According to the given information,

Thus, 'E' is codes as '5'.

Hence, "Option 2" is the correct answer.

According to the given information,

Thus, 'poet' is codes as 'dl'.

Hence, "Option 1" is the correct answer.

Given: 

Shyam starts from point A and drives 11 km towards the east.

He then takes a right turn, drives 5 km, turns right and drives 12 km.

He then takes a right turn and drives 10 km.

He takes a final right turn, drives 1 km and stops at point P.

Thus, Shyam should drive 5 km (10 km - 5 km) in the south direction in order to reach point A again.

Hence, "Option 1" is the correct answer.

The correct answer is Registering a combined total of 1000 fours and sixes in IPL history.

Key Points

• Virat Kohli became the first player in IPL history to achieve the milestone of registering a combined total of 1000 fours and sixes as of April 15, 2025.
• The milestone includes a career record of over 850 fours and 150 sixes, showcasing his consistency and dominance as a batsman in the league.
• Kohli has been a part of the IPL since its inception in 2008 and has represented Royal Challengers Bangalore (RCB) throughout his IPL career.
• This achievement underscores Kohli's role as one of the most prolific run-scorers in IPL history, further solidifying his legacy in T20 cricket.
• He has also been the leading run-scorer in IPL history, with over 7000 runs to his name as of 2025.

Additional Information

• Indian Premier League (IPL):
• The IPL is a professional T20 cricket league in India, founded in 2008 by the Board of Control for Cricket in India (BCCI).
• It is one of the most popular and lucrative cricket leagues globally, featuring players from across the world.
• The league consists of 10 franchise teams representing different cities in India (as of 2025).
• Notable records in the IPL include most runs, most wickets, and highest individual scores in a match.
• Virat Kohli:
• Virat Kohli is regarded as one of the greatest batsmen of all time, known for his consistency across all formats of cricket.
• He has represented India in all three formats and has captained the national team across various tournaments.
• Kohli holds several records, including being the fastest to 8000, 9000, 10000, 11000, and 12000 ODI runs.
• In IPL, he holds the record for the most runs scored in a single season (973 runs in 2016).
• T20 Cricket:
• T20 cricket is a shorter format of the game, with each team playing a maximum of 20 overs.
• It emphasizes aggressive batting, innovative bowling, and quick fielding to achieve results within a few hours.
• The format has gained immense popularity due to its fast-paced nature and entertainment value.
• Milestones in IPL:
• Several players have achieved unique milestones, including Chris Gayle (most sixes in IPL history) and Lasith Malinga (most wickets in IPL history).
• Milestones like 1000 fours and sixes reflect a player's ability to consistently score boundaries, a critical skill in T20 cricket.
• Such records highlight the evolution of cricket as a sport and the growing emphasis on strike rates and scoring efficiency.

Shortcut Trick

Net Profit% can be calculated using the successive percentage formula when Mark-up% and Discount% are known.

Formula: Profit% = M − D − (M × D) ÷ 100, where M = Mark-up% and D = Discount%.

M = 25% and D = 12%.

Profit% = 25 − 12 − (25 × 12) ÷ 100 = 13 − (300 ÷ 100) = 13 − 3 = 10%.

∴ The correct answer is 10%.

Alternate Method

Given → Marked Price (MP) = ₹3,100, Mark-up = 25% above CP, Discount = 12%. Formulas: CP = MP × 100 ÷ (100 + Mark-up%) | SP = MP × (100 − D%) ÷ 100 | Profit% = (SP − CP) ÷ CP × 100.

⇒ Let Cost Price (CP) = ₹100. ⇒ Marked Price (MP) = 100 + 25% of 100 = ₹125. ⇒ Selling Price (SP) = 125 − 12% of 125 = 125 − (12 ÷ 100 × 125) = 125 − 15 = ₹110. ⇒ Profit = SP − CP = 110 − 100 = ₹10. ⇒ Profit% = (10 ÷ 100) × 100 = 10%.

∴ The correct answer is 10%.

Additional Information

Marked Price and Discount

Discount is always calculated on the Marked Price. SP = MP × (100 − Discount%) ÷ 100.

Effective Change

When a value is increased by x% and then decreased by y%, the net change is given by (x − y − xy/100)%.

Given: 56 – 12 × 4 ÷ 9 + 5 = ?

According to the question, after ‘+’ and ‘–’ are interchanged, and ‘×’ and ‘÷’ are interchanged:

56 – 12 × 4 ÷ 9 + 5 = ? ⇒ 56 + 12 ÷ 4 × 9 – 5 = ?

⇒ 56 + 12 ÷ 4 × 9 – 5 = ?

⇒ 56 + 3 × 9 – 5 = ?

⇒ 56 + 27 – 5 = ?

⇒ 83 – 5 = ?

⇒ 78 = ?

Hence, "Option 2" is the correct answer.

The logic followed here is:

Given: 

11 - 12 - 13 - 26

11 + 1 = 12

12 + 1 = 13

13 × 2 = 26

And,

19 - 20 - 21 - 42

19 + 1 = 20

20 + 1 = 21

21 × 2 = 42

So, checking each option one by one:

Option 1) 4 - 5 - 6 - 10

4 + 1 = 5

5 + 1 = 6

6 × 2 = 12 ≠ 10

Option 2) 7 - 8 - 9 - 18

7 + 1 = 8

8 + 1 = 9

9 × 2 = 18

Option 3) 3 - 4 - 5 - 12

3 + 1 = 4

4 + 1 = 5

5 × 2 = 10 ≠ 12

Option 4) 9 - 10 - 11 - 24

9 + 1 = 10

10 + 1 = 11

11 × 2 = 22 ≠ 24

Thus, out of all the options '7 - 8 - 9 - 18' follows the same logic as given.

Hence, "Option 2" is the correct answer.

Shortcut Trick

Apply the Empirical Formula: Mean = (3 × Median − Mode) ÷ 2.

Substitute the given values: Mean = (3 × 65 − 52.7) ÷ 2.

Mean = (195 − 52.7) ÷ 2 = 142.3 ÷ 2 = 71.15.

Rounding to one decimal place, we get 71.2.

∴ The correct answer is 71.2.

Alternate Method

Given: Mode = 52.7 and Median = 65.

Formula Used: Mode = 3 × Median − 2 × Mean

⇒ 52.7 = 3 × 65 − 2 × Mean

⇒ 52.7 = 195 − 2 × Mean

⇒ 2 × Mean = 195 − 52.7

⇒ 2 × Mean = 142.3

⇒ Mean = 142.3 ÷ 2

⇒ Mean = 71.15 ≈ 71.2

∴ The correct answer is 71.2.

Additional Information

Empirical Relationship

The relationship Mode = 3 Median − 2 Mean is an approximation used for unimodal and moderately skewed distributions.

The correct answer is Aurobindo Ghosh.

Key Points

• Aurobindo Ghosh is primarily associated with the Extremist faction of the Indian National Congress, not the Moderates.
• He played a significant role in promoting radical nationalism and advocating for complete independence rather than gradual reforms.
• During the early 1900s, Aurobindo Ghosh emerged as a key leader of the Extremists alongside Bal Gangadhar Tilak and Bipin Chandra Pal.
• His political philosophy included the use of passive resistance and boycotts to oppose British rule.
• He later retired from active politics and shifted his focus to spirituality, establishing the Sri Aurobindo Ashram in Puducherry.

Additional Information

• Moderates in the Indian National Congress
• Moderates were a group of leaders in the Congress who believed in achieving political reforms through constitutional and peaceful methods.
• Key leaders included Dadabhai Naoroji, Gopal Krishna Gokhale and Ferozshah Mehta.
• Their primary aim was to secure greater representation for Indians in the legislative councils and administrative reforms.
• They often relied on petitions, speeches, and lobbying to achieve their goals.
• Extremists in the Indian National Congress
• Extremists were a faction within the Congress that emerged in the early 1900s, advocating for direct action and complete independence.
• Key leaders included Bal Gangadhar Tilak, Bipin Chandra Pal, and Lala Lajpat Rai.
• They used methods like boycotts, Swadeshi movement, and mass mobilization to challenge British rule.
• The split between Moderates and Extremists occurred at the Surat Session of the Congress in 1907.
• Dadabhai Naoroji
• Known as the "Grand Old Man of India," Dadabhai Naoroji was a prominent Moderate leader.
• He authored the book "Poverty and Un-British Rule in India," highlighting the economic drain caused by British policies.
• He was the first Indian to be elected to the British Parliament in 1892.
• Gopal Krishna Gokhale
• A Moderate leader and mentor to Mahatma Gandhi, Gokhale was a staunch advocate of social reforms and education.
• He founded the Servants of India Society to promote social welfare and national awakening.

The correct answer is Jhajjar-Bachauli Wildlife Sanctuary.

Key Points

• The Jhajjar-Bachauli Wildlife Sanctuary is located in Punjab, India, and is known for its rich biodiversity and ecological significance.
• In March 2025, the Punjab government proposed developing this sanctuary into a leopard safari to promote eco-tourism and conservation efforts.
• The leopard safari is expected to attract tourists and raise awareness about wildlife conservation in the region.
• This initiative aligns with the state's efforts to enhance eco-tourism and create sustainable development opportunities for local communities.
• The sanctuary is home to various wildlife species, including leopards, and offers a natural habitat conducive to their growth and protection.

Additional Information

• Eco-Tourism:
• Eco-tourism refers to responsible travel to natural areas that conserve the environment and sustain the well-being of local people.
• It promotes awareness about conservation and helps generate income for local communities.
• Leopards in India:
• The Indian leopard (Panthera pardus fusca) is a subspecies of leopard found across the Indian subcontinent.
• Leopards are listed as "Vulnerable" on the IUCN Red List due to habitat loss and poaching.
• Conservation initiatives, including protected areas and safaris, play a crucial role in their survival.
• Wildlife Sanctuaries in Punjab:
• Punjab has several wildlife sanctuaries, including Harike Wildlife Sanctuary, Abohar Wildlife Sanctuary, and Jhajjar-Bachauli Wildlife Sanctuary.
• These sanctuaries are vital for preserving biodiversity and serve as key locations for conservation and tourism.
• Sustainable Development:
• Sustainable development aims to meet the needs of the present without compromising the ability of future generations to meet their own needs.
• Eco-tourism initiatives like leopard safaris are examples of sustainable practices that benefit both the environment and local communities.

Shortcut Trick

Apply the successive percentage change formula: Net change = a + b + (a × b)/100

Here, reduction (a) = −16% and increase (b) = +10%.

Net change = −16 + 10 + [(−16 × 10) / 100]

Net change = −6 − 1.6 = −7.6%

Negative sign indicates a lower salary.

∴ The correct answer is 7.6%.

Alternate Method

Given: Initial reduction = 16%, Subsequent increase = 10%.

⇒ Let initial salary = 100 units

⇒ Salary after 16% reduction = 100 − 16 = 84 units

⇒ Salary after 10% increase = 84 + (10% of 84)

⇒ New salary = 84 + 8.4 = 92.4 units

⇒ Difference from initial = 100 − 92.4 = 7.6 units

⇒ Percentage lower = (7.6 / 100) × 100 = 7.6%

∴ The correct answer is 7.6%.

Additional Information

Successive Percentage Change

When a value is changed by x% and then by y%, the effective change is given by (x + y + xy/100)%. Use positive values for increase and negative for decrease.

Multiplying Factor Method

Final Value = Initial Value × (100−r₁)/100 × (100+r₂)/100. For this question: 100 × 0.84 × 1.1 = 92.4.

Equal Increase and Decrease

If a value is increased by x% and then decreased by x%, there is always a net decrease of (x²/100)%.

Shortcut Trick

For the largest cone in a cube of side a:

Diameter of cone = Height of cone = side of cube = 8 cm.

Radius r = 8/2 = 4 cm and height h = 8 cm.

Volume = (1/3) × (22/7) × 4² × 8 = (1/3) × (22/7) × 128 = 2816 / 21.

∴ The correct answer is 134 (2/21) cm³.

Alternate Method

Given:

Edge of the cube (a) = 8 cm.

Formula Used:

Volume of Right Circular Cone = (1/3) π r² h

Calculations:

⇒ When a cone is cut from a cube, its base diameter equals the cube's edge and its height equals the cube's edge.

⇒ Radius (r) = 8 ÷ 2 = 4 cm

⇒ Height (h) = 8 cm

⇒ Volume = (1/3) × (22/7) × (4)² × 8

⇒ Volume = (1/3) × (22/7) × 16 × 8

⇒ Volume = 2816 ÷ 21

⇒ Volume = 134 (2/21) cm³

∴ The correct answer is 134 (2/21) cm³.

Additional Information

Volume of largest Sphere in a Cube

The diameter of the largest sphere that can fit inside a cube is equal to the side of the cube (a). Volume = (4/3) π (a/2)³.

Volume of largest Cylinder in a Cube

For the largest cylinder, the diameter and height are both equal to the side of the cube (a). Volume = π (a/2)² a.

Slant Height of Cone

The slant height (l) is given by the Pythagorean relation l = √(r² + h²).

The correct answer is Click on Alt + Enter key.

Key Points

• Alt + Enter is not a valid keyboard shortcut to open the Find and Replace function in Microsoft Word.
• Microsoft Word provides specific methods to search and replace text, such as using the Ctrl + H shortcut or accessing the 'Replace' option from the 'Home' tab.
• Users can also locate the Find and Replace feature under the 'Edit' menu in older versions of Microsoft Word.
• Valid shortcuts for Find and Replace in Microsoft Word include Ctrl + H for replacing text and Ctrl + F for finding text.
• The 'Replace' option in the 'Home' tab is accessible in the ribbon interface of modern versions of Microsoft Word.

Additional Information

• Find and Replace in Microsoft Word:
• This feature allows users to locate specific text and replace it with other text or formatting.
• It is commonly used for correcting errors, updating documents, or applying consistent formatting.
• The Find and Replace dialog box offers options such as case sensitivity, wildcards, and advanced search criteria.
• Keyboard Shortcuts in Microsoft Word:
• Keyboard shortcuts enhance productivity by providing quick access to commonly used features.
• Examples include Ctrl + S for saving, Ctrl + P for printing, and Ctrl + Z for undoing actions.
• Microsoft Word supports customizable shortcuts for advanced users.
• Ribbon Interface:
• Introduced in Microsoft Word 2007, the ribbon interface replaced traditional menus and toolbars.
• It organizes features into tabs and groups for easier navigation.
• The 'Home' tab is one of the most frequently used tabs and includes options for text formatting, paragraph settings, and editing tools.
• Version Compatibility:
• The methods to access Find and Replace may vary across different versions of Microsoft Word.
• Older versions (pre-2007) may use menu-based navigation, while newer versions (2007 and later) use ribbon-based navigation.
• Understanding version-specific features ensures effective use of the software.

The correct answer is They move faster.

Key Points

• When a substance is heated, its particles gain kinetic energy, causing them to move faster.
• Heating increases the temperature, which directly affects the motion of particles in solids, liquids, and gases.
• In solids, the particles vibrate more vigorously around their fixed positions as the temperature rises.
• In liquids and gases, the particles move faster and spread out, leading to processes like expansion and changes in state (e.g., evaporation).
• This phenomenon is explained by the Kinetic Theory of Matter, which states that particles are in constant motion and their energy depends on temperature.

Additional Information

• Kinetic Energy:
• The energy possessed by a particle due to its motion.
• It increases with temperature, causing faster movement of particles.
• Expansion on Heating:
• Substances generally expand when heated due to increased particle motion.
• This property is utilized in applications like thermometers.
• Phase Changes:
• Heating can cause substances to change state, such as solid to liquid (melting) or liquid to gas (evaporation).
• This occurs because particles move faster and overcome intermolecular forces.
• Kinetic Theory of Matter:
• A scientific theory explaining the behavior of particles in matter based on their kinetic energy.
• States that temperature is a measure of the average kinetic energy of particles.
• Brownian Motion:
• An observable phenomenon in liquids and gases where particles move randomly due to collisions.
• It becomes more prominent as particles gain energy from heating.

Shortcut Trick

List the first 10 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Calculate the total sum: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 129

Find the average by dividing the sum by the count: 129 ÷ 10 = 12.9

∴ The correct answer is 12.9.

Alternate Method

Given: The first 10 prime numbers.

Formula Used: Average = (Sum of all observations) ÷ (Total number of observations)

⇒ First 10 Prime Numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

⇒ Sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29

⇒ Sum = 129

⇒ Total Count (n) = 10

⇒ Average = 129 ÷ 10

⇒ Average = 12.9

∴ The correct answer is 12.9.

Additional Information

Prime Numbers

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Smallest Prime Number

The number 2 is the smallest prime number and the only even prime number in the set of all primes.

Composite Numbers

Numbers that have more than two factors are called composite numbers. Note that 1 is neither prime nor composite.

The correct answer is France.

Key Points

• The 78th Cannes Film Festival is scheduled to take place in May 2025 in Cannes, France.
• Cannes, a city on the French Riviera, has been hosting the prestigious Cannes Film Festival since its inception in 1946.
• This international film festival is one of the most recognized and celebrated events in the global film industry, attracting filmmakers, actors, and critics worldwide.
• The festival showcases films from various genres and cultures, emphasizing artistic excellence and creative storytelling.
• The main award given at the Cannes Film Festival is the Palme d'Or (Golden Palm), which honors the best film in the competition.

Additional Information

• Cannes Film Festival
• The Cannes Film Festival is an annual event that takes place in May in Cannes, France.
• It is one of the "Big Three" film festivals, alongside the Venice Film Festival and the Berlin International Film Festival.
• Founded in 1946, the festival is renowned for its red-carpet premieres and exclusive screenings.
• The event is organized by the French Ministry of Culture and a dedicated board of directors.
• Palme d'Or
• The Palme d'Or is the highest prize awarded at the Cannes Film Festival.
• This prestigious award was introduced in 1955, replacing the Grand Prix du Festival International du Film.
• The trophy is made of 24-carat gold and is a symbol of cinematic excellence.
• Notable winners include films like "Parasite" (2019) and "Pulp Fiction" (1994).
• French Riviera
• The French Riviera, also known as the Côte d'Azur, is a Mediterranean coastline in southeastern France.
• It is famous for its glamorous lifestyle, luxury resorts, and cultural heritage.
• Cannes is one of the key cities in the French Riviera, alongside Nice, Saint-Tropez, and Monaco.
• Global Significance of Cannes
• The Cannes Film Festival is a major platform for launching films that gain international recognition.
• It provides opportunities for networking and collaboration among filmmakers, producers, and distributors.
• Beyond cinema, the festival significantly boosts tourism and the local economy in Cannes.

The correct answer is 1971.

Key Points

• Privy purses were annual payments made to the rulers of erstwhile princely states as part of the integration of these states into the Indian Union post-independence.
• These payments were guaranteed under Articles 291 and 362 of the Indian Constitution to ensure the cooperation of princely states during the process of integration.
• In 1971, under the leadership of Prime Minister Indira Gandhi, the 26th Amendment to the Constitution of India was enacted, officially abolishing privy purses.
• The 26th Amendment removed Articles 291 and 362 from the Constitution and abolished the recognition of rulers as well as their privileges.
• The move was part of the broader effort to promote equality and eliminate the remnants of feudalism in independent India.

Additional Information

• Privy Purses:
• Privy purses were monetary allowances given to the rulers of princely states as part of their agreement to join India.
• The amount varied based on the size, revenue, and status of the princely state.
• 26th Constitutional Amendment:
• This amendment was passed in 1971 and removed Articles 291 and 362 from the Indian Constitution.
• It ended the recognition of princely states and abolished all privileges, titles, and privy purses associated with them.
• Significance of Abolition:
• The abolition of privy purses was seen as a step toward reducing inequality and strengthening the democratic fabric of India.
• It also marked the end of any feudal privileges and ensured that all citizens were treated equally under the law.
• Integration of Princely States:
• Post-independence, there were more than 550 princely states in India.
• Sardar Vallabhbhai Patel and V.P. Menon played key roles in integrating these states into the Indian Union through diplomacy and negotiation.

Given: A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 6.

1) F lives on an even numbered floor but not 6.

2) The sum of floors on which F and C live is 3.

3) The sum of floors on which D and F live is 7.

4. B lives immediately above A.

After positioning B and A only one position is left which will be occupied by the only person left i.e. E.

Thus, one person live between B and F.

Hence, "Option 1" is the correct answer.

Given:

Simplify: 127 - [7 × (1 - 5 + 4)] ÷ 91

Formula used:

Follow BODMAS (Bracket, Order, Division, Multiplication, Addition, Subtraction)

Calculation:

127 - [7 × (1 - 5 + 4)] ÷ 91

⇒ 127 - [7 × (1 - 1)] ÷ 91

⇒ 127 - [7 × 0] ÷ 91

⇒ 127 - 0 ÷ 91

⇒ 127 - 0

⇒ 127

∴ The correct answer is option (4).

Decoding symbols:

Given: M + N ÷ O × P – Q

M + N → M is the mother of N.

N ÷ O → N is the father of O.

O × P → O is the wife of P.

P – Q → P is the brother of Q.

Thus, M is Q's brother's wife's father's mother.

Hence, the correct answer is "Option 4"

The logic followed here is:

Hence, "Option 2" is the correct answer.

The correct answer is 500 GW.

Key Points

• India has set an ambitious target of achieving 500 GW of renewable energy installed capacity by the year 2030.
• This target includes contributions from various renewable sources such as solar, wind, hydropower, and biomass.
• The initiative is part of India's commitment under the Paris Agreement to combat climate change and reduce carbon emissions.
• India aims to fulfill 50% of its energy requirements from renewable sources by 2030.
• As of 2023, India has already achieved around 125 GW of renewable energy capacity, showcasing significant progress toward the 2030 goal.

Additional Information

• National Solar Mission (NSM):
• Launched in 2010, NSM is part of India's National Action Plan on Climate Change (NAPCC).
• It aims to establish India as a global leader in solar energy by achieving a target of 100 GW of solar capacity by 2022.
• Paris Agreement:
• An international treaty adopted in 2015 to combat climate change.
• India pledged to reduce its carbon intensity by 33-35% by 2030 compared to 2005 levels.
• Renewable energy targets are a key component of India's commitment under this agreement.
• International Solar Alliance (ISA):
• Founded by India and France in 2015, ISA is a treaty-based intergovernmental organization.
• Its objective is to promote the use of solar energy globally and mobilize financial resources for its expansion.
• Green Energy Corridor Project:
• A government initiative to integrate renewable energy into India's power grid.
• The project involves setting up transmission networks to handle renewable energy efficiently.

Shortcut Trick Identify the right triangle triplet by observing the gap between sides. The sides are x − 26, x − 13, and x (where x is the hypotenuse). The common difference is 13. Scaling the standard 5, 12, 13 triplet by 13: 5×13, 12×13, 13×13 → 65, 156, 169. Here 169 − 13 = 156 and 169 − 26 = 143 (does not match 65). Using x = 78: Sides are 78 − 26 = 52, 78 − 13 = 65, and 78 (Not a triplet). Using x = 39: 13, 26, 39 (No). Correct triplet calculation: x2 = (x−13)2 + (x−26)2 → x = 65. Sides: 39, 52, 65 (Scaled 3, 4, 5 triplet by 13). Area = 1/2 × 39 × 52 = 39 × 26 = 1014 cm2. ∴ The correct answer is 1014 cm2.

Alternate Method Given: Sides are (x − 26), (x − 13) and hypotenuse x. Formula: Base2 + Perpendicular2 = Hypotenuse2

⇒ (x − 26)2 + (x − 13)2 = x2 ⇒ (x2 − 52x + 676) + (x2 − 26x + 169) = x2 ⇒ 2x2 − 78x + 845 = x2 ⇒ x2 − 78x + 845 = 0 ⇒ x2 − 65x − 13x + 845 = 0 ⇒ x(x − 65) − 13(x − 65) = 0 ⇒ (x − 65)(x − 13) = 0 ⇒ x = 65 (Since x − 26 must be positive, x > 26) ⇒ Base = 65 − 26 = 39 cm, Height = 65 − 13 = 52 cm ⇒ Area = 1/2 × Base × Height = 1/2 × 39 × 52 ⇒ Area = 39 × 26 = 1014 cm2 ∴ The correct answer is 1014 cm2.

Additional Information Pythagorean Triplets Common triplets like (3, 4, 5), (5, 12, 13), and (8, 15, 17) can be scaled by a constant k to find other right triangles (3k, 4k, 5k). Area of Right Triangle The area is always half the product of the two shorter sides (legs): Area = 1/2 × a × b. Quadratic Roots Shortcut For x2 − (sum of roots)x + (product of roots) = 0, identify factors of the constant that add up to the middle coefficient.

Given:

Expression: 6893.5 × 603.3 × 0.3019

Formula used:

For two products to be equal, the overall decimal place shifts must balance out.

Calculations:

Original expression's decimal shifts (relative to integer):

6893.5 (1 place left) × 603.3 (1 place left) × 0.3019 (4 places left)

Total left shift = 1 + 1 + 4 = 6 places.

Let's examine the options for a total 6-place left shift:

Option 1: 6.8935 (4 left) × 60.33 (2 left) × 30.19 (2 right)

Net shift = 4 + 2 - 2 = 4 places left. (Incorrect)

Option 2: 6.8935 (4 left) × 6.033 (3 left) × 301.9 (1 right)

Net shift = 4 + 3 - 1 = 6 places left. (Correct)

Wait, let me re-evaluate the shifts from the original numbers, not relative to integers. This is about comparing the original product to the product of the options.

Let P = 6893.5 × 603.3 × 0.3019

Option 1: 6.8935 × 60.33 × 30.19

(6893.5 / 1000) × (603.3 / 10) × (0.3019 × 100)

= P × (1/1000) × (1/10) × 100 = P × (100/10000) = P / 100 (Incorrect)

Option 2: 6.8935 × 6.033 × 301.9

(6893.5 / 1000) × (603.3 / 100) × (0.3019 × 1000)

= P × (1/1000) × (1/100) × 1000 = P × (1000/100000) = P / 100 (Incorrect)

Option 3: 68.935 × 6033 × 3.019

(6893.5 / 100) × (603.3 × 10) × (0.3019 × 10)

= P × (1/100) × 10 × 10 = P × (100/100) = P × 1 (Correct)

Option 4: 689.35 × 603.3 × 301.9

(6893.5 / 10) × 603.3 × (0.3019 × 1000)

= P × (1/10) × 1 × 1000 = P × (1000/10) = P × 100 (Incorrect)

∴ The correct answer is option 3.

Alternate Method 

Given:

Expression: 6893.5 × 603.3 × 0.3019

Formula used:

When we shift the decimal point in all numbers such that the overall scaling factor remains 1, the product stays the same.

Calculation:

Original numbers:

6893.5 = 68.935 × 100

603.3 = 6033 ÷ 10

0.3019 = 3.019 ÷ 10

Let's adjust them oppositely to balance the product:

6893.5 ÷ 100 = 68.935   $\rightarrow$ ÷100

603.3 × 10 = 6033   $\rightarrow$ ×10

0.3019 × 10 = 3.019   $\rightarrow$ ×10

Overall scaling factor:

⇒ (÷100) × (×10) × (×10) = ÷100 × 100 = 1

Therefore, the product remains the same.

∴ The correct answer is option (3): 68.935 × 6033 × 3.019.

The correct answer is Internet connectivity.

Key Points

• The Multidimensional Poverty Index (MPI) is calculated using ten indicators across three broad dimensions: health, education, and standard of living.
• The indicators under the health dimension include nutrition and child mortality.
• Under the education dimension, the indicators used are years of schooling and school attendance.
• The standard of living dimension includes indicators such as access to electricity, drinking water, sanitation, cooking fuel, housing, and asset ownership.
• Internet connectivity is not one of the indicators used in calculating the MPI, as it focuses on basic needs and capabilities rather than technological access.

Additional Information

• Multidimensional Poverty Index (MPI):
• Developed by the Oxford Poverty and Human Development Initiative (OPHI) and the United Nations Development Programme (UNDP).
• Aims to provide a more comprehensive measure of poverty beyond just income levels.
• It captures the overlapping deprivations individuals or households face across multiple dimensions.
• Dimensions and Indicators:
• Health: Nutrition, Child Mortality.
• Education: Years of Schooling, School Attendance.
• Standard of Living: Cooking Fuel, Sanitation, Drinking Water, Electricity, Housing, Assets.
• Global MPI Reports:
• The MPI is included in the Human Development Reports released annually by the UNDP.
• It provides valuable insights into poverty trends and is used for policymaking and international comparisons.
• Focus on Basic Needs:
• The MPI emphasizes fundamental human needs such as health, education, and basic living standards.
• Technological access, including internet connectivity, is not included as it is not considered a core indicator of poverty reduction.

The correct answer is fat-soluble vitamins.

Key Points

• Bile is essential for the emulsification of fats, which allows for the digestion and absorption of fat-soluble vitamins such as Vitamins A, D, E, and K.
• Without bile, fats remain undigested, and the absorption of fat-soluble vitamins in the small intestine becomes impaired.
• Fat-soluble vitamins require the presence of dietary fats and bile salts to form micelles, which facilitate their absorption into the intestinal cells.
• A deficiency in bile production can lead to health issues such as night blindness (Vitamin A deficiency), rickets (Vitamin D deficiency), and clotting disorders (Vitamin K deficiency).
• Patients with bile production issues may require medical interventions like bile supplements or dietary modifications to ensure proper nutrient absorption.

Additional Information

• Bile and Its Role:
• Bile is produced by the liver and stored in the gallbladder, released into the small intestine during digestion.
• It contains bile salts, cholesterol, and waste products like bilirubin, which help in fat digestion and the excretion of waste.
• Fat-Soluble Vitamins:
• Fat-soluble vitamins include Vitamins A, D, E, and K, which are stored in the liver and fatty tissues for later use.
• These vitamins are crucial for vision (A), bone health (D), antioxidation (E), and blood clotting (K).
• Micelle Formation:
• Bile salts help in the formation of micelles, which are tiny droplets that make fats and fat-soluble vitamins soluble in the watery environment of the intestine.
• This process is critical for their absorption across the intestinal lining.
• Diseases Linked to Bile Deficiency:
• Conditions like gallstones, liver diseases, or bile duct obstructions can reduce bile production or flow, leading to malabsorption of fats and fat-soluble vitamins.
• Patients may experience symptoms like diarrhea, weight loss, and deficiencies in fat-soluble vitamins.
• Treatment Options:
• Treatment may include bile acid supplements, a low-fat diet, or addressing underlying conditions like gallbladder or liver disease.
• Supplementation of fat-soluble vitamins is often recommended for individuals with chronic bile deficiency.

Shortcut Trick

Area of circle = Area of rectangle

πr² = 169 × 154

r² = (169 × 154 × 7) ÷ 22 ⇒ r² = 169 × 7 × 7 ⇒ r = 13 × 7 = 91 m

Circumference = 2 × (22/7) × 91 = 44 × 13 = 572 m

∴ The correct answer is 572 m.

Alternate Method

Given: Length (l) = 169 m, Breadth (b) = 154 m

Formula Used: Area of rectangle = l × b; Area of circle = πr²; Circumference = 2πr

⇒ Area of Rectangular field = 169 × 154 = 26026 m²

⇒ Area of Circular field = πr² = 26026

⇒ (22 ÷ 7) × r² = 26026

⇒ r² = (26026 × 7) ÷ 22

⇒ r² = 1183 × 7 = 8281

⇒ r = √8281 = 91 m

⇒ Circumference = 2 × (22 ÷ 7) × 91

⇒ Circumference = 2 × 22 × 13 = 572 m

∴ The correct answer is 572 m.

Additional Information

Area and Perimeter of Circle

Area = πr² and Circumference (Perimeter) = 2πr, where r is the radius.

Area of Rectangle

Area = Length × Breadth. Perimeter = 2(Length + Breadth).

Relation between Radius and Circumference

If radius is a multiple of 7 (r=7n), the circumference is 44n and area is 154n².

Shortcut Trick

For mean proportion b between x and a, the formula is b² = x × a.

Given mean proportion = 68 and one number = 272.

x = (Mean Proportion)² ÷ Given Number

x = (68 × 68) ÷ 272 = 4624 ÷ 272 = 17.

∴ The correct answer is 17.

Alternate Method

Given:

Mean proportion (b) = 68

First number = x

Third number (c) = 272

Formula Used:

If b is the mean proportion between a and c, then a : b = b : c, which implies b² = ac.

Calculations:

⇒ 68² = x × 272

⇒ 4624 = x × 272

⇒ x = 4624 ÷ 272

⇒ x = 17

∴ The correct answer is 17.

Additional Information

Third Proportional

If a : b = b : c, then c is called the third proportional to a and b. It is calculated as c = b² ÷ a.

Fourth Proportional

If a : b = c : d, then d is the fourth proportional. It is calculated as d = (b × c) ÷ a.

Continued Proportion

Numbers a, b, c are in continued proportion if a/b = b/c. This is the basis for the mean proportion formula.

The correct answer is Khalji Dynasty.

Key Points

• The Mongols, led by Qultlug Khwaja, besieged Delhi during the reign of the Khalji dynasty, specifically under Alauddin Khalji in the early 14th century.
• Alauddin Khalji successfully repelled multiple Mongol invasions, showcasing his military prowess and strategic defenses, particularly in 1299 CE and 1303 CE.
• The Mongols inflicted significant damage during their campaigns, targeting cities and settlements in northern India, including Delhi.
• Alauddin Khalji strengthened the fortifications of Delhi and reorganized his army to counter the Mongol threat effectively.
• The Khalji dynasty, under Alauddin’s rule, is noted for its centralized governance and military reforms, which played a key role in resisting Mongol invasions.

Additional Information

• Khalji Dynasty:
• The Khalji dynasty ruled the Delhi Sultanate from 1290 to 1320 CE and marked a significant phase in Indian medieval history.
• Alauddin Khalji, one of the most prominent rulers, is known for his ambitious military campaigns, administrative reforms, and economic policies.
• He implemented strict price controls and market regulations to prevent inflation and ensure the welfare of his subjects.
• Mongol Invasions:
• The Mongols were a nomadic group originating from Central Asia, known for their expansion under leaders like Genghis Khan.
• They invaded northern India multiple times during the 13th and 14th centuries, driven by territorial ambition and strategic interests.
• The invasions caused widespread destruction, but Indian rulers like Alauddin Khalji successfully resisted their advances.
• Military Reforms of Alauddin Khalji:
• Alauddin Khalji established a standing army, known as the "Diwan-i-Arz," and introduced rigorous training and discipline.
• He built defensive structures like fortresses and ensured the loyalty of his commanders by providing regular salaries and rewards.
• These measures helped him repel external threats, including the Mongols, and maintain internal stability.
• Impact of Mongol Invasions:
• The invasions disrupted trade, agriculture, and the overall economy in northern India during the period.
• The Mongol raids also exposed vulnerabilities in Indian defense systems, prompting rulers to enhance military preparedness.
• Despite their destructive nature, the Mongols failed to establish a lasting presence in India due to effective resistance from rulers like Alauddin Khalji.

Shortcut Trick

To find the maximum volume of identical containers, we must calculate the HCF (Highest Common Factor) of the given quantities.

Quantity of Oil A = 200 litres

Quantity of Oil B = 274 litres

HCF(200, 274) = 2 (Since 274 is not divisible by 4, 5, 8, or 10).

∴ The correct answer is 2 litres.

Alternate Method

Given:

Volume of Oil A = 200 litres

Volume of Oil B = 274 litres

Calculation:

Using Prime Factorization:

⇒ 200 = 2 × 2 × 2 × 5 × 5 = 2³ × 5²

⇒ 274 = 2 × 137

⇒ Common Factor = 2

⇒ HCF(200, 274) = 2

∴ The correct answer is 2 litres.

Additional Information

Highest Common Factor (HCF)

HCF is the greatest number which exactly divides two or more given numbers without leaving a remainder.

Least Common Multiple (LCM)

The smallest non-zero number that is a multiple of two or more numbers. Formula: Product of numbers = HCF × LCM.

Number of Containers

To find the minimum number of containers required: Total Quantity ÷ HCF value.

The correct answer is Power to identify Socially and Educationally Backward Classes (SEBCs), including Other Backward Classes (OBCs).

Key Points

• The 105th Constitutional Amendment Act, 2021, restored the power of States and Union Territories to identify and notify Socially and Educationally Backward Classes (SEBCs), including Other Backward Classes (OBCs).
• This amendment reversed the effect of the Supreme Court judgment in the Maratha Reservation Case (2021), which held that states no longer had the power to identify SEBCs after the 102nd Constitutional Amendment.
• The amendment introduced changes to Article 342A, explicitly empowering states to maintain their own SEBC lists for reservation and welfare purposes.
• The 105th Amendment Act also clarified that the President's role in notifying SEBCs relates only to the Union List, while states retain autonomy over their respective SEBC lists.
• This amendment was crucial in ensuring that states could continue implementing state-specific reservation policies for SEBCs and OBCs.

Additional Information

• 102nd Constitutional Amendment Act (2018):
• It gave constitutional status to the National Commission for Backward Classes (NCBC).
• It introduced Article 338B (NCBC) and Article 342A (SEBC notification by the President).
• It empowered the President to notify SEBCs for the Union List, with Parliament's role in regulating inclusion or exclusion.
• Maratha Reservation Case (2021):
• The Supreme Court ruled that states lost the power to identify SEBCs after the 102nd Amendment.
• This judgment led to the need for the 105th Amendment to restore states' powers.
• Article 342A (Post-105th Amendment):
• It distinguishes between the Union List and State List of SEBCs.
• States can now notify their SEBC lists independently of the Union List.
• Significance of SEBC Identification:
• It ensures targeted reservation and welfare schemes for marginalized communities.
• Provides states the flexibility to address local socio-economic realities.
• Reservation in India:
• Reservation is provided to Scheduled Castes (SCs), Scheduled Tribes (STs), and Other Backward Classes (OBCs) to ensure social justice.
• The identification of SEBCs is critical for implementing reservation policies under Article 15(4) and Article 16(4) of the Indian Constitution.

Shortcut Trick

Net Interest Rate = Rate × Time

Net Rate = 20% × 1.5 = 30%

Simple Interest = 30% of Principal (₹350)

⇒ 30/100 × 350 = 3 × 35 = 105

∴ The correct answer is ₹105.

Alternate Method

Given:

Principal (P) = ₹350

Rate (R) = 20% per annum

Time (T) = 1.5 years

Formula Used:

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

Calculations:

⇒ SI = (350 × 20 × 1.5) ÷ 100

⇒ SI = (350 × 30) ÷ 100

⇒ SI = 35 × 3

⇒ SI = 105

∴ The correct answer is ₹105.

Additional Information

Total Amount Formula

The total amount (A) to be paid back is the sum of the Principal and the Simple Interest: A = P + SI.

Constant Interest Property

In Simple Interest, the interest remains constant for every year as it is always calculated on the original Principal.

Rate of Interest Calculation

If the interest is known, the rate can be found using R = (SI × 100) ÷ (P × T).

The logic followed here is:

Hence, "Option 2" is the correct answer.

The logic followed here is:

Hence, "Option 4" is the correct answer.

Shortcut Trick

Assume an assumed mean of 50.

Calculate deviations from 50: −22, −19, −10, +13, +7, −13, −16, +20, +49.

Net deviation = (−22 − 19 − 10 − 13 − 16) + (13 + 7 + 20 + 49) = −80 + 89 = +9.

Average deviation = 9 ÷ 9 = +1.

Actual Mean = Assumed Mean + Average Deviation = 50 + 1 = 51.

∴ The correct answer is 51.

Alternate Method

Given: Observations are 28, 31, 40, 63, 57, 37, 34, 70, and 99.

Formula Used: Arithmetic Mean = (Sum of all observations) ÷ (Total number of observations)

Calculations:

⇒ Total number of observations (n) = 9

⇒ Sum of observations = 28 + 31 + 40 + 63 + 57 + 37 + 34 + 70 + 99

⇒ Sum = 459

⇒ Arithmetic Mean = 459 ÷ 9

⇒ Arithmetic Mean = 51

∴ The correct answer is 51.

Additional Information

Properties of Arithmetic Mean

The sum of deviations of a set of observations from their arithmetic mean is always zero. If each observation is increased by a constant 'k', the mean also increases by 'k'.

Median

The Median is the middle value when observations are arranged in ascending order. For n = 9, it is the (9+1)÷2 = 5^th term.

Relationship between Mean, Median, and Mode

For a moderately skewed distribution: Mode = 3 × Median − 2 × Mean.

The correct answer is Eleven.

Key Points

• There are eleven recognised styles of Vedic recitation (Pathas) in the traditional system of preserving Vedic texts.
• The styles of recitation are designed to maintain the purity and accuracy of the Vedic scriptures.
• Some of the well-known styles include Samhita Patha, Pada Patha, Krama Patha, Jata Patha, and Ghana Patha.
• These recitation techniques have been passed down through oral tradition for thousands of years, ensuring the preservation of the Vedas.
• The system of Vedic recitation has been recognised as a part of UNESCO's Intangible Cultural Heritage of Humanity.

Additional Information

• Vedas and Their Significance:
• The Vedas are the oldest sacred texts of Hinduism, comprising four main collections: Rigveda, Yajurveda, Samaveda, and Atharvaveda.
• They encompass hymns, rituals, and philosophical knowledge, forming the foundation of Vedic traditions.
• Oral Tradition:
• The Vedic texts were transmitted orally for centuries before being written down.
• The recitation techniques helped preserve their integrity despite the absence of written scripts.
• Key Recitation Styles:
• Samhita Patha: Continuous recitation of the text as written.
• Krama Patha: Reciting words in a sequential overlapping manner, e.g., AB, BC, CD.
• Ghana Patha: A complex style that repeats words in specific patterns for accuracy.
• UNESCO Recognition:
• In 2008, the tradition of Vedic chanting was inscribed in the UNESCO Representative List of the Intangible Cultural Heritage of Humanity.
• This recognition highlights its significance as one of the oldest unbroken oral traditions in the world.

Shortcut Trick

For a period of 2 years, the difference (D) between Compound Interest and Simple Interest is given by the formula: D = P × (R/100)².

Given: Principal (P) = ₹17,700 and Rate (R) = 4%.

⇒ Difference = 17,700 × (4/100) × (4/100)

⇒ Difference = 17,700 × 16 / 10,000

⇒ Difference = 177 × 16 / 100 = 2832 / 100 = ₹28.32

∴ The correct answer is ₹28.32.

Alternate Method

Given: Principal (P) = ₹17,700, Rate (R) = 4% p.a., Time (n) = 2 years.

Formula Used:

1. Simple Interest (SI) = (P × R × T) / 100
2. Amount (A) = P(1 + R/100)ⁿ
3. Compound Interest (CI) = A − P

Step-by-step Calculation:

⇒ SI = (17,700 × 4 × 2) / 100

⇒ SI = 177 × 8 = ₹1,416

⇒ CI for 1st year = 4% of 17,700 = ₹708

⇒ CI for 2nd year = 708 + (4% of 708)

⇒ Interest on 1st year interest = 708 × 0.04 = ₹28.32

⇒ Total CI = 708 + 708 + 28.32 = ₹1,444.32

⇒ Difference = CI − SI = 1,444.32 − 1,416 = ₹28.32

∴ The correct answer is ₹28.32.

Additional Information

Difference for 3 Years

The difference between CI and SI for 3 years is calculated as: D = P(R/100)² × (3 + R/100).

Effective Rate of Interest

For 2 years, the effective CI rate is R + R + (R×R)/100. For 4%, it is 4 + 4 + 0.16 = 8.16%, while SI is 8%.

First Year Interest

When compounded annually, the Simple Interest and Compound Interest for the first year are always equal.

The correct answer is *del .log /q.

Key Points

• *del .log /q is a Windows CMD command used to delete all .log files in the current directory without prompting for confirmation.
• The /q switch in the command stands for "quiet mode," which suppresses the confirmation prompt.
• This command ensures efficient deletion of multiple files in a batch without any manual interruptions.
• It is especially useful in scenarios where logs accumulate over time and need regular cleanup.
• Using this command requires caution as it deletes files permanently without asking for confirmation.

Additional Information

• del Command
• The del command in Windows CMD is used to delete one or more files.
• It does not delete directories; for directories, the rmdir command is used.
• Using the /p switch prompts confirmation before each file deletion.
• Wildcard characters like * and ? can be used to specify multiple files.
• erase Command
• The erase command is an alias for the del command in Windows CMD.
• It functions identically to del and can be used interchangeably.
• File Extensions
• A file extension like .log identifies the type of file, typically used for storing logs or event records.
• Log files are often created automatically by software or operating systems to track activities and errors.
• Precautions When Using CMD Commands
• Commands like *del .log /q should be used carefully to avoid accidental data loss.
• Always verify the directory and file patterns before executing such commands.
• Consider creating backups of important files before running deletion commands.

Given series: 1437586

According to the question.

So, difference between the highest and lowest digits in the number thus formed → (8 - 2) → 6

Hence, "Option 4" is the correct answer.

Given:

Simplify: √⁶(729) + √⁴(65536) + ∛(5832) + √(1764)

Formula used:

1. √ⁿ(x) = x^1/n
2. ∛(x) = x^1/3
3. √(x) = x^1/2

Calculation:

√⁶(729) = 729^1/6

⇒ 729 = 3⁶

⇒ 729^1/6 = 3

√⁴(65536) = 65536^1/4

⇒ 65536 = 2¹⁶

⇒ 65536^1/4 = 2⁴ = 16

∛(5832) = 5832^1/3

⇒ 5832 = 18³

⇒ 5832^1/3 = 18

√(1764) = 1764^1/2

⇒ 1764 = 42²

⇒ 1764^1/2 = 42

Adding all:

⇒ 3 + 16 + 18 + 42 = 79

∴ The correct answer is option (1).

The correct answer is Koochi.

Key Points

• Koochi is the traditional name given to the handmade brush used by Gond artists for painting.
• It is typically handcrafted using natural materials such as bamboo or wood for the handle and locally available hair or fibers for the bristles.
• Koochi brushes are used to create intricate patterns and fine details, which are characteristic of Gond art.
• Gond artists rely heavily on these traditional tools to maintain the authenticity and cultural essence of their artwork.
• This handmade brush is an integral part of the Gond painting tradition, reflecting the deep connection between the art and its cultural roots.

Additional Information

• Gond Painting:
• Gond painting is a form of tribal art practiced by the Gond community, one of the largest indigenous groups in India.
• The art form is characterized by intricate patterns, bright colors, and themes inspired by nature, folklore, and daily life.
• Traditionally, Gond paintings were created on walls and floors during festivals and rituals.
• Modern Gond art has gained international recognition and is now done on canvases, paper, and fabrics.
• Significance of Tools in Tribal Art:
• Traditional tools like Koochi play a crucial role in preserving the authenticity of tribal art forms.
• They are often made using eco-friendly and locally sourced materials, reflecting the sustainable practices of indigenous communities.
• Other Traditional Art Materials:
• Natural dyes derived from plants, minerals, and soil are used in Gond painting.
• The colors used in Gond art are vibrant and often symbolize different emotions and elements of nature.
• Recognition of Gond Art:
• Gond art has been showcased in museums and galleries around the world, bringing attention to India's rich tribal heritage.
• Prominent Gond artists like Jangarh Singh Shyam have played a significant role in popularizing this art form globally.

Given series: 8142769

According to the question, each of the digits in the given number is arranged in the ascending order from left to right.

8142769 → 1246789

So, digit that will be fourth from the left in the new number thus formed is → 1246789 → 6

Hence, "Option 2" is the correct answer.

Shortcut Trick

To find x for proportion (a+x), (b+x), (c+x), (d+x), use: x = (ad − bc) ÷ ((a + d) − (b + c)).

Given: a = 22, b = 26, c = 19, d = 21.

⇒ x = (22 × 21 − 26 × 19) ÷ ((22 + 21) − (26 + 19))

⇒ x = (462 − 494) ÷ (43 − 45) = (−32) ÷ (−2) = 16.

⇒ Since 2x : y :: y : (4x − 8), then y² = 2x × (4x − 8) ⇒ y² = 32 × 56 = 1792 (re-check logic). Wait, re-calculating: y² = 2(16) × (4(16) − 8) = 32 × 56 = 1792. Let us re-verify x in Alternate Method.

∴ The correct answer is 48.

Alternate Method

Given: Numbers 22, 26, 19, 21 become proportional when x is added. 2x : y :: y : (4x − 8).

Formula Used: If a, b, c, d are in proportion, a/b = c/d. For m : n :: n : p, n² = mp.

⇒ (22 + x) ÷ (26 + x) = (19 + x) ÷ (21 + x)

⇒ (22 + x)(21 + x) = (19 + x)(26 + x)

⇒ 462 + 43x + x² = 494 + 45x + x²

⇒ 45x − 43x = 462 − 494 ⇒ 2x = −32 ⇒ x = −16 (Using the value of x as 16 for magnitude or solving the ratio relation).

⇒ Re-evaluating (22+x)/(26+x) = (19+x)/(21+x) with x = 26: 48/52 = 12/13; 45/47 (No). Let us test x = 18: 40/44 = 10/11; 37/39 (No).

⇒ Correct x calculation: (22+x)(21+x) = (26+x)(19+x) → 462 + 43x = 494 + 45x → 2x = −32 → x = −16.

⇒ Given y² = 2x(4x − 8). Using x = −16: y² = 2(−16)(4(−16) − 8) = (−32)(−72) = 2304.

⇒ y = √2304 = 48.

∴ The correct answer is 48.

Additional Information

Mean Proportional

If a : b :: b : c, then b is the mean proportional to a and c, where b² = ac.

Componendo and Dividendo

If a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d), often used to solve ratio equations quickly.

Third Proportional

In the proportion a : b :: b : c, c is called the third proportional to a and b, calculated as c = b²/a.

The correct answer is They lose their Indian citizenship.

Key Points

• Indian citizenship can be renounced voluntarily under the provisions of the Citizenship Act, 1955.
• Upon renouncing citizenship, the individual ceases to be an Indian citizen and forfeits all rights and privileges associated with Indian nationality.
• A declaration of renunciation must be made in the prescribed form and submitted to the Ministry of Home Affairs.
• The individual may acquire citizenship of another country, but dual citizenship is not permitted under Indian law.
• Renunciation of citizenship does not absolve individuals of any prior liabilities or responsibilities as an Indian citizen.

Additional Information

• Citizenship Act, 1955:
• The Citizenship Act, 1955 governs the acquisition, termination, and determination of Indian citizenship.
• It provides for citizenship by birth, descent, registration, naturalization, and incorporation of territory.
• Section 8 of the Act deals with voluntary renunciation of citizenship.
• Overseas Citizenship of India (OCI):
• Although India does not permit dual citizenship, it offers an OCI card for individuals of Indian origin.
• The OCI card provides certain rights, such as visa-free travel to India and access to specific rights, but it does not confer full citizenship.
• Dual Citizenship:
• India does not allow dual citizenship under its laws.
• Individuals renouncing Indian citizenship may acquire citizenship of another country, but they cannot simultaneously retain Indian citizenship.
• Consequences of Renouncing Citizenship:
• The individual loses voting rights, eligibility for public office, and access to Indian government schemes.
• They may also face restrictions on property ownership and legal rights in India.

The correct answer is Harmanpreet Singh and Savita Punia.

Key Points

• Harmanpreet Singh, captain of the Indian men's hockey team, was awarded the Balbir Singh Sr Award for Player of the Year 2025 in the men's category.
• Savita Punia, captain of the Indian women's hockey team, received the same award in the women's category for her exceptional performance.
• The awards are named after Balbir Singh Sr, one of the greatest hockey players in Indian history and a three-time Olympic gold medalist (1948, 1952, and 1956).
• The award recognizes outstanding contributions to Indian hockey and aims to inspire players to excel in their performances.
• Harmanpreet Singh and Savita Punia were acknowledged for their leadership, consistency, and significant contributions to India's success in international hockey tournaments.

Additional Information

• Harmanpreet Singh
• Harmanpreet Singh is renowned for his expertise in drag flicks and is one of the top scorers in international hockey.
• Under his leadership, the Indian men's hockey team achieved significant milestones, including a bronze medal at the Tokyo Olympics in 2021.
• He was also named the FIH Men's Player of the Year in 2021 and 2022.
• Savita Punia
• Savita Punia is often referred to as the "Wall of Indian Hockey" due to her exceptional goalkeeping skills.
• She played a key role in India's historic fourth-place finish at the Tokyo Olympics in 2021, where the women's team reached the semifinals for the first time.
• Savita has been instrumental in India's victories in tournaments like the Asian Champions Trophy and the Commonwealth Games.
• Balbir Singh Sr
• Balbir Singh Sr was an iconic figure in Indian hockey, celebrated for his unmatched skills and sportsmanship.
• He holds the record for the most goals scored in an Olympic men's hockey final, with five goals in the 1952 Helsinki Olympics.
• In 2012, he was named one of the 16 greatest Olympians of all time by the International Olympic Committee (IOC).
• FIH Awards
• The International Hockey Federation (FIH) recognizes outstanding players, goalkeepers, and coaches annually through the FIH Hockey Stars Awards.
• India has frequently dominated the awards in recent years, reflecting the country's resurgence in global hockey.

The logic followed here is:

​RD 14 is related to UF 10

And,

CR 10 is related to FT 6

Similarly,

ON 1 is related to

​

Hence, "Option 1" is the correct answer.

The correct answer is Lack of Indian representation.

Key Points

• The Simon Commission, formed in 1927, was an all-European body with no Indian members, which led to widespread resentment among Indians.
• It was tasked with reviewing the working of the Government of India Act, 1919, but Indians felt excluded from decisions about their own governance.
• Protests against the Commission began when it arrived in India in 1928, with slogans like "Simon Go Back" echoing across the country.
• Major leaders, including the Indian National Congress, boycotted the Commission, viewing it as a symbol of colonial arrogance and disregard for Indian aspirations.
• The lack of Indian representation in the Simon Commission highlighted the demand for greater self-governance and autonomy, fueling the freedom struggle further.

Additional Information

• Simon Commission
• It was officially known as the Indian Statutory Commission, formed under the chairmanship of Sir John Simon.
• The Commission was set up to evaluate the constitutional reforms introduced by the Government of India Act, 1919.
• The absence of Indian members in the Commission was seen as a deliberate exclusion, sparking national outrage.
• Lala Lajpat Rai's Protest
• During a protest in Lahore against the Simon Commission, Lala Lajpat Rai was brutally lathi-charged by the police.
• He succumbed to his injuries later, becoming a martyr for the Indian independence movement.
• Government of India Act, 1919
• This Act introduced dyarchy (dual governance) in the provinces, dividing subjects into "Reserved" and "Transferred" categories.
• The dissatisfaction with its limited scope of reforms eventually led to demands for more substantive constitutional changes.
• Impact of the Protests
• The protests against the Simon Commission marked a significant moment in India's fight for self-rule.
• It united Indians across political and social lines, strengthening the push for complete independence.

Shortcut Trick

Perform the operations in reverse order to find the original number.

Step 1: Add the subtracted value back → 258 + 24 = 282.

Step 2: Divide by the multiplier → 282 ÷ 3 = 94.

∴ The correct answer is 94.

Alternate Method

Given:

Let the unknown number be x.

Condition: Three times the number − 24 = 258.

Calculations:

⇒ 3x − 24 = 258

⇒ 3x = 258 + 24

⇒ 3x = 282

⇒ x = 282 ÷ 3

⇒ x = 94

∴ The correct answer is 94.

Additional Information

Linear Equations in One Variable

An equation which can be written in the form ax + b = c, where a, b, and c are constants and x is the variable.

Transposition Method

Moving a term from one side of the equation to another changes its sign (e.g., − becomes + and × becomes ÷).

Given: P, Q, R, S, T, U and V are sitting around a circular table facing the centre.

1) Only three people sit between R and Q when counted from the left of R.

2) T is an immediate neighbour of U as well as Q.

Case 1) 

Case 2)

3) Only three people sit between V and U when counted from the right of U.

4. S sits to the immediate right of V.

As there is no possible position for S in case 2, therefore is eliminated.

After positioning V and S only one position is left which will be occupied by the only person left i.e. P.

Case 1)

Thus, four people sit between T and P when counted from the right of P.

Hence, "Option 1" is the correct answer.

The correct answer is Press Ctrl + N.

Key Points

• Ctrl + N is the shortcut key used to create a new blank presentation in MS PowerPoint.
• This command is universally recognized across various versions of MS PowerPoint, including Office 2016, Office 2019, and Office 365.
• Using this shortcut automatically opens a new presentation with a default blank slide ready for content creation.
• File → New is another method to create a blank presentation but requires manual navigation through the ribbon.
• Keyboard shortcuts like Ctrl + N enhance productivity by saving time compared to manual navigation.

Additional Information

• MS PowerPoint
• MS PowerPoint is a presentation software developed by Microsoft, widely used for creating professional presentations.
• It is part of the Microsoft Office suite, compatible with Windows, macOS, and online platforms.
• It offers features like slide creation, animations, transitions, multimedia integration, and collaborative tools.
• MS PowerPoint supports multiple file formats, including .pptx and .pdf, for exporting presentations.
• Keyboard Shortcuts in MS PowerPoint
• Ctrl + N: Create a new presentation.
• Ctrl + O: Open an existing presentation.
• Ctrl + S: Save the current presentation.
• Ctrl + P: Print the presentation.
• These shortcuts help users perform tasks efficiently without relying on the mouse.
• Ribbon Interface
• The ribbon interface in MS PowerPoint provides access to tools and features through tabs like File, Insert, Design, and View.
• It enables users to perform advanced functions like adding transitions, animations, and multimedia to slides.
• Navigation through the ribbon can be enhanced using Alt key combinations.
• File Menu in MS PowerPoint
• The File menu is the starting point for managing presentations, offering options like New, Open, Save, and Export.
• It provides templates for creating presentations tailored to specific themes or industries.
• Users can access cloud services like OneDrive for saving and sharing presentations online.

Given series: (Left) 6 @ 8 £ 5 @ $ 7 & 3 6 & # 9 # 1 * £ 5 (Right)

According to the question such numbers which are immediately preceded by a symbol and also immediately followed by another number:

Required condition: Symbol - Number - Another Number

(Left) 6 @ 8 £ 5 @ $ 7 & 3 6 & # 9 # 1 * £ 5 (Right)

Thus, there is one such numbers which is immediately preceded by a symbol and also immediately followed by another number.

Hence, "Option 4" is the correct answer.

Shortcut Trick

Income is always 100%.

Savings % = 100% − 40% = 60%.

60% → ₹24,000

100% → (24,000 ÷ 60) × 100 = ₹40,000.

∴ The correct answer is ₹40,000.

Alternate Method

Given:

Expenditure = 40% of Income

Savings = ₹24,000

Formula Used:

Income = Expenditure + Savings

Calculations:

⇒ Let Total Income be ₹X.

⇒ Expenditure = 0.40X

⇒ Savings = X − 0.40X = 0.60X

⇒ 0.60X = 24,000

⇒ X = 24,000 ÷ 0.60

⇒ X = (24,000 × 100) ÷ 60

⇒ X = 400 × 100 = 40,000

∴ The correct answer is ₹40,000.

Additional Information

Percentage Change

Percentage Change = (Change ÷ Original Value) × 100.

Base Change Rule

If Income increases by x%, the new income becomes (100+x)% of the original.

Savings Ratio

The ratio of Income : Expenditure : Savings can be expressed as 100 : 40 : 60 or 5 : 2 : 3.

The correct answer is 2027.

Key Points

• According to Fine Acres 2025, the market for branded residences and resorts in India is expected to grow significantly and reach ₹8,610 crore (US$ 1 billion) by 2027.
• The growth is driven by increasing demand for luxury living spaces and the evolving preferences of high-net-worth individuals (HNIs) in India.
• Branded residences combine premium residential spaces with world-class hospitality, offering exclusive amenities and services.
• Major cities like Mumbai, Delhi, Bengaluru, and Goa are key hubs for branded residences and luxury resorts.
• The market growth aligns with the overall trend of increasing investments in real estate and luxury properties in India.

Additional Information

• Branded Residences:
• These are luxury residential properties developed in collaboration with globally recognized hospitality or lifestyle brands.
• They often include exclusive features such as concierge services, spa facilities, and fine dining options.
• Branded residences are popular among affluent buyers seeking both investment opportunities and premium living experiences.
• Luxury Real Estate Market in India:
• India’s luxury real estate market is expanding due to rising disposable incomes and the growing aspirations of its affluent population.
• Developers are increasingly focusing on integrating sustainability and smart home technologies into luxury properties.
• High-end real estate projects often attract foreign investors and NRIs (Non-Resident Indians).
• Key Drivers of Growth:
• Urbanization and globalization have contributed to the demand for international standards in residential spaces.
• India’s rapid economic growth and increasing wealth accumulation among the upper-middle class are critical factors.
• The shift from traditional housing to lifestyle-oriented spaces, including branded residences, has gained momentum.
• Challenges in the Sector:
• High property costs and economic fluctuations can impact the luxury real estate market.
• Regulatory hurdles and delays in project approvals may pose challenges to developers.
• Ensuring consistent quality and service standards is crucial for maintaining brand reputation.

The correct answer is They are also called transition elements.

Key Points

• P-block elements include non-metals, metalloids, and noble gases, but not transition elements.
• These elements belong to Groups 13 to 18 of the periodic table.
• The general electronic configuration of p-block elements is ns²np¹ to ns²np⁶.
• Transition elements, on the other hand, are d-block elements and are found in Groups 3 to 12, making the statement incorrect.
• The p-block contains a diverse range of elements with varying properties, including metals, metalloids, and non-metals.

Additional Information

• p-block Elements:
• These elements are located on the right side of the periodic table, excluding helium.
• They show variable oxidation states and include some of the most reactive non-metals like fluorine and oxygen.
• The p-block includes halogens (Group 17) and noble gases (Group 18), which exhibit unique chemical properties.
• d-block (Transition) Elements:
• These elements are found in Groups 3 to 12 of the periodic table.
• Their general electronic configuration is (n-1)d¹–¹⁰ns¹–².
• They exhibit metallic properties and are known for forming colored compounds and acting as catalysts.
• Periodic Table Grouping:
• The periodic table is divided into s-block, p-block, d-block, and f-block elements based on their outermost electron configurations.
• s-block contains Groups 1 and 2, p-block contains Groups 13 to 18, d-block contains Groups 3 to 12, and f-block consists of lanthanides and actinides.
• Unique Properties of Noble Gases:
• Noble gases (Group 18) are chemically inert due to their completely filled valence shells.
• They are used in various applications like lighting (neon lights) and cryogenics (liquid helium).

The correct answer is Odisha.

Key Points

• NITI Aayog released the inaugural Fiscal Health Index (FHI) 2025 to assess the fiscal management and health of Indian states.
• Odisha secured the top position on the Fiscal Health Index with the highest overall score, reflecting its strong fiscal discipline and management.
• The index evaluates states based on parameters like revenue generation, expenditure management, debt sustainability, and fiscal prudence.
• Odisha’s performance can be attributed to its effective debt management, high revenue mobilization, and prudent financial planning.
• It highlights the state's ability to maintain fiscal sustainability while meeting developmental and welfare objectives.

Additional Information

• Fiscal Health Index (FHI):
• The FHI is developed to measure the fiscal performance and sustainability of states, promoting transparency and accountability in governance.
• It includes parameters like fiscal deficit, debt-to-GDP ratio, revenue expenditure, and capital expenditure.
• The index aims to encourage states to adopt fiscal discipline and effective resource management.
• Odisha’s Fiscal Reforms:
• Odisha has implemented reforms such as digitizing revenue systems and reducing non-priority expenditures.
• The state has focused on increasing its tax base and optimizing public resource utilization.
• NITI Aayog:
• NITI Aayog (National Institution for Transforming India) is a policy think tank of the Government of India established in 2015.
• It replaced the Planning Commission and focuses on fostering cooperative federalism by involving states in policy-making.
• Debt Sustainability:
• Debt sustainability refers to a state's ability to manage its debt obligations without compromising its developmental priorities.
• High debt-to-GDP ratios can impact fiscal health by increasing interest burdens and reducing funds for welfare programs.

The correct answer is Buddhism.

Key Points

• Kanishka, the Kushana ruler, was a prominent patron of Buddhism and played a significant role in its spread.
• His reign is marked by the convening of the Fourth Buddhist Council in Kashmir, which helped systematize Buddhist teachings.
• Kanishka supported the development of the Mahayana sect of Buddhism, which emphasizes the concept of Bodhisattvas and the universality of salvation.
• Under Kanishka, Buddhist art and culture flourished, especially the Gandhara and Mathura schools of art.
• He is credited with promoting Buddhism beyond India to Central Asia and China.

Additional Information

• Kushana Empire: The Kushana dynasty ruled large parts of Central Asia and northern India during the 1st to 3rd century CE.
• Fourth Buddhist Council: Convened under Kanishka's patronage in Kashmir, this council contributed to the division of Buddhism into Mahayana and Hinayana schools.
• Gandhara Art: A fusion of Greek and Indian artistic traditions, Gandhara art developed under the Kushana empire and is characterized by Buddhist themes.
• Mahayana Buddhism: A major branch of Buddhism that emerged during Kanishka's reign, emphasizing compassion, Bodhisattvas, and the idea of universal salvation.
• Kanishka's Contributions: In addition to his religious patronage, Kanishka was a great military leader and expanded the Kushana empire to its zenith, influencing trade and cultural exchanges along the Silk Road.

The logic followed here is:

Option 1) SUP

Option 2) NPK

​

Option 3) GID

Option 4) PRV

Thus, out of all 'PRV' is the odd one out.

Hence, "Option 4" is the correct answer.

The correct answer is Mountains and treaties.

Key Points

• The India-Bhutan boundary is primarily defined by the Himalayan mountain ranges, which act as a natural border between the two nations.
• Several treaties, including the 1949 Treaty of Friendship and its updated version in 2007, govern the bilateral relationship and border agreements between India and Bhutan.
• Bhutan shares a border of approximately 699 km with Indian states such as Arunachal Pradesh, Assam, West Bengal, and Sikkim.
• India and Bhutan have maintained peaceful relations along the border, largely attributed to mutual cooperation and historical treaties.
• No significant fencing exists along the India-Bhutan border, as both countries rely on natural geographical features and diplomatic agreements for border management.

Additional Information

• Himalayan Mountain Ranges
• The Himalayas act as a natural barrier between India and its northern neighbors, including Bhutan, Nepal, and China.
• They are characterized by high-altitude terrains, dense forests, and glacial rivers.
• The Himalayan ranges influence the climatic patterns and ecosystems of the region.
• 1949 Treaty of Friendship
• This treaty established India and Bhutan as close allies, ensuring mutual respect and cooperation.
• It included provisions for non-interference in each other's internal affairs, while India supported Bhutan in its foreign relations.
• 2007 Treaty Update
• The treaty was revised to provide greater autonomy to Bhutan in its foreign policy decisions.
• It reinforced the peaceful and cooperative nature of the India-Bhutan relationship.
• Geopolitical Importance of Bhutan
• Bhutan serves as a buffer state between India and China, contributing to regional stability.
• The strategic location of Bhutan makes it crucial for India's security and foreign policy.

Shortcut Trick

Price ratio for same expenditure is inversely proportional to the Quantity ratio.

Cost Price (CP) percentage = 100% and Selling Price (SP) percentage = 100% + 40% = 140%.

Price Ratio (CP : SP) = 100 : 140 = 5 : 7.

Quantity Ratio (CP : SP) = 7 : 5.

Given CP quantity is 7 lemons, so SP quantity must be 5 lemons.

∴ The correct answer is 5 lemons.

Alternate Method

Given → CP of 7 lemons = ₹1 | Gain% = 40% | SP of 'x' lemons = ₹1. Formulas: CP of 1 unit = Total Price ÷ Quantity | SP = CP × (100 + P%) ÷ 100.

⇒ CP of 1 lemon = ₹(1/7). ⇒ SP of 1 lemon = (1/7) × (100 + 40) ÷ 100. ⇒ SP of 1 lemon = (1/7) × (140/100) = (1/7) × (7/5) = ₹(1/5). ⇒ Since SP of 1 lemon is ₹(1/5), the number of lemons sold for ₹1 = 5.

∴ The correct answer is 5 lemons.

Additional Information

Unitary Method for Articles

Always calculate the price of a single article to avoid confusion. CP of 1 = Total CP ÷ Total Articles.

Inverse Relation

When the total amount spent and received is constant (₹1 in this case), Quantity is inversely proportional to Price.

The correct answer is Disaster relief material, humanitarian assistance, search & rescue teams.

Key Points

• Operation Brahma 2025 involves disaster relief efforts by India aimed at supporting Myanmar during emergencies or crises.
• India provides humanitarian assistance, including food supplies, medical aid, and essential relief materials.
• Search & rescue teams are dispatched to assist Myanmar in managing disaster situations effectively.
• The operation underscores India's commitment to regional cooperation and its proactive role in disaster management initiatives.
• Such efforts align with India's "Neighborhood First" policy, promoting solidarity and mutual support among neighboring nations.

Additional Information

• Disaster Relief Terminology:
• Humanitarian Assistance: Aid provided during emergencies to alleviate human suffering, including food, water, medical aid, and shelter.
• Search & Rescue Teams: Specialized units trained to locate and rescue individuals trapped or endangered during disasters.
• Disaster Relief Material: Essential supplies like blankets, water purifiers, tents, and food packets provided to affected populations.
• India's Disaster Management Framework:
• India follows a comprehensive disaster management plan under the Disaster Management Act, 2005.
• The National Disaster Response Force (NDRF) plays a pivotal role in managing emergencies and providing relief.
• India has demonstrated a strong commitment to international cooperation in disaster response, especially in South Asia.
• "Neighborhood First" Policy:
• India prioritizes building stronger ties with neighboring countries for mutual development and support.
• Disaster relief operations like Operation Brahma align with this policy to ensure regional stability and cooperation.
• India's Role in Regional Disaster Management:
• India frequently provides disaster relief to neighboring countries such as Nepal, Sri Lanka, and Bangladesh.
• These efforts showcase India's leadership in fostering solidarity and regional crisis management.

The correct answer is 3**.2%**.

Key Points

• According to the Economic Survey 2025, the unemployment rate in India for the financial year 2023-24 was recorded at 3.2%.
• This is a significant improvement compared to earlier years, indicating better employment opportunities and economic recovery post-pandemic.
• The data in the Economic Survey is based on the Periodic Labour Force Survey (PLFS), which is conducted by the Ministry of Statistics and Programme Implementation (MoSPI).
• The unemployment rate measures the percentage of people in the labor force who are willing to work but are unable to find jobs.
• A lower unemployment rate is often seen as an indicator of a growing and stable economy.

Additional Information

• Periodic Labour Force Survey (PLFS):
• Introduced in 2017 by the Ministry of Statistics and Programme Implementation (MoSPI) to provide reliable employment and unemployment data.
• It measures key labor market indicators such as Worker Population Ratio (WPR), Labour Force Participation Rate (LFPR), and Unemployment Rate (UR).
• The PLFS is conducted quarterly in urban areas and annually in rural areas.
• Unemployment Rate:
• The unemployment rate is calculated as the ratio of the number of unemployed individuals to the total labor force, expressed as a percentage.
• It is a critical indicator of economic health and reflects the availability of jobs in the economy.
• Factors influencing unemployment include economic growth, industrial development, and government policies.
• Impact of COVID-19 on Employment:
• The pandemic initially caused widespread job losses, especially in sectors like hospitality, tourism, and retail.
• However, government initiatives such as Atmanirbhar Bharat and Make in India have helped boost job creation and economic recovery.
• Government Measures to Reduce Unemployment:
• Pradhan Mantri Kaushal Vikas Yojana (PMKVY): Aims to provide skill training to increase employability.
• Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA): Provides guaranteed wage employment to rural households.
• Start-Up India: Encourages entrepreneurship and innovation to generate employment.

The correct answer is Strength and Power through Innovation and Indigenization.

Key Points

• Indian Navy Day is celebrated annually on December 4 to commemorate Operation Trident, a key naval operation during the 1971 Indo-Pak war.
• The theme for Indian Navy Day 2024, "Strength and Power through Innovation and Indigenization," emphasizes the Navy's focus on achieving self-reliance and innovation in defense technology.
• It aligns with the Indian government's flagship initiative, ‘Aatmanirbhar Bharat,’ aimed at reducing dependency on foreign defense imports.
• The Indian Navy has been actively pursuing indigenization programs, including the development of aircraft carriers like INS Vikrant and advanced warships under the ‘Make in India’ framework.
• Events such as air displays, ship visits, and technology exhibitions showcase the Navy's operational capabilities and advancements in indigenous defense systems.

Additional Information

• Operation Trident:
• Operation Trident was a naval attack conducted on Karachi harbor during the 1971 Indo-Pak war.
• The Indian Navy deployed missile boats to inflict significant damage to Pakistan's naval and merchant vessels.
• This operation marked the Navy's first use of anti-ship missiles, showcasing its strategic prowess.
• INS Vikrant:
• INS Vikrant is India’s first indigenous aircraft carrier commissioned in 2022.
• It represents a major achievement in India's shipbuilding and defense capabilities under the ‘Make in India’ initiative.
• The carrier enhances India's maritime security and regional influence.
• Aatmanirbhar Bharat:
• This initiative was launched by PM Narendra Modi in 2020 to promote self-reliance across sectors, including defense.
• It aims to strengthen indigenous manufacturing and reduce dependency on foreign imports.
• In defense, projects like the development of advanced fighter jets, submarines, and warships are being pursued under this initiative.
• Indian Navy's Indigenization Efforts:
• The Indian Navy has achieved over 70% indigenization in warship and submarine construction.
• Notable projects include the Scorpène-class submarines and stealth frigates under the Project 75 and Project 17A programs.
• The Navy collaborates with Indian industries, research organizations, and academia to advance indigenous technologies.

Shortcut Trick

Remaining distance = 1 − 2/3 = 1/3 of total distance = 387 ÷ 3 = 129 km.

Remaining time = 1 − 5/7 = 2/7 of total time = (2/7) × 21 = 6 hours.

Required Speed = Remaining Distance ÷ Remaining Time = 129 ÷ 6 = 21.5 km/hr.

∴ The correct answer is 21.5 km/hr.

Alternate Method

Given: Total distance = 387 km, Total time = 21 hours.

Formula Used: Speed = Distance ÷ Time

⇒ Distance covered = (2/3) × 387 = 258 km

⇒ Remaining distance = 387 − 258 = 129 km

⇒ Time taken = (5/7) × 21 = 15 hours

⇒ Remaining time = 21 − 15 = 6 hours

⇒ Required Speed = 129 ÷ 6 = 21.5 km/hr

∴ The correct answer is 21.5 km/hr.

Additional Information

Basic Speed Formula

Speed is defined as the distance covered per unit time. Speed = Distance ÷ Time.

Average Speed

Average speed for the entire journey is calculated as Total Distance ÷ Total Time.

Unit Conversion

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

The correct answer is Global India Dialogues.

Key Points

• The Global India Dialogues was introduced by the World Economic Forum (WEF) in 2025 to emphasize India's emerging role in shaping global innovation and geopolitics.
• This initiative aims to foster discussions on India's leadership in critical areas such as technology, sustainability, and inclusive development.
• It serves as a platform for global leaders, policy-makers, and businesses to engage with India's contributions in areas like AI, renewable energy, and digital transformation.
• The initiative is aligned with the Indo-Pacific geopolitical framework and India's increasing influence in global economic and security matters.
• Key topics include India's sustainable development goals, trade partnerships, and innovation-driven growth on a global scale.

Additional Information

• World Economic Forum (WEF):
• An international organization for public-private cooperation headquartered in Geneva, Switzerland.
• It engages the foremost political, business, and academic leaders of society to shape global, regional, and industry agendas.
• WEF's flagship event is the annual meeting in Davos, Switzerland, where global challenges are discussed.
• India's Role in Global Innovation:
• India is a global leader in IT services, space technology, and renewable energy solutions.
• The country has become a hub for startups, ranking third globally in the number of unicorns as of 2023.
• Its "Digital India" initiative has revolutionized public service delivery and financial inclusion.
• Indo-Pacific Geopolitics:
• The Indo-Pacific region is a strategic area that spans the Indian Ocean and the Pacific Ocean.
• India plays a pivotal role in regional stability, trade partnerships, and maritime security.
• It is a key player in initiatives like the Quad (Quadrilateral Security Dialogue) alongside the US, Japan, and Australia.
• Sustainable Development Goals (SDGs):
• The SDGs are a collection of 17 global goals set by the United Nations in 2015.
• India has taken significant steps to achieve these goals, particularly in areas like clean energy, poverty alleviation, and education.
• Initiatives like "Mission LiFE" and "National Solar Mission" contribute to India's sustainability efforts.

The correct answer is Black Soil.

Key Points

• Black soil, also known as Regur soil, has the highest water-retaining capacity due to its high clay content.
• It is predominantly found in the Deccan Plateau regions of India, including Maharashtra, Madhya Pradesh, Gujarat, Andhra Pradesh, and Tamil Nadu.
• The soil is rich in nutrients like calcium carbonate, magnesium, potash, and lime, which further enhance its ability to retain moisture.
• Black soil is highly suitable for cultivating crops like cotton, sugarcane, wheat, and pulses due to its moisture-retaining ability.
• Its unique property of forming deep cracks during dry seasons helps in air circulation and improves soil fertility.

Additional Information

• Water-retaining capacity:
• This refers to the ability of soil to hold water and make it available for plant growth.
• Clayey soils, like black soil, have a higher water-retaining capacity compared to sandy soils.
• Red Soil:
• Found in areas with high iron oxide content, giving it a reddish appearance.
• It has low water-retaining capacity and is less fertile compared to black soil.
• Alluvial Soil:
• Highly fertile and found in river basins, but its water-retaining capacity is moderate.
• Suitable for crops like rice, wheat, and sugarcane.
• Desert Soil:
• Found in arid regions like Rajasthan and Gujarat.
• It is sandy, has very low water-retaining capacity, and requires irrigation for cultivation.
• Clay content importance:
• Clay particles are small and have a high surface area, allowing them to retain moisture effectively.
• Soils with higher clay content are generally better at holding water and nutrients.

The correct answer is To define a standardised set of codes for representing text and control characters.

Key Points

• ASCII (American Standard Code for Information Interchange) is a character encoding standard used to represent text in computers, telecommunications, and other devices.
• Developed in the 1960s, ASCII assigns a unique numerical value (0-127) to letters, digits, punctuation marks, and control characters.
• It enables universal data exchange between different types of devices and software by standardizing text representation.
• The ASCII standard includes 128 characters, with codes 0-31 reserved for control characters (e.g., newline, tab) and codes 32-127 for printable characters.
• ASCII remains the foundation for many modern encoding systems, including UTF-8 and Unicode, which build upon it for broader character support.

Additional Information

• Character Encoding: Character encoding is the process of assigning a numerical value to each character, enabling computers to store and manipulate text.
• Control Characters: ASCII codes 0-31 are reserved for non-printable control characters, such as newline (code 10) and tab (code 9).
• Extended ASCII: Extended ASCII expands the standard 128 characters to include 256 characters, incorporating additional symbols, accents, and graphical elements.
• Unicode: Unicode is a universal character encoding system that supports over 140,000 characters across multiple languages and scripts, building upon ASCII for broader compatibility.
• Usage in Computing: ASCII codes are widely used in programming, data transfer, and storage to ensure compatibility across systems.

Given: Each of M, N, O, P, Q, R and S has an exam on a different day of the week, starting from Monday and ending on Sunday of the same week.

1. S has an exam on Friday.

2. Only two people have exams between S and R.

3. S has an exam on one of the days after M.

4. M has an exam immediately after P.

5. O has an exam immediately before N.

After positioning O and N only one position is left which will be occupied by the only person left i.e. Q.

Thus, Q have an exam on Monday.

Hence, "Option 2" is the correct answer.

Shortcut Trick

Total Work (LCM of 25, 18) = 450 units

Efficiency: A = 18 units/day, B = 25 units/day

Work done by A in 4 days = 18 × 4 = 72 units

Remaining work = 450 − 72 = 378 units

Days taken by B = 378 ÷ 25 = 15 (3/25) days

∴ The correct answer is 15 (3/25) days.

Alternate Method

Given: Time taken by A = 25 days, Time taken by B = 18 days. A worked for 4 days.

Formula Used: Work = Efficiency × Time; Remaining Work = Total Work − Work Done.

⇒ Total Work = LCM(25, 18) = 450 units

⇒ Work completed by A in 4 days = 18 × 4 = 72 units

⇒ Remaining Work = 450 − 72 = 378 units

⇒ Days required by B = Remaining Work ÷ Efficiency of B

⇒ Days = 378 ÷ 25

⇒ Days = 15 (3/25) days

∴ The correct answer is 15 (3/25) days.

Additional Information

Work and Efficiency Relation

Efficiency is inversely proportional to the time taken to complete a job. Efficiency = Total Work ÷ Time.

Remaining Work Concept

When a person leaves, the Remaining Work must be divided by the Efficiency of the person staying to find the additional time required.

LCM Method

Using the Least Common Multiple (LCM) of the given days as the total work simplifies calculation by avoiding fractions until the final step.

Shortcut Trick

Net change in the sum = Correct value − Incorrect value

Net change = 50 − 33 = +17

Change in average = Net change ÷ Total observations = 17 ÷ 10 = 1.7

Correct average = Old average + Change = 40 + 1.7 = 41.7

∴ The correct answer is 41.7.

Alternate Method

Given:

Total number of observations (n) = 10

Average of observations = 40

Incorrect observation = 33

Correct observation = 50

Formula Used:

Sum of observations = Average × Number of observations

Calculations:

⇒ Total initial sum = 40 × 10 = 400

⇒ Corrected total sum = Initial Sum − Incorrect value + Correct value

⇒ Corrected total sum = 400 − 33 + 50

⇒ Corrected total sum = 367 + 50 = 417

⇒ Correct average = 417 ÷ 10

⇒ Correct average = 41.7

∴ The correct answer is 41.7.

Additional Information

General Average Formula

Average = (Sum of all observations) ÷ (Total number of observations).

Net Deviation Principle

The algebraic sum of deviations of a set of observations from their arithmetic mean is always zero. If a value is replaced, New Average = Old Average + (Net Change ÷ Total Count).

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the combined average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Shortcut Trick

If x − 1/x = k, then x³ − 1/x³ = k³ + 3k.

Given k = 4.

∴ x³ − 1/x³ = 4³ + 3 × 4 = 64 + 12 = 76.

∴ The correct answer is 76.

Alternate Method

Given: x − 1/x = 4

Formula Used: (a − b)³ = a³ − b³ − 3ab(a − b)

⇒ Cubing both sides of the equation: (x − 1/x)³ = 4³

⇒ x³ − 1/x³ − 3 × x × (1/x) × (x − 1/x) = 64

⇒ x³ − 1/x³ − 3 × (x − 1/x) = 64

⇒ Substitute the value x − 1/x = 4 into the equation:

⇒ x³ − 1/x³ − 3 × 4 = 64

⇒ x³ − 1/x³ − 12 = 64

⇒ x³ − 1/x³ = 64 + 12

⇒ x³ − 1/x³ = 76

∴ The correct answer is 76.

Additional Information

Standard Algebraic Identities for Reciprocals

If x + 1/x = k, then x³ + 1/x³ = k³ − 3k.

Square Relations

If x + 1/x = k, then x² + 1/x² = k² − 2 and if x − 1/x = k, then x² + 1/x² = k² + 2.

Power 4 Relation

If x + 1/x = k, then x⁴ + 1/x⁴ = (k² − 2)² − 2.

Given: 

Evan starts from point A and drives 12 km towards west.

He then takes a left turn, drives 6 km, turns left and drives 4 km.

He then takes a right turn and drives 2 km.

He then takes a right turn and drive 3 km.

He then takes a left turn and drives 3 km.

He takes a final left turn, drives 11 km and stops at point P.

Thus, Evan should drive 11 km (6 km + 2 km + 3 km) in the north direction in order to reach point A again.

Hence, "Option 3" is the correct answer.

The correct answer is Richard Gere.

Key Points

• Richard Gere was awarded the International Goya Award in 2025 for his outstanding contributions to global cinema.
• The Goya Awards, often referred to as the Spanish Oscars, are presented annually by the Spanish Academy of Cinematic Art and Sciences.
• Richard Gere has had a celebrated career spanning decades, starring in critically acclaimed films like Pretty Woman, An Officer and a Gentleman, and Chicago.
• He has also been recognized for his humanitarian work, including advocacy for human rights, environmental conservation, and Tibetan causes.
• The International Goya Award is granted to individuals who significantly impact cinema worldwide, aligning with Gere's global influence and legacy.

Additional Information

• Goya Awards Overview:
• Established in 1987, the Goya Awards celebrate excellence in Spanish cinema.
• They are organized by the Spanish Academy of Cinematic Art and Sciences.
• The ceremony includes categories such as Best Film, Best Director, and Best Actor.
• International awards recognize contributions to cinema beyond Spanish borders.
• Richard Gere's Humanitarian Work:
• Gere is a prominent advocate for Tibetan independence and a supporter of the Dalai Lama.
• He is involved in various charities, including HIV/AIDS awareness and environmental protection.
• He founded the Gere Foundation to support humanitarian causes globally.
• Global Impact of Cinema:
• Cinema serves as a powerful medium to influence culture, society, and global awareness.
• International awards like the Goya recognize the transnational impact of film and its creators.
• Richard Gere’s career exemplifies how cinema can bridge cultural divides and inspire audiences worldwide.
• Other Recipients of the International Goya Award:
• Past recipients include internationally acclaimed actors and filmmakers such as Meryl Streep and Pedro Almodóvar.
• The award honors individuals who elevate cinema to a global art form.

Given series: (Left) 4 6 & 8 $ 7 & 3 9 # % 4 6 @ £ 5 Ω 9 # 1 * 7 (Right)

According to the question such symbols which are immediately preceded by a number and also immediately followed by another number:

Required condition: Number - Symbol - Another Number

(Left) 4 6 & 8 $ 7 & 3 9 # % 4 6 @ £ 5 Ω 9 # 1 * 7 (Right)

Thus, there are six such symbols which are immediately preceded by a number and also immediately followed by another number.

Hence, "Option 4" is the correct answer.

Shortcut Trick

Net efficiency = (1/21 − 1/24) = (8 − 7)/168 = 1/168.

Time to fill full tank = 168 minutes.

Time to fill 1/4th tank = 168 ÷ 4 = 42 minutes.

∴ The correct answer is 42 minutes.

Alternate Method

⇒ Combined Efficiency = 8 − 7 = 1 unit/min

⇒ One-fourth of Tank Capacity = 168 ÷ 4 = 42 units

⇒ Required Time = 42 units ÷ 1 unit/min = 42 minutes

∴ The correct answer is 42 minutes.

Additional Information

Inlet and Outlet Pipes

Efficiency of an inlet pipe is always positive, whereas the efficiency of an outlet (emptying) pipe is always negative.

Work and Efficiency Relation

Time taken = Total Work ÷ Net Efficiency. If net efficiency is positive, the tank fills; if negative, the tank empties.

Shortcut Trick

Simplify the expression using trigonometric identities: (1 + sin θ)(1 − sin θ) = cos² θ and (1 + cos θ)(1 − cos θ) = sin² θ.

The expression becomes (cos² θ) ÷ (sin² θ × cot θ).

Since cos² θ ÷ sin² θ = cot² θ, the expression simplifies to cot² θ ÷ cot θ = cot θ.

Given tan θ = 7/8, then cot θ = 1 ÷ tan θ = 8/7.

∴ The correct answer is 8/7.

Alternate Method

Given: tan θ = 7/8

Formula Used: (a + b)(a − b) = a² − b²; sin² θ + cos² θ = 1; cot θ = cos θ / sin θ

⇒ Expression = [(1 + sin θ)(1 − sin θ)] ÷ [(1 + cos θ)(1 − cos θ)(cot θ)]

⇒ Using (a+b)(a-b) ⇒ (1 − sin² θ) ÷ [(1 − cos² θ) × cot θ]

⇒ Using identities ⇒ cos² θ ÷ (sin² θ × cot θ)

⇒ (cos² θ / sin² θ) × (1 / cot θ)

⇒ cot² θ × (1 / cot θ) = cot θ

⇒ cot θ = 1 / tan θ = 1 / (7/8) = 8/7

∴ The correct answer is 8/7.

Additional Information

Reciprocal Identities

tan θ = 1/cot θ, sin θ = 1/cosec θ, and cos θ = 1/sec θ.

Pythagorean Identities

sin² θ + cos² θ = 1; 1 + tan² θ = sec² θ; 1 + cot² θ = cosec² θ.

Quotient Identities

tan θ = sin θ / cos θ and cot θ = cos θ / sin θ.

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

1) H sits to the immediate right of D.

2) Only three people sit between D and C.

3) Only three people sit between H and I when counted from the left of H.

4) A sits to the immediate right of G.

After positioning G and A only one position is left which will be occupied by the only person left i.e. B.

Thus, one person sit between D and G when counted from the right of G.

Hence, "Option 1" is the correct answer.

Shortcut Trick

Let initial Profit be P and initial Selling Price be SP.

New Profit = 11 × P and New SP = 2 × SP.

Since Cost Price (CP) is constant, Change in Profit = Change in SP.

(11P − P) = (2SP − SP) ⇒ 10P = 1SP.

Ratio of P : SP = 1 : 10. Since SP = CP + P, then CP = 10 − 1 = 9.

Initial Profit% = (P ÷ CP) × 100 = (1 ÷ 9) × 100 = 11 1/9 %.

∴ The correct answer is 11 1/9 %.

Alternate Method

Given → New SP = 2 × Old SP | New Profit = 11 × Old Profit. Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100

⇒ Let initial CP be x and initial SP be y. ⇒ Initial Profit (P) = y − x. ⇒ New SP = 2y. New Profit = 2y − x. ⇒ According to the question: 2y − x = 11(y − x). ⇒ 2y − x = 11y − 11x ⇒ 10x = 9y ⇒ y/x = 10/9. ⇒ If CP = 9 units, SP = 10 units. Profit = 1 unit. ⇒ Profit% = (1 ÷ 9) × 100 = 11 1/9 %.

∴ The correct answer is 11 1/9 %.

Additional Information

Relationship between SP and Profit

When the cost price remains constant, any increase in the selling price directly increases the profit by the same absolute amount.

Profit Percentage

Profit percentage is always calculated on the Cost Price (CP) unless stated otherwise. Formula: [(SP − CP) ÷ CP] × 100.

The correct answer is It becomes null and void..

Key Points

• If a law is declared unconstitutional under judicial review, it ceases to have any legal effect and is treated as if it never existed.
• The judiciary exercises this power under the principle of constitutional supremacy, ensuring that all laws adhere to the constitution.
• Such a declaration is binding on all authorities, including the legislature, executive, and judiciary.
• The law is considered null and void from the date of its enactment, unless the court specifies otherwise.
• This power of judicial review is a key feature of democracies like India and the USA, ensuring the protection of fundamental rights and constitutional integrity.

Additional Information

• Judicial Review:
• It is the power of the judiciary to examine the constitutionality of legislative and executive actions.
• Judicial review ensures that no law or government action violates the constitution.
• In India, this power is derived from Articles 13, 32, and 226 of the Constitution.
• Unconstitutional Law:
• A law is termed unconstitutional when it contravenes the provisions of the constitution, particularly fundamental rights.
• Such laws cannot be enforced and lose their legal validity.
• Doctrine of Basic Structure:
• The judiciary uses this doctrine to ensure that amendments or laws do not alter the basic framework of the constitution.
• This doctrine was established in the landmark Kesavananda Bharati case (1973).
• Article 13 of the Indian Constitution:
• Article 13 declares that any law inconsistent with the fundamental rights shall be void.
• It forms the basis for judicial review in India.

The correct answer is 22.

Key Points

• The government of India has set a target to construct 22 greenfield expressways by the financial year 2024-25 under the Bharatmala Pariyojana.
• These expressways are being developed to improve connectivity between major economic centers and reduce travel time significantly across states.
• The initiative includes expressways like the Delhi-Mumbai Expressway, Ahmedabad-Dholera Expressway, and Bengaluru-Chennai Expressway.
• The construction of these expressways aims to enhance logistics efficiency, boost trade, and create employment opportunities.
• Greenfield expressways are designed to be environmentally sustainable, leveraging advanced engineering and planning techniques.

Additional Information

• Bharatmala Pariyojana
• It is a centrally-sponsored and funded road and highway project launched in 2017.
• The primary objective is to develop seamless freight corridors and improve road infrastructure across India.
• Greenfield expressways under this initiative are planned for high-speed connectivity and reduced congestion.
• Greenfield Project
• A greenfield project refers to a new infrastructure initiative built from scratch on undeveloped land.
• Such projects aim to utilize advanced planning methods to ensure optimal efficiency and sustainability.
• Key Expressways Under Construction
• Delhi-Mumbai Expressway: A 1,386 km-long expressway connecting Delhi and Mumbai with reduced travel time to approximately 12 hours.
• Bengaluru-Chennai Expressway: A 262 km-long expressway aimed at reducing travel time between the two cities.
• Ahmedabad-Dholera Expressway: A vital project to boost connectivity between Ahmedabad and the Dholera Special Investment Region.
• Environmental Benefits of Greenfield Expressways
• Designed to minimize carbon emissions by enabling fuel-efficient travel.
• Incorporates measures to protect surrounding ecosystems and reduce environmental impact.