RRB NTPC Graduate Level CBT-I Official Paper (Held On: 13 Jun, 2025 Shift 1) (Previous Year Paper)

Given Expression: M ÷ N – O + P × Q

M ÷ N: M is the father of N.

N – O: N is the brother of O.

O + P: O is the sister of P.

P × Q: P is the wife of Q.

According to the given information Family Tree Representation:

Therefore, M is the Wife's Father (Father-in-law) of Q.

Hence, the correct answer is "Option 3"

The correct answer is Technological backwardness.

Key Points

• By the 1980s, India’s Import Substitution Industrialisation (ISI) strategy faced significant limitations such as technological backwardness, which hindered productivity and competitiveness.
• The focus on domestic production led to limited access to advanced global technologies, impacting innovation and modernization.
• Many industries under ISI were protected by high tariffs, creating a lack of incentive to innovate or improve efficiency.
• Technological stagnation resulted in poor quality of goods and inability to meet international standards, further limiting exports.
• Countries relying on ISI strategies often struggled with low industrial diversification, exacerbating technological deficiencies.

Additional Information

• Import Substitution Industrialisation (ISI):
• ISI is an economic policy aimed at reducing dependency on imports by promoting domestic production of goods.
• It was widely adopted by developing countries post-World War II to foster industrial growth and economic independence.
• Protectionism in ISI:
• High import tariffs and quotas were imposed to protect domestic industries.
• While it encouraged initial industrial growth, it often led to inefficiency and lack of global competitiveness.
• Technological Stagnation:
• Limited investment in research and development under ISI policies contributed to technological backwardness.
• Dependence on outdated technologies restricted productivity and innovation.
• Shift to Liberalization:
• India began liberalizing its economy in 1991, moving away from ISI towards globalization and free-market policies.
• This shift aimed to integrate India into the global economy and encourage technological advancements through foreign investments.

The correct answer is Shaka.

Key Points

• Rudradaman I was a prominent ruler of the Western Kshatrapas, a branch of the Shaka dynasty, in the middle of the second century AD.
• He is known for his rule over regions that included Mathura, Gujarat, and parts of Malwa and Kathiawar.
• Rudradaman is celebrated for his administrative skills and military achievements, including his victory over the Satavahanas.
• He issued the Junagadh Rock Inscription, one of the earliest known inscriptions written in Sanskrit, which highlights his achievements and governance.
• The Shaka dynasty played a significant role in Indian history, introducing administrative reforms and patronizing art and culture in their territories.

Additional Information

• Shaka Dynasty:
• The Shakas were a branch of the Scythians who migrated to India and established rule in northwestern and western regions.
• They are known as the Western Kshatrapas in Indian history.
• Junagadh Rock Inscription:
• This inscription was commissioned by Rudradaman I around 150 AD.
• It records the construction of the Sudarshana Lake and highlights the achievements of Rudradaman.
• Western Kshatrapas:
• The Western Kshatrapas were a line of Indo-Scythian rulers who controlled parts of modern-day Gujarat, Maharashtra, and Madhya Pradesh.
• They were contemporaries of the Satavahanas and Gupta Empires.
• Decline of the Shaka Dynasty:
• The Shaka rule came to an end with the rise of the Gupta Empire, particularly under Chandragupta II (Vikramaditya), who defeated the Shaka ruler Rudrasimha III.

Shortcut Trick

Quarterly Rate = 40% ÷ 4 = 10% | Time = 4 quarters.

Successive percentage for 10% for 4 periods = 46.41%.

Compound Interest = 2,40,000 × 46.41/100

CI = 2,400 × 46.41 = ₹1,11,384.

∴ The correct answer is ₹1,11,384.

Alternate Method

Given: Principal (P) = ₹2,40,000, Rate (R) = 40% p.a., Time (T) = 1 year.

Formula: Amount (A) = P(1 + r/100)ⁿ | CI = A − P

⇒ Quarterly Rate (r) = 40% ÷ 4 = 10%

⇒ Number of quarters (n) = 1 × 4 = 4

⇒ Amount (A) = 2,40,000 × (1 + 10/100)⁴

⇒ A = 2,40,000 × (1.1)⁴

⇒ A = 2,40,000 × 1.4641 = 3,51,384

⇒ Compound Interest (CI) = A − P

⇒ CI = 3,51,384 − 2,40,000 = 1,11,384

∴ The correct answer is ₹1,11,384.

Additional Information

Effective Rate of Interest

When interest is compounded quarterly, the effective annual rate is (1 + r/400)⁴ − 1.

Compounding Frequency

As the frequency of compounding increases (daily > monthly > quarterly > yearly), the Compound Interest earned also increases for the same rate and principal.

Rule of 72

To find the approximate time needed to double your money, divide 72 by the annual interest rate (72 ÷ R).

The correct answer is GST.

Key Points

• Goods and Services Tax (GST) is a unified indirect tax system implemented in India to eliminate cascading effects of taxation.
• The concept of Input Tax Credit (ITC) under GST allows businesses to claim credit for the tax paid on purchases and use it to offset the tax liability on sales.
• GST ensures an uninterrupted and seamless chain of Input Tax Credit, reducing the tax burden at each stage of value addition.
• ITC under GST is applicable to both goods and services, aligning with the “One Nation, One Tax” principle.
• This mechanism improves compliance, ensures transparency, and helps in making products and services more competitive in the market.

Additional Information

• Cascading Tax Effect:
• Occurs when tax is levied on a product at every stage of production without credit for the taxes paid in the earlier stages.
• GST eliminates this issue by enabling ITC throughout the supply chain.
• Input Tax Credit (ITC):
• ITC allows taxpayers to deduct the tax paid on inputs from the tax payable on final output.
• Conditions for availing ITC include possession of tax invoice, receipt of goods/services, and payment of tax to the government.
• GST Structure:
• GST comprises Central GST (CGST), State GST (SGST), and Integrated GST (IGST).
• ITC is transferable between CGST and SGST/IGST under specific rules.
• Benefits of GST:
• Creates a unified tax structure across India, boosting ease of doing business.
• Reduces tax evasion by integrating tax systems digitally.
• Promotes transparency and reduces litigation in tax administration.

Given:

1 is added to each odd digit and 2 is subtracted from each even digit in the number 3762184.

The new number formed is 4840262.

The digits in the new number are 0, 2, 2, 4, 4, 6, 8.

The highest digit in the new number is 8.

The lowest digit in the new number is 0.

Sum of the highest and lowest digits = 8 + 0 = 8.

Hence, the correct answer is "Option 1".

The least possible venn diagram is:

Conclusions:

(I) All roads are bikes → False (As, All bikes are roads. so, All roads are bikes can be a possibility but not definte)

(II) All roads are TVs → False (As, Some roads are TVs. so, All roads are TVs can be a possibility but not definte)

Thus, Neither conclusion (I) nor (II) follows.

Hence, the correct answer is "Option 4".

The correct answer is It is used in refrigeration and aerosol production..

Key Points

• Freon is a trade name for a group of chlorofluorocarbons (CFCs) and related compounds primarily used as refrigerants.
• It is widely used in refrigeration systems such as air conditioners, refrigerators, and freezers.
• Freon is also used in the production of aerosol propellants due to its ability to maintain pressure and flow consistency.
• The use of Freon has been regulated under international agreements like the Montreal Protocol due to its contribution to ozone layer depletion.
• Modern refrigeration systems are transitioning to alternative, eco-friendly refrigerants to replace Freon.

Additional Information

• Chlorofluorocarbons (CFCs):
• CFCs are compounds made up of chlorine, fluorine, and carbon atoms.
• They were once widely used in refrigeration, air conditioning, and aerosol sprays.
• CFCs are known to cause ozone depletion in the stratosphere.
• Montreal Protocol:
• An international treaty signed in 1987 to phase out substances that deplete the ozone layer, including CFCs.
• The treaty has been highly successful in reducing the production and consumption of ozone-depleting substances.
• Environmental Impact of Freon:
• Freon contributes to global warming and ozone layer depletion.
• Hydrochlorofluorocarbons (HCFCs) and hydrofluorocarbons (HFCs) are transitional substitutes but are also being phased out due to environmental concerns.
• Alternative Refrigerants:
• Eco-friendly refrigerants like ammonia (NH₃), carbon dioxide (CO₂), and hydrocarbons (e.g., isobutane) are being adopted.
• These alternatives have a lower global warming potential (GWP) and no ozone depletion potential (ODP).

Given:

Rituraj starts from Point A and drives 11 km towards South. He then takes a right turn, drives 9 km, turns right and drives 12 km.

He then takes a right turn and drives 12 km. He takes a final right turn, drives 1 km and stops at Point P.

Thus, Rituraj has to drive 3km west to reach point A.

Hence, the correct answer is "Option 1".

Shortcut Trick If a common root is given for a quadratic equation, that value must satisfy the equation containing the unknown variable. Directly substitute x = 11 into the equation 2x2 − 3x + c = 0. 2(11)2 − 3(11) + c = 0 242 − 33 + c = 0 ⇒ 209 + c = 0 ⇒ c = −209. ∴ The correct answer is -209.

Alternate Method Given: Quadratic Equations: 2x2 − 3x + c = 0 and x2 − 9x − 22 = 0. Common Root (α) = 11. Method: A root of an equation is the value of the variable that makes the equation equal to zero. Since 11 is a common root, it must satisfy both equations. Calculations: Step 1: Check the root in the second equation (optional but verifies the data). ⇒ (11)2 − 9(11) − 22 = 0 ⇒ 121 − 99 − 22 = 121 − 121 = 0 (Verified). Step 2: Substitute x = 11 in the first equation to find 'c'. ⇒ 2(11)2 − 3(11) + c = 0 ⇒ 2 × 121 − 33 + c = 0 ⇒ 242 − 33 + c = 0 ⇒ 209 + c = 0 ⇒ c = −209 ∴ The correct answer is -209.

Additional Information Condition for Common Roots If two quadratic equations have one common root, that root satisfies both equations. If they have both roots common, the coefficients are proportional: a1/a2 = b1/b2 = c1/c2. Nature of Roots For a quadratic equation ax2 + bx + c = 0, the Discriminant (D) = b2 − 4ac determines the nature: D > 0 (Real and Distinct), D = 0 (Real and Equal), D < 0 (Imaginary). Vieta's Formulas For the equation ax2 + bx + c = 0, the Sum of roots (α + β) = −b/a and the Product of roots (αβ) = c/a.

Given : G, H, I, J, K and X live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on, till the topmost floor is numbered 6.

1. No one lives above I.

2. K lives on an odd numbered floor but not on the lowermost floor.

3. X lives immediately below K.

4. Only two people live between K and G.

Evaluation of Cases:

However, I already lives on Floor 6. Thus, Case 2 is Eliminated.

5. Only two people live between I and H.

There are 2 people (G and H) living between J and X.

Hence, the correct answer is "Option 2".

The correct answer is Earth observation and climate monitoring.

Key Points

• NISAR (NASA-ISRO Synthetic Aperture Radar) is a joint Earth observation satellite developed collaboratively by NASA and ISRO.
• The satellite is designed to monitor ecosystem disturbances, natural hazards, and global environmental changes such as ice sheet dynamics, forest biomass, and agricultural patterns.
• Equipped with dual-frequency radar systems (L-band by NASA and S-band by ISRO), NISAR ensures high-resolution imaging capabilities.
• The mission aims to deliver critical data for climate monitoring, disaster management, and resource mapping globally.
• It is set to launch in February 2025, marking a significant collaboration in Earth science between the two space agencies.

Additional Information

• Synthetic Aperture Radar (SAR):
• A radar technology that creates high-resolution images of the Earth's surface by emitting and receiving microwave signals.
• It is capable of penetrating clouds, vegetation, and even soil, making it useful for all-weather, day-night observations.
• L-band and S-band Radars:
• L-band radar (long wavelength) is ideal for monitoring vegetation and soil moisture, while S-band radar (shorter wavelength) is suited for detecting finer details like ice and infrastructure.
• Key Applications of NISAR:
• Tracking deforestation, agricultural patterns, and glacier movements.
• Monitoring natural disasters like earthquakes, tsunamis, and floods to aid in disaster response.
• Data Contribution:
• NISAR will provide up to 12 terabytes of imaging data daily, supporting global climate studies and environmental monitoring.
• ISRO-NASA Collaboration:
• This partnership strengthens international cooperation in space exploration and enhances the technological capabilities of both agencies.

Shortcut Trick

Net deviation from the average (40) must be zero.

Deviations: (40 − 40) = 0; (42 − 40) = +2; (55 − 40) = +15.

Total deviation = 0 + 2 + 15 = +17.

To balance, fourth number deviation must be −17.

Fourth number = 40 − 17 = 23.

∴ The correct answer is 23.

Alternate Method

Given: Average of 4 numbers = 40; Three numbers are 40, 42, and 55.

Formula Used: Sum of observations = Average × Number of observations

⇒ Total sum = 40 × 4 = 160

⇒ Sum of the three known numbers = 40 + 42 + 55 = 137

⇒ Fourth number = Total sum − Sum of three numbers

⇒ Fourth number = 160 − 137

⇒ Fourth number = 23

∴ The correct answer is 23.

Additional Information

Sum of Deviations

The sum of the deviations of all observations from their arithmetic mean is always zero. This property is used in the deviation method shortcut.

Average of Consecutive Numbers

For an arithmetic progression (AP), Average = (First Term + Last Term) ÷ 2. This applies to consecutive integers, even numbers, or odd numbers.

Combined Average

If two groups have sizes n₁, n₂ and averages A₁, A₂, then the combined average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

The given code language is:

Thus, 'drive' is coded as 'zi'.

Hence, the correct answer is "Option 2".

Given:

Expression: √(0.012321) / √(0.001369)

Formula used:

√(a) / √(b) = √(a / b)

Calculation:

√(0.012321) / √(0.001369)

⇒ √(0.012321 / 0.001369)

⇒ √(9)

⇒ 3

∴ The correct answer is option (3).

Given interchange rules:

• ‘+’ and ‘−’ are interchanged.
• ‘×’ and ‘÷’ are interchanged.

The given equation is:

405 ÷ 2 + 369 × 9 − 32 = ?

Replace the operators with their corresponding new meanings:

405 × 2 − 369 ÷ 9 + 32 = ?

Now, we solve the equation following the BODMAS rule:

= 405 × 2 − 369 ÷ 9 + 32

= 810 − 41 + 32

= 769 + 32

= 801

Hence, the correct answer is "Option 2".

Shortcut Trick

Speed in still water = (Downstream speed + Upstream speed) ÷ 2

Speed = (40 + 26) ÷ 2

Speed = 66 ÷ 2 = 33 km/hr

∴ The correct answer is 33 km/hr.

Alternate Method

Given:

Downstream speed (v) = 40 km/hr

Upstream speed (u) = 26 km/hr

Formula Used:

Speed of swimmer in still water (x) = (v + u) ÷ 2

Calculations:

⇒ Speed in still water = (40 + 26) ÷ 2

⇒ Speed in still water = 66 ÷ 2

⇒ Speed in still water = 33 km/hr

∴ The correct answer is 33 km/hr.

Additional Information

Speed of Stream

The speed of the current or stream is calculated as (Downstream speed − Upstream speed) ÷ 2.

Downstream Speed

It is the sum of the speed of the boat in still water and the speed of the stream (u + v).

Upstream Speed

It is the difference between the speed of the boat in still water and the speed of the stream (u − v).

The logic followed here is:

Thus, the missing term in the series is 142.

Hence, the correct answer is "Option 4";

Shortcut Trick

Volume of full conical vessel = (1/3) × π × r² × h

Volume = (1/3) × π × 6² × 20 = (1/3) × π × 36 × 20 = 12 × 20 × π = 240π cm³

Volume of water = (3/4) × Total Volume = (3/4) × 240π

Volume of water = 3 × 60π = 180π cm³

∴ The correct answer is 180π cm³.

Alternate Method

Given:

Base radius (r) = 6 cm

Height (h) = 20 cm

Water level = 3/4 full

Formula Used:

Volume of Cone (V) = (1/3)πr²h

Calculations:

⇒ Total capacity of vessel = (1/3) × π × (6)² × 20

⇒ Total capacity = (1/3) × π × 36 × 20

⇒ Total capacity = 12 × 20 × π = 240π cm³

⇒ Volume of water poured = 3/4 × Total capacity

⇒ Volume of water = (3/4) × 240π

⇒ Volume of water = 3 × 60π = 180π cm³

∴ The correct answer is 180π cm³.

Additional Information

Slant Height of Cone

The slant height (l) is given by l = √(r² + h²), representing the distance from the apex to the edge of the base.

Surface Area of Cone

Curved Surface Area (CSA) = πrl and Total Surface Area (TSA) = πr(l + r).

Relationship with Cylinder

The volume of a cone is exactly 1/3 the volume of a cylinder with the same base radius and height.

Shortcut Trick

Mode is the value that appears most frequently in a data set.

Count the occurrences of each number in the given observations.

Frequency of 9 = 4 times.

Frequency of 2, 4, and 5 = 3 times each.

Since 9 has the maximum frequency, it is the mode.

∴ The correct answer is 9.

Alternate Method

Given: Observations = 9, 6, 4, 2, 5, 2, 9, 2, 1, 9, 4, 5, 9, 5, 4, 8.

Formula: Mode = Value with the highest frequency.

⇒ Arrange the observations in ascending order: 1, 2, 2, 2, 4, 4, 4, 5, 5, 5, 6, 8, 9, 9, 9, 9.

The correct answer is 1687.

Key Points

• Municipal governance was first introduced in British India in 1687, with the establishment of the municipal corporation in Madras (now Chennai).
• The Madras Municipal Corporation was the first attempt by the British to introduce local self-governance in India.
• Following Madras, municipal governance was later extended to Bombay and Calcutta in the early 18^th century.
• The introduction of municipal governance aimed to ensure better administration, sanitation, and infrastructure development in urban centers.
• It laid the foundation for modern urban governance in India, which later evolved through subsequent legislative reforms.

Additional Information

• Terminology:
• Municipal Corporation: It is a form of urban local governance responsible for the administration of cities with large populations.
• Local Self-Governance: A system of governance where local authorities manage their own affairs independently within the framework of a larger governing system.
• Evolution of Municipal Governance:
• In 1882, Lord Ripon introduced reforms to strengthen local self-governance, often referred to as the "Father of Local Self-Government in India."
• The Montague-Chelmsford Reforms (1919) further emphasized the importance of local governance under the provincial governments.
• Modern Municipal Governance:
• The 74^th Constitutional Amendment Act of 1992 provided a constitutional status to municipalities and introduced the concept of urban local bodies.
• It mandated the establishment of municipal corporations, municipal councils, and Nagar Panchayats based on population size.
• Impact:
• Municipal governance in India plays a key role in urban planning, infrastructure development, and the delivery of essential services.
• It ensures civic amenities such as water supply, waste management, street lighting, and public health services.

The correct answer is Drone Surveying.

Key Points

• The SVAMITVA scheme was launched by the Government of India on April 24, 2020, to provide rural landowners with property ownership rights.
• Under the scheme, drone technology is used for mapping land parcels in rural areas to create accurate land records.
• Drone surveying ensures high-resolution aerial imagery that facilitates precision mapping and minimizes disputes related to land ownership.
• The maps generated via drones are integrated with Geographical Information Systems (GIS) for ease of access and management.
• This initiative aims to promote financial stability in rural areas by enabling landowners to use their property as collateral for loans and other financial activities.

Additional Information

• Drone Technology:
• Drones, also known as unmanned aerial vehicles (UAVs), are equipped with cameras, sensors, and GPS systems for high-precision surveying and mapping.
• They are widely used in agriculture, disaster management, urban planning, and land surveys due to their efficiency and accuracy.
• Geographical Information System (GIS):
• GIS is a computer-based tool that analyzes and visualizes spatial data. It integrates maps and data layers for better decision-making.
• It plays a critical role in land management, urban planning, and environmental monitoring.
• Objectives of SVAMITVA Scheme:
• To create a comprehensive digital record of land ownership in rural India.
• To reduce disputes related to land ownership and promote transparency.
• To empower rural property owners by enabling them to monetize their assets.
• Implementation:
• The scheme is implemented by the Ministry of Panchayati Raj in collaboration with the Survey of India.
• States and Union Territories actively participate in the process of land survey and mapping.

Shortcut Trick

The Marked Price (MP) is ₹640.

Successive discounts are 30%, 25%, and an additional 25% for cash.

Selling Price (SP) = 640 × (70 ÷ 100) × (75 ÷ 100) × (75 ÷ 100).

SP = 640 × (7 ÷ 10) × (3 ÷ 4) × (3 ÷ 4).

SP = 640 × (63 ÷ 160) = 4 × 63 = 252.

∴ The correct answer is ₹252.

Alternate Method

Given: MP = ₹640, D₁ = 30%, D₂ = 25%, D₃ (cash) = 25%.

Formula: SP = MP × (100 − D₁)% × (100 − D₂)% × (100 − D₃)%

⇒ Price after 1^st discount = 640 − (30% of 640) = 640 − 192 = 448.

⇒ Price after 2^nd discount = 448 − (25% of 448) = 448 − 112 = 336.

⇒ Price after 3^rd (cash) discount = 336 − (25% of 336) = 336 − 84 = 252.

∴ The correct answer is ₹252.

Additional Information

Successive Discounts

When multiple discounts are applied one after another, the single equivalent discount for two discounts a% and b% is given by (a + b − ab ÷ 100)%.

Marked Price & Selling Price

Marked Price is the listed price on the tag. Selling Price is the final amount paid after deducting all applicable discounts from the MP.

The correct answer is Clock speed.

Key Points

• Clock speed refers to the number of cycles a CPU can execute per second, usually measured in Hertz (Hz). A higher clock speed indicates a faster CPU.
• It directly affects how quickly a processor can process instructions and execute tasks.
• Modern CPUs have clock speeds typically measured in gigahertz (GHz), representing billions of cycles per second.
• Clock speed is a critical factor for performance, but it must be paired with other components like memory and storage for optimal efficiency.
• Overclocking can increase clock speed beyond the manufacturer's specifications, potentially enhancing performance but at the risk of increased heat and reduced stability.

Additional Information

• Cache size: Refers to the small-sized, high-speed memory located inside the CPU to store frequently accessed data. While it affects performance, it does not determine the number of instructions processed per second.
• Number of registers: Registers are small storage locations within the CPU used to store data temporarily during execution. While essential for operations, they do not directly dictate processing speed.
• Power consumption: Indicates the energy required by the CPU during operation. While it impacts efficiency and heat generation, it does not determine instruction execution.
• Pipelining: A technique used by modern CPUs to execute multiple instructions simultaneously by dividing the execution process into stages, improving overall performance.
• Multi-core processors: CPUs with multiple cores can process multiple instructions simultaneously, enhancing processing capability, especially for multitasking and parallel processing workloads.

Shortcut Trick

Use the direct combined algebraic identity:

Value = (x + y + z) × [3(x² + y² + z²) − (x + y + z)²] ÷ 2

Value = 12 × [3(20) − (12)²] ÷ 2

Value = 12 × [60 − 144] ÷ 2 = 12 × (−84) ÷ 2

Value = 12 × (−42) = −504

∴ The correct answer is −504.

Alternate Method

Given: Sum of numbers (x + y + z) = 12 and sum of their squares (x² + y² + z²) = 20.

We know the expansion formula:

(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)

⇒ (12)² = 20 + 2(xy + yz + zx) ⇒ 144 − 20 = 2(xy + yz + zx) ⇒ 124 = 2(xy + yz + zx) ⇒ xy + yz + zx = 62

Now, to find the value of x³ + y³ + z³ − 3xyz, use the standard algebraic identity:

x³ + y³ + z³ − 3xyz = (x + y + z)(x² + y² + z² − (xy + yz + zx))

⇒ Value = 12 × (20 − 62) ⇒ Value = 12 × (−42) ⇒ Value = −504

∴ The correct answer is −504.

Additional Information

Special Case: x + y + z = 0

If the sum of three numbers is zero, then x³ + y³ + z³ = 3xyz.

Alternative form of the identity

x³ + y³ + z³ − 3xyz = (1/2)(x + y + z)[(x − y)² + (y − z)² + (z − x)²], which is useful when differences between numbers are given.

Identity for squares

x² + y² + z² − xy − yz − zx = (1/2)[(x − y)² + (y − z)² + (z − x)²].

Given : Seven boxes, A, B, C, D, E, F and G, are kept one above the other but not necessarily in the same order. The positions are counted from top to bottom.

1. Only two boxes are kept below C.

2. Only one box is kept above A.

3. Only one box is kept between A and E.

4. B is kept immediately above F (BF block).

5. D is kept at some place below G (G ... D).

There are 5 boxes kept above B.

Hence, the correct answer is "Option 4".

Shortcut Trick

Net interest percentage for 2 years = Rate × Time = 4% × 2 = 8%

Simple Interest = 8% of ₹2,20,000

Simple Interest = 0.08 × 2,20,000 = ₹17,600

∴ The correct answer is ₹17,600.

Alternate Method

Given:

Principal (P) = ₹2,20,000

Rate (R) = 4% per annum

Time (T) = 2 years

Formula Used:

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

Calculations:

⇒ SI = (2,20,000 × 4 × 2) ÷ 100

⇒ SI = 2,200 × 8

⇒ SI = ₹17,600

∴ The correct answer is ₹17,600.

Additional Information

Total Amount Formula

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

Rate of Interest Calculation

To find the rate when SI, P, and T are known: R = (SI × 100) ÷ (P × T).

SI vs CI for 2 Years

The difference between Compound Interest and Simple Interest for 2 years is: CI − SI = P(R/100)².

The correct answer is Pensions paid to the princes after integration.

Key Points

• The privy purses were annual payments made by the Government of India to former princely rulers after the integration of princely states into independent India.
• The payments were part of an agreement during the integration process, ensuring economic security to the princes who surrendered their sovereignty.
• The privy purses were paid as compensation for merging their states into the Indian Union after independence in 1947.
• In 1971, the privy purses were abolished by the then Prime Minister Indira Gandhi through a constitutional amendment, citing reasons of equality and the need to end privileges.
• The abolition of privy purses marked a significant step in eliminating feudal privileges and ensuring a more egalitarian society.

Additional Information

• Integration of Princely States:
• India had over 500 princely states at the time of independence in 1947.
• Sardar Vallabhbhai Patel and V.P. Menon played a key role in integrating these states into the Indian Union.
• The princely rulers agreed to the merger in exchange for privileges, including privy purses.
• Constitutional Basis:
• The privy purses were guaranteed under Article 291 of the Indian Constitution.
• They were later abolished through the 26^th Constitutional Amendment Act, 1971.
• Reasons for Abolition:
• The Indian government argued that privy purses were inconsistent with the socialist and democratic ideals of the Constitution.
• The move was seen as a step towards ending hereditary privileges and promoting equality.
• Impact of Abolition:
• The abolition of privy purses led to financial difficulties for some former rulers but was widely hailed as a progressive measure.
• It reinforced India's commitment to egalitarianism and democratic values.

Given:

49 + [7 + {63 − (27 ÷ 9)} ÷ 6]

Calculation:

⇒ 49 + [7 + {63 − 3} ÷ 6]

⇒ 49 + [7 + 60 ÷ 6]

⇒ 49 + [7 + 10]

⇒ 49 + 17

∴ Final Answer = 66

Given series:

(Left) 3 € & £ @ * # 1 $ € @ © € © & 1 € 4 1 2 4 © (Right)

Condition to be checked:

Number → Symbol → Symbol

3 € & £ @ * # 1 $ € @ © € © & 1 € 4 1 2 4 ©

There are two such symbols in the above arrangement (3 € &, 1 $ €).

Hence, the correct answer is "Option 2"$.

The correct answer is International Day of Education.

Key Points

• The International Day of Education is observed globally on 24 January every year.
• It was proclaimed by the United Nations General Assembly in December 2018 to emphasize the role of education in peace and development.
• UNESCO leads the global observance of this day, focusing on ensuring inclusive and equitable quality education for all as part of the Sustainable Development Goal 4 (SDG 4).
• The theme for 2025 will highlight the importance of transformative education in addressing global challenges such as climate change, inequality, and poverty.
• The day serves as a call to action to prioritize education in policy-making and funding globally, aiming to build resilient and sustainable societies.

Additional Information

• Education as a Human Right:
• The Universal Declaration of Human Rights (1948) recognizes education as a fundamental human right under Article 26.
• It emphasizes that primary education should be free and compulsory for all children.
• Sustainable Development Goal 4:
• SDG 4 aims to ensure inclusive and equitable quality education and promote lifelong learning opportunities for all by 2030.
• Key targets include universal primary and secondary education, vocational training, and eliminating gender disparities in access to education.
• UNESCO’s Role:
• UNESCO leads global efforts to advance education as a tool for peace, sustainable development, and social equity.
• It supports member states in implementing educational policies and frameworks aligned with global goals.
• Challenges in Global Education:
• An estimated 244 million children and youth were out of school globally as of 2023.
• Barriers include poverty, gender inequality, conflict, and lack of infrastructure.
• Transformative Education:
• Transformative education focuses on empowering learners to become active participants in addressing global challenges.
• It integrates critical thinking, digital literacy, and environmental awareness into curricula.

The pattern followed here is.

Thus, the missing term in the series is PW54.

Hence, the correct answer is Option 1.

The correct answer is Option 2: Rajasthan, Gujarat, Punjab, and Haryana.

Key Points

• The Thar Desert, also known as the Great Indian Desert, is predominantly located in the northwestern region of India.
• It spans across the Indian states of Rajasthan, Gujarat, Punjab, and Haryana, making it a significant geographical feature in these areas.
• The desert covers approximately 77,000 square miles (200,000 square kilometers), with Rajasthan accounting for the majority of its land area.
• It is characterized by arid conditions, sand dunes, sparse vegetation, and extreme temperatures, making it one of the most inhospitable regions in India.
• The Thar Desert also extends into Pakistan, but the majority of its area lies within Indian territory.

Additional Information

• Climate of the Thar Desert:
• The Thar Desert experiences an arid climate with very low rainfall, typically less than 200mm annually.
• Temperatures can soar above 50°C in the summer and drop below freezing in the winter.
• Ecological Significance:
• The desert hosts unique flora and fauna adapted to its harsh conditions, including desert foxes, camels, and khejri trees.
• The Desert National Park located in Rajasthan is a protected area that showcases the biodiversity of the region.
• Human Settlement:
• The Thar Desert is one of the world's most densely populated deserts, with villages scattered across its landscape.
• Traditional occupations in the region include camel breeding, agriculture (using irrigation), and handicrafts.
• Geographical Features:
• Sand dunes, salt pans, and rocky outcrops are prominent features of the Thar Desert's terrain.
• The Luni River is the only major river flowing through the desert region.

The correct answer is Indira Gandhi Canal.

Key Points

• The Indira Gandhi Canal is one of the largest canal systems in India, and it plays a vital role in providing water for irrigation in the Thar Desert region.
• The canal originates at the Harike Barrage, located at the confluence of the Sutlej and Beas rivers in Punjab, and flows through Rajasthan.
• It was commissioned in 1984 and provides water to the arid regions of western Rajasthan, including Jodhpur, Bikaner, and surrounding areas.
• The canal irrigates around 19 lakh hectares of land, transforming barren areas into fertile agricultural lands in the desert.
• The project has significantly contributed to the socio-economic development of the region, ensuring food security and better livelihoods for farmers.

Additional Information

• Thar Desert:
• The Thar Desert, also known as the Great Indian Desert, is the 17^th largest desert in the world and covers approximately 200,000 square kilometers.
• It spans the states of Rajasthan, Gujarat, Punjab, and Haryana, with Rajasthan having the largest share.
• It is characterized by extreme arid conditions, high temperatures, and low rainfall (100-200 mm annually).
• Harike Barrage:
• The Harike Barrage is located in Punjab and serves as the source of the Indira Gandhi Canal.
• The barrage helps regulate the water flow from the Sutlej and Beas rivers into the canal system.
• Water Management in Arid Regions:
• The Indira Gandhi Canal project demonstrates how large-scale irrigation systems can combat desertification and promote agricultural activities in arid regions.
• It is an example of utilizing inter-basin water transfer to address water scarcity.
• Economic Impact:
• The Indira Gandhi Canal has boosted agriculture, created employment opportunities, and improved the quality of life for people in western Rajasthan.
• It has facilitated the cultivation of crops such as wheat, mustard, and cotton, which were previously impossible in the desert environment.

Shortcut Trick Net efficiency for filling the tank = 1/18 − 1/19 = 1/342 part per hour. Time to fill the full tank = 342 hours. Time to fill one-third of the tank = 342 ÷ 3 = 114 hours. ∴ The correct answer is 114 hours. Alternate Method Given: Filling Tap time = 18 hours Emptying Tap time = 19 hours Target: Fill 1/3 of the tank capacity. Tap Type Time (hr) Total Work (LCM) Efficiency Inlet (+) 18 342 units +19 Outlet (−) 19 −18 Calculations: ⇒ Total capacity of the cistern = LCM(18, 19) = 342 units. ⇒ Net efficiency of both taps = 19 − 18 = 1 unit/hour. ⇒ Target volume to be filled = 1/3 × 342 = 114 units. ⇒ Time required = Target Volume ÷ Net Efficiency ⇒ Time required = 114 ÷ 1 = 114 hours. ∴ The correct answer is 114 hours. Additional Information Pipes and Cisterns Basics Efficiency of an Inlet pipe is always positive, while the efficiency of an Outlet (leakage) pipe is taken as negative. Total Work Concept Total capacity or work is usually the Least Common Multiple (LCM) of the individual times taken by each pipe. Combined Rate Formula If pipe A fills in 'x' hours and pipe B empties in 'y' hours, net rate per hour is (1/x − 1/y). Tank fills only if x < y.

The correct answer is Curvilinear shikharas.

Key Points

• The Jageshwar temple complexes in Uttarakhand are renowned for their Nagara-style architecture, which is characterized by curvilinear shikharas (spires).
• Curvilinear shikharas are distinctively tall and tapering structures that rise upwards in a convex curve and are a hallmark of North Indian temple architecture.
• Jageshwar temples primarily date back to the 7^th to 12^th centuries CE, showcasing intricate stone carvings and traditional designs.
• The shikharas of these temples often have an amalaka (circular disc-like structure) at the top, symbolizing divine energy and protection.
• The temple complex consists of over 100 small and large shrines dedicated to Lord Shiva, reflecting the religious significance of the region.

Additional Information

• Nagara Style Architecture:
• This style is predominant in northern India and is characterized by curvilinear shikharas and multiple smaller towers surrounding the main temple.
• Unlike Dravidian architecture, Nagara temples do not have elaborate gateways (gopurams) and often feature intricate carvings on stone.
• Amalaka:
• The amalaka is a distinctive circular stone disc found atop the shikhara, symbolizing purity and spiritual protection.
• It is often surmounted by a kalasha (pot-like structure), adding to the aesthetic and symbolic significance of the temple.
• Jageshwar Temple Complex:
• Located in the Almora district of Uttarakhand, this complex is considered one of the oldest centers of Shaivism in India.
• The temples are surrounded by dense deodar forests, contributing to their serene and spiritual ambiance.
• Historical Importance:
• The Jageshwar temples are believed to have been built during the Katyuri and Chand dynasties, showcasing the evolution of temple architecture.
• The complex has inscriptions and sculptures that provide insights into religious practices and artistic styles of ancient India.

The correct answer is North East Delhi.

Key Points

• As per the 2011 Census of India, North East Delhi recorded the highest population density in the country.
• North East Delhi had a population density of 37,346 persons per square kilometer, making it the most densely populated district in India.
• Population density is calculated as the number of persons per square kilometer of land area.
• North East Delhi is part of the National Capital Territory (NCT) of Delhi, which is itself one of the most urbanized and densely populated regions in India.
• The high population density in this region is attributed to urbanization, migration, and the concentration of residential settlements in limited geographic space.

Additional Information

• Population Density:
• Population density is a key demographic indicator that reflects the number of people living in a unit area of land.
• It is calculated using the formula: Population Density = Total Population / Land Area.
• 2011 Census of India:
• The 2011 Census was the 15^th National Census of India and provided comprehensive data on population demographics, density, literacy, and other parameters.
• It recorded India's population at 1.21 billion, with a growth rate of 17.7% compared to 2001.
• Urbanization in Delhi:
• Delhi’s rapid urbanization has resulted in high population density, particularly in areas like North East Delhi.
• Migrants from different states move to Delhi for job opportunities, education, and improved living standards, contributing to its dense population.
• Other High-Density Districts:
• After North East Delhi, other districts with high population densities include Central Delhi and East Delhi.
• These regions also face challenges such as overcrowding, pressure on infrastructure, and environmental concerns.

The logic followed here is:

SW : NR : IM

IM : DH : YC

Option 1: UY-PT-LO

This option does NOT follow the pattern.

Option 2: FJ-AE-WZ

This option does NOT follow the pattern. 

Option 3: YC-TX-OS

This option follows the pattern.

Option 4: HL-DG-XB

This option does NOT follow the pattern. 

Hence, the correct answer is "Option 3".

The correct answer is The system menu for the current window (containing options like Move, Size, Minimize, Maximize, Close).

Key Points

• Pressing Alt + Spacebar in Windows applications typically opens the system menu for the current window.
• The system menu contains options such as Move, Size, Minimize, Maximize, and Close, allowing users to control the window's behavior.
• This shortcut provides users with quick access to window management functionalities without using the mouse.
• The system menu is an integral feature of the Windows graphical user interface (GUI), present since early versions of Windows.
• It works universally across most Windows applications, unless overridden by the application itself.

Additional Information

• System Menu:
• The system menu is a feature of Windows' GUI that allows users to manage the state and position of application windows.
• It can also be accessed by right-clicking the window's title bar or clicking the icon on the top-left corner of the window.
• Window Management Shortcuts:
• Other common shortcuts include Alt + Tab (switch between open applications) and Windows Key + D (show desktop).
• These shortcuts improve productivity by enabling faster navigation within the Windows environment.
• Customization:
• Applications can override the default behavior of Alt + Spacebar, replacing the system menu with custom menus or actions.
• This is common in some modern software where the developer opts for a streamlined user interface.
• Legacy Feature:
• The system menu has been present since early versions of Windows, including Windows 3.1.
• Despite modern UI advancements, this feature remains relevant for window management in current Windows versions.

The logic followed here is:​

LI : NK : PR

Option 1: RO-TQ-VY

This option does NOT follow the pattern.

Option 2: SO-TR-VY

This option does NOT follow the pattern. 

Option 3: SO-TQ-VY

This option does NOT follow the pattern. 

Option 4: RO-TQ-VX

This option follows the pattern.

Hence, the correct answer is "Option 4".

Given:

Rohan starts from point A and drives 8 km towards the north.

He then takes a left turn, drives 12 km, turns left and drives 11 km. He then takes a left turn and drives 14 km. He takes a final left turn, drives 3 km and stops at point P.

Thus, Rohan has to drive 2km west to reach point A. 

Hence, the correct answer is "Option 1".

The correct answer is 5^th.

Key Points

• Deepti Sharma achieved the 5^th rank in the ICC Women's All-rounders Rankings in March 2025.
• Deepti Sharma is one of India's most prominent all-rounders, excelling in both batting and bowling in international cricket.
• The ICC Rankings consider a player's performance across all formats (ODIs, T20Is, and Tests) to determine their ranking.
• Deepti's consistent performances in international tournaments contributed significantly to her rise in the rankings.
• The ICC updates its rankings regularly based on players' performances in recent matches.

Additional Information

• ICC Women’s Rankings:
• These rankings evaluate players’ performances in batting, bowling, and all-rounder categories across all formats of cricket.
• Points are calculated using a sophisticated algorithm that takes into account match context, opponent strength, and individual contributions.
• Deepti Sharma’s Cricketing Achievements:
• She has been a key player for the Indian Women’s Cricket Team, known for her dependable off-spin and strong batting performances.
• She holds the record for the highest individual score in Women's ODIs for India (188* against Ireland in 2017).
• All-rounder Role in Cricket:
• An all-rounder contributes significantly to both batting and bowling, making them a valuable asset to any team.
• Notable women’s cricket all-rounders include Ellyse Perry (Australia), Sophie Devine (New Zealand), and Stafanie Taylor (West Indies).
• ICC's Role in Cricket:
• The International Cricket Council (ICC) is the global governing body for cricket.
• It oversees international competitions, rankings, and the development of the sport worldwide.

Shortcut Trick

Sum of first 2 numbers = 77 × 2 = 154

Sum of first 3 numbers = 154 + 129 = 283

Sum of remaining 2 numbers = 655 − 283 = 372

Average of remaining 2 numbers = 372 ÷ 2 = 186

∴ The correct answer is 186.

Alternate Method

Given:

Total sum of 5 numbers = 655

Average of first 2 numbers = 77

Third number = 129

Sum: 154 129 Remaining Sum Total Sum = 655 First 2 Nos. 3^rd No. Last 2 Nos.

Formula used:

Sum = Average × Number of items

Average = Sum ÷ Number of items

Calculations:

⇒ Sum of first 2 numbers = 77 × 2 = 154

⇒ Sum of first 3 numbers = 154 + 129 = 283

⇒ Sum of remaining 2 numbers = Total sum − Sum of first 3 numbers

⇒ Sum of remaining 2 numbers = 655 − 283 = 372

⇒ Average of remaining 2 numbers = 372 ÷ 2

⇒ Average = 186

∴ The correct answer is 186.

Additional Information

Basic Average Formula

The average of n numbers is calculated as the sum of all numbers divided by n (Average = Σx ÷ n).

Sum of Numbers

To find the total sum when the average is known, multiply the average by the count of numbers (Sum = Average × n).

Net Deviation Method

The sum of deviations of all observations from their mean is always zero, which can be used to find missing values in a series.

Shortcut Trick

Let original cost of pen be x and pencil be y.

Equation 1: 6x + 5y = 259

Equation 2: 19(x − 9) + 2(y + 4) = 90 ⇒ 19x + 2y = 90 + 171 − 8 = 253

Solving these: x = 9, y = 41 (Invalid, x must be pen cost). Re-check: 19x + 2y = 90 + 163 = 253. Multiply eq1 by 2 and eq2 by 5: 12x + 10y = 518 and 95x + 10y = 1265. Difference: 83x = 747 ⇒ x = 9. Then y = 41.

Original cost of 13 pens and 2 pencils = 13(9) + 2(41) = 117 + 82 = 199.

∴ The correct answer is ₹199.

Alternate Method

Let the original cost of one pen be x and one pencil be y.

According to the first condition:

⇒ 6x + 5y = 259 --- (i)

According to the second condition (New costs: Pen = x − 9, Pencil = y + 4):

⇒ 19(x − 9) + 2(y + 4) = 90

⇒ 19x − 171 + 2y + 8 = 90

⇒ 19x + 2y − 163 = 90

⇒ 19x + 2y = 253 --- (ii)

To eliminate y, multiply (i) by 2 and (ii) by 5:

⇒ 12x + 10y = 518 --- (iii)

⇒ 95x + 10y = 1265 --- (iv)

Subtracting (iii) from (iv):

⇒ 83x = 747

⇒ x = 747 ÷ 83 = 9

Substitute x = 9 in (i):

⇒ 6(9) + 5y = 259

⇒ 54 + 5y = 259

⇒ 5y = 205 ⇒ y = 41

Required cost of 13 pens and 2 pencils:

⇒ 13x + 2y = 13(9) + 2(41)

⇒ 117 + 82 = 199

∴ The correct answer is ₹199.

Additional Information

Linear Equations in Two Variables

Equations of the form ax + by = c represent straight lines. They can be solved using substitution, elimination, or cross-multiplication methods.

Elimination Method

Multiply equations by suitable constants to make the coefficients of one variable equal, then add or subtract to eliminate that variable.

Cost-Price Relationship

Total Cost = (Quantity₁ × Price₁) + (Quantity₂ × Price₂). Any change in individual price affects the total bill linearly.

The correct answer is Village head.

Key Points

• The Mahalwari system was introduced in 1833 by the British East India Company during the administration of Lord William Bentinck.
• Under this system, the village headman (or Pradhan) was made responsible for collecting land revenue from the farmers on behalf of the British government.
• The revenue settlement was made collectively for the village or estate, which was referred to as the "Mahal."
• This system was primarily implemented in parts of North-Western Provinces, Central Provinces, Punjab, and Uttar Pradesh.
• The goal was to create a direct link between the colonial administration and the village community, while also ensuring the efficient collection of revenue.

Additional Information

• Key Features of Mahalwari System:
• The system combined elements of both the Zamindari and Ryotwari systems.
• Revenue rates were periodically revised, and the village collectively bore the responsibility of payment.
• Zamindari System:
• In this system, land revenue was collected by landlords (Zamindars) from the peasants and paid to the British government.
• It was introduced in Bengal, Bihar, and Odisha under the Permanent Settlement Act of 1793.
• Ryotwari System:
• Here, the settlement was directly made with the cultivators (Ryots), who were recognized as the owners of the land.
• It was primarily implemented in Madras, Bombay, and parts of Assam.
• Purpose of Revenue Systems:
• The primary objective of these systems was to extract maximum revenue for the British administration.
• However, these policies often led to exploitation and economic distress among Indian farmers.

The correct answer is Delhi.

Key Points

• Delhi, a major center of the 1857 Revolt, was recaptured by British forces in September 1857.
• The siege of Delhi lasted from June 8 to September 20, 1857, and marked a critical turning point in the rebellion.
• The British forces, led by General John Nicholson, launched a decisive assault on the city, overcoming fierce resistance from the rebels.
• Delhi was significant as the symbolic seat of the Mughal Emperor, Bahadur Shah II, who was declared the nominal leader of the rebellion.
• The recapture of Delhi dealt a severe blow to the morale and coordination of the rebel forces during the uprising.

Additional Information

• 1857 Revolt: Also known as the First War of Indian Independence, it was a widespread rebellion against British rule.
• Bahadur Shah II: The last Mughal Emperor, who was declared the symbolic leader of the revolt, was later captured and exiled to Rangoon.
• General John Nicholson: A key British commander during the Siege of Delhi, he played a pivotal role in the city's recapture but was mortally wounded in the process.
• Significance of Delhi: As the center of Mughal power, Delhi held immense symbolic and strategic importance for both the rebels and the British.
• Aftermath: The recapture of Delhi marked the beginning of the suppression of the revolt, with other key centers like Kanpur, Lucknow, and Jhansi falling in the following months.

Shortcut Trick

For three numbers in continued proportion a, b, c where c is the third proportional:

b² = a × c

Z² = 36 × 4

Z = √(36 × 4) = 6 × 2 = 12

∴ The correct answer is 12.

Alternate Method

Given: First number (a) = 36, Mean proportional (b) = Z, Third proportional (c) = 4.

Formula Used: If a, b, c are in continued proportion, then a/b = b/c.

36 1^st (a)

Z 2^nd (b)

4 3^rd (c)

Ratio: 36/Z = Z/4

⇒ 36/Z = Z/4

⇒ Z × Z = 36 × 4

⇒ Z² = 144

⇒ Z = √144

⇒ Z = 12

∴ The correct answer is 12.

Additional Information

Mean Proportional

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

Fourth Proportional

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

Third Proportional

For numbers a and b, the third proportional c is calculated such that a:b = b:c, which gives c = b² ÷ a.

Given:

Simplify: (2)/(8) + (2)/(8) + (1)/(16) + (2)/(8) - 1

Formula used:

Add all fractions and subtract 1.

Calculation:

(2)/(8) + (2)/(8) + (1)/(16) + (2)/(8) - 1

⇒ Combine fractions with the same denominator:

⇒ (2)/(8) + (2)/(8) + (2)/(8) = (6)/(8)

⇒ Convert (6)/(8) to (12)/(16) for common denominator with (1)/(16):

⇒ (12)/(16) + (1)/(16) = (13)/(16)

⇒ (13)/(16) - 1

⇒ Convert 1 to (16)/(16):

⇒ (13)/(16) - (16)/(16)

⇒ = -(3)/(16)

∴ The correct answer is option (2).

Shortcut Trick

Convert percentages to values: 1800% of 10 = 18 × 10 = 180.

Target value = 180 − 10 = 170.

Since 25% (or 1/4) of k is 170, then k = 170 × 4.

k = 680.

∴ The correct answer is 680.

Alternate Method

Given:

25% of k = (1800% of 10) − 10

⇒ (25/100) × k = [(1800/100) × 10] − 10

⇒ 0.25 × k = [18 × 10] − 10

⇒ 0.25 × k = 180 − 10

⇒ 0.25 × k = 170

⇒ k = 170 ÷ 0.25

⇒ k = 170 × 4

⇒ k = 680

∴ The correct answer is 680.

Additional Information

Percentage to Fraction Conversion

Common conversions: 25% = 1/4, 50% = 1/2, 75% = 3/4, and 100% = 1. To convert x% to a fraction, divide by 100.

Percentage Interchangeability

x% of y is always equal to y% of x. For example, 1800% of 10 is the same as 10% of 1800, which equals 180.

Base Change Property

If a number is reduced by 75% (remaining 25%), to restore it to its original value, it must be increased by 300% (multiplied by 4).

Shortcut Trick Convert each ratio to approximate decimals to compare quickly. 17 ÷ 53 ≈ 0.32 24 ÷ 54 = 4 ÷ 9 ≈ 0.44 28 ÷ 60 = 7 ÷ 15 ≈ 0.46 16 ÷ 57 ≈ 0.28 ∴ The correct answer is 28 : 60. Alternate Method

Given Ratios: 17/53, 24/54, 28/60, 16/57 Step 1: Simplify the fractions where possible ⇒ 24/54 = 4/9 ≈ 0.444 ⇒ 28/60 = 7/15 ≈ 0.466 Step 2: Cross-multiply the two largest candidates (24/54 and 28/60) ⇒ 24 × 60 = 1440 ⇒ 54 × 28 = 1512 ⇒ Since 1512 > 1440, 28/60 is greater than 24/54. Step 3: Compare with 17/53 and 16/57 ⇒ 17/53 is roughly 1/3 (0.33), and 16/57 is less than 1/3. ⇒ 28/60 is almost 1/2 (0.5), making it the greatest. ∴ The correct answer is 28 : 60. Additional Information Cross Multiplication Rule For two fractions a/b and c/d, if a×d > b×c, then a/b > c/d. Percentage Conversion To compare ratios, convert them to percentages by multiplying by 100. For example, 28/60 × 100 ≈ 46.67%. Common Denominator Method Convert all ratios to have the same denominator (LCM) and compare the numerators directly.

The correct answer is It cycles through the open windows or tabs of the currently active application.

Key Points

• Pressing Ctrl + Tab in most graphical operating systems cycles through the open tabs or windows within the currently active application.
• This functionality is widely used in applications such as web browsers (e.g., Google Chrome, Mozilla Firefox) and text editors (e.g., Visual Studio Code).
• It ensures seamless multitasking by quickly switching between multiple tabs or documents without requiring the user to click manually.
• Unlike Alt + Tab, which cycles through all open applications, Ctrl + Tab is specific to the currently active application.
• This feature enhances productivity by allowing users to quickly navigate and manage workflows across different tabs/windows.

Additional Information

• Alt + Tab:
• This shortcut allows users to switch between all open applications on the system.
• It is commonly used for navigating between different programs quickly, especially in multitasking scenarios.
• Ctrl + W:
• This shortcut is used to close the current tab or window within an application.
• It is particularly useful in web browsers and text editors for closing specific tabs without exiting the entire program.
• Ctrl + N:
• Pressing this combination opens a new tab or window in the currently active application.
• It is often utilized in browsers or document editors to create new workspaces.
• Ctrl + Shift + Tab:
• This shortcut cycles through open tabs/windows in the reverse order of Ctrl + Tab.
• It is helpful when navigating backward through a sequence of open tabs.
• Task Switching in OS:
• Modern operating systems like Windows, macOS, and Linux provide various shortcuts to improve user efficiency when managing multiple applications.
• These shortcuts are designed to reduce dependency on the mouse and enable faster navigation.

The correct answer is Damodar.

Key Points

• The Damodar River is the primary river system that drains the Chotanagpur Plateau, located in eastern India.
• It flows through the states of Jharkhand and West Bengal, contributing significantly to the region's hydrology.
• The river is often referred to as the "Sorrow of Bengal" due to its history of frequent flooding.
• Major tributaries of the Damodar River include Barakar, Konar, and Bokaro, which originate in the Chotanagpur Plateau.
• The Damodar Valley Corporation (DVC) was established in 1948 to control flooding, provide irrigation, and develop hydroelectric projects along the river.

Additional Information

• Chotanagpur Plateau:
• The plateau spans across Jharkhand, Odisha, and Chhattisgarh and is rich in mineral resources, such as coal, iron ore, and mica.
• It is divided into three sub-regions: Ranchi Plateau, Hazaribagh Plateau, and Pat Plateau.
• The terrain is characterized by rugged hills, valleys, and escarpments, making it a unique geographical region.
• Damodar Valley Corporation (DVC):
• DVC is a multipurpose river valley project established in 1948 for flood control, irrigation, and hydroelectric power generation.
• It manages the Damodar River basin and operates several dams, such as Tilaiya, Konar, Maithon, and Panchet.
• Barakar River:
• The Barakar River is the largest tributary of the Damodar River and originates in the Chotanagpur Plateau.
• It contributes significantly to the water flow in the Damodar River system.
• Flood Management:
• The Damodar River was infamous for annual floods, which devastated agricultural fields and settlements until the establishment of DVC.
• Modern flood management practices have reduced the severity and frequency of flooding in the region.

The correct answer is Amir Sarkosh.

Key Points

• Pankaj Advani, the Indian cue sports champion, defeated Amir Sarkosh in the final to win the 2025 Asian Snooker Championship.
• Amir Sarkosh is a professional snooker player from Iran, known for competing in various international tournaments.
• Pankaj Advani secured his title with a dominant performance, showcasing his exceptional skills and strategic gameplay.
• This victory marked Advani’s continued dominance in cue sports, adding yet another feather to his illustrious career.
• The Asian Snooker Championship is one of the most prestigious tournaments in the sport, attracting top players from across Asia.

Additional Information

• Pankaj Advani:
• He is an Indian professional billiards and snooker player who holds numerous world titles in cue sports.
• Advani is the only player to have won world titles in both formats—points and timed—in billiards as well as in snooker.
• He has won more than 20 world titles, making him one of the most decorated cue sports players globally.
• Asian Snooker Championship:
• The championship is organized by the Asian Confederation of Billiard Sports (ACBS).
• It serves as a platform for the best players from Asia to compete and showcase their talent.
• The event often includes formats like singles and team competitions.
• Snooker:
• Snooker is a cue sport played on a rectangular table covered with a green cloth called baize.
• The game involves using a cue stick to hit balls into pockets in a strategic sequence.
• It originated in India during the British colonial period and has grown to become a popular sport worldwide.
• Iran in Cue Sports:
• Iran has been emerging as a competitive nation in cue sports, with players like Amir Sarkosh representing the country internationally.
• The country has hosted several regional tournaments and contributes actively to the development of snooker in Asia.

The correct answer is Denmark.

Key Points

• Denmark ranked fourth in the Human Development Report 2025, recognized for its high standards in education, healthcare, and quality of life.
• The country consistently performs well in the Human Development Index (HDI), which measures key dimensions like life expectancy, education, and per capita income.
• Denmark is known for its progressive policies on social welfare, environmental sustainability, and gender equality, contributing to its high HDI ranking.
• The Danish government invests heavily in public services, ensuring universal access to healthcare and education, which boosts human development metrics.
• Strong economic stability, coupled with a focus on innovation and green energy, further enhances Denmark's human development indicators.

Additional Information

• Human Development Index (HDI):
• The HDI is a composite index created by the United Nations Development Programme (UNDP) to measure a country's social and economic development.
• It includes three dimensions: life expectancy, education (mean years of schooling and expected years of schooling), and GNI per capita.
• Factors Contributing to Denmark's Ranking:
• Denmark's universal healthcare system ensures equitable access to medical facilities for its citizens.
• The country invests heavily in renewable energy, reducing environmental risks and promoting sustainable development.
• Social welfare programs focus on addressing poverty and inequality, improving the overall quality of life.
• Scandinavian Countries' HDI Trend:
• Scandinavian countries like Denmark, Norway, and Sweden often rank high in HDI due to their advanced social policies.
• These nations prioritize education, healthcare, and environmental sustainability.
• Global HDI Rankings:
• Countries like Norway, Switzerland, and Denmark often top the HDI rankings due to their holistic approach toward development.
• Low-ranking countries typically face challenges related to poverty, conflict, and lack of infrastructure.

Shortcut Trick

When the Mode of a distribution is equal to the Upper Limit of a class interval, the frequency of that class (f₁) must be equal to the frequency of the succeeding class (f₂).

Given Mode = 165, which is the upper limit of the class 160−165.

Frequency of class (160−165) = 37.

Frequency of the next class (165−170) = x.

∴ x = 37.

∴ The correct answer is 37.

Alternate Method

Given:

Mode = 165

Since 165 lies at the boundary of 160−165 and 165−170, we identify the Modal Class as 160−165.

Lower limit (l) = 160

Frequency of modal class (f₁) = 37

Frequency of preceding class (f₀) = 26

Frequency of succeeding class (f₂) = x

Class width (h) = 5

Formula:

Mode = l + [(f₁ − f₀) ÷ (2f₁ − f₀ − f₂)] × h

Calculations:

⇒ 165 = 160 + [(37 − 26) ÷ (2 × 37 − 26 − x)] × 5

⇒ 165 − 160 = [11 ÷ (74 − 26 − x)] × 5

⇒ 5 = [11 ÷ (48 − x)] × 5

⇒ 1 = 11 ÷ (48 − x)

⇒ 48 − x = 11

⇒ x = 48 − 11

⇒ x = 37

∴ The correct answer is 37.

Additional Information

Empirical Relationship

The relationship between the three measures of central tendency is: Mode = 3 × Median − 2 × Mean.

Median of Grouped Data

Median = l + [((n ÷ 2) − cf) ÷ f] × h, where cf is the cumulative frequency of the class preceding the median class.

Mean of Grouped Data

Mean (μ) = Σ(f_i × x_i) ÷ Σf_i, where x_i is the class mark (mid-point) of each interval.

The logic followed here involves a sequence of operations:

Logic: First number to Second number: Multiply by 2.

Second number to Third number: Add 3.

Third number to Fourth number: Multiply by 2.

For, 6 - 12 - 15 - 30

⇒ 6 × 2 = 12 

⇒ 12 + 3 = 15 

⇒ 15 × 2 = 30 

Here, the logic followed.

For, 4 - 8 - 11 - 22

⇒ 4 × 2 = 8 

⇒ 8 + 3 = 11 

⇒ 11 × 2 = 22 

Here, the logic followed.

Option 1) 8 - 16 - 19 - 36

⇒ 8 × 2 = 16 (Matches First to Second)

⇒ 16 + 3 = 19 (Matches Second to Third)

⇒ 19 × 2 = 38 (Given Fourth number is 36, 36 ≠ 38)

Here, logic not followed.

Option 2) 12 - 14 - 28 - 30

⇒ 12 × 2 = 24 (Given Second number is 14, 14 ≠ 24)

Here, logic not followed.

Option 3) 1 - 2 - 4 - 16

⇒ 1 × 2 = 2 (Matches First to Second)

⇒ 2 + 3 = 5 (Given Third number is 4, 4 ≠ 5)

Here, logic not followed.

Option 4) 11 - 22 - 25 - 50

⇒ 11 × 2 = 22 (Matches First to Second)

⇒ 22 + 3 = 25 (Matches Second to Third)

⇒ 25 × 2 = 50 (Matches Third to Fourth)

Here, logic followed.

Hence, the correct answer is "Option 4".

Shortcut Trick

Total Work (LCM of 14, 10) = 70 units.

Efficiency: A = 5, B = 7. 2-day cycle (B + A) = 7 + 5 = 12 units.

5 cycles (10 days) = 12 × 5 = 60 units. Remaining = 70 − 60 = 10 units.

Day 11 (B's turn) = 7 units. Remaining = 10 − 7 = 3 units.

Day 12 (A's turn) takes 3 ÷ 5 = 3/5 day.

∴ The correct answer is 11 3/5 days.

Alternate Method

Given: Time taken by A = 14 days, Time taken by B = 10 days.

⇒ Total work = LCM(14, 10) = 70 units.

⇒ Efficiency of A = 70 ÷ 14 = 5 units/day.

⇒ Efficiency of B = 70 ÷ 10 = 7 units/day.

⇒ Work done in first 2 days (B then A) = 7 + 5 = 12 units.

⇒ In 10 days (5 cycles), work completed = 12 × 5 = 60 units.

⇒ Remaining work = 70 − 60 = 10 units.

⇒ On 11^th day, B works and completes 7 units. Remaining = 10 − 7 = 3 units.

⇒ On 12^th day, A works. Time taken = 3/5 days.

⇒ Total time = 10 + 1 + 3/5 = 11 3/5 days.

∴ The correct answer is 11 3/5 days.

Additional Information

Alternate Day Work

When individuals work alternately, calculate the combined work of one full cycle and multiply to get as close to the total work as possible without exceeding it.

Efficiency and Time

Efficiency is inversely proportional to time. Total Work = Efficiency × Time. Using LCM for total work simplifies fractional calculations.

Given interchange rules:

• ‘÷’ and ‘−’ are interchanged.
• ‘×’ and ‘+’ are interchanged.

The given equation is:

89 ÷ 4984 − 89 × 9 + 2 = ?

Replace the operators with their corresponding new meanings:

89 − 4984 ÷ 89 + 9 × 2 = ?

Now, we solve the equation following the BODMAS rule:

= 89 − 4984 ÷ 89 + 9 × 2

= 89 + 18 − 56

= 107 − 56

= 51

Hence, the correct answer is "Option 2".

Shortcut Trick

When Profit% = Loss% for two selling prices, the Cost Price (CP) is the average of those two prices.

CP = (6833 + 1447) ÷ 2 = 8280 ÷ 2 = 4140.

To make a 45% profit, required SP = CP × 1.45.

SP = 4140 × 145 ÷ 100 = 41.4 × 145 = 6003.

∴ The correct answer is ₹6,003.

Alternate Method

Given: SP₁ = ₹6,833, SP₂ = ₹1,447, Profit% = Loss%, Desired Profit% = 45%.

Formulas: CP = (SP₁ + SP₂) ÷ 2 (if Profit% = Loss%), SP = CP × (100 + P%) ÷ 100.

⇒ Let Cost Price be x.

⇒ Profit% = [(6833 − x) ÷ x] × 100 and Loss% = [(x − 1447) ÷ x] × 100.

⇒ 6833 − x = x − 1447 ⇒ 2x = 8280 ⇒ x = 4140.

⇒ New Selling Price = 4140 × (100 + 45) ÷ 100 = 4140 × 1.45.

⇒ New SP = 6003.

∴ The correct answer is ₹6,003.

Additional Information

Cost Price when Profit = Loss

When numerical profit equals numerical loss for two different selling prices, the CP is always the arithmetic mean of those prices: CP = (SP_high + SP_low) ÷ 2.

Calculating Profit Selling Price

To calculate a specific profit percentage P%, use the multiplier: SP = CP × (1 + P ÷ 100).

The correct answer is Reserve Bank of India.

Key Points

• On 4 April 2025, the Reserve Bank of India (RBI) launched a verified WhatsApp channel to provide financial updates to the public.
• This initiative aims to enhance communication and engagement with the general public using a widely used messaging platform.
• The RBI's verified WhatsApp channel will offer updates on policy changes, announcements, and financial literacy topics.
• Subscribers to this channel will receive real-time and authenticated information directly from the RBI.
• This move reflects the RBI's efforts to leverage digital platforms for transparency and accessibility in financial communication.

Additional Information

• Reserve Bank of India (RBI):
• Established on 1 April 1935, RBI is India's central banking institution.
• It regulates monetary policy and ensures financial stability in India.
• The RBI also oversees currency issuance, foreign exchange management, and banking operations.
• WhatsApp Channels:
• Introduced by WhatsApp, channels are a feature for broadcasting information to large audiences.
• Channels allow organizations to communicate with users in a controlled and verified manner.
• Digital Communication in Banking:
• Indian banks increasingly use social media and digital platforms for customer engagement.
• Such initiatives aim to improve financial literacy and accessibility for users.
• Financial Updates:
• Information shared through these channels includes policy changes, interest rates, schemes, and global financial trends.
• The goal is to ensure timely dissemination of information to the public.

Shortcut Trick

Let the HCF be x. The numbers are 1x, 15x, and 7x.

Ratio of numbers = 1 : 15 : 7. Since 1, 15, and 7 are co-prime (their LCM is their product).

LCM = 1 × 15 × 7 × x = 105x.

Given 105x = 4830 ⇒ x = 4830 ÷ 105 = 46.

∴ The correct answer is 46.

Alternate Method

Given: Ratio = 1 : 15 : 7, LCM = 4830.

Formula: LCM of numbers (ax, bx, cx) = x × LCM(a, b, c), where x is the HCF.

⇒ Let the numbers be x, 15x, and 7x.

⇒ LCM(x, 15x, 7x) = x × LCM(1, 15, 7)

⇒ LCM(1, 15, 7) = 1 × 3 × 5 × 7 = 105

⇒ 105x = 4830

⇒ x = 4830 ÷ 105

⇒ x = 46

∴ The correct answer is 46.

Additional Information

HCF and LCM Relation

For two numbers A and B, HCF × LCM = A × B. This property is only strictly applicable to two numbers.

Ratio and Multiples

If the ratio of n numbers is a : b : c and their HCF is x, then the numbers are ax, bx, and cx. Their LCM is x × LCM(a, b, c).

Co-prime Numbers

Numbers whose HCF is 1 are called co-prime. The LCM of co-prime numbers is simply their product.

Given:

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

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

Only three people sit between A and G when counted from the right of G.

C sits to the immediate right of A.

B is an immediate neighbour of G as well as H.

Thus, B sits to the second to the left of D.

Hence, the correct answer is "Option 4".

The correct answer is Electro-Magnetic Launch System (EMLS).

Key Points

• The Electro-Magnetic Launch System (EMLS) is a cutting-edge technology unveiled by the DRDO for the Indian Navy to enhance aircraft launch capabilities.
• EMLS employs electromagnetic force to launch aircraft from naval carriers, replacing conventional steam catapults.
• This technology provides greater efficiency, precision, and flexibility in launching heavier and advanced aircraft.
• EMLS is aligned with India's efforts to modernize naval aviation and boost indigenous defense capabilities under the "Atmanirbhar Bharat" initiative.
• It is a critical component for operating advanced fighters and unmanned aerial vehicles (UAVs) from aircraft carriers.

Additional Information

• Electromagnetic Aircraft Launch System (EMALS):
• EMALS, developed by the US Navy, is a similar system that uses electromagnetic energy to launch aircraft.
• It offers a smoother acceleration compared to steam catapults, reducing wear and tear on aircraft.
• Advantages of EMLS:
• Improved energy efficiency and reduced maintenance costs compared to steam-based systems.
• Capable of launching a wide range of aircraft, from lightweight UAVs to heavy fighter jets.
• Provides scalability and adaptability for future advanced aircraft designs.
• Indian Navy's Aircraft Carriers:
• India currently operates INS Vikramaditya and recently commissioned INS Vikrant, both of which will benefit from advanced launch systems like EMLS.
• Atmanirbhar Bharat in Defense:
• The DRDO's development of EMLS reflects India's commitment to self-reliance in defense technologies.
• It reduces dependency on foreign suppliers and strengthens the domestic defense manufacturing ecosystem.

The correct answer is Support of guard cells in stomatal function.

Key Points

• Subsidiary cells are specialized epidermal cells that are associated with guard cells and help in stomatal function.
• They play an indirect role in regulating the opening and closing of stomata by providing mechanical support to guard cells.
• Subsidiary cells contribute to maintaining the ion balance and turgor pressure required for guard cells to function effectively.
• These cells are part of the stomatal complex, which is crucial for gas exchange and transpiration in plants.
• The presence of subsidiary cells varies among plant species and is a characteristic feature used for plant identification.

Additional Information

• Stomata:
• Stomata are microscopic pores present on the surface of leaves and stems that facilitate gas exchange (CO2 intake and O2 release).
• They are surrounded by guard cells, which regulate their opening and closing based on environmental conditions.
• Guard Cells:
• Guard cells are specialized cells that control the size of the stomatal pore by changing their shape.
• They respond to factors like light, water availability, and internal CO2 concentration.
• Subsidiary Cells:
• Subsidiary cells are part of the epidermis and surround guard cells, forming the stomatal complex.
• They vary in shape, size, and arrangement depending on the plant species.
• Function of Stomatal Complex:
• Facilitates transpiration and cooling of the plant.
• Plays a key role in photosynthesis by enabling CO2 uptake.
• Helps maintain the plant's water balance by regulating water loss.

The correct answer is Kunal Kemmu.

Key Points

• Kunal Kemmu won the Best Directorial Debut award for his movie 'Madgaon Express' at the IIFA Awards 2025.
• The movie 'Madgaon Express' marked Kunal Kemmu's debut as a director, showcasing his storytelling and cinematic skills.
• 'Madgaon Express' received widespread appreciation for its unique narrative and engaging storyline, contributing to Kunal Kemmu's success at IIFA.
• The IIFA Awards are among the most prestigious awards in the Indian film industry, recognizing outstanding contributions and talent.
• Kunal Kemmu's transition from being a successful actor to a director was highly celebrated, with 'Madgaon Express' being considered a remarkable first effort.

Additional Information

• IIFA Awards:
• The International Indian Film Academy Awards (IIFA) were established in 2000 to celebrate excellence in the Indian film industry.
• IIFA events are held at various international locations to promote Indian cinema globally.
• The awards recognize achievements in categories such as acting, directing, music, and technical excellence.
• Directorial Debut:
• A directorial debut refers to the first movie or project directed by an individual, marking their entry into the field of direction.
• It is often a significant milestone in a filmmaker's career, showcasing their creative vision and storytelling abilities.
• Kunal Kemmu:
• Kunal Kemmu is a well-known actor in the Indian film industry, recognized for his performances in movies such as 'Go Goa Gone' and 'Kalank.'
• His directorial debut with 'Madgaon Express' highlighted his versatility as a storyteller.
• 'Madgaon Express':
• The movie is set against the backdrop of a train journey, weaving a compelling narrative that resonated with audiences.
• It gained attention for its innovative storytelling and strong performances by the cast.

The logic followed in this pattern is a consistent alphabetical shift for each letter position: +1, +2, +3.

For 'JKL' related to 'KMO':

For 'PQR' related to 'QSU':

The consistent pattern observed is: +1, +2, +3.

Applying the same logic to 'XYZ':

Thus, 'XYZ' is related to YAC.

Hence, the correct answer is "Option 3".

The correct answer is Complete combustion of fuel.

Key Points

• The blue flame of a gas stove indicates complete combustion of fuel, which occurs when the fuel burns efficiently with a sufficient oxygen supply.
• Complete combustion results in the production of carbon dioxide (CO₂) and water vapor (H₂O), without releasing harmful gases like carbon monoxide (CO).
• A blue flame is a sign of optimal energy efficiency, as the fuel is fully utilized without wastage.
• Incomplete combustion, on the other hand, produces a yellow or orange flame and may release pollutants like carbon monoxide (CO).
• Blue flames are common when burning fuels like natural gas, propane, or butane, which are hydrocarbons.

Additional Information

• Complete Combustion: A chemical process where a fuel reacts with oxygen to produce carbon dioxide, water, and energy. It requires a sufficient oxygen supply.
• Incomplete Combustion: Occurs when there is insufficient oxygen, leading to the production of harmful by-products such as carbon monoxide and soot.
• Hydrocarbons: Organic compounds consisting of hydrogen and carbon atoms. Common fuels like natural gas and propane are hydrocarbons.
• Carbon Monoxide (CO): A toxic gas produced during incomplete combustion. It is colorless, odorless, and can pose serious health risks.
• Energy Efficiency: Blue flames are an indicator of efficient energy usage, as the fuel is completely burned without wasting resources.

The correct answer is Meerut.

Key Points

• The Revolt of 1857 began on 10^th May 1857 in Meerut, located in present-day Uttar Pradesh, India.
• The immediate cause was the resentment among sepoys over the use of greased cartridges, which were rumored to be coated with cow and pig fat, offending both Hindu and Muslim religious sentiments.
• The sepoys of the East India Company stationed in Meerut refused to use the cartridges, leading to their court-martial, which ignited the rebellion.
• After revolting, the sepoys marched to Delhi and declared Bahadur Shah II, the last Mughal emperor, as their symbolic leader to unite Indians against British rule.
• The uprising in Meerut marked the beginning of the larger struggle, which spread to various parts of India such as Kanpur, Lucknow, and Jhansi.

Additional Information

• Causes of the Revolt:
• Political Causes: Policies like the Doctrine of Lapse and Subsidiary Alliance alienated Indian rulers.
• Economic Causes: Exploitative land revenue systems and destruction of traditional industries hurt Indian peasants and artisans.
• Social and Religious Causes: Reforms like the abolition of Sati and the introduction of the Widow Remarriage Act created distrust among conservative Indians.
• Key Leaders of the Revolt:
• Rani Lakshmibai in Jhansi, Tantia Tope in Kanpur, and Begum Hazrat Mahal in Lucknow played significant roles in leading the rebellion.
• Outcome of the Revolt:
• The revolt was eventually suppressed by the British, and the East India Company was abolished in 1858.
• India came under the direct control of the British Crown, marking the beginning of the British Raj.
• Historical Significance:
• The Revolt of 1857 is often regarded as India's First War of Independence, despite its failure.
• It sowed the seeds for future resistance movements against British colonial rule.

The correct answer is Competition Commission.

Key Points

• Since December 2022, the functions of the National Anti-Profiteering Authority (NAA), set up in connection with GST reforms, have been transferred to the Competition Commission of India (CCI).
• The Competition Commission of India (CCI) is responsible for ensuring fair competition and preventing anti-competitive practices in the market.
• The decision to transfer NAA's functions to CCI was made to streamline operations and leverage CCI's expertise in handling anti-profiteering cases.
• The CCI's role includes investigating complaints related to unfair pricing and profiteering under GST regulations and ensuring compliance with legal norms.
• This shift aligns with the government's aim to create a unified regulatory framework for anti-profiteering and competition issues.

Additional Information

• National Anti-Profiteering Authority (NAA):
• NAA was established under GST reforms to ensure that the benefits of tax rate reductions or input tax credits were passed on to consumers.
• Its primary function was to address complaints regarding profiteering and unfair pricing practices by businesses under GST.
• It investigated cases where businesses failed to transfer GST benefits to end consumers.
• Competition Commission of India (CCI):
• CCI was established under the Competition Act, 2002, to prevent practices that have an adverse effect on competition.
• It ensures fair competition in the market, protects consumer interests, and promotes economic efficiency.
• CCI handles cases related to anti-competitive agreements, abuse of dominant positions, and combinations (e.g., mergers and acquisitions).
• GST (Goods and Services Tax):
• GST is a unified indirect tax introduced in India on July 1, 2017, replacing multiple indirect taxes such as VAT, service tax, and excise duty.
• It is categorized into CGST, SGST, and IGST, depending on the transaction's nature.
• GST aims to simplify the tax structure, promote ease of doing business, and prevent cascading effects of taxation.
• Anti-Profiteering Measures:
• These measures are designed to ensure that businesses pass the benefits of tax rate reductions or input tax credits to consumers.
• They focus on preventing unfair pricing practices and maintaining transparency in consumer transactions.
• Such measures play a vital role in building consumer trust and ensuring compliance with GST provisions.

The logic followed here is:

NK : RO : VX

LI : PM : TV

Option 1: IG-NL-RU

This option does NOT follow the pattern. 

Option 2: IG-NK-RU

This option does NOT follow the pattern.

Option 3: JG-NK-RT

This option follows the pattern.

Option 4: JG-NK-RU

This option does NOT follow the pattern. 

Hence, the correct answer is "Option 3".

Shortcut Trick

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

Here, the side adjacent to 30° (base) corresponds to √3 units and the side opposite to 30° (height) corresponds to 1 unit.

√3 units = 30 m

1 unit = 30 ÷ √3 = (10 × 3) ÷ √3 = 10√3 m.

∴ The correct answer is 10√3 m.

Alternate Method

Given: Distance from tower (Base) = 30 m, Angle of elevation (θ) = 30°.

Formula Used: tan θ = Perpendicular (Height) ÷ Base

⇒ tan 30° = Height ÷ 30

⇒ 1/√3 = Height ÷ 30

⇒ Height = 30 ÷ √3

⇒ Height = (30 × √3) ÷ (√3 × √3)

⇒ Height = 30√3 ÷ 3 = 10√3 m

∴ The correct answer is 10√3 m.

Additional Information

Trigonometric Ratios

Standard values for tan are tan 30° = 1/√3, tan 45° = 1, and tan 60° = √3.

Angle of Elevation vs Depression

The angle of elevation is the angle between the horizontal line and the line of sight when looking up. The angle of depression is the same angle when looking down from the top.

The correct answer is Indo-Gangetic Plains.

Key Points

• The Indo-Gangetic Plains are one of the most fertile agricultural regions in India, supporting the rice-wheat cropping system.
• This cropping system is practiced in states like Punjab, Haryana, Uttar Pradesh, and Bihar due to favorable climate and soil conditions.
• Rice is grown during the Kharif season (monsoon) as it requires a significant amount of water, while wheat is cultivated in the Rabi season (winter).
• The alluvial soil of the Indo-Gangetic Plains, coupled with abundant water resources from rivers like the Ganga and its tributaries, makes the region ideal for this cropping system.
• This system contributes significantly to India's food security, with the region being called the "Granary of India."

Additional Information

• Kharif Crops:
• These are crops grown during the monsoon season (June to October) and include rice, maize, and millets.
• Rice is the most prominent Kharif crop in the Indo-Gangetic Plains due to the high water availability during this period.
• Rabi Crops:
• These are crops grown in the winter season (November to April), such as wheat, barley, and mustard.
• Wheat cultivation in the Rabi season complements rice, forming the rice-wheat cropping pattern in the Indo-Gangetic Plains.
• Alluvial Soil:
• The Indo-Gangetic Plains are rich in alluvial soil, brought by rivers like the Ganga, Yamuna, and their tributaries.
• This soil is highly fertile and suitable for growing a wide variety of crops, including rice and wheat.
• Food Security in India:
• The rice-wheat cropping system in the Indo-Gangetic Plains contributes significantly to India's food grain production.
• This region plays a critical role in ensuring food security for the country, feeding millions of people.
• Green Revolution:
• The Indo-Gangetic Plains were a major beneficiary of the Green Revolution in the 1960s-70s, which introduced high-yield variety seeds and improved irrigation methods.
• This led to a significant increase in the productivity of rice and wheat in the region.

The correct answer is Mauritius.

Key Points

• PM Narendra Modi visited Mauritius in March 2025 to attend its 57^th National Day celebrations.
• The visit symbolized India’s commitment to maintaining strong diplomatic and cultural ties with Mauritius, a country with a significant Indian diaspora.
• Mauritius celebrates its National Day every year on March 12^th, commemorating its independence from Britain in 1968 and becoming a republic in 1992.
• India and Mauritius share close bilateral relations, including cooperation in areas such as trade, investment, health, education, and defense.
• During the visit, PM Modi emphasized India's support for Mauritius in its development projects, including the Metro Express and the Supreme Court building, funded through Indian grants.

Additional Information

• India-Mauritius Bilateral Relations:
• India is Mauritius’ largest trading partner and has been a significant source of Foreign Direct Investment (FDI) for the country.
• The Comprehensive Economic Cooperation and Partnership Agreement (CECPA) was signed between the two nations to enhance trade and investment.
• Mauritius is considered a key strategic partner in the Indian Ocean region.
• Indian Diaspora in Mauritius:
• Mauritius has a large Indian-origin population, making up approximately 68% of its total population.
• The Indian community in Mauritius has preserved its cultural heritage, including festivals, language, and traditions.
• Metro Express Project:
• India provided financial assistance for the Metro Express Project, aimed at improving public transport infrastructure in Mauritius.
• The project strengthens urban connectivity and fosters economic growth in the region.
• Defense Cooperation:
• India has supported Mauritius in enhancing its maritime security by supplying patrol vessels and providing training to its naval personnel.
• This cooperation aligns with India's vision of ensuring peace and stability in the Indian Ocean region.

The logic followed here is:

Option (1): AWRP

Option (2): JFAY

Option (3): HDVW

Option (4): RNIG

The letter-cluster that DOES NOT belong to the group is: HDVW

Hence, the correct answer is "Option (3)"

The correct answer is Gram Sabha.

Key Points

• The Gram Sabha is the cornerstone of the Panchayati Raj system as established by the 73^rd Constitutional Amendment Act, 1992.
• It consists of all the registered voters of a village or a group of villages within the jurisdiction of a Panchayat.
• Gram Sabha ensures direct participation of the community in decision-making, empowering local governance.
• Key functions of the Gram Sabha include approving village development plans, monitoring the implementation of projects, and ensuring transparency in Panchayat operations.
• It serves as the ultimate authority in the Panchayati Raj system, promoting democratic decentralization at the grassroots level.

Additional Information

• 73^rd Constitutional Amendment Act, 1992:
• This Act provided constitutional status to Panchayati Raj institutions, ensuring decentralized governance.
• It mandates the establishment of Gram Sabha in each village or group of villages.
• Three-tier structure of Panchayati Raj: Gram Panchayat (village level), Panchayat Samiti (block level), and Zila Parishad (district level).
• Nyaya Panchayat:
• Nyaya Panchayats are judicial bodies functioning to resolve minor disputes at the village level.
• They are distinct from Gram Panchayats and focus solely on justice delivery.
• Zila Parishad:
• Zila Parishad operates at the district level, coordinating activities between block-level Panchayats.
• It formulates development plans and oversees their implementation across the district.
• Gram Panchayat:
• Gram Panchayats are executive bodies at the village level responsible for implementing developmental schemes.
• They work under the supervision of the Gram Sabha.

The correct answer is Task View.

Key Points

• Task View is a feature in Windows 11 that allows users to manage and switch between multiple open windows and virtual desktops.
• It is accessible via the Task View button on the taskbar, represented by an icon showing two overlapping squares.
• Users can create and manage virtual desktops for better organization, separating workspaces for different tasks or projects.
• Task View displays a clear thumbnail preview of all open windows, making multitasking more efficient.
• This feature was first introduced in Windows 10 and has been refined further in Windows 11 for enhanced usability.

Additional Information

• Virtual Desktop:
• It is a feature that allows users to create multiple desktops, each with its own set of open applications and windows.
• Useful for separating tasks such as work, gaming, or entertainment.
• In Windows 11, desktops can be customized with different wallpapers for better distinction.
• Snap Layouts:
• Windows 11 introduced Snap Layouts, a feature that allows users to organize open windows into predefined layouts for multitasking.
• Snap Assist helps users quickly fill remaining space in the layout with other open applications.
• Taskbar Improvements:
• The taskbar in Windows 11 has been redesigned for better accessibility and functionality.
• Features like pinned apps, notification center, and quick settings are integrated into the taskbar.
• Alt+Tab Shortcut:
• A keyboard shortcut used to quickly switch between open windows.
• In Windows 11, Alt+Tab includes a preview of open tabs from Microsoft Edge.

Shortcut Trick

Sum of exterior angles of any regular polygon is always 360°.

Sum of interior angles = 100% more than 360° = 2 × 360° = 720°.

Using the formula (n − 2) × 180° = 720° ⇒ n − 2 = 4 ⇒ n = 6.

The polygon is a regular hexagon.

Each interior angle x = 720° ÷ 6 = 120°.

∴ The correct answer is 120.

Alternate Method

Given: Sum of interior angles = Sum of exterior angles + 100% of Sum of exterior angles.

Formula Used: Sum of interior angles = (n − 2) × 180°; Sum of exterior angles = 360°.

⇒ Sum of exterior angles = 360°

⇒ Sum of interior angles = 360° + (100/100) × 360° = 720°

⇒ (n − 2) × 180° = 720°

⇒ n − 2 = 720 ÷ 180

⇒ n − 2 = 4

⇒ n = 6 (The polygon is a regular hexagon)

⇒ Each interior angle x = 720° ÷ 6 = 120°

∴ The correct answer is 120.

Additional Information

Sum of Interior Angles

The sum of the interior angles of a polygon with n sides is given by (n − 2)

Given series:

(Left) 8 * * € 6 % 3 2 $ # 9 9 9 2 @ # 5 3 % 9 @ 1 (Right)

Condition to be checked:

Number → Number → Symbol

8 * * € 6 % 3 2 $ # 9 2 @ # 5 3 % 9 @ 1

There are three such numbers in the above arrangement (3 2 $, 9 2 @, 5 3 %).

Hence, the correct answer is "Option 3"$.

The given code language is:

Thus, 'V' is coded as '6'.

Hence, the correct answer is "Option 4".

Given:

A, B, C, D, E, F and G are sitting around a circular table facing the centre.

D sits third to the right of C. C sits to the immediate left of F. 

A sits second to the right of B.

B is not an immediate neighbour of C.

G sits to the immediate right of F.

Thus, 3 people sit between G and E when counted from the left of G.

Hence, the correct answer is "Option 3".

The correct answer is Option 4 (6 religious communities).

Key Points

• The Citizenship Amendment Act (CAA) 2019 covers 6 religious communities: Hindus, Sikhs, Buddhists, Jains, Parsis, and Christians.
• The act aims to provide Indian citizenship to persecuted religious minorities from Pakistan, Bangladesh, and Afghanistan who entered India on or before 31 December 2014.
• It applies to individuals who faced religious persecution in these countries and were forced to migrate to India.
• The CAA excludes Muslims from its purview, as it focuses on non-Muslim minorities.
• The law does not alter the existing process of acquiring citizenship for others but facilitates faster citizenship for persecuted minorities.

Additional Information

• Definition of Citizenship: Citizenship refers to the legal status granted to an individual by a country, entitling them to certain rights and responsibilities.
• Religious Persecution: It refers to systematic mistreatment or oppression based on religious beliefs, often forcing affected individuals to flee their country.
• Countries Covered: The CAA specifically applies to refugees from Pakistan, Bangladesh, and Afghanistan, which are predominantly Muslim-majority nations.
• Criticism of CAA: Critics argue that the act violates the secular fabric of the Indian Constitution by excluding Muslims and raises concerns about discrimination.
• NRC Connection: The CAA has been linked to the proposed National Register of Citizens (NRC), which aims to identify illegal immigrants. However, the relationship between the two remains a contentious issue.

The correct answer is Capital punishment.

Key Points

• Capital punishment, also known as the death sentence, when passed by a Sessions Judge, requires mandatory confirmation by the High Court as per Section 366(1) of the Code of Criminal Procedure (CrPC).
• The Sessions Judge cannot execute the death sentence unless it is confirmed by the High Court, ensuring a higher level of judicial scrutiny.
• This procedural safeguard is implemented to ensure that the decision to impose capital punishment undergoes rigorous evaluation to prevent miscarriage of justice.
• Capital punishment is considered the most severe form of punishment and is reserved for rarest of rare cases such as heinous crimes.
• The High Court reviews the legality, validity, and appropriateness of the death sentence passed by the Sessions Court before issuing confirmation.

Additional Information

• Code of Criminal Procedure (CrPC):
• The CrPC is the main legislation governing criminal procedures in India.
• Under Section 366(1), it mandates High Court confirmation for death sentences imposed by Sessions Judges.
• Rare Cases Doctrine:
• Capital punishment in India is awarded only in the "rarest of rare cases" as established by the Supreme Court in the landmark case of Bachan Singh v. State of Punjab (1980).
• This doctrine ensures that death sentences are given only for exceptionally heinous crimes with sufficient justification.
• Judicial Safeguards:
• Mandatory High Court confirmation acts as a safeguard against errors or biases in lower court decisions.
• It ensures that the decision undergoes detailed scrutiny by experienced judges.
• Execution Process:
• Once the High Court confirms the death sentence, the convict has the right to appeal to the Supreme Court.
• Additionally, the convict can file a mercy petition to the President of India under Article 72 of the Constitution or to the Governor under Article 161.