RRB NTPC (UG) CBT-I Official Paper (Held On 08 May, 2026 Shift 3) (Previous Year Paper)

Shortcut Trick

Let the total capacity of the cistern be the LCM of (10, 20, 12) = 60 units.

Combined Efficiency: (A+B) = 6, (B+C) = 3, (C+A) = 5.

Summing them: 2(A+B+C) = 6 + 3 + 5 = 14 ⇒ A+B+C = 7 units/hr.

Efficiency of Pipe B = (A+B+C) − (C+A) = 7 − 5 = 2 units/hr.

Time taken by B = 60 ÷ 2 = 30 hr.

∴ The correct answer is 30 hr.

Alternate Method

Given:

Time taken by (Pipe A + Pipe B) = 10 hr

Time taken by (Pipe B + Pipe C) = 20 hr

Time taken by (Pipe C + Pipe A) = 12 hr

Formula Used:

Efficiency = Total Work ÷ Time taken

Calculations:

⇒ Adding efficiencies: (A + B) + (B + C) + (C + A) = 6 + 3 + 5

⇒ 2(A + B + C) = 14

⇒ A + B + C = 14 ÷ 2 = 7 units/hr

⇒ We know efficiency of (C + A) = 5 units/hr

⇒ Efficiency of B = (A + B + C) − (C + A) = 7 − 5 = 2 units/hr

⇒ Time taken by Pipe B alone = Total Work ÷ Efficiency of B

⇒ Time = 60 ÷ 2 = 30 hr

∴ The correct answer is 30 hr.

Additional Information

Combined Efficiency Rule

When pipes work in pairs, the sum of their individual efficiencies is half the sum of their pairwise efficiencies: (A+B+C) = [(A+B) + (B+C) + (C+A)] ÷ 2.

Pipes and Cisterns Basics

Inlet pipes perform positive work (filling), while outlet pipes perform negative work (emptying). Total work is the volume of the tank/cistern.

Time and Work Relation

Time taken and efficiency are inversely proportional to each other. Time = 1 ÷ Efficiency (for constant work).

Shortcut Trick

Approximate Effective Discount for each Scheme:

(A) 21 + 8 − (21 × 8 / 100) = 27.32%

(B) Successive 38%, 42%, 30% → clearly much higher than 50% (≈ 74.8%)

(C) Weighted Average = [(8 × 17) + (2 × 20)] ÷ 10 = 17.6%

(D) Buy 10 Get 7 Free = [7 ÷ (10 + 7)] × 100 ≈ 41.18%

Comparing the values, 17.6% is the lowest discount, making it the least beneficial.

∴ The correct answer is C.

Alternate Method

Given:

⇒ Total Toys to buy = 10

⇒ Let Marked Price (MP) of 1 toy = ₹100

⇒ Total Marked Price for 10 toys = ₹1000

Formula Used:

⇒ Successive Discount = a + b − (ab/100)

⇒ Buy X Get Y Free Discount % = [Y ÷ (X + Y)] × 100

Calculations:

Scheme (A): Successive 21% and 8%

⇒ Effective Discount = 21 + 8 − (21 × 8 / 100) = 29 − 1.68 = 27.32%

Scheme (B): Successive 38%, 42%, 30%

⇒ First two: 38 + 42 − (38 × 42 / 100) = 80 − 15.96 = 64.04%

⇒ Final: 64.04 + 30 − (64.04 × 30 / 100) = 94.04 − 19.21 = 74.83%

Scheme (C): 17% on first 8, 20% on next 2

⇒ Discount on 8 toys = 8 × 17 = ₹136

⇒ Discount on 2 toys = 2 × 20 = ₹40

⇒ Total Discount = 136 + 40 = ₹176

⇒ Effective % = (176 ÷ 1000) × 100 = 17.6%

Scheme (D): Buy 10 Get 7 Free

⇒ Effective Discount % = [7 ÷ (10 + 7)] × 100 = (7 ÷ 17) × 100 ≈ 41.18%

⇒ Comparing all schemes, 17.6% is the minimum discount.

∴ The correct answer is C.

Additional Information

Successive Discounts

When multiple discounts are applied one after another, the total discount is always less than the sum of individual percentages. Formula: a + b − (ab/100).

Buy X Get Y Free

The effective discount percentage in such offers is calculated as: [Free Items ÷ Total Items (Bought + Free)] × 100.

Least Beneficial vs Most Beneficial

For a customer, the least beneficial scheme is the one offering the lowest effective discount percentage, while the most beneficial offers the highest.

Shortcut Trick

Convert decimals to fractions for faster calculation: 0.25 = 1/4 and 0.5 = 1/2.

Numerator: (1/4) × 1.6 = 0.4

Denominator: 0.04 × (1/2) = 0.02

Result = 0.4 ÷ 0.02 = 40 ÷ 2 = 20

∴ The correct answer is 20.

Alternate Method

Given: (0.25 × 1.6) ÷ (0.04 × 0.5)

Method Used: Apply the BODMAS rule (perform operations inside Brackets first).

⇒ Step 1 (First bracket): 0.25 × 1.6 = 0.400 = 0.4

⇒ Step 2 (Second bracket): 0.04 × 0.5 = 0.020 = 0.02

⇒ Step 3 (Division): 0.4 ÷ 0.02

⇒ To remove the decimal from the divisor, multiply both numerator and denominator by 100.

⇒ (0.4 × 100) ÷ (0.02 × 100) = 40 ÷ 2

⇒ Result = 20

∴ The correct answer is 20.

Additional Information

BODMAS Rule

It stands for Brackets, Of, Division, Multiplication, Addition, and Subtraction. Operations must be performed in this specific order to get the correct result.

Multiplying Decimals

Multiply the numbers as if they were whole numbers, then place the decimal point in the product so that it has the same number of decimal places as the sum of the decimal places in the factors.

Dividing by Decimals

Move the decimal point in the divisor to the right until it is a whole number, and move the decimal point in the dividend the same number of places to the right before dividing.

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Total Distance = 100 + 150 + 50 = 300 km

Total Time = (100/50) + (150/60) + (50/40) = 2 + 2.5 + 1.25 = 5.75 hours

Average Speed = 300 ÷ 5.75 ≈ 52.17 km/h

∴ The correct answer is 52.17 km/h.

Alternate Method

Given:

Distance₁ = 100 km, Speed₁ = 50 km/h

Distance₂ = 150 km, Speed₂ = 60 km/h

Distance₃ = 50 km, Speed₃ = 40 km/h

Formula Used:

Time = Distance ÷ Speed

Average Speed = (Total Distance) ÷ (Total Time)

Calculations:

⇒ Time for first part (t₁) = 100 ÷ 50 = 2 hours

⇒ Time for second part (t₂) = 150 ÷ 60 = 2.5 hours

⇒ Time for third part (t₃) = 50 ÷ 40 = 1.25 hours

⇒ Total Time (T) = 2 + 2.5 + 1.25 = 5.75 hours

⇒ Average Speed = 300 ÷ 5.75

⇒ Average Speed = 30000 ÷ 575 = 1200 ÷ 23

⇒ Average Speed ≈ 52.1739... km/h

∴ The correct answer is 52.17 km/h.

Additional Information

Average Speed for Equal Distances

When a journey is divided into two equal distances with speeds x and y, the Average Speed is the harmonic mean: (2 × x × y) ÷ (x + y).

Average Speed for Equal Time Intervals

If an object travels at speed x for time T and then at speed y for the same time T, the Average Speed is the arithmetic mean: (x + y) ÷ 2.

Unit Conversion

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

Shortcut Trick

Assume the total quantity is 12 units (LCM of 3 and 4).

Net profit/loss units = (1/3 × 12 × 20) + (1/4 × 12 × (−10)) + (5/12 × 12 × 0)

Net effect = 80 − 30 + 0 = 50 units.

Overall percentage = 50 ÷ 12 = 25/6 = 4 ¹/₆%.

∴ The correct answer is 4 ¹/₆% profit.

Alternate Method

Given: Total Cost Price (CP) = ₹2400

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

⇒ Profit on first part = (1/3) × 2400 × 20% = 800 × 0.20 = ₹160

⇒ Loss on second part = (1/4) × 2400 × 10% = 600 × 0.10 = ₹60

⇒ Remaining goods = 1 − (1/3 + 1/4) = 1 − 7/12 = 5/12

⇒ Profit/Loss on remaining part = (5/12) × 2400 × 0 = ₹0

⇒ Total Net Profit = 160 − 60 + 0 = ₹100

⇒ Overall Profit Percentage = (100 ÷ 2400) × 100 = 100/24 = 25/6 = 4 ¹/₆%

∴ The correct answer is 4 ¹/₆% profit.

Additional Information

Weighted Average Profit/Loss

When goods are sold in parts, the net profit/loss percentage is the weighted average: % = (w₁p₁ + w₂p₂ + ...) ÷ (w₁ + w₂ + ...).

Cost Price Selling

Selling an item at its Cost Price (CP) implies there is no profit and no loss (0% change).

Fractional Parts Calculation

Always ensure the sum of all fractional parts equals 1 (e.g., 1/3 + 1/4 + 5/12 = 12/12 = 1).

Shortcut Trick

Let the HCF of the three numbers be x.

The numbers are then 3x, 7x, and 2x.

LCM of (3x, 7x, 2x) = x × LCM(3, 7, 2) = x × 42.

Given, 42x = 8820.

x = 8820 ÷ 42 = 210.

∴ The correct answer is 210.

Alternate Method

Given:

Ratio of three numbers = 3 : 7 : 2

LCM of the numbers = 8820

Formula Used:

If numbers are in the ratio a : b : c, then the numbers can be represented as ax, bx, and cx, where x is their HCF.

The LCM of these numbers = x × LCM(a, b, c).

Calculations:

⇒ Let the numbers be 3x, 7x, and 2x.

⇒ LCM(3, 7, 2) = 3 × 7 × 2 = 42 (as they are co-prime).

⇒ LCM of (3x, 7x, 2x) = 42x.

⇒ 42x = 8820.

⇒ x = 8820 ÷ 42.

⇒ x = 210.

∴ The correct answer is 210.

Additional Information

HCF (Highest Common Factor)

The greatest number that divides two or more numbers without leaving a remainder.

LCM (Least Common Multiple)

The smallest non-zero number that is a multiple of two or more numbers.

Product Rule for Two Numbers

For any two numbers A and B: A × B = HCF(A, B) × LCM(A, B).

Co-prime Numbers

Two or more numbers are co-prime if their HCF is 1. Their LCM is simply the product of the numbers.

Shortcut Trick

Effective Interest Rate for 2 years at 4% = 4 + 4 + (4 × 4)/100 = 8.16%.

Given that 8.16% of the Principal (y) = ₹765.

The Total Amount (A) percentage = 100% + 8.16% = 108.16%.

⇒ Amount = (765 ÷ 8.16) × 108.16

⇒ Amount = 93.75 × 108.16 = ₹10,140.

∴ The correct answer is ₹10,140.

Alternate Method

Given: Principal (P) = ₹y, Rate (R) = 4% p.a., Time (n) = 2 years, Compound Interest (CI) = ₹765.

Formula Used: CI = P[(1 + R/100)ⁿ − 1] and Amount (A) = P + CI

⇒ 765 = y[(1 + 4/100)² − 1]

⇒ 765 = y[(1 + 1/25)² − 1]

⇒ 765 = y[(26/25)² − 1]

⇒ 765 = y[676/625 − 1]

⇒ 765 = y[(676 − 625)/625]

⇒ 765 = y[51/625]

⇒ y = (765 × 625) ÷ 51

⇒ y = 15 × 625 = ₹9,375

⇒ Amount (A) = Principal (y) + CI

⇒ A = 9,375 + 765 = ₹10,140

∴ The correct answer is ₹10,140.

Additional Information

Compound Interest Formula

The amount A is calculated as A = P(1 + r/100)ⁿ, where P is principal, r is rate, and n is time.

Effective Rate for 2 Years

The net percentage interest for two years is given by x + y + (xy/100), where x and y are annual rates.

Difference between CI and SI

For 2 years, the difference between Compound Interest and Simple Interest is P(R/100)².

Shortcut Trick

Net percentage change = a + b + (ab ÷ 100)

Here, a = +12% and b = −10%

Net change = 12 − 10 + (12 × (−10) ÷ 100) = 2 − 1.2 = 0.8%

Given, 0.8% increase = ₹1,584

Original Salary (100%) = (1,584 ÷ 0.8) × 100 = 1,980 × 100 = ₹1,98,000

∴ The correct answer is ₹1,98,000.

Alternate Method

Given:

First year revision = increased by 12%

Second year revision = decreased by 10%

Increase in original monthly salary = ₹1,584

Formula Used:

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

Calculations:

Let Sangeeta's salary be ₹x.

⇒ Salary after 1st year = x × (112 ÷ 100) = 1.12x

⇒ Salary after 2nd year = 1.12x × (90 ÷ 100) = 1.008x

⇒ Total increase in salary = 1.008x − x = 0.008x

⇒ 0.008x = 1,584

⇒ x = 1,584 ÷ 0.008

⇒ x = 1,584,000 ÷ 8

⇒ x = 1,98,000

∴ The correct answer is ₹1,98,000.

Additional Information

Successive Percentage Change

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

Multiplying Factor Method

For an increase of r%, the factor is (1 + r/100). For a decrease, the factor is (1 − r/100). Final value = Initial value × Factor₁ × Factor₂.

Base Value Property

Percentage changes are always calculated on the preceding value in a series of successive changes, not on the original base value each time.

Shortcut Trick

Convert science-to-total ratios into decimals to compare proportions:

Batch A: 5 ÷ (5 + 8) = 5/13 ≈ 0.3846

Batch B: 7 ÷ (7 + 11) = 7/18 ≈ 0.3888

Batch C: 3 ÷ (3 + 5) = 3/8 = 0.3750

Since 0.3888 > 0.3846 > 0.3750, Batch B has the highest proportion.

∴ The correct answer is Batch B.

Alternate Method

Given:

Ratio of Science to Arts students:

Batch A = 5 : 8 | Batch B = 7 : 11 | Batch C = 3 : 5

Formula Used:

Proportion of Science students = Science ÷ (Science + Arts)

Calculations:

⇒ Batch A proportion = 5 / (5 + 8) = 5/13

⇒ Batch B proportion = 7 / (7 + 11) = 7/18

⇒ Batch C proportion = 3 / (3 + 5) = 3/8

⇒ Comparing 5/13 and 7/18 by cross-multiplication: 5 × 18 = 90 and 7 × 13 = 91. Since 91 > 90, Batch B > Batch A.

⇒ Comparing 7/18 and 3/8 by cross-multiplication: 7 × 8 = 56 and 3 × 18 = 54. Since 56 > 54, Batch B > Batch C.

⇒ Batch B has the highest proportion of science students.

∴ The correct answer is Batch B.

Additional Information

Ratio to Proportion Conversion

If the ratio of two components is a:b, the proportion of the first component in the total is given by a/(a+b).

Comparing Fractions Shortcut

To compare a/b and c/d without division, compare the products (a × d) and (b × c). If ad > bc, then a c/d.

Percentage Share

The percentage share of a component is (Value / Total) × 100, which is useful for comparing proportions across different group sizes.

Shortcut Trick

Let Marked Price (MP) = 100 units.

Cost Price (CP) = 100 − 20% = 80 units.

Selling Price (SP) = 80 + 40% of 80 = 112 units.

Difference (SP − MP) = 112 − 100 = 12 units → ₹10.

Marked Price = (10 ÷ 12) × 100 = 1000 ÷ 12 = 83.33.

∴ The correct answer is ₹83.33.

Alternate Method

Given:

Discount on Marked Price = 20%

Selling Price (SP) = Marked Price (MP) + ₹10

Profit Percentage = 40%

⇒ Let the Marked Price be x.

⇒ Cost Price (CP) = x − 20% of x = 0.8x.

⇒ Selling Price (SP) = x + 10.

⇒ Profit = SP − CP = (x + 10) − 0.8x = 0.2x + 10.

⇒ Profit Percentage = (Profit ÷ CP) × 100

⇒ 40 = [(0.2x + 10) ÷ 0.8x] × 100

⇒ 0.40 = (0.2x + 10) ÷ 0.8x

⇒ 0.32x = 0.2x + 10

⇒ 0.12x = 10

⇒ x = 10 ÷ 0.12 = 83.333...

∴ The correct answer is ₹83.33.

Additional Information

Relationship between CP and MP

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

Successive Discounts

Two successive discounts of a% and b% are equivalent to a single discount of [a + b − (a × b)/100]%.

Mark-up Percentage

Mark-up % = [(MP − CP) ÷ CP] × 100. It represents how much more the Marked Price is compared to the Cost Price.

Shortcut Trick

Total Work (LCM of 12 and 39) = 156 units.

Efficiencies: A = 13, B = 4.

Work done by (A + B) in 4 days = (13 + 4) × 4 = 68 units.

Remaining work = 156 − 68 = 88 units.

Time taken by B = 88 ÷ 4 = 22 days.

∴ The correct answer is 22 days.

Alternate Method

Given:

Time taken by A = 12 days

Time taken by B = 39 days

Formula Used:

Efficiency = Total Work ÷ Time

Remaining Work = Total Work − Work Completed

Calculations:

⇒ Total efficiency of A and B = 13 + 4 = 17 units/day

⇒ Work done by A and B together in 4 days = 17 × 4 = 68 units

⇒ Remaining work to be done = 156 − 68 = 88 units

⇒ A leaves, so B completes the 88 units of work.

⇒ Time taken by B = 88 ÷ 4 = 22 days

∴ The correct answer is 22 days.

Additional Information

Pipes & Cisterns

Similar logic applies to pipes where inlet pipes have positive efficiency and outlet pipes have negative efficiency.

Work & Wages

Wages are distributed among workers in the ratio of their efficiency or the total work done by each.

Alternate Day Work

When people work on alternate days, calculate the work done in one complete cycle (e.g., 2 days) to find the total time.

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete the work (Efficiency ∝ 1 ÷ Time).

Shortcut Trick

Total interest percentage for 3 years = 7.5% × 3 = 22.5%

Total Amount percentage = 100% (Principal) + 22.5% (Interest) = 122.5%

Amount = 122.5% of ₹8,000

Amount = 1.225 × 8000 = ₹9,800

∴ The correct answer is ₹9800.

Alternate Method

Given:

Principal (P) = ₹8,000

Rate of Interest (R) = 7.5% per annum

Time (T) = 3 years

Formula Used:

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

Amount (A) = Principal (P) + Simple Interest (SI)

Calculations:

⇒ SI = (8000 × 7.5 × 3) ÷ 100

⇒ SI = 80 × 22.5

⇒ SI = ₹1,800

⇒ Amount = 8000 + 1800

⇒ Amount = ₹9,800

∴ The correct answer is ₹9800.

Additional Information

Simple Interest Concept

Simple Interest is calculated only on the initial principal amount throughout the entire period. SI = P × R × T / 100.

Amount in SI

The total value after adding interest to the principal is called the Amount. A = P(1 + RT/100).

SI vs CI Difference

For the first year, SI and Compound Interest (CI) are equal if interest is compounded annually. From the second year, CI > SI because interest is earned on interest.

Shortcut Trick

Convert the given target ratio 3:2 into decimal form: 3 ÷ 2 = 1.5.

Check the decimal values of the options:

60/45 ≈ 1.33 | 45/20 = 2.25 | 35/25 = 1.4 | 120/80 = 1.5.

Since 120/80 matches the decimal value 1.5, it is equivalent to 3:2.

∴ The correct answer is 120:80.

Alternate Method

Given: Target Ratio = 3 : 2

Formula Used: Simplest form of a ratio is obtained by dividing both terms by their Highest Common Factor (HCF).

⇒ Option 1: 60 : 45 (HCF = 15) ⇒ (60 ÷ 15) : (45 ÷ 15) = 4 : 3

⇒ Option 2: 45 : 20 (HCF = 5) ⇒ (45 ÷ 5) : (20 ÷ 5) = 9 : 4

⇒ Option 3: 35 : 25 (HCF = 5) ⇒ (35 ÷ 5) : (25 ÷ 5) = 7 : 5

⇒ Option 4: 120 : 80 (HCF = 40) ⇒ (120 ÷ 40) : (80 ÷ 40) = 3 : 2

∴ The correct answer is 120:80.

Additional Information

Simplest Form of Ratio

A ratio a:b is in its simplest form if the HCF of a and b is 1. To simplify, divide both terms by their common factors.

Equivalent Ratios

Ratios that represent the same relationship between numbers are called equivalent ratios. They can be found by multiplying or dividing both terms by the same non-zero number.

Proportion

When two ratios are equal, they are said to be in proportion. For a:b = c:d, the product of extremes (a×d) equals the product of means (b×c).

Shortcut Trick

In a 30°−60°−90° right-angled triangle, the sides are in the ratio 1 : √3 : 2.

The base (adjacent to 60°) corresponds to 1 unit.

Given, 1 unit = 15 m.

The ladder (hypotenuse) corresponds to 2 units.

Length of ladder = 2 × 15 = 30 m.

∴ The correct answer is 30 m.

Alternate Method

Given:

Angle of elevation of the ladder with the ground (θ) = 60°

Distance of the foot of the ladder from the wall (Base) = 15 m

Formula Used:

In a right-angled triangle, cos θ = Base / Hypotenuse

Calculations:

Let the length of the ladder be L.

⇒ cos 60° = 15 / L

⇒ 1 / 2 = 15 / L

⇒ L = 15 × 2

⇒ L = 30 m

∴ The correct answer is 30 m.

Additional Information

Trigonometric Ratios

Fundamental ratios in a right triangle: sin θ = P/H, cos θ = B/H, and tan θ = P/B (where P = Perpendicular, B = Base, H = Hypotenuse).

Standard Values of Cosine

Common values include cos 0° = 1, cos 30° = √3/2, cos 45° = 1/√2, cos 60° = 1/2, and cos 90° = 0.

Pythagoras Theorem

In any right-angled triangle, the relationship between the sides is given by H² = P² + B².

30-60-90 Triangle Rule

For a triangle with angles 30°, 60°, and 90°, the side lengths are always in the ratio x : x√3 : 2x.

Shortcut Trick

When Distance is constant, Speed is inversely proportional to Time.

Ratio of Time = 5 : 6 → Ratio of Speed = 6 : 5.

Original Speed = 300 ÷ 5 = 60 km/h.

Here, 6 units = 60 km/h ⇒ 1 unit (change) = 10 km/h.

Since the ratio decreases from 6 to 5, the speed decreases.

∴ The correct answer is 10 km/h decrease.

Alternate Method

Given:

Distance (D) = 300 km

Initial Time (T₁) = 5 hr

New Time (T₂) = 6 hr

Formula Used:

Speed (S) = Distance (D) ÷ Time (T)

Calculations:

⇒ Initial Speed (S₁) = 300 ÷ 5 = 60 km/h

⇒ New Speed (S₂) = 300 ÷ 6 = 50 km/h

⇒ Change in Speed = Initial Speed − New Speed

⇒ Change = 60 − 50 = 10 km/h

⇒ Since the new speed is lower, there is a decrease of 10 km/h.

∴ The correct answer is 10 km/h decrease.

Additional Information

Speed-Time Relation

For a fixed distance, Speed and Time are inversely proportional. If time increases by a certain factor, speed must decrease by the same factor to cover the same distance.

Average Speed

Average Speed is calculated as the Total Distance divided by the Total Time taken for the entire journey. Formula: Average Speed = (Total Distance) ÷ (Total Time).

Unit Conversion

To convert Speed from km/h to m/s, multiply the value by 5/18. To convert from m/s to km/h, multiply the value by 18/5.

Shortcut Trick

A number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places is 0 or a multiple of 11.

Check 3,762: (2 + 7) − (6 + 3) = 9 − 9 = 0.

Since the result is 0, the number 3,762 is divisible by 11.

∴ The correct answer is 3,762.

Alternate Method

Given: Numbers are 3,762, 7,393, 4,915, and 6,184.

Divisibility Rule of 11: Let the digits of a number be checked from right to left. The difference (Sum of digits at positions 1, 3, 5...) − (Sum of digits at positions 2, 4, 6...) must be 0, 11, 22, etc.

⇒ For 3,762: (2 + 7) − (6 + 3) = 9 − 9 = 0 (Divisible)

⇒ For 7,393: (3 + 3) − (9 + 7) = 6 − 16 = −10 (Not divisible)

⇒ For 4,915: (5 + 9) − (1 + 4) = 14 − 5 = 9 (Not divisible)

⇒ For 6,184: (4 + 1) − (8 + 6) = 5 − 14 = −9 (Not divisible)

∴ The correct answer is 3,762.

Additional Information

Divisibility by 3 and 9

A number is divisible by 3 or 9 if the sum of its digits is divisible by 3 or 9, respectively.

Divisibility by 4

A number is divisible by 4 if the last two digits of the number are divisible by 4.

Divisibility by 8

A number is divisible by 8 if the last three digits of the number are divisible by 8.

Shortcut Trick

Check if the sum of terms is zero: 23 + (−14) + (−9) = 23 − 23 = 0.

Apply the Algebraic Identity: If a + b + c = 0, then a³ + b³ + c³ = 3abc.

Calculation: 3 × 23 × (−14) × (−9) = 3 × 23 × 126.

Result: 69 × 126 = 8694.

∴ The correct answer is 8694.

Alternate Method

Given:

a = 23

b = −14

c = −9

Formula Used:

a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)

Calculations:

⇒ First, evaluate the sum (a + b + c):

⇒ 23 + (−14) + (−9) = 23 − 14 − 9 = 0

⇒ Since the sum is zero, the right side of the identity becomes zero.

⇒ a³ + b³ + c³ − 3abc = 0 × (a² + b² + c² − ab − bc − ca) = 0

⇒ a³ + b³ + c³ = 3abc

⇒ Substitute the values: 3 × 23 × (−14) × (−9)

⇒ 3 × 23 × 126

⇒ 69 × 126 = 8694

∴ The correct answer is 8694.

Additional Information

Conditional Algebraic Identity

The identity a³ + b³ + c³ = 3abc holds true if and only if a + b + c = 0 or a = b = c.

General Expansion

The expression a² + b² + c² − ab − bc − ca can be rewritten as 1/2[(a−b)² + (b−c)² + (c−a)²], which is always non-negative for real numbers.

Trinomial Square

Another useful identity is (a + b + c)² = a² + b² + c² + 2(ab + bc + ca).

Shortcut Trick

Surface area of a sphere = π × d²

Area = 3.14 × 10 × 10 = 314 m²

Total cost = Area × rate = 314 × 5

∴ The correct answer is ₹1570.

Alternate Method

Given: Internal Diameter (d) = 10 m, Rate of coating = ₹5 per m², π = 3.14

Formula Used: Surface Area of a Sphere = 4πr²; Total Cost = Area × Rate

Calculations:

⇒ Radius (r) = Diameter ÷ 2 = 10 ÷ 2 = 5 m

⇒ Internal Surface Area = 4 × 3.14 × (5)²

⇒ Area = 4 × 3.14 × 25

⇒ Area = 100 × 3.14 = 314 m²

⇒ Total Cost = 314 × 5

⇒ Total Cost = ₹1570

∴ The correct answer is ₹1570.

Additional Information

Volume of a Sphere

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.

Hemisphere Surface Area

For a hemisphere, the Curved Surface Area (CSA) is 2πr² and the Total Surface Area (TSA) is 3πr².

Surface Area in terms of Diameter

The total surface area of a sphere can also be written as πd², which often simplifies calculations when the diameter is known.

Shortcut Trick

Use the Ratio Method for successive changes:

Year 2015 (10% increase): 10 → 11

Year 2016 (15% decrease): 20 → 17 (since 15% = 3/20)

Overall Ratio: (10 × 20) : (11 × 17) = 200 : 187

Given final value: 187 units = 1,87,000 ⇒ 1 unit = 1,000

Initial Population = 200 × 1,000 = 2,00,000

∴ The correct answer is 2,00,000.

Alternate Method

Let the Initial Population in the beginning of 2015 be P.

⇒ Population after 10% increase in 2015 = P × (1 + 10/100) = 1.1P

⇒ Population after 15% decrease in 2016 = 1.1P × (1 − 15/100)

⇒ Population at the end of 2016 = 1.1P × 0.85 = 0.935P

⇒ According to the question: 0.935P = 1,87,000

⇒ P = 1,87,000 ÷ 0.935

⇒ P = (1,87,000 × 1,000) ÷ 935

⇒ P = 200 × 1,000 = 2,00,000

∴ The correct answer is 2,00,000.

Additional Information

Successive Percentage Change Formula

For two successive changes of a% and b%, the effective net change is [a + b + (a × b)/100]%. Use positive for increase and negative for decrease.

Multiplier Method

Final Value = Initial Value × (1 ± r₁/100) × (1 ± r₂/100). This is widely used in population growth and depreciation problems.

Population Growth

If the population increases at a constant rate r% per annum, the population after n years is P(1 + r/100)ⁿ.

Shortcut Trick

In an isosceles triangle, angles opposite to equal sides are equal.

Given XY = XZ, therefore the base angles ∠Y = ∠Z.

Sum of angles in a triangle = 180°.

∠X + 2 × ∠Z = 180° ⇒ 40° + 2 × ∠Z = 180°.

2 × ∠Z = 140° ⇒ ∠Z = 70°.

∴ The correct answer is 70°.

Alternate Method

Given:

In ΔXYZ, XY = XZ and vertex angle ∠X = 40°.

Formula Used:

1. Isosceles Triangle Property: Angles opposite to equal sides are equal.
2. Angle Sum Property: The sum of all interior angles of a triangle is 180°.

Calculations:

⇒ In ΔXYZ, since XY = XZ, it is an isosceles triangle.

⇒ ∠Y = ∠Z (Property of isosceles triangles)

⇒ ∠X + ∠Y + ∠Z = 180° (Angle sum property)

⇒ 40° + ∠Z + ∠Z = 180°

⇒ 40° + 2 × ∠Z = 180°

⇒ 2 × ∠Z = 180° − 40°

⇒ 2 × ∠Z = 140°

⇒ ∠Z = 140° ÷ 2

⇒ ∠Z = 70°

∴ The correct answer is 70°.

Additional Information

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent (Equal sides ↔ Equal angles).

Triangle Angle Sum Theorem

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

Exterior Angle Property

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

Shortcut Trick

Marked Price per pair = ₹2800.

Discounted Price (DP) per pair = 82% of 2800 = ₹2296.

Special offer allows 5 pairs at full DP and 2 pairs at 50% DP (which is 1 pair at full DP).

Total effective cost for 7 pairs = (5 + 1) × 2296 = 6 × 2296.

Total Cost = ₹13,776.

∴ The correct answer is ₹13,776.

Alternate Method

Given:

Marked Price (MP) of a pair of shoes = ₹2800

Trade Discount = 18%

Quantity 1 = 5 pairs at discounted price

Quantity 2 = 2 pairs at 50% of discounted price

Formula Used:

Discounted Price = MP × (100 − Discount%) / 100

Total Cost = (Quantity₁ × Price₁) + (Quantity₂ × Price₂)

Calculations:

⇒ Trade Discount amount = 18% of 2800 = 0.18 × 2800 = ₹504

⇒ Discounted Price (DP) per pair = 2800 − 504 = ₹2296

⇒ Cost of first 5 pairs = 5 × 2296 = ₹11,480

⇒ Cost of next 2 pairs = 2 × (50% of 2296) = 2 × 1148 = ₹2,296

⇒ Total Cost for 7 pairs = 11480 + 2296 = ₹13,776

∴ The correct answer is ₹13,776.

Additional Information

Marked Price and Selling Price

Selling Price (SP) is calculated as MP − Discount. If multiple items have different discounts, the total SP is the sum of individual SPs.

Successive Discounts

When two discounts d₁% and d₂% are applied successively, the effective discount is (d₁ + d₂ − (d₁×d₂)/100)%.

Trade Discount vs Cash Discount

Trade discount is given on the list price at the time of sale, while cash discount is offered for immediate or early payment.

Shortcut Trick

Direct calculation: Age of A = 2 × (Age of B) + 5

Given Person B is 15 years old.

Age of Person A = (2 × 15) + 5 = 30 + 5

Age of Person A = 35 years

∴ The correct answer is 35 years.

Alternate Method

Given:

Present age of Person B = 15 years

Present age of Person A = 5 years more than twice the age of Person B

Formula Used:

Age_A = (2 × Age_B) + 5

Calculations:

⇒ Age of Person B = 15 years

⇒ Twice the age of Person B = 2 × 15 = 30 years

⇒ Age of Person A = 30 + 5

⇒ Age of Person A = 35 years

∴ The correct answer is 35 years.

Additional Information

Linear Equations in Age Problems

Age relations such as 'twice as old' or 'n years older' are formulated as linear equations (y = mx + c) where m is the multiplier and c is the constant difference.

Constant Difference Rule

The difference between the ages of two individuals always remains constant, regardless of the number of years that pass.

Ratio Method

For complex age problems, ratios are used by finding a common multiplier (k) to satisfy the given conditions for different time periods.

Shortcut Trick

Break the expression into three parts using the VBODMAS rule.

Part 1: {(16/36) ÷ (16/4)} = (4/9) ÷ 4 = 1/9.

Part 2: ((2/7) × (14/6) + 5/12) = (2/3 + 5/12) = 13/12.

Part 3: (4/7) ÷ (39/12 of 12/7) = (4/7) ÷ (39/7) = 4/39.

Final: (1/9 ÷ 13/12) + 4/39 = (1/9 × 12/13) + 4/39 = 4/39 + 4/39 = 8/39.

∴ The correct answer is 8/39.

Alternate Method

Given: {(16/36) ÷ (16/4)} ÷ ((2/7) × (14/6) + (5/12)) + (4/7) ÷ (39/12) of (12/7)

Formula Used: Order of operations follows VBODMAS (Vinculum, Brackets, Of, Division, Multiplication, Addition, Subtraction).

⇒ Simplify first bracket: (16/36) ÷ (16/4) = 4/9 ÷ 4 = 4/9 × 1/4 = 1/9

⇒ Simplify inner part of second group: (2/7 × 14/6) = 2/7 × 7/3 = 2/3

⇒ Complete second bracket: 2/3 + 5/12 = 8/12 + 5/12 = 13/12

⇒ Simplify Of operation: (39/12) of (12/7) = 39/12 × 12/7 = 39/7

⇒ Remaining expression: (1/9 ÷ 13/12) + (4/7 ÷ 39/7)

⇒ Perform divisions: (1/9 × 12/13) + (4/7 × 7/39) = 4/39 + 4/39

⇒ Final Addition: 8/39

∴ The correct answer is 8/39.

Additional Information

The VBODMAS Rule

It ensures mathematical consistency by prioritizing Brackets then Of (which is a form of multiplication) over Division and Multiplication.

Fraction Division

Dividing by a fraction is equivalent to multiplying by its reciprocal (inverted form): a/b ÷ c/d = a/b × d/c.

Common Denominators

When adding fractions like 2/3 and 5/12, find the LCM of denominators (12) to create a common base before adding numerators.

Shortcut Trick

Identify common base 5 and use the Net Power rule.

Net Power = (Power of term 1 + Power of term 2) − Power of denominator.

Calculation: [3x + 2(x − 1)] − (4x − 1).

⇒ (3x + 2x − 2) − 4x + 1 = 5x − 2 − 4x + 1 = x − 1.

The resulting expression is 5^x-1.

∴ The correct answer is 5^x-1.

Alternate Method

Given: [5^3x × (5²)^(x-1)] ÷ 5^4x-1

Formula Used: (a^m)ⁿ = a^m×n | a^m × aⁿ = a^m+n | a^m ÷ aⁿ = a^m−n

Step-by-step Simplification:

⇒ [5^3x × 5^2(x-1)] ÷ 5^4x-1

⇒ [5^3x × 5^2x-2] ÷ 5^4x-1

⇒ 5^{(3x + 2x − 2)} ÷ 5^4x-1

⇒ 5^{(5x − 2)} ÷ 5^4x-1

⇒ 5^{(5x − 2) − (4x − 1)}

⇒ 5^{5x − 2 − 4x + 1}

⇒ 5^{x − 1}

∴ The correct answer is 5^x-1.

Additional Information

Product and Quotient Laws

When multiplying terms with the same base, add their exponents (a^m × aⁿ = a^m+n). When dividing, subtract them (a^m ÷ aⁿ = a^m−n).

Power of a Power Rule

Raising a power to another power requires multiplying the exponents: (a^m)ⁿ = a^m×n.

Negative Exponents

Any non-zero base raised to a negative power is the reciprocal: a⁻ⁿ = 1/aⁿ.

Zero Exponent Rule

Any non-zero base raised to the power of zero is always 1: a⁰ = 1.

Shortcut Trick

Identify the increase in average: 25,500 − 24,000 = ₹1,500.

Income of new employee = New average + (Initial number of employees × Increase in average).

Income = 25,500 + (6 × 1,500) = 25,500 + 9,000 = ₹34,500.

∴ The correct answer is ₹34,500.

Alternate Method

Given:

Initial number of employees = 6 | Initial average income = ₹24,000

Final number of employees = 7 | Final average income = ₹25,500

Formula Used:

Total Income = Average Income × Number of Employees

Calculations:

⇒ Total monthly income of 6 employees = 6 × 24,000 = ₹1,44,000

⇒ Total monthly income of 7 employees = 7 × 25,500 = ₹1,78,500

⇒ Monthly income of the new employee = Total (7 employees) − Total (6 employees)

⇒ Monthly income = 1,78,500 − 1,44,000 = ₹34,500

∴ The correct answer is ₹34,500.

Additional Information

Net Deviation Concept

The sum of deviations of all observations from their arithmetic mean is always zero.

Weighted Average

When two groups are combined, the combined average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Inclusion and Exclusion

If adding a new member increases the average, the new member's value is higher than the original average.

Shortcut Trick

Divisor = 5 × Remainder = 5 × 56 = 280

Quotient = Divisor ÷ 14 = 280 ÷ 14 = 20

Dividend = (Divisor × Quotient) + Remainder

Dividend = (280 × 20) + 56 = 5600 + 56 = 5656

∴ The correct answer is 5656.

Alternate Method

Given:

Remainder (r) = 56

Divisor (d) = 5 × Remainder

Divisor (d) = 14 × Quotient (q)

Formula Used:

Dividend = (Divisor × Quotient) + Remainder

Calculations:

⇒ Divisor = 5 × 56 = 280

⇒ 14 × Quotient = 280

⇒ Quotient = 280 ÷ 14 = 20

⇒ Dividend = (280 × 20) + 56

⇒ Dividend = 5600 + 56

⇒ Dividend = 5656

∴ The correct answer is 5656.

Additional Information

Division Algorithm

For any two whole numbers, the dividend is always equal to the product of the divisor and quotient plus the remainder.

Remainder Property

The remainder must always be greater than or equal to 0 and strictly less than the divisor (0 ≤ r < d).

Euclid's Division Lemma

It states that for any two positive integers a and b, there exist unique integers q and r such that a = bq + r.

Shortcut Trick

The ratio of surface areas of two spheres is equal to the square of the ratio of their radii.

Radius of Sphere A : Radius of Sphere B = 6 : 3 = 2 : 1

Surface Area Ratio = (2)² : (1)² = 4 : 1

∴ The correct answer is 4:1.

Alternate Method

Given:

Radius of Sphere A (r₁) = 6 cm

Radius of Sphere B (r₂) = 3 cm

Formula Used:

Surface Area (S) of a sphere = 4πr²

Calculations:

⇒ Surface Area of Sphere A (S₁) = 4 × π × (6)²

⇒ S₁ = 4 × π × 36 = 144π cm²

⇒ Surface Area of Sphere B (S₂) = 4 × π × (3)²

⇒ S₂ = 4 × π × 9 = 36π cm²

⇒ Ratio = S₁ : S₂ = 144π : 36π

⇒ Ratio = 144 / 36 = 4 / 1

∴ The correct answer is 4:1.

Additional Information

Volume of a Sphere

The volume (V) of a sphere is given by the formula V = (4/3)πr³.

Ratio of Volumes

The ratio of the volumes of two spheres is equal to the cube of the ratio of their radii: V₁/V₂ = (r₁/r₂)³.

Hemisphere Properties

For a hemisphere, the Curved Surface Area = 2πr² and the Total Surface Area = 3πr².

Shortcut Trick

Summing both conditions: (8 + 5) Mangoes + (5 + 8) Oranges = 164 + 148

⇒ 13 (Mangoes + Oranges) = ₹312

⇒ 1 (Mango + Orange) = 312 ÷ 13 = ₹24

⇒ 3 (Mangoes + Oranges) = 3 × 24 = ₹72

∴ The correct answer is ₹72.

Alternate Method

Given:

Cost of 8 mangoes and 5 oranges = ₹164

Cost of 5 mangoes and 8 oranges = ₹148

Formula Used:

Symmetrical Linear Equations: Add equations when coefficients are interchanged.

Calculations:

⇒ Let cost of 1 mango be M and 1 orange be O.

⇒ 8M + 5O = 164 --- (Equation 1)

⇒ 5M + 8O = 148 --- (Equation 2)

⇒ Adding Eq(1) and Eq(2): (8M + 5M) + (5O + 8O) = 164 + 148

⇒ 13M + 13O = 312

⇒ 13(M + O) = 312

⇒ M + O = 312 ÷ 13 = 24

⇒ Cost of 3 mangoes and 3 oranges = 3 × (M + O)

⇒ 3 × 24 = 72

∴ The correct answer is ₹72.

Additional Information

Linear Equations in Two Variables

Equations expressed in the form ax + by = c, where a and b are coefficients and c is a constant.

Symmetrical Coefficients Property

When coefficients are interchanged (ax + by = m and bx + ay = n), adding them directly gives a simplified value for (x + y).

Unitary Method

A problem-solving technique where you first find the value of a single unit and then multiply it by the required quantity.

Shortcut Trick

In a distribution with two values, the mean acts as the balance point.

Difference between first value (10) and mean (12.5) = 12.5 − 10 = 2.5

Difference between second value (15) and mean (12.5) = 15 − 12.5 = 2.5

Since the deviations are equal in magnitude (2.5), the frequencies must also be equal.

Given first frequency = 5, therefore p = 5.

∴ The correct answer is 5.

Alternate Method

Given:

Mean (χ) = 12.5

Values (x_i): 10, 15

Frequencies (f_i): 5, p

Formula Used:

Arithmetic Mean (χ) = ∑f_ix_i ÷ ∑f_i

Calculations:

⇒ 12.5 = (10 × 5 + 15 × p) ÷ (5 + p)

⇒ 12.5 × (5 + p) = 50 + 15p

⇒ 62.5 + 12.5p = 50 + 15p

⇒ 62.5 − 50 = 15p − 12.5p

⇒ 12.5 = 2.5p

⇒ p = 12.5 ÷ 2.5

⇒ p = 5

∴ The correct answer is 5.

Additional Information

Properties of Arithmetic Mean

The algebraic sum of deviations of a set of observations from their arithmetic mean is always zero. ∑f_i(x_i − χ) = 0.

Weighted Average Formula

When different values have different importance or frequency, the weighted mean is calculated as χ_w = (w₁x₁ + w₂x₂ + ... + w_nx_n) ÷ (w₁ + w₂ + ... + w_n).

Change of Origin and Scale

If every observation is increased by 'a', the mean increases by 'a'. If every observation is multiplied by 'k', the mean is multiplied by 'k'.

Shortcut Trick

The Third Proportional of a and b is calculated as b² ÷ a.

First, find m: m = (20 × 20) ÷ 4 = 100.

Then, find n: n = (50 × 50) ÷ 100 = 25.

∴ The correct answer is 25.

Alternate Method

Given:

First pair: 4, 20 and m are in continuous proportion.

Second pair: m, 50 and n are in continuous proportion.

Formula Used:

If a, b, c are in continuous proportion, then a : b = b : c ⇒ c = b² ÷ a.

Calculations:

⇒ For the first set: 4 : 20 = 20 : m

⇒ m = (20 × 20) ÷ 4

⇒ m = 400 ÷ 4 = 100

⇒ For the second set: 100 : 50 = 50 : n

⇒ n = (50 × 50) ÷ 100

⇒ n = 2500 ÷ 100 = 25

∴ The correct answer is 25.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is calculated as √(a × b).

Fourth Proportional

If four numbers a, b, c, and d are in proportion (a : b :: c : d), then the fourth proportional d = (b × c) ÷ a.

Continued Proportion

Three numbers are in continued proportion if the ratio of the first to the second is equal to the ratio of the second to the third (a/b = b/c).

The correct answer is West Bengal.

Key Points

• In India, particularly in states like West Bengal, Assam, and Odisha, the prevailing climatic conditions allow for the cultivation of three distinct crops of rice within a single agricultural year.
• The three varieties are identified based on their seasonal cycles and are locally named Aus, Aman, and Boro.
• Aman is the primary winter rice crop. It is typically sown during the onset of the Southwest Monsoon in June and July and harvested between November and December. It occupies the largest portion of the total rice area in the state.
• Aus is referred to as autumn rice. It is sown during the pre-monsoon period in May and June and harvested in the autumn months of September and October.
• Boro is known as summer rice. This variety is sown in the winter (November to January) and harvested in the summer (April to May). Its cultivation is heavily reliant on assured irrigation facilities during the dry season.
• The fertile alluvial soil and the hot, humid climate of the lower Gangetic plains in West Bengal provide the ideal environment for this intensive cropping pattern.

 Additional Information

• Rice (Oryza sativa):
• It is the staple food crop for a significant majority of India’s population and is primarily a Kharif crop.
• Growth requires high temperatures (above 25°C), high humidity, and annual rainfall exceeding 100 cm.
• West Bengal is consistently among the top producers of rice in India, contributing significantly to the national food security.
• Geographical Context of Other Options:
• In Manipur and Nagaland, rice is often grown using Jhum (shifting) cultivation or terrace farming in hilly terrains, where a single crop is more common due to topographical constraints.
• While Bihar is a major rice producer, the specific nomenclature and systematic triple-cropping of Aus, Aman, and Boro are most traditionally associated with the Bengal delta region.

The correct answer is Indian Statistical Institute (ISI).

Key Points

• The Ministry of Statistics and Programme Implementation (MoSPI) has introduced a draft bill to amend the Indian Statistical Institute Act, 1959, aiming to modernize the governance and administrative framework of the Indian Statistical Institute (ISI).
• The Indian Statistical Institute was established by the legendary statistician Prasanta Chandra Mahalanobis on December 17, 1931, and was later declared an Institution of National Importance by an Act of Parliament in 1959.
• As the institute approaches its centenary year in 2031, the government seeks to restructure its organizational hierarchy to enhance efficiency and accountability in its academic and research pursuits.
• A significant proposal in the draft bill includes the redesignation of the head of the institute from Director to Director General, bringing it in line with the leadership structure of other elite scientific and research organizations in India.
• The proposed legislation also focuses on reforming the ISI Council, which is the apex governing body, to improve the decision-making process and integrate modern management practices within the premier statistical body.

 Additional Information

• National Sample Survey Office (NSSO) and Central Statistics Office (CSO):
• The NSSO was previously responsible for conducting large-scale nationwide sample surveys on various socio-economic aspects.
• The CSO was the nodal agency for coordinating statistical activities and preparing National Accounts, including Gross Domestic Product (GDP) estimates.
• In May 2019, the Government of India merged the NSSO and the CSO to form a unified National Statistical Office (NSO) under the MoSPI.
• Ministry of Statistics & Programme Implementation (MoSPI):
• This ministry consists of two wings: the Statistics Wing (NSO) and the Programme Implementation Wing.
• It is responsible for the release of key economic indicators such as the Index of Industrial Production (IIP) and the Consumer Price Index (CPI).
• The ministry also monitors the progress of Central Sector Projects costing 150 crore rupees and above.

The correct answer is Puducherry.

Key Points

• The Government of Union Territories Act, 1963 was enacted by the Parliament to provide for Legislative Assemblies and Councils of Ministers for certain Union Territories (UTs).
• This Act was a direct consequence of the 14th Constitutional Amendment Act, 1962, which introduced Article 239A to the Indian Constitution, allowing Parliament to create a local legislature for UTs.
• Puducherry (then Pondicherry) was officially granted its own legislature through this Act in 1963, shortly after its de jure transfer from French administration to India.
• The Legislative Assembly of Puducherry consists of 30 members chosen by direct election and up to 3 members nominated by the Central Government.
• Initially, the Act also provided legislatures for Himachal Pradesh, Manipur, Tripura, and Goa, Daman and Diu, though most of these territories eventually achieved full statehood.

 Additional Information

• Delhi:
• While it has a legislature, it was not established by the 1963 Act. It was granted a Legislative Assembly through the 69th Constitutional Amendment Act, 1991 and Article 239AA.
• The Government of National Capital Territory of Delhi Act, 1991 provides the legal framework for its governance.
• Chandigarh:
• Created as a Union Territory in 1966 via the Punjab Reorganisation Act to serve as a shared capital.
• It is governed by an Administrator and does not have its own legislature or Council of Ministers.
• Andaman & Nicobar Islands:
• Established as a Union Territory in 1956, it is administered directly by the President through a Lieutenant Governor.
• It remains a UT without a Legislative Assembly.

The correct answer is Vijayanagara Empire.

Key Points

• Hampi, situated on the southern bank of the Tungabhadra River in the state of Karnataka, served as the magnificent capital of the Vijayanagara Empire from 1336 to 1565 AD.
• The empire was founded by two brothers, Harihara I and Bukka Raya I, belonging to the Sangama Dynasty, who established a stronghold against the expansion of the northern Sultanates.
• The city reached its cultural and territorial peak during the reign of Krishnadevaraya (1509–1529 AD), who is considered the most powerful ruler of the Tuluva Dynasty.
• Hampi was renowned globally for its architectural brilliance, featuring massive fortifications, complex Dravidian-style temples, and innovative urban planning including aqueducts and markets.
• The prosperity of the city came to a violent end in 1565 following the Battle of Talikota, where a coalition of Deccan Sultanates (Bijapur, Golconda, Ahmednagar, and Bidar) defeated and subsequently plundered the capital.
• In recognition of its historical and architectural significance, UNESCO designated the group of monuments at Hampi as a World Heritage Site in 1986.

 Additional Information

• Gupta Empire:
• Often referred to as the Golden Age of India (4th to 6th century CE), its primary capital was located at Pataliputra (modern-day Patna).
• Known for advancements in Sanskrit literature, astronomy, and the decimal system.
• Mughal Empire:
• An empire of Central Asian origin established by Babur in 1526.
• The empire’s prominent capitals included Agra, Fatehpur Sikri, and Shahjahanabad (Old Delhi).
• Maurya Empire:
• Founded by Chandragupta Maurya in 322 BCE, it was the first pan-Indian empire.
• Its administrative center and capital was Pataliputra, and it is most famous for the reign of Ashoka the Great.
• Virupaksha Temple:
• One of the oldest structures in Hampi, dedicated to Lord Shiva, which remained an active place of worship even after the city was abandoned.

The correct answer is System software.

Key Points

• System software is a comprehensive category of computer programs designed to operate and control the computer hardware directly while providing a platform for application software to run.
• It serves as the fundamental intermediary layer between the physical circuitry of the machine and the end-user, ensuring that hardware resources like the Central Processing Unit (CPU), Random Access Memory (RAM), and storage units are managed efficiently.
• The primary role of system software is to handle low-level tasks such as memory management, process scheduling, and file system organization, which are essential for the overall stability and performance of the computer.
• By providing standardized Application Programming Interfaces (APIs) and system calls, it allows developers to create software that can interact with complex hardware without needing to know the specific technical details of the underlying components.
• This software type typically initiates during the booting process and remains active in the background throughout the entire computing session to monitor system health and resource allocation.

 Additional Information

• Application Software:
• These are end-user programs developed to perform specific, non-computing tasks such as word processing, spreadsheet management, or web browsing.
• Unlike system software, these programs interact mostly with the Operating System rather than the hardware directly.
• Utility Software:
• A subset of system software focused on the optimization, configuration, and maintenance of the computer system.
• Common examples include antivirus software, disk defragmenters, and backup utilities that help keep the system running securely and smoothly.
• Driver Software:
• Also known as device drivers, these are specialized components of system software that act as translators between the Operating System and external peripherals.
• They allow the OS to recognize and utilize hardware like graphics cards, printers, and scanners by providing specific instruction sets.

The correct answer is Process Management.

Key Points

• Process Management is the fundamental function of an Operating System (OS) responsible for managing the execution of multiple tasks, ensuring that the Central Processing Unit (CPU) is utilized efficiently.
• The specific task of allocating CPU time is known as CPU Scheduling. The OS uses a Short-term Scheduler to select which process in the 'Ready' state will be executed next by the processor.
• The concept of sharing CPU cycles among various users or programs emerged with the development of Multiprogramming and Time-Sharing Systems in the 1960s, specifically with systems like Multics and IBM OS/360.
• To manage this, the OS maintains a Process Control Block (PCB) for each process, which contains essential data like the Process State, Program Counter, and CPU Registers.
• When switching from one process to another, the OS performs a Context Switch, saving the current state of the running process and loading the saved state of the next process to be executed.
• Modern operating systems like Linux utilize advanced algorithms such as the Completely Fair Scheduler (CFS) to ensure that every process gets a fair share of processor time, minimizing latency and starvation.

 Additional Information

• Memory Management:
• This function involves managing the Primary Memory (RAM). It keeps track of which parts of memory are currently in use and by whom.
• It performs Memory Allocation and Deallocation, ensuring processes do not interfere with each other's address spaces through techniques like Paging and Segmentation.
• Device Management:
• The OS manages Input/Output (I/O) devices such as printers, disks, and monitors using Device Drivers.
• It acts as an intermediary between the hardware and the software, managing I/O Queues and Interrupts.
• File Management:
• This involves the management of Secondary Storage. It handles File Creation, Deletion, and Directory Structures.
• It implements Access Control lists to protect data and maintains the File Allocation Table (FAT) or New Technology File System (NTFS) structures.

The correct answer is Railways.

Key Points

• Railways serve as the principal mode of transportation for freight in India, particularly for heavy and bulky goods over long distances, due to their immense load-bearing capacity and cost-efficiency.
• The Indian Railways network is one of the largest in the world, spanning over 68,000 kilometers, which allows for the seamless movement of materials between mineral-rich zones and industrial hubs.
• Bulk commodities like coal, iron ore, cement, food grains, and fertilizers constitute the majority of the freight traffic, as rail transport can carry massive volumes in a single trip compared to other modes.
• From a technical perspective, a single freight train can carry a load equivalent to approximately 70 to 100 trucks, making it far more energy-efficient and reducing the logistics cost per tonne-kilometer for the national economy.
• The development of Dedicated Freight Corridors (DFC), such as the Eastern and Western DFCs, has been specifically designed to increase the speed and efficiency of heavy goods movement across the country.

 Additional Information

• Waterways:
• While scientifically the cheapest mode of transport, Inland Waterways in India are limited by the navigability of rivers and seasonal water levels, currently carrying a much smaller share of bulk freight compared to rail.
• Roadways:
• Best suited for short to medium distances and providing door-to-door service, but they become economically unviable for extremely heavy bulk goods over long stretches due to high fuel consumption.
• Airways:
• The most expensive mode, utilized primarily for perishable goods, high-value electronics, or emergency supplies, and is unsuitable for heavy industrial raw materials.

The correct answer is 44th Amendment.

Key Points

• The Right to Property was originally established as a Fundamental Right under Article 19(1)(f), which guaranteed citizens the right to acquire, hold, and dispose of property, and Article 31, which provided protection against the compulsory acquisition of property.
• The 44th Amendment Act, 1978, enacted by the Janata Party Government led by Morarji Desai, deleted Article 19(1)(f) and Article 31 from the list of Fundamental Rights in Part III of the Indian Constitution.
• The amendment inserted a new Article 300A in Part XII of the Constitution, which states that 'no person shall be deprived of his property save by authority of law', thereby restoring it as a Legal Right or Constitutional Right.
• As a result of this change, a citizen cannot directly approach the Supreme Court under Article 32 for the enforcement of the right to property, although they can still seek remedies through the High Courts under Article 226.
• This shift allowed the state to implement land reforms and acquire private property for public purposes more effectively, provided such actions are backed by valid legislation.

 Additional Information

• 42nd Amendment Act (1976):
• Commonly referred to as the Mini-Constitution, it introduced significant changes including the addition of Socialist, Secular, and Integrity to the Preamble.
• It also established Fundamental Duties for citizens under Part IV-A (Article 51A).
• 48th Amendment Act (1984):
• This amendment was specifically concerned with the extension of President's Rule in the state of Punjab beyond the normal one-year period due to internal disturbances.
• 46th Amendment Act (1982):
• Addressed legal complexities regarding the Sales Tax on the transfer of property in goods involved in the execution of works contracts and the delivery of goods on hire-purchase.

The correct answer is Introduction of the Enfield rifle with cartridges feared to contain animal fat.

Key Points

• The immediate cause of the 1857 Uprising was the introduction of the Enfield P-53 Rifle, which required a new type of greased cartridge.
• To load the rifle, sepoys had to bite off the ends of these cartridges, which were rumored to be lubricated with tallow (cow fat) and lard (pig fat).
• This caused massive outrage as the cow is sacred to Hindus, while the pig is considered unclean in Islam; hence, both communities felt their religious sentiments were being intentionally violated by the British East India Company.
• The first major sign of resistance occurred in Barrackpore on March 29, 1857, when Mangal Pandey of the 34th Native Infantry attacked his officers, leading to his execution on April 8, 1857.
• The full-scale mutiny eventually erupted on May 10, 1857, at the military station in Meerut, from where the soldiers marched to Delhi to proclaim Bahadur Shah Zafar as their leader.

 Additional Information

• While the greased cartridges were the trigger, other underlying causes contributed to the revolt:
• General Service Enlistment Act of 1856: This act mandated that all recruits of the Bengal Army must be willing to serve overseas, which many Upper-caste Hindus believed would lead to a loss of caste (crossing the Kala Pani).
• Doctrine of Lapse: Introduced by Lord Dalhousie, this policy allowed the British to annex princely states like Jhansi, Satara, and Nagpur if the ruler died without a natural male heir.
• Religious Reforms: The abolition of Sati (1829), the Widow Remarriage Act (1856), and the activities of Christian Missionaries were viewed as direct interference in Indian social and religious customs.
• Economic Exploitation: Heavy land revenue demands and the destruction of local handicrafts led to widespread rural distress.

The correct answer is Prakrit.

Key Points

• Ashokan Inscriptions: The majority of the edicts issued by the Mauryan Emperor Ashoka (reigned c. 268−232 BCE) were composed in Prakrit. These inscriptions were strategically placed across the Indian subcontinent to propagate his philosophy of Dhamma in the vernacular language of the common people.
• Hathigumpha Inscription: King Kharavela of the Chedi Dynasty (Mahameghavahana) of Kalinga inscribed his achievements in the Hathigumpha Inscription at Udayagiri, Odisha. This 17-line record is written in Prakrit using the Brahmi script.
• Language vs. Script: It is essential to note that while the language was Prakrit, the scripts varied. Most inscriptions used Brahmi, but in the northwestern regions, Kharoshthi, Greek, and Aramaic were also employed to reach local populations.
• Administrative Use: During the 3rd and 2nd centuries BCE, Prakrit served as the primary language for royal proclamations and administrative records, preceding the dominance of Classical Sanskrit in later centuries.

 Additional Information

• Pali
• Commonly associated with the Theravada Buddhist canon and the Tipitaka.
• While linguistically related to Prakrit, it was not the formal language used in the Ashokan or Kharavela inscriptions.
• Sanskrit
• The use of Sanskrit in royal inscriptions became prominent later, notably with the Junagadh Rock Inscription of Rudradaman I around 150 CE.
• It eventually became the court language during the Gupta Empire.
• Evolution of Writing
• The Brahmi script used in these Prakrit inscriptions is the ancestor of most modern Indian scripts, including Devanagari, Bengali, and Tamil.

The correct answer is Printed Circuit Board.

Key Points

• A Printed Circuit Board (PCB) is a rigid structure that physically supports and electrically connects electronic components using conductive pathways, tracks, or signal traces etched from copper sheets.
• In the context of a Computer System, the most significant PCB is the Motherboard (also known as the mainboard or system board), which serves as the backbone for connecting the Central Processing Unit (CPU), Random Access Memory (RAM), and all other internal hardware.
• PCBs are typically manufactured using a non-conductive substrate material, most frequently FR-4, which is a flame-retardant fiberglass-reinforced epoxy laminate.
• The primary function of a PCB is to ensure a stable electrical connection between components like transistors, capacitors, and microprocessors, while providing a compact and reliable layout for complex circuitry.
• The production of PCBs involves a process called photolithography or chemical etching to remove unwanted copper, leaving only the required circuit traces that define the electronic architecture of the device.

 Additional Information

• Structural Layers of a PCB:
• Solder Mask: The outermost layer (typically green) that protects the copper traces from oxidation and prevents solder bridges during component assembly.
• Silkscreen: A layer of ink traces used to print labels, component identifiers (reference designators), and logos for easier maintenance and repair.
• Process Control Block:
• In the domain of Operating Systems (software), the acronym PCB can also refer to a Process Control Block, which is a data structure used by the Kernel to store information about a specific active process.
• Evolution of Circuitry:
• Before PCBs, circuits were built using point-to-point wiring, which was highly susceptible to short circuits and mechanical failure as complexity increased. The transition to PCBs allowed for the miniaturization of modern laptops, smartphones, and high-performance servers.

The correct answer is Non-volatile and larger in storage capacity.

Key Points

• Secondary memory, frequently referred to as auxiliary memory or external storage, is designed to store data and programs permanently. Unlike primary memory, it is not directly accessible by the Central Processing Unit (CPU); instead, data must be loaded into the Random Access Memory (RAM) via Input/Output channels before execution.
• A fundamental attribute of secondary memory is that it is non-volatile. This ensures that all stored information, including the Operating System (OS), software applications, and personal files, remains intact even after the computer is powered down or in the event of a power failure.
• Secondary memory devices offer a vastly larger storage capacity compared to main memory. While RAM typically ranges from 4 GB to 64 GB in modern personal computers, secondary storage solutions such as Hard Disk Drives (HDD) and Solid State Drives (SSD) commonly provide capacities ranging from 256 GB to several terabytes (TB).
• In the memory hierarchy, secondary storage is positioned below primary memory because it is significantly slower in terms of data access speed but much more cost-effective per gigabyte of storage, allowing for the mass retention of data.

 Additional Information

• Primary Memory (RAM):
• It is volatile, meaning it loses all data once the power supply is disconnected.
• It facilitates high-speed data transfer as it is directly connected to the CPU via the memory bus.
• Common Secondary Storage Devices:
• Magnetic Storage: Includes Hard Disk Drives (HDD) and Magnetic Tapes, which use magnetic fields to read and write data.
• Optical Storage: Includes CD-ROMs, DVDs, and Blu-ray Discs, which utilize laser technology for data retrieval.
• Flash Memory: Includes Solid State Drives (SSD), USB Flash Drives, and SD Cards, which are faster and more durable than traditional mechanical disks due to the absence of moving parts.
• Direct Memory Access (DMA): This is a feature that allows certain hardware subsystems to access main system memory independently of the CPU, but it does not apply to the CPU directly executing instructions from secondary storage.

The correct answer is Al₂(SO₄)₃.

Key Points

• The chemical formula of Aluminium Sulphate is determined using the valency or oxidation state of the constituent ions to ensure the resulting compound is electrically neutral.
• Aluminium (Al) is a group 13 element and typically forms a cation with a charge of +3 (Al³⁺), meaning it loses three electrons to achieve a stable octet.
• The Sulphate ion (SO₄) is a polyatomic anion consisting of one sulphur atom and four oxygen atoms, carrying a collective charge of -2 (SO₄²⁻).
• Applying the criss-cross method, the numerical value of the charge of the Aluminium ion (3) becomes the subscript for the Sulphate ion, and the numerical value of the charge of the Sulphate ion (2) becomes the subscript for the Aluminium ion.
• To balance the total charge: 2 × (+3) + 3 × (−2) = 0. Therefore, two aluminium atoms combine with three sulphate groups to form Al₂(SO₄)₃.

 Additional Information

• Properties and Characteristics:
• Molar Mass: The anhydrous form of Aluminium Sulphate has a molar mass of approximately 342.15 g/mol.
• Physical Appearance: It usually appears as a white crystalline solid or powder and is highly hygroscopic, meaning it readily absorbs moisture from the air.
• Solubility: It is highly soluble in water but virtually insoluble in ethanol. When dissolved in water, it undergoes hydrolysis to form an acidic solution.
• Industrial Uses:
• Water Purification: It acts as a coagulant, causing impurities to clump together (flocculation) so they can be easily filtered out.
• Paper Industry: Used as a sizing agent to adjust the paper's absorbency and improve its printability.
• Textile Dyeing: Functions as a mordant, helping dyes adhere to fabric fibers like cotton.

The correct answer is Bilateral Investment Treaty - BIT.

Key Points

• The Bilateral Investment Treaty (BIT) between India and Uzbekistan was signed on September 24, 2024, in Tashkent. This agreement represents a significant step in deepening economic cooperation and providing a secure legal framework for investors from both nations.
• The treaty was signed by the Union Minister for Finance and Corporate Affairs of India, Nirmala Sitharaman, and the Deputy Prime Minister of Uzbekistan, Jamshid Khodjaev, during the Minister’s visit to attend the 9th Annual Meeting of the Board of Governors of the Asian Infrastructure Investment Bank (AIIB) held in Samarkand.
• The BIT is designed to protect investments against non-commercial risks, ensuring fair and equitable treatment and protection from expropriation without adequate compensation. It replaces the previous Bilateral Investment Promotion and Protection Agreement (BIPPA) between the two countries.
• After both governments completed the necessary domestic ratification procedures, the treaty officially came into force in May 2025, establishing a predictable investment climate and facilitating greater capital flows into sectors like pharmaceuticals, information technology, and infrastructure.

 Additional Information

• Bilateral Investment Treaty (BIT):
• This treaty is based on the 2015 Model BIT of India, which includes an Investor-State Dispute Settlement (ISDS) mechanism, requiring investors to exhaust local remedies for a specified period before moving to international arbitration.
• It aligns with India’s Connect Central Asia Policy, aimed at strengthening ties with resource-rich Central Asian Republics.
• Comprehensive Economic Partnership Agreement (CEPA):
• A CEPA is a comprehensive free trade agreement that covers trade in goods, services, and investment. India has signed such agreements with the UAE and Mauritius, but the agreement with Uzbekistan in 2024 was specifically a BIT.
• Double Taxation Avoidance Agreement (DTAA):
• A DTAA is a tax treaty between two countries to avoid the same income being taxed twice. India and Uzbekistan already have a DTAA in place, which was originally signed in 1993 and subsequently updated.

The correct answer is 1950.

Key Points

• The Planning Commission of India was established on 15 March 1950 through an executive resolution of the Government of India.
• It was created based on the recommendations of the Advisory Planning Board, which was constituted in 1946 under the chairmanship of K.C. Neogy.
• The organization functioned as an extra-constitutional and non-statutory body, meaning its existence was not defined by the Constitution of India nor created by an Act of Parliament.
• The Prime Minister of India served as the Ex-officio Chairman of the commission; Pandit Jawaharlal Nehru was its first chairman, while Gulzarilal Nanda served as the first Deputy Chairman.
• Its primary mandate was to formulate Five-Year Plans to promote the balanced and effective utilization of the country's resources for economic development.

 Additional Information

• NITI Aayog (National Institution for Transforming India):
• Established on 1 January 2015, it replaced the Planning Commission to better serve the needs of a modern India.
• It serves as the premier policy Think Tank of the Union Government, providing both directional and policy inputs.
• Unlike the Planning Commission which followed a top-down approach, NITI Aayog emphasizes a bottom-up approach and the spirit of Cooperative Federalism.
• National Development Council (NDC):
• Formed on 6 August 1952, the NDC was the apex body responsible for the final approval of the Five-Year Plans prepared by the Planning Commission.
• The First Five-Year Plan:
• Launched in 1951 (covering the period 1951−1956), it was based on the Harrod-Domar model and focused primarily on the development of the agricultural sector.

The correct answer is 42nd Constitutional Amendment Act.

Key Points

• The 42nd Constitutional Amendment Act, enacted in 1976 during the Internal Emergency under the Indira Gandhi administration, is the most extensive amendment in the history of the Indian Constitution.
• This amendment is famously known as the Mini-Constitution because it introduced massive changes to the constitutional structure, including the Preamble, Fundamental Rights, and Directive Principles.
• For the first and only time since the adoption of the Constitution, the Preamble was amended to include three new terms: Socialist, Secular, and Integrity.
• The insertion of the word Socialist was intended to emphasize the egalitarian goals of the Indian state, specifically Democratic Socialism, which aims to end poverty, ignorance, disease, and inequality of opportunity.
• The addition of Socialist formally aligned the Preamble with the Directive Principles of State Policy, particularly Article 39, which seeks the equitable distribution of material resources.
• Unlike the communistic socialism of the Soviet model, Indian Socialism is a Gandhian-Marxist blend that favors a mixed economy where the private and public sectors co-exist.

 Additional Information

• 38th Constitutional Amendment Act (1975):
• Empowered the President to declare a state of Emergency that would be non-justiciable in a court of law.
• Ensured that Ordinances promulgated by the President or Governors could not be challenged in court.
• 44th Constitutional Amendment Act (1978):
• Enacted by the Janata Government to undo several controversial changes brought by the 42nd Amendment.
• It removed the Right to Property from the list of Fundamental Rights and made it a Legal Right under Article 300A.
• 86th Constitutional Amendment Act (2002):
• Inserted Article 21A, making Free and Compulsory Education a Fundamental Right for children aged 6 to 14 years.
• Added a new Fundamental Duty under Article 51A(k) for parents and guardians.

The correct answer is Aw - Deciduous forests and tree-shredded grasslands.

Key Points

• BWh represents the Subtropical Hot Desert climate. The letter B stands for arid climates, W for desert (Wüste), and h for hot. This climate is characterized by high temperatures and extremely low precipitation, supporting xerophytic vegetation like cacti and thorny bushes rather than a dense evergreen canopy. Hence, statement 1 is incorrect.
• ET stands for the Tundra climate within the Polar (E) group. In this climate, the average temperature of the warmest month is between 0°C and 10°C. The vegetation consists of mosses, lichens, and stunted shrubs, while tropical rainforests are associated with the Af climate. Hence, statement 2 is incorrect.
• Aw denotes the Tropical Savanna climate. It is defined by a distinct dry season (usually in winter) and a wet season. The vegetation comprises deciduous forests that shed leaves during the dry period and grasslands interspersed with trees (often referred to as savanna). Hence, statement 3 is correct.
• Cfa refers to the Humid Subtropical climate, characterized by hot, humid summers and mild winters with rainfall occurring throughout the year. Cold deserts (BWk) and permafrost (EF/ET) are found in much colder or more arid latitudinal zones. Hence, statement 4 is incorrect.

 Additional Information

• Koeppen Climate Classification System: Developed by Wladimir Koeppen in 1884, it categorizes climates based on monthly and annual averages of temperature and precipitation.
• Group A (Tropical Humid): Tropical climates where the average temperature of every month is 18°C or higher.
• Af: Tropical Wet (Rainforest).
• Am: Tropical Monsoon.
• Aw: Tropical Wet and Dry (Savanna).
• Group B (Dry Climates): Regions where potential evapotranspiration exceeds precipitation.
• BSh: Semi-arid Steppe.
• BWk: Mid-latitude Cold Desert.
• Group C (Warm Temperate): Mid-latitude climates with mild winters; the coldest month average is between −3°C and 18°C.

The correct answer is Sushil Kumar.

Key Points

• Sushil Kumar is a former Indian freestyle wrestler who holds the distinction of being the first athlete from independent India to win two individual Olympic medals.
• He secured his first Olympic Bronze medal at the 2008 Beijing Olympics in the 66 kg freestyle category, ending a 56-year drought for India in Olympic wrestling since Kashaba Dadasaheb Jadhav won bronze in 1952.
• He achieved his second Olympic medal, a Silver, at the 2012 London Olympics, where he served as the flag bearer for the Indian contingent during the opening ceremony.
• In 2010, at the FILA World Wrestling Championships held in Moscow, he created history by becoming the first Indian wrestler to win a World Championship Gold medal.
• He was honored with India s highest sporting award, the Major Dhyan Chand Khel Ratna (formerly Rajiv Gandhi Khel Ratna), in 2009 for his exceptional contributions to the sport.

 Additional Information

• Geeta Phogat:
• She is the first Indian female wrestler to win a Gold medal in wrestling at the Commonwealth Games (Delhi 2010).
• She was also the first Indian woman wrestler to qualify for the Olympic Games (London 2012).
• Col. Rajyavardhan Singh Rathore:
• An acclaimed shooter who won India s first individual Silver medal at the Olympics post-independence during the 2004 Athens Games in the Double Trap event.
• He later transitioned into politics and served as the Minister of State (Independent Charge) for Youth Affairs and Sports.
• Bajrang Punia:
• A highly decorated freestyle wrestler who won the Bronze medal at the 2020 Tokyo Olympics in the 65 kg category.
• He holds the record for being the only Indian wrestler to win four medals at the World Wrestling Championships (one silver and three bronze).

The correct answer is ₹2,000 crore.

Key Points

• The Rural Infrastructure Development Fund (RIDF) was established by the Government of India during the financial year 1995-96.
• The primary motive behind creating this fund was to provide low-cost credit to State Governments and State-owned corporations to help them complete ongoing rural infrastructure projects that were stalled due to a lack of resources.
• The National Bank for Agriculture and Rural Development (NABARD) is the designated authority responsible for the administration and operational management of the RIDF.
• When the fund was launched under the RIDF I tranche in 1995-96, it began with an initial corpus of ₹2,000 crore.

 Additional Information

• Funding Mechanism:
• The corpus of the RIDF is generated from the shortfall in lending to the Priority Sector (specifically agriculture) by Scheduled Commercial Banks.
• Banks that do not meet their Priority Sector Lending (PSL) targets are required to contribute to the fund as per the guidelines issued by the Reserve Bank of India (RBI).
• Scope and Coverage:
• Initially, the fund focused primarily on irrigation projects.
• Currently, it covers 39 eligible activities classified into three main categories: Agriculture and Related Sectors, Social Sector, and Rural Connectivity (roads and bridges).
• The Agriculture Sector accounts for a significant portion of the total sanctions, aiming to boost rural productivity and employment.
• Evolution of the Corpus:
• Since its inception with ₹2,000 crore, the annual allocation for the RIDF is announced in the Union Budget every year.
• The allocation has increased multi-fold over the years; for instance, the allocation for RIDF XXVII (2021-22) reached ₹40,000 crore to support rural growth.

The correct answer is Akbar.

Key Points

• The Zabti system, also known as the Dahshala system, was the most organized land revenue mechanism introduced during the reign of Emperor Akbar around 1580-1582.
• The system was developed and implemented by Akbar's Finance Minister, Raja Todar Mal, who was a brilliant administrator previously associated with Sher Shah Suri.
• Under this method, the revenue was fixed based on the average yield of land and the prevailing prices over the preceding ten years.
• It required a systematic measurement of land using a standardized unit called the Ilahi Gaz and a measuring tool made of bamboo called the Tanab.
• Revenue was collected strictly in cash, which helped the Mughal state maintain a stable treasury and facilitated the expansion of the imperial military and administrative machinery.
• The system was prevalent in the core provinces of the Mughal Empire, including Agra, Delhi, Lahore, Allahabad, and Malwa, where the administration could maintain detailed records.

 Additional Information

• Land Classification: To ensure fair taxation, land was divided into four categories based on the frequency of cultivation:
• Polaj: Fertile land that was cultivated every year and never left fallow.
• Parauti: Land left fallow for a year or two to recover its natural fertility.
• Chachar: Land that remained uncultivated for three to four years.
• Banjar: Inferior land that remained out of cultivation for five years or more.
• Babar and Humayun: As the early Mughal rulers, they were primarily focused on territorial consolidation and military defense; hence, they did not establish a long-term administrative revenue framework like the Zabti.
• Aurangzeb: During his later reign, the agrarian system faced severe stress due to high revenue demands and the Jagirdari crisis, where the available land (Paibaqi) was insufficient to meet the grants required for the growing number of Mansabdars.

The correct answer is Proteins.

Key Points

• Pepsin is a powerful enzyme found in Gastric Juice that initiates the digestion of proteins by breaking them down into smaller units called Peptones and Proteoses.
• It is secreted by the Chief Cells (peptic cells) of the stomach lining in an inactive proenzyme form known as Pepsinogen.
• The activation of Pepsinogen into Pepsin requires an acidic medium, which is provided by Hydrochloric Acid (HCl) secreted by the Oxyntic Cells (parietal cells).
• The stomach maintains a highly acidic pH level (approximately 1.8), which is the optimum environment for Pepsin to function efficiently as an Endopeptidase.
• By hydrolyzing internal peptide bonds, Pepsin transforms long-chain complex Proteins into shorter polypeptide chains, facilitating further digestion in the Small Intestine.

 Additional Information

• Carbohydrates:
• Digestion begins in the Buccal Cavity through the action of Salivary Amylase (Ptyalin).
• Final breakdown into simple sugars like Glucose occurs in the small intestine via Pancreatic Amylase and Disaccharidases.
• Fats:
• Requires Emulsification by Bile Salts produced in the Liver and stored in the Gallbladder.
• The enzyme Lipase, primarily from the Pancreas, breaks down fats into Fatty Acids and Glycerol.
• Vitamins:
• These are Micronutrients essential for metabolic functions but do not require enzymatic breakdown for energy.
• They are absorbed directly in the Small Intestine, specifically in the Ileum for Vitamin B₁₂.

The correct answer is Lichchhavi.

Key Points

• Chandragupta I (reigned c. 319–335 CE) was the son of Ghatotkacha and the first powerful ruler of the Gupta dynasty to adopt the imperial title of Maharajadhiraja (King of Kings).
• He significantly elevated his political status and the influence of the Gupta Empire by marrying Princess Kumaradevi of the Lichchhavi tribe, an ancient and prestigious Kshatriya clan.
• The Lichchhavis were a dominant power in Vaishali (modern-day Bihar), and this matrimonial alliance provided the Guptas with substantial territorial and political leverage over the Magadha region.
• To commemorate this union, Chandragupta I issued a special series of gold coins known as the King-and-Queen type (or Chandragupta-Kumaradevi type), featuring the names and portraits of both the King and the Queen.
• The prestige associated with the Lichchhavi lineage was so high that their son, Samudragupta, proudly referred to himself as Lichchhavi-dauhitra (grandson of the Lichchhavis) in his famous Allahabad Pillar Inscription (Prayag Prashasti).

 Additional Information

• Avanti:
• An ancient Indian Mahajanapada located in the Malwa region with its capital at Ujjain. It was later annexed into the Gupta Empire during the reign of Chandragupta II.
• Panchala:
• A historical region in the Ganges-Yamuna Doab of Northern India, known for being one of the sixteen Mahajanapadas mentioned in ancient Buddhist and Jain texts.
• Gandhara:
• A region situated in present-day Afghanistan and Pakistan, famous for its unique Gandhara School of Art and the ancient learning center at Takshashila.

The correct answer is Ultrasound.

Key Points

• The human auditory system is sensitive to a specific range of vibrations known as the audible range, which typically spans from 20 Hz to 20,000 Hz.
• Sound waves with frequencies that surpass the upper limit of 20,000 Hz (or 20 kHz) are scientifically classified as ultrasound or ultrasonic waves.
• While these waves are physically identical to audible sound in terms of propagation, they are inaudible to the human ear because the tympanic membrane cannot vibrate at such high speeds.
• Many animals, including bats, dolphins, and porpoises, have the biological capability to produce and hear ultrasound, utilizing it for echolocation to hunt and navigate.
• The Hertz (Hz) is the standard SI unit of frequency, representing the number of cycles per second; thus, ultrasound involves over 20,000 vibrations every second.

 Additional Information

• Infrasound:
• Refers to sound waves with a frequency below 20 Hz, which is the lower limit of human hearing.
• Sources include seismic waves from earthquakes, volcanic eruptions, and ocean tides.
• Large mammals like elephants and rhinoceroses communicate using infrasonic signals over vast distances.
• Supersonic:
• This term describes the velocity of an object rather than its frequency. An object is supersonic if it travels faster than the speed of sound (approximately 343 m/s in air).
• When an aircraft reaches supersonic speeds, it produces a sonic boom due to the accumulation of shock waves.
• Tones:
• A tone is a sound that consists of a single, pure frequency. Most musical sounds are actually "notes," which combine a fundamental frequency with several harmonics.
• Practical Applications of Ultrasound:
• Medical Imaging: Utilized in sonography to visualize fetuses and internal organs without ionizing radiation.
• SONAR: Used by submarines and ships to detect underwater obstacles and measure the depth of the sea.
• Industrial Cleaning: High-frequency vibrations are used to remove contaminants from delicate electronic components and surgical instruments.

The correct answer is Flight acceptance hot testing of the CE20.

Key Points

• On March 14, 2025, the Indian Space Research Organisation (ISRO) successfully conducted the flight acceptance hot testing of the CE20 cryogenic engine, marking a pivotal advancement in India's propulsion capabilities.
• This specific engine is identified for the LVM3-M6 mission, which is the sixth operational mission of the Launch Vehicle Mark-3 (LVM3).
• The test was carried out at the ISRO Propulsion Complex (IPRC) in Mahendragiri, Tamil Nadu, which is the primary facility for testing liquid propulsion systems.
• A major achievement of this session was firing the engine for a duration of 100 seconds under non-vacuum (sea-level) conditions, significantly exceeding previous limitations.
• The test utilized an innovative Nozzle Protection System (NPS), which allowed for longer firing durations without the risk of flow separation or thermal damage that typically occurs when testing high-area-ratio nozzles at sea level.
• Before this development, flight acceptance tests were typically conducted at the High-Altitude Test (HAT) facility with a maximum duration of 25 seconds due to the complexity of maintaining vacuum conditions.

 Additional Information

• CE20 Cryogenic Engine:
• It is India's first indigenous cryogenic engine to use a Gas Generator cycle, providing high thrust to the Cryogenic Upper Stage (C25) of the LVM3.
• It operates using Liquid Oxygen (LOX) as the oxidizer and Liquid Hydrogen (LH2) as the fuel, delivering the high specific impulse necessary for heavy-lift missions.
• The CE20 has been successfully human-rated for the upcoming Gaganyaan mission, demonstrating its high reliability and safety standards.
• Other Milestones in March 2025:
• On March 28, 2025, ISRO reached another milestone by conducting the first successful hot test of the Semi-cryogenic Engine Power Head Test Article (PHTA).
• The semi-cryogenic engine is designed to use Refined Kerosene (ISROSENE) and Liquid Oxygen, aiming to boost the payload capacity of the LVM3 from 4 tonnes to 6 tonnes for GTO missions.

Concept:

The Ministry of Environment, Forest and Climate Change (MoEFCC) has introduced a specific legal framework to address the long-standing issue of toxic and hazardous substance contamination in soil and water. These rules provide a systematic, time-bound procedure for handling sites that pose a risk to human health and the environment due to historical industrial activities or waste dumping.

Key Points:

• Notification: The rules were notified on July 24, 2025, under the powers conferred by the Environment (Protection) Act, 1986.
• Process Stages: The framework involves Identification (listing suspected sites), Determination (conducting preliminary and detailed assessments to confirm contamination levels), and Remediation (executing cleanup plans).
• Accountability: They incorporate the 'Polluter Pays' principle, holding the responsible party liable for the costs of restoration.
• Thresholds: Sites are declared 'contaminated' if hazardous substance concentrations exceed the response levels specified in the rules.

Important Provisions:

• The State Pollution Control Boards (SPCBs) and Pollution Control Committees (PCCs) are responsible for the technical assessment and declaration of these sites.
• A centralized online portal is used to maintain an inventory of suspected, probable, and confirmed contaminated sites.
• Exclusions include sites affected strictly by radioactive waste, mining operations, or marine oil spills, which are governed by other specific acts unless contaminants exceed the response levels defined in these new rules.

Final Answer: The rules that define the process of identification, determination, and remediation of contaminated sites are the Environment Protection (Management of Contaminated Sites) Rules, 2025.

The correct answer is Widow Remarriage Association.

Key Points

• Mahadev Govind Ranade, often hailed as the Socrates of Maharashtra, was a distinguished Indian scholar, social reformer, and a judge of the Bombay High Court.
• He founded the Widow Remarriage Association in 1861 (also known as Punarvivahottejak Mandali) to promote the welfare of widows and encourage their remarriage, following the Hindu Widows Remarriage Act of 1856.
• Ranade was a primary leader of the Prarthana Samaj in Bombay, which focused on social reforms such as the education of women and the abolition of the caste system and child marriage.
• He established the Poona Sarvajanik Sabha in 1870, an organization aimed at representing the interests of the peasantry and acting as a mediator between the people and the British Government.
• He was a founding member of the Indian National Congress (1885) and initiated the Indian National Social Conference in 1887, which addressed social issues on a national platform.
• Known as the Father of Indian Economics, he advocated for state intervention to foster industrialization and economic growth in India.

 Additional Information

• Brahmo Samaj:
• Founded by Raja Ram Mohan Roy in 1828 in Calcutta.
• It was the first major reform movement in Hinduism, advocating for monotheism and the abolition of Sati.
• Arya Samaj:
• Established by Swami Dayanand Saraswati in 1875 in Bombay.
• It promoted the infallible authority of the Vedas and introduced the Shuddhi movement to bring back converts to the Hindu fold.
• Indian National Congress:
• Founded in December 1885 at Gokuldas Tejpal Sanskrit College, Bombay.
• The organization was founded by Allan Octavian Hume (A.O. Hume), a retired British civil servant, with Womesh Chandra Bonnerjee serving as its first President.

The correct answer is To attract foreign investment.

Key Points

• The 1991 Economic Reforms were launched to tackle a severe Balance of Payments (BoP) crisis, where foreign exchange reserves had dropped to levels barely sufficient for two weeks of imports.
• Tax incentives, such as tax holidays and reduced corporate tax rates, were designed to lower the cost of entry for Multi-National Corporations (MNCs) and Foreign Institutional Investors (FIIs).
• The primary objective was to encourage the inflow of Foreign Direct Investment (FDI) to supplement domestic capital, which was insufficient to fund industrial growth and infrastructure development.
• These incentives were intended to facilitate the transfer of advanced technology and modern managerial practices from developed nations to the Indian industrial sector.
• By attracting foreign capital, the government aimed to modernize the manufacturing sector and make Indian products more competitive in the global market.

 Additional Information

• Liberalization:
• Involved the dismantling of the License-Permit Raj, allowing private players to enter sectors previously reserved for the government.
• Reduced the statutory liquidity ratio (SLR) and cash reserve ratio (CRR) to increase the lending capacity of banks.
• Globalization:
• Aimed at integrating the Indian economy with the World Economy by reducing import tariffs and export duties.
• Encouraged the convertibility of the rupee on the current account to facilitate smoother international trade.
• Privatization:
• Focused on the disinvestment of Public Sector Undertakings (PSUs) to improve efficiency through private ownership and management.
• Shifted the government's role from a producer to a regulator and facilitator of economic activity.

The correct answer is Article 43.

Key Points

• Article 43 of the Indian Constitution mandates that the State shall endeavor to secure, by suitable legislation or economic organization, a living wage and conditions of work ensuring a decent standard of life for all workers.
• This article covers all categories of workers, including those in the agricultural and industrial sectors, ensuring they have full enjoyment of leisure and social and cultural opportunities.
• The concept of a living wage is more comprehensive than a minimum wage, as it aims to provide for the basic requirements of a family, including food, clothing, housing, and education for children.
• Furthermore, Article 43 specifically mentions the promotion of cottage industries on an individual or cooperative basis in rural areas, reflecting the Gandhian Principles within the Directive Principles of State Policy.

 Additional Information

• Article 41:
• Directs the State to ensure the right to work, to education, and to public assistance in cases of unemployment, old age, sickness, and disablement.
• Article 42:
• Requires the State to make provisions for securing just and humane conditions of work and for maternity relief.
• Article 47:
• Focuses on the duty of the State to raise the level of nutrition and the standard of living of its people and the improvement of public health.
• It also includes the endeavor to bring about the prohibition of the consumption of intoxicating drinks and drugs.

The correct answer is France.

Key Points

• In February 2025, India and France strengthened their long-standing bilateral ties by signing a joint declaration to establish a partnership focused on Advanced and Small Modular Nuclear Reactors (SMRs).
• The agreement was formalized between India's Department of Atomic Energy (DAE) and the French Commissariat à l’énergie atomique et aux énergies alternatives (CEA).
• The partnership aims to facilitate technical cooperation, joint research, and development of low-carbon nuclear technologies to support industrial decarbonization and energy security.
• This initiative is a critical component of the Horizon 2047 roadmap, which outlines the strategic cooperation between the two nations for the next 25 years.
• The focus on Small Modular Reactors (SMRs) highlights a shift towards more flexible, cost-effective, and safer nuclear power solutions compared to traditional large-scale reactors.

 Additional Information

• Small Modular Reactors (SMRs):
• These are advanced nuclear reactors with a power capacity of up to 300 MW(e) per unit.
• They are characterized by their modular design, allowing for factory fabrication and easier transportation to remote sites.
• SMRs offer enhanced safety features, such as passive cooling systems that do not require human intervention or external power.
• India-France Nuclear History:
• France was the first country to sign a Civil Nuclear Cooperation Agreement with India in 2008 after the Nuclear Suppliers Group (NSG) waiver.
• The two countries are already collaborating on the Jaitapur Nuclear Power Project in Maharashtra, which aims to install six Evolutionary Power Reactors (EPRs) with a total capacity of 9.6 GW.
• The Strategic Partnership between India and France was established in 1998, covering defense, space, and nuclear energy.

The correct answer is Panchayats and Municipalities.

Key Points

• The State Election Commission (SEC) is a constitutional body created under the 73rd and 74th Constitutional Amendment Acts of 1992 to ensure the autonomous conduct of local government elections.
• According to Article 243K of the Constitution of India, the superintendence, direction, and control of the preparation of electoral rolls and the conduct of all elections to the Panchayats (Gram Panchayats, Panchayat Samitis, and Zilla Parishads) are vested in the State Election Commission.
• Similarly, Article 243ZA mandates that the SEC is responsible for conducting and supervising elections to Municipalities, including Municipal Corporations, Municipal Councils, and Nagar Panchayats.
• The State Election Commissioner is appointed by the Governor of the state, and their conditions of service and tenure are determined by state laws, providing them with a status equivalent to a High Court Judge regarding removal procedures.

 Additional Information

• Election Commission of India (ECI):
• Established under Article 324, the ECI is an independent constitutional authority responsible for administering election processes at the national and state levels.
• The ECI conducts elections for the Lok Sabha, Rajya Sabha, State Legislative Assemblies, and State Legislative Councils.
• It is also the sole authority for conducting the elections of the President and Vice-President of India.
• Jurisdiction Differences:
• While the ECI manages parliamentary and legislative elections, it has no role in Panchayati Raj Institutions or Urban Local Bodies.
• The State Election Commission functions independently of the Election Commission of India for the specific purpose of Local Self-Government.

The correct answer is Sulphur dioxide.

Key Points

• Acid rain refers to any form of precipitation, including rain, snow, or fog, that contains elevated levels of nitric and sulphuric acids.
• The primary chemical responsible for this phenomenon is Sulphur dioxide (SO₂), which is released into the atmosphere through the combustion of fossil fuels (like coal and oil) in power plants and industrial boilers.
• Once in the atmosphere, SO₂ reacts with water vapor, oxygen, and other chemicals to form Sulphuric acid (H₂SO₄), which eventually falls to the ground as acid rain.
• While normal rainwater is slightly acidic with a pH value of about 5.6 (due to dissolved Carbon dioxide), acid rain typically has a pH value between 4.2 and 4.4.
• The environmental impact of acid rain includes the acidification of aquatic environments, damage to forest vegetation, and the chemical weathering of stone buildings and cultural monuments like the Taj Mahal.

 Additional Information

• Carbon monoxide (CO):
• A colorless, odorless, and highly toxic gas produced by the incomplete combustion of carbon-based fuels.
• It does not directly contribute to acid rain but poses significant health risks by reducing the oxygen-carrying capacity of blood.
• Ozone (O₃):
• Found in the troposphere, it acts as a secondary pollutant and a major component of photochemical smog.
• While it helps catalyze some atmospheric oxidation processes, it is not a direct precursor to acid rain formation.
• Ammonia (NH₃):
• An alkaline gas primarily emitted from agricultural activities, livestock management, and fertilizer use.
• In the atmosphere, it can act as a buffering agent to neutralize acidic compounds, though its deposition can still lead to soil and water issues.

The correct answer is Kerala.

Key Points

• Tholpavakoothu is a traditional ritualistic shadow puppetry art form that originated and is primarily practiced in the state of Kerala, specifically in the districts of Palakkad, Thrissur, and Malappuram.
• The name is a compound of three Malayalam words: Thol meaning leather, Pava meaning puppet, and Koothu meaning play or performance.
• It is traditionally performed in specially constructed permanent theaters called Koothumadams located within the premises of Bhadrakali temples, as an offering to the goddess.
• The performance is based on the Kamba Ramayana, the Tamil version of the epic written by the poet Kambar, spanning across 21 parts over 21 nights.
• The puppets are crafted from deer skin, meticulously perforated to create intricate patterns that project shadows onto a white cloth screen when illuminated by coconut-shell oil lamps (Chirathu).

 Additional Information

• Puppetry Traditions in Other States:
• Andhra Pradesh: Known for Tholu Bommalata, where puppets are large, multicolored, and translucent, creating vibrant shadows.
• Odisha: Known for Ravana Chhaya, which uses puppets made from a single piece of leather without jointed limbs, resulting in opaque, non-colored shadows.
• West Bengal: Famous for various string and rod puppetry forms like Putul Nautch and Danger Putul Nach, often performed during local fairs.
• Karnataka: Practices Togalu Gombeyaata, a shadow puppet form similar to those in Andhra Pradesh but with distinct regional stylistic variations.
• Tamil Nadu: Has a similar form called Tholpavai Koothu, which shares historical roots with the Kerala tradition but has evolved differently in its musical and linguistic execution.

The correct answer is Ecosystem.

Key Points

• An ecosystem is considered the structural and functional unit of nature because it encompasses the complex interactions between living organisms and their physical environment.
• The term was coined by A.G. Tansley in 1935 to describe a self-regulating and self-sustaining system.
• The structural features of an ecosystem consist of biotic components (producers, consumers, and decomposers) and abiotic components (temperature, light, water, and soil).
• The functional aspects of an ecosystem include energy flow, nutrient cycling, productivity, and decomposition, which ensure the continuity of life within a specific geographical area.
• Ecosystems can vary significantly in scale, ranging from a small pond or a single tree to vast biomes like tropical rainforests or the entire biosphere.

 Additional Information

• Environment:
• It refers to the sum total of all external conditions (physical, chemical, and biological) that surround and influence an organism.
• While it provides the setting for life, it lacks the specific internal functional cycles that define an ecosystem.
• Cell:
• The cell is the fundamental structural and functional unit of life or living organisms, not of nature as a whole.
• All living things are composed of cells, and the study of these units is known as Cytology.
• Ecology:
• Ecology is the scientific study of the relationships and interactions between organisms and their environment.
• The concept was popularized by Ernst Haeckel in 1866, who defined it as the study of the economy of nature.

The correct answer is ET - Tundra climate.

Key Points

• The Tundra climate (ET) is a polar climate characterized by extremely cold temperatures where the warmest month has an average temperature between 0°C and 10°C.
• The defining soil characteristic of this region is permafrost, which refers to ground, including rock or soil, that remains at or below 0°C for at least two consecutive years.
• Due to the presence of permafrost and a very short growing season, deep-rooted trees cannot survive; instead, the landscape is dominated by low-lying vegetation such as mosses, lichens, and small sedges.
• In the Koppen climate classification, the ET designation is primarily found in the high latitudes of the Northern Hemisphere, covering the Arctic coastal fringes of North America, Eurasia, and the Antarctic Peninsula.
• The moisture levels in these regions are low, making it a polar desert, but the low evaporation rates allow the soil to remain moist or waterlogged during the brief summer thaw.

 Additional Information

• Cfb - Marine West Coast Climate:
• Characterized by mild winters and cool summers with high humidity and year-round precipitation.
• Supports dense temperate forests, including both deciduous and coniferous trees, primarily in Western Europe and the Pacific Northwest.
• Aw - Tropical Wet and Dry Climate:
• Also known as the Savanna climate, it features a distinct dry season during the winter months.
• The vegetation consists of tall grasses and scattered, drought-resistant trees like the Acacia or Baobab.
• BSh - Subtropical Steppe Climate:
• A semi-arid climate that serves as a transition zone between desert (BW) and more humid climates.
• It experiences high temperatures and erratic rainfall, supporting short-grass prairies and xerophytic shrubs.

The correct answer is Chandrapur and Bhandara.

Key Points

• Iron ore deposits in Maharashtra are geographically concentrated in two primary zones: the Eastern Vidarbha region and the South Konkan region.
• The Eastern Vidarbha belt includes districts such as Chandrapur, Gadchiroli, Gondia, and Bhandara, where minerals are found in ancient Metamorphic rock formations.
• In Chandrapur, high-grade Hematite iron ore is extracted from prominent localities such as Lohara, Asola, Dewalgaon, and Pipalgaon.
• Bhandara district contributes to the state mineral wealth with significant deposits located in areas like Khursipar and Pauni, often found in association with other metallic minerals.
• The iron ore in these regions is valued for its high iron content, typically ranging between 55% and 65%, making it suitable for industrial steel production.

 Additional Information

• Sindhudurg District:
• Located in the Konkan region, it is a major producer of iron ore, particularly in the Redi area, which facilitates easy export through its coastal proximity.
• Deccan Trap Basalt:
• Regions like Aurangabad, Jalna, Pune, and Thane are largely covered by Basaltic lava flows, which are generally devoid of significant metallic mineral deposits like iron ore.
• Industrial Importance:
• The availability of Iron Ore along with Coal in the Vidarbha region has led to the establishment of several Sponge Iron plants and Steel industries in Chandrapur.
• Manganese and Coal:
• The Nagpur-Bhandara belt is also internationally recognized for the production of Manganese, while the Wardha Valley is the primary source of Coal in the state.

The correct answer is BIRSA 101.

Key Points

• BIRSA 101 is India’s first indigenous CRISPR-Cas9 based gene therapy specifically designed to provide a curative treatment for Sickle Cell Disease (SCD).
• Launched in November 2025, the therapy represents a major breakthrough in India’s Atmanirbhar Bharat initiative in the field of advanced biotechnology and genomic medicine.
• The therapy was developed through a collaborative research effort led by the Council of Scientific and Industrial Research (CSIR) and the Institute of Genomics and Integrative Biology (IGIB), aimed at making expensive gene treatments affordable for the Indian population.
• The treatment mechanism involves harvesting the patient’s own hematopoietic stem cells, using CRISPR technology to edit the HBB gene or induce fetal hemoglobin (HbF), and then re-infusing them to produce healthy red blood cells.
• The naming of BIRSA 101 pays tribute to the tribal leader Birsa Munda, reflecting the therapy's primary target demographic, as Sickle Cell Disease disproportionately affects Scheduled Tribes across the tribal belt of India.

 Additional Information

• Sickle Cell Disease (SCD):
• It is an inherited genetic blood disorder where red blood cells become rigid and sickle-shaped, leading to anemia, organ damage, and vaso-occlusive crises.
• India has the second-highest global burden of SCD, with a high prevalence in states like Madhya Pradesh, Gujarat, and Chhattisgarh.
• CRISPR Technology:
• Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR) serves as a molecular scissor to edit DNA with high precision.
• It utilizes a guide RNA to identify the target genetic sequence and the Cas9 enzyme to execute the cut, allowing for the correction of genetic mutations.
• National Sickle Cell Anaemia Elimination Mission:
• Announced in the Union Budget 2023-24 and launched in July 2023, the mission aims to eliminate the disease as a public health threat by 2047.
• The mission focuses on universal screening of approximately 7 crore people in the age group of 0−40 years in 17 high-burden states.

The correct answer is Combining emissions, energy use and expert-reviewed climate policy data.

Key Points

• The Climate Change Performance Index (CCPI) 2025 is an independent monitoring tool that evaluates the climate protection performance of 63 countries and the European Union, which together account for more than 90% of global greenhouse gas emissions.
• The assessment framework is divided into four distinct categories with specific weightings: Greenhouse Gas (GHG) Emissions (40%), Renewable Energy (20%), Energy Use (20%), and Climate Policy (20%).
• The GHG Emissions indicator tracks current emission levels, recent trends, and the alignment of national 2030 targets with the Paris Agreement goal of limiting global warming to 1.5 degrees Celsius.
• The Climate Policy component is unique because it incorporates qualitative data through expert-reviewed assessments provided by approximately 450 climate and energy experts from non-governmental organizations and think tanks.
• The index uses a standardized methodology to provide a comparable score for each country, determining whether their progress is Very High, High, Medium, Low, or Very Low.

 Additional Information

• Publication and Authorship:
• The index is published annually by Germanwatch, the NewClimate Institute, and the Climate Action Network (CAN) International.
• The CCPI 2025 report was officially released during the COP29 summit held in Baku, Azerbaijan.
• Methodological Limitations of Other Approaches:
• Renewable Energy statistics only: This metric alone is insufficient as it does not account for the total carbon footprint or energy efficiency.
• Forest Cover and National Targets: While important for carbon sequestration, forest data is not a primary pillar of the CCPI, which prioritizes energy-related emissions and systemic decarbonization.
• Opinion Polls: Public sentiment is not a factor in the CCPI; it relies strictly on hard data from the International Energy Agency (IEA) and professional policy critiques.