RRB NTPC (UG) CBT-I Official Paper (Held On 16 Jun, 2026 Shift 3) (Previous Year Paper)

Shortcut Trick

In a parallelogram, opposite angles are equal and adjacent angles are supplementary (sum is 180°).

Given angle = 70°

Opposite angle = 70°

Adjacent angle = 180° − 70° = 110°

Angle opposite to the adjacent angle = 110°

The other three angles are 70°, 110°, and 110°.

∴ The correct answer is 70°, 110°, 110°.

Alternate Method

Given:

One angle of the parallelogram = 70°

Formula used:

1. Sum of adjacent angles of a parallelogram = 180°
2. Opposite angles of a parallelogram are equal.

Let the parallelogram be ABCD where ∠A = 70°.

⇒ ∠A + ∠B = 180° (Adjacent angles are supplementary)

⇒ 70° + ∠B = 180°

⇒ ∠B = 180° − 70°

⇒ ∠B = 110°

Since opposite angles are equal:

⇒ ∠C = ∠A = 70°

⇒ ∠D = ∠B = 110°

∴ The other three angles are 110°, 70°, and 110° (which can be written as 70°, 110°, 110°).

∴ The correct answer is 70°, 110°, 110°.

Additional Information

Sum of Interior Angles

For any quadrilateral, including a parallelogram, the sum of all interior angles is always 360°.

Properties of Diagonals

The diagonals of a parallelogram bisect each other, although they are not necessarily equal in length unless it is a rectangle.

Consecutive Angles

Any pair of consecutive angles in a parallelogram will always sum to 180° because they are interior angles on the same side of a transversal cutting parallel lines.

Shortcut Trick

The Effective Rate of interest for 2 years at 8% compounded annually = 8 + 8 + (8 × 8)/100 = 16.64%.

Total Compound Interest = 16.64% of ₹5,000.

⇒ CI = 5000 × (16.64 / 100) = 50 × 16.64 = ₹832.

∴ The correct answer is ₹832.

Alternate Method

Given:

Principal (P) = ₹5,000

Rate (R) = 8% per annum

Time (T) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)^T

Compound Interest (CI) = A − P

Calculations:

⇒ A = 5000 × (1 + 8/100)²

⇒ A = 5000 × (108/100) × (108/100)

⇒ A = 5000 × 1.08 × 1.08

⇒ A = 5000 × 1.1664

⇒ A = ₹5,832

⇒ CI = 5832 − 5000

⇒ CI = ₹832

∴ The correct answer is ₹832.

Additional Information

Difference between CI and SI

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

Effective Percentage Method

The net change for two successive percentage increases of a% and b% is calculated as [a + b + (ab/100)]%.

Compounding Periods

If interest is compounded half-yearly, the rate is halved (R/2) and the time is doubled (2n) in the standard formula.

Shortcut Trick

Net Multiplier = (1 + 20%) × (1 + 25%)

⇒ Multiplier = 1.20 × 1.25 = 1.5

Shopkeeper Cost Price = B pays ÷ Net Multiplier

⇒ CP = 3,000 ÷ 1.5 = 2,000

∴ The correct answer is ₹2,000.

Alternate Method

Given:

Amount paid by B = ₹3,000

Profit made by A = 25%

Profit made by shopkeeper = 20%

Calculations:

Let the cost price for the shopkeeper be x.

The shopkeeper sells it to A at 20% profit:

⇒ Cost price for A = x × (120 ÷ 100) = 1.2x

A sells it to B at 25% profit:

⇒ Cost price for B = (1.2x) × (125 ÷ 100)

⇒ 3,000 = 1.2x × 1.25

⇒ 3,000 = 1.5x

⇒ x = 3,000 ÷ 1.5

⇒ x = 2,000

∴ The correct answer is ₹2,000.

Additional Information

Successive Profit Percentage

When there are two successive profits of a% and b%, the effective profit percentage is given by [a + b + (a × b ÷ 100)]%.

Cost Price and Selling Price Relation

Selling Price (SP) = CP × (100 + Profit%) ÷ 100. Conversely, Cost Price (CP) = SP × 100 ÷ (100 + Profit%).

Chain Rule in Profit and Loss

In a chain of transactions, the final price = Initial CP × (1 + r₁) × (1 + r₂) × ... × (1 + r_n), where r is the profit/loss fraction.

Shortcut Trick

To find the least beneficial scheme, we calculate the effective discount percentage for each case when buying 9 toys.

Scheme A: 27% + 39% − (27 × 39 / 100) ≈ 55.47%

Scheme B: (39% + 7% − 2.73%) then with 40% → effective ≈ 65.96%

Scheme C: Flat 26% for the first 9 toys → 26%

Scheme D: 7 free on 9 items → (7 / 16) × 100 ≈ 43.75%

Comparing all, Scheme C provides the lowest discount (26%).

∴ The correct answer is Scheme C.

Alternate Method

Given: Number of toys to be bought = 9. We evaluate the discount % for each scheme.

Formula Used:

1. Successive Discounts (x, y): d_eff = x + y − (xy/100)
2. Buy X Get Y Free: d_eff = [Y / (X + Y)] × 100

Calculations:

Scheme A: Successive 27% and 39%

⇒ d = 27 + 39 − (27 × 39 / 100) = 66 − 10.53 = 55.47%

Scheme B: Successive 39%, 7%, and 40%

⇒ Remainder factor = (1 − 0.39) × (1 − 0.07) × (1 − 0.40)

⇒ 0.61 × 0.93 × 0.60 = 0.34038

⇒ Effective Discount = (1 − 0.34038) × 100 = 65.96%

Scheme C: 26% discount on first 9 toys

⇒ Since customer buys exactly 9 toys, the discount is a flat 26%.

Scheme D: 7 toys free on buying 9 toys

⇒ Total items = 9 + 7 = 16 | Free items = 7

⇒ Discount % = (7 / 16) × 100 = 43.75%

The least beneficial scheme for the customer is the one with the minimum discount percentage.

⇒ 26% (C) < 43.75% (D) < 55.47% (A) < 65.96% (B)

∴ The correct answer is Scheme C.

Additional Information

Successive Discount Rule

For multiple discounts, the final price is P × (1−d₁/100) × (1−d₂/100) ... Total discount = 100 − [100 × (Product of remainders)].

Buy X Get Y Free

Effective Discount % = [Free Items / (Purchased Items + Free Items)] × 100.

Comparison of Schemes

The scheme most beneficial to the customer is the one with the highest discount, while the scheme most beneficial to the shopkeeper is the one with the lowest discount.

Shortcut Trick

Total Distance = 200 + 300 = 500 m

Relative Speed (Opposite) = 500 ÷ 20 = 25 m/s

Relative Speed (Same) = 500 ÷ 48 = 10.417 m/s

Faster Speed = (25 + 10.417) ÷ 2 = 17.708 m/s = 17.708 × 18/5 km/h

Faster Speed = 63.75 km/h

∴ The correct answer is 63.75 km/h.

Alternate Method

Given:

⇒ Length of Train P (L₁) = 200 m

⇒ Length of Train Q (L₂) = 300 m

⇒ Time taken in same direction (T_same) = 48 sec

⇒ Time taken in opposite direction (T_opp) = 20 sec

Formula Used:

⇒ Relative Speed (Opposite) = (L₁ + L₂) ÷ T_opp = S_f + S_s

⇒ Relative Speed (Same) = (L₁ + L₂) ÷ T_same = S_f − S_s

Calculations:

⇒ Total distance to be covered in both cases = 200 + 300 = 500 m

⇒ Let Faster Train Speed = S_f and Slower Train Speed = S_s

⇒ S_f + S_s = 500 ÷ 20 = 25 m/s −−− (1)

⇒ S_f − S_s = 500 ÷ 48 = 125/12 m/s −−− (2)

⇒ Adding (1) and (2): 2 × S_f = 25 + 125/12

⇒ 2 × S_f = (300 + 125) ÷ 12 = 425 ÷ 12

⇒ S_f = 425 ÷ 24 m/s

⇒ To convert to km/h: S_f = (425 ÷ 24) × (18 ÷ 5)

⇒ S_f = 85 × (3 ÷ 4) = 255 ÷ 4 = 63.75 km/h

∴ The correct answer is 63.75 km/h.

Additional Information

Relative Speed Concept

When two objects move in the opposite direction, their relative speed is the sum (u + v). When they move in the same direction, it is the difference (u − v).

Unit Conversion

To convert speed from meters per second (m/s) to kilometers per hour (km/h), multiply by 18/5 or 3.6.

Crossing Distance

The total distance covered when two trains cross each other is always the sum of their lengths (L₁ + L₂), regardless of their direction.

Shortcut Trick

The given sequence 3, 7, 11, ..., 51 is an Arithmetic Progression (AP).

For any AP, the Arithmetic Mean is simply the average of the first term and the last term.

First term (a) = 3, Last term (l) = 51

Arithmetic Mean = (a + l) ÷ 2 = (3 + 51) ÷ 2 = 54 ÷ 2 = 27.

∴ The correct answer is 27.

Alternate Method

Given: First term (a) = 3, Common difference (d) = 7 − 3 = 4, Last term (l) = 51

Formula Used: n = [(l − a) ÷ d] + 1; Sum (S_n) = (n ÷ 2) × (a + l); Mean = Sum ÷ n

⇒ Number of terms (n): 51 = 3 + (n − 1) × 4

⇒ 48 = (n − 1) × 4 ⇒ 12 = n − 1 ⇒ n = 13

⇒ Sum (S_n): (13 ÷ 2) × (3 + 51) = 6.5 × 54 = 351

⇒ Arithmetic Mean: 351 ÷ 13 = 27

∴ The correct answer is 27.

Additional Information

Properties of Arithmetic Progression (AP)

In an AP, the arithmetic mean is always equal to the median of the series. For a symmetric distribution or linear sequence, Mean = Median = (First + Last) ÷ 2.

General Term of an AP

The n^th term is calculated as a_n = a + (n − 1)d, where 'a' is the first term and 'd' is the common difference.

Sum of n terms

The sum of the first n terms of an AP can also be expressed as S_n = (n ÷ 2) × [2a + (n − 1)d].

Shortcut Trick

LCM of 54, 81, and 108 = 324 units (Total Capacity).

Efficiency of C = 6, D = 4, and Net (C+D−E) = 3.

Efficiency of Drain E = (6 + 4) − 3 = 7 units/min.

Time for E = 324 ÷ 7 = 46.2857... ≈ 46.29 min.

∴ The correct answer is 46.29 min.

Alternate Method

Given: Filling time for Tap C = 54 min, Tap D = 81 min. Combined filling time with Drain E = 108 min.

Formula: Net Efficiency = Efficiency of Filling Taps − Efficiency of Emptying Taps

⇒ Efficiency of Drain E = Efficiency(C) + Efficiency(D) − Efficiency(C + D − E)

⇒ Efficiency of Drain E = 6 + 4 − 3 = 7 units/min.

⇒ Time required by Drain E alone = Total Work ÷ Efficiency of E

⇒ Time = 324 ÷ 7

⇒ Time ≈ 46.29 min.

∴ The correct answer is 46.29 min.

Additional Information

Pipes and Cisterns Principle

If a pipe fills a tank in 'x' hours and another empties it in 'y' hours, the net work in 1 hour is (1/x − 1/y).

Efficiency and Time

Efficiency is inversely proportional to the time taken to complete the work (E ∝ 1/T).

Negative Work

An outlet pipe (drain) performs negative work because it removes water from the cistern.

Shortcut Trick

Net price after 20% discount = 24,000 × 80% = ₹19,200

Final Selling Price after additional ₹800 reduction = 19,200 − 800 = ₹18,400

∴ The correct answer is ₹18,400.

Alternate Method

Given:

Marked Price (MP) of the washing machine = ₹24,000

Festival Discount percentage = 20%

Additional cash discount = ₹800

Formula Used:

Selling Price (SP) = [MP × (100 − Discount%)/100] − Additional Discount

Calculations:

⇒ Price after 20% discount = 24,000 − (20% of 24,000)

⇒ Price after 20% discount = 24,000 − (20/100 × 24,000)

⇒ Price after 20% discount = 24,000 − 4,800 = ₹19,200

⇒ Final Selling Price = 19,200 − 800

⇒ Final Selling Price = ₹18,400

∴ The correct answer is ₹18,400.

Additional Information

Marked Price (MP)

The price printed on the label of an item before any discount is applied. It is also known as List Price or Tag Price.

Net Discount Formula

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

Selling Price (SP) Calculation

SP = MP − Discount. If profit is given, SP = CP + Profit. If loss is given, SP = CP − Loss.

Shortcut Trick

Use the Algebraic Identity: (Difference)² = (Sum)² − 4 × (Product)

⇒ (Difference)² = (44)² − 4 × 228

⇒ (Difference)² = 1936 − 912 = 1024

⇒ Difference = √1024 = 32

∴ The correct answer is 32.

Alternate Method

Given:

Sum of two positive numbers (x + y) = 44

Product of two positive numbers (xy) = 228

Formula Used:

(x − y)² = (x + y)² − 4xy

Calculations:

⇒ (x − y)² = (44)² − 4 × 228

⇒ (x − y)² = 1936 − 912

⇒ (x − y)² = 1024

⇒ x − y = √1024

⇒ x − y = 32

∴ The correct answer is 32.

Additional Information

Fundamental Algebraic Identities

1. (x + y)² = x² + y² + 2xy
   
2. (x − y)² = x² + y² − 2xy

Relationship between Sum, Difference, and Product

(x + y)² − (x − y)² = 4xy. This identity is extremely useful for finding the Difference when the Sum and Product are known.

Quadratic Roots Property

If x and y are roots of a quadratic equation t² − (Sum)t + (Product) = 0, then the Difference between the roots is √D, where D = (Sum)² − 4(Product).

Shortcut Trick

Total Height (Building + Tower) = Distance × tan(Angle to Top)

Total Height = 70 × tan(60°) = 70√3 m

Tower Height = Total Height − Building Height

Tower Height = 70√3 − 30 m

∴ The correct answer is 70√3 − 30 m.

Alternate Method

Given:

Height of the building (BT) = 30 m

Distance from the point (P) to the building (B) = 70 m

Angle of elevation to top of tower (C) = 60°

Angle of elevation to bottom of tower (T) = 30°

Formula Used:

In a right-angled triangle, tan θ = Perpendicular / Base

Calculations:

Let the height of the tower be h.

In right-angled triangle ΔPBC (Base to Top of Tower):

⇒ tan 60° = BC / PB

⇒ √3 = (BT + TC) / 70

⇒ √3 = (30 + h) / 70

⇒ 30 + h = 70 × √3

⇒ h = 70√3 − 30

∴ The correct answer is 70√3 − 30 m.

Additional Information

Angle of Elevation

The angle formed between the horizontal line and the line of sight when an observer looks at an object above the horizontal level.

Trigonometric Ratios

Standard values used in height and distance problems: tan 30° = 1/√3, tan 45° = 1, and tan 60° = √3.

Total Height Relation

For a structure placed on a base, the total height from the ground is the sum of the base height and the structure height (H = h_base + h_object).

Shortcut Trick

If third proportional of a and b is c, then c = b² ÷ a.

TP₁ (36, 48) = (48 × 48) ÷ 36 = 64.

TP₂ (49, 64) = (64 × 64) ÷ 49.

Ratio = 64 : (64 × 64 ÷ 49) = 1 : (64 ÷ 49) = 49 : 64.

∴ The correct answer is 49:64.

Alternate Method

Given:

First pair: a₁ = 36, b₁ = 48

Second pair: a₂ = 49, b₂ = 64

Formula Used:

For two numbers a and b, the third proportional x is calculated as: a : b = b : x ⇒ x = b² ÷ a.

Calculations:

⇒ Let x be the third proportional of 36 and 48.

⇒ x = (48 × 48) ÷ 36

⇒ x = 2304 ÷ 36 = 64

⇒ Let y be the third proportional of 49 and 64.

⇒ y = (64 × 64) ÷ 49 = 4096 ÷ 49

⇒ Required Ratio = x : y = 64 : (4096 ÷ 49)

⇒ Ratio = (64 × 49) : 4096

⇒ Ratio = 3136 : 4096

⇒ Simplifying by dividing both terms by 64: (3136 ÷ 64) : (4096 ÷ 64)

⇒ Ratio = 49 : 64

⇒ This result corresponds to the value given in Option (3).

∴ The correct answer is 49:64.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(a × b). It is the value x such that a : x = x : b.

Fourth Proportional

For four numbers a, b, c, and d in proportion (a : b = c : d), d is the fourth proportional, calculated as d = (b × c) ÷ a.

Ratio and Proportion Properties

If a/b = c/d, then by Invertendo b/a = d/c, and by Alternando a/c = b/d.

Shortcut Trick

Difference in ratio units between Bala and Amit = 7 − 5 = 2 units.

Given that 2 units = ₹3,600 ⇒ 1 unit = ₹1,800.

Chetan total savings = 9 units = 9 × 1,800 = ₹16,200.

∴ The correct answer is ₹16,200.

Alternate Method

Given: Savings ratio of Amit, Bala, and Chetan = 5 : 7 : 9. Bala savings − Amit savings = ₹3,600.

⇒ Let the savings of Amit, Bala, and Chetan be 5x, 7x, and 9x respectively. ⇒ According to the question, Bala savings − Amit savings = 3600. ⇒ 7x − 5x = 3600. ⇒ 2x = 3600. ⇒ x = 3600 ÷ 2 = 1800. ⇒ Chetan total savings = 9x. ⇒ Chetan total savings = 9 × 1800. ⇒ Total = ₹16,200.

∴ The correct answer is ₹16,200.

Additional Information

Ratio and Proportion

A ratio represents how many times one number contains another. For a ratio a:b:c, actual values can be expressed as ax, bx, and cx.

Unitary Method

This method involves finding the value of one unit by dividing a known quantity by its ratio parts, then multiplying by the desired ratio parts.

Compound Ratio

When two or more ratios are multiplied term by term (a:b and c:d), the resulting ratio (ac:bd) is called the compound ratio.

Shortcut Trick

Assume all 8 notebooks are of the first type.

The extra cost for the 5 Type 2 notebooks is 5 × ₹20 = ₹100.

Subtract this excess from the total: ₹420 − ₹100 = ₹320.

Cost of one Type 1 notebook = 320 ÷ 8 = ₹40.

∴ The correct answer is ₹40.

Alternate Method

Given:

Quantity of Type 1 = 3 | Quantity of Type 2 = 5

Total Cost of 3 Type 1 and 5 Type 2 = ₹420

Price Difference: Type 2 = Type 1 + ₹20

Formula Used:

Total Price = (n₁ × p₁) + (n₂ × p₂)

Let the cost of one Type 1 notebook be x.

⇒ Cost of one Type 2 notebook = x + 20

⇒ 3 × x + 5 × (x + 20) = 420

⇒ 3x + 5x + 100 = 420

⇒ 8x = 420 − 100

⇒ 8x = 320

⇒ x = 320 ÷ 8

⇒ x = 40

∴ The correct answer is ₹40.

Additional Information

Linear Equation in One Variable

An equation which can be written in the form ax + b = 0, where a and b are real numbers and a ≠ 0.

Substitution Method

A strategy for solving systems of equations by expressing one variable in terms of the other to reduce the number of variables.

Price-Quantity Relation

Total Expenditure is always the product of the Price per unit and the Quantity purchased (E = P × Q).

Shortcut Trick

For two successive discounts of x% and y%, the net percentage reduction is given by the formula: (x + y − (x × y) / 100)%.

⇒ Net Discount = (10 + 20 − (10 × 20) / 100)%

⇒ Net Discount = (30 − 2)%

⇒ Net Discount = 28%

∴ The correct answer is 28%.

Alternate Method

Given:

First successive discount = 10%

Second successive discount = 20%

Let the Marked Price (MP) of the item be 100.

⇒ Price after first discount (10%) = 100 − (10% of 100)

⇒ Price after first discount = 100 − 10 = 90

⇒ Price after second discount (20%) = 90 − (20% of 90)

⇒ Price after second discount = 90 − (0.20 × 90) = 90 − 18

⇒ Final Selling Price (SP) = 72

⇒ Net percentage reduction = ((MP − Final SP) / MP) × 100

⇒ Net reduction = ((100 − 72) / 100) × 100 = 28%

∴ The correct answer is 28%.

Additional Information

Three Successive Discounts

For three successive discounts of a%, b%, and c%, first find the net discount of a and b, then use that result with c to find the total net discount.

Successive Percentage Change Formula

The effective change for successive variations x% and y% is (x + y + (xy/100))%. Use positive values for increase and negative for decrease/discount.

Multiplier Method

Final Value = Initial Value × (1 − d₁/100) × (1 − d₂/100). For 10% and 20% discounts, the multiplier is 0.9 × 0.8 = 0.72, implying a 28% reduction.

Shortcut Trick

Tap 2 fills the cistern in 13 hr and Tap 3 empties it in 13 hr, so their efficiencies cancel out.

The net filling is effectively done by Tap 1 alone at its original rate.

Tap 1 fills the entire cistern in 4 hr.

Time required to fill one-fourth of the cistern = Total time ÷ 4 = 4 hr ÷ 4 = 1 hr.

∴ The correct answer is 1 hr.

Alternate Method

Given:

Time taken by Tap A to fill = 4 hr

Time taken by Tap B to fill = 13 hr

Time taken by Tap C to empty = 13 hr

Formula Used:

Efficiency = Total Work ÷ Time Taken

Calculations:

⇒ Total capacity of the cistern = LCM(4, 13, 13) = 52 units

⇒ Net efficiency when all taps are open = 13 + 4 − 4 = 13 units/hr

⇒ Target to fill one-fourth of the cistern = 52 ÷ 4 = 13 units

⇒ Time taken = Target Work ÷ Net Efficiency

⇒ Time taken = 13 ÷ 13 = 1 hr

∴ The correct answer is 1 hr.

Additional Information

Negative Efficiency

In pipe and cistern problems, the efficiency of an outlet pipe (or emptying tap) is always treated as negative because it reduces the total work done.

Net Filling Rate

When multiple pipes work together, the net rate of filling is the algebraic sum of their individual rates: Net Rate = ∑(Inlet Rates) − ∑(Outlet Rates).

Total Capacity via LCM

Assume the total capacity of the tank/cistern as the Least Common Multiple (LCM) of the individual times taken by each pipe to simplify efficiency calculations.

Given:

The exponential equation is 6^x − 6^x−1 = 30

Formula used:

a^m−n = a^m ÷ aⁿ

Calculations:

6^x − 6^x−1 = 30

⇒ 6^x − (6^x ÷ 6¹) = 30

⇒ 6^x × (1 − 1/6) = 30

⇒ 6^x × (5/6) = 30

⇒ 6^x = (30 × 6) ÷ 5

⇒ 6^x = 6 × 6

⇒ 6^x = 36

⇒ 6^x = 6²

⇒ x = 2

To find the value of (2x − 1) ÷ (2x + 3), we substitute x = 2 in the expression:

⇒ (2 × 2 − 1) ÷ (2 × 2 + 3)

⇒ (4 − 1) ÷ (4 + 3)

⇒ 3/7

∴ The correct answer is option (4).

Shortcut Trick

To check divisibility by 11, calculate the difference between the sum of digits at odd places and the sum of digits at even places.

For 978626: Sum of digits at odd places (1^st, 3^rd, 5^th) = 9 + 8 + 2 = 19.

Sum of digits at even places (2^nd, 4^th, 6^th) = 7 + 6 + 6 = 19.

Difference = 19 − 19 = 0. If the difference is 0 or a multiple of 11, the number is divisible by 11.

∴ The correct answer is 978626.

Alternate Method

Given: Options (1) 869756, (2) 978626, (3) 447255, (4) 112044.

Formula: A number is divisible by 11 if (Sum of digits at odd places) − (Sum of digits at even places) = 0, 11, 22, ...

Let us check each option systematically:

⇒ For 869756: (8 + 9 + 5) − (6 + 7 + 6) = 22 − 19 = 3 (Not divisible by 11)

⇒ For 978626: (9 + 8 + 2) − (7 + 6 + 6) = 19 − 19 = 0 (Divisible by 11)

⇒ For 447255: (4 + 7 + 5) − (4 + 2 + 5) = 16 − 11 = 5 (Not divisible by 11)

⇒ For 112044: (1 + 2 + 4) − (1 + 0 + 4) = 7 − 5 = 2 (Not divisible by 11)

∴ The correct answer is 978626.

Additional Information

Divisibility Rule of 11

A number is divisible by 11 if the alternating sum of its digits (d₁ − d₂ + d₃ − d₄ ...) is a multiple of 11 (including 0).

Divisibility Rule of 9

A number is divisible by 9 if the sum of all its digits is divisible by 9.

Divisibility Rule of 3

A number is divisible by 3 if the sum of its digits is a multiple of 3.

Divisibility Rule of 7

Double the last digit and subtract it from the rest of the number; if the result is divisible by 7, the original number is also divisible by 7.

Shortcut Trick

Both numbers must be divisible by their HCF (15), which eliminates options 2 and 4.

The Product of two numbers must equal HCF × LCM = 15 × 225 = 3375.

Testing Option 1: 45 × 75 = 3375 (Matches).

Testing Option 3: 15 × 75 = 1125 (Incorrect).

∴ The correct answer is 45 and 75.

Alternate Method

Given: HCF = 15 and LCM = 225.

Formula Used: Product of two numbers = HCF × LCM

⇒ Let the numbers be 15a and 15b, where a and b are co-prime.

⇒ 15a × 15b = 15 × 225

⇒ 225 × ab = 3375

⇒ ab = 3375 ÷ 225 = 15

⇒ Possible co-prime pairs for (a, b) are (1, 15) and (3, 5).

⇒ Case 1: (15 × 1, 15 × 15) = (15, 225)

⇒ Case 2: (15 × 3, 15 × 5) = (45, 75)

⇒ Comparing with the given options, the pair is 45 and 75.

∴ The correct answer is 45 and 75.

Additional Information

HCF and LCM Relation

For any two positive integers a and b, the relationship is always HCF(a, b) × LCM(a, b) = a × b.

Divisibility Property

The HCF of any group of numbers is always a factor of their LCM.

Co-prime Factorization

If HCF = h, the numbers can be expressed as hx and hy, where LCM = hxy and x, y are co-prime integers.

Shortcut Trick

Assume the base average is 24.

Calculate deviations: (18 − 24) = −6, (20 − 24) = −4, (25 − 24) = +1, (27 − 24) = +3.

Net deviation of 4 numbers = −6 − 4 + 1 + 3 = −6.

To maintain the average, the fifth number must balance this: 24 − (−6) = 30.

∴ The correct answer is 30.

Alternate Method

Given: Average of 5 numbers = 24, Four numbers are 18, 20, 25, and 27.

Formula: Sum = Average × Count of numbers

⇒ Total sum of 5 numbers = 24 × 5 = 120

⇒ Sum of 4 given numbers = 18 + 20 + 25 + 27 = 90

⇒ Let the fifth number be x.

⇒ 90 + x = 120

⇒ x = 120 − 90

⇒ x = 30

∴ The correct answer is 30.

Additional Information

Weighted Average

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

Arithmetic Progression Average

For numbers in an AP (equal gaps), the average is simply (First term + Last term) ÷ 2 or the middle term.

Effect of Constant Change

If each number in a set is increased, decreased, multiplied, or divided by a constant k, the new average also changes by the same constant k.

Shortcut Trick

Given: 1.2x = 0.5y ⇒ x/y = 0.5/1.2 = 5/12

Let x = 5 and y = 12

Required value = (x + y) / (x − y) = (5 + 12) / (5 − 12) = 17 / (−7)

∴ The correct answer is −17/7.

Alternate Method

Given: 1.2x = 0.5y

Formula Used: Ratio and Proportion properties.

⇒ 1.2x = 0.5y

⇒ x / y = 0.5 / 1.2

⇒ x / y = 5 / 12

⇒ Let x = 5k and y = 12k

⇒ (x + y) / (x − y) = (5k + 12k) / (5k − 12k)

⇒ (x + y) / (x − y) = 17k / (−7k)

⇒ (x + y) / (x − y) = −17 / 7

∴ The correct answer is −17/7.

Additional Information

Componendo and Dividendo

If a/b = c/d, then (a + b)/(a − b) = (c + d)/(c − d). This is useful for solving fractional equations quickly.

Ratio Substitution

In homogeneous expressions like (x+y)/(x-y), the actual values of x and y are not needed; only their ratio is sufficient to find the result.

Decimal to Fraction

Always convert decimals to simple fractions (e.g., 0.5 = 1/2, 1.2 = 6/5) to avoid calculation errors in ratios.

Shortcut Trick

Profit 25% = 1/4 in fraction form.

For a dishonest dealer selling at cost price, the Weight Ratio is the inverse of the Price Ratio.

Price Ratio (CP : SP) = 4 : 5 ⇒ Weight Ratio (False : True) = 4 : 5.

Given True Weight (5 units) = 1000 gm.

1 unit = 200 gm ⇒ Actual Weight (4 units) = 4 × 200 = 800 gm.

∴ The correct answer is 800 gm.

Alternate Method

Given:

Claimed sale at cost price (CP).

Profit percentage = 25%.

Standard True Weight = 1 kg = 1000 gm.

Formula Used:

Profit % = [(True Weight − False Weight) ÷ False Weight] × 100

Calculations:

Let the false weight used be x gm.

⇒ 25 = [(1000 − x) ÷ x] × 100

⇒ 25 ÷ 100 = (1000 − x) ÷ x

⇒ 1 ÷ 4 = (1000 − x) ÷ x

⇒ x = 4 × (1000 − x)

⇒ x = 4000 − 4x

⇒ 5x = 4000

⇒ x = 800 gm

∴ The correct answer is 800 gm.

Additional Information

Dishonest Dealer Concept

When a shopkeeper sells at CP but uses less weight, the Profit % = (Error ÷ Actual Value Given) × 100.

Dual Profit Scenario

If the dealer marks up the price by P% and also uses a false weight, Net Profit % = [((100+P) × True Weight) ÷ False Weight] − 100.

Inverse Proportion Rule

Profit % and weight given are inversely related; to gain 25% (1/4), the weight must be reduced to 4/5 of the original.

Shortcut Trick

Total interest percentage = Rate × Time = 16% × 3 = 48%.

Since 48% of the Principal = ₹1,320.

Principal (100%) = (1320 ÷ 48) × 100 = 27.5 × 100 = ₹2,750.

∴ The correct answer is ₹2,750.

Alternate Method

Given:

Simple Interest (SI) = ₹1,320

Time (T) = 3 years

Rate (R) = 16% per annum

Formula used:

Principal (P) = (SI × 100) ÷ (R × T)

⇒ P = (1320 × 100) ÷ (16 × 3)

⇒ P = 132000 ÷ 48

⇒ P = 2750

∴ The correct answer is ₹2,750.

Additional Information

Total Amount in Simple Interest

The total amount (A) is the sum of the principal and the interest earned: A = P + SI = P × (1 + RT/100).

SI vs CI for First Year

For the first year, if the interest is compounded annually, the Simple Interest and Compound Interest are always equal.

Difference between CI and SI for 2 Years

The difference between Compound Interest and Simple Interest for 2 years is given by the formula: Difference = P × (R/100)².

Shortcut Trick

In problems involving Sum (S) and Difference (D) of two values, the larger value (Mother's age) is calculated as:

Mother's age = (Sum + Difference) ÷ 2

⇒ Mother's age = (52 + 24) ÷ 2

⇒ Mother's age = 76 ÷ 2 = 38 years.

∴ The correct answer is 38 years.

Alternate Method

Given:

Sum of Mother's age (M) and Daughter's age (D) = 52 years

Difference between their ages = 24 years

Let the Mother's age be M and the Daughter's age be D.

According to the question:

1. M + D = 52

2. M − D = 24

By adding equation (1) and equation (2):

⇒ (M + D) + (M − D) = 52 + 24

⇒ 2M = 76

⇒ M = 76 ÷ 2

⇒ M = 38 years.

∴ The correct answer is 38 years.

Additional Information

Linear Equations in Two Variables

Equations of the form x + y = A and x − y = B can be solved quickly by finding x = (A + B) ÷ 2 and y = (A − B) ÷ 2.

Age Difference Property

The difference between the ages of two people remains constant regardless of how many years pass or how many years ago it was.

Finding the Smaller Value

To find the younger person's age (Daughter), subtract the difference from the sum and divide by 2: (52 − 24) ÷ 2 = 14 years.

Shortcut Trick

Convert all numbers into like decimals: 7.0, 12.4, and 1.0.

Remove the decimal point to treat them as whole numbers: 70, 124, and 10.

Calculate the LCM of 70, 124, and 10 using prime factorization.

LCM(70, 124, 10) = 4340.

Divide the result by 10 to place the decimal point back: 4340 ÷ 10 = 434.

∴ The correct answer is 434.

Alternate Method

Given: The numbers are 7, 12.4, and 1.

Formula Used: LCM of Fractions = LCM(Numerators) ÷ HCF(Denominators).

⇒ Represent numbers as fractions: 7 = 7/1, 12.4 = 124/10 = 62/5, 1 = 1/1.

⇒ To find the LCM of 7/1, 62/5, and 1/1, find the LCM of numerators (7, 62, 1) and HCF of denominators (1, 5, 1).

⇒ LCM(7, 62, 1) = 7 × 62 = 434 (since 7 and 62 have no common factors).

⇒ HCF(1, 5, 1) = 1.

⇒ Required LCM = 434 ÷ 1 = 434.

∴ The correct answer is 434.

Additional Information

LCM of Fractions

The Least Common Multiple of a set of fractions is given by the formula: LCM = LCM of Numerators ÷ HCF of Denominators.

HCF of Fractions

The Highest Common Factor of a set of fractions is given by the formula: HCF = HCF of Numerators ÷ LCM of Denominators.

LCM of Decimals

To find the LCM of decimals, first convert all numbers into like decimals (equal decimal places) and then find the LCM as if they were integers, finally adjusting the decimal point.

Shortcut Trick

Net multiplier = (1 + 0.20) × (1 − 0.10) × (1 + 0.15)

Net multiplier = 1.20 × 0.90 × 1.15 = 1.08 × 1.15 = 1.242

Overall percentage change = (1.242 − 1) × 100 = 24.2%

∴ The correct answer is 24.2% increase.

Alternate Method

Given: Year 1 change = 20% increase; Year 2 change = 10% decrease; Year 3 change = 15% increase.

Formula: Final Revenue = Initial Revenue × (100 + r₁)/100 × (100 + r₂)/100 × (100 + r₃)/100

⇒ Let the initial Revenue be 100 units.

⇒ Revenue after 1st year = 100 + (20% of 100) = 120 units.

⇒ Revenue after 2nd year = 120 − (10% of 120) = 120 − 12 = 108 units.

⇒ Revenue after 3rd year = 108 + (15% of 108) = 108 + 16.2 = 124.2 units.

⇒ Overall percentage change = 124.2 − 100 = 24.2%.

∴ The correct answer is 24.2% increase.

Additional Information

Successive Percentage Formula

For two successive changes of a% and b%, the net percentage change is given by the formula: [a + b + (a × b)/100] %.

Multiplying Factor Method

An x% increase corresponds to a multiplier of (1 + x/100), while an x% decrease corresponds to a multiplier of (1 − x/100). The product of these factors gives the final result.

Base Value Adjustment

In successive changes, each percentage change is applied to the updated value from the previous step, not the original starting value.

Shortcut Trick

Metal Volume = π(R² − r²)h = 396

Given thickness (R − r) = 1 ⇒ (R − r)(R + r) = 9 ⇒ R + r = 9

Solving R − r = 1 and R + r = 9 gives inner radius (r) = 4 units.

Inner volume = πr²h = (22/7) × 16 × 14 = 704 cubic units.

∴ The correct answer is 704 cubic units.

Alternate Method

Given: Length (h) = 14 units, Thickness (t) = 1 unit, Metal Volume = 396 cubic units.

Formula Used: Volume of metal = πh(R² − r²); Inner volume = πr²h

Let the inner radius be r units and outer radius be R units.

⇒ Thickness = R − r = 1 unit ⇒ R = r + 1

⇒ Volume of metal = π × (R² − r²) × h

⇒ 396 = (22/7) × ((r + 1)² − r²) × 14

⇒ 396 = 22 × (r² + 2r + 1 − r²) × 2

⇒ 396 = 44 × (2r + 1)

⇒ 2r + 1 = 396 ÷ 44

⇒ 2r + 1 = 9

⇒ 2r = 8 ⇒ r = 4 units

⇒ Inner volume = πr²h

⇒ Inner volume = (22/7) × 4² × 14

⇒ Inner volume = 22 × 16 × 2 = 704 cubic units

∴ The correct answer is 704 cubic units.

Additional Information

Volume of Hollow Cylinder

The volume of the material in a hollow cylinder is given by V = πh(R² − r²), where R is the outer radius and r is the inner radius.

Total Surface Area (TSA)

The Total Surface Area of a hollow cylinder is the sum of the inner CSA, outer CSA, and the area of the two circular rings: TSA = 2πh(R + r) + 2π(R² − r²).

Thickness Property

The thickness (t) is the difference between the outer radius and the inner radius: t = R − r.

Shortcut Trick

Rise in water level (h) = (Total volume of 30 spheres) ÷ (Area of cylinder base)

h = [30 × (4/3) × π × 7³] ÷ [π × 20²]

h = [40 × 343] ÷ 400

h = 13720 ÷ 400 = 34.3 cm

∴ The correct answer is 34.3 cm.

Alternate Method

Given:

Radius of cylindrical tank (R) = 20 cm

Radius of each solid sphere (r) = 7 cm

Number of solid spheres (n) = 30

Formula Used:

Volume of cylinder = π × R² × h

Volume of sphere = (4/3) × π × r³

Calculations:

Let the rise in water level in the cylinder be h cm.

When the spheres are completely immersed, the volume of water displaced is equal to the total volume of the 30 spheres:

⇒ Volume of water risen in cylinder = 30 × Volume of one sphere

⇒ π × R² × h = 30 × (4/3) × π × r³

Canceling π from both sides:

⇒ R² × h = 10 × 4 × r³

⇒ 20² × h = 40 × 7³

⇒ 400 × h = 40 × 343

⇒ 400 × h = 13720

⇒ h = 13720 ÷ 400

⇒ h = 34.3 cm

∴ The correct answer is

Shortcut Trick

Let the total distance be the LCM of denominators (5 and 4) = 20 units.

Distance by train = 3/5 × 20 = 12 units.

Distance by car = 1/4 × 20 = 5 units.

Remaining distance on foot = 20 − (12 + 5) = 3 units.

Given that 3 units = 300 m ⇒ 1 unit = 100 m.

Total distance = 20 units = 2000 m = 2 km.

∴ The correct answer is 2 km.

Alternate Method

Let the total distance from home to office be d meters.

Distance traveled by train = 3/5 of d

Distance traveled by car = 1/4 of d

Distance traveled on foot = 300 m

⇒ Train distance + Car distance + Foot distance = Total distance

⇒ (3/5) × d + (1/4) × d + 300 = d

⇒ 300 = d − (3/5 + 1/4) × d

⇒ 300 = d − [(12 + 5) / 20] × d

⇒ 300 = d − (17/20) × d

⇒ 300 = (3/20) × d

⇒ d = (300 × 20) ÷ 3

⇒ d = 2000 m

Converting meters into kilometers:

⇒ d = 2000 ÷ 1000 = 2 km

∴ The correct answer is 2 km.

Additional Information

Fraction of a Whole

The sum of all fractional parts of any quantity is always equal to 1. The remaining fraction is calculated as 1 − (sum of known fractions).

Unit Conversion

To convert distance from meters to kilometers, divide the value by 1000 (since 1 km = 1000 m).

Distance-Speed-Time Relation

Distance is directly proportional to speed and time: Distance = Speed × Time.

Given:

2^x+1 × 4^y−2 = 32

x = 3y

Formula used:

a^m × aⁿ = a^m+n

(a^m)ⁿ = a^mn

Calculation:

Expressing the equation in base 2:

2^x+1 × (2²)^y−2 = 2⁵

⇒ 2^x+1 × 2^2(y−2) = 2⁵

⇒ 2^x+1 × 2^2y−4 = 2⁵

⇒ 2^x+1+2y−4 = 2⁵

⇒ 2^x+2y−3 = 2⁵

Comparing the exponents:

⇒ x + 2y − 3 = 5

⇒ x + 2y = 8

Substituting x = 3y from the given data:

⇒ 3y + 2y = 8

⇒ 5y = 8

⇒ y = 8/5

⇒ y = 1.6

∴ The correct answer is option (3).

Shortcut Trick

A's age after 8 years = 32 years.

A's present age = 32 − 8 = 24 years.

Ratio of present ages A : B = 4 : 5.

4 units → 24 years ⇒ 1 unit = 6 years.

B's present age = 5 units × 6 = 30 years.

∴ The correct answer is 30 years.

Alternate Method

Given:

Ratio of present ages of A and B = 4 : 5

Age of A after 8 years = 32 years

Calculations:

Let the present age of A be 4x and B be 5x.

According to the question, A's age after 8 years is 32.

⇒ 4x + 8 = 32

⇒ 4x = 32 − 8

⇒ 4x = 24

⇒ x = 24 ÷ 4

⇒ x = 6

Now, calculate B's present age:

⇒ B's present age = 5x

⇒ B's present age = 5 × 6 = 30 years.

Therefore, the value matches Option (2).

∴ The correct answer is 30 years.

Additional Information

Constant Age Difference

The difference between the ages of two persons always remains constant, regardless of how many years pass or have passed.

Ratio Scaling

If the ratio of ages is given as a:b, and the age of one person is known, the other can be found using the unitary method (Age ÷ Ratio Part × Required Part).

Future and Past Ages

To find age 'n' years after, add 'n' to the present age. To find age 'n' years ago, subtract 'n' from the present age.

The correct answer is Marine deposits and wood fossils.

Key Points

• The Great Indian Desert, also known as the Thar Desert, has a geological history that reveals it was once submerged under the sea during the Mesozoic era, specifically during the Jurassic and Cretaceous periods.
• The presence of extensive marine deposits in the Jaisalmer and Bikaner regions serves as primary evidence of ancient marine transgressions where the Tethys Sea covered large parts of western Rajasthan.
• Evidence of this maritime past is preserved at the Akal Wood Fossil Park, located about 17 km from Jaisalmer, which contains petrified remains of gymnosperms and other trees dating back nearly 180 million years.
• The discovery of fossilized ammonites, bivalves, and other marine invertebrates within the sedimentary rock layers confirms that the region supported a diverse marine ecosystem before tectonic shifts caused the sea to retreat.
• Geologists have identified that the desert floor consists of sedimentary rocks like sandstones, limestones, and shales, which are characteristic of shallow marine environments and coastal deltas from the Mesozoic and Cenozoic eras.

 Additional Information

• Other options do not serve as evidence for this specific geological phenomenon:
• Black soil:
• Also known as Regur soil, it is typically formed from the weathering of basaltic volcanic rocks.
• It is predominantly found in the Deccan Trap region, covering states like Maharashtra and Madhya Pradesh, rather than being an indicator of marine history in the Thar.
• Glacial deposits:
• These are sediments like tillites transported and deposited by glaciers.
• While found in the Himalayas or related to the Permo-Carboniferous glaciation of Gondwanaland, they are not the defining evidence for the Mesozoic sea in the Thar.
• Volcanic ash layers:
• These originate from explosive volcanic eruptions.
• While some volcanic activity occurred during the Deccan eruptions, they do not prove the existence of an ancient sea bed compared to the direct evidence of fossilized marine life.

The correct answer is Article 359.

Key Points

• Article 359 of the Indian Constitution empowers the President to suspend the right to move any court for the enforcement of the Fundamental Rights guaranteed by Part III during a National Emergency.
• Unlike Article 358, which automatically suspends the rights under Article 19, Article 359 does not automatically suspend any right; it only authorizes the President to issue a specific order naming the rights whose enforcement is to be suspended.
• The 44th Amendment Act of 1978 introduced a crucial safeguard, stipulating that the President cannot suspend the right to move the court for the enforcement of rights guaranteed by Article 20 (Protection in respect of conviction for offences) and Article 21 (Protection of life and personal liberty).
• A Presidential Order issued under this Article may extend to the whole or any part of the territory of India and must be laid before each House of Parliament for approval as soon as possible after it is made.
• While Article 358 only operates in the case of an External Emergency (war or external aggression), Article 359 can be invoked during both External and Internal Emergencies (armed rebellion).

 Additional Information

• Article 358:
• Relates specifically to the suspension of the provisions of Article 19.
• Suspension is automatic and occurs the moment a National Emergency is proclaimed on grounds of war or external aggression.
• Article 356:
• Provisions regarding the failure of constitutional machinery in states, commonly referred to as President's Rule.
• It allows the Union Government to take direct control of a state executive.
• Article 357:
• Deals with the exercise of legislative powers under a proclamation issued under Article 356.
• It permits Parliament to confer the power to make laws for the state on the President or other specified authorities.

The correct answer is Kesavananda Bharati case.

Key Points

• The Kesavananda Bharati v. State of Kerala (1973) is a landmark judgment in which the Supreme Court of India introduced the Basic Structure doctrine.
• A special bench of 13 judges, which is the largest ever constituted in the history of the Indian judiciary, heard the case for 68 days and delivered the judgment on April 24, 1973.
• By a slim majority of 7:6, the court held that while Parliament has wide powers to amend the Constitution under Article 368, these powers are not absolute and cannot be used to destroy or emasculate the basic structure or essential features of the document.
• The case challenged the validity of the 24th, 25th, and 29th Constitutional Amendment Acts, which were enacted by the government to bypass previous judicial restrictions on land reforms and property rights.
• The ruling identified several features as part of the basic structure, including Democracy, Secularism, Federalism, Rule of Law, and Judicial Review, ensuring they remain beyond the reach of parliamentary modification.

 Additional Information

• Shankari Prasad case (1951)
• This was the first case to challenge the 1st Constitutional Amendment Act.
• The Supreme Court ruled that the power of Parliament to amend the Constitution under Article 368 included the power to amend Fundamental Rights.
• Golaknath case (1967)
• An 11-judge bench overturned the previous stance and ruled that Fundamental Rights are transcendental and cannot be abridged by Parliament.
• The court stated that an amendment under Article 368 is a 'law' within the meaning of Article 13(2) and thus cannot violate Fundamental Rights.
• Minerva Mills case (1980)
• The Supreme Court reaffirmed and applied the Basic Structure doctrine to strike down portions of the 42nd Amendment Act.
• It established that the limited amending power of Parliament is itself a part of the basic structure, and emphasized the balance between Fundamental Rights and Directive Principles.

The correct answer is India.

Key Points

• The Prime Minister of India, Narendra Modi, was conferred the prestigious Speaker of the Knesset Medal during his high-profile state visit to Israel in February 2026.
• The medal was presented by the Speaker of the Knesset, the national legislature of Israel, in a special ceremony held at the parliament building in Jerusalem.
• This honor was bestowed upon the Indian Prime Minister to recognize his visionary leadership and his instrumental role in elevating India-Israel relations to a comprehensive Strategic Partnership.
• The visit in February 2026 marked a significant milestone, reinforcing cooperation in critical areas such as defense technology, semiconductor manufacturing, water management, and space exploration.
• The award reflects the deep-rooted democratic values shared by both nations and honors India as a key stabilizing force in the Indo-Pacific and the Middle East (West Asia) regions.

 Additional Information

• The Knesset:
• It is the unicameral legislature of Israel, consisting of 120 members elected for four-year terms.
• The Speaker of the Knesset is the presiding officer of the house, responsible for maintaining the dignity of the parliament and representing it in international forums.
• India-Israel Strategic Partnership:
• The relationship was upgraded to a Strategic Partnership during PM Modi’s historic first visit to Israel in July 2017.
• India is one of the largest buyers of Israeli military equipment, and both nations collaborate through the I2U2 Group (India, Israel, UAE, USA).
• Other Countries Mentioned:
• Spain: While Spain maintains diplomatic ties with Israel, its Prime Minister was not the recipient of this specific legislative honor in early 2026.
• Luxembourg: A key member of the European Union that focuses on financial and digital cooperation with Israel, but did not receive the Speaker's Medal in this timeframe.
• Belgium: Known for its role in the EU and NATO, Belgium's diplomatic interactions with Israel in 2026 were centered on trade rather than high-level parliamentary medals.

The correct answer is Reducing the maximum processor state (clock speed/frequency) to cap the peak computational capacity and thermal output.

Key Points

• The Power Saver plan in the Windows Operating System is a pre-configured power scheme designed to maximize battery life by prioritizing energy efficiency over hardware performance.
• The primary technical mechanism utilized is Processor Power Management (PPM), specifically the adjustment of the Maximum Processor State within the system's power settings.
• By capping the maximum processor state (often to values like 50% or 70%), the OS forces the Central Processing Unit (CPU) to operate at a lower clock frequency than its rated base or boost speed.
• This reduction in frequency is coupled with Dynamic Voltage Scaling, where the operating voltage is lowered; since power consumption is proportional to the square of the voltage (P ∝ V² × f), this results in significant energy savings and reduced thermal output.
• Because the CPU executes fewer cycles per second, the time required to complete computational tasks increases, leading to the reduced system responsiveness and lag observed by the user.
• This mechanism effectively disables or limits high-performance features such as Intel Turbo Boost or AMD Precision Boost, ensuring the processor stays within a low-power P-state.

 Additional Information

• Understanding Incorrect Mechanisms:
• Cache Memory Flushing:
• Aggressively flushing the L1, L2, or L3 cache would actually increase power consumption and latency, as the CPU would be forced to fetch data from the much slower and power-intensive System RAM or Virtual Memory.
• Disabling the GPU:
• The OS does not entirely disable the Graphics Processing Unit (GPU) as it is required for the Desktop Window Manager (DWM) to render the UI; however, it may switch from a discrete GPU to an Integrated GPU (iGPU) to save power.
• Hard Disk Spin-down:
• While increasing the frequency of HDD spin-down saves mechanical energy, it primarily affects storage latency rather than the overall peak computational capacity of the system.
• Related Technical Concepts:
• Thermal Design Power (TDP): By limiting the processor state, the system ensures the CPU operates well below its maximum TDP, preventing the cooling fans from spinning at high speeds, which further conserves battery.
• Idle States (C-States): In addition to limiting active performance, the Power Saver plan encourages the processor to enter deeper C-states (sleep states) more rapidly when no tasks are being processed.

The correct answer is Hibernate.

Key Points

• Hibernate is a power management mode in Windows 11 designed to save the current state of the Operating System, including all open applications and documents, to the Hard Disk Drive (HDD) or Solid State Drive (SSD).
• When this mode is activated, the system writes the contents of the Random Access Memory (RAM) into a hidden file located in the root directory of the system drive named hiberfil.sys.
• Unlike Sleep mode, which requires a small amount of power to keep data active in the volatile RAM, Hibernate uses zero power because the computer is physically powered down after the data transfer to storage is complete.
• It is particularly useful for laptop users who need to stop working for an extended period without a power source, as it ensures that the session is preserved even if the battery drains completely.
• When the user triggers a Power On, the Windows Boot Loader reads the data from the storage drive and restores it to the RAM, allowing the user to resume work exactly where they left off.

 Additional Information

• Shut Down:
• This process closes all running programs, logs out the user, and clears the RAM entirely before cutting power to the hardware.
• In Windows 11, if Fast Startup is enabled, it saves a small part of the Kernel state to the disk to speed up the next boot process.
• Restart:
• This command initiates a full Shut Down followed by an immediate boot-up sequence.
• It is the standard procedure for clearing temporary software conflicts and finalizing the installation of system updates or device drivers.
• Sleep:
• Often confused with hibernation, this is a low-power state where data is kept in the RAM for near-instant wake times.
• If power is lost while in this mode, any unsaved data that was not previously backed up to the Hard Drive will be lost.

The correct answer is Antarctica.

Key Points

• Antarctica is globally recognized as the highest continent in terms of average elevation, reaching approximately 2,300 meters (roughly 7,500 feet) above mean sea level.
• This distinction is not due to the height of its bedrock, but rather the presence of massive, permanent ice sheets that cover approximately 98% of the landmass.
• The Antarctic Ice Sheet has an average thickness of about 1.9 kilometers (1.2 miles), and in certain locations, the ice reaches depths of nearly 4.8 kilometers.
• Without this thick layer of ice, Antarctica would likely be the lowest continent, as the weight of the ice causes isostatic depression, pushing much of the continental crust below sea level.
• In contrast, other continents consist primarily of exposed rock and soil, with their average elevations calculated based on their varied terrain of mountains, plateaus, and plains.

 Additional Information

• Asia:
• While home to the world’s highest point, Mount Everest (8,848.86 meters), its vast plains and lowlands result in an average elevation of approximately 950 meters.
• Africa:
• Characterized by extensive plateaus and the East African Highlands, its average elevation is roughly 600 meters.
• South America:
• Despite containing the Andes Mountains, the longest continental mountain range, the continent maintains an average elevation of about 590 meters.
• Europe:
• Considered the lowest continent by average elevation, standing at only 300 meters, largely due to the massive North European Plain.

The correct answer is Kharavela.

Key Points

• Kharavela was the third and most illustrious ruler of the Mahameghavahana dynasty, also referred to as the Chedi dynasty of Kalinga.
• He reigned during the 1st or 2nd century BCE, significantly expanding the power of Kalinga (modern-day Odisha) following the disintegration of the Mauryan Empire.
• The primary historical source for his reign is the Hathigumpha inscription, a seventeen-line record carved in the Udayagiri Hills near Bhubaneswar.
• The inscription provides a chronological account of his first thirteen years, mentioning his military victories over the Satavahanas, the Indo-Greek king Demetrius, and various Tamil kingdoms.
• A staunch follower of Jainism, Kharavela is credited with retrieving the Kalinga Jina idol from Magadha and constructing rock-cut caves for Jain monks at Udayagiri and Khandagiri.

 Additional Information

• Gautamiputra Satakarni:
• The 23rd ruler and the most powerful king of the Satavahana dynasty, who ruled the Deccan and Central India.
• He is celebrated in the Nashik inscription for destroying the Saka, Yavana, and Pahlava rulers and restoring the glory of the Satavahanas.
• Kanishka:
• The greatest emperor of the Kushan dynasty, who ruled over a vast territory spanning Central Asia and North India.
• He is famous for starting the Saka Era in 78 CE and convening the Fourth Buddhist Council in Kashmir to resolve sectarian disputes.
• Pushyamitra Shunga:
• The founder of the Shunga dynasty, who ascended the throne in 185 BCE after assassinating the last Maurya emperor, Brihadratha.
• He was a champion of Brahmanical traditions and performed two Ashvamedha (horse) sacrifices to assert his imperial authority.

The correct answer is Intensity.

Key Points

• Sound intensity is scientifically defined as the amount of sound energy passing through a unit area per unit time (per second) in a direction perpendicular to that area.
• The relationship is mathematically expressed as I = P / A, where I is intensity, P is sound power (energy per second), and A is the surface area.
• Intensity is an objective physical quantity that can be accurately measured using instruments, regardless of the listener’s hearing sensitivity.
• The S.I. unit of sound intensity is Watt per square meter (W/m²).
• The intensity of sound is directly proportional to the square of the amplitude of the vibration. This means if the amplitude of the wave is tripled, the intensity increases by a factor of nine.
• While intensity is often associated with loudness, they are not the same; loudness is the subjective physiological response of the human ear to the intensity of sound.

 Additional Information

• Frequency
• It is the number of complete oscillations or cycles of a sound wave produced in one second.
• The unit of frequency is Hertz (Hz). It determines the pitch of the sound but is independent of the energy-per-area measurement.
• Pitch
• It is the subjective perception of the frequency of a sound by the human brain.
• Sounds with higher frequencies are perceived as high-pitched (shrill), while sounds with lower frequencies are perceived as low-pitched (flat).
• Echo
• An echo is the reflection of sound that reaches the listener shortly after the direct sound.
• To distinguish an echo from the original sound, the reflected sound must reach the ear at least 0.1 seconds later, requiring a minimum distance of approximately 17.2 meters in air at room temperature.

The correct answer is Radiation.

Key Points

• Radiation is the unique method of heat transfer that does not require any material medium (solid, liquid, or gas) to propagate, allowing energy to travel through the vacuum of space.
• Energy from the Sun is transmitted in the form of electromagnetic waves, primarily consisting of visible light, infrared radiation (heat), and ultraviolet rays.
• Because the vast expanse between the Sun and the Earth is nearly a perfect vacuum, other methods like conduction or convection are impossible as they rely on molecular interaction or fluid movement.
• Thermal radiation travels at the speed of light, which is approximately 3 × 10⁸ meters per second, ensuring that solar energy reaches Earth in about 8 minutes and 20 seconds.
• Once these electromagnetic waves strike the Earth's atmosphere and surface, the energy is absorbed by molecules, increasing their kinetic energy and resulting in a rise in temperature.

 Additional Information

• Conduction
• This is the transfer of heat through direct contact between substances.
• It occurs as faster-moving molecules collide with slower ones, passing thermal energy through a medium, typically effective in solids like metals.
• Convection
• It involves the mass movement of molecules within fluids, which includes both liquids and gases.
• Heated fluid becomes less dense and rises, while cooler, denser fluid sinks, creating convection currents that distribute heat.
• Insulation
• This is not a heat transfer method but rather the process of reducing heat flow between objects.
• Thermal insulators like fiberglass, wool, or trapped air are used to inhabit the transfer of energy via conduction or convection.

The correct answer is Battle of Plassey.

Key Points

• The Battle of Plassey was fought on June 23, 1757, on the banks of the Bhagirathi River in Bengal.
• The conflict occurred between the British East India Company, commanded by Robert Clive, and the Nawab of Bengal, Siraj-ud-Daulah.
• A primary reason for the British victory was the secret alliance between Robert Clive and Mir Jafar, the commander of the Nawab’s army, who defected during the battle.
• The victory transformed the British East India Company from a commercial entity into a dominant political and military force in India, establishing its first major foothold in the wealthy province of Bengal.
• Following the battle, the British gained immense wealth from the Bengal treasury and were granted significant land and revenue rights, facilitating their subsequent expansion.

 Additional Information

• Battle of Buxar (1764):
• This battle was fought between the British and the combined forces of Mir Qasim (Nawab of Bengal), Shuja-ud-Daulah (Nawab of Awadh), and the Mughal Emperor Shah Alam II.
• It consolidated British control over northern India and led to the Treaty of Allahabad (1765), which granted the Company the Diwani rights to collect taxes from Bengal, Bihar, and Odisha.
• Battle of Wandiwash (1760):
• A decisive engagement during the Third Carnatic War between the British and the French.
• The British victory led by Sir Eyre Coote effectively ended French colonial ambitions in India.
• Battle of Panipat:
• The Third Battle of Panipat (1761) was fought between the Maratha Empire and the Afghan forces of Ahmad Shah Abdali.
• While it resulted in a Maratha defeat, it significantly weakened indigenous powers, indirectly aiding British ascendancy.

The correct answer is Sanjay Malhotra.

Key Points

• The Appointments Committee of the Cabinet (ACC) approved the appointment of Sanjay Malhotra as the 26th Governor of the Reserve Bank of India (RBI) on December 9, 2024.
• He officially assumed his duties on December 11, 2024, succeeding Shaktikanta Das, who served as the 25th Governor for a tenure spanning six years from 2018 to 2024.
• Sanjay Malhotra is a veteran 1990-batch Indian Administrative Service (IAS) officer belonging to the Rajasthan cadre.
• Before his elevation to the central bank's top post, he served as the Secretary in the Department of Revenue, Ministry of Finance, where he played a pivotal role in tax administration and policy.
• His appointment is for a period of three years from the date of assuming charge or until further orders.

 Additional Information

• Michael Patra:
• He is a career central banker currently serving as a Deputy Governor of the Reserve Bank of India.
• He is a vital member of the Monetary Policy Committee (MPC) and is known for his expertise in macroeconomic policy and inflation targeting.
• Poonam Gupta:
• She serves as the Director General of the National Council of Applied Economic Research (NCAER) and is a member of the Economic Advisory Council to the Prime Minister (PMEAC).
• Raghuram Rajan:
• He was the 23rd Governor of the RBI, serving from 2013 to 2016, and is a world-renowned economist.
• RBI Governor Appointment:
• The Governor is appointed by the Government of India under the provisions of Section 8 of the Reserve Bank of India Act, 1934.
• The first Governor of the RBI was Sir Osborne Smith (1935), and the first Indian to hold the post was C.D. Deshmukh (1943).

The correct answer is Accelerate socio-economic reforms.

Key Points

• The Twenty Point Programme (TPP) was first launched by Prime Minister Indira Gandhi on July 1, 1975, with the primary objective of improving the quality of life of the poor and underprivileged sections of society.
• The programme was designed to facilitate growth with social justice by addressing critical areas such as land reforms, liquidating rural indebtedness, and ensuring the abolition of bonded labor.
• It focused on increasing agricultural production, implementing a land ceiling, and providing housing sites for the landless, which were essential components of the socio-economic reform agenda of that era.
• The initiative was closely linked to the Fifth Five-Year Plan and the slogan of Garibi Hatao (Eradicate Poverty), aiming to provide basic necessities like clean drinking water, health, and education to the rural masses.
• The programme sought to redistribute resources and curb economic inequalities by socializing urban land and preventing the hoarding of essential commodities. Hence, the primary aim was to accelerate socio-economic reforms.

 Additional Information

• Evolution of TPP:
• The programme has been restructured multiple times in 1982, 1986, and most recently in 2006 (known as TPP-2006) to address contemporary challenges.
• The Ministry of Statistics and Programme Implementation (MoSPI) is the nodal agency responsible for monitoring the implementation of the programme across various states.
• Distinction from Other Economic Shifts:
• Liberalize trade policies and Promote foreign direct investment were the core features of the New Economic Policy introduced in 1991, commonly known as LPG (Liberalization, Privatization, and Globalization) reforms.
• The 1975 programme was launched during the Emergency and focused on domestic social welfare rather than market-oriented liberalization or reducing government borrowing.

The correct answer is Ctrl + C.

Key Points

• The keyboard shortcut Ctrl + C is the primary command used in Graphical User Interfaces (GUI) to duplicate Selected Text, Images, or Files without removing them from their original location.
• When this shortcut is executed, the operating system places a copy of the selected data into a temporary storage area known as the Clipboard, which resides in the Random Access Memory (RAM).
• This command follows the Common User Access (CUA) standards, making it a universal shortcut across Windows, Linux, and various application softwares like Microsoft Office and Web Browsers.
• Unlike the Cut command, Ctrl + C is a non-destructive process that ensures the integrity of the source data while allowing for replication in another environment or document.
• In certain Command-Line Interfaces (CLI), such as the Linux Terminal, the same key combination is often used to send a SIGINT (Signal Interrupt) to stop a running program, though its primary role in desktop computing remains copying.

 Additional Information

• Ctrl + F
• This shortcut activates the Find or Search utility, enabling users to locate specific keywords or character strings within a Document, PDF, or Webpage.
• Ctrl + S
• Known as the Save command, this shortcut writes the current state of a file from the Volatile Memory to a Permanent Storage Device like an SSD or HDD.
• Ctrl + V
• This is the Paste shortcut, which retrieves the content currently held in the System Clipboard and inserts it into the current cursor position or active window.

The correct answer is Fantasy With Truth.

Key Points

• Dr. L. Subramaniam, a world-renowned Indian violinist, composer, and conductor, achieved a significant milestone in his career when he received a Grammy Award nomination in 1981.
• The nominated album, Fantasy With Truth, is a landmark recording in the Global Fusion genre, showcasing his ability to blend the intricate gamakas of Carnatic music with the improvisational freedom of Western Jazz.
• This nomination in the Best Jazz Fusion Performance category highlighted the violin as a versatile lead instrument capable of transcending cultural boundaries and standard orchestral roles.
• The album features collaborations with prominent international artists, reinforcing Dr. Subramaniam's reputation as a bridge between Eastern and Western musical traditions.

 Additional Information

• Dr. L. Subramaniam:
• Commonly referred to as the God of Indian Violin, he has composed major symphonic works and film scores, including the soundtrack for Salaam Bombay!.
• He was awarded the Padma Shri in 1988 and the Padma Bhushan in 2001 by the Government of India for his exceptional contribution to the arts.
• He is the founder of the Lakshminarayana Global Music Festival, which promotes cross-cultural artistic exchange.
• West Meets East:
• This is a famous collaborative album series featuring sitar maestro Pandit Ravi Shankar and violinist Yehudi Menuhin, which began in 1966 and won a Grammy Award in 1967.
• Indo-Jazz Fusion:
• Dr. Subramaniam is considered a pioneer of this movement, often working with legends such as George Harrison, Stephan Grappelli, and Jean-Luc Ponty to create a new musical vocabulary.

The correct answer is 67.0.

Key Points

• India achieved an overall score of 67.0 in the SDG Index 2025, reflecting its incremental progress toward the United Nations 2030 Agenda.
• The SDG Index is a featured component of the Sustainable Development Report, which is published annually by the Sustainable Development Solutions Network (SDSN) to track the performance of all 193 UN Member States.
• A score of 67.0 indicates that India is approximately 67 percent of the way toward achieving the optimal target across the 17 Sustainable Development Goals (SDGs), where a score of 100 represents full achievement.
• India has demonstrated significant resilience and improvement in specific areas such as SDG 12 (Responsible Consumption and Production) and SDG 13 (Climate Action), while continuing to face challenges in SDG 2 (Zero Hunger) and SDG 5 (Gender Equality).
• The index provides a quantitative framework for comparing national progress, helping policymakers identify gaps in socio-economic development and environmental sustainability.

 Additional Information

• Sustainable Development Solutions Network (SDSN):
• It was launched in 2012 under the auspices of the UN Secretary-General to mobilize global scientific and technological expertise.
• The organization is currently led by Professor Jeffrey Sachs and focuses on practical problem solving for sustainable development.
• Comparison with SDG India Index:
• The SDG India Index is a separate sub-national monitoring tool developed by NITI Aayog, which usually reports different scores based on localized indicators and a specialized methodology.
• While the Global SDG Index focuses on international comparability, the NITI Aayog version focuses on competitive federalism among Indian States and Union Territories.
• The 17 Goals:
• These goals were adopted in September 2015 as a universal call to action to end poverty, protect the planet, and ensure that by 2030 all people enjoy peace and prosperity.
• Key goals include No Poverty (Goal 1), Quality Education (Goal 4), Affordable and Clean Energy (Goal 7), and Decent Work and Economic Growth (Goal 8).

The correct answer is Introduction of separate electorates for Muslims.

Key Points

• The Indian Councils Act of 1909, popularly known as the Morley-Minto Reforms, introduced the system of separate electorates based on religion. Under this provision, Muslim members were to be elected exclusively by Muslim voters, thereby institutionalizing communal representation in the Indian political system.
• This act effectively legalized communalism in India, and Lord Minto came to be known as the Father of Communal Electorate for his role in implementing this divisive electoral policy.
• The reform significantly increased the size of the Legislative Councils at both the Central and Provincial levels, where the number of members in the Central Legislative Council was raised from 16 to 60.
• It empowered members of the Legislative Council to ask supplementary questions and move resolutions on the Budget, expanding the deliberative functions of the legislative bodies beyond mere discussion.
• The act provided for the first time for the association of Indians with the Executive Councils of the Viceroy and Governors, leading to the appointment of Satyendra Prasad Sinha as the first Indian member of the Viceroy’s Executive Council.

 Additional Information

• Historical Context of Other Options:
• The Supreme Court in India was first established at Calcutta through the Regulating Act of 1773, with Sir Elijah Impey as the first Chief Justice.
• Universal voting rights or Universal Adult Franchise was not granted during the British Raj; it was formally adopted only with the enforcement of the Constitution of India on January 26, 1950.
• The position of the Viceroy was created by the Government of India Act 1858 following the Revolt of 1857 and remained the supreme executive authority until the Indian Independence Act of 1947.
• The Government of India Act 1919 (Montagu-Chelmsford Reforms) later introduced Dyarchy in the provinces and expanded the principle of communal representation to Sikhs, Indian Christians, and Anglo-Indians.

The correct answer is Kalinga style.

Key Points

• The Jagannath Temple in Puri, Odisha, is a monumental example of the Kalinga style of architecture, which is a specialized sub-branch of the broader Nagara (North Indian) tradition.
• This architectural style is characterized by three distinct types of temples: Rekha Deula (tall curvilinear tower), Pidha Deula (pyramidal roofed square porch), and Khakhara Deula (rectangular temple with a barrel-vaulted roof).
• The main sanctum of the Jagannath Temple is a Rekha Deula, while the assembly hall or porch, known as the Jagamohana, follows the Pidha Deula structure.
• Construction was initiated in the 12th century by King Anantavarman Chodaganga Deva of the Eastern Ganga Dynasty, showcasing the pinnacle of Odishan stone masonry.
• The temple complex is enclosed by two massive concentric walls: the outer Meghanada Pacheri and the inner Kurma Bheda, which protect the sacred deities Jagannath, Balabhadra, and Subhadra.

 Additional Information

• Dravidian style
• Origin: Developed primarily in South India under dynasties like the Cholas and Pallavas.
• Features: Characterized by a pyramid-like tower called a Vimana and massive gateways known as Gopurams.
• Hoysala Style
• Origin: Flourished in Karnataka between the 11th and 14th centuries.
• Features: Distinguished by a stellate (star-shaped) ground plan and extremely intricate carvings on chloritic schist (soapstone).
• Vesara style
• Origin: Emerged in the Deccan region, particularly under the Later Chalukyas and Rashtrakutas.
• Features: A hybrid style that harmoniously combines elements of both the Nagara and Dravidian architectural traditions.

The correct answer is 1985.

Key Points

• The Central Administrative Tribunal (CAT) was established under the Administrative Tribunals Act, 1985, following the 42nd Amendment Act, 1976 of the Constitution of India.
• The tribunal was officially inaugurated on November 1, 1985, during the tenure of the Rajiv Gandhi government to provide specialized adjudication for service-related disputes.
• The constitutional backing for the CAT is found in Article 323-A, which empowers the Parliament to establish administrative tribunals for the adjudication of disputes relating to recruitment and conditions of service.
• Its primary objective is to offer a speedy and inexpensive justice delivery mechanism to employees of the Central Government, thereby reducing the workload of the regular civil courts.

 Additional Information

• Jurisdiction and Scope:
• The CAT exercises original jurisdiction over service matters concerning members of the All-India Services, Central Civil Services, and civilian employees of the Defense Services.
• It does not have jurisdiction over members of the Armed Forces, officers and servants of the Supreme Court, and the secretarial staff of the Parliament.
• Legal Framework and Composition:
• The tribunal is a multi-member body consisting of a Chairman and various Members (Judicial and Administrative), all of whom are appointed by the President of India.
• In its proceedings, the tribunal is not bound by the technicalities of the Code of Civil Procedure, 1908, but is governed by the Principles of Natural Justice.
• Following the L. Chandra Kumar Case (1997), the decisions of the CAT can be challenged before the Division Bench of the respective High Court through a writ petition.

The correct answer is 52.5 %.

Key Points

• The Worker Population Ratio (WPR) is defined as the percentage of employed persons in the total population, providing a primary indicator of the level of employment in the country.
• As per the Periodic Labour Force Survey (PLFS) Quarterly Bulletin covering the period October – December 2025, the WPR for persons aged 15 years and above in India was recorded at 52.5%.
• The data is compiled and released by the National Statistical Office (NSO), which operates under the Ministry of Statistics and Programme Implementation (MoSPI).
• The survey utilizes the Current Weekly Status (CWS) approach for quarterly reports, which classifies a person as employed if they worked for at least one hour on any day during the seven-day reference period preceding the interview.
• An increasing WPR trend signifies an expansion in employment opportunities and higher participation of the population in economic activities.

 Additional Information

• Periodic Labour Force Survey (PLFS):
• Launched in April 2017 to provide more frequent labor market data.
• Objectives include estimating employment and unemployment indicators in the short time interval of three months for urban areas and annually for both rural and urban areas.
• Key indicators tracked include Labour Force Participation Rate (LFPR), Worker Population Ratio (WPR), and Unemployment Rate (UR).
• The 15+ age group is the standard demographic used to measure the active labor force, excluding children and early adolescents from the primary employment statistics.

The correct answer is Energy = Power times Time.

Key Points

• Electrical Energy represents the total work done by an electric current in maintaining the flow of charge through a circuit for a given duration.
• Electric Power (P) is defined as the rate at which electrical energy is consumed or dissipated in an electrical circuit. It is mathematically expressed as Power = Energy / Time.
• By rearranging the fundamental definition of power, Electrical Energy (E) can be calculated as the product of the power consumed and the time interval over which it is used: Energy = Power × Time.
• In the International System of Units (SI), energy is measured in Joules (J). One Joule is defined as the energy transferred when a power of one Watt (W) is applied for one Second (s).
• This relationship is fundamental for calculating electricity bills, where the total energy consumption is determined by the wattage of appliances and their duration of operation.

 Additional Information

• Power Components:
• Electric Power itself is the product of Voltage (V) and Current (I). Therefore, energy can also be expressed as Energy = Voltage × Current × Time.
• The unit of power is the Watt, named after the Scottish inventor James Watt.
• Commercial Unit of Energy:
• The Kilowatt-hour (kWh) is the standard unit for commercial electricity consumption, often referred to as a Unit.
• One Kilowatt-hour is equal to 1000 Watts used for one hour (3600 seconds), which equates to 3.6 × 10⁶ Joules.
• Ohm’s Law and Energy:
• According to Ohm’s Law, Voltage = Current × Resistance. Substituting this into the energy formula yields Energy = I² × R × t, known as Joule’s Law of Heating.
• This formula explains how electrical energy is converted into heat energy in resistors.

The correct answer is Governor.

Key Points

• According to the Constitution of India, the Governor is the de jure head (legal or nominal head) of the state executive, similar to the President at the Union level.
• Article 153 states that there shall be a Governor for each state, although the 7th Constitutional Amendment Act (1956) facilitated the appointment of the same person for two or more states.
• Article 154 mandates that the executive power of the State shall be vested in the Governor and shall be exercised by him either directly or through officers subordinate to him.
• While the Governor is the constitutional head, the Chief Minister is the de facto (real) executive head who leads the Council of Ministers.
• All executive actions of the Government of a State are formally taken in the name of the Governor as per the provisions of Article 166.
• The Governor acts as a vital link between the Union Government and the State Government, ensuring that the state administration is carried out in accordance with the Constitution.

 Additional Information

• Governor’s Appointment and Tenure:
• The Governor is appointed by the President of India by warrant under his hand and seal (Article 155).
• A person must be a citizen of India and have completed at least 35 years of age to be eligible for the post.
• The Governor holds office during the pleasure of the President, with a standard term of five years.
• Chief Minister:
• The Chief Minister is the head of the elected government and is appointed by the Governor under Article 164.
• Chief Justice of High Court:
• The Chief Justice is the highest judicial authority in the state, appointed by the President under Article 217.

The correct answer is Boycott of schools, courts, and councils alongside the adoption of khadi.

Key Points

• The Calcutta Session of the Indian National Congress was a special session held in September 1920, presided over by Lala Lajpat Rai.
• During this session, Mahatma Gandhi introduced the resolution for the Non-Cooperation Movement (NCM) to address grievances related to the Jallianwala Bagh Massacre and the Khilafat Movement.
• The core strategy involved a phased withdrawal of support from British institutions, specifically targeting the boycott of government schools and colleges, British law courts, and the Legislative Councils established under the 1919 Reforms.
• The strategy also emphasized economic self-reliance through the boycott of foreign cloth and the proactive adoption of Khadi (hand-spun cloth) and the Charkha (spinning wheel) to revive the domestic textile industry.
• This session marked the transition of the Congress from a middle-class pressure group into a mass movement by integrating social, political, and economic boycotts.

 Additional Information

• Nagpur Session (December 1920):
• The Non-Cooperation program approved at Calcutta was formally ratified here, and the Congress goal was changed from constitutional means to Swaraj (Self-Rule).
• Legislative Councils and Swarajists:
• While the 1920 strategy demanded a total boycott, leaders like C.R. Das and Motilal Nehru later formed the Swaraj Party in 1923 to contest elections and negotiate reforms from within the councils.
• Ahimsa and Non-Violence:
• Gandhi’s strategy was strictly based on Non-Violence (Ahimsa), making the establishment of armed village guards or any form of violent resistance fundamentally incompatible with his philosophy of Satyagraha.
• Educational Impact:
• The boycott led to the establishment of National Institutions such as Jamia Millia Islamia, Kashi Vidyapeeth, and Gujarat Vidyapeeth to provide alternative education to students.

The correct answer is 2022.

Key Points

• The Pune Metro Rail Project was officially inaugurated by Prime Minister Narendra Modi on March 6, 2022.
• During the inauguration, the Prime Minister flagged off the metro service on two priority stretches: the 7-kilometer section from Pimpri Chinchwad Municipal Corporation (PCMC) to Phugewadi and the 5-kilometer section from Vanaz to Garware College.
• The project is a significant infrastructure development for Maharashtra, designed to provide a world-class, environment-friendly Mass Rapid Transit System (MRTS) to the citizens of Pune and Pimpri Chinchwad.
• The total length of the Pune Metro project is approximately 32.2 kilometers, comprising two corridors: the Purple Line (Line 1) and the Aqua Line (Line 2).
• While the project was inaugurated in 2022, the foundation stone for the same was laid by Prime Minister Narendra Modi several years earlier, on December 24, 2016.

 Additional Information

• Project Execution and Features:
• The project is executed by the Maharashtra Metro Rail Corporation Limited (MAHA-METRO), which is a joint venture between the Government of India and the Government of Maharashtra.
• The Pune Metro is notable for its sustainable features, including solar energy generation at stations and the use of lightweight aluminum-body coaches manufactured under the Make in India initiative.
• It aims to integrate with other modes of transport such as the Pune Suburban Railway, city bus services (PMPML), and the Pune Railway Station to ensure seamless multi-modal connectivity.
• The project has an estimated completion cost of over 11,400 crore rupees and is funded through a combination of equity and loans from international agencies like the European Investment Bank (EIB) and Agence Française de Développement (AFD).

Therefore, the correct option is 2.

The correct answer is Uttar Pradesh.

Key Points

• The Bateshwar Fair is a prominent annual event held in the town of Bateshwar, located in the Agra district of Uttar Pradesh.
• Geographically, the fair is situated on the banks of the Yamuna River, a site famous for its complex of 101 Shiva temples arranged in a crescent shape along the riverfront.
• The fair typically commences a few days before the festival of Deepawali and continues for a duration of nearly three weeks, reaching its religious peak on Kartika Purnima.
• It is recognized as one of the largest cattle fairs in North India, serving as a major hub for the trading of camels, horses, cows, and buffaloes.
• The fair carries immense spiritual significance, as thousands of devotees perform ritualistic baths in the Yamuna and offer prayers at the Bateshwar Mahadev temple.

 Additional Information

• Bihar:
• This state is home to the Sonepur Cattle Fair, also known as the Harihar Kshetra Mela, which is considered the largest animal fair in Asia.
• Madhya Pradesh:
• The state hosts several major cultural and religious events, such as the Ujjain Simhastha Kumbh and the Gwalior Trade Fair, but it is not the site of the Bateshwar animal fair.
• Chhattisgarh:
• Known for the Bastar Dussehra and the Rajim Kumbh Mela, the state's festivals focus on tribal heritage and religious congregations at the confluence of the Mahanadi, Pairi, and Sondur rivers.
• Historical Context:
• The Bateshwar temples are believed to have been patronized by the Bhadauria kings, reflecting the Maratha and Chauhan architectural influences common in western Uttar Pradesh.

The correct answer is Secondary sector.

Key Points

• The Secondary sector encompasses activities where natural products are transformed into other forms through manufacturing processes, typically within industrial units or workshops.
• This sector is often referred to as the industrial sector because it involves the processing of raw materials to produce semi-finished or finished goods.
• Cotton textile production is a key example of secondary activity; it involves using raw cotton (a primary product) to spin yarn and subsequently weave textile fabric.
• Iron and steel manufacturing is a foundational heavy industry within this sector, utilizing iron ore to produce steel, which serves as a vital input for various other industries like infrastructure and automobiles.
• In the Indian economy, the secondary sector is essential for value addition and contributes approximately 25% to 30% to the Gross Domestic Product (GDP).

 Additional Information

• Economic Classification in India:
• Primary sector: Focuses on the direct extraction and use of natural resources. Key activities include agriculture, forestry, fishing, and mining.
• Tertiary sector: Also known as the service sector, it provides support services to the primary and secondary sectors. It includes banking, transportation, trade, and communication.
• Quaternary sector: A specialized component of the tertiary sector that involves knowledge-based services. Examples include Information Technology (IT), Research and Development (R&D), and financial planning.

The correct answer is Make in India.

Key Points

• Safran Group, a French multinational aerospace and defense corporation, has significantly integrated its supply chain within the Indian ecosystem to support major ISRO and DRDO projects.
• The Gaganyaan mission, which aims to demonstrate India's human spaceflight capability, involves high-end technological collaboration and localized production of critical components.
• The projected 70% revenue boost for Safran India by 2025 is driven by the establishment of large-scale manufacturing and MRO (Maintenance, Repair, and Overhaul) facilities in cities like Hyderabad and Bengaluru.
• This strategic growth is a direct alignment with the Make in India initiative, which encourages global firms to manufacture products domestically to foster a self-reliant aerospace and defense sector.

 Additional Information

• Make in India Initiative
• Launched in September 2014 to transform India into a global design and manufacturing hub.
• Focuses on 27 sectors, with Aviation and Space being primary pillars for technological advancement.
• It facilitates Foreign Direct Investment (FDI) and protects intellectual property to build a best-in-class manufacturing infrastructure.
• Safran's Presence in India
• Safran operates the largest MRO facility for LEAP engines in India to service commercial airlines.
• The company is a key partner in the Rafale fighter jet program, providing the M88 engines and other critical avionics.
• Gaganyaan Mission Details
• The mission aims to launch a crew of three members to an orbit of 400 km for a duration of 3 days.
• It is a cornerstone for the future Indian Space Station and interplanetary explorations.

The correct answer is education sector.

Key Points

• The Gross Enrolment Ratio (GER) is a critical statistical measure used within the education sector to determine the number of students enrolled in school at different grade levels, such as primary, secondary, and tertiary education.
• It is calculated by dividing the number of students enrolled in a specific level of education, regardless of age, by the population of the official age group corresponding to that level, and then multiplying the result by 100.
• The GER serves as an indicator of the educational capacity of a country and the extent of participation in the schooling system by the eligible population.
• A unique characteristic of this ratio is that it can exceed 100%; this occurs when students who are older or younger than the official age group (due to late entry or grade repetition) are enrolled in that specific level.
• In the context of Higher Education in India, the All India Survey on Higher Education (AISHE) is the primary report that tracks and publishes the GER data annually.

 Additional Information

• Education Sector Targets:
• The National Education Policy (NEP) 2020 has set a target to increase the Gross Enrolment Ratio in higher education, including vocational education, from 26.3% (2018) to 50% by the year 2035.
• Health Sector:
• Utilizes metrics such as Infant Mortality Rate (IMR), Maternal Mortality Ratio (MMR), and Life Expectancy to gauge public welfare, which are conceptually distinct from enrolment ratios.
• Banking Sector:
• Focuses on financial liquidity and stability through indicators like the Cash Reserve Ratio (CRR), Statutory Liquidity Ratio (SLR), and Capital Adequacy Ratio (CAR).
• Transport Sector:
• Evaluates efficiency using metrics like Operating Ratio, Load Factor, and Network Density, which relate to logistics and infrastructure rather than human capital development.

The correct answer is South Korea.

Key Points

• In October 2025, the government of South Korea conferred its highest national honor, the Grand Order of Mugunghwa, upon U.S. President Donald Trump during his diplomatic visit.
• The award ceremony took place on October 29, 2025, in the historic city of Gyeongju, which served as the capital of the ancient Silla Kingdom, on the sidelines of the APEC 2025 Leaders' Summit.
• South Korean President Lee Jae Myung personally presented the decoration to Donald Trump, making him the first U.S. President to receive this prestigious distinction.
• The honor was awarded in recognition of Trump's contributions to regional security, his role as a peacemaker on the Korean Peninsula, and his efforts in enhancing bilateral economic cooperation.
• As part of the ceremonial gesture, Trump was also gifted a symbolic replica of the Cheonmachong gold crown, an ancient Silla Dynasty artifact representing national pride and unity.

 Additional Information

• Grand Order of Mugunghwa:
• Instituted on August 13, 1949, it stands as the highest of all Korean orders and is superior to the Order of National Foundation.
• It is named after the Mugunghwa (Hibiscus syriacus), South Korea's national flower, which symbolizes resilience and the nation's eternal spirit.
• The award is exceptionally granted to foreign heads of state or their spouses who have rendered distinguished service to the Republic of Korea.
• Incorrect Options Context:
• China: The highest award for foreigners is the Order of Friendship, which was not the subject of this 2025 conferment.
• Japan: Japan's highest honor is the Supreme Order of the Chrysanthemum, typically reserved for monarchs and exceptional heads of state.
• Bhutan: The kingdom's highest civilian honor is the Order of the Dragon King (Druk Gyalpo).

The correct answer is Microcontroller.

Key Points

• A Microcontroller (MCU) is a highly integrated Integrated Circuit (IC) designed to govern specific operations within an Embedded System.
• It is often referred to as a 'computer on a chip' because it integrates a Central Processing Unit (CPU), Volatile Memory (RAM), and Non-volatile Memory (ROM or Flash) into a single compact silicon die.
• The primary design goal of a microcontroller is to provide a self-contained unit that includes Input/Output (I/O) Peripherals, such as Timers, Serial Communication Ports, and Analog-to-Digital Converters (ADC), which are necessary for interacting with sensors and actuators.
• Unlike a Microprocessor, which requires external components like a Northbridge or separate memory modules to function, the microcontroller combines these features to reduce Power Consumption, physical size, and overall system cost.
• Microcontrollers are widely utilized in Real-time Applications where specific, repetitive tasks are performed, such as in Automobile Engine Control Systems, Medical Devices, and Remote Controls.

 Additional Information

• Motherboard
• The Motherboard is the main Printed Circuit Board (PCB) in a general-purpose computer (like a PC or Laptop) that serves as a backbone for connecting various discrete components.
• It contains Sockets for the CPU, slots for RAM modules, and interfaces for Storage Devices (SATA/NVMe), but it is not a single integrated chip itself.
• System Bus
• A System Bus is a communication system that transfers data between the internal components of a computer.
• It typically consists of three main parts: the Data Bus (carries actual data), the Address Bus (specifies where data should go), and the Control Bus (carries commands from the CPU).
• Microprocessor vs. Microcontroller
• A Microprocessor consists only of a CPU and is designed for high-speed, general-purpose computing tasks found in personal computers.
• In contrast, Microcontrollers are task-specific, emphasizing Energy Efficiency and Integration rather than raw computational power.

The correct answer is Iron Ore.

Key Points

• Kudremukh is a mountain range located in the Chikmagalur district of Karnataka, situated within the Western Ghats, which is a UNESCO World Heritage Site.
• The name Kudremukh literally translates to Horse-face in the Kannada language, describing the unique shape of one of the highest peaks in the region.
• The region is world-renowned for housing one of the largest deposits of Magnetite iron ore in the world, which is a high-grade mineral known for its magnetic properties.
• The Kudremukh Iron Ore Company Limited (KIOCL), a Public Sector Undertaking (PSU), was established in 1976 to exploit these massive mineral resources.
• For logistical efficiency, the ore was transported in the form of slurry through a 110 km long pipeline to the New Mangalore Port for international export.
• Due to environmental concerns regarding the biodiversity of the Kudremukh National Park, the Supreme Court of India ordered the cessation of mining operations in December 2005.

 Additional Information

• Copper:
• In Karnataka, copper deposits are primarily found in Ingaldhal within the Chitradurga district.
• Significant Indian copper reserves are located in Malanjkhand (Madhya Pradesh) and Khetri (Rajasthan).
• Bauxite:
• This is the primary ore for Aluminium production.
• In Karnataka, it is extracted from the Belagavi and Chikmagalur districts, particularly around the Baba Budan hills.
• Manganese:
• Karnataka is a major producer of manganese ore in India.
• Large-scale deposits are concentrated in the Sandur belt of Ballari district, as well as in Shimoga and Tumakuru.

The correct answer is Delhi High Court.

Key Points

• The Delhi High Court officially issued a notification regarding its calendar for the year 2025, wherein it declared 26 December 2025 (Friday) as a court holiday.
• By declaring this date a holiday, the court has advanced the commencement of its Winter Vacation, which will now effectively begin on 26 December 2025 and continue until 31 December 2025.
• This administrative decision was made under the powers vested in the Chief Justice and the Registry of the High Court to regulate the judicial calendar and ensure a structured recess for the judiciary and the legal fraternity.
• The notification ensures that both the High Court and the Subordinate Courts under its jurisdiction in the National Capital Territory of Delhi follow the revised schedule for the winter break.
• Typically, Christmas (December 25) is a standard holiday, and by declaring December 26 as a holiday, the court bridged the gap to create a continuous Winter Vacation period.
• The decision was communicated through a circular issued by the Registrar General, citing the administrative requirements and the approved List of Holidays for the calendar year 2025.

 Additional Information

• Delhi High Court Establishment and Structure:
• The Delhi High Court was established on 31 October 1966, following the enactment of the Delhi High Court Act, 1966.
• It serves as the highest judicial authority within the National Capital Territory (NCT) of Delhi.
• The court currently has a sanctioned strength of 60 judges, comprising 45 permanent judges and 15 additional judges.
• The administrative control over the District Courts and other subordinate judiciary in Delhi is exercised by the High Court through its Full Court and Administrative Committees.
• Judicial Vacations in India:
• High Courts in India are empowered under Article 225 of the Constitution of India and their respective High Court Rules to determine their working days and vacation schedules.
• Vacations are categorized into Summer Vacation (usually in May-June) and Winter Vacation (usually in late December).
• During these periods, Vacation Benches are constituted to hear urgent matters, such as habeas corpus petitions, stay orders, and bail applications.

The correct answer is 29 subjects for Panchayats.

Key Points

• The 11th Schedule was added to the Constitution of India by the 73rd Constitutional Amendment Act of 1992, which institutionalized the Panchayati Raj system.
• It contains a list of 29 subjects or functional items over which the Panchayats have the power to plan and implement schemes for economic development and social justice.
• This schedule is linked directly to Article 243-G of the Constitution, which defines the powers, authority, and responsibilities of Panchayats.
• The subjects mentioned in the schedule include Agriculture, Land Improvement, Minor Irrigation, Animal Husbandry, Fisheries, Social Forestry, Small-scale Industries, Rural Housing, and Drinking Water.
• The inclusion of this schedule aimed to decentralize power and ensure the participation of the rural population in the democratic process at the grassroots level.

 Additional Information

• 12th Schedule:
• It was added by the 74th Constitutional Amendment Act, 1992.
• It contains 18 functional items related to the powers and responsibilities of Municipalities (Urban Local Bodies) under Article 243-W.
• Concurrent List:
• It is part of the 7th Schedule of the Constitution, which divides legislative powers between the Union and the States.
• It contains subjects like Education, Forests, and Marriage, where both the Parliament and State Legislatures can make laws.
• Fundamental Duties:
• These are contained in Part IV-A and Article 51A of the Constitution.
• They were added by the 42nd Amendment Act, 1976, based on the recommendations of the Swaran Singh Committee; currently, there are 11 duties.

The correct answer is Sitar.

Key Points

• Pandit Ravi Shankar (1920–2012) was a legendary Indian sitar virtuoso and a globally acclaimed composer who became the most well-known proponent of Hindustani classical music in the 20th century.
• He was a disciple of Acharya Allauddin Khan, the founder of the Maihar gharana, under whom he underwent rigorous training in the traditional Gurukul system.
• The Sitar is a plucked stringed instrument used mainly in Hindustani music; Shankar is credited with introducing several innovations to the instrument's design and playing style, particularly the use of the bass strings (kharaj) to enhance the Alap section.
• His international fame peaked in the 1960s through his association with George Harrison of The Beatles, which led to a global Sitar explosion and performances at iconic events like the Monterey Pop Festival (1967) and Woodstock (1969).
• For his immense contributions, he was honored with the Bharat Ratna, India's highest civilian award, in 1999, and he received five Grammy Awards, including a posthumous Lifetime Achievement Award in 2013.

 Additional Information

• Flute
• In the context of Indian Classical Music, the Bansuri (bamboo flute) is the primary instrument.
• Renowned masters of this instrument include Pandit Hariprasad Chaurasia and Pannalal Ghosh.
• Tabla
• A pair of hand drums (the Dayan and Bayan) used for rhythm in Hindustani music.
• Legendary exponents include Ustad Zakir Hussain, Ustad Alla Rakha, and Pandit Kishan Maharaj.
• Sarod
• A fretless stringed instrument known for its deep, introspective sound and continuous slides (meend).
• Prominent virtuosos include Ustad Amjad Ali Khan, Ustad Ali Akbar Khan, and Amaan Ali Bangash.

The correct answer is High fiscal and current account deficits.

Key Points

• The 1991 Economic Crisis in India was a severe Balance of Payments (BoP) crisis resulting from a long period of macroeconomic mismanagement during the 1980s.
• A primary driver was the high fiscal deficit, which reached 8.4% of GDP in 1990-91. This was caused by the government living far beyond its means, funded by internal and external borrowings.
• Simultaneously, the current account deficit (CAD) widened significantly, reaching about 3% of GDP. This meant India was importing far more goods and services than it was exporting, leading to a massive drain on foreign exchange reserves.
• The Gulf War (1990-91) acted as an immediate catalyst, causing a sharp spike in global oil prices and a sudden drop in remittances from Indian workers in West Asia, further straining the BoP position.
• By mid-1991, India's foreign exchange reserves had dropped to approximately $1.2 billion, an amount barely sufficient to sustain two weeks of essential imports.

 Additional Information

• Incorrect Factors:
• Agricultural Surplus: India did not have an agricultural surplus that triggered the crisis; instead, the economy suffered from high inflation, which peaked at nearly 17% in 1991.
• Oil Price Drop: Contrary to a drop, the Gulf War led to a massive oil price hike, which was a major external shock to India’s economy.
• Increase in Gold Reserves: Gold reserves were not increasing; the crisis was so dire that the government had to pledge 67 tonnes of gold to the Bank of England and the Union Bank of Switzerland to avoid a sovereign default.
• Policy Transformation:
• The crisis necessitated a loan from the IMF and World Bank, which came with conditions to restructure the economy.
• This led to the New Economic Policy of 1991, introducing Liberalization, Privatization, and Globalization (LPG) to open up the Indian economy to international competition.

The correct answer is Russian Revolution.

Key Points

• The Preamble of the Indian Constitution declares the resolve to secure for all its citizens Justice in three distinct forms: Social, Economic, and Political.
• These ideals of Justice were inspired by the Russian Revolution of 1917, which sought to create a society based on egalitarian principles and the end of exploitation.
• Social Justice implies that the Constitution aims to create a society without discrimination based on caste, creed, religion, sex, or place of birth, ensuring the improvement of conditions for backward classes and women.
• Economic Justice refers to the elimination of glaring inequalities in wealth, income, and property, ensuring that economic resources are distributed to serve the common good.
• Political Justice ensures that all citizens have equal opportunities to participate in the political process, including the right to vote and access to public offices without discrimination.
• The Preamble acts as an introductory statement that sets out the guiding principles and philosophy of the Constitution of India.

 Additional Information

• French Revolution (1789):
• The Indian Constitution borrowed the ideals of Liberty, Equality, and Fraternity from the French Revolution.
• It emphasized the rights of man and the republican form of government.
• American Revolution (1776):
• This revolution influenced the concept of a Written Constitution and the inclusion of a Bill of Rights (transformed into Fundamental Rights in India).
• Other features borrowed from the USA include the Independence of the Judiciary and Judicial Review.
• Glorious Revolution (1688):
• Occurring in England, it established the Supremacy of Parliament over the monarchy.
• It laid the foundation for the Parliamentary form of government that India adopted from the British Constitution.

The correct answer is Prabhakarvardhana.

Key Points

• Prabhakarvardhana was the first significant and powerful king of the Pushyabhuti dynasty, also known as the Vardhana dynasty, ruling from Thanesar (modern-day Haryana) during the late 6th century.
• He was the first ruler of the dynasty to assume imperial titles such as Maharajadhiraja (King of Kings) and Parama-bhattaraka, marking the transition of the family from local feudatories to independent sovereigns.
• In the historical text Harshacharita, written by the court poet Banabhatta, he is famously described using the epithet Huna-harina-kesari, which translates to 'a lion to the Huna deer', indicating his decisive military victories over the invading Hunas.
• His military campaigns significantly strengthened the Pushyabhuti position in Northern India, as he is also credited with defeating or intimidating the rulers of Sindh, Gandhara, Lata, and Malwa.
• By successfully repelling the Huna tribes, who had previously caused the decline of the Gupta Empire, Prabhakarvardhana established a stable and powerful foundation for his successors, Rajyavardhana and Harshavardhana.

 Additional Information

• Rajyavardhana:
• He was the eldest son of Prabhakarvardhana and ascended the throne in 605 CE.
• He defeated the Malwa king Devagupta but was treacherously murdered by Shashanka, the ruler of Gauda (Bengal).
• Harshavardhana:
• The most illustrious ruler of the dynasty, he reigned from 606 to 647 CE and shifted the capital to Kannauj.
• He was a great patron of Buddhism and authored famous Sanskrit plays including Ratnavali, Nagananda, and Priyadarsika.
• Naravardhana:
• Regarded as the earliest known ancestor and the founder of the Pushyabhuti line.
• He was a minor chieftain and a feudatory, likely under the Imperial Guptas or the Maukhari kings, lacking the sovereign power achieved by his descendants.