The correct answer is Inconsistent use of slide masters and templates.

Key Points

• Inconsistent use of slide masters and templates can lead to a lack of uniformity in design, making the presentation appear unprofessional and reducing its credibility.
• Proper use of slide masters ensures consistent formatting, including font styles, colors, and layouts throughout the presentation.
• Templates provide a structured and visually appealing design, contributing to the clarity and impact of the presentation.
• Disorganized or conflicting slide designs may distract the audience, undermining the content's effectiveness and overall message delivery.
• Maintaining design consistency aligns with best practices for creating high-quality presentations that convey professionalism and attention to detail.

Additional Information

• Slide Masters:
• Slide masters are pre-designed layouts that control the appearance of slides in a presentation.
• Using slide masters ensures uniformity in font styles, colors, and layout across multiple slides.
• They save time by allowing users to apply consistent formatting without manually editing each slide.
• Templates:
• Templates are pre-designed slide decks that provide a cohesive visual structure.
• They allow users to focus on content creation rather than design elements.
• Templates are especially useful for maintaining brand identity in corporate presentations.
• Best Practices for PowerPoint Presentations:
• Limit the use of animations and transitions to avoid distracting the audience.
• Ensure text is legible by using appropriate font sizes and contrasting colors.
• Include visuals like charts and images to complement the content and aid understanding.
• Proofread content thoroughly to avoid grammatical errors or inconsistencies.
• Impact of Poor Design:
• Poor design choices can divert attention from the presentation's core message.
• It may result in disengagement from the audience and a loss of credibility.
• Professionally designed presentations foster trust and enhance the speaker's authority.

Given:

72 \div \left[ \frac{4}{2} \times \left{ 9 + 2 - \left( 4 + 7 - \left( 1 + 8 \right) \right) \right} \right]

Formula used:

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

Calculation:

72 \div \left[ \frac{4}{2} \times \left{ 9 + 2 - \left( 4 + 7 - \left( 1 + 8 \right) \right) \right} \right]

⇒ (72 \div \left[ 2 \times \left{ 9 + 2 - (4 + 7 - 9) \right} \right] )

⇒ (72 \div \left[ 2 \times \left{ 9 + 2 - (11 - 9) \right} \right] )

⇒ (72 \div \left[ 2 \times \left{ 9 + 2 - 2 \right} \right] )

⇒ $(72 \div \left[ 2 \times 9 \right] )$

⇒ $(72 \div 18)$

⇒ 4

∴ The correct answer is 4.

The correct answer is 1818.

Key Points

• The Bhil rebellion, led by prominent leaders such as Kazi Singh and Bhima Naik, started in 1818.
• This tribal uprising occurred in the regions of Khandesh, which is now part of modern-day Maharashtra and Madhya Pradesh.
• The Bhils revolted against British colonial rule due to exploitation, loss of autonomy, and oppressive revenue policies.
• The rebellion was fueled by the marginalization of the Bhil community and the British seizure of their traditional lands and forests.
• Despite being tribal guerrilla fighters, the Bhils faced significant challenges in sustaining the rebellion against the superior British forces.

Additional Information

• Bhil Community:
• The Bhils are one of the largest tribal communities in India, primarily inhabiting the western and central parts of the country.
• Traditionally, they relied on agriculture, hunting, and forest resources for sustenance.
• Their distinct cultural identity includes traditional attire, unique art forms, and tribal governance systems.
• Causes of Tribal Rebellions:
• The British colonial policies often disrupted tribal autonomy and traditional ways of life.
• Exploitation by landlords, moneylenders, and revenue officials further aggravated tribal discontent.
• Forced labor and displacement from ancestral lands were recurring issues for tribal communities.
• Impact of the Bhil Rebellion:
• Although the rebellion was eventually suppressed, it highlighted the resilience and resistance of the Bhil community.
• The British implemented certain conciliatory measures, such as appointing Bhil leaders in administrative roles, to pacify the community.
• Other Tribal Movements:
• The Bhil rebellion was one of many tribal uprisings during British rule, such as the Santhal rebellion (1855-1856) and the Munda rebellion (1899-1900).
• These movements were significant in shaping India's freedom struggle by exposing the exploitative colonial practices.

Shortcut Trick

90% of Tank Capacity = 50 litres

10% of Tank Capacity (Remaining) = (50 ÷ 90) × 10 litres

⇒ 50 ÷ 9 = 5.555... litres

Total petrol needed to fill = 50 + 5.555... = 55.56 litres

∴ The correct answer is 55.56 litres.

Alternate Method

Given:

Petrol poured = 50 litres

Empty percentage = 10%

Filled percentage = 100% − 10% = 90%

⇒ Let the total capacity of the tank be x litres.

⇒ 90% of x = 50

⇒ (90/100) × x = 50

⇒ x = (50 × 100) ÷ 90

⇒ x = 500 ÷ 9 = 55.555... litres

⇒ Rounded to two decimal places, x ≈ 55.56 litres

∴ The correct answer is 55.56 litres.

Additional Information

Percentage Change

Percentage change = (Difference ÷ Original Value) × 100. Useful for calculating capacity fluctuations.

Base Value Concept

Always identify the 100% value (total capacity) before calculating parts (filled or empty portions).

Rounding Rules

If the third decimal digit is 5 or more, increase the second decimal digit by 1 (e.g., 5.555... becomes 5.56).

Given: Suraj ranked 18^th from the top and 67^th from the bottom in his class.

Suraj's rank from the top = 18^th

Suraj's rank from the bottom = 67^th

Total number of students in his class = Suraj's rank from the top + Suraj's rank from the bottom - 1

= 18 + 67 - 1

= 84

Hence, "Option 4" is the correct answer.

The correct answer is 0.19.

Key Points

• According to the Global Debt Report 2025, the share of central bank holdings of domestic sovereign bonds in OECD countries in 2024 was 19% (0.19).
• OECD countries represent economically advanced nations, including key players such as the US, UK, Japan, and European Union member states.
• The significant holding of domestic sovereign bonds by central banks highlights their role in stabilizing economies and managing fiscal policies.
• The increase in central bank holdings has been influenced by quantitative easing policies implemented during economic downturns.
• This share underscores the growing reliance on central banks to provide liquidity and maintain economic stability.

Additional Information

• OECD (Organisation for Economic Co-operation and Development):
• An intergovernmental organization established in 1961 to promote economic progress and global trade.
• It consists of 38 member countries, mostly developed economies.
• OECD provides a platform for economic analysis and policy recommendations.
• Domestic Sovereign Bonds:
• Sovereign bonds are debt securities issued by governments to finance their expenditures.
• Domestic sovereign bonds are denominated in the issuing country’s local currency.
• Central banks often purchase these bonds as part of monetary policy measures.
• Quantitative Easing (QE):
• A monetary policy tool used by central banks to inject liquidity into the economy.
• Involves large-scale purchases of government bonds and other securities.
• Aimed at reducing interest rates and stimulating economic growth.
• Economic Stability and Liquidity Management:
• Central banks play a key role in maintaining economic stability by controlling inflation and managing liquidity.
• Purchasing sovereign bonds is one method to ensure adequate liquidity in financial markets.

The correct answer is Lorenz Curve.

Key Points

• The Lorenz Curve is a graphical representation that illustrates the distribution of income or wealth among individuals or households in a population.
• It is used to measure income inequality, where the degree of deviation from the line of perfect equality (the diagonal line) indicates the level of inequality.
• The closer the Lorenz Curve is to the diagonal line, the more equal the income distribution; the farther it is, the greater the inequality.
• The curve is often used in conjunction with the Gini Coefficient, which quantifies the level of income inequality as a single numerical value.
• Developed by Max Lorenz in 1905, this tool remains a cornerstone in economic studies related to inequality and social welfare.

Additional Information

• Gini Coefficient:
• The Gini Coefficient is a numerical measure derived from the Lorenz Curve, ranging from 0 to 1.
• A Gini Coefficient of 0 indicates perfect equality, while a value of 1 indicates perfect inequality.
• It is widely used by economists and policymakers to compare income inequality across regions or countries.
• Dependency Ratio:
• This is a demographic metric that indicates the ratio of dependents (young and elderly) to the working-age population.
• While important for understanding economic pressures, it does not measure income inequality.
• Consumer Price Index (CPI):
• CPI measures changes in the price level of a basket of consumer goods and services purchased by households over time.
• It is a key indicator of inflation, not income distribution.
• Labour Force Participation Rate (LFPR):
• LFPR measures the proportion of the working-age population that is either employed or actively seeking employment.
• It provides insights into labor market dynamics but does not reflect income inequality.
• Historical Context of Income Inequality Studies:
• The study of income inequality gained prominence during the 20^th century as economists sought to understand its implications on economic growth and social stability.
• Tools like the Lorenz Curve and Gini Coefficient remain fundamental to these analyses.

The correct answer is Common Ion Effect.

Key Points

• Common ion effect occurs when a solution already contains ions that are present in the solute being added, reducing the solubility of the solute due to ion interference.
• In the case of CH₃COOH, the addition of CH₃COONa introduces acetate ions (CH₃COO⁻), which are common to both the acid and the salt.
• The presence of acetate ions shifts the dissociation equilibrium of CH₃COOH to the left, decreasing the concentration of hydrogen ions and reducing its solubility.
• This phenomenon is explained by Le Chatelier's Principle, where the equilibrium adjusts to counter the increase in concentration of common ions.
• The common ion effect is a key concept in acid-base chemistry, particularly in buffer solutions and solubility equilibria.

Additional Information

• Le Chatelier's Principle:
• This principle states that if a dynamic equilibrium is disturbed by changing conditions, the position of equilibrium shifts to counteract the change.
• In the case of the common ion effect, the equilibrium adjusts to reduce the concentration of the added common ion.
• Buffer Solutions:
• Buffers are solutions that resist changes in pH upon the addition of small amounts of acid or base.
• The common ion effect plays a crucial role in maintaining the pH stability of buffers.
• Applications of Common Ion Effect:
• Used in analytical chemistry for selective precipitation of ions.
• Helps in controlling the solubility of compounds in pharmaceutical formulations.
• Important in maintaining pH stability in biological systems.
• Solubility Equilibrium:
• Describes the balance between dissolved ions and undissolved solid in a saturated solution.
• The common ion effect influences solubility equilibrium by altering the ionic concentrations.

The correct answer is Ctrl + S.

Key Points

• Ctrl + S is the standard keyboard shortcut used in MS Excel, as well as most other software, to save the current file or workbook.
• When pressed, this shortcut ensures that the changes made to the workbook are stored in the file on the disk, preventing data loss.
• If the file is being saved for the first time, the "Save As" dialog box will appear to allow the user to specify the file name and location.
• This shortcut is part of the universally accepted Microsoft Office commands, ensuring consistency across various Office applications like Word, PowerPoint, and Excel.
• Using shortcuts like Ctrl + S improves productivity and minimizes the risk of losing unsaved work due to unexpected interruptions.

Additional Information

• Other Common Keyboard Shortcuts in MS Excel:
• Ctrl + N: Creates a new workbook.
• Ctrl + O: Opens an existing workbook.
• Ctrl + P: Opens the print dialog box for printing the workbook.
• Ctrl + Z: Undoes the last action.
• Ctrl + Y: Redoes the last undone action.
• AutoSave Feature:
• Microsoft Excel's AutoSave feature automatically saves changes to the workbook at regular intervals (if enabled).
• It is particularly useful when working on cloud-based platforms like OneDrive.
• Save As Command:
• Accessible via F12 or the File menu, this command allows users to save the file with a different name or in a different format.
• It is commonly used when creating multiple versions of a file.
• File Formats in MS Excel:
• Excel files can be saved in various formats, including .xlsx (default), .xls (Excel 97-2003), .csv (comma-separated values), and .pdf.
• Choosing the correct format is essential for compatibility and specific use cases.
• Importance of Regular Saving:
• Regularly saving your work ensures protection against unexpected system crashes, power outages, or accidental file closures.
• Experts recommend using Ctrl + S frequently during long working sessions to minimize data loss risks.

Shortcut Trick

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

Mean = (3 × 62 − 36.3) ÷ 2

Mean = (186 − 36.3) ÷ 2

Mean = 149.7 ÷ 2 = 74.85

∴ The correct answer is 74.85.

Alternate Method

Given: Mode = 36.3 and Median = 62.

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

⇒ 36.3 = 3 × 62 − 2 × Mean

⇒ 36.3 = 186 − 2 × Mean

⇒ 2 × Mean = 186 − 36.3

⇒ 2 × Mean = 149.7

⇒ Mean = 149.7 ÷ 2

⇒ Mean = 74.85

∴ The correct answer is 74.85.

Additional Information

Empirical Relationship

For a moderately skewed distribution, the relationship between central tendencies is Mode = 3 Median − 2 Mean.

Symmetrical Distribution

In a perfectly symmetrical distribution (like a Normal Distribution), the Mean, Median, and Mode coincide at the same point (Mean = Median = Mode).

Skewness and Central Tendency

In a positively skewed distribution, Mean > Median > Mode. In a negatively skewed distribution, Mode > Median > Mean.

Shortcut Trick For two people running in opposite directions on a circular track, the number of meeting points is the sum of the simplified ratio of their speeds. Ratio of time taken by Siddharth and Yash = 85 : 45 Ratio of speed of Siddharth and Yash = 45 : 85 = 9 : 17 Number of distinct meeting points = 9 + 17 = 26 ∴ The correct answer is 26. Alternate Method Given: Length of circular track = 2295 m Time taken by Siddharth (T1) = 85 s Time taken by Yash (T2) = 45 s

Calculations: ⇒ Speed of Siddharth (S1) = Distance ÷ T1 = 2295 ÷ 85 = 27 m/s ⇒ Speed of Yash (S2) = Distance ÷ T2 = 2295 ÷ 45 = 51 m/s ⇒ Ratio of Speeds (S1 : S2) = 27 : 51 ⇒ Simplify the ratio by dividing by 3: 27/3 : 51/3 = 9 : 17 ⇒ Let the simplified ratio be a : b, where a = 9 and b = 17. ⇒ Since they move in opposite directions, total meeting points = a + b ⇒ Meeting points = 9 + 17 = 26 ∴ The correct answer is 26. Additional Information Meeting Points in Same Direction If two people move in the same direction with speeds in simplified ratio a : b (where a > b), the number of distinct meeting points is |a − b|. Time of First Meeting The time taken for the first meeting anywhere on the track is L ÷ (S1 + S2) for opposite directions and L ÷ |S1 − S2| for same direction, where L is track length. Time of Meeting at Start Point The time when they meet for the first time at the starting point is given by LCM of the time taken by each person to complete one full round.

Shortcut Trick

For a cubic equation ax³ + bx² + cx + d = 0, the sum and product of roots are given by:

Sum of roots = −b/a and Product of roots = −d/a.

In the given equation 4x³ − 8x² − 13x + 19 = 0, we have a = 4, b = −8, and d = 19.

Sum = −(−8)/4 = 2 and Product = −19/4.

∴ The correct answer is 2, −19/4.

Alternate Method

Given:

Cubic Equation: 4x³ − 8x² − 13x + 19 = 0

Formula Used:

For ax³ + bx² + cx + d = 0:

Sum of roots (α + β + γ) = − (coefficient of x²) / (coefficient of x³)

Product of roots (αβγ) = − (constant term) / (coefficient of x³)

Calculations:

⇒ Comparing with standard form, a = 4, b = −8, c = −13, d = 19

⇒ Sum of all roots = −b/a = −(−8)/4

⇒ Sum of all roots = 8/4 = 2

⇒ Product of all roots = −d/a = −(19)/4

⇒ Product of all roots = −19/4

∴ The correct answer is 2, −19/4.

Additional Information

Sum of roots taken two at a time

For a cubic equation, the sum of product of roots taken two at a time (αβ + βγ + γα) is equal to c/a.

Quadratic Equation Roots

For a quadratic equation ax² + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a.

Vieta's Formulas

These formulas relate the coefficients of a polynomial to sums and products of its roots, where signs alternate (+, −, +, −...).

Shortcut Trick

If all subgroups in a population have the same average value, the combined average of the entire population will remain the same, regardless of the number of items in each subgroup.

Average of 12 students = 60

Average of the rest (18 students) = 60

Since both groups have an average of 60, the total class average is simply 60.

∴ The correct answer is 60.

Alternate Method

Given:

Total students in the class = 30

Average score of 12 students = 60

Average score of the remaining students = 60

Formula Used:

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

Calculations:

⇒ Total score of 12 students = 12 × 60 = 720

⇒ Remaining students = 30 − 12 = 18

⇒ Total score of 18 students = 18 × 60 = 1080

⇒ Total score of the class = 720 + 1080 = 1800

⇒ Average score of the class = 1800 ÷ 30

⇒ Average score of the class = 60

∴ The correct answer is 60.

Additional Information

Weighted Average Formula

When two groups are combined, the resulting average is A_avg = (n₁×A₁ + n₂×A₂) ÷ (n₁ + n₂), where n is the count and A is the average.

Constant Average Property

If every individual in a group has the same value 'x', the average of the group is always 'x'. Adding more groups with average 'x' will not change the overall average.

Deviation Principle

The sum of deviations of all observations from their arithmetic mean is always zero. This helps in finding the average of large datasets by assuming a base value.

According to the given information,

Thus, 'flag' is coded as 'tc'.

Hence, "Option 4" is the correct answer.

Given:

$\left( \frac{11}{10} \right)^7 \times \left( \frac{10}{11} \right)^{10} \times \left( \frac{11}{10} \right)^9 = \left( \frac{10}{11} \right)^{3m+17}$

Formula used:

$a^m \times a^n = a^{m+n}$ and $\left( \frac{a}{b} \right)^n = \left( \frac{b}{a} \right)^{-n}$

Calculation:

Combine powers of same base:

$\left( \frac{11}{10} \right)^7 \times \left( \frac{11}{10} \right)^9 = \left( \frac{11}{10} \right)^{16}$

Now the expression becomes:

$\left( \frac{11}{10} \right)^{16} \times \left( \frac{10}{11} \right)^{10}$

Write everything in base $\left( \frac{10}{11} \right)$:

$\left( \frac{11}{10} \right)^{16} = \left( \frac{10}{11} \right)^{-16}$

So the full expression becomes:

$\left( \frac{10}{11} \right)^{-16} \times \left( \frac{10}{11} \right)^{10} = \left( \frac{10}{11} \right)^{-6}$

Now equating powers:

$-6 = 3m + 17$

⇒ $3m = -6 - 17 = -23$

⇒ $m = \frac{-23}{3}$

∴ The correct answer is $-\frac{23}{3}$

The logic followed here is:

Option 1) URO

Option 2) TQN

Option 3) KIE

Option 4) WTQ

Thus, out of all the options 'KIE' is the odd one.

Hence, "Option 3" is the correct answer.

Shortcut Trick

In a proportion a : b :: c : d, the Product of Extremes equals the Product of Means.

Ratio of 9.8 : 14.7 simplified is 2 : 3 (both divisible by 4.9).

Since the first ratio is 2 : 3, the second ratio 15 : x must also be 2 : 3.

2 units → 15, so 1 unit → 7.5. Therefore, 3 units → 3 × 7.5 = 22.5.

∴ The correct answer is 22.5.

Alternate Method

Given Proportion: 9.8 : 14.7 :: 15 : x

Formula used: Product of extremes = Product of means (a × d = b × c)

⇒ 9.8 × x = 14.7 × 15

⇒ x = (14.7 × 15) ÷ 9.8

⇒ x = 220.5 ÷ 9.8

⇒ x = 22.5

∴ The correct answer is 22.5.

Additional Information

Fourth Proportional

In the expression a : b :: c : d, d is called the fourth proportional to a, b, and c. It is calculated as d = (b × c) ÷ a.

Mean Proportional

The mean proportional between two numbers a and b is √(a × b). It satisfies the ratio a : x :: x : b.

Third Proportional

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

Shortcut Trick

In ΔBDC, since BD ⊥ AC, ∠C = 90° − ∠DBC = 90° − 22° = 68°.

In ΔAEC, ∠AEB is the exterior angle at vertex E because B, E, C are collinear.

By the Exterior Angle Theorem, ∠AEB = ∠CAE + ∠C.

⇒ ∠AEB = 36° + 68° = 104°.

∴ The correct answer is 104°.

Alternate Method

Given: In ΔABC, BD ⊥ AC at D, ∠DBC = 22°, and ∠CAE = 36° where E is on BC.

Formula Used: Sum of angles in a triangle = 180°; Linear pair of angles sum to 180°.

In ΔBDC:

⇒ ∠BDC = 90° (Since BD ⊥ AC)

⇒ ∠BCD + ∠DBC + ∠BDC = 180°

⇒ ∠BCD + 22° + 90° = 180°

⇒ ∠BCD = 180° − 112° = 68°

In ΔAEC:

⇒ ∠CAE = 36° (Given)

⇒ ∠ACE = ∠BCD = 68°

⇒ ∠AEC = 180° − (∠CAE + ∠ACE)

⇒ ∠AEC = 180° − (36° + 68°) = 180° − 104° = 76°

Since B, E, C lie on a straight line:

⇒ ∠AEB + ∠AEC = 180° (Linear pair)

⇒ ∠AEB = 180° − 76° = 104°

∴ The correct answer is 104°.

Additional Information

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

Angle Sum Property

The sum of the interior angles of any triangle is always 180°.

Linear Pair Postulate

If two angles form a linear pair, then the measures of the angles add up to 180°.

Given:

Pravenesh starts from point A and drives 12 km towards the south.

He then takes a right turn, drives 7 km, turns right and drives 14 km.

He then takes a right turn and drives 10 km.

He takes a final right turn, drives 2 km and stops at point P.

Thus, Pravenesh should drive 3 km (10 km - 7 km) in the west direction in order to reach point A again.

Hence, "Option 4" is the correct answer.

Shortcut Trick

Net filling time = (a × b) ÷ (b − a), where a is filling time and b is emptying time.

Net time = (9 × 90) ÷ (90 − 9)

Net time = 810 ÷ 81 = 10 minutes.

∴ The correct answer is 10 minutes.

Alternate Method

⇒ Combined Efficiency = 10 − 1 = 9 units/minute.

⇒ Time taken to fill tank = Total Work ÷ Combined Efficiency

⇒ Time = 90 ÷ 9 = 10 minutes.

∴ The correct answer is 10 minutes.

Additional Information

Pipes and Cisterns Efficiency

Efficiency of a filling pipe is taken as positive (+), while the efficiency of an emptying pipe (leak) is taken as negative (−).

Net Work Formula

If pipe A fills in x hours and pipe B empties in y hours, the net work in 1 hour is (1/x − 1/y). If the result is positive, the tank is filling; if negative, the tank is emptying.

The correct answer is Bhangar.

Key Points

• Bhangar is the older alluvium found in the Northern Plains of India.
• It is characterized by its slightly elevated terraces compared to the newer alluvium, known as Khadar.
• The soil in the Bhangar region is generally less fertile due to the presence of lime nodules, locally called kankar.
• This region is usually found farther away from river courses and is more stable as compared to the younger Khadar regions.
• Bhangar plays a crucial role in agriculture but often requires more effort to improve soil fertility compared to Khadar.

Additional Information

• Khadar: The newer alluvium deposited by rivers during floods, forming fertile plains ideal for agriculture.
• Bhabar: A narrow belt of coarse gravel and pebbles situated at the foothills of the Himalayas, where rivers disappear due to high porosity.
• Terai: A marshy region located south of the Bhabar belt, where rivers re-emerge, supporting dense vegetation and rich biodiversity.
• Alluvium: Sediments deposited by rivers, categorized into older (Bhangar) and newer (Khadar) based on their time of deposition and fertility.
• The Northern Plains of India are formed by the deposition of sediments brought by the Ganga, Brahmaputra, and Indus river systems.

Shortcut Trick To find x for proportion (a, b, c, d): x = (ad − bc) ÷ (b + c − a − d) x = (20 × 16 − 34 × 11) ÷ (34 + 11 − 20 − 16) = (320 − 374) ÷ (45 − 36) = −54 ÷ 9 = −6 Substitute x = −6 in 3x : y :: y : (2x − 6) ⇒ y2 = 3x(2x − 6) = 3(−6)(2(−6) − 6) = −18 × −18 = 324 y = √324 = 18 (since y > 0) ∴ The correct answer is 18. Alternate Method

Given: Numbers (20+x), (34+x), (11+x), (16+x) are in proportion. Formula Used: a/b = c/d and y2 = ac if a : y :: y : c ⇒ (20 + x) ÷ (34 + x) = (11 + x) ÷ (16 + x) ⇒ (20 + x)(16 + x) = (11 + x)(34 + x) ⇒ 320 + 20x + 16x + x2 = 374 + 11x + 34x + x2 ⇒ 320 + 36x = 374 + 45x ⇒ 45x − 36x = 320 − 374 ⇒ 9x = −54 ⇒ x = −6 ⇒ Now, 3x : y :: y : (2x − 6) ⇒ y2 = 3x × (2x − 6) ⇒ y2 = 3(−6) × (2(−6) − 6) = −18 × (−12 − 6) = −18 × −18 ⇒ y2 = 324 ⇒ y = √324 = 18 ∴ The correct answer is 18. Additional Information Mean Proportional If b is the mean proportional between a and c, then a : b :: b : c, which implies b2 = ac. Basic Proportion Rule Four numbers a, b, c, d are in proportion if a × d = b × c (Product of extremes = Product of means). Third Proportional In the proportion a : b :: b : c, the term c is called the third proportional to a and b, where c = b2/a.

The correct answer is Ethics, mental phenomena, and psychological insights.

Key Points

• The Abhidhamma Pitaka is one of the three sections of the Tripitaka, the foundational texts of Theravāda Buddhism.
• It focuses on philosophical and psychological analysis of the mind, mental phenomena, and ethical principles.
• It provides a detailed categorization of mental states, cognitive processes, and ethical behavior.
• Unlike the Sutta Pitaka, which contains discourses, the Abhidhamma Pitaka offers a more systematic and analytical approach to Buddhist teachings.
• It is considered a scholarly and advanced text, aimed primarily at monks and serious students of Buddhist philosophy.

Additional Information

• Tripitaka (Three Baskets):
• The Tripitaka consists of three main collections: Vinaya Pitaka (rules for monastic discipline), Sutta Pitaka (Buddha's discourses), and Abhidhamma Pitaka (philosophical and psychological analysis).
• It forms the doctrinal foundation of Theravāda Buddhism and is written in Pali.
• Abhidhamma Pitaka Structure:
• Contains seven books, such as Dhammasangani, Vibhanga, and Patthana, which systematically explore mental and physical phenomena.
• Focuses on understanding reality through an analysis of consciousness, perception, and causality.
• Role in Buddhist Practice:
• The Abhidhamma Pitaka helps practitioners cultivate insight (vipassana) into the nature of reality and achieve liberation (nirvana).
• It is used as a guide for meditation and ethical living, emphasizing mindfulness and understanding of mental states.
• Psychological Insights:
• Offers a detailed examination of the mind, emotions, and thought processes, making it highly relevant in modern psychological studies.
• Its teachings on impermanence (anicca), suffering (dukkha), and non-self (anatta) are central to Buddhist philosophy.

Shortcut Trick

To check divisibility by 71, use the oscillator method where the osculator for 71 is 7.

Multiply the last digit by 7 and subtract it from the remaining number.

For 5609: 560 − (9 × 7) = 560 − 63 = 497.

Repeat: 49 − (7 × 7) = 49 − 49 = 0. Since the result is 0, the number is divisible.

∴ The correct answer is 5609.

Alternate Method

Given: Numbers (1) 6010, (2) 6121, (3) 5603, (4) 5609 and divisor 71.

Calculation:

⇒ Check 6010: 6010 ÷ 71 ≈ 84.64 (Not divisible)

⇒ Check 6121: 6121 ÷ 71 ≈ 86.21 (Not divisible)

⇒ Check 5603: 5603 ÷ 71 ≈ 78.91 (Not divisible)

⇒ Check 5609: 5609 ÷ 71 = 79

⇒ 71 × 70 = 4970

⇒ 5609 − 4970 = 639

⇒ 71 × 9 = 639

⇒ 4970 + 639 = 5609

∴ The correct answer is 5609.

Additional Information

Negative Osculators

For a prime number ending in 1 like 71, the negative osculator is (71−1)/10 = 7. Subtract (last digit × 7) from the rest of the number.

Divisibility by Prime Numbers

Divisibility for any prime p can be checked using the formula 10k ± 1 to find the osculator value used for reducing large numbers.

Decoding signs:

Given: 9 ÷ 12 × 450 + 8208 − 18 = ?

9 ÷ 12 × 450 + 8208 − 18 = ? ⇒ 9 × 12 + 450 − 8208 ÷ 18 = ?

⇒ 9 × 12 + 450 − 8208 ÷ 18 = ?

⇒ 9 × 12 + 450 − 456 = ?

⇒ 108 + 450 − 456 = ?

⇒ 558 − 456 = ?

⇒ 102 = ?

Hence, "Option 2" is the correct answer.

The logic followed here is:

Given: # : AIP :: MRV : %

Option 1) # = ELR, % = QUX → ELR : AIP :: MRV : QUX

Option 2) # = WFN, % = QUX → WFN : AIP :: MRV : QUX

Option 3) # = IOT, % = WFN → IOT : AIP :: MRV : WFN

Option 4) # = QUX, % = ELR → QUX : AIP :: MRV : ELR

Hence, "Option 2" is the correct answer.

The correct answer is northern and eastern parts of India with the northwestern region.

Key Points

• Uttarapatha was one of the most important trade routes in ancient India, especially during the post-Mauryan period.
• It connected the northern and eastern regions of India with the northwestern region, facilitating trade and cultural exchanges.
• This route extended from the Gangetic plains to the northwestern regions, including Taxila and regions in present-day Pakistan.
• Uttarapatha was a crucial trade corridor for goods like textiles, spices, and precious metals.
• It also played a role in the spread of Buddhism and other cultural influences along its path during the post-Mauryan period.

Additional Information

• Other Major Ancient Trade Routes:
• Dakshinapatha: Connected the southern regions of India to the northern parts.
• Silk Route: Facilitated trade between India, Central Asia, and China, primarily for silk, spices, and precious stones.
• Grand Trunk Road: An important ancient route later developed into a major highway during the Mughal period.
• Taxila's Role:
• Taxila, located near Uttarapatha, was a major center for trade and learning during ancient times.
• It served as a hub for merchants traveling along Uttarapatha.
• Post-Mauryan Period:
• The post-Mauryan period saw significant trade activity along Uttarapatha under rulers like the Shungas, Kushans, and Satavahanas.
• It was during this period that Indian merchants actively engaged in international trade.
• Buddhism's Spread:
• Uttarapatha played a role in the spread of Buddhism to Central Asia and beyond.
• Buddhist monks often traveled along this route to propagate teachings.

The correct answer is TAPAS.

Key Points

• TAPAS is a Medium Altitude Long Endurance (MALE) unmanned aerial vehicle (UAV) developed by the Defence Research and Development Organisation (DRDO) in India.
• The UAV is designed for surveillance, reconnaissance, and intelligence gathering over extended periods.
• TAPAS was showcased at the Drone Industry Conclave 2025 as a significant step towards India's self-reliance in drone technology.
• It can operate at altitudes of up to 30,000 feet and has an endurance of over 24 hours, making it suitable for both military and civilian applications.
• The drone integrates advanced systems such as electro-optical payloads, synthetic aperture radar, and satellite communication capabilities.

Additional Information

• Medium Altitude Long Endurance (MALE) UAVs
• MALE UAVs are designed to operate at altitudes ranging from 10,000 to 30,000 feet.
• These drones are capable of long-duration flights, often exceeding 24 hours, making them ideal for extended missions.
• They are widely used for surveillance, reconnaissance, and intelligence gathering, particularly in defense and border monitoring.
• DRDO's Role in UAV Development
• The Defence Research and Development Organisation (DRDO) is India's premier research agency focused on defense technology.
• It has developed several UAVs, including TAPAS, RUSTOM, and NETRA, to strengthen India's indigenous drone capabilities.
• DRDO collaborates with other agencies and private industries to integrate cutting-edge technologies into its UAV projects.
• Applications of TAPAS
• Military: Border surveillance, anti-terror operations, and intelligence gathering.
• Civilian: Disaster management, agriculture monitoring, and search-and-rescue operations.
• Scientific: Environmental data collection and weather monitoring.
• Other UAVs Developed by DRDO
• RUSTOM: Another MALE UAV designed for tactical missions and surveillance.
• NETRA: A small quadcopter UAV used for surveillance in urban areas.
• AURA: An autonomous stealth UAV under development for advanced military applications.

The correct answer is By an Act of Parliament.

Key Points

• Municipal Corporations in Union Territories (UTs) are established through Acts passed by the Parliament of India, as UTs are governed directly by the Central Government.
• Unlike states, which have their own legislative assemblies, Union Territories are administered by the President of India through appointed administrators.
• The Parliament enacts laws to create and regulate municipal corporations in UTs, ensuring they fulfill the functions of urban local governance.
• For example, the New Delhi Municipal Council (NDMC) operates under the New Delhi Municipal Council Act, 1994, passed by Parliament.
• This framework ensures consistency and uniformity in governance across UTs, considering their unique administrative structures.

Additional Information

• Municipal Corporation:
• It is a form of urban local government that governs cities with a population exceeding 1 million.
• Municipal corporations are responsible for providing civic amenities such as water supply, waste management, roads, and public health services.
• They are governed by elected representatives (councillors) and an appointed municipal commissioner.
• Union Territories:
• Union Territories are regions in India directly governed by the Central Government.
• Currently, India has 8 Union Territories, including Delhi, Chandigarh, and Puducherry.
• Some UTs, like Delhi and Puducherry, have partial statehood with legislative assemblies.
• New Delhi Municipal Council (NDMC):
• The NDMC is a municipal council governing the central area of New Delhi.
• It was constituted under the New Delhi Municipal Council Act, 1994, passed by Parliament.
• The council is chaired by a government-appointed officer, typically an IAS officer.
• Constitutional Provisions:
• The 74^th Constitutional Amendment Act, 1992, provides the framework for urban local governance in India.
• However, in Union Territories, Parliament has the authority to legislate municipal laws under Article 239 of the Constitution.

The logic followed here is:

4 is related to 10 → 4 + 6 = 10

And,

34 is related to 40 → 34 + 6 = 40

Similarly,

66 is related to → 66 + 6 = 72

Hence, "Option 1" is the correct answer.

Shortcut Trick

Assume an average of 100 to calculate net deviation.

Deviations from 100: +208, +27, −10, −55, +25, +3.

Sum of deviations = 208 + 27 − 10 − 55 + 25 + 3 = +198.

Average adjustment = 198 ÷ 6 = +33.

Final Average = Assumed Mean + Adjustment = 100 + 33 = 133.

∴ The correct answer is 133.

Alternate Method

Given: A set of six numbers: 308, 127, 90, 45, 125, and 103.

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

⇒ Total Sum = 308 + 127 + 90 + 45 + 125 + 103

⇒ Sum = 798

⇒ Number of terms (n) = 6

⇒ Average = 798 ÷ 6

⇒ Average = 133

∴ The correct answer is 133.

Additional Information

Properties of Average

If each given observation is increased or decreased by a constant value k, the new average will also be increased or decreased by k.

Weighted Average

When components have different frequencies, the weighted mean is used: A = (Σw_ix_i) ÷ (Σw_i).

Consecutive Numbers

For a set of numbers in Arithmetic Progression (AP), the average is always the middle term or (First term + Last term) ÷ 2.

The logic followed here is:

Given: # : EKN :: RVN : %

Option 1) # = DMK, % = SZQ → DMK : EKN :: RVN : SZQ

Option 2) # = DHL, % = SYP → DHL : EKN :: RVN : SYP

Option 3) # = CML, % = PZT → CML : EKN :: RVN : PZT

Option 4) # = CIK, % = PYR → CIK : EKN :: RVN : PYR

Hence, "Option 2" is the correct answer.

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

1) Only E is kept above D.

2) Only two boxes are kept above C.

3) C is kept immediately above F.

4) G is kept immediately above B.

5) G is not kept in third position from the bottom.

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

Thus, five boxes are kept above G.

Hence, "Option 2" is the correct answer.

The correct answer is Guide Western Disturbances into India.

Key Points

• Westerly Jet Streams are fast-moving air currents in the upper atmosphere that significantly influence weather patterns during winter.
• These jet streams play a key role in guiding Western Disturbances, which are extratropical storms originating in the Mediterranean region, into the Indian subcontinent.
• Western Disturbances bring rainfall and snowfall to northern and northwestern India during winter, particularly in the states of Jammu & Kashmir, Himachal Pradesh, and Uttarakhand.
• The Westerly Jet Streams are strongest during winter months due to the temperature gradient between the tropics and polar regions.
• These jet streams significantly influence agricultural activities in India, as the precipitation from Western Disturbances supports Rabi crops like wheat and barley.

Additional Information

• Western Disturbances:
• Western Disturbances are weather systems characterized by low-pressure areas and are carried into India by Westerly Jet Streams.
• They originate over the Mediterranean Sea, Caspian Sea, and Black Sea regions.
• These disturbances cause rainfall and snowfall in the Himalayan region during winter months.
• They are crucial for maintaining the winter crop cycle in northern India.
• Jet Streams:
• Jet streams are narrow bands of strong winds in the upper levels of the atmosphere.
• They are typically found at altitudes of 9-12 km above the Earth's surface.
• Jet streams are caused by the temperature contrast between tropical and polar regions.
• The two major jet streams influencing India are the Westerly Jet Stream (winter) and the Easterly Jet Stream (summer).
• Impact on Indian Climate:
• In winter, Westerly Jet Streams guide Western Disturbances, causing rainfall over northwestern India and the Himalayas.
• In summer, the Easterly Jet Streams contribute to the onset of the Indian monsoon.
• Jet streams significantly affect the distribution and intensity of rainfall in India.
• They also influence temperature patterns and seasonal shifts in weather systems.
• Rabi Crops:
• Rabi crops are winter crops sown in October-November and harvested in March-April.
• Wheat, barley, mustard, and peas are examples of Rabi crops.
• Rainfall from Western Disturbances during winter is essential for their cultivation.
• Regions dependent on Rabi crops are particularly affected by variations in Westerly Jet Streams.

The logic followed here is:

Hence, "Option 2" is the correct answer.

The correct answer is Carboxyl and amino groups.

Key Points

• A peptide bond is a covalent bond formed between the carboxyl group of one amino acid and the amino group of another.
• The reaction is a condensation reaction, resulting in the release of a water molecule.
• This bond forms the backbone of proteins, linking individual amino acids into a polypeptide chain.
• The carboxyl group (-COOH) contributes the carbon atom, while the amino group (-NH2) contributes the nitrogen atom to the peptide bond.
• These functional groups are essential in protein synthesis, which occurs in ribosomes during translation in living cells.

Additional Information

• Amino Acids:
• Amino acids are organic molecules that serve as the building blocks of proteins.
• Each amino acid contains an amino group (-NH2), a carboxyl group (-COOH), a hydrogen atom, and a unique side chain (R-group).
• There are 20 standard amino acids, classified as essential or non-essential based on whether the human body can synthesize them.
• Peptide Bond Formation:
• Peptide bonds are formed during a process called translation, which takes place in ribosomes.
• Enzymes known as peptidyl transferases catalyze the formation of peptide bonds.
• Peptide bonds are strong and have partial double-bond character, restricting rotation around the bond.
• Proteins:
• Proteins are polymers of amino acids linked by peptide bonds, folded into specific three-dimensional structures.
• They perform a variety of functions, including enzymatic activity, structural roles, and signaling.
• Hydrolysis of Peptide Bonds:
• Peptide bonds can be broken down via hydrolysis, which involves the addition of water.
• This process is catalyzed by enzymes such as proteases, which are important in digestion and protein recycling.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

(I) Some warriors are leaders → Does not follow (As all leaders are knights and some knights are warriors. So it is possible but not definite)

(II) Some politicians are knights → Follow (As all warriors are politicians and some knights are warriors. As some part pf knights is common with warriors which whole comes in politicians, therefore it is true.)

∴ Here, Only conclusion (II) follows.​

Hence, the correct answer is "Option 4".

The correct answer is conciliatory.

Key Points

• Lok Adalat proceedings are non-adversarial and conciliatory, aiming to resolve disputes amicably without prolonged litigation.
• It is governed under the Legal Services Authorities Act, 1987, which promotes alternative dispute resolution mechanisms.
• Lok Adalats encourage mutual agreement and compromise between disputing parties, ensuring faster and cost-effective justice.
• Decisions made in Lok Adalats are binding, and there is no provision for appeal against the award, ensuring finality of the resolution.
• This mechanism is particularly effective in resolving civil cases, matrimonial disputes, and minor criminal offenses, reducing the burden on regular courts.

Additional Information

• Lok Adalat:
• Lok Adalat translates to "People's Court" and is part of India's judicial system aimed at providing speedy justice.
• It operates under the National Legal Services Authority (NALSA).
• Cases resolved include disputes related to motor accident claims, family issues, and unpaid debts.
• Conciliatory Proceedings:
• Conciliation is a voluntary process where parties come to an agreement with the assistance of a neutral third party.
• It is less formal than mediation and involves facilitating communication between disputants.
• Legal Services Authorities Act, 1987:
• It provides the statutory basis for organizing Lok Adalats and ensuring legal aid to weaker sections of society.
• The Act aims to promote justice on the basis of equal opportunity.
• Advantages of Lok Adalats:
• Ensures resolution without prolonged litigation, saving time and money.
• Encourages amicable settlements and reduces animosity between parties.
• Reduces the burden on conventional courts.

Shortcut Trick

Ratio of Covered Distance to Remaining Distance = 4 : 3

Total Ratio parts = 4 + 3 = 7 units → 35 km

1 unit = 5 km ∴ Covered Distance = 4 × 5 = 20 km

Time = 4 hours 15 minutes = 4.25 hours

Speed = 20 ÷ 4.25 ≈ 4.7 km/hr

∴ The correct answer is 4.7 km/hr.

Alternate Method

Given: Total Distance = 35 km, Time = 4 hours 15 minutes.

Formula Used: Speed = Distance ÷ Time

⇒ Let remaining distance be x.

⇒ Covered distance = 4/3 × x

⇒ Total Distance = x + 4/3 × x = 7x/3

⇒ 7x/3 = 35 ⇒ x = (35 × 3) ÷ 7 = 15 km

⇒ Covered Distance = 35 − 15 = 20 km

⇒ Time taken = 4 + 15/60 = 4.25 hours

⇒ Speed = 20 ÷ 4.25 = 4.7058...

∴ The correct answer is 4.7 km/hr.

Additional Information

Time Conversion

To convert minutes to hours, divide by 60. Example: 15 min = 15/60 = 0.25 hours.

Average Speed

Average Speed = Total Distance ÷ Total Time taken for the journey.

Rounding Decimals

When rounding to one decimal place, check the second decimal; if it is 5 or more, increase the first decimal by 1.

Shortcut Trick

If Curved Surface Area (CSA) is half of Total Surface Area (TSA), then CSA = Sum of Area of two bases.

2πrh = 2πr²

This directly implies Radius (r) = Height (h).

Given h = 128 cm, therefore r = 128 cm.

∴ The correct answer is 128 cm.

Alternate Method

Given:

Height (h) of the cylinder = 128 cm

Condition: Curved Surface Area = 1/2 × Total Surface Area

Formulas Used:

Curved Surface Area (CSA) = 2πrh

Total Surface Area (TSA) = 2πr(h + r)

Calculations:

⇒ 2πrh = 1/2 × [2πr(h + r)]

⇒ 2πrh = πr(h + r)

⇒ 2h = h + r

⇒ 2h − h = r

⇒ r = h

⇒ r = 128 cm

∴ The correct answer is 128 cm.

Additional Information

Volume of Cylinder

The amount of space occupied by a cylinder is given by V = πr²h.

Base Area

The area of one circular base of a cylinder is πr².

Relation when CSA = 1/3 TSA

If CSA is one-third of TSA, then 2πrh = 1/3[2πr(h+r)], which simplifies to r = 2h.

Shortcut Trick

Profit on First Pen: Let Marked Price be CP × (1 + 0.75). Net SP = MP × (1 − 0.14).

Effective Profit 1 = 444 × [1.75 × 0.86 − 1] = 444 × 0.505 = 224.22.

Profit on Second Pen = 356 × 48% = 356 × 0.48 = 170.88.

Total Profit = 224.22 + 170.88 = 395.10.

∴ The correct answer is ₹395.10.

Alternate Method

Given → CP₁ = ₹444, Mark-up = 75%, Discount = 14%, CP₂ = ₹356, Profit%₂ = 48%. Formulas: Profit = SP − CP | SP = CP × (100 + P%) ÷ 100 × (100 − D%) ÷ 100

⇒ For the first pen, Mark-up Price = 444 + (75% of 444) = 444 + 333 = ₹777. ⇒ Selling Price of first pen = 777 − (14% of 777) = 777 − 108.78 = ₹668.22. ⇒ Profit from first pen = 668.22 − 444 = ₹224.22. ⇒ Profit from the second pen = 48% of 356 = 0.48 × 356 = ₹170.88. ⇒ Total Profit = 224.22 + 170.88 = ₹395.10.

∴ The correct answer is ₹395.10.

Additional Information

Effective Profit Percentage

When a markup (m%) and then a discount (d%) is applied, the net profit% is given by the formula: [m − d − (m × d) ÷ 100].

Marked Price and Selling Price

The relationship between CP and SP through MP is SP = CP × (1 + markup%) × (1 − discount%).

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

1) H sits third to the left of G.

2. I sits to the immediate right of G

3) I sits second to the left of D.

4) Only two people sit between D and A when counted from the left of A.

5) B is not an immediate neighbor of H.

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

Thus, I sits third to the right of C.

Hence, "Option 2" is the correct answer.

Shortcut Trick

Convert speed to m/min: 2.7 km/hr × (1000/60) = 45 m/min.

Volume per minute = Area of cross-section × Speed in m/min.

Volume = (20 × 36) × 45 = 720 × 45 = 32,400 m³.

∴ The correct answer is 32,400 m³.

Alternate Method

Given: Depth (h) = 20 m, Width (b) = 36 m, Speed = 2.7 km/hr.

Formula Used: Volume of water per unit time = Area × Velocity.

⇒ Speed of flow in m/hr = 2.7 × 1000 = 2700 m/hr.

⇒ Speed of flow per minute = 2700 ÷ 60 = 45 m/min.

⇒ Cross-sectional area of river = Depth × Width = 20 × 36 = 720 m².

⇒ Volume of water per minute = Area × Length of water column in 1 min.

⇒ Volume = 720 × 45 = 32,400 m³.

∴ The correct answer is 32,400 m³.

Additional Information

Flow Rate Measurement

The volume of water flowing through a channel is calculated as the product of the cross-sectional area (Area = Width × Depth) and the flow velocity (Speed).

Unit Conversion

To convert km/hr to m/min, multiply by 1000/60 or 50/3. To convert m³ to Liters, remember 1 m³ = 1000 Liters.

Volume of a Cuboid

Since the river is treated as a rectangular channel, the volume is V = l × b × h, where 'l' is the distance water travels in the given time.

Shortcut Trick

Since Δ ABC ∼ Δ XYZ, the ratio of their perimeters is equal to the ratio of their corresponding sides.

Ratio of corresponding sides = AB ÷ XY = 6 ÷ 8 = 3 ÷ 4

Perimeter of Δ XYZ = XY + YZ + ZX = 8 + 12 + 16 = 36 cm

Perimeter of Δ ABC = (3 ÷ 4) × 36 = 27 cm

∴ The correct answer is 27 cm.

Alternate Method

Given:

AB = 6 cm, XY = 8 cm, YZ = 12 cm, ZX = 16 cm

Δ ABC ∼ Δ XYZ

Formula Used:

For similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding sides:

AB ÷ XY = BC ÷ YZ = CA ÷ ZX = Perimeter(Δ ABC) ÷ Perimeter(Δ XYZ)

Calculations:

⇒ Perimeter of Δ XYZ = XY + YZ + ZX

⇒ Perimeter of Δ XYZ = 8 + 12 + 16 = 36 cm

⇒ Since Δ ABC ∼ Δ XYZ, we have:

⇒ Perimeter of Δ ABC ÷ Perimeter of Δ XYZ = AB ÷ XY

⇒ Perimeter of Δ ABC ÷ 36 = 6 ÷ 8

⇒ Perimeter of Δ ABC ÷ 36 = 3 ÷ 4

⇒ Perimeter of Δ ABC = (3 ÷ 4) × 36

⇒ Perimeter of Δ ABC = 3 × 9 = 27 cm

Explanation of incorrect options:

Option (1) 34 cm: Incorrect, as the perimeter must be exactly 27 cm based on the similarity ratio of 3/4.

Option (2) 24 cm: Incorrect, as 24 cm would correspond to a similarity ratio of 2/3, which does not match AB/XY = 6/8 = 3/4.

Option (4) 32 cm: Incorrect, as 32 cm does not satisfy the similarity ratio of 3/4.

∴ The correct answer is 27 cm.

Additional Information

Properties of Similar Triangles

If two triangles are similar, the ratio of their corresponding sides is equal to the ratio of their perimeters, altitudes, medians, and angle bisectors.

Area Ratio Theorem

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides: Area(Δ ABC) ÷ Area(Δ XYZ) = (AB ÷ XY)².

Similarity Criteria

Two triangles are similar if they satisfy Angle-Angle (AA), Side-Angle-Side (SAS), or Side-Side-Side (SSS) similarity conditions.

Given:

Manoj starts from Point A and drives 13 km towards west.

He then takes a right turn, drives 2 km, turns right and drives 7 km.

He then takes a left turn and drives 5 km.

He takes a final right turn, drives 6 km and stops at Point P.

Thus, Manoj should drive 7 km (5 km + 2 km) in the south direction in order to reach point A again.

Hence, "Option 2" is the correct answer.

The correct answer is Great Big Beautiful Life.

Key Points

• Great Big Beautiful Life is a contemporary romance novel by Emily Henry, a bestselling author known for her witty and emotionally rich storytelling.
• The plot follows two rival writers, Daphne Vincent and Miles Nowak, competing to secure the rights to write the biography of a notorious heiress, Margaret Ives.
• Published on April 1, 2025, the book has created buzz for its mix of sharp humor and heartfelt drama.
• The narrative shifts between glamorous city backdrops and intimate personal moments, exploring themes of ambition, truth, and the complexities of love in competitive creative circles.
• Early reviews predict it will be a bestseller, praising its dynamic characters and layered, engaging storyline.

Additional Information

• Emily Henry
• Emily Henry is a New York Times bestselling author, known for her works in contemporary romance and fiction genres.
• Some of her other notable works include Beach Read (2020) and People We Meet on Vacation (2021).
• Her books often feature complex, relatable characters and explore themes of love, self-discovery, and personal growth.
• Contemporary Romance Genre
• This genre focuses on love stories set in modern times, often involving relatable characters and realistic settings.
• It is characterized by themes of personal growth, emotional connections, and overcoming obstacles in relationships.
• Authors like Emily Henry, Christina Lauren, and Colleen Hoover are prominent figures in this genre.
• Notorious Heiress Biographies
• Biographies of heiresses often explore themes of wealth, privilege, scandal, and societal expectations.
• Such stories have captivated audiences due to their blend of glamour and intrigue.
• Examples include works on figures like Gloria Vanderbilt and Barbara Hutton, whose lives were marked by both fortune and public scrutiny.
• Reception of Book Lovers
• The novel has received critical acclaim for its witty dialogue and heartfelt storytelling.
• It appeals to fans of romance and literary fiction, making it a favorite among book clubs and casual readers alike.
• Emily Henry’s writing style is often praised for blending humor with emotional depth, creating memorable characters and narratives.

The logic followed here is:

Hence, "Option 2" is the correct answer.

Given series: (Left) 4 @ 7 4 £ 9 9 # @ 1 4 $ % 4 3 8 2 © © 1 5 # (Right)

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

Required condition: Number - Number - Number

(Left) 4 @ 7 4 £ 9 9 # @ 1 4 $ % 4 3 8 2 © © 1 5 # (Right)

Thus, there are two such numbers are there which are immediately preceded by a number and also immediately followed by a number.

Hence, "Option 3" is the correct answer.

The correct answer is Palamu Tiger Reserve.

Key Points

• Palamu Tiger Reserve is located in the Latehar district of Jharkhand and was one of the first nine tiger reserves declared under Project Tiger in 1973.
• The relocation of Jaigir village is part of efforts to reduce human-wildlife conflict and ensure conservation of the core area of the reserve.
• Jaigir is the first village within the core area of Palamu Tiger Reserve that has been successfully relocated to minimize anthropogenic pressures on wildlife habitats.
• The process of relocation involved financial compensation and support to villagers for rehabilitation outside the reserve's core area.
• The initiative aligns with the National Tiger Conservation Authority's (NTCA) guidelines for sustainable conservation practices.

Additional Information

• Project Tiger:
• Launched by the Government of India in 1973 to conserve the tiger population and its habitat.
• Project Tiger is administered by the National Tiger Conservation Authority (NTCA).
• It covers 53 tiger reserves across India as of 2023.
• Core and Buffer Zones:
• Tiger reserves are divided into core and buffer zones for effective management.
• The core zone is strictly protected for wildlife conservation, while the buffer zone accommodates regulated human activities.
• National Tiger Conservation Authority (NTCA):
• NTCA was established in 2005 to strengthen tiger conservation efforts in India.
• It oversees the implementation of Project Tiger and ensures compliance with wildlife protection laws.
• Human-Wildlife Conflict:
• Human-wildlife conflict arises due to overlapping habitats and competition for resources between humans and wildlife.
• Relocation of villages from protected areas is a common strategy to mitigate such conflicts.

The correct answer is Madras Presidency.

Key Points

• The Poligar Rebellion occurred in the Madras Presidency during the late 18^th and early 19^th centuries.
• Poligars were feudal chieftains under the Nayak and Vijayanagar rulers who controlled forts and commanded independent armies in South India.
• The rebellion was triggered when the British East India Company tried to abolish the military and land rights of Poligars.
• Key figures in the rebellion include Kattabomman and other Poligar leaders who resisted British authority.
• The suppression of the rebellion led to the consolidation of British power in South India and the dismantling of feudal structures in the region.

Additional Information

• Poligars:
• Poligars were local chieftains who collected taxes and maintained law and order in their respective territories.
• They were known for their military prowess and control over fortified regions.
• Madras Presidency:
• The Madras Presidency was a major administrative division of British India, covering most of South India.
• It was a hub for rebellions like the Poligar Revolt due to strong regional resistance against British policies.
• Kattabomman:
• Kattabomman was a prominent Poligar leader from Tamil Nadu who opposed British control.
• He became a symbol of resistance and is remembered for his courage and defiance against colonial rule.
• Impact of the Rebellion:
• The suppression of Poligars marked the decline of feudal autonomy in South India.
• The rebellion highlighted the growing discontent against British policies and led to stricter administrative measures.

The correct answer is Nagaland and Arunachal Pradesh.

Key Points

• The Konyak tribe is primarily found in the northeastern states of Nagaland and parts of Arunachal Pradesh.
• They are one of the largest tribes in Nagaland, predominantly residing in the Mon district.
• The Konyaks are traditionally known as fierce warriors and have a unique culture, including their practice of headhunting in the past.
• Their tribal identity is marked by tattoos, which symbolize their achievements and social status.
• They are skilled in handicrafts, blacksmithing, and agriculture, contributing significantly to their local economy.

Additional Information

• Head-Hunting Practice:
• The Konyak tribe was historically known for its practice of headhunting, which was a significant cultural ritual symbolizing bravery and strength.
• This practice ended decades ago due to the influence of Christianity and modern governance.
• Traditional Attire and Tattoos:
• Konyak men and women wear distinctive tribal attire adorned with beads, feathers, and ornaments.
• Their facial and body tattoos were traditionally earned after successful headhunting expeditions.
• Aoling Festival:
• The Konyak tribe celebrates the Aoling festival, marking the arrival of spring and the start of the agricultural season.
• It is observed in the first week of April and includes traditional dances, songs, and rituals.
• Language and Culture:
• The Konyak tribe speaks the Konyak language, which belongs to the Tibeto-Burman language family.
• They are known for preserving their indigenous traditions and oral folklore passed down through generations.

Given equation: 8 ÷ 7 + 56 × 14 − 2 = ?

According to the question, after '+' and '−' are interchanged and '×' and '÷' are interchanged:

8 ÷ 7 + 56 × 14 − 2 = ? ⇒ 8 × 7 − 56 ÷ 14 + 2 = ?

⇒ 8 × 7 − 56 ÷ 14 + 2 = ?

⇒ 8 × 7 − 4 + 2 = ?

⇒ 56 + 2 − 4 = ?

⇒ 58 − 4 = ?

⇒ 54 = ?

Hence, "Option 1" is the correct answer.

The correct answer is Medical device manufacturers.

Key Points

• In September 2024, the Uniform Code of Pharmaceutical Marketing Practices (UCPMP) extended its guidelines to medical device manufacturers for ethical marketing and promotion practices.
• The UCPMP aims to regulate and ensure transparency in interactions between pharmaceutical companies and healthcare professionals, now including medical device manufacturers.
• The extension of UCPMP to medical device manufacturers highlights the growing importance of ethical considerations in the healthcare and medical device industry.
• Under these guidelines, medical device manufacturers are expected to adhere to ethical standards in advertising, promotions, and interactions with healthcare providers.
• This move aligns with the government's efforts to strengthen accountability and safeguard patient interests in the healthcare sector.

Additional Information

• Uniform Code of Pharmaceutical Marketing Practices (UCPMP)
• The UCPMP was introduced by the Department of Pharmaceuticals, Government of India, to regulate marketing practices in the pharmaceutical industry.
• It seeks to prevent unethical practices such as excessive gifts, inducements, or sponsorships offered to healthcare professionals.
• It emphasizes transparency, accountability, and ethical promotional practices in the healthcare sector.
• Medical Devices Industry in India
• India has one of the fastest-growing medical device markets globally, valued at approximately USD 11 billion in 2022.
• The sector is regulated by the Central Drugs Standard Control Organization (CDSCO) under the Drugs and Cosmetics Act.
• Medical devices range from diagnostic tools and surgical instruments to advanced imaging and therapeutic equipment.
• Ethical Marketing Practices
• Ethical marketing ensures that healthcare products are promoted in a manner that prioritizes patient welfare and safety.
• It includes accurate representation of product benefits, avoiding misleading claims, and transparent interactions with healthcare professionals.
• Impact of UCPMP Extension
• The inclusion of medical device manufacturers under UCPMP guidelines is expected to enhance trust among healthcare providers and patients.
• It promotes fair competition and deters unethical practices within the medical device industry.

The correct answer is 1911.

Key Points

• The Partition of Bengal was implemented by the British in 1905 under Lord Curzon’s administration, dividing Bengal into East Bengal and Assam, and West Bengal.
• It faced fierce opposition from Indian leaders and the general public, leading to protests, boycotts, and the Swadeshi Movement.
• Due to the intense backlash, the British annulled the partition in 1911 during the Delhi Durbar held to commemorate King George V's coronation.
• Post-annulment, Bengal was reunited, but Bihar and Orissa were carved out as separate provinces to ease administrative challenges.
• The annulment symbolized the growing strength of Indian nationalism and the organized resistance against British policies.

Additional Information

• Partition of Bengal (1905):
• The division was justified by the British as an administrative necessity due to Bengal’s large size and population.
• East Bengal was predominantly Muslim, while West Bengal had a Hindu majority, leading to communal undertones in the partition.
• Swadeshi Movement:
• A key response to the partition, promoting the boycott of British goods and the use of indigenous products.
• It marked the beginning of organized nationalist movements in India.
• Delhi Durbar (1911):
• It was a grand event to mark the coronation of King George V and Queen Mary.
• During this event, the British announced the annulment of the Partition of Bengal and the transfer of the capital from Calcutta to Delhi.
• Impact on Indian Nationalism:
• The partition and its annulment highlighted the importance of mass movements and unity among Indians.
• It strengthened the resolve of Indian leaders to fight for independence and helped unite various communities.

Shortcut Trick

Given cot θ = 3/4 (Base/Perpendicular), so sin θ = 4/5.

Apply direct formula: sin 3θ = 3 sin θ − 4 sin³θ.

⇒ sin 3θ = 3(4/5) − 4(4/5)³ = 12/5 − 256/125.

⇒ (300 − 256)/125 = 44/125.

∴ The correct answer is 44/125.

Alternate Method

Given: cot θ = 3/4

Formula Used: sin 3θ = 3 sin θ − 4 sin³θ

⇒ In a right-angled triangle, if cot θ = Base/Perpendicular = 3/4,

⇒ Hypotenuse (H) = √(3² + 4²) = √(9 + 16) = 5.

⇒ sin θ = Perpendicular/Hypotenuse = 4/5.

⇒ sin 3θ = 3(4/5) − 4(4/5)³

⇒ sin 3θ = 12/5 − 4(64/125)

⇒ sin 3θ = 12/5 − 256/125

⇒ sin 3θ = (12 × 25 − 256) / 125

⇒ sin 3θ = (300 − 256) / 125 = 44/125.

∴ The correct answer is 44/125.

Additional Information

Multiple Angle Formulas

cos 3θ = 4 cos³θ − 3 cos θ and tan 3θ = (3 tan θ − tan³θ) / (1 − 3 tan²θ).

Pythagorean Triplet

The numbers (3, 4, 5) form a Pythagorean triplet where 3² + 4² = 5².

Trigonometric Ratios

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

Given series: (Left) @ 5 4 £ 8 & © £ * 2 5 9 $6 £ 4 * 8$ 4 % * (Right)

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

Required condition: Number - Symbols - Number

(Left) @ 5 4 £ 8 & © £ * 2 5 9 $6 £ 4 * 8$ 4 % * (Right)

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

Hence, "Option 2" is the correct answer.

The correct answer is Article 32.

Key Points

• Article 32 of the Indian Constitution empowers the Supreme Court to issue writs for the enforcement of Fundamental Rights.
• Writs under Article 32 include Habeas Corpus, Mandamus, Prohibition, Certiorari, and Quo Warranto.
• It is often referred to as the "heart and soul" of the Constitution, as described by Dr. B.R. Ambedkar, for safeguarding fundamental rights.
• This article provides the right to individuals to directly approach the Supreme Court in case of violation of their Fundamental Rights.
• The jurisdiction of Article 32 makes the Supreme Court the guardian and protector of Fundamental Rights.

Additional Information

• Habeas Corpus: A writ to produce a person before the court to ensure they are not detained unlawfully.
• Mandamus: A writ issued to a public official or body to perform a duty that they are legally obligated to fulfill.
• Prohibition: A writ issued by a higher court to prevent a lower court or tribunal from exceeding its jurisdiction.
• Certiorari: A writ issued by a higher court to review the decision or proceedings of a lower court or tribunal.
• Quo Warranto: A writ to question the legality of a person holding a public office.
• Besides Article 32, High Courts are empowered to issue writs under Article 226, but the scope of Article 226 is wider as it includes not just Fundamental Rights but also other legal rights.
• The right to constitutional remedies, as provided under Article 32, is itself a Fundamental Right, ensuring citizens' access to justice.
• In certain situations, the enforcement of Fundamental Rights under Article 32 may be suspended during the proclamation of Emergency under Article 359 of the Constitution.

Given equation: 43 + 15 ÷ 2 – 12 × 4 = ?

According to the question, after '+' and '−' are interchanged and '×' and '÷' are interchanged:

43 + 15 ÷ 2 – 12 × 4 = ? ⇒ 43 – 15 × 2 + 12 ÷ 4 = ?

⇒ 43 – 15 × 2 + 12 ÷ 4 = ?

⇒ 43 – 15 × 2 + 3 = ?

⇒ 43 + 3 – 30 = ?

⇒ 46 – 30 = ?

⇒ 16 = ?

Hence, "Option 4" is the correct answer.

The correct answer is Shaktikanta Das.

Key Points

• Shaktikanta Das, the former Governor of the Reserve Bank of India (RBI), is recognized for his significant contributions to India's financial and economic policies.
• He was appointed as the Principal Secretary-2 to PM Narendra Modi in February 2025, reinforcing his pivotal role in India's economic governance.
• Shaktikanta Das has served in various key positions, including Secretary of the Department of Economic Affairs and Secretary of Revenue in the Ministry of Finance.
• He played a crucial role in implementing economic reforms, such as the Goods and Services Tax (GST) and measures to strengthen fiscal policy frameworks.
• Das’s appointment aligns with the government’s commitment to leveraging experienced policymakers for enhancing governance and driving economic growth.

Additional Information

• Principal Secretary Role
• The Principal Secretary is one of the most senior bureaucratic positions in India, directly responsible for advising the Prime Minister on policy matters and implementation strategies.
• Principal Secretaries often coordinate among ministries and departments, ensuring seamless execution of government initiatives.
• The appointment reflects trust in the individual’s expertise, experience, and ability to manage critical national issues.
• Shaktikanta Das's Contributions
• He spearheaded the demonetization initiative in November 2016, playing a key role in its implementation and communication strategy.
• Das has been instrumental in shaping India’s Monetary Policy Framework during his tenure at RBI.
• Under his leadership, RBI has focused on financial inclusion initiatives, improving access to banking services for underserved populations.
• RBI's Role in Economic Governance
• The Reserve Bank of India (RBI) is responsible for regulating the monetary policy, ensuring the stability of the financial system, and promoting economic growth.
• Key functions include controlling inflation, managing currency supply, and ensuring liquidity in the economy.
• Economic Reforms in India
• India has witnessed significant economic reforms, such as GST, Insolvency and Bankruptcy Code (IBC), and fiscal consolidation measures.
• These reforms aim to streamline taxation, improve ease of doing business, and strengthen the financial system.

Shortcut Trick

Since the total expenditure (₹1) is constant, the quantity is inversely proportional to the price.

Price ratio (CP : SP) = 100 : 120 = 5 : 6.

Quantity ratio (CP : SP) = 6 : 5.

Given SP quantity = 5 units = 5 chocolates.

∴ CP quantity = 6 units = 6 chocolates.

∴ The correct answer is 6 chocolates.

Alternate Method

Given: Selling Price (SP) of 5 chocolates = ₹1, Profit % = 20%.

Formulas: CP = [SP × 100] ÷ [100 + Profit%]

⇒ SP of 1 chocolate = ₹(1/5).

⇒ CP of 1 chocolate = [(1/5) × 100] ÷ (100 + 20).

⇒ CP of 1 chocolate = [20] ÷ 120 = ₹(1/6).

⇒ Since CP of 1 chocolate is ₹(1/6), the number of chocolates bought for ₹1 = 6.

∴ The correct answer is 6 chocolates.

Additional Information

Price and Consumption Relationship

When the total expenditure remains constant, the quantity (consumption) is inversely proportional to the price per unit. Formula: Price × Quantity = Expenditure.

Profit and Loss on Unit Basis

It is always easier to calculate the Cost Price or Selling Price for a single unit to avoid confusion with bulk quantities.

The correct answer is Click inside a text placeholder and start typing.

Key Points

• In MS PowerPoint, a text placeholder is a predefined area on the slide where text can be added easily.
• To add text, simply click inside the text placeholder and start typing your content.
• Placeholders are commonly found in slide layouts such as title slides, content slides, or bullet list slides.
• Text placeholders are designed to help maintain a consistent slide design and formatting throughout the presentation.
• Users can customize the font, color, size, and alignment of the text after typing to match their requirements.

Additional Information

• Text Placeholder:
• It is a box with dotted or dashed borders visible in slide layouts.
• Placeholders can also hold images, charts, tables, or other elements, but their default purpose is often text input.
• Slide Layouts:
• Each slide layout in MS PowerPoint determines the positioning of placeholders for title, content, and other elements.
• Common layouts include "Title Slide," "Title and Content," and "Two Content."
• Keyboard Shortcut Tips:
• There is no direct shortcut like Ctrl + T to add text; placeholders must be clicked manually.
• However, users can use shortcuts like Ctrl + A to select all text or Ctrl + E to center-align text.
• Custom Text Boxes:
• If no placeholder exists, users can insert a custom text box via the "Insert" tab.
• Select "Text Box," click on the slide, and then type text into the custom box.
• Formatting Options:
• Text formatting options are available under the "Home" tab in the Ribbon.
• Users can adjust font styles, apply bold/italic/underline effects, and change text colors.

The correct answer is Shift + Delete.

Key Points

• The Shift + Delete keyboard shortcut in Windows OS permanently deletes a file without sending it to the Recycle Bin.
• This action bypasses the Recycle Bin, making recovery of the file more difficult unless specialized software is used.
• It is a quick method to remove unwanted files permanently and save disk space.
• Users are advised to exercise caution while using this shortcut, as accidental deletions may require advanced recovery tools.
• Files deleted using this method do not consume space in the Recycle Bin and are immediately removed from the file system.

Additional Information

• Recycle Bin
• The Recycle Bin is a feature in Windows OS used to temporarily store deleted files.
• Files moved to the Recycle Bin can be restored unless the bin is emptied.
• It serves as a safeguard against accidental deletions.
• File Recovery
• Files permanently deleted using Shift + Delete can sometimes be recovered using third-party recovery tools.
• Examples of such tools include Recuva, EaseUS Data Recovery Wizard, and Disk Drill.
• File System
• The file system in Windows OS (e.g., NTFS, FAT32) manages how data is stored and retrieved on storage devices.
• Permanently deleted files are marked as free space in the file system and may be overwritten by new data.
• Best Practices
• Always double-check before using Shift + Delete to ensure important files are not deleted accidentally.
• Maintain regular backups to avoid permanent data loss.

Shortcut Trick

Check the options against the condition: 5 years ago, Father was 4 times Son.

Option (1) 32, 8 → 5 yrs ago: 27, 3 (9 times) ×

Option (2) 50, 20 → 5 yrs ago: 45, 15 (3 times) ×

Option (3) 45, 15 → 5 yrs ago: 40, 10 (4 times) ✓

Second condition check: (15+15) : 45 = 30 : 45 = 2 : 3 ✓

∴ The correct answer is 45:15 years.

Alternate Method

Given: Ratio after 15 yrs (Son) to Present (Father) = 2 : 3. Ratio 5 yrs ago F : S = 4 : 1.

⇒ Let ages 5 years ago be Father = 4x and Son = x.

⇒ Present age of Father = 4x + 5 and Son = x + 5.

⇒ Son's age after 15 years = (x + 5) + 15 = x + 20.

⇒ According to question: (x + 20) / (4x + 5) = 2 / 3

⇒ 3(x + 20) = 2(4x + 5)

⇒ 3x + 60 = 8x + 10

⇒ 5x = 50 ⇒ x = 10.

⇒ Present Father = 4(10) + 5 = 45 years.

⇒ Present Son = 10 + 5 = 15 years.

∴ The correct answer is 45:15 years.

Additional Information

Age Ratio Constant Difference

The numerical difference between the ages of two persons always remains constant regardless of the number of years passed.

Present Age Conversion

If age 'n' years ago is x, present age is x + n. If age after 'n' years is y, present age is y − n.

Shortcut Trick

The given ages form an Arithmetic Progression (AP) with common difference d = 5 and number of terms n = 6.

Shortcut formula for Standard Deviation (σ) of an AP: σ = d × √[(n² − 1) / 12]

σ = 5 × √[(6² − 1) / 12] = 5 × √(35 / 12) = 5 × √2.9167

σ ≈ 5 × 1.7078 = 8.539

∴ The correct answer is 8.54 years.

Alternate Method

Given: Ages = 25, 30, 35, 40, 45, 50 | Number of people (N) = 6.

Formula: Standard Deviation (σ) = √[Σ(x − μ)² / N], where μ is the mean.

⇒ Mean (μ) = (25 + 30 + 35 + 40 + 45 + 50) / 6 = 225 / 6

The correct answer is Joule.

Key Points

• The SI (International System of Units) unit of energy is the Joule (symbol: J).
• One Joule is defined as the energy transferred when a force of one newton moves an object by one meter.
• The Joule is named after the physicist James Prescott Joule, who contributed significantly to the study of energy.
• 1 Joule is equivalent to 1 Newton-meter (N·m) or 1 kg·m²/s² in base SI units.
• Joule is used to measure various forms of energy, including kinetic energy, potential energy, thermal energy, and electrical energy.

Additional Information

• Watt:
• Watt (W) is the SI unit of power, not energy.
• 1 Watt is defined as 1 Joule per second (1 W = 1 J/s).
• Kelvin:
• Kelvin (K) is the SI unit of temperature, not energy.
• It is used to measure the thermodynamic temperature scale.
• Newton:
• Newton (N) is the SI unit of force, not energy.
• 1 Newton is the force required to accelerate a 1 kg mass by 1 meter per second squared (1 N = 1 kg·m/s²).
• Relationship Between Energy and Work:
• Energy is the capacity to do work, and work is the transfer of energy.
• Both energy and work are measured in Joules.
• Other Common Units of Energy:
• Calorie (cal): Commonly used in food energy, 1 cal = 4.184 Joules.
• Electronvolt (eV): Used in atomic and particle physics, 1 eV = 1.602 × 10⁻¹⁹ Joules.

The correct answer is Chairperson and five members.

Key Points

• The National Human Rights Commission (NHRC) of India consists of a Chairperson and five full-time members.
• The Chairperson is typically a retired Chief Justice of India, ensuring the highest level of judicial oversight in human rights matters.
• The five members include four full-time members and one ex-officio member who serves as the Chairperson of the National Commission for Scheduled Castes, Scheduled Tribes, Minorities, and Women.
• The NHRC was established on 12 October 1993 under the Protection of Human Rights Act, 1993.
• It aims to protect and promote human rights in India, including rights related to life, liberty, equality, and dignity of individuals.

Additional Information

• Human Rights:
• Human rights are fundamental rights that protect the dignity and freedom of individuals.
• They include rights such as freedom of speech, equality before the law, and protection against discrimination.
• Protection of Human Rights Act, 1993:
• This act provides for the establishment of the NHRC and State Human Rights Commissions (SHRCs).
• It outlines the powers and functions of the NHRC, including investigating human rights violations and recommending corrective measures.
• Functions of NHRC:
• Investigating complaints of human rights violations.
• Conducting inquiries, recommending reforms, and promoting awareness of human rights.
• It also reviews acts that may result in the violation of human rights and suggests remedies.
• Composition of NHRC:
• Chairperson: A retired Chief Justice of India.
• Four full-time members: Including individuals with judicial and human rights expertise.
• Ex-officio members from relevant commissions representing vulnerable sections of society.

The correct answer is Aag Ka Darya.

Key Points

• Aag Ka Darya (River of Fire) was written by Qurratulain Hyder in 1959 and is considered one of the most important works in Urdu literature.
• The novel spans over two millennia, exploring the cultural, social, and political history of the Indian subcontinent.
• It is known for its profound examination of the effects of the Partition of India (1947) on individuals and society.
• The book delves deeply into themes of identity, displacement, and the continuity of civilization, connecting ancient and modern times.
• Qurratulain Hyder is often referred to as the "Grande Dame of Urdu Literature" for her contribution to the literary world.

Additional Information

• Partition of India (1947):
• The partition led to the division of British India into two independent dominions, India and Pakistan, causing massive displacement and communal violence.
• It remains one of the most significant and tragic events in South Asian history, affecting millions of lives.
• Qurratulain Hyder:
• Born in 1927, Hyder was an iconic Urdu novelist, short story writer, and translator, who received numerous accolades for her work, including the Jnanpith Award.
• Her literary contributions include novels like "Mere Bhi Sanamkhane" and "Kar e Jahan Daraz Hai."
• Aag Ka Darya - Literary Style:
• The novel utilizes a multi-layered narrative structure, intertwining historical and fictional elements.
• It incorporates characters from different time periods, blending personal stories with historical events.
• Urdu Literature:
• Urdu literature has a rich tradition of poetry and prose, with notable works in genres such as ghazals, novels, and short stories.
• Writers like Mirza Ghalib, Saadat Hasan Manto, and Ismat Chughtai have made significant contributions to Urdu literature.

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

1) Both Q and V are immediate neighbours of S.

2. V sits third to the left of T.

3) R sits to the immediate left of T.

4) U is not an immediate neighbour of V.

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

Thus, four people sit between S and U when counted from the right of S.

Hence, "Option 3" is the correct answer.

The correct answer is Tube wells and canals.

Key Points

• Tube wells and canals account for the largest share of irrigation in India, contributing significantly to agricultural productivity.
• Canals are prominent irrigation sources in areas like Punjab, Haryana, and Uttar Pradesh due to their extensive network and water availability.
• Tube wells rely on groundwater extraction, making them widely used in regions with low surface water availability, such as Rajasthan and parts of Maharashtra.
• The Green Revolution further promoted the use of tube wells and canals, especially in northern India, to ensure reliable water supply for high-yield crops.
• Together, tube wells and canals irrigate a significant portion of India's agricultural land, ensuring food security for the growing population.

Additional Information

• Canal Irrigation:
• Canals are artificial waterways that distribute water from rivers or reservoirs to agricultural fields.
• They are particularly effective in regions with flat terrain and abundant surface water sources.
• India has an extensive canal network, with major projects like the Indira Gandhi Canal in Rajasthan.
• Tube Wells:
• Tube wells are deep bore wells equipped with pumps to extract groundwater for irrigation.
• They are widely used in areas where surface water sources are scarce or unreliable.
• Excessive use of tube wells has led to groundwater depletion in certain regions, necessitating sustainable practices.
• Rainwater Harvesting:
• Rainwater harvesting involves collecting and storing rainwater for irrigation and other purposes.
• Though beneficial, it is a secondary source of irrigation compared to tube wells and canals in India.
• Tank Irrigation:
• Tanks are small water reservoirs used primarily in southern states like Tamil Nadu and Karnataka.
• They provide water for irrigation during dry seasons but have limited coverage compared to tube wells and canals.

Shortcut Trick

Total Expenditure % = 30% + 25% + 15% + 16% = 86%

Savings % = 100% − 86% = 14%

14% of Salary = ₹42,000

100% (Total Salary) = (42000 ÷ 14) × 100 = 3000 × 100 = ₹3,00,000

∴ The correct answer is ₹3,00,000.

Alternate Method

Given:

House Rent = 30% | Food = 25% | Medical = 15% | Others = 16%

Monthly Savings = ₹42,000

Calculations:

⇒ Total spending = 30 + 25 + 15 + 16 = 86%

⇒ Let total monthly salary be S.

⇒ Savings = S − (86% of S) = 14% of S

⇒ 14/100 × S = 42,000

⇒ S = (42,000 × 100) ÷ 14

⇒ S = 3,000 × 100 = 3,00,000

∴ The correct answer is ₹3,00,000.

Additional Information

Percentage Expenditure

When percentages are given on the total salary, simply add them to find total expenditure. Savings % = 100% − Total Expenditure %.

Remaining Balance Concept

If the question states % of remaining salary, use the successive formula: Final = Initial × (1 − r₁/100) × (1 − r₂/100).

Base Value Calculation

Total Value = (Given Value ÷ Percentage of that Value) × 100.

The correct answer is To propose strategies for enhancing India's role in global automotive value chains.

Key Points

• The report by NITI Aayog aims to outline strategic measures for enhancing India's participation in global automotive value chains.
• It focuses on aligning India's automotive industry policies with global standards to boost competitiveness and innovation.
• Key areas addressed include technology adoption, skill development, and fostering collaboration between stakeholders.
• The report emphasizes strengthening exports, improving supply chain efficiency, and leveraging India's manufacturing capacity.
• Promoting sustainable practices and integrating advanced technologies like electric vehicles (EVs) and autonomous systems are highlighted as vital strategies.

Additional Information

• Global Value Chains (GVCs):
• GVCs refer to the international division of production, where different stages of the manufacturing process are carried out in various countries.
• Participation in GVCs helps nations integrate into the global economy and enhance their trade competitiveness.
• India's Automotive Industry:
• India is the world's fourth-largest automotive market and a major exporter of vehicles and auto components.
• The industry contributes significantly to India's GDP and provides employment to millions of workers.
• Electric Vehicles (EVs) and Sustainability:
• EVs are a critical focus area in India's automotive strategy to reduce dependence on fossil fuels and promote sustainability.
• India aims to achieve 30% EV penetration by 2030 under its National Electric Mobility Mission Plan (NEMMP).
• Skill Development in the Automotive Sector:
• Upskilling and reskilling workers are essential to adapt to technological changes in the automotive industry.
• Initiatives like the Automotive Skills Development Council (ASDC) work towards training the workforce for emerging technologies.

The logic followed here is:

Hence, "Option 4" is the correct answer.

The correct answer is Dr. R Balasubramaniam.

Key Points

• Dr. R Balasubramaniam is the author of the book 'Power Within: The Leadership Legacy of Narendra Modi', which reflects on PM Modi's leadership values and principles.
• The book captures the journey of Narendra Modi's leadership and its transformative impact on the nation and governance.
• Dr. R Balasubramaniam is a leadership expert and founder of the Swami Vivekananda Youth Movement (SVYM), an organization working towards community development and education.
• The book examines leadership lessons from the life of PM Modi, particularly focusing on decision-making, resilience, and public service.
• It is widely appreciated for its insights into political leadership and provides actionable principles for leaders across domains.

Additional Information

• Dr. R Balasubramaniam
• He is a public policy expert, leadership trainer, and social worker with decades of experience in grassroots development.
• He has served on several government committees and advisory boards, including the Lokpal Search Committee in India.
• Dr. Balasubramaniam is the author of several other books focused on leadership and social transformation.
• Leadership Legacy
• The concept of leadership legacy emphasizes the long-term impact of a leader's actions on their organization, community, or nation.
• PM Narendra Modi's leadership is often characterized by visionary policy-making, resilience, and grassroots connection.
• Swami Vivekananda Youth Movement (SVYM)
• A non-profit organization founded by Dr. R Balasubramaniam in 1984, based on the teachings of Swami Vivekananda.
• It focuses on healthcare, education, and leadership development in rural and tribal communities.
• Books on PM Modi's Leadership
• Several books have been written about PM Narendra Modi's governance, including 'The Modi Effect' by Lance Price and 'Narendra Modi: The Man, The Times' by Nilanjan Mukhopadhyay.
• These books explore various aspects of Modi's leadership style, policy initiatives, and political strategies.

The correct answer is Chaman Arora.

Key Points

• Chaman Arora won the Sahitya Akademi Award 2024 for his work in Dogri literature.
• The awarded book, titled 'Ik Hor Ashwthama', is a notable contribution to the Dogri literary tradition.
• The Sahitya Akademi Award recognizes exceptional literary works in 24 Indian languages, including Dogri.
• This prestigious award is presented annually by the Sahitya Akademi, India's National Academy of Letters.
• The award includes a cash prize of ₹1,00,000, along with a citation and a memento.

Additional Information

• Sahitya Akademi Award:
• Established in 1954, the award celebrates literary excellence in India's diverse languages.
• It is aimed at promoting and preserving India's rich linguistic heritage.
• The award encompasses genres like novels, poetry, short stories, essays, and plays.
• Only works published in the preceding five years are eligible for nomination.
• Dogri Language:
• Dogri is one of the 22 scheduled languages recognized by the Indian Constitution.
• It is primarily spoken in the Jammu region of Jammu & Kashmir.
• The language is known for its rich oral tradition and vibrant folk literature.
• Dogri gained official recognition as a scheduled language in 2003.
• Literary Significance of 'Ik Hor Ashwthama':
• 'Ik Hor Ashwthama' draws inspiration from Indian mythology, exploring themes of immortality and human conflict.
• The book is celebrated for its powerful storytelling and unique narrative structure.
• It reflects contemporary societal issues through the lens of Dogri literature.
• Sahitya Akademi:
• The Sahitya Akademi operates under the Ministry of Culture, Government of India.
• It also organizes literary seminars, workshops, and fellowships to promote literary activities across India.

Decoding the Symbols:

Given: M + N − O × P ÷ Q

M + N → M is the mother of N.

N − O → N is the brother of O. 

O × P → O is the wife of P.

P ÷ Q → P is the father of Q.

Thus, M is Q's maternal grandmother or mother's mother.

Hence, "Option 1" is the correct answer.

The logic followed here is:

Given: 

JAY : MDB

And,

PAN : SDQ

Similarly,

Option 3) UPC : XSF

Hence, "Option 3" is the correct answer.

The correct answer is Cristiano Ronaldo.

Key Points

• Cristiano Ronaldo became the first footballer to score 900 professional career goals, including goals scored for both club and country, in April 2025.
• The milestone was achieved during his tenure with Al-Nassr, the Saudi Arabian club he joined in 2023 after leaving Manchester United.
• Ronaldo is widely regarded as one of the greatest football players of all time, consistently breaking records in his illustrious career.
• His goals include contributions to clubs such as Sporting CP, Manchester United, Real Madrid, Juventus, and Al-Nassr, as well as the Portuguese national team.
• As of 2025, Ronaldo remains the all-time leading scorer for the UEFA Champions League and the Portuguese national team.

Additional Information

• Professional Career Goals:
• This statistic encompasses all goals scored in official matches for clubs and national teams, including league games, domestic cups, international tournaments, and qualifiers.
• Other notable players nearing this milestone include Lionel Messi, who remains a close competitor in terms of career goals.
• Ronaldo's Career Highlights:
• He has won five Ballon d'Or awards, recognizing him as the best player in the world.
• He holds the record for the most goals scored in a single UEFA Champions League season (17 goals in 2013-14).
• Ronaldo is the first player in history to win league titles in England, Spain, and Italy.
• Influence on Modern Football:
• Ronaldo's exceptional goal-scoring ability, athleticism, and dedication to fitness have set a benchmark for upcoming footballers.
• He is a global icon, with sponsorships from brands like Nike, and has built his own CR7 brand.
• Al-Nassr and Saudi Pro League:
• Ronaldo joined Al-Nassr in 2023, marking a significant shift in his career to the Saudi Pro League.
• His presence has increased the global visibility of the league and attracted other international players to the region.

The logic followed here is:

Hence, "Option 4" is the correct answer.

Alternate Method

The correct answer is ₹1,59,964 crore.

Key Points

• The budget allocation for the Ministry of Rural Development for the fiscal year 2023-24 was ₹1,59,964 crore.
• This allocation was aimed at improving rural infrastructure, livelihood creation, and poverty alleviation in rural areas.
• Key schemes under the Ministry of Rural Development include Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA), Pradhan Mantri Gram Sadak Yojana (PMGSY), and National Social Assistance Programme.
• The increased funding reflects the government's emphasis on strengthening rural development programs to ensure sustainable growth.
• It supports initiatives aimed at bridging the urban-rural divide and enhancing the quality of life in rural regions.

Additional Information

• Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA)
• MGNREGA is a flagship rural employment scheme that guarantees at least 100 days of wage employment in a financial year to rural households.
• It focuses on creating durable assets such as roads, water conservation structures, and irrigation facilities.
• The scheme plays a crucial role in poverty alleviation and empowering rural communities.
• Pradhan Mantri Gram Sadak Yojana (PMGSY)
• PMGSY aims to provide all-weather road connectivity to unconnected villages in India.
• The scheme is instrumental in improving access to markets, healthcare, and education in rural areas.
• It contributes significantly to rural infrastructure development and economic growth.
• National Social Assistance Programme (NSAP)
• NSAP provides financial assistance to the elderly, widows, and persons with disabilities in the form of pensions.
• The program is a part of India's social safety net for vulnerable sections of society.
• It aims to ensure minimum income support and dignity for marginalized individuals.
• Importance of Rural Development
• Rural development is crucial for reducing poverty and unemployment in rural areas.
• Investments in rural infrastructure, education, and healthcare help bridge the urban-rural divide.
• It fosters sustainable economic growth and improves the quality of life for the rural population.

The correct answer is The Foreigners Act, 1946.

Key Points

• The Immigration and Foreigners Bill, 2025, was enacted to modernize and consolidate laws governing immigration, foreigners, and their regulation in India.
• The legislation specifically repealed The Foreigners Act, 1946, which had been the primary legal framework governing the entry, stay, and deportation of foreigners in India for decades.
• The Foreigners Act, 1946, was considered outdated and inadequate to address the complexities of contemporary immigration and border security challenges.
• The new bill aims to establish a more comprehensive and technology-driven approach to managing immigration and foreigner-related matters.
• The bill introduces provisions for e-governance, better monitoring of foreign nationals, and streamlined deportation processes.

Additional Information

• The Foreigners Act, 1946:
• It was enacted by the British Government to regulate the entry, presence, and departure of foreigners in India.
• The Act empowered the government to declare any foreign national as an illegal immigrant and deport them.
• The Act also provided for powers to arrest, detain, or restrict the movement of foreigners under certain circumstances.
• Immigration Challenges in India:
• India faces significant immigration challenges, including illegal migration across porous borders with neighboring countries like Bangladesh and Myanmar.
• The lack of a modern and unified immigration framework has hindered efficient regulation and monitoring of foreign nationals.
• Key Features of the Immigration and Foreigners Bill, 2025:
• Introduces a centralized database for monitoring the entry and exit of foreign nationals.
• Enhances penalties for violation of immigration laws.
• Establishes dedicated immigration courts to expedite the resolution of disputes and deportation cases.
• Related Legislation:
• The Emigration Act, 1983, governs the emigration of Indian nationals for overseas employment and remains unaffected by the new bill.
• The Citizenship Act, 1955, deals with the acquisition and termination of Indian citizenship and is also separate from the Immigration and Foreigners Bill.