RRB NTPC (UG) CBT-I Official Paper (Held On 15 Jun, 2026 Shift 1) (Previous Year Paper)

Shortcut Trick

Equate decimal places: Total numerator places = 13, Total denominator places = 12, resulting in a factor of 10⁻¹.

Identify powers: 6859 = 19³, 54872 = 38³ = (2 × 19)³, and 1156 = 34² = (2 × 17)².

Simplify the ratios: (19/38)³ × (34/17)² × (64000/1600) × 0.1 = (1/8) × 4 × 40 × 0.1 = 2.

Calculate the final root: √2 ≈ 1.414.

∴ The correct answer is 1.414.

Alternate Method

Given Expression: √( (0.6859 × 0.1156 × 0.64000) / (0.289 × 0.1600 × 0.54872) )

⇒ Count total decimal places in Numerator: 4 + 4 + 5 = 13.

⇒ Count total decimal places in Denominator: 3 + 4 + 5 = 12.

⇒ Remove decimals by adjusting powers of 10: √( (6859 × 1156 × 64000) / (289 × 1600 × 54872) × 10⁻¹ )

⇒ Simplify the large numbers using prime factorization: 6859 = 19³, 1156 = 34², 289 = 17², 54872 = 38³.

⇒ √( (19³ × 34² × 40) / (17² × 38³ × 10) )

⇒ √( (19³ × (2 × 17)² × 40) / (17² × (2 × 19)³ × 10) )

⇒ √( (19³ × 4 × 17² × 40) / (17² × 8 × 19³ × 10) )

⇒ Cancel common terms: √( (4 × 40) / (8 × 10) ) = √(160 / 80) = √2

⇒ Square root of 2 up to three decimal places = 1.414

∴ The correct answer is 1.414.

Additional Information

Cubes of Numbers

Memorizing cubes up to 20 is crucial for simplification: 19³ = 6859 and 38³ = 54872.

Square Root Constants

Standard square root values frequently used in exams: √2 ≈ 1.414 and √3 ≈ 1.732.

Power and Indices Rule

For any numbers a and b: (a × b)ⁿ = aⁿ × bⁿ. This helps in simplifying ratios like (34/17)² = 2² = 4.

Shortcut Trick

Relative Speed (opposite direction) = 55 + 65 = 120 km/h

Total distance to be covered = 160 + 140 = 300 m

Time = Total Distance ÷ Relative Speed

Time = 300 ÷ (120 × 5/18) = 300 ÷ (100/3) = 9 sec

∴ The correct answer is 9 sec.

Alternate Method

Given:

Length of Train 1 (L₁) = 160 m

Length of Train 2 (L₂) = 140 m

Speed of Train 1 (S₁) = 55 km/h

Speed of Train 2 (S₂) = 65 km/h

Formula Used:

Time taken to cross = (L₁ + L₂) ÷ (S₁ + S₂)

Calculations:

⇒ Total Distance = 160 + 140 = 300 m

⇒ Relative Speed = 55 + 65 = 120 km/h

⇒ Convert speed to m/s = 120 × (5/18) m/s

⇒ Relative Speed = 600/18 = 100/3 m/s

⇒ Time = 300 ÷ (100/3)

⇒ Time = (300 × 3) ÷ 100

⇒ Time = 900 ÷ 100 = 9 sec

∴ The correct answer is 9 sec.

Additional Information

Relative Speed in Opposite Directions

When two objects move towards each other or in opposite directions, their relative speed is the sum of their individual speeds: V_rel = S₁ + S₂.

Unit Conversion Factor

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

Crossing a Stationary Object

When a train crosses a pole or a standing man, the distance covered is equal to the length of the train itself.

Shortcut Trick

Given difference (x − y) = 20 and mean proportional √xy = 24.

Square of mean proportional: xy = 24² = 576.

Using the identity: (x + y)² = (x − y)² + 4xy

⇒ (x + y)² = 20² + 4 × 576 = 400 + 2304 = 2704.

⇒ Sum (x + y) = √2704 = 52.

∴ The correct answer is 52.

Alternate Method

Let the two positive numbers be 'a' and 'b' (where a > b).

Given:

Difference between numbers (a − b) = 20

Mean proportional between a and b = 24

Formula Used:

1. Mean Proportional = √(a × b)

2. (a + b)² = (a − b)² + 4ab

⇒ From mean proportional definition: √ab = 24

⇒ Squaring both sides: ab = 24 × 24 = 576

⇒ We know that (a + b)² = (a − b)² + 4ab

⇒ (a + b)² = (20)² + 4 × 576

⇒ (a + b)² = 400 + 2304

⇒ (a + b)² = 2704

⇒ a + b = √2704

⇒ a + b = 52

∴ The correct answer is 52.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is the square root of their product, expressed as x = √ab.

Third Proportional

If a, b, and c are in continued proportion (a:b = b:c), then c is called the third proportional, where c = b² ÷ a.

Algebraic Relationship

The relationship between the sum and difference of two numbers is given by the identity (a + b)² − (a − b)² = 4ab.

Shortcut Trick

Combined efficiency of P and Q = 1/16, and efficiency of P alone = 1/24.

Work done by P and Q together in 4 days = 4 ÷ 16 = 1/4 of total work.

Remaining work to be finished by P alone = 1 − 1/4 = 3/4.

More days required by P = (3/4) × 24 = 18 days.

∴ The correct answer is 18 days.

Alternate Method

Given: P and Q can complete the task in 16 days; P alone takes 24 days; they work together for 4 days.

Formula Used: Total Work = LCM of individual days; Efficiency = Total Work ÷ Time.

⇒ Total work (LCM of 16 and 24) = 48 units.

⇒ Efficiency of P + Q = 48 ÷ 16 = 3 units/day.

⇒ Efficiency of P alone = 48 ÷ 24 = 2 units/day.

⇒ Work completed by P and Q in 4 days = 3 units/day × 4 days = 12 units.

⇒ Remaining work = 48 − 12 = 36 units.

⇒ Additional days for P alone = 36 units ÷ 2 units/day = 18 days.

∴ The correct answer is 18 days.

Additional Information

Work and Efficiency Relationship

Efficiency is inversely proportional to the time taken (E ∝ 1/T). If a person is twice as efficient, they take half the time.

Combined Efficiency

The total efficiency of multiple workers is the sum of their individual efficiencies (E_Total = E₁ + E₂ + ...).

Pipes and Cisterns Analogy

The same LCM and efficiency method applies to tank-filling problems, where inlet pipes perform positive work and outlet pipes perform negative work.

Shortcut Trick

Net deviation from the overall Average Height (164 cm) must be zero.

Deviation for Class A = (160 − 164) × 24 = −96

Deviation for Class B = (168 − 164) × 20 = +80

Total deviation (A + B) = −16. To balance, Class C must provide a deviation of +16.

Deviation per student in Class C = 165 − 164 = +1.

Number of students in Class C = 16 ÷ 1 = 16.

∴ The correct answer is 16.

Alternate Method

Given:

Class A: n_A = 24, Avg_A = 160 cm

Class B: n_B = 20, Avg_B = 168 cm

Class C: n_C = x, Avg_C = 165 cm

Overall Average = 164 cm

Formula Used:

Overall Average = (n_A × Avg_A + n_B × Avg_B + n_C × Avg_C) ÷ (n_A + n_B + n_C)

Calculations:

⇒ 164 = (24 × 160 + 20 × 168 + x × 165) ÷ (24 + 20 + x)

⇒ 164 = (3840 + 3360 + 165x) ÷ (44 + x)

⇒ 164(44 + x) = 7200 + 165x

⇒ 7216 + 164x = 7200 + 165x

⇒ 7216 − 7200 = 165x − 164x

⇒ x = 16

∴ The correct answer is 16.

Additional Information

Weighted Average Formula

The combined average of multiple groups is calculated as A_w = (n₁a₁ + n₂a₂ + ... + n_ka_k) ÷ (n₁ + n₂ + ... + n_k).

Deviation Method

The sum of deviations of all observations from their arithmetic mean is always zero. This property helps in finding missing values or averages quickly.

Average Property

The combined average must always lie between the lowest and the highest individual group averages. In this case, 160 < 164 < 168.

Shortcut Trick

Total Volume = 30 × 20 × 8 = 4800 cm³

Remaining Volume = 90% of 4800 = 4320 cm³

Volume of 1 Cube = 4³ = 64 cm³

Number of Cubes = 4320 ÷ 64 = 67.5 → 67 complete cubes

∴ The correct answer is 67.

Alternate Method

Given:

Dimensions of the solid cuboid = 30 cm × 20 cm × 8 cm

Material lost during melting = 10%

Side of the identical cubes = 4 cm

Calculations:

⇒ Total volume of the cuboid = Length × Breadth × Height

⇒ Volume = 30 × 20 × 8 = 4800 cm³

⇒ Volume of material lost = 10% of 4800 = (10 ÷ 100) × 4800 = 480 cm³

⇒ Volume of remaining metal = 4800 − 480 = 4320 cm³

⇒ Volume of one small cube = (Side)³ = 4³ = 64 cm³

⇒ Number of cubes formed = Remaining Volume ÷ Volume of one cube

⇒ Number of cubes = 4320 ÷ 64

⇒ Number of cubes = 67.5

⇒ Since we need the number of complete cubes, we take the integer part.

∴ The correct answer is 67.

Additional Information

Volume of Solid Shapes

For a cuboid, Volume = L × B × H. For a cube, Volume = a³. During melting and recasting, total volume remains constant unless a percentage loss is specified.

Material Loss Calculation

If x% of material is lost, the usable volume is (100 − x)% of the initial volume. Usable Volume = V_initial × (1 − x/100).

Complete Units Rule

When calculating the number of discrete items formed from a bulk material, always round down to the nearest whole number if the result is a fraction.

Shortcut Trick

Calculate total interest percentage: Interest = 2529.60 − 1860 = 669.60

Total Interest % = (669.60 / 1860) × 100 = 36%

Since the rate is 12% per year, Time (T) = Total % / Rate per annum

T = 36% / 12% = 3 years

∴ The correct answer is 3 years.

Alternate Method

Given:

Principal (P) = ₹1,860

Amount (A) = ₹2,529.60

Rate (R) = 12% p.a.

Formula Used: Simple Interest (SI) = (P × R × T) / 100

⇒ Simple Interest (SI) = Amount − Principal

⇒ SI = 2529.60 − 1860 = 669.60

⇒ 669.60 = (1860 × 12 × T) / 100

⇒ 669.60 = 18.6 × 12 × T

⇒ 669.60 = 223.2 × T

⇒ T = 669.60 / 223.2

⇒ T = 3 years

∴ The correct answer is 3 years.

Additional Information

Simple Interest Formula

The basic formula is SI = (P × R × T) / 100, where P is Principal, R is Rate, and T is Time.

Amount Calculation

Total Amount (A) = Principal (P) + Simple Interest (SI). It can also be expressed as A = P(1 + RT/100).

Finding Rate of Interest

If time and interest are known, the rate can be calculated as R = (SI × 100) / (P × T).

Shortcut Trick

Apply the Successive Percentage Change formula: Net % change = x + y + (xy/100).

Here, x = +25% (increase) and y = −20% (decrease).

Net change = 25 − 20 + [25 × (−20) / 100] = 5 − 5 = 0%.

Since the net change is 0%, the final salary remains the same as the initial salary.

∴ The correct answer is ₹58,000.

Alternate Method

Given:

Initial Salary = ₹58,000

First Change = 25% Increase

Second Change = 20% Decrease

Step 1: Calculate salary after 25% increase

⇒ Salary after increase = 58,000 + (25/100 × 58,000)

⇒ Salary after increase = 58,000 + 14,500 = ₹72,500

Step 2: Calculate salary after 20% decrease on the new amount

⇒ Final Salary = 72,500 − (20/100 × 72,500)

⇒ Final Salary = 72,500 − 14,500

⇒ Final Salary = ₹58,000

∴ The correct answer is ₹58,000.

Additional Information

Successive Percentage Formula

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

Multiplier Method

Final Value = Initial Value × (1 ± r₁/100) × (1 ± r₂/100). In this case: 58,000 × 1.25 × 0.80 = 58,000 × 1 = 58,000.

Base Change Property

An increase of 25% (1/4) followed by a decrease of 20% (1/5) results in no change because (5/4) × (4/5) = 1.

Shortcut Trick

The Total Surface Area (TSA) of a cube follows the formula 6 × a².

Since the side is 94 cm, the unit digit of 94² is 6 (4 × 4 = 16).

Multiplying by 6, the final unit digit must be 6 (6 × 6 = 36).

Estimating: 94² is slightly less than 100² (10,000), so TSA is slightly less than 60,000.

Calculation: 6 × 8836 = 53016.

∴ The correct answer is 53,016 cm².

Alternate Method

Given:

The side length (a) of the cube is 94 cm.

Formula Used:

Total Surface Area of a cube = 6 × (side)²

Calculations:

⇒ TSA = 6 × (94)²

⇒ TSA = 6 × (94 × 94)

⇒ 94² = (100 − 6)² = 10000 − 1200 + 36 = 8836

⇒ TSA = 6 × 8836

⇒ TSA = 53016 cm²

∴ The correct answer is 53,016 cm².

Additional Information

Volume of a Cube

The volume represents the total capacity of the cube and is calculated as a³.

Lateral Surface Area (LSA)

The LSA refers to the area of only the four side faces (excluding top and bottom), given by 4 × a².

Body Diagonal of a Cube

The length of the longest rod that can be placed inside a cube is a√3.

Face Diagonal of a Cube

The diagonal of any single square face of the cube is calculated as a√2.

Shortcut Trick

Total work = LCM(12, 30) = 60 units.

Efficiency of A = 5 units/day, B = 2 units/day.

Work done by both in 2 days = (5 + 2) × 2 = 14 units.

Remaining work = 60 − 14 = 46 units.

Time taken by B alone = 46 ÷ 2 = 23 days.

∴ The correct answer is 23 days.

Alternate Method

Given: A completes work in 12 days and B in 30 days.

⇒ Total work (LCM of 12 and 30) = 60 units.

⇒ Work completed by A and B together in 2 days = (5 + 2) × 2 = 14 units.

⇒ Remaining work to be done by B = 60 − 14 = 46 units.

⇒ Time taken by B to complete the remaining work = Remaining Work ÷ Efficiency of B

⇒ Time = 46 ÷ 2 = 23 days.

∴ The correct answer is 23 days.

Additional Information

Relationship between Efficiency and Time

Efficiency is inversely proportional to Time. If time ratio is x : y, the efficiency ratio is y : x.

Work & Wages

Wages are generally distributed in the ratio of the work done by each person, which is the product of Efficiency × Time.

Total Work Calculation

Total work can be assumed as any multiple of the given days, but LCM is preferred to keep efficiencies in whole numbers.

Shortcut Trick

Total difference in the daily wage bill = Excess + Shortfall = 4000 + 2000 = ₹6000.

Difference in daily pay per worker = 500 − 450 = ₹50.

Total temporary workers = Total Difference ÷ Difference per Worker = 6000 ÷ 50 = 120.

∴ The correct answer is 120.

Alternate Method

Given: Pay Rate₁ = ₹500, Pay Rate₂ = ₹450, Budget Excess = ₹4,000, Budget Shortfall = ₹2,000.

Formula Used: Total Wage Bill = Number of Workers × Daily Pay Rate

⇒ Let n be the number of workers and B be the company’s budget.

⇒ Case 1: 500 × n = B + 4000

⇒ Case 2: 450 × n = B − 2000

⇒ Subtracting Case 2 from Case 1: (500n − 450n) = (B + 4000) − (B − 2000)

⇒ 50n = 4000 + 2000

⇒ 50n = 6000

⇒ n = 6000 ÷ 50 = 120.

∴ The correct answer is 120.

Additional Information

Excess and Deficit Rule

When comparing two scenarios where one results in an excess (E) and the other in a shortfall or deficit (D), the total difference between the two conditions is calculated as (E + D).

Linear Equations in One Variable

These problems follow the standard form ax + b = c, where x represents the unknown quantity (like the number of workers) and can be solved by isolating the variable.

Rate-Quantity Relationship

The change in total value is equal to the quantity multiplied by the change in rate: ΔTotal = Quantity × ΔRate.

Given:

(32 ÷ 0.8 × x) − 72 = 720 ÷ (4 × 5 + 10)

Formula used:

Solve using the BODMAS rule (Bracket, Of, Division, Multiplication, Addition, Subtraction).

Calculation:

Let the missing value be x.

(32 ÷ 0.8 × x) − 72 = 720 ÷ (4 × 5 + 10)

⇒ (40 × x) − 72 = 720 ÷ (20 + 10)

⇒ 40 × x − 72 = 720 ÷ 30

⇒ 40 × x − 72 = 24

⇒ 40 × x = 24 + 72

⇒ 40 × x = 96

⇒ x = 96 ÷ 40

⇒ x = 2.4

∴ The correct answer is option (3).

Shortcut Trick

The Third Proportional of two numbers a and b is given by the formula b² ÷ a.

⇒ Third Proportional = (16 × 16) ÷ 8

⇒ 256 ÷ 8 = 32

∴ The correct answer is 32.

Alternate Method

Given:

First number (a) = 8

Second number (b) = 16

Formula Used:

If three numbers a, b, and c are in continued proportion, then:

a : b :: b : c

⇒ a ÷ b = b ÷ c

Calculations:

⇒ Let the third proportional be x.

⇒ 8 : 16 :: 16 : x

⇒ 8 ÷ 16 = 16 ÷ x

⇒ 1 ÷ 2 = 16 ÷ x

⇒ x = 16 × 2

⇒ x = 32

∴ The correct answer is 32.

Additional Information

Mean Proportional

The Mean Proportional between two numbers a and b is calculated as √(a × b).

Fourth Proportional

For three numbers a, b, and c, the fourth proportional (x) satisfies a : b = c : x, which means x = (b × c) ÷ a.

Continued Proportion

Three quantities are in continued proportion if the ratio of the first to the second is equal to the ratio of the second to the third.

Shortcut Trick

List integers that leave remainder 2 when divided by 5: 2, 7, 12, 17, 22, ...

List integers that leave remainder 3 when divided by 7: 3, 10, 17, 24, ...

Identify the first common number that appears in both sequences.

The smallest positive integer satisfying both conditions is 17.

∴ The correct answer is 17.

Alternate Method

Given:

Number (N) ÷ 5 → Remainder = 2

Number (N) ÷ 7 → Remainder = 3

Step-by-step Calculation:

⇒ Let N = 5k + 2 and N = 7m + 3

⇒ 5k + 2 = 7m + 3

⇒ 5k = 7m + 1

⇒ If m = 1, 5k = 8 (Not an integer)

⇒ If m = 2, 5k = 7(2) + 1 = 15

⇒ k = 15 ÷ 5 = 3

⇒ Smallest N = 5(3) + 2 = 17

∴ The correct answer is 17.

Additional Information

Chinese Remainder Theorem (CRT)

CRT provides a systematic way to solve systems of linear congruences with pairwise coprime moduli like 5 and 7.

General Form of Solution

The general solution for such problems is N = (LCM(d₁, d₂) × n) + x, where x is the smallest positive integer and n = 0, 1, 2...

Successive Division Method

For larger numbers, use N = d₁k + r₁ and substitute into the second congruence to solve for k iteratively.

Shortcut Trick

Ratio of the two complementary angles is 3 : 2 (since 2 × Angle₁ = 3 × Angle₂).

Total units = 3 + 2 = 5 units.

Given, total sum = 90º (complementary property).

5 units = 90º ⇒ 1 unit = 18º.

Larger angle = 3 units = 3 × 18º = 54º.

∴ The correct answer is 54º.

Alternate Method

Given:

Sum of two angles = 90º

Relationship: 2 × (One angle) = 3 × (Other angle)

Formula Used:

For Complementary Angles, θ₁ + θ₂ = 90º.

Calculations:

Let the two angles be x and y.

⇒ x + y = 90º    ---(i)

⇒ 2x = 3y    ---(ii)

⇒ x = 3y / 2

Substituting the value of x in equation (i):

⇒ (3y / 2) + y = 90º

⇒ (3y + 2y) / 2 = 90º

⇒ 5y / 2 = 90º

⇒ 5y = 180º

⇒ y = 36º

Now, finding the value of x:

⇒ x = 90º − 36º

⇒ x = 54º

Comparing 54º and 36º, the larger angle is 54º.

∴ The correct answer is 54º.

Additional Information

Complementary Angles

Two angles are called complementary if their sum is exactly 90º. Each angle is the complement of the other.

Supplementary Angles

Two angles are called supplementary if their sum is exactly 180º. They form a linear pair when placed adjacently on a straight line.

Adjacent Angles

Angles that have a common vertex and a common side but do not overlap are known as adjacent angles.

Shortcut Trick

Convert decimals into their simplest fractions: 5 = 5/1, 8.3 = 83/10, and 0.19 = 19/100.

Formula: LCM of fractions = LCM of Numerators ÷ HCF of Denominators.

LCM(5, 83, 19) = 5 × 83 × 19 = 7885 (since all are co-prime).

HCF(1, 10, 100) = 1.

Result = 7885 ÷ 1 = 7885.

∴ The correct answer is 7885.

Alternate Method

Given: Numbers are 5, 8.3, and 0.19.

Formula Used: To find the LCM of decimals, equalize the number of decimal places and find the LCM of the resulting integers.

⇒ Step 1: Make decimal places equal: 5.00, 8.30, 0.19.

⇒ Step 2: Treat them as integers: 500, 830, and 19.

⇒ Step 3: Find prime factors:

⇒ 500 = 2² × 5³

⇒ 830 = 2 × 5 × 83

⇒ 19 = 19 (Prime)

⇒ Step 4: LCM = Highest powers of all prime factors = 2² × 5³ × 83 × 19.

⇒ LCM = 4 × 125 × 83 × 19 = 500 × 1577 = 788500.

⇒ Step 5: Adjust decimal: 788500 ÷ 100 = 7885.

∴ The correct answer is 7885.

Additional Information

LCM of Fractions

The Least Common Multiple (LCM) of a set of fractions is given by: (LCM of Numerators) ÷ (HCF of Denominators).

HCF of Fractions

The Highest Common Factor (HCF) of a set of fractions is given by: (HCF of Numerators) ÷ (LCM of Denominators).

Co-prime Numbers

Numbers that have only 1 as a common factor are co-prime. The LCM of co-prime numbers is always equal to their product.

Shortcut Trick

When an object covers equal distances at different speeds, the Average Speed is the Harmonic Mean of the speeds.

Average Speed = 3 ÷ (1/v₁ + 1/v₂ + 1/v₃)

⇒ Average Speed = 3 ÷ (1/40 + 1/60 + 1/120)

⇒ Average Speed = 3 ÷ (6/120) = 3 × 20 = 60 km/hr.

∴ The correct answer is 60 km/hr.

Alternate Method

Given: Three segments of 40 km each. Speeds = 40 km/hr, 60 km/hr, and 120 km/hr.

Formula Used: Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance = 40 + 40 + 40 = 120 km

⇒ Time for 1^st segment (t₁) = 40 ÷ 40 = 1 hour

⇒ Time for 2^nd segment (t₂) = 40 ÷ 60 = 2/3 hour

⇒ Time for 3^rd segment (t₃) = 40 ÷ 120 = 1/3 hour

⇒ Total Time = 1 + 2/3 + 1/3 = 1 + 1 = 2 hours

⇒ Average Speed = 120 ÷ 2 = 60 km/hr

∴ The correct answer is 60 km/hr.

Additional Information

Two Equal Distance Segments

If a journey is divided into two equal halves with speeds x and y, the average speed is 2xy ÷ (x + y).

Unequal Distance Segments

For unequal distances d₁, d₂, ... with speeds v₁, v₂, ..., Average Speed = (d₁ + d₂ + ...) ÷ (d₁/v₁ + d₂/v₂ + ...).

Unit Conversion

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

Shortcut Trick

Use the Weighted Average method for calculation.

Ratio of goods quantity = 50% : (40% of 50%) : (Remaining 30%) = 50 : 20 : 30 = 5 : 2 : 3

Overall Profit x% = (5 × 36 + 2 × 14 + 3 × (−21)) ÷ (5 + 2 + 3)

x = (180 + 28 − 63) ÷ 10 = 145 ÷ 10 = 14.5%

∴ The correct answer is 14.5%.

Alternate Method

Given: 50% goods at 36% profit, 40% of remaining (50%) at 14% profit, and still remaining (30%) at 21% loss.

Formula Used: Overall Profit% = (Total Profit ÷ Total CP) × 100

Let the Total Cost Price (CP) of 100 units of goods be ₹100.

⇒ Case 1: CP = ₹50 | Profit = 36% of 50 = 50 × 0.36 = ₹18

⇒ Remaining goods = 100 − 50 = 50 units

⇒ Case 2: CP = 40% of 50 = 20 units | Profit = 14% of 20 = 20 × 0.14 = ₹2.8

⇒ Still Remaining goods = 50 − 20 = 30 units

⇒ Case 3: CP = 30 units | Loss = 21% of 30 = 30 × 0.21 = ₹6.3 (Loss is −6.3)

⇒ Total Profit = 18 + 2.8 − 6.3 = 14.5

⇒ x% = (14.5 ÷ 100) × 100 = 14.5%

∴ The correct answer is 14.5%.

Additional Information

Weighted Average Profit/Loss

Overall Profit % = (n₁p₁ + n₂p₂ + ... + n_kp_k) ÷ (n₁ + n₂ + ... + n_k), where n is quantity and p is profit percentage (negative for loss).

Successive Changes vs Parts

When goods are divided into parts, we use weighted averages. When one value changes multiple times, we use successive percentage formula: a + b + (ab/100).

Profit and Loss Basics

Profit % = (Profit ÷ CP) × 100 | SP = CP × (100 + P%) ÷ 100. Always calculate profit and loss on the Cost Price (CP) unless stated otherwise.

Shortcut Trick

The Total Sum is simply the product of the Average and the Total count of numbers.

Total Sum = Average × Number of items

Total Sum = 7 × 3 = 21

∴ The correct answer is 21.

Alternate Method

Given:

Average of three numbers = 7

Number of quantities (n) = 3

Formula Used:

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

Calculations:

⇒ 7 = (Sum of three numbers) ÷ 3

⇒ Sum of three numbers = 7 × 3

⇒ Sum of three numbers = 21

∴ The correct answer is 21.

Additional Information

Arithmetic Mean

The most common type of average, calculated by adding all numbers in a set and dividing by the count of numbers.

Weighted Average

Used when different values have different levels of importance or frequency: (w₁x₁ + w₂x₂) ÷ (w₁ + w₂).

Average of Consecutive Numbers

For a series in Arithmetic Progression (AP), the average is simply (First Term + Last Term) ÷ 2.

Shortcut Trick

Use the algebraic identity: (Difference)² = (Sum)² − 4 × (Product)

⇒ (Difference)² = 27² − 4 × 176

⇒ (Difference)² = 729 − 704 = 25

⇒ Difference = √25 = 5

∴ The correct answer is 5.

Alternate Method

Given: Sum of two numbers = 27, Product = 176.

Formula Used: Factorisation method to find the numbers x and y such that x + y = 27 and xy = 176.

⇒ Let the two positive numbers be x and y.

⇒ x + y = 27 and x × y = 176.

⇒ Factorizing 176 to find pairs whose sum is 27: 176 = 1 × 176, 2 × 88, 4 × 44, 8 × 22, 11 × 16.

⇒ Since 11 + 16 = 27, the numbers are 16 and 11.

⇒ Positive difference = 16 − 11 = 5.

∴ The correct answer is 5.

Additional Information

Algebraic Relationship

The core relationship between sum, product, and difference is given by (x + y)² − (x − y)² = 4xy.

Quadratic Equation Formulation

If sum (S) and product (P) of two numbers are known, the numbers are the roots of the quadratic equation t² − St + P = 0.

Nature of Roots

For the difference to be a rational number, the value (Sum² − 4 × Product) must be a perfect square.

Shortcut Trick

Effective capital ratio (Investment × Time):

A : B : C = (1,21,500 × 12) : (1,02,060 × 9) : (97,200 × 6 + 72,700 × 6)

A : B : C = 14,58,000 : 9,18,540 : 10,19,400 = 24,300 : 15,309 : 16,990

Sum of ratio parts = 24,300 + 15,309 + 16,990 = 56,599 units

Total profit = ₹1,69,797 ⇒ 1 unit = ₹3

Difference (A − B) = (24,300 − 15,309) × 3 = 8,991 × 3 = ₹26,973.

∴ The correct answer is ₹26,973.

Alternate Method

Given:

Investment of A = ₹1,21,500 for 12 months

Investment of B = ₹1,02,060 for 9 months

Investment of C = ₹97,200 for 6 months and (₹97,200 − ₹24,500) = ₹72,700 for 6 months

Total Profit = ₹1,69,797

Formula: Profit Share Ratio = (Investment₁ × Time₁) : (Investment₂ × Time₂)

Calculations:

⇒ Equivalent Capital of A = 1,21,500 × 12 = 14,58,000

⇒ Equivalent Capital of B = 1,02,060 × 9 = 9,18,540

⇒ Equivalent Capital of C = (97,200 × 6) + (72,700 × 6) = 5,83,200 + 4,36,200 = 10,19,400

⇒ Ratio A : B : C = 14,58,000 : 9,18,540 : 10,19,400

⇒ Dividing by common factor 60: 24,300 : 15,309 : 16,990

⇒ Sum of ratios = 24,300 + 15,309 + 16,990 = 56,599

⇒ Total Profit = ₹1,69,797

⇒ Value of 1 unit = 1,69,797 ÷ 56,599 = ₹3

⇒ Difference between share of A and B = (24,300 − 15,309) units

⇒ Difference = 8,991 × 3 = ₹26,973

∴ The correct answer is ₹26,973.

Additional Information

Basic Partnership Law

Profit is always distributed in the ratio of the product of Capital (C) and Time (T), i.e., P₁ : P₂ = C₁×T₁ : C₂×T₂.

Effective Capital for Multiple Transactions

When a partner changes investment mid-term, effective capital = (C₁×T₁ + C₂×T₂ + ...), where T is the duration for each capital amount.

Calculating Unknown Shares

Individual Profit = (Individual Ratio Part ÷ Total Ratio Sum) × Total Profit.

Shortcut Trick

Total Simple Interest for 3 years = 20% × 3 = 60%.

Total Amount = 100% (Principal) + 60% (Interest) = 160% = ₹5,280.

Simple Interest for 2 years = 20% × 2 = 40%.

Required SI = (5,280 ÷ 160%) × 40% = 5,280 ÷ 4 = ₹1,320.

∴ The correct answer is ₹1,320.

Alternate Method

Given:

Amount (A) = ₹5,280, Rate (R) = 20% p.a., Time (T₁) = 3 years.

Formula Used:

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

Amount (A) = Principal (P) + SI = P × (1 + (R × T) ÷ 100)

Calculations:

⇒ 5,280 = P × (1 + (20 × 3) ÷ 100)

⇒ 5,280 = P × (1 + 0.6)

⇒ 5,280 = 1.6P

⇒ Principal (P) = 5,280 ÷ 1.6 = ₹3,300

⇒ Simple Interest for 2 years (T₂ = 2) = (3,300 × 20 × 2) ÷ 100

⇒ SI = 33 × 40 = ₹1,320

∴ The correct answer is ₹1,320.

Additional Information

Simple Interest Properties

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

Principal Formula

The Principal can be calculated if the Amount, Rate, and Time are known: P = (A × 100) ÷ (100 + RT).

SI vs CI

For the first year (if compounded annually), Simple Interest and Compound Interest are equal for the same principal and rate.

Shortcut Trick

The largest 6-digit number is 999999.

Divide 999999 by 96 to find the remainder.

999999 ÷ 96 gives a remainder of 63.

Subtract this remainder from 999999 to get the largest divisible number.

999999 − 63 = 999936.

∴ The correct answer is 999936.

Alternate Method

Given: Divisor = 96, Largest 6-digit number = 999999.

Formula: Required Number = (Largest n-digit number) − (Remainder when largest n-digit number is divided by divisor).

⇒ Largest 6-digit number = 999999

⇒ Dividing 999999 by 96:

⇒ 999999 = 10416 × 96 + 63

⇒ Remainder = 63

⇒ Required number = 999999 − 63

⇒ Required number = 999936

∴ The correct answer is 999936.

Additional Information

Divisibility Rule for 96

A number is divisible by 96 if it is divisible by both 3 (sum of digits) and 32 (last 5 digits divisible by 32).

Smallest n-digit number divisible by x

Required number = Smallest n-digit number + (x − remainder), where remainder is obtained by dividing the smallest n-digit number by x.

Division Algorithm

Dividend = (Divisor × Quotient) + Remainder. For perfect divisibility, the remainder must be zero.

Shortcut Trick

Assume the initial price of fuel is 100.

Final Price = 100 × (0.55) × (0.75) × (0.85) × (1.45)

Final Price = 100 × 0.50840625 = 50.840625

Net percentage decrease = 100 − 50.840625 = 49.159375%

Rounding to 2 decimal places, we get 49.16%.

∴ The correct answer is 49.16%.

Alternate Method

Given:

Initial changes: 45% decrease, 25% decrease, 15% decrease.

Fourth month change: 45% increase.

Formula Used:

Final Value = Initial Value × (1 − r₁/100) × (1 − r₂/100) × (1 − r₃/100) × (1 + r₄/100)

Calculations:

⇒ Let Initial Price = 100

⇒ Price after 1^st month = 100 − 45% of 100 = 55

⇒ Price after 2^nd month = 55 − 25% of 55 = 55 − 13.75 = 41.25

⇒ Price after 3^rd month = 41.25 − 15% of 41.25 = 41.25 − 6.1875 = 35.0625

⇒ Price after 4^th month = 35.0625 + 45% of 35.0625 = 35.0625 + 15.778125 = 50.840625

⇒ Net Percentage Decrease = 100 − 50.840625 = 49.159375%

⇒ Rounding to two decimal places = 49.16%

∴ The correct answer is 49.16%.

Additional Information

Successive Percentage Change

For two successive changes of a% and b%, the net change is given by (a + b + ab/100)%. Use negative values for decrease.

Multiplying Factor Concept

To find the final value after an x% change, multiply the base by (1 ± x/100). For multiple changes, multiply all factors sequentially.

Rounding Rules

When rounding to 2 decimal places, if the third decimal digit is 5 or greater, round up the second digit.

Shortcut Trick

Let Cost Price (CP) = 100.

Marked Price (MP) = 100 + 120 = 220.

To gain 43%, Selling Price (SP) must be 143.

Discount needed = MP − SP = 220 − 143 = 77.

Discount % = (77 ÷ 220) × 100 = 35%.

∴ The correct answer is 35%.

Alternate Method

Given:

Markup = 120% above Cost Price (CP)

Required Gain (Profit) = 43%

Formula Used:

1. Marked Price (MP) = CP × (100 + Markup%) ÷ 100
2. Selling Price (SP) = CP × (100 + Profit%) ÷ 100
3. Discount % = [(MP − SP) ÷ MP] × 100

Calculations:

⇒ Let CP = 100

⇒ MP = 100 + (120% of 100) = 100 + 120 = 220

⇒ SP = 100 + (43% of 100) = 100 + 43 = 143

⇒ Discount = MP − SP = 220 − 143 = 77

⇒ Discount % = (77 ÷ 220) × 100

⇒ Discount % = (7 ÷ 20) × 100 = 7 × 5 = 35%

∴ The correct answer is 35%.

Additional Information

Relationship between CP and MP

The ratio of Cost Price to Marked Price is directly related to the profit and discount: CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%).

Net Percentage Change Formula

The overall profit or loss can be calculated using the successive percentage change formula: Net % = Markup − Discount − (Markup × Discount ÷ 100).

Discount Calculation

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

Shortcut Trick

The effective price after successive discounts is: MP × 70% × 88% = SP.

MP × 0.7 × 0.88 = ₹2,464

MP × 0.616 = ₹2,464

MP = 2,464 ÷ 0.616 = ₹4,000.

∴ The correct answer is ₹4,000.

Alternate Method

Given:

Trade Discount = 30%

Scheme Discount = 12%

Selling Price (SP) = ₹2,464

Formula Used:

Final SP = MP × (100 − d₁)/100 × (100 − d₂)/100

Calculations:

⇒ Let the Marked Price (MP) of the electric kettle be M.

⇒ Price after 30% trade discount = M × (100 − 30) ÷ 100 = 0.70M.

⇒ Final Selling Price after 12% scheme discount = 0.70M × (100 − 12) ÷ 100.

⇒ 2,464 = 0.70M × 0.88

⇒ 2,464 = 0.616 × M

⇒ M = 2,464 ÷ 0.616

⇒ M = 4,000

∴ The correct answer is ₹4,000.

Additional Information

Single Equivalent Discount

For two successive discounts of a% and b%, the single equivalent discount is [a + b − (a × b)/100]%.

Relation between MP and CP

The ratio between Marked Price and Cost Price is given by: MP/CP = (100 + Profit%)/(100 − Discount%).

Basis of Discount

A discount (whether trade or scheme) is always calculated on the current Marked Price or the preceding balance price in a chain.

Shortcut Trick

Break the expression into three parts: Part 1 is √36 = 6.

Part 2 is √(324 ÷ 81) = √4 = 2.

Part 3: Count decimal places. Top has 6, Bottom has 8. Net adjustment is 10² in the numerator.

Simplify: √[(95 ÷ 19) × (85 ÷ 17) × (189 ÷ 21) × 100] = √(5 × 5 × 9 × 100) = 150.

Total Sum = 6 + 2 + 150 = 158.

∴ The correct answer is 158.

Alternate Method

Given Expression: √36 + √(324 ÷ 81) + √((9.5 × 0.0085 × 18.9) ÷ (0.021 × 0.0017 × 1.9))

The expression involves square roots and decimal simplification. We solve each term step-by-step:

⇒ Term 1: √36 = 6

⇒ Term 2: √(324 ÷ 81) = √4 = 2

⇒ Term 3: To simplify √((9.5 × 0.0085 × 18.9) ÷ (0.021 × 0.0017 × 1.9)), remove decimals by multiplying both numerator and denominator by 10⁸.

⇒ √((95 × 85 × 189 × 100) ÷ (21 × 17 × 19))

⇒ √((95 ÷ 19) × (85 ÷ 17) × (189 ÷ 21) × 100)

⇒ √(5 × 5 × 9 × 100)

⇒ √(22500) = 150

Now, add all the simplified values obtained from the steps above:

⇒ 6 + 2 + 150 = 158

∴ The correct answer is 158.

Additional Information

BODMAS Rule

Always prioritize Orders (roots and exponents) before addition and subtraction to ensure correct arithmetic evaluation.

Decimal Shift in Fractions

When dividing decimals, shift the decimal point to the right in both the numerator and denominator by the same number of places to simplify into whole numbers.

Square Root of Products

The property √(a × b × c) = √a × √b × √c allows for the factorization of large numbers under a root for easier calculation.

Shortcut Trick

Ratio 5 years ago (M:S) = 7 : 1 (Difference = 6 units)

Current Ratio (M:S) = 4 : 1 (Difference = 3 units)

Equalize differences by multiplying current ratio by 2 → 8 : 2

Change in son's age units from 5 years ago to now = 2 − 1 = 1 unit → 5 years

Son's present age = 2 units = 2 × 5 = 10 years.

∴ The correct answer is 10 years.

Alternate Method

Given:

Current age of man is four times the age of his son.

Five years ago, the man was seven times older than his son.

Formula Used:

Age difference and ratio calculation using linear equations.

Calculations:

⇒ Let the son's present age be S years.

⇒ Therefore, the man's present age is 4S years.

⇒ Five years ago, son's age = (S − 5) years.

⇒ Five years ago, man's age = (4S − 5) years.

⇒ According to the condition: (4S − 5) = 7 × (S − 5)

⇒ 4S − 5 = 7S − 35

⇒ 35 − 5 = 7S − 4S

⇒ 30 = 3S

⇒ S = 10

∴ The correct answer is 10 years.

Additional Information

Age Difference Constant Rule

The numerical difference between the ages of two people always remains the same, regardless of how many years pass.

Ratio Scaling

When solving age problems using ratios, always ensure the unit difference between the two ratios is equalized relative to the time gap.

General Age Formula

If the present age is X, then age 'n' years ago is (X − n) and age after 'n' years is (X + n).

Shortcut Trick

Ratio of Cost Price (CP) for P to Q = 100 : 125 = 4 : 5

Ratio of CP for Q to R = 100 : 40 = 5 : 2

Combined ratio P : Q : R = 4 : 5 : 2

Given R paid 2 units = ₹5,166

1 unit = ₹2,583 ⇒ P purchased for 4 units = 4 × 2,583 = ₹10,332

∴ The correct answer is ₹10,332.

Alternate Method

Given:

Price paid by R = ₹5,166

Profit percentage of P = 25%

Loss percentage of Q = 60%

Formula Used:

Selling Price (SP) = Cost Price (CP) × (100 ± Profit/Loss%)/100

Calculations:

⇒ Let the purchase price of the item for P be x.

⇒ P sells it to Q at 25% profit, so CP of Q = x × (125/100) = 1.25x

⇒ Q sells it to R at 60% loss, so CP of R = 1.25x × (1 − 60/100)

⇒ CP of R = 1.25x × 0.40 = 0.5x

⇒ Given that R paid ₹5,166, therefore: 0.5x = 5,166

⇒ x = 5,166 ÷ 0.5 = 5,166 × 2

⇒ x = 10,332

∴ The correct answer is ₹10,332.

Additional Information

Successive Percentage Change

When a value changes by a% and then by b%, the effective percentage change is given by (a + b + ab/100)%.

Fractional Conversion

Profit of 25% is equivalent to a multiplier of 5/4 (1 + 1/4), and a loss of 60% is equivalent to a multiplier of 2/5 (1 − 3/5).

Final Price Formula

Final Price = Initial Price × (100 ± r₁)/100 × (100 ± r₂)/100 × ... × (100 ± r_n)/100.

Shortcut Trick

In a standard 30°−60°−90° right-angled triangle, the ratio of sides opposite to the angles is 1 : √3 : 2.

The side opposite to 30° (building height) corresponds to 1 unit = 100√3 m.

The side opposite to 60° (horizontal distance) corresponds to √3 units.

⇒ Horizontal distance = 100√3 × √3 = 300 m.

∴ The correct answer is 300 m.

Alternate Method

Given:

Height of the building (AB) = 100√3 m

Angle of depression from the top of the building to the bicycle = 30°

Since the horizontal ground is parallel to the horizontal line of sight from the top, the angle of elevation of the top of the building from the bicycle (Angle ACB) = 30° (alternate interior angles).

Let the horizontal distance from the base of the building to the bicycle (BC) = d

Formula Used:

In a right-angled triangle ABC:

tan(θ) = Opposite Side ÷ Adjacent Side

Calculations:

In right-angled triangle ABC:

⇒ tan(30°) = AB ÷ BC

⇒ 1 ÷ √3 = 100√3 ÷ d

⇒ d = 100√3 × √3

⇒ d = 100 × 3

⇒ d = 300 m

∴ The correct answer is 300 m.

Additional Information

Angle of Elevation and Depression

The angle of elevation is measured upwards from the horizontal line, while the angle of depression is measured downwards. They are equal in magnitude because of alternate interior angles.

Standard Trigonometric Ratios for Height & Distance

Common ratio values to remember: tan(30°) = 1/√3, tan(45°) = 1, and tan(60°) =

The correct answer is ₹50,000.

Key Points

• In a landmark ruling in 2025, the Supreme Court of India reinforced the financial security of women by setting a permanent monthly alimony benchmark of ₹50,000 for a divorced wife who remains unmarried.
• The Apex Court emphasized that maintenance is not a matter of charity but a fundamental right derived from the principle of Social Justice, ensuring that a woman is not left in a state of destitution after the dissolution of marriage.
• The judgment clarified that the amount of ₹50,000 was determined considering the rising Cost of Living and the Inflation Index, aiming to provide a basic standard of living that aligns with the husband's financial status and the wife's previous lifestyle.
• This decision is rooted in the interpretation of Section 125 of the Criminal Procedure Code (CrPC), now integrated into the Bharatiya Nagarik Suraksha Sanhita (BNSS), which mandates the husband to provide support to a wife who is unable to maintain herself.
• The court highlighted that the 'unmarried' status of the divorced wife necessitates continuous support until her remarriage or change in financial circumstances, making the ₹50,000 sum a fixed monthly obligation for the respondent.

 Additional Information

• Permanent Alimony:
• It refers to the allowance ordered by the court to be paid by one spouse to the other after the Decree of Divorce is passed.
• Under Section 25 of the Hindu Marriage Act, 1955, the court has the authority to grant permanent alimony and maintenance at the time of passing any decree.
• Factors Influencing Alimony Quantum:
• Standard of Living: The Supreme Court has consistently held that a wife is entitled to the same comfort level she enjoyed in her Matrimonial Home.
• Financial Capacity: The Net Taxable Income, assets, and liabilities of the husband are critical determinants for the final amount.
• Duration of Marriage: Longer durations often lead to higher alimony settlements due to the increased dependency established over time.
• Interim Maintenance:
• Distinguished from permanent alimony, this is the amount paid during the pendency of the Matrimonial Suit to cover immediate legal and living expenses.

The correct answer is President of India.

Key Points

• The Speaker Pro Tem is a temporary post created to preside over the first few sittings of a newly elected Lok Sabha until a permanent Speaker is elected.
• According to Article 99 of the Indian Constitution, every member of either House of Parliament must, before taking their seat, make and subscribe an oath or affirmation before the President or some person appointed by him.
• The President of India appoints the Speaker Pro Tem and administers the oath of office to him/her, usually at the Rashtrapati Bhavan, before the first session of the new House begins.
• By convention, the most senior member of the Lok Sabha (in terms of number of years/terms served) is chosen for this position to ensure the smooth transition of parliamentary proceedings.
• The primary duties of the Speaker Pro Tem include presiding over the first meeting of the Lok Sabha, administering the oath to all other newly elected members, and enabling the election of the permanent Speaker.

 Additional Information

• Chief Justice of India:
• Responsible for administering the oath of office to the President of India under Article 60.
• Does not have a constitutional role in the administration of oaths for members of the Legislature.
• Vice President of India:
• Acts as the Ex-officio Chairman of the Rajya Sabha.
• The oath of the Vice President is administered by the President or a person appointed by him.
• Cabinet Secretary:
• The highest-ranking civil servant and the administrative head of the Cabinet Secretariat.
• Functions as the chief coordinator of the Government of India but holds no constitutional authority regarding parliamentary oaths.
• Nature of Office:
• The office of Speaker Pro Tem is strictly temporary and ceases to exist the moment the House elects its permanent Speaker under Article 93.

The correct answer is Konkan → Karnataka → Malabar.

Key Points

• The Western Coastal Plain of India is a narrow strip of land situated between the Western Ghats and the Arabian Sea, extending from the Gulf of Kachchh in the north to Kanyakumari in the south.
• The Konkan Coast constitutes the northern segment of the western coastline. It stretches from Daman in the north to Goa in the south, covering the coastal districts of Maharashtra and Goa. It is characterized by a rugged and indented coastline.
• The Karnataka Coast, also referred to as the Kanara Coast, is the middle section located south of the Konkan region. It extends from Goa to Mangalore along the state of Karnataka.
• The Malabar Coast forms the southernmost part of the western coastal plains, stretching from Mangalore to the southern tip of the peninsula at Kanyakumari. This region primarily falls within the state of Kerala and is known for its extensive backwaters or Kayals.
• Therefore, the correct geographical sequence from north to south along the western coast is the Konkan Coast, followed by the Karnataka Coast, and finally the Malabar Coast.

 Additional Information

• Kathiawar Coast:
• This section is located in Gujarat, specifically around the Saurashtra peninsula. It lies to the north of the Konkan Coast and is bounded by the Gulf of Kachchh and the Gulf of Khambhat.
• Comparison with the Eastern Coast:
• The Eastern Coastal Plain is broader than the western coast and is divided into the Northern Circars (between the Mahanadi and Krishna rivers) and the Coromandel Coast (stretching from the Krishna river to Kanyakumari).
• Geomorphological Features:
• The western coast is an example of a submerged coast, which provides natural deep-water harbors. Major ports such as Kandla, Mumbai, Marmagao, and Kochi are located along this coastline.

The correct answer is Application software.

Key Points

• Application software consists of programs designed to perform specific tasks for users, rather than simply managing the computer system itself.
• Microsoft Word is categorized as a word processor used for creating, editing, and formatting text documents.
• Microsoft Excel is a spreadsheet application utilized for data organization, mathematical calculations, and financial analysis using a grid of cells.
• Microsoft PowerPoint is a presentation program that allows users to create visual slide decks for business or educational purposes.
• These programs are considered end-user software because they allow individuals to produce specific outputs like documents, charts, and presentations.
• Application software requires an Operating System to run, as it does not communicate directly with the computer hardware.

 Additional Information

• System software:
• Responsible for managing and controlling the hardware components so that application software can perform its tasks.
• Core examples include Operating Systems (OS) like Windows 11, Linux, and macOS, as well as utility software like disk defragmenters.
• Hardware components:
• The physical, tangible parts of a computer system such as the Central Processing Unit (CPU), Hard Disk Drive (HDD), and Monitor.
• Booting programs:
• Specific sets of instructions, such as the BIOS (Basic Input/Output System) or UEFI, that load the operating system into the RAM when the computer is turned on.

The correct answer is Mesolithic.

Key Points

• The Mesolithic phase, also referred to as the Middle Stone Age, represents a transitional period between the Palaeolithic and Neolithic eras, beginning approximately around 10,000 BCE in India.
• The most defining technological advancement of this period was the production of microliths, which are tiny, highly specialized stone tools made from crypto-crystalline silica such as chert, chalcedony, agate, and jasper.
• These tools are typically very small, ranging from 1 cm to 8 cm in length, and are classified into geometrical shapes (like triangles, trapezes, and lunates or crescents) and non-geometrical shapes.
• Microliths were rarely used alone; they were designed to be hafted into wooden or bone handles to create composite tools like spearheads, arrowheads, knives, and sickles.
• In the Indian context, major Mesolithic sites include Bagor in Rajasthan (one of the largest Mesolithic sites), Adamgarh in Madhya Pradesh, Langhnaj in Gujarat, and Sarai Nahar Rai in Uttar Pradesh.
• This era witnessed a shift towards more efficient hunting-gathering and the early beginnings of animal domestication, as evidenced by findings at Bagor and Adamgarh.

 Additional Information

• Lower Palaeolithic
• Characterized by the Acheulian culture involving large, heavy stone tools.
• Common implements included hand-axes, cleavers, and choppers used for butchering and digging.
• Middle Palaeolithic
• Marked by a transition to flake-based tool industries.
• Key tools included scrapers, borers, and points made using the Levallois technique.
• Early Iron Age
• Associated with the introduction of iron metallurgy following the Bronze Age.
• In India, this period is often linked with the Painted Grey Ware (PGW) culture in the North and Megalithic cultures in the South.

The correct answer is Gandhi-Irwin Pact.

Key Points

• The Gandhi-Irwin Pact was a landmark political agreement signed on March 5, 1931, between Mahatma Gandhi and the Viceroy of India, Lord Irwin, before the Second Round Table Conference in London.
• The pact led to the suspension of the Civil Disobedience Movement, which had gained massive momentum following the Salt Satyagraha and the Dandi March of 1930.
• Key provisions of the pact included the release of all political prisoners not charged with violence, the return of confiscated properties to their owners, and the right of people in coastal villages to make salt for personal consumption without paying tax.
• In exchange, the Indian National Congress agreed to discontinue the movement and participate in the Second Round Table Conference to discuss constitutional reforms for India.
• The pact was significant as it placed the Indian National Congress on an equal footing with the British Government for the first time during negotiations.

 Additional Information

• Poona Pact (1932):
• This was an agreement between Mahatma Gandhi and Dr. B.R. Ambedkar on behalf of the depressed classes and upper-caste Hindus.
• It resulted in the reservation of seats for the Depressed Classes in provincial and central legislatures instead of separate electorates.
• Lucknow Pact (1916):
• An agreement reached between the Indian National Congress and the All India Muslim League at a joint session held in Lucknow.
• It established a joint front to demand self-government from the British and accepted the principle of separate electorates for Muslims.
• Lahore Session (1929):
• Presided over by Jawaharlal Nehru, this session is famous for passing the resolution of Purna Swaraj or Complete Independence, which set the stage for the Civil Disobedience Movement.

The correct answer is It was intended to divide people on communal lines and weaken the growing nationalist movement..

Key Points

• The Partition of Bengal was announced on July 19, 1905, by the then Viceroy of India, Lord Curzon, and it officially came into effect on October 16, 1905.
• While the British administration cited administrative convenience as the official reason, the actual strategic intent was to stifle the rising tide of Indian nationalism, as Bengal was the nerve center of political consciousness and anti-colonial resistance.
• The territorial reorganization was designed to create a communal rift by establishing a Muslim-majority province in the East (Eastern Bengal and Assam) and a Hindu-majority province in the West (Western Bengal, Bihar, and Odisha).
• By making the Bengali-speaking population a minority in their own province and fostering religious divisions, the colonial government aimed to implement the classic Divide and Rule policy to weaken the unified front of the Indian National Congress.
• Nationalist leaders recognized this as a deliberate attempt to destroy Bengali unity and communal harmony, leading to the launch of the Swadeshi and Boycott movements, which marked a new phase in the struggle for Swaraj.

 Additional Information

• Swadeshi Movement:
• It was a direct reaction to the 1905 Partition, emphasizing the use of indigenous goods and the burning of foreign-made cloth to exert economic pressure on the British.
• 1911 Annulment:
• Due to the intense and sustained political agitation, the partition was eventually annulled by Lord Hardinge during the Delhi Durbar in 1911.
• Administrative Rationale:
• The British argued that the Bengal Presidency was too large, with a population of nearly 78 million, making it difficult for a single Lieutenant-Governor to manage effectively.
• Shift of Capital:
• In 1911, alongside the annulment of the partition, the British shifted the capital of colonial India from Calcutta to Delhi to ensure better administrative control and move away from the revolutionary hotbed of Bengal.

The correct answer is Protozoan.

Key Points

• Malaria is a life-threatening infectious disease caused by parasites of the genus Plasmodium. These parasites are microscopic, single-celled eukaryotic organisms classified as protozoans.
• The infection is primarily transmitted to humans through the bite of an infected female Anopheles mosquito. The mosquito serves as the vector, carrying the parasite from one human host to another.
• During the bite, the mosquito injects the parasite in the form of sporozoites into the bloodstream. These sporozoites travel to the liver, where they mature and multiply.
• After the liver stage, the parasites (now called merozoites) enter the red blood cells (erythrocytes). Their multiplication inside these cells leads to the destruction of the red blood cells, which is a hallmark of the disease.
• The clinical symptoms, including recurring high fever, chills, and sweating, are caused by the release of a metabolic waste product called hemozoin when the infected red blood cells rupture.

 Additional Information

• Bacteria:
• These are prokaryotic organisms that cause diseases such as Typhoid, Tuberculosis, and Cholera. Unlike malaria, bacterial infections are generally treated with antibiotics.
• Fungi:
• Fungi are eukaryotic organisms that include yeasts and molds. They are responsible for common skin diseases like Ringworm and Athlete’s foot, but they do not cause malaria.
• Virus:
• Viruses are non-living infectious particles that require a host cell to replicate. They cause diseases like Dengue, Hepatitis, and COVID-19. While Dengue is also mosquito-borne, its pathogen is a virus, not a protozoan.
• There are several species of Plasmodium that cause malaria in humans, including P. falciparum, P. vivax, P. ovale, and P. malariae, with P. falciparum being the most lethal.

Therefore, the pathogen responsible for the transmission and development of malaria is a protozoan.

The correct answer is Hubballi.

Key Points

• The South Western Railway (SWR) is one of the 19 railway zones in India, which was created by reorganizing the existing Southern Railway and South Central Railway zones.
• The zone officially commenced its operations on April 1, 2003, with its headquarters established in Hubballi (formerly known as Hubli) in the state of Karnataka.
• Geographically, the South Western Railway zone covers a vast majority of the railway network in Karnataka, and extends its jurisdiction to parts of Tamil Nadu, Andhra Pradesh, and Goa.
• The administrative structure of this zone is divided into three functional divisions: Hubballi, Bengaluru, and Mysuru.
• Hubballi is a significant railway landmark, as it houses one of the oldest and largest Carriage and Wagon Workshops in the Indian Railways network, established in 1885.
• The city is also home to the Shree Siddharoodha Swamiji Hubballi Junction, which holds the record for the world s longest railway platform as of 2023.

 Additional Information

• Jaipur:
• It serves as the headquarters of the North Western Railway (NWR) zone.
• This zone was also formed in 2002 and comprises divisions like Jaipur, Ajmer, Bikaner, and Jodhpur.
• Mumbai:
• Mumbai is a major railway nerve center, hosting the headquarters for two zones: the Central Railway (CR) at Chhatrapati Shivaji Maharaj Terminus and the Western Railway (WR) at Churchgate.
• Jabalpur:
• Located in Madhya Pradesh, it is the headquarters of the West Central Railway (WCR) zone.
• The WCR zone includes the Jabalpur, Bhopal, and Kota divisions.

The correct answer is It resulted from reduced trade and rising land grants replacing cash payments..

Key Points

• The post-Gupta period (6^th century CE to 1000 CE) was characterized by a distinct shift from a centralized monetary economy to a decentralized agrarian structure.
• A primary cause for the decline in metallic coinage was the slump in long-distance trade, particularly with the Roman Empire and Central Asia, which reduced the influx of gold and silver.
• Economic historians like R.S. Sharma argue that the emergence of Indian Feudalism led to the practice of land grants. Rulers began donating land to Brahmins (Agraharas) and state officials as a substitute for cash salaries.
• This transition promoted a closed, self-sufficient village economy where local production met local needs, significantly diminishing the necessity for a circulating metallic currency for daily transactions.

 Additional Information

• Currency Alternatives:
• While high-value gold and silver coins became scarce, cowrie shells (shells used as money) and copper coins became the standard medium for small-scale local exchange.
• Gupta Coinage:
• The Gupta Dynasty was famous for its high-quality gold coins (Dinaras); however, toward the end of their rule, coins showed increasing debasement (mixing gold with inferior metals), signaling economic distress.
• Urban Decay:
• The decline of trade led to urban centers falling into ruin, forcing merchants and artisans to move to rural areas, which further solidified land-based wealth over monetary wealth.

The correct answer is 2003.

Key Points

• The 89^th Constitutional Amendment Act was enacted in the year 2003 to bifurcate the combined National Commission for Scheduled Castes and Scheduled Tribes.
• This amendment specifically aimed at creating a dedicated National Commission for Scheduled Castes (NCSC) under Article 338 of the Indian Constitution.
• The act also inserted a new Article 338A, which led to the establishment of the National Commission for Scheduled Tribes (NCST).
• This legislative change was passed by the Parliament in 2003 and received the Presidential assent shortly thereafter, officially coming into force on February 19, 2004.
• Before this amendment, the 65^th Constitutional Amendment Act, 1990 had replaced the one-man Special Officer with a multi-member National Commission for SCs and STs.

 Additional Information

• National Commission for Scheduled Castes (NCSC):
• It is a constitutional body responsible for safeguarding the interests of the Scheduled Castes in India.
• The commission consists of a Chairperson, a Vice-Chairperson, and three other members, all of whom are appointed by the President of India by warrant under his hand and seal.
• Their primary function is to investigate and monitor all matters relating to the safeguards provided for the Scheduled Castes under the Constitution or any other law.
• The commission has all the powers of a civil court while investigating any matter or inquiring into any complaint.
• Reasons for Bifurcation:
• The social and educational conditions of Scheduled Tribes were considered significantly different from Scheduled Castes, as STs often face issues related to geographical isolation and cultural preservation, whereas SCs face issues related to social exclusion like untouchability.
• Separating the commissions allowed for a more focused approach toward the specific development and welfare schemes tailored for each group.

Therefore, the correct option is 2.

The correct answer is Only 2, 3 and 4.

Key Points

• Marathi: As of December 2022, this language did not hold the official classical status. Although the Maharashtra Government submitted a proposal based on the Rangnath Pathare Committee report, the Union Cabinet only granted it Classical Language status later in October 2024. Hence, statement 1 is incorrect.
• Tamil: It was the very first language in India to be accorded the Classical Language status in 2004. The criteria for this selection include high antiquity of early texts and a recorded history spanning over 1500 to 2000 years. Hence, statement 2 is correct.
• Sanskrit: This language was declared classical in 2005. It is recognized for its extraordinary contribution to Indian heritage, particularly through the Vedas, Upanishads, and classical literature that influenced several other linguistic traditions. Hence, statement 3 is correct.
• Odia: It was officially added to the list in February 2014, becoming the sixth language to receive this distinction. It was the first language from the Indo-Aryan group, other than Sanskrit, to be recognized as classical during that period. Hence, statement 4 is correct.

 Additional Information

• As of December 2022, there were a total of six languages recognized as classical by the Ministry of Culture:
• Tamil (declared in 2004).
• Sanskrit (declared in 2005).
• Kannada (declared in 2008).
• Telugu (declared in 2008).
• Malayalam (declared in 2013).
• Odia (declared in 2014).
• The Linguistic Experts Committee, constituted by the Ministry of Culture, evaluates the eligibility of languages based on original literary traditions that are not borrowed from another speech community.
• Benefits of this status include the establishment of a Center of Excellence for Studies in Classical Languages and the provision for the University Grants Commission (UGC) to create professional chairs in Central Universities for these specific languages.

The correct answer is Geneva, Switzerland.

Key Points

• The 353^rd Session of the Governing Body of the International Labour Organization (ILO) is scheduled to be held in March 2025.
• This session, like most regular meetings of the executive council, takes place at the ILO Headquarters in Geneva, Switzerland.
• The Governing Body is the executive organ of the ILO and meets three times a year, specifically in March, June, and October/November, to make decisions on ILO policy, the agenda of the International Labour Conference, and the draft Programme and Budget.
• During these sessions, representatives discuss global labor standards, the protection of workers rights, and the implementation of international labor conventions.

 Additional Information

• International Labour Organization (ILO):
• It was founded in 1919 under the Treaty of Versailles as an affiliated agency of the League of Nations.
• In 1946, it became the first specialized agency associated with the United Nations (UN).
• The organization is unique due to its tripartite structure, which involves governments, employers, and workers from 187 Member States in its decision-making processes.
• The ILO was awarded the Nobel Peace Prize in 1969 for its work in improving fraternity and peace among nations through social justice.
• The current Director-General of the ILO (as of 2024-2025) is Gilbert F. Houngbo, who was elected by the Governing Body.

The correct answer is Madhya Pradesh.

Key Points

• The Khelo India Water Sports Festival 2025 was officially organized in Srinagar, Jammu and Kashmir, primarily hosted at the Water Sports Center located on the banks of Nigeen Lake and Dal Lake.
• Madhya Pradesh emerged as the dominant force in the competition, securing the highest number of gold medals across various aquatic disciplines, which cemented its position at the top of the overall medal tally.
• The state contingent displayed exceptional prowess in Canoeing, Kayaking, and Rowing, sweeping several podium finishes in both the men’s and women’s categories.
• This victory is a testament to the state’s focused investment in aquatic sports, outperforming other prominent states like Kerala and Maharashtra that have traditionally been strong in water-based events.
• The festival was part of the Khelo India initiative by the Ministry of Youth Affairs and Sports, aimed at promoting specialized sporting disciplines and identifying Olympic-level talent at the grassroots level.

 Additional Information

• Infrastructure and Training Excellence:
• The Madhya Pradesh State Water Sports Academy, based in Bhopal, is credited with the state’s success; it provides international-standard high-performance training and features world-class equipment for athletes.
• The academy has a history of producing athletes who represent India at the Asian Games and World Championships, particularly in Slalom and Sprint events.
• The 2025 Festival in Srinagar served as a crucial qualifying and scouting ground for upcoming national and international aquatic championships.
• While Kerala is famous for its Vallam Kali (Snake Boat Race) and Maharashtra for its coastal sports, Madhya Pradesh has successfully created a systematic technical training model that prioritizes Olympic-format water sports.

The correct answer is Climate Smart Cities Assessment Framework.

Key Points

• The Climate Smart Cities Assessment Framework (CSCAF) was launched in February 2019 by the Ministry of Housing and Urban Affairs (MoHUA) as a part of the Smart Cities Mission.
• It serves as a first-of-its-kind public assessment tool designed to provide a clear roadmap for Indian cities to combat climate change through planned investments and policy interventions.
• The framework evaluates urban performance across 28 indicators categorized into five key thematic areas: Energy and Green Buildings, Urban Planning, Green Cover & Biodiversity, Mobility and Air Quality, Water Management, and Waste Management.
• By using this framework, cities can assess their current climate situation and adopt data-driven strategies to improve their climate resilience and overall sustainability.
• The second version, CSCAF 2.0, was later launched in September 2020 to further refine the assessment parameters and encourage broader participation from 126 cities, including all Smart Cities and capital cities.

 Additional Information

• National Action Plan on Climate Change (NAPCC)
• Launched in June 2008, it is a comprehensive strategy created by the Prime Minister Council on Climate Change to address the challenges of global warming.
• It outlines eight national missions focusing on solar energy, enhanced energy efficiency, sustainable habitat, water, Himalayan ecosystems, green India, sustainable agriculture, and strategic knowledge for climate change.
• National Mission on Sustainable Habitat (NMSH)
• Approved in 2010, it is one of the eight core missions under the NAPCC framework managed by the MoHUA.
• It focuses on making cities sustainable by promoting energy efficiency in the residential and commercial sectors, improving urban waste management, and enhancing public transport systems.

The correct answer is Step-wells for water conservation.

Key Points

• Dholavira, located on Khadir Bet island in the Kutch Desert Wildlife Sanctuary of Gujarat, is distinguished by its extraordinary water management system.
• Archaeologists discovered a massive, rectangular step-well at the site, measuring approximately 73.4 meters in length, 29.3 meters in width, and 10 meters in depth.
• This prehistoric step-well is nearly three times the size of the Great Bath at Mohenjo-daro and represents one of the earliest and most sophisticated examples of hydraulic engineering in the ancient world.
• The site features a series of 16 interconnected reservoirs and stone-cut dams designed to conserve every drop of rainwater in an otherwise arid environment.
• The presence of these rock-cut water structures highlights the transition from simple well-culture to advanced water harvesting, making it a unique architectural hallmark of this specific Harappan city.

 Additional Information

• City Planning and Structure:
• Unlike most Harappan cities which were divided into two parts (the Citadel and the Lower Town), Dholavira was uniquely divided into three sections: the Citadel, the Middle Town, and the Lower Town.
• The city was protected by massive stone fortifications, whereas most other Indus sites primarily used mud-bricks for defensive walls.
• The Dholavira Signboard:
• One of the most significant archaeological finds at the site is a large inscription consisting of ten large-sized signs of the Harappan script, often called the Dholavira Signboard.
• This discovery is unique because most Indus Valley scripts are found on small seals or pottery fragments rather than large public displays.
• General Harappan Features:
• While complex drainage systems and large fortifications are present in Dholavira, they are common traits across major sites like Harappa, Mohenjo-daro, and Kalibangan.
• Pictorial murals are not a standard architectural feature of the Indus Valley Civilization, which focused more on terracotta figurines and steatite seals.

The correct answer is Provide rural road connectivity.

Key Points

• The Pradhan Mantri Gram Sadak Yojana (PMGSY) was launched on 25^th December 2000 by the Government of India under the leadership of the then Prime Minister Atal Bihari Vajpayee.
• It is a Centrally Sponsored Scheme implemented by the Ministry of Rural Development to provide all-weather road access to unconnected rural habitations.
• The primary mandate is to provide a single all-weather road (with necessary culverts and cross-drainage structures) that is operable throughout the year.
• The scheme specifically targets habitations with a population size of 500 persons and above in plain areas and 250 persons and above in Hill States, Desert Areas, Tribal Areas, and Backward Districts.
• By improving rural road connectivity, the initiative aims to facilitate better access to markets, healthcare, education, and other essential social services, thereby reducing rural poverty.
• The program has expanded through subsequent phases such as PMGSY-II (launched in 2013) and PMGSY-III (approved in 2019) to consolidate and upgrade the existing Rural Through Routes.

 Additional Information

• Build national highways:
• National highways are managed by the Ministry of Road Transport and Highways (MoRTH) and the National Highways Authority of India (NHAI).
• The Bharatmala Pariyojana is the flagship program focused on the development of economic corridors and international connectivity.
• Connect Waterways:
• The development of inland waterways is governed by the Inland Waterways Authority of India (IWAI) under the National Waterways Act, 2016.
• The Sagarmala Project focuses on port-led development and optimizing the use of India's coastline and navigable rivers.
• Promote bullet trains:
• High-speed rail development is the responsibility of the National High Speed Rail Corporation Limited (NHSRCL) under the Ministry of Railways.
• The Mumbai-Ahmedabad High Speed Rail (MAHSR) is India's first sanctioned bullet train project.

The correct answer is To control fiscal deficits.

Key Points

• The Fiscal Responsibility and Budget Management (FRBM) Act was enacted in August 2003 to institutionalize financial discipline and reduce the fiscal deficit of the Indian government.
• Its primary objective is to ensure inter-generational equity in fiscal management and long-term macro-economic stability by achieving a balanced budget over time.
• The Act originally mandated the Central Government to reduce the fiscal deficit to a target of 3% of the GDP and to eliminate the revenue deficit entirely.
• It requires the government to lay three specific policy statements before Parliament: the Medium-term Fiscal Policy Statement, the Fiscal Policy Strategy Statement, and the Macro-economic Framework Statement.
• The act also aims to provide the Reserve Bank of India (RBI) with greater autonomy in managing inflation by prohibiting the government from borrowing directly from the RBI.

 Additional Information

• Fiscal Deficit Components:
• Fiscal Deficit is the difference between total expenditure and non-debt receipts, representing the total borrowing needs of the government.
• Revenue Deficit refers to the excess of revenue expenditure over revenue receipts, signifying that the government is borrowing to fund daily consumption.
• N.K. Singh Committee (2016):
• This committee was formed to review the FRBM Act and recommended a debt-to-GDP ratio of 60% (40% for the Centre and 20% for States) by the year 2023.
• It introduced the Escape Clause, allowing the government to deviate from the fiscal deficit target by up to 0.5% in cases of national security, structural reforms, or major calamities.

The correct answer is Objectives Resolution.

Key Points

• The Preamble of the Indian Constitution is based on the Objectives Resolution, which was drafted and moved in the Constituent Assembly by Pandit Jawaharlal Nehru on December 13, 1946.
• The resolution outlined the fundamental commitments of the Constituent Assembly to create an independent, sovereign, and democratic India.
• It served as a guiding roadmap for the framing of the Constitution, emphasizing values such as social, economic, and political justice, equality of status and opportunity, and freedom of thought, expression, belief, faith, and worship.
• The Constituent Assembly officially and unanimously adopted the Objectives Resolution on January 22, 1947.
• The core philosophy and idealistic essence of this resolution were ultimately distilled into the Preamble, which serves as the Identity Card of the Constitution.

 Additional Information

• Fundamental Rights Resolution:
• Historically associated with the Karachi Session of the Indian National Congress in 1931, which was presided over by Sardar Vallabhbhai Patel and emphasized civil liberties and economic programs.
• Directive Principles Resolution:
• The Directive Principles of State Policy (DPSP) are contained in Part IV (Articles 36−51). These were borrowed from the Irish Constitution and aim to establish a welfare state.
• Fundamental Duties Resolution:
• These were not part of the original document but were added to Part IV-A (Article 51A) by the 42^nd Constitutional Amendment Act, 1976, following the recommendations of the Swaran Singh Committee.
• The Preamble has been amended only once till date, in 1976, to include the words Socialist, Secular, and Integrity.

The correct answer is 1909.

Key Points

• The Indian Council Act of 1909 is popularly known as the Morley-Minto Reforms, named after the then Secretary of State for India, Lord Morley, and the Viceroy of India, Lord Minto.
• The most landmark and controversial provision of this Act was the introduction of separate electorates for Muslims, which allowed Muslim representatives to be elected only by Muslim voters.
• By granting communal representation, the Act effectively institutionalized the divide and rule policy, which later significantly influenced the socio-political fabric of India.
• Due to the introduction of this communal voting system, Lord Minto became known in historical texts as the Father of Communal Electorate.
• The Act increased the size of the Legislative Councils at both the Central and Provincial levels; for instance, the number of members in the Central Legislative Council was raised from 16 to 60.
• It also marked the first time an Indian was appointed to the Viceroy’s Executive Council, with Satyendra Prasad Sinha joining as a Law Member.

 Additional Information

• Indian Council Act of 1861:
• Introduced the Portfolio System, where individual members of the executive council were placed in charge of specific departments.
• Started the process of decentralization by restoring legislative powers to the Madras and Bombay presidencies.
• Authorized the Viceroy to issue ordinances in times of emergency, which would have the force of law for six months.
• Indian Council Act of 1862 (Implementation context):
• Under the provisions of the 1861 Act, Lord Canning nominated three Indians—the Raja of Benares, the Maharaja of Patiala, and Sir Dinkar Rao—to the newly constituted Legislative Council.
• 1903:
• While not associated with a specific Indian Council Act, this year is notable for the Delhi Durbar organized by Lord Curzon to celebrate the coronation of King Edward VII.

The correct answer is AgCl and AgBr.

Key Points

• Silver Bromide (AgBr) and Silver Chloride (AgCl) are the primary light-sensitive chemicals used in black and white photography. They belong to a group of compounds known as silver halides.
• When these compounds are exposed to light, they undergo a photochemical decomposition reaction. In this process, the silver halide crystals absorb photons, causing the silver ions to be reduced to metallic silver.
• The chemical equation for the decomposition of Silver Chloride is: 2AgCl(s) + Sunlight → 2Ag(s) + Cl₂(g). The white silver chloride turns greyish due to the formation of silver metal.
• The chemical equation for Silver Bromide is: 2AgBr(s) + Sunlight → 2Ag(s) + Br₂(g). In this reaction, the pale yellow silver bromide decomposes into metallic silver and bromine gas.
• In the photographic process, the areas of the film exposed to more light contain more silver metal, which creates the dark parts of the negative, while unexposed areas remain clear after processing.

 Additional Information

• Silver Halides:
• These are compounds formed between Silver (Ag) and Halogens (Group 17 elements like Chlorine, Bromine, and Iodine).
• AgBr is the most widely used halide in photographic emulsions because it has the optimal level of sensitivity to light.
• AgCl is often used in photographic printing paper rather than the film itself, as it is less sensitive than bromide but produces finer detail.
• Photodecomposition:
• This is a type of decomposition reaction where a single reactant breaks down into two or more products in the presence of photons (light energy).
• This reaction is endothermic in nature as it requires the absorption of energy to break chemical bonds.
• Aside from photography, photolysis plays a critical role in ozone layer formation and photosynthesis in plants.

The correct answer is The Malabar Coast.

Key Points

• The Malabar Coast constitutes the southwestern shoreline of the Indian subcontinent, primarily spanning the state of Kerala and the coastal regions of Karnataka.
• It is geographically distinguished by its extensive backwaters, locally referred to as Kayals, which are a chain of brackish lagoons and lakes linked by man-made and natural canals.
• The formation of these lagoons is a result of the depositional work of ocean currents and waves, which created barrier islands that trapped the discharge of numerous rivers flowing down from the Western Ghats.
• Vembanad Lake, situated on this coast, is the longest lake in India and serves as the largest wetland system in the country, covering an area of approximately 2,033 square kilometers.
• These backwaters are critical for the local economy, supporting inland navigation, traditional fishing, and the unique Kuttanad farming system, where cultivation happens below sea level.
• Geologically, the Malabar Coast is a submergent coast in its southern reaches but shows evidence of emergence in other parts, characterized by narrow alluvial plains and sand dunes.

 Additional Information

• The Coromandel Coast
• This refers to the southeastern coastal region of India, stretching from the False Divi Point to Kanyakumari.
• Unlike the west coast, it is broader and features large deltas formed by the Kaveri, Krishna, and Godavari rivers.
• It is notably famous for receiving heavy rainfall during the North-East Monsoon or Retreating Monsoon season.
• The Northern Circars
• This is a geographical division of the Eastern Coastal Plain lying between the Mahanadi and Krishna rivers.
• It encompasses the coastal regions of Odisha and northern Andhra Pradesh, characterized by the Chilika Lake, the largest brackish water lagoon in India.
• The Andhra Coast
• Part of the Eastern Coastal Plain, it is known for its fertile alluvial soil and the presence of the Kolleru Lake, a major freshwater lake located between the Krishna and Godavari deltas.

The correct answer is Article 76.

Key Points

• Article 76 of the Indian Constitution deals with the appointment, duties, and tenure of the Attorney General of India.
• The Attorney General is appointed by the President of India and acts as the Chief Legal Advisor to the Government of India.
• To qualify for this post, a person must be qualified to be appointed as a Judge of the Supreme Court, implying they must be a citizen of India with specific judicial or legal experience.
• The Attorney General holds office during the pleasure of the President, meaning there is no fixed tenure mentioned in the Constitution.
• Under this article, the Attorney General has the right of audience in all courts in the territory of India and the right to participate in Parliamentary proceedings without the right to vote.

 Additional Information

• Article 165:
• Provides for the appointment of the Advocate General for the State.
• The Advocate General is the highest legal officer at the state level, appointed by the Governor.
• Article 211:
• Imposes a restriction on discussion in the State Legislature.
• It mandates that no discussion shall take place in the Legislature of a State with respect to the conduct of any Judge of the Supreme Court or of a High Court in the discharge of his duties.
• Article 240:
• Vests the President with the power to make regulations for the peace, progress, and good government of certain Union Territories.
• This includes territories like the Andaman and Nicobar Islands, Lakshadweep, and Dadra and Nagar Haveli and Daman and Diu.

The correct answer is Shirley Botchwey.

Key Points

• Shirley Ayorkor Botchwey is the current Commonwealth Secretary-General, having been elected to the position during the Commonwealth Heads of Government Meeting (CHOGM) held in Samoa in October 2024.
• She officially assumed office in April 2025, succeeding Baroness Patricia Scotland, and made history as the first African woman to lead the 56-nation intergovernmental organization.
• In September 2025, she presided over the 25^th Commonwealth Foreign Affairs Ministers Meeting (CFAMM) in New York, which traditionally takes place on the sidelines of the United Nations General Assembly (UNGA).
• During this high-level meeting, Shirley Botchwey advocated for climate finance, youth empowerment, and the economic resilience of Small Island Developing States (SIDS), which constitute a significant portion of the Commonwealth membership.
• As the leader of the Commonwealth Secretariat, her role involves managing the administrative functions of the organization and facilitating cooperation between member states on global issues.

 Additional Information

• Patricia Scotland:
• She served as the 6^th Commonwealth Secretary-General from 2016 to 2025.
• A legal expert from Dominica, she was the first woman to hold the office and championed the Commonwealth Blue Charter for ocean protection.
• Ngozi Okonjo-Iweala:
• She is the Director-General of the World Trade Organization (WTO), appointed in March 2021.
• A renowned Nigerian economist, she previously served as Nigeria's Finance Minister and Foreign Minister, but has not held the position of Commonwealth Secretary-General.
• Kamalesh Sharma:
• An Indian diplomat who served as the 5^th Commonwealth Secretary-General from 2008 to 2016.
• He was instrumental in the adoption of the Commonwealth Charter in 2012, which outlines the core values of the organization.

The correct answer is Three-tier.

Key Points

• The Balwantrai Mehta Committee was appointed by the Government of India in January 1957 to examine the working of the Community Development Programme (1952) and the National Extension Service (1953).
• The committee submitted its report in November 1957 and recommended the establishment of the scheme of Democratic Decentralization, which eventually came to be known as Panchayati Raj.
• The specific recommendation was for a three-tier Panchayati Raj system consisting of the Gram Panchayat at the village level, the Panchayat Samiti at the block level, and the Zila Parishad at the district level.
• The Gram Panchayat was to be constituted with directly elected representatives, whereas the Panchayat Samiti and Zila Parishad were to be formed with indirectly elected members.
• The committee envisioned the Panchayat Samiti as the executive body and the Zila Parishad as the advisory, coordinating, and supervisory body, chaired by the District Collector.
• Following these recommendations, Rajasthan became the first state to adopt the system, inaugurated in Nagaur district on October 2, 1959, by the then Prime Minister Jawaharlal Nehru.

 Additional Information

• Two-tier system:
• This was recommended by the Ashok Mehta Committee in 1978, which suggested a Zila Parishad at the district level and a Mandal Panchayat (representing a group of villages) to replace the three-tier structure.
• Four-tier system:
• The G.V.K. Rao Committee (1985) observed that the Panchayati Raj had become grass without roots due to bureaucratization and suggested a four-tier structure including State-level Council, Zila Parishad, Mandal Panchayat, and Gram Sabha.
• L.M. Singhvi Committee (1986):
• This committee recommended that Panchayati Raj institutions should be constitutionally recognized and protected to ensure regular elections and financial autonomy.
• 73^rd Constitutional Amendment Act, 1992:
• This act gave constitutional status to the Panchayati Raj system, mandating a three-tier system for all states with a population of over 20 lakh, adding Part IX and the Eleventh Schedule to the Constitution of India.

The correct answer is IIT Madras.

Key Points

• Coal India Limited (CIL), a Maharatna Public Sector Undertaking, has partnered with the Indian Institute of Technology Madras (IIT Madras) to establish the Coal India Limited Centre for Sustainable Energy (CILCSE).
• The primary objective of this collaboration is to drive research and development in sustainable energy solutions, addressing the global need for cleaner energy and decarbonization.
• The center focuses on specialized domains such as Carbon Capture, Utilization, and Storage (CCUS), Green Hydrogen, and Coal Gasification to ensure energy security while minimizing environmental impact.
• This initiative is strategically aligned with the Government of India's vision of achieving Net Zero emissions by 2070 and supports the objectives of the National Green Hydrogen Mission.
• The partnership facilitates an industry-academia interface, allowing CIL to leverage the technical expertise of IIT Madras to transition from a coal-centric company to a diversified energy entity.

 Additional Information

• Coal India Limited (CIL):
• It is the largest coal producer in the world and functions under the Ministry of Coal, headquartered in Kolkata, West Bengal.
• CIL is increasingly investing in solar power and renewable energy projects to transition toward a sustainable business model.
• IIT Madras:
• Located in Chennai, it has consistently maintained the top rank in the Engineering category of the National Institutional Ranking Framework (NIRF).
• The institute is renowned for its IIT Madras Research Park, which fosters innovation and start-up ecosystems in deep-tech and energy sectors.

The correct answer is Goal 7.

Key Points

• Sustainable Development Goal 7 (SDG 7) is one of the 17 goals established by the United Nations in 2015 as part of the 2030 Agenda for Sustainable Development.
• The primary mission of Goal 7 is to ensure universal access to affordable, reliable, sustainable, and modern energy for all individuals globally by the year 2030.
• It targets a significant increase in the global share of renewable energy sources, such as solar, wind, and geothermal power, to transition away from fossil fuels.
• Another critical objective is doubling the global rate of improvement in energy efficiency, which involves optimizing energy consumption across industrial, transportation, and residential sectors.
• Access to clean energy is considered a fundamental driver for progress in other areas, including poverty reduction, food security, health, and climate mitigation.
• The goal also emphasizes international cooperation to facilitate access to clean energy research and technology, including advanced fossil-fuel technologies with lower emissions.

 Additional Information

• Sustainable Development Goal 5:
• Focuses on achieving gender equality and empowering all women and girls.
• Aims to end all forms of discrimination, violence, and harmful practices like forced marriage and female genital mutilation.
• Sustainable Development Goal 9:
• Concentrates on building resilient infrastructure, promoting inclusive and sustainable industrialization, and fostering innovation.
• It encourages scientific research and upgrades the technological capabilities of industrial sectors in all countries.
• Sustainable Development Goal 13:
• Urges taking immediate and collective action to combat climate change and its devastating environmental impacts.
• Includes targets for strengthening resilience and adaptive capacity to climate-related hazards and natural disasters.

The correct answer is Convex Lens.

Key Points

• Hypermetropia, commonly referred to as long-sightedness, is a refractive defect of the eye where light rays from nearby objects do not converge soon enough and instead focus at a point behind the retina.
• This condition occurs when the axial length of the eyeball is too short or the crystalline lens lacks sufficient curvature, resulting in a focal length that is too long for the eye's physical dimensions.
• A Convex Lens is a converging lens that is thicker at the center than at the edges. It works by bending incoming light rays inward before they reach the eye's natural lens.
• By adding a convex lens, the overall optical power of the eye is increased. This additional convergence ensures that the focal point is pulled forward and placed precisely on the retina, allowing for clear near vision.
• The power of the corrective lens required is measured in Dioptres (D) and is expressed as a positive value for Hypermetropia.

 Additional Information

• Concave Lens:
• This is a diverging lens used to correct Myopia (short-sightedness).
• In a myopic eye, light focuses in front of the retina because the eyeball is too long or the lens is too curved; the concave lens spreads the rays out to shift the focus back onto the retina.
• Cylindrical Lens:
• These lenses have different powers in different meridians and are primarily used to correct Astigmatism.
• Astigmatism is caused by an irregular, non-spherical curvature of the cornea or lens, leading to distorted images.
• Photochromic Lenses:
• These are specialized lenses that darken when exposed to Ultraviolet (UV) radiation and clear up in the absence of UV light.
• They typically contain silver halide molecules and are used for light sensitivity and sun protection rather than specific refractive correction.

The correct answer is Article 235.

Key Points

• Article 235 of the Indian Constitution explicitly grants the High Court the power of control over subordinate courts within its territorial jurisdiction.
• This provision is located in Part VI, Chapter VI of the Constitution, which specifically addresses the structure and administration of Subordinate Courts.
• The scope of 'control' vested in the High Court includes administrative matters such as the posting, promotion, and the grant of leave to individuals belonging to the judicial service of a State.
• It applies to all judicial officers holding posts inferior to the rank of District Judge, ensuring that their career progression and disciplinary matters are handled by the judiciary rather than the Executive.
• The Supreme Court of India has historically interpreted this article to include disciplinary control, which allows the High Court to conduct inquiries and recommend transfers or removals to protect judicial independence.

 Additional Information

• Article 308:
• It is the opening article of Part XIV, which deals with Services under the Union and the States.
• It provides the interpretation of the term 'State' specifically for the provisions contained within this part of the Constitution.
• Article 115:
• It pertains to Financial Matters of the Union Government within Part V.
• It details the procedure for Supplementary, additional or excess grants when the funds authorized for a service are found insufficient or a need arises for a new service.
• Article 107:
• It outlines the provisions as to introduction and passing of Bills in the Parliament.
• It establishes that a Bill (excluding Money Bills) may originate in either the Lok Sabha or the Rajya Sabha and must be agreed upon by both Houses to proceed.
• Article 233:
• This related article deals with the appointment of District Judges by the Governor of the State in consultation with the High Court.

The correct answer is Correcting balance of payment imbalances and controlling inflationary pressures.

Key Points

• The New Economic Policy (NEP) launched in July 1991 by the Indian government was a response to a severe economic crisis characterized by a massive Balance of Payments (BoP) deficit and skyrocketing inflation.
• The policy framework was broadly divided into two sets of measures: Stabilisation Measures and Structural Reform Measures.
• Stabilisation Measures were short-term in nature and were intended to correct the immediate weaknesses of the economy, specifically by restoring macro-economic stability.
• The first immediate objective was to improve the foreign exchange reserves to ensure India could meet its international payment obligations and avoid a sovereign default.
• The second objective was to control the inflationary pressures by regulating the money supply and fiscal deficit, as the inflation rate had reached double digits (approximately 17%) by 1991.
• These measures were a prerequisite for receiving financial assistance from international agencies like the International Monetary Fund (IMF) and the World Bank.

 Additional Information

• Structural Reform Measures
• These were long-term policies aimed at improving the efficiency of the economy and increasing its international competitiveness.
• They included the famous LPG model: Liberalisation, Privatisation, and Globalisation.
• Disinvestment: This involves the government selling its equity in Public Sector Enterprises (PSEs) to private investors to reduce state control and improve corporate governance.
• Foreign Direct Investment (FDI): Policy changes were made to allow greater automatic approval for foreign capital to improve technological standards and capital availability.
• Trade Policy Reforms: These involved the removal of licensing for imports and the reduction of high tariff rates to integrate the Indian economy with the global market.

The correct answer is Amaravati Quantum Valley.

Key Points

• The Amaravati Quantum Valley was officially announced in April 2025 as a specialized economic and technological zone in Andhra Pradesh, designed to serve as India’s first major quantum computing hub.
• This project is part of a broader state initiative to transform the Amaravati capital region into a global center for deep-tech research, bridging the gap between academic theory and commercial quantum applications.
• The valley focuses on the development of quantum hardware, including superconducting qubits and photonic circuits, aiming to build intermediate-scale quantum computers with 50 to 100 physical qubits.
• It establishes a collaborative ecosystem involving Tier-1 research institutions, global technology giants, and specialized startups to drive innovation in Quantum Information Science and Technology (QIST).
• The announcement marks a significant milestone in India’s domestic capabilities, reducing reliance on foreign quantum infrastructure and aligning with the Make in India vision for frontier technologies.

 Additional Information

• National Quantum Mission (NQM):
• Approved by the Union Cabinet in 2023 with an outlay of over 6,000 crore, the mission aims to seed, nurture, and scale up scientific and industrial R&D in quantum technology.
• It targets the development of quantum communication networks over a distance of 2,000 km and the creation of highly sensitive quantum sensors for navigation and healthcare.
• Core Domains of Quantum Technology:
• Quantum Computing: Utilizing superposition and entanglement to solve complex problems in optimization and drug discovery that are unsolvable by classical supercomputers.
• Quantum Cryptography: Implementing Quantum Key Distribution (QKD) to provide unhackable communication channels for national security and banking sectors.
• Quantum Materials: Engineering novel materials with topological properties for the next generation of electronic devices.

The correct answer is 15 lakh saplings in the state.

Key Points

• Seva Parv 2025, also widely celebrated as Seva Pakhwada (Service Fortnight), was observed from September 17, 2025, marking the birthday of Prime Minister Narendra Modi, until October 2, 2025, the birth anniversary of Mahatma Gandhi.
• As part of the nationwide Sustainable Development Goal (SDG) linked drive, the Government of Uttar Pradesh established a specific target to plant 15 lakh saplings across the state during this 15-day window.
• This initiative was closely integrated with the Ek Ped Maa Ke Naam (A Tree in Mother’s Name) campaign, which aims to enhance Indias carbon sink and promote climate resilience in alignment with SDG 13 (Climate Action).
• The plantation drive targeted various locations, including Panchayat lands, educational institutions, and urban forest zones, to ensure a balanced increase in the green cover of the state.
• The Department of Forest and the Department of Rural Development were the primary agencies responsible for executing this massive plantation exercise to meet the 15 lakh milestone within the stipulated timeframe.

 Additional Information

• Seva Parv / Seva Pakhwada:
• It is an annual event focused on public service, social welfare, and environmental conservation activities.
• Key activities include blood donation camps, cleanliness drives under Swachh Bharat Abhiyan, and awareness programs on vocal for local.
• Environmental Targets of Uttar Pradesh:
• Uttar Pradesh has consistently set high benchmarks for afforestation, often targeting over 35 crore saplings during the monsoon season (Van Mahotsav).
• The 15 lakh target for the Seva Parv serves as a supplementary micro-campaign to sustain momentum for the state’s Green Mission.
• The state utilizes the Geographic Information System (GIS) and e-Nagarpalika portals to monitor the survival rate of the planted saplings.

The correct answer is Automation.

Key Points

• Automation refers to the ability of a computer to perform a series of operations or tasks without human intervention once the initial program or instructions are provided and executed.
• The Control Unit (CU) within the Central Processing Unit (CPU) facilitates this by managing the Fetch-Decode-Execute cycle, allowing the computer to move from one instruction to the next in the Instruction Set automatically.
• This characteristic is essential for complex computations and high-speed data processing, where a machine can run batch jobs, system updates, or background processes independently until a logical end-point is reached.
• In modern computing, automation enables Artificial Intelligence (AI) and Robotic Process Automation (RPA) to handle sophisticated workflows, significantly increasing operational efficiency and reducing the likelihood of human error.

 Additional Information

• Diligence:
• This represents the reliability and consistency of a computer system.
• Unlike humans, computers do not suffer from fatigue, boredom, or lack of concentration, allowing them to perform millions of calculations per second for extended periods.
• Accuracy:
• Computers deliver extremely high precision in their results, often calculating up to several decimal places without error.
• The degree of accuracy is governed by the GIGO (Garbage In, Garbage Out) principle, meaning the computer is only as accurate as the input data and software logic provided to it.
• Portability:
• This refers to the ability of hardware or software to be transferred from one location or platform to another with minimal modification.
• In the context of programming languages, it signifies the ability of code to run across various operating systems such as Linux, Windows, and macOS.

The correct answer is Ctrl + S.

Key Points

• The Ctrl + S shortcut is the universal command used in the Windows operating system and most productivity applications (such as Microsoft Word, Excel, and Notepad) to trigger the Save function.
• When a user types or edits a document, the data is stored in the Random Access Memory (RAM), which is volatile memory; this means any unsaved data will be permanently wiped if the computer loses power or the Operating System crashes.
• Pressing Ctrl + S initiates a command to write the data from the volatile RAM to a non-volatile storage device, such as a Hard Disk Drive (HDD) or Solid State Drive (SSD), ensuring data persistence.
• Regularly using this shortcut is considered a critical computing best practice to minimize the risk of losing significant progress due to hardware failures or software glitches.
• As per the provided choices, Option (3) correctly identifies Ctrl + S as the essential tool for maintaining document safety. Hence, Ctrl + S is the correct answer.

 Additional Information

• Ctrl + V:
• Function: This is the Paste shortcut.
• Usage: It takes the content currently stored in the system Clipboard and inserts it into the document at the location of the insertion point.
• Ctrl + C:
• Function: This is the Copy shortcut.
• Usage: It duplicates selected text or objects and stores them in the Clipboard while leaving the original content intact.
• Ctrl + X:
• Function: This is the Cut shortcut.
• Usage: It removes the selected text or object from its original location and moves it to the Clipboard for later pasting.
• F12 Key:
• Function: In many Office applications, this serves as the Save As shortcut.
• Usage: It allows the user to save an existing file with a new name, a different file extension (like PDF or TXT), or in a different directory.

The correct answer is Marathi.

Key Points

• On October 3, 2024, the Union Cabinet, chaired by Prime Minister Narendra Modi, officially approved the conferment of Classical Language status to Marathi along with four other languages.
• The recognition was part of a historic decision to elevate Marathi, Pali, Prakrit, Assamese, and Bengali to the status of Classical Languages, acknowledging their deep historical roots and literary significance.
• The Government of India follows specific criteria for this designation, including high antiquity of early texts or recorded history spanning 1500 to 2000 years and a body of ancient literature that is considered a valuable heritage by generations of speakers.
• The proposal for Marathi was long-standing, backed by extensive research demonstrating that its linguistic and literary traditions are original and not borrowed from another speech community.
• With this inclusion, Marathi joins an elite group of Indian languages that receive special support for research, preservation, and promotion from the Ministry of Education.

 Additional Information

• Evolution of Classical Languages in India:
• Tamil was the first language to be accorded the status in 2004.
• Sanskrit was recognized in 2005, followed by Telugu and Kannada in 2008.
• Malayalam was designated in 2013, and Odia received the status in 2014.
• As of October 2024, the total number of recognized Classical Languages in India has reached 11.
• Benefits of the Status:
• The Ministry of Education provides two major annual International Awards for scholars of eminence in these languages.
• A Centre of Excellence for Studies in Classical Languages is established to promote academic research and documentation.
• The University Grants Commission (UGC) is requested to create a certain number of Professional Chairs for Classical Languages in Central Universities.
• Incorrect Options Context:
• Kannada: Conferred classical status in 2008.
• Tamil: Conferred classical status in 2004.
• Odia: Conferred classical status in 2014.

The correct answer is Brussels.

Key Points

• On March 6, 2025, the leaders of the European Union (EU) convened an extraordinary summit in Brussels to deliberate on the critical security challenges posed by the situation in Ukraine and the broader European security framework.
• Brussels serves as the administrative heart and the permanent seat of the European Council, where the heads of state or government of the 27 EU member states meet to define the Union's political direction and security priorities.
• The summit specifically focused on the European Peace Facility (EPF), the scaling up of the European defense industry, and the provision of long-term security guarantees to support Ukraine against external aggression.
• Holding the summit in Brussels allowed for immediate coordination with NATO leadership, as both organizations are headquartered in the city, emphasizing transatlantic unity and a collective response to security threats.
• Meetings typically take place at the Europa building, which is equipped with high-security facilities designed for crisis management and sensitive diplomatic negotiations between EU leaders and the President of the European Council.

 Additional Information

• Vienna:
• While Vienna is a prominent international diplomatic hub hosting the OSCE (Organization for Security and Co-operation in Europe) and the IAEA, it is not the official venue for European Council summits.
• Paris:
• Paris and nearby Versailles have hosted informal EU summits in the past, particularly in early 2022, but standard extraordinary sessions concerning security policy are generally centralized in Brussels.
• Berlin:
• As the capital of the EU's largest economy, Berlin is central to European diplomacy and Weimar Triangle talks, but formal plenary sessions of the 27 member states are hosted at the EU's institutional headquarters.

The correct answer is Computers became smaller and faster.

Key Points

• The transition from Vacuum Tubes in the first generation to Transistors in the second generation initiated a significant reduction in physical footprint and heat generation.
• The development of Integrated Circuits (ICs) during the third generation allowed for thousands of components to be placed on a single silicon chip, drastically increasing processing speed and reliability.
• Advancements in Microprocessor technology, specifically Very Large Scale Integration (VLSI), enabled the compression of an entire Central Processing Unit (CPU) onto a single chip, leading to the miniaturization seen in modern laptops and smartphones.
• As the physical distance between electronic components decreased, the time required for electrical signals to travel was reduced, resulting in higher clock speeds and the ability to perform billions of instructions per second (BIPS).
• Successive generations have consistently improved energy efficiency and memory density, allowing computers to store more data and operate faster while consuming less power than their predecessors.

 Additional Information

• Computer Generations Breakdown:
• First Generation (1940-1956): Utilized Vacuum Tubes; these machines like ENIAC and UNIVAC were room-sized and frequently overheated.
• Second Generation (1956-1963): Replaced tubes with Transistors, making computers smaller, faster, cheaper, and more energy-efficient.
• Third Generation (1964-1971): Introduced Integrated Circuits (ICs), which increased speed and efficiency by mounting many transistors on Silicon Chips.
• Fourth Generation (1971-Present): Characterized by Microprocessors and VLSI technology; this era saw the birth of Personal Computers (PCs) like the Altair 8800 and Apple II.
• Fifth Generation (Present and Beyond): Focuses on Artificial Intelligence (AI), Ultra Large Scale Integration (ULSI), and Parallel Processing to achieve human-like computing capabilities.