4950

Vivek’s share = (1620 / 4950) × 1540

= (18 / 55) × 1540 = 28 × 18 = 504

∴ Answer = ₹504

Alternate Method

Given:

Siddharth = ₹1570, Lata = ₹1760, Vivek = ₹1620

Total profit = ₹1540

Formula used:

Profit share ∝ Investment

Calculation:

⇒ Ratio = 1570 : 1760 : 1620

⇒ Total investment = 1570 + 1760 + 1620 = 4950

⇒ Vivek’s share = (1620 / 4950) × 1540

⇒ Simplify ⇒ (18 / 55) × 1540

⇒ = 18 × 28 = 504

∴ The correct answer is ₹504.

Additional Information

Partnership Rule

Profit is divided in ratio of investments (if time is same).

Simplification

Divide ratio by common factor to ease calculation.

Fraction Trick

Convert ratio into fraction of total to find share.

Quick Tip

Always simplify before multiplying.

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

D sits fourth to the right of O.

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

B sits third to the right of C.

Q is an immediate neighbor of B and R.

 

 

So, people between P and Q are O and B → 2 people

Hence, the correct answer is "Option 1".

The logic followed here is:

thus, "110" will replace the question mark in the given series.

Hence, the correct option is "Option 2".

The correct answer is Sustainable Harnessing and Advancement of Nuclear Energy for Transforming India (SHANTI) Bill.

Key Points

• The Sustainable Harnessing and Advancement of Nuclear Energy for Transforming India (SHANTI) Bill was conceptualized to overhaul the legal framework governing civil nuclear energy in India, receiving the President's assent in 2025.
• The primary objective of this legislation is to consolidate existing laws, primarily updating the provisions of the Atomic Energy Act, 1962, to align with modern energy security needs and climate goals.
• A landmark feature of the SHANTI Bill is the formal provision for private sector participation in the nuclear power sector, which was previously a government monopoly under the Department of Atomic Energy (DAE).
• The bill facilitates the development of Bharat Small Reactors (BSRs) and Small Modular Reactors (SMRs) through Public-Private Partnerships (PPPs), aiming to increase the share of nuclear energy in India's total energy mix.
• It provides a streamlined regulatory framework for the licensing, operation, and decommissioning of nuclear plants, ensuring that safety standards are maintained by the Atomic Energy Regulatory Board (AERB) while encouraging innovation and investment.

Additional Information

• Bharat Small Reactors (BSRs): These are indigenous small-scale nuclear reactors designed to be safer, cost-effective, and quicker to deploy than traditional large-scale Pressurized Heavy Water Reactors (PHWRs). They are ideal for industrial captive power and decentralized energy grids.
• Atomic Energy Act, 1962: This was the foundational legislation that governed the production, control, and use of atomic energy in India. The SHANTI Bill seeks to address the limitations of this 63-year-old act to allow non-government entities to enter the field of power generation.
• Energy Transition and Net Zero: India has committed to reaching Net Zero emissions by the year 2070. Nuclear energy is considered a clean, baseload power source essential for fulfilling the Panchamrit targets announced at COP26.
• Nuclear Power Corporation of India Limited (NPCIL): As a Public Sector Undertaking (PSU) under the DAE, NPCIL has been the sole operator of commercial nuclear power plants. Under the new bill, NPCIL is expected to play a mentorship and collaborative role with private players.
• Global Context: Many countries like the USA, France, and China have already integrated private investment in their nuclear sectors. India's shift towards this model aims to attract global technology and domestic capital.

Important Points

• Budgetary Foundation: The precursor to this bill was the Union Budget 2024-25, where the Finance Minister announced that the Government of India would partner with the private sector for R&D and the setting up of Bharat Small Reactors.
• Three-Stage Nuclear Program: India continues to follow its three-stage nuclear power program formulated by Dr. Homi J. Bhabha, utilizing Uranium, Plutonium, and eventually Thorium (of which India has the world's largest reserves in monazite sands in Kerala and Odisha).
• Installed Capacity: As of recent data, India's installed nuclear capacity stands at approximately 7,480 MW, with a target to reach 22,480 MW by the year 2031-32 through the addition of several 700 MW PHWR units and VVER units at Kudankulam.
• Civil Liability for Nuclear Damage (CLND) Act, 2010: This act remains a critical component of the legal landscape, defining operator liability and compensation in the rare event of a nuclear incident, which is a key consideration for private investors under the SHANTI Bill.