The correct answer is Copy and Paste.

Key Points

• Copy and Paste is a widely used command in MS Word and other text editing software to duplicate text and place it in another location within the document or across documents.
• Users can select the text, right-click to copy, and then paste it at the desired location using the right-click menu or shortcut keys (Ctrl+C and Ctrl+V).
• This command allows users to retain the original text while creating a duplicate copy, ensuring no data is lost.
• Copy and Paste is applicable to not just text but also images, tables, and other elements in MS Word.
• It simplifies repetitive tasks and enhances productivity by eliminating the need for retyping or recreating content.

Additional Information

• Cut vs. Copy:
• The Cut command (Ctrl+X) removes the selected text or object from its original location and allows it to be pasted elsewhere.
• Copy (Ctrl+C), on the other hand, creates a duplicate while leaving the original content intact.
• Drag and Drop Functionality:
• Users can drag selected text or objects and drop them into a new location within the same document.
• This method is quick but lacks the precision of Copy and Paste for cross-document transfers.
• Paste Special:
• Paste Special allows users to control the formatting of copied content when pasting.
• For example, users can paste as plain text, formatted text, or in other specified formats.
• Shortcut Keys in MS Word:
• Common shortcuts include Ctrl+C (Copy), Ctrl+V (Paste), Ctrl+X (Cut), and Ctrl+Z (Undo).
• These shortcuts are designed to enhance user efficiency and streamline text manipulation tasks.
• Clipboard Functionality:
• The Clipboard temporarily stores copied or cut items, allowing users to paste them multiple times.
• In MS Word, the Clipboard can hold multiple items, offering extended flexibility for editing tasks.

The correct answer is 836.

Key Points

• The Andaman and Nicobar Islands are a group of islands located in the Bay of Bengal, consisting of a total of 836 islands/islets/rocky outcrops as per the Andaman and Nicobar Administration.
• The archipelago is divided into two groups: the Andaman Islands (north) and the Nicobar Islands (south).
• These islands are known for their rich biodiversity, unique flora and fauna, and strategic importance for India's maritime boundaries.
• Of the 836 islands, only a fraction are inhabited, while the majority remain pristine and untouched.
• These islands form a vital ecological hotspot and are protected under various environmental laws and conservation programs.

Additional Information

• Geographical Significance
• The Andaman and Nicobar Islands lie at the juncture of the Bay of Bengal and the Andaman Sea, making them strategically important for India's defense and trade.
• They act as a natural barrier to the Indian coastline, protecting it from potential threats and offering a vantage point for maritime surveillance.
• Biodiversity
• The islands are part of the Indo-Malayan eco-zone, hosting a variety of endemic species, including rare birds, reptiles, and marine life.
• The tropical rainforests here support diverse ecosystems, with mangroves playing a key role in stabilizing coastal environments.
• Tribes of the Islands
• The islands are home to indigenous tribes such as the Great Andamanese, Onge, Jarwa, and Sentinelese.
• These tribes have distinct cultural practices and lifestyles, and efforts are made to preserve their heritage and isolation.
• Tourism and Conservation
• The islands are a popular tourist destination, known for their beaches, coral reefs, and adventure activities like scuba diving.
• Significant areas are designated as protected zones, such as the Mahatma Gandhi Marine National Park, to conserve the delicate ecosystems.

The correct answer is 48^th Amendment Act.

Key Points

• The 48^th Amendment Act of 1984 did not amend any provisions related to the Directive Principles of State Policy (DPSP).
• This amendment was enacted to extend the President's Rule in the state of Punjab beyond the one-year limit prescribed under Article 356(5) of the Indian Constitution.
• It dealt specifically with the political situation in Punjab and had no relevance to the Directive Principles of State Policy.
• In contrast, amendments like the 42^nd Amendment Act and 86^th Amendment Act directly addressed and modified provisions of the DPSP.
• The 42^nd Amendment Act, for instance, added new principles, while the 86^th Amendment Act integrated the right to education for children under Article 21A, influencing related DPSPs.

Additional Information

• Directive Principles of State Policy (DPSP):
• Enshrined in Part IV (Articles 36-51) of the Indian Constitution, DPSPs aim to establish a welfare state by guiding the government in policy-making.
• They are non-justiciable, meaning they cannot be enforced in a court of law, but they are fundamental in governance.
• Examples include provisions for social welfare, equitable distribution of resources, and environmental conservation.
• 42^nd Amendment Act (1976):
• Known as the "Mini-Constitution," it made significant changes to the DPSP.
• Added Articles 39A (Equal justice and free legal aid), 43A (Workers' participation in management), and 48A (Protection of the environment).
• Shifted the focus towards socialism and environmental sustainability.
• 86^th Amendment Act (2002):
• Introduced Article 21A, making the right to education a fundamental right for children aged 6 to 14 years.
• Modified Article 45 under DPSP to focus on early childhood care for children below six years.
• 97^th Amendment Act (2011):
• Added a new DPSP under Article 43B, emphasizing the promotion of cooperative societies.
• Aimed to strengthen cooperative movements in India by ensuring their democratic functioning.

The correct answer is Plateau regions.

Key Points

• Plateau regions in India, such as the Deccan Plateau, are characterized by hard rock formations and non-alluvial soil, making them unsuitable for tube-well irrigation.
• Tube-well irrigation requires soft, porous, and permeable alluvial soil to facilitate water extraction, which is not present in plateau regions.
• These regions often lack sufficient groundwater recharge due to rocky terrain and limited aquifer systems.
• In contrast, regions like Punjab, Western Uttar Pradesh, and Coastal Plains have fertile alluvial soil and abundant groundwater, making them ideal for tube-well irrigation.
• Farmers in plateau regions primarily depend on rainfall or surface water sources such as tanks, reservoirs, and rivers for irrigation.

Additional Information

• Alluvial Soil and Irrigation:
• Alluvial soil is formed by river deposits and is rich in nutrients, making it fertile and ideal for agriculture.
• Its porous structure allows easy water percolation, which facilitates the use of tube-well irrigation.
• Groundwater and Aquifers:
• Groundwater is stored in aquifers, which are layers of permeable rock or sediment that can hold and transmit water.
• Plateau regions typically have fractured or impermeable rocks that hinder groundwater storage and extraction.
• Deccan Plateau Characteristics:
• It is composed of igneous and metamorphic rocks, which are hard and non-porous.
• These features limit the region’s ability to support groundwater-based irrigation systems like tube-wells.
• Alternative Irrigation in Plateau Regions:
• Farmers rely on surface irrigation methods such as canals, tanks, and rainwater harvesting to meet their agricultural water needs.
• Government initiatives promote micro-irrigation techniques like drip and sprinkler systems to optimize water use in these areas.
• Indian Irrigation Practices:
• Approximately 48% of India’s net sown area relies on irrigation, with tube-wells being a major source in alluvial regions.
• Regions unsuitable for tube-well irrigation often implement watershed development projects to improve water availability.

Shortcut Trick

Apply the Inverse Proportion rule: M₁ × T₁ = M₂ × T₂

Here, 23 pipes × 29 minutes = 47 pipes × Time

Time = (23 × 29) ÷ 47 = 667 ÷ 47

Time ≈ 14.19 minutes

∴ The correct answer is 14.19 minutes.

Alternate Method

Given:

Initial number of pipes (M₁) = 23

Initial time (T₁) = 29 minutes

Final number of pipes (M₂) = 47

Formula Used:

Total Work = Number of Pipes × Time taken

Calculations:

⇒ Total capacity of tank = 23 × 29 units

⇒ Total capacity = 667 units

⇒ Time taken by 47 pipes = Total capacity ÷ Number of pipes

⇒ Time = 667 ÷ 47

⇒ Time = 14.19148...

⇒ Time ≈ 14.19 minutes (rounded off to two decimal places)

∴ The correct answer is 14.19 minutes.

Additional Information

Inverse Variation

In Pipes and Cisterns, the number of pipes is inversely proportional to the time taken to fill the tank (if all pipes have the same efficiency).

Chain Rule Formula

The general formula is M₁D₁H₁/W₁ = M₂D₂H₂/W₂, where M is efficiency/pipes, D is days/minutes, and W is work/capacity.

The correct answer is Myanmar.

Key Points

• Arunachal Pradesh is located in the northeastern region of India, sharing its eastern border with Myanmar.
• The border between Arunachal Pradesh and Myanmar is demarcated by the India-Myanmar International Boundary.
• The border region is characterized by dense forests and mountainous terrain, making it strategically and geographically significant.
• Arunachal Pradesh also shares international borders with China to the north and Bhutan to the west, but Myanmar lies directly to its east.
• This area includes tribal communities and is part of the larger Indo-Burma biodiversity hotspot.

Additional Information

• Bordering States and Countries:
• Arunachal Pradesh shares its borders with three countries: China, Bhutan, and Myanmar.
• It also shares state borders with Assam and Nagaland within India.
• McMahon Line:
• The McMahon Line is the de facto boundary between India and China in Arunachal Pradesh.
• This line is a source of territorial disputes between India and China.
• Tribal Diversity:
• Arunachal Pradesh is home to numerous indigenous tribes, including the Adi, Nyishi, Apatani, and Mishmi tribes.
• These tribes have unique cultures, traditions, and languages.
• Strategic Importance:
• Arunachal Pradesh holds strategic importance for India due to its location at the tri-junction of India, China, and Myanmar.
• It is critical for India’s border security and regional connectivity initiatives.

The correct answer is Centre on Integrated Rural Development for Asia and Pacific (CIRDAP).

Key Points

• The Ministry of Rural Development in India collaborates with the Centre on Integrated Rural Development for Asia and the Pacific (CIRDAP) to advance rural development initiatives in the Asia-Pacific region.
• CIRDAP was established in 1979 at the initiative of the Food and Agriculture Organization (FAO) of the United Nations to promote integrated rural development.
• The organization has its headquarters in Dhaka, Bangladesh, and works with member countries to strengthen rural development policies and practices.
• India is a founding member of CIRDAP and actively contributes to its programs focusing on poverty alleviation, sustainable agriculture, and rural infrastructure development.
• CIRDAP functions as a platform for knowledge-sharing, capacity-building, and technical cooperation among its 15 member countries, including India, Bangladesh, Sri Lanka, and others.

Additional Information

• CIRDAP Member Countries
• CIRDAP has 15 member countries, which include Afghanistan, Bangladesh, Bhutan, India, Indonesia, Iran, Laos, Malaysia, Myanmar, Nepal, Pakistan, the Philippines, Sri Lanka, Thailand, and Vietnam.
• These countries collaborate on rural development strategies and share best practices to improve living conditions in rural areas.
• Integrated Rural Development
• Integrated rural development involves a holistic approach to improving economic, social, and environmental conditions in rural areas.
• It focuses on sectors such as agriculture, education, health, infrastructure, and community participation to ensure sustainable development.
• Role of FAO
• The Food and Agriculture Organization (FAO) of the United Nations was instrumental in the establishment of CIRDAP, emphasizing its commitment to eradicating hunger and promoting rural development globally.
• FAO continues to provide technical support and guidance to CIRDAP and its member countries.
• India and CIRDAP
• India’s Ministry of Rural Development plays a pivotal role in supporting CIRDAP by offering expertise, resources, and research inputs.
• India often hosts training programs, workshops, and conferences under the aegis of CIRDAP to foster regional cooperation in rural development.

Shortcut Trick

Assume initial distance is 44 km (LCM of 11 and 44).

Total Distance = 44 (forward 1) + 88 (forward 2) + 132 (return) = 264 km.

Total Time = Total Distance ÷ Average Speed = 264 ÷ 34 = 132/17 hours.

Forward Time = (44/11) + (88/44) = 4 + 2 = 6 hours.

Return Speed = 132 ÷ (132/17 − 6) = 132 ÷ (30/17) = 132 × 17 ÷ 30 = 74.8 km/hr.

∴ The correct answer is 74.8 km/hr.

Alternate Method

Given: Forward speed 1 = 11 km/hr, Forward speed 2 = 44 km/hr, Avg Speed = 34 km/hr.

Formula Used: Average Speed = Total Distance ÷ Total Time

⇒ Let first distance be D. Second distance = 2D. Total return distance = 3D.

⇒ Total Distance = D + 2D + 3D = 6D.

⇒ Total Time = (D/11) + (2D/44) + (3D/V) = (4D+2D)/44 + 3D/V = 6D/44 + 3D/V = 3D/22 + 3D/V.

⇒ 34 = 6D ÷ (3D/22 + 3D/V) = 6D ÷ [3D(1/22 + 1/V)]

⇒ 34 = 2 ÷ ( (V + 22) / 22V )

⇒ 34 = 44V ÷ (V + 22)

⇒ 34(V + 22) = 44V ⇒ 34V + 748 = 44V

⇒ 10V = 748 ⇒ V = 74.8 km/hr.

∴ The correct answer is 74.8 km/hr.

Additional Information

Average Speed Formula

For different distances d₁, d₂, d₃... with speeds s₁, s₂, s₃..., Average Speed = (Σd) ÷ (Σd/s).

Special Case: Equal Distances

When two equal distances are covered at speeds a and b, the average speed is (2ab) ÷ (a + b).

Unit Conversion

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

The logic followed here is:

(33, 429, 13) → 33 × 13 = 429

And,

(44, 220, 5) → 44 × 5 = 220

So, checking each option one by one:

Option 1) (20, 363, 18) → 20 × 18 = 360 ≠ 363

Option 2) (4, 23, 5) → 4 × 5 = 20 ≠ 23

Option 3) (43, 903, 21) → 43 × 21 = 903

Option 4) (30, 363, 12) → 30 × 12 = 360 ≠ 363

Hence, "Option 3" is the correct answer.

The logic followed here is:

Option 1) CG - LP

Option 2) QS - OQ

​

Option 3) SU - QS

Option 4) MO - KM

Thus, out of all 'CG - LP' is the odd one out.

Hence, "Option 1" is the correct answer.

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

1. Only one person sits between P and V when counted from the right of P.

2) Only one person sits between V and U.

3) Only one person sits between P and Q. 

4) Only two people sit between R and U. 

5) Only one person sits between T and Q. 

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

Thus, five sit between S and P when counted from the left of S.

Hence, "Option 4" is the correct answer.

Given Table:

According to the given condition:

Given: 7 6 @ 1 3 &

Here, no rule applies here.

7 → coded as W 

6 → coded as K

@ → coded as Z 

1 → coded as R

3 → coded as T

& → coded as N

So, 7 6 @ 1 3 & → Coded as W K Z R T N

Hence, "Option 4" is the correct answer.

Shortcut Trick

Savings = 40% ⇒ Expenditure = 100% − 40% = 60%

60% units = ₹960

1% unit = 960 ÷ 60 = 16

100% units (Income) = 16 × 100 = ₹1600

∴ The correct answer is ₹1600.

Alternate Method

Given:

Savings percentage = 40%

Expenditure = ₹960

Formula Used:

Income = Expenditure + Savings

Calculations:

⇒ Let the total income be ₹x.

⇒ Savings = 40% of x

⇒ Expenditure = Income − Savings

⇒ Expenditure = 100% − 40% = 60% of x

⇒ 60/100 × x = 960

⇒ 0.6x = 960

⇒ x = 960 ÷ 0.6

⇒ x = 1600

∴ The correct answer is ₹1600.

Additional Information

Percentage Change

To calculate percentage change, use the formula: (Change ÷ Original Value) × 100.

Income Components

In most aptitude problems, Income is always considered as the sum of Expenditure and Savings (I = E + S).

Base Value

Income is generally treated as the base (100%) when calculating percentage savings or percentage expenditure.

Given: 

Kapil starts from point A and drives 9 km towards west.

He then takes a right turn, drives 1 km, turns right and drives 5 km.

He then takes a left turn and drives 3 km.

He then takes a left turn and drive 5 km.

He then takes a right turn and drives 8 km.

He takes a final right turn, drives 9 km and stops at point P. 

Thus, Kapil should drive 12 km (1 km + 3 km + 8 km) in the south direction in order to reach point A again.

Hence, "Option 4" is the correct answer.

Shortcut Trick

Assume the total quantity is 3 units. 1 unit is sold at 10% loss (−10%).

To get a 20% gain on the whole transaction (3 units), total profit needed = 3 × 20% = 60%.

Remaining units = 3 − 1 = 2 units.

Profit needed from remaining units = Total Profit − Profit/Loss already made = 60% − (−10%) = 70%.

Gain percentage on remainder = 70% ÷ 2 = 35%.

∴ The correct answer is 35%.

Alternate Method

Given: Total CP = ₹450 | Loss on 1/3^rd part = 10% | Overall Gain = 20%. Formulas: Profit = SP − CP | SP = CP × (100 + P%) ÷ 100 | SP = CP × (100 − L%) ÷ 100.

⇒ Total SP required = 450 × (120 ÷ 100) = ₹540. ⇒ CP of 1/3^rd goods = 450 × (1 ÷ 3) = ₹150. ⇒ SP of 1/3^rd goods at 10% loss = 150 × (90 ÷ 100) = ₹135. ⇒ Remaining SP needed = 540 − 135 = ₹405. ⇒ CP of remaining 2/3^rd goods = 450 − 150 = ₹300. ⇒ Profit required on remaining = 405 − 300 = ₹105. ⇒ Profit % on remaining = (105 ÷ 300) × 100 = 35%. ∴ The correct answer is 35%.

Additional Information

Weighted Average Method

For parts of goods, Overall % = (n₁ × p₁ + n₂ × p₂) ÷ (n₁ + n₂), where p is profit/loss %.

Profit and Loss on Parts

When the total CP is given but the question asks for a percentage, the actual CP value does not affect the final percentage result.

The logic followed here is:

Given: # : QVR :: CHD : %

Option 1) # = LJM, % = NHG → LJM : QVR :: CHD : NHG

Option 2) # = GYT, % = NYU → GYT : QVR :: CHD : NYU

​

Option 3) # = PMM, % = JUY → PMM : QVR :: CHD : JUY

Option 4) # = LQM, % = HMI → LQM : QVR :: CHD : HMI

Hence, "Option 4" is the correct answer.

The correct answer is Margins.

Key Points

• The Margins feature in MS Word allows users to set the blank space between the text and the edges of the page.
• Margins can be adjusted by navigating to Layout > Margins, where predefined options like Normal, Narrow, Wide, and custom settings are available.
• Changing the margins affects the document layout, helping users manage text density and page appearance efficiently.
• Proper margin settings are crucial for ensuring readability, consistency, and adherence to document formatting standards, such as those required for academic or professional submissions.
• MS Word allows users to set margins individually for each side of the page: top, bottom, left, and right.

Additional Information

• Page Layout Tab in MS Word:
• The Page Layout tab includes essential formatting options like Margins, Orientation, Size, Columns, and Page Borders.
• It enables users to customize the overall appearance and structure of the document.
• Other Margin Types:
• MS Word allows for the creation of gutter margins, which provide extra space for binding documents.
• Mirror margins are used for documents intended for double-sided printing, ensuring symmetry between facing pages.
• Document Orientation:
• Orientation options (Portrait and Landscape) can complement margin settings to optimize document appearance.
• Portrait orientation is vertical, while Landscape orientation is horizontal.
• Page Borders vs. Margins:
• While margins define blank space around text, Page Borders add decorative or functional lines around the page’s edges.
• Page Borders are customizable under the Design tab in MS Word.
• Importance of Margins:
• Proper margins improve visual appeal and help maintain a professional appearance in documents.
• They are crucial for printing, ensuring text does not get cut off or overlap binding areas.

The correct answer is Sayyid Dynasty.

Key Points

• The Sayyid Dynasty ruled the Delhi Sultanate from 1414 to 1451 CE and was established after the decline of the Tughlaq Dynasty.
• Yahya bin Ahmad Sirhindi, in his famous work Tarikh-i-Mubarak Shahi, claimed that the founder of the Sayyid Dynasty, Khizr Khan, was a descendant of the Prophet Muhammad.
• Khizr Khan was appointed as the governor of Multan by Timur (Tamerlane) and later established his rule in Delhi in 1414 CE.
• The dynasty is called "Sayyid" due to the belief that its rulers were Sayyids, descendants of the Prophet Muhammad, which is a title signifying high religious and social status in Islamic tradition.
• After Khizr Khan, his successors, including Mubarak Shah, Muhammad Shah, and Ala-ud-Din Alam Shah, ruled until the dynasty was overthrown by the Lodi Dynasty in 1451 CE.

Additional Information

• Delhi Sultanate
• The Delhi Sultanate refers to a series of Muslim dynasties that ruled over large parts of India from 1206 to 1526 CE.
• The Sultanate saw five main dynasties: Slave (Mamluk), Khilji, Tughlaq, Sayyid, and Lodi dynasties.
• The Sayyid Dynasty was the fourth dynasty of the Delhi Sultanate.
• Khizr Khan
• Khizr Khan was the founder of the Sayyid Dynasty and ruled from 1414 to 1421 CE.
• He did not assume the title of Sultan and continued to acknowledge the suzerainty of Timur's successors in Central Asia.
• He focused on consolidating power in Delhi and surrounding areas rather than expanding the empire.
• Significance of Sayyid Title
• The title "Sayyid" denotes a person who claims direct lineage to the Prophet Muhammad through his grandsons Hasan and Husayn.
• This lineage is considered sacred in Islamic culture and conveys religious and social prestige.
• Decline of the Sayyid Dynasty
• The Sayyid Dynasty faced continuous challenges, including revolts and weakened central authority.
• The last ruler, Ala-ud-Din Alam Shah, voluntarily abdicated the throne in favor of Bahlul Lodi in 1451 CE, marking the end of the dynasty.

Given: 36 ÷ 15 − 175 × 5 + 11 = ?

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

36 ÷ 15 − 175 × 5 + 11 = ? ⇒ 36 × 15 + 175 ÷ 5 − 11 = ?

⇒ 36 × 15 + 175 ÷ 5 − 11 = ?

⇒ 36 × 15 + 35 − 11 = ?

⇒ 540 + 35 − 11 = ?

⇒ 575 − 11 = ?

⇒ 564 = ?

Hence, "Option 4" is the correct answer.

The correct answer is Pulse Polio First Dose.

Key Points

• National Vaccination Day is observed in India on 16^th March every year.
• It was initiated to commemorate the first-ever administration of the Oral Polio Vaccine (OPV) in India on 16 March 1995.
• The Pulse Polio Immunization (PPI) program was launched in 1995 with the aim of eradicating polio in India by vaccinating all children under the age of five.
• The program became one of the most successful vaccination initiatives, leading to India being declared polio-free by the World Health Organization (WHO) in 2014.
• This milestone is remembered annually to raise awareness about the importance of vaccination in preventing diseases.

Additional Information

• Pulse Polio Immunization Program
• Launched in 1995 under the Global Polio Eradication Initiative (GPEI).
• It involved administering two drops of the Oral Polio Vaccine (OPV) to children under five, irrespective of their previous vaccination status.
• The program focused on high-risk areas and rapid response to polio outbreaks.
• It played a crucial role in achieving a polio-free status for India, certified by WHO in 2014.
• Global Polio Eradication Initiative (GPEI)
• A public-private partnership launched in 1988 with the goal of eradicating polio worldwide.
• Key partners include WHO, UNICEF, Rotary International, CDC, and the Bill & Melinda Gates Foundation.
• Since its launch, the number of polio cases globally has decreased by over 99%.
• Importance of Vaccination
• Vaccination is one of the most effective ways to prevent infectious diseases.
• It helps develop immunity by mimicking an infection without causing illness.
• Mass vaccination campaigns like Pulse Polio have saved millions of lives worldwide.
• Eradication of Polio in India
• India reported its last polio case in January 2011 in West Bengal.
• On 27 March 2014, WHO certified the Southeast Asia Region, including India, as polio-free.
• India's success was attributed to strong government commitment, community participation, and support from global health organizations.

According to the given information,

Thus, 'are' is coded as 'zl'.

Hence, "Option 3" is the correct answer.

The logic followed here is:

Given: # : QYE :: BHP : %

Option 1) # = GEU, % = RNF → GEU : QYE :: BHP : RNF

Option 2) # = WKK, % = LBZ → WKK : QYE :: BHP : LBZ

​

Option 3) # = LBZ, % = GEU → LBZ : QYE :: BHP : GEU

Option 4) # = RNF, % = WKK → RNF : QYE :: BHP : WKK

Hence, "Option 3" is the correct answer.

The logic followed here is:

​​​

Hence, "Option 2" is the correct answer.

The logic followed here is:

Given: 

KF-MH-OQ

And,

ID-KF-MO

Similarly,

Option 1) GB-ID-KM

​

​

Hence, "Option 1" is the correct answer.

The correct answer is Fixed-wing UAVs and Swarm drones.

Key Points

• The Defence Research and Development Organisation (DRDO) successfully demonstrated the Directed Energy Weapon (DEW) Mk-II(A) during trials in 2025.
• The DEW Mk-II(A) effectively neutralized Fixed-wing Unmanned Aerial Vehicles (UAVs) and Swarm drones, showcasing its operational capabilities against advanced aerial threats.
• The system employs laser-based technology to disable or destroy aerial targets by disrupting their onboard electronics or structure.
• These trials highlighted India’s advancements in non-kinetic warfare technologies, positioning DRDO among the global leaders in Directed Energy Weapons development.
• The DEW Mk-II(A) was specifically designed to counter emerging threats from drones, which are increasingly being used in military and surveillance applications.

Additional Information

• Directed Energy Weapons (DEWs):
• DEWs are a class of weapons that emit energy in a focused direction to damage or disable targets.
• Common types of DEWs include laser weapons, microwave weapons, and particle beam weapons.
• They offer advantages such as precision targeting, minimal collateral damage, and low operational costs once deployed.
• Fixed-wing UAVs:
• Fixed-wing UAVs are unmanned aerial systems that use wings like traditional airplanes for flight.
• They are commonly used for surveillance, reconnaissance, and delivery applications due to their long flight range and efficiency.
• Swarm Drones:
• Swarm drones refer to a coordinated group of drones that operate together to achieve a common objective.
• These are often used for military operations, search-and-rescue missions, and surveillance.
• Swarm drones leverage artificial intelligence and communication systems to coordinate their movements.
• India’s DEW Program:
• India has been developing Directed Energy Weapons under DRDO’s Advanced Weapons and Technology program.
• These systems are part of the country’s effort to counter modern threats like drones, missiles, and other aerial platforms.
• Global DEW Development:
• Countries such as the USA, China, and Russia are actively developing DEWs for military applications.
• These weapons are considered critical for next-generation warfare due to their ability to neutralize high-speed and agile threats.

Shortcut Trick To find the roots of 5m2 + 18m + 16 = 0, identify two numbers with product (5 × 16) = 80 and sum = 18. The numbers are 10 and 8. Shortcut: Divide these numbers by the coefficient of m2 (5) and reverse their signs. Roots = −(10/5) and −(8/5) ⇒ −2 and −8/5. ∴ The correct answer is −8/5 and −2.

Alternate Method Given: The quadratic equation is 5m2 + 18m + 16 = 0. Formula: We use the factorisation method by splitting the middle term. ⇒ 5m2 + 10m + 8m + 16 = 0 ⇒ 5m(m + 2) + 8(m + 2) = 0 ⇒ (5m + 8)(m + 2) = 0 Setting each factor to zero: ⇒ 5m + 8 = 0 ⇒ m = −8/5 ⇒ m + 2 = 0 ⇒ m = −2 The roots of the equation are −8/5 and −2. ∴ The correct answer is −8/5 and −2.

Additional Information Discriminant and Nature of Roots For ax2 + bx + c = 0, the discriminant D = b2 − 4ac determines the nature of roots. If D > 0, roots are real and distinct; if D = 0, roots are real and equal. Sum and Product of Roots The Sum of roots (α + β) = −b/a and the Product of roots (αβ) = c/a. Quadratic Formula Roots can also be found using x = [−b ± √(b2 − 4ac)] / 2a.

Shortcut Trick

Ratio of Shan's share (S) to Piyush's share (P) is given by (1 + R/100)^Δt : 1.

Here, difference in time (Δt) = 20 − 19 = 1 year and Rate (R) = 8%.

Ratio S : P = (1 + 8/100)¹ : 1 ⇒ 108 : 100 ⇒ 27 : 25.

Total units = 27 + 25 = 52 units → ₹1,612.

1 unit = 1612 ÷ 52 = ₹31.

Shan's share = 27 × 31 = ₹837.

∴ The correct answer is ₹837.

Alternate Method

Given:

Total Principal = ₹1,612 | Rate (R) = 8% p.a.

Time for Shan (n₁) = 19 years | Time for Piyush (n₂) = 20 years.

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Let the amount given to Shan be S and to Piyush be P.

⇒ S(1 + 8/100)¹⁹ = P(1 + 8/100)²⁰

⇒ S = P(1 + 8/100)²⁰⁻¹⁹

⇒ S = P(108/100)

⇒ S/P = 27/25

⇒ S = [27 / (27 + 25)] × 1612

⇒ S = (27 / 52) × 1612

⇒ S = 27 × 31

⇒ S = ₹837

∴ The correct answer is ₹837.

Additional Information

Compound Interest Ratio Rule

When a sum is divided such that amounts are equal after T₁ and T₂ years, the ratio of shares is (1 + R/100)^T₂−T₁ : 1.

Effective Rate for CI

For a rate R% for 2 years, the effective rate is R + R + (R×R)/100 %.

Successive Percentage Change

Compound interest is essentially a successive percentage increase on the principal amount every year.

Given:

Simplify: 81 + (76)/(2) + 42 - 86

Formula used:

Basic arithmetic operations

Calculation:

⇒ 81 + (76)/(2) + 42 - 86

⇒ 81 + 38 + 42 - 86

⇒ 81 + 38 - 44

⇒ 75

∴ The correct answer is option (4).

The correct answer is Union Government.

Key Points

• The Union Government is responsible for deciding citizenship in newly added territories to India as per the provisions of the Constitution and relevant laws.
• Article 11 of the Indian Constitution empowers Parliament to regulate the right of citizenship by law.
• The Citizenship Act of 1955, enacted by the Union Government, lays out the legal framework for acquiring, renouncing, and determining citizenship in India.
• In cases where new territories are added to India, the Union Government decides citizenship based on the provisions outlined in the Citizenship Act.
• International agreements or treaties governing territorial addition may also influence citizenship decisions, which are implemented by the Union Government.

Additional Information

• Article 5-11 of the Indian Constitution:
• These articles govern citizenship provisions in India.
• Article 11 explicitly empowers Parliament to make laws regulating citizenship.
• The Citizenship Act, 1955:
• It is the primary law governing citizenship in India.
• It includes provisions for citizenship by birth, descent, registration, naturalization, and incorporation of territory.
• Incorporation of Territory:
• When a new territory is added to India, its residents may be granted Indian citizenship based on legal provisions.
• The Union Government decides the criteria and implementation process for granting citizenship.
• International Treaties and Agreements:
• Territorial additions often occur due to international agreements or treaties.
• The Union Government ensures compliance with these agreements while determining citizenship for affected residents.
• Judicial Oversight:
• In case of disputes or challenges, the Supreme Court of India may interpret constitutional provisions related to citizenship.
• However, the primary authority remains with the Union Government.

Shortcut Trick

Use the relationship: (100 + Profit%) ÷ (100 − Discount%) = MP ÷ CP.

Given Profit = 71% and Discount = 10%.

MP ÷ CP = (100 + 71) ÷ (100 − 10) = 171 ÷ 90 = 19 ÷ 10.

Marked up value = 19 − 10 = 9 units on a base of 10.

Markup percentage X = (9 ÷ 10) × 100 = 90%.

∴ The correct answer is 90.

Alternate Method

Given → Discount = 10%, Profit = 71%, Markup = X%. Formulas: SP = CP × (100 + Profit%) ÷ 100 | SP = MP × (100 − Discount%) ÷ 100.

⇒ Let Cost Price (CP) be 100. ⇒ Since gain is 71%, Selling Price (SP) = 100 + 71 = 171. ⇒ Discount is 10%, so SP = 90% of Marked Price (MP). ⇒ 171 = 0.90 × MP ⇒ MP = 171 ÷ 0.9 = 190. ⇒ Markup (X) = MP − CP = 190 − 100 = 90. ⇒ Since CP was 100, the markup percentage X = 90%.

∴ The correct answer is 90.

Additional Information

Markup and Discount Relation

The effective percentage change can be calculated using the formula: Net % = a + b + (ab ÷ 100), where 'a' is markup % and 'b' is discount % (negative).

Marked Price (MP)

MP is the price printed on the label. Discount is always calculated on MP, while Profit/Loss is calculated on CP.

The logic followed here is:

Given: 

BAIL - ALIB - LIAB

And,

DEAF - EFAD - FAED

Similarly,

Option 3) BOLD - ODLB - DLOB

​

​​

Hence, "Option 3" is the correct answer.

Shortcut Trick

Given: X ∝ A² and A ∝ 1/Y.

Combining these, X ∝ (1/Y)² ⇒ X ∝ 1/Y².

Relationship: X₁ × Y₁² = X₂ × Y₂².

97 × 6² = X₂ × 2² ⇒ 97 × 36 = X₂ × 4.

X₂ = 97 × 9 = 873.

∴ The correct answer is 873.

Alternate Method

Given: X₁ = 97, Y₁ = 6, Y₂ = 2.

Formula Used: X = k/Y² or X₁Y₁² = X₂Y₂²

⇒ X ∝ A² and A ∝ 1/Y ⇒ A² ∝ 1/Y²

⇒ Therefore, X ∝ 1/Y²

⇒ 97 = k / 6²

⇒ k = 97 × 36

⇒ X₂ = k / 2²

⇒ X₂ = (97 × 36) ÷ 4

⇒ X₂ = 97 × 9 = 873

∴ The correct answer is 873.

Additional Information

Direct Proportionality

If y ∝ x, then y = kx. The ratio y/x remains constant for all pairs of variables.

Inverse Proportionality

If y ∝ 1/x, then xy = k. The product of the two variables remains constant.

Joint Variation

When a variable depends on two or more other variables, such as z ∝ xy, leading to z = kxy.

The correct answer is Bihar.

Key Points

• 'Tirabhukti' is an ancient term mentioned in Gupta inscriptions referring to a region in present-day Bihar.
• The term is derived from Sanskrit, where 'Tira' means bank and 'Bhukti' means enjoyment or territory, signifying a region associated with riverbanks.
• This region was strategically important during the Gupta Empire due to its fertile plains and proximity to the Ganges River.
• Historical records suggest that 'Tirabhukti' was part of the administrative structure of the Gupta dynasty, which divided its empire into several provinces or 'Bhuktis.'
• Prominent cities in the region during the Gupta period include Pataliputra (modern-day Patna) and Vaishali.

Additional Information

• Gupta Empire:
• The Gupta Empire (circa 320-550 CE) is considered a golden age of Indian culture, art, science, and literature.
• It was marked by significant advancements in mathematics, astronomy, and medicine.
• The administrative divisions of the empire included provinces called 'Bhuktis,' which were further subdivided into districts called 'Vishayas.'
• Pataliputra:
• Located in modern-day Patna, Pataliputra was a major political and cultural center during the Gupta period.
• It served as the capital of several ancient Indian dynasties, including the Mauryas and the Guptas.
• Vaishali:
• An ancient city in Bihar, Vaishali was significant during the Gupta period and earlier.
• It is known for its connection to Buddhism and Jainism, with Lord Mahavira spending much of his life there.
• Gupta Inscriptions:
• These inscriptions provide critical insights into the administrative, social, and economic structure of the Gupta Empire.
• They are primarily written in Sanskrit and often carved on stone and metal surfaces.

The correct answer is Niger.

Key Points

• Niger became the first African country to be acknowledged by the World Health Organization (WHO) for successfully eliminating onchocerciasis (river blindness) in early 2025.
• The WHO recognition came after Niger conducted extensive public health campaigns aimed at eradicating the disease, which is caused by the parasitic worm Onchocerca volvulus.
• The elimination was achieved through sustained mass drug administration (MDA) programs using ivermectin, a drug that targets the parasite and interrupts its transmission cycle.
• This achievement highlights Niger's commitment to combating neglected tropical diseases (NTDs) and improving public health infrastructure.
• Onchocerciasis primarily affects communities living near fast-flowing rivers in sub-Saharan Africa, leading to severe itching, skin lesions, and in extreme cases, blindness.

Additional Information

• Onchocerciasis (River Blindness):
• It is a neglected tropical disease caused by the parasite Onchocerca volvulus, which is transmitted to humans through the bites of infected blackflies (genus Simulium).
• Symptoms include severe itching, skin changes, and visual impairment that can lead to permanent blindness.
• The disease predominantly affects rural communities in Africa but also occurs in some regions of Latin America and Yemen.
• Ivermectin:
• Ivermectin is an antiparasitic medication that has been instrumental in controlling and eradicating onchocerciasis.
• It works by killing the microfilariae (larval stage of the parasite), thereby reducing transmission and disease progression.
• WHO's mass drug administration programs distribute ivermectin free of cost in endemic regions.
• Neglected Tropical Diseases (NTDs):
• NTDs are a group of diseases that disproportionately affect impoverished populations in tropical and subtropical regions.
• Examples include onchocerciasis, lymphatic filariasis, leprosy, and schistosomiasis.
• Global initiatives such as WHO’s NTD Roadmap aim to eliminate or control these diseases by 2030.
• Global Health Impact:
• Eliminating onchocerciasis in Niger sets a precedent for other African nations to strengthen their disease elimination efforts.
• It aligns with the Sustainable Development Goals (SDGs), particularly SDG 3, which focuses on ensuring healthy lives and promoting well-being for all.

The correct answer is Denmark.

Key Points

• Denmark has been consistently leading global climate change rankings due to its strong policies and commitment to achieving carbon neutrality by 2050.
• The country excels in renewable energy use, particularly wind energy, which contributes significantly to its electricity generation.
• Denmark’s ambitious climate policies include the Climate Act, which legally binds the country to reduce greenhouse gas emissions by 70% by 2030 (compared to 1990 levels).
• Its high ranking in the Climate Change Performance Index 2025 is attributed to its proactive measures in renewable energy, energy efficiency, and international cooperation on climate issues.
• The Climate Change Performance Index evaluates countries based on greenhouse gas emissions, renewable energy, energy use, and climate policy, with Denmark scoring high across all categories.

Additional Information

• Climate Change Performance Index (CCPI):
• The CCPI is an independent monitoring tool used to track the climate protection performance of 60 countries and the European Union.
• The index is jointly published by Germanwatch, the NewClimate Institute, and the Climate Action Network (CAN).
• It evaluates countries based on four key categories: greenhouse gas emissions (40%), renewable energy (20%), energy use (20%), and climate policy (20%).
• The CCPI aims to enhance transparency in international climate politics and encourage countries to adopt stronger climate measures.
• Denmark's Renewable Energy Leadership:
• Denmark is a global leader in wind energy, with wind turbines accounting for over 40% of its electricity production.
• The country has invested heavily in offshore wind farms and plans to build artificial energy islands to harness more renewable energy.
• Denmark’s energy transition is supported by governmental policies and public-private partnerships in the green energy sector.
• Paris Agreement:
• An international treaty adopted in 2015 to combat climate change by limiting global warming to well below 2°C above pre-industrial levels, aiming for 1.5°C.
• Countries are required to submit nationally determined contributions (NDCs) outlining their climate action plans.
• Denmark’s commitment to the Paris Agreement is reflected in its ambitious national targets and initiatives to reduce emissions.
• Carbon Neutrality:
• Carbon neutrality, also known as net-zero emissions, refers to achieving a balance between emitted and absorbed greenhouse gases.
• Denmark aims to become carbon neutral by 2050, with interim targets like the 70% reduction in emissions by 2030.
• The country is adopting technologies such as carbon capture and storage (CCS) and increasing its reliance on renewable energy to meet these goals.

The correct answer is Kolkata-Lucknow Industrial Corridor.

Key Points

• The Kolkata-Lucknow Industrial Corridor is not an officially planned industrial corridor under the Government of India’s infrastructure initiatives.
• Key industrial corridors currently planned include the Delhi-Mumbai Industrial Corridor (DMIC), Chennai-Bengaluru Industrial Corridor (CBIC), and Vizag-Chennai Industrial Corridor (VCIC).
• The industrial corridors aim to enhance economic growth, create jobs, and strengthen infrastructure by connecting key cities and manufacturing hubs.
• The DMIC project is one of the largest infrastructure initiatives, spanning six states and focusing on high-tech industrial zones.
• Other planned corridors include the Amritsar-Kolkata Industrial Corridor (AKIC) and the Bengaluru-Mumbai Industrial Corridor (BMIC), which are integral to India's economic strategy.

Additional Information

• Delhi-Mumbai Industrial Corridor (DMIC)
• A flagship project aimed at developing an industrial zone across six states in India.
• It spans approximately 1,500 km between Delhi and Mumbai, focusing on manufacturing and logistics.
• DMIC is expected to boost GDP growth and generate millions of jobs.
• Vizag-Chennai Industrial Corridor (VCIC)
• Part of the East Coast Economic Corridor (ECEC), connecting Andhra Pradesh and Tamil Nadu.
• It aims to enhance manufacturing competitiveness and create economic opportunities along the eastern coastline.
• Chennai-Bengaluru Industrial Corridor (CBIC)
• Links Chennai and Bengaluru to facilitate industrial development, particularly in the automotive and electronics sectors.
• Focuses on creating high-quality infrastructure and promoting investments.
• Industrial Corridor Concept
• Industrial corridors are regions planned for economic development through industrialization and infrastructure connectivity.
• They aim to attract foreign direct investment (FDI) and promote domestic manufacturing under initiatives like "Make in India."

Given: Kavish ranked 38^th from the top and 15^th from the bottom in his class.

Kavish's rank from the top = 38^th

Kavish's rank from the bottom = 15^th

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

= 38 + 15 - 1 → 52^nd

Hence, "Option 4" is the correct answer.

Shortcut Trick

Volume of Cone = (1/3) × π × r² × h

160π = (1/3) × π × r² × 30

160 = 10 × r² ⇒ r² = 16 ⇒ r = 4 cm

Diameter = 2 × r = 2 × 4 = 8 cm

∴ The correct answer is 8 cm.

Alternate Method

Given:

Height (h) of the cone = 30 cm

Volume (V) of the cone = 160π cm³

Formula Used:

Volume of a right circular cone = (1/3)πr²h

Calculations:

⇒ 160π = (1/3) × π × r² × 30

⇒ 160 = 10 × r²

⇒ r² = 160 / 10

⇒ r² = 16

⇒ r = √16 = 4 cm

⇒ Diameter (d) = 2 × radius (r)

⇒ d = 2 × 4 = 8 cm

∴ The correct answer is 8 cm.

Additional Information

Slant Height of Cone

The slant height (l) is given by the relation l = √(r² + h²).

Curved Surface Area (CSA)

The CSA of a right circular cone is given by the formula π × r × l.

Total Surface Area (TSA)

The TSA of a cone includes the base area: TSA = πrl + πr² = πr(l + r).

Shortcut Trick

Ratio of Covered Distance to Remaining Distance = 7 : 9.

Total distance ratio = 7 + 9 = 16 units → 54 km.

Covered distance = (7 ÷ 16) × 54 = 23.625 km.

Time = 1 hour 15 minutes = 1.25 hours.

Speed = 23.625 ÷ 1.25 = 18.9 km/hr.

∴ The correct answer is 18.9 km/hr.

Alternate Method

Given: Total distance = 54 km, Time = 1 hour 15 minutes.

Formula Used: Speed = Distance ÷ Time

⇒ Let Remaining Distance be 'x' km.

⇒ Distance Covered = (7/9) × x

⇒ Total Distance = x + (7x/9) = 16x/9

⇒ 16x/9 = 54

⇒ x = (54 × 9) ÷ 16 = 30.375 km (Remaining)

⇒ Distance Covered = 54 − 30.375 = 23.625 km

⇒ Time = 1 + (15/60) = 1.25 hours

⇒ Speed = 23.625 ÷ 1.25 = 18.9 km/hr

∴ The correct answer is 18.9 km/hr.

Additional Information

Time Conversion

To convert minutes to hours, divide by 60. For example, 15 minutes = 15/60 = 0.25 hours.

Ratio Application

If a part is a fraction (a/b) of the remaining, the total is represented by (a + b) units.

Average Speed

Average Speed = Total Distance Covered ÷ Total Time Taken.

The correct answer is Giddha.

Key Points

• Giddha is a traditional folk dance performed by women in Punjab, India.
• It is considered the female counterpart of Bhangra, which is primarily performed by men.
• Giddha is characterized by vibrant costumes, rhythmic clapping, and lively singing of folk songs known as boliyan.
• The dance portrays various themes such as social issues, daily life, and playful teasing, making it a celebration of Punjabi culture.
• Giddha does not rely on instrumental music; instead, participants sing while clapping to maintain rhythm.

Additional Information

• Bhangra:
• Bhangra is a folk dance originating from Punjab, performed by men to celebrate harvest festivals.
• It involves vigorous movements, including jumps and spins, accompanied by the sound of dhol drums.
• Bhangra has gained popularity worldwide and is frequently performed at cultural events.
• Boliyan:
• Boliyan are short, traditional Punjabi folk songs sung during dances like Giddha and Bhangra.
• They often convey emotions, humor, and themes of daily life or social issues.
• Costumes in Giddha:
• Women wear colorful Punjabi suits, adorned with heavy jewelry and accessories.
• The attire reflects the rich cultural heritage of Punjab.
• Regional Folk Dances of India:
• Ghoomar: A traditional dance from Rajasthan performed by women in circular movements.
• Kalbelia: A folk dance of the Kalbelia community in Rajasthan, known for its serpent-like movements.
• Garba: A Gujarati folk dance performed during Navratri celebrations.

Shortcut Trick

Put θ = 45° directly into the expression.

⇒ 3 + tan² 45° + cot² 45° − sec² 45° cosec² 45°

⇒ 3 + 1² + 1² − (√2)² × (√2)²

⇒ 3 + 1 + 1 − 2 × 2 = 5 − 4 = 1

∴ The correct answer is 1.

Alternate Method

Given:

Expression: 3 + tan² θ + cot² θ − sec² θ cosec² θ

Formula Used:

1 + tan² θ = sec² θ

1 + cot² θ = cosec² θ

sec² θ cosec² θ = sec² θ + cosec² θ

Calculations:

⇒ 3 + tan² θ + cot² θ − sec² θ cosec² θ

We can rewrite 3 as 1 + 1 + 1:

⇒ 1 + (1 + tan² θ) + (1 + cot² θ) − sec² θ cosec² θ

⇒ 1 + sec² θ + cosec² θ − sec² θ cosec² θ

Since sec² θ cosec² θ = sec² θ + cosec² θ:

⇒ 1 + (sec² θ + cosec² θ) − (sec² θ + cosec² θ)

⇒ 1

∴ The correct answer is 1.

Additional Information

Trigonometric Identities

The three fundamental Pythagorean identities are sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

Product to Sum Identity

The identity sec² θ cosec² θ = sec² θ + cosec² θ is extremely useful for simplifying complex trigonometric algebraic expressions.

Shortcut Trick

For any two similar triangles, the ratio of their areas is always equal to the square of the ratio of their corresponding sides.

Given the ratio of corresponding sides = 15 : 14

∴ Ratio of their areas = 15² : 14² = 225 : 196

∴ The correct answer is 225 : 196.

Alternate Method

Given:

The ratio of the lengths of two corresponding sides of two similar triangles = 15 : 14

Formula Used:

According to the Area of Similar Triangles Theorem, if two triangles are similar, then the ratio of the areas of both triangles is proportional to the square of the ratio of their corresponding sides:

Area₁ ÷ Area₂ = (Side₁ ÷ Side₂)²

Calculations:

Let the two similar triangles be Triangle 1 and Triangle 2.

Let the corresponding sides of the two triangles be s₁ and s₂ respectively.

⇒ s₁ : s₂ = 15 : 14

Let the areas of the two triangles be A₁ and A₂ respectively.

Using the theorem of similar triangles:

⇒ A₁ ÷ A₂ = (s₁ ÷ s₂)²

⇒ A₁ ÷ A₂ = (15 ÷ 14)²

⇒ A₁ ÷ A₂ = 15² ÷ 14²

⇒ A₁ ÷ A₂ = 225 ÷ 196

⇒ A₁ : A₂ = 225 : 196

Option Analysis:

Option (1) 226 : 197 is incorrect because it does not represent the squares of 15 and 14.

Option (2) 15 : 14 is incorrect because it represents the ratio of the sides, not the ratio of the areas.

Option (3) 225 : 196 is correct because it is the exact ratio of the squares of the corresponding sides (15² : 14²).

Option (4) 15√15 : 14 is incorrect because it does not follow the square relation of similar triangles.

∴ The correct answer is 225 : 196.

Additional Information

Ratio of Perimeters of Similar Triangles

The ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides (s₁ : s₂).

Ratio of Altitudes and Medians

The ratio of corresponding altitudes, medians, and angle bisectors of two similar triangles is also equal to the ratio of their corresponding sides.

Area of Similar Triangles Theorem

If ΔABC ≈ ΔPQR, then Area(ΔABC) ÷ Area(ΔPQR) = (AB ÷ PQ)² = (BC ÷ QR)² = (AC ÷ PR)².

The correct answer is Devlali, Maharashtra.

Key Points

• The joint military exercise "Agni Warrior 2024" was conducted between India and Singapore in November 2024.
• The exercise was held at the Devlali Field Firing Ranges in Maharashtra, India.
• Agni Warrior is a bilateral artillery exercise aimed at enhancing interoperability and sharing expertise between the two nations’ armed forces.
• The exercise involves training on advanced artillery systems, simulation exercises, and live firing drills.
• It is part of the ongoing defense cooperation and long-standing strategic partnership between India and Singapore.

Additional Information

• Devlali Field Firing Ranges
• Located in Maharashtra, India, Devlali is one of the oldest military centers in India, established by the British in 1861.
• It is a key location for artillery training and testing due to its expansive area and infrastructure.
• India-Singapore Defense Relations
• India and Singapore have a strong defense partnership, with regular joint exercises in all three domains: army, navy, and air force.
• Key exercises include SIMBEX (navy), Bold Kurukshetra (army), and Joint Staff Talks.
• Artillery Modernization in India
• India has been modernizing its artillery systems with platforms like the K9 Vajra, M777 Howitzer, and Dhanush.
• These advancements aim to enhance India’s long-range precision strike capabilities.
• Significance of Joint Military Exercises
• Joint exercises like Agni Warrior improve mutual trust and understanding between countries.
• They also enhance operational readiness and technical expertise in handling modern weapon systems.

The correct answer is 1.2044 × 1024.

Key Points

• The number of molecules in a substance is calculated using Avogadro's number (6.022 × 10²³ molecules/mol).
• In this question, we are given 2 moles of CO₂.
• To find the number of molecules, multiply the number of moles by Avogadro's number: 2 × 6.022 × 10²³ = 12.044 × 10²³ = 1.2044 × 10²⁴ molecules.
• Hence, 12.044 × 10²³ molecules are present in 2 moles of CO₂.
• This calculation is based on the fundamental concept of mole and Avogadro's constant.

Additional Information

• Avogadro's Number:
• Avogadro's number (6.022 × 10²³) represents the number of particles (atoms, molecules, or ions) in one mole of a substance.
• It is a fundamental constant in chemistry.
• Mole Concept:
• A mole is a unit in chemistry used to express amounts of a chemical substance.
• One mole of any substance contains exactly 6.022 × 10²³ particles.
• Carbon Dioxide (CO₂):
• It is a molecule composed of one carbon atom and two oxygen atoms.
• It is a major greenhouse gas and is essential for the process of photosynthesis in plants.
• Applications of Avogadro's Number:
• Used to calculate the number of particles in a given amount of substance.
• Helps in determining molar mass and molecular formulas in stoichiometry.

Shortcut Trick

Apply the Successive Percentage formula: a + b + (a × b)/100

Here, a = −16% (reduction) and b = +11% (increase).

Net change = −16 + 11 + (−16 × 11)/100 = −5 − 1.76 = −6.76%.

The negative sign indicates that the final salary is lower.

∴ The correct answer is 6.76%.

Alternate Method

Given: Initial reduction = 16%, Subsequent increase = 11%.

⇒ Let the initial salary be 100.

⇒ Salary after 16% reduction = 100 − 16 = 84.

⇒ Salary after 11% increase = 84 + (11% of 84) = 84 + 9.24 = 93.24.

⇒ Total decrease = 100 − 93.24 = 6.76.

⇒ Percentage lower = (6.76 / 100) × 100 = 6.76%.

∴ The correct answer is 6.76%.

Additional Information

Successive Percentage Formula

For two successive changes of x% and y%, the net effective change is given by [x + y + (xy/100)]%.

Base Value Change

In percentage problems, 100 is often the best assumed base value to simplify calculations as percentage values directly represent absolute values.

Net Decrease vs Net Increase

If the final result of the successive formula is positive, it indicates a net increase; if negative, it indicates a net decrease or lower value.

Shortcut Trick

Assume the Mean (A) is 44.

Calculate deviations (d = x − A): −30, −18, 0, 17, 40.

Calculate net deviation (Σfd): 91(−30) + 78(−18) + 95(0) + 36(17) + 98(40) = 398.

Total frequency (Σf) = 91 + 78 + 95 + 36 + 98 = 398.

Mean = A + (Σfd ÷ Σf) = 44 + (398 ÷ 398) = 45.

∴ The correct answer is 45.

Alternate Method

Given: Marks (x) and Number of Students (f).

Formula: Mean (x̄) = Σf_ix_i ÷ Σf_i

⇒ Total Students (Σf) = 91 + 78 + 95 + 36 + 98 = 398

The correct answer is Only 1 and 3.

Key Points

• The Congress-Jammu and Kashmir National Conference (JKNC) alliance secured a majority with 48 seats, making them the key power holders in the 2024 Assembly elections.
• Voter turnout in the 2024 Jammu and Kashmir Assembly elections was recorded at 63.88%, reflecting a significant increase compared to the voter turnout in the most recent Lok Sabha elections.
• The BJP did not emerge as the single largest party, as the Congress-JKNC alliance surpassed its seat count.
• The newly elected assembly in Jammu and Kashmir does not hold full legislative powers equivalent to other Indian states, as Jammu and Kashmir remains a Union Territory after the abrogation of Article 370 in August 2019.
• Statements 1 and 3 are correct, accurately reflecting the outcomes of the 2024 elections.

Additional Information

• Jammu and Kashmir Assembly: After the abrogation of Article 370 in 2019, Jammu and Kashmir was reorganized into two Union Territories: Jammu and Kashmir, and Ladakh.
• Congress-JKNC Alliance: Historically, both parties have played significant roles in the political landscape of Jammu and Kashmir, often aligning to counter BJP influence in the region.
• Voter Turnout Trends: An increase in voter turnout signifies heightened political engagement and interest among citizens, often influenced by key local and national issues.
• BJP Performance: The BJP has historically aimed to expand its influence in Jammu and Kashmir, but in the 2024 Assembly elections, it fell short in securing a majority.
• Union Territory Status: Jammu and Kashmir continues to function under a Union Territory framework, meaning its legislative assembly has limited powers compared to full-fledged states like Maharashtra or Tamil Nadu.

The logic followed here is:

Hence, the correct answer is "Option 1".

Decoding signs:

Given: 5 × 39 ÷ 1407 − 3 + 11562 = ?

5 × 39 ÷ 1407 − 3 + 11562 = ? ⇒ 5 + 39 × 1407 ÷ 3 - 11562 = ?

⇒ 5 + 39 × 1407 ÷ 3 - 11562 = ?

⇒ 5 + 39 × 469 - 11562 = ?

⇒ 5 + 18291 - 11562 = ?

⇒ 18296 - 11562 = ?

⇒ 6734 = ?

Hence, "Option 1" is the correct answer.

Shortcut Trick

For a recurring decimal like 8.2727..., let x = 8.2727...

Write as integer + fraction: 8 + 0.2727...

Shortcut for 0.ab... = ab/99: 0.2727... = 27/99

Simplified fraction: 8 + 3/11 = (88 + 3) / 11 = 91/11

∴ The correct answer is 91/11.

Alternate Method

Given: Decimal value = 8.272727...

Formula Used: Conversion of non-terminating repeating decimal to vulgar fraction.

⇒ Let x = 8.272727... (Equation 1)

⇒ Multiplying Equation 1 by 100:

⇒ 100x = 827.272727... (Equation 2)

⇒ Subtracting Equation 1 from Equation 2:

⇒ 100x − x = 827.272727... − 8.272727...

⇒ 99x = 819

⇒ x = 819 ÷ 99

⇒ Dividing both numerator and denominator by 9:

⇒ x = 91/11

∴ The correct answer is 91/11.

Additional Information

Pure Recurring Decimals

A decimal in which all digits after the decimal point repeat. Example: 0.aaaa... = a/9 or 0.abab... = ab/99.

Mixed Recurring Decimals

A decimal where some digits after the decimal point do not repeat and some do. Example: 0.abcbc... = (abc − a) / 990.

Rational Number Property

Every recurring decimal is a rational number and can be expressed in the form p/q, where q ≠ 0.

The correct answer is 2.0.

Key Points

• The Total Fertility Rate (TFR) in India as per the National Family Health Survey - 5 (2019-21) is 2.0, which is below the replacement level of fertility (2.1).
• This marks a significant decline from the TFR of 2.2 reported during NFHS-4 (2015-16).
• The TFR decline is an indicator of increasing awareness about family planning and better access to contraceptive methods.
• The survey also highlights that urban areas have a lower TFR (1.6) compared to rural areas (2.1).
• State-specific trends reveal that several states, including Kerala, Tamil Nadu, and Punjab, have achieved TFR levels below replacement.

Additional Information

• Total Fertility Rate (TFR):
• TFR is defined as the average number of children a woman would have during her lifetime.
• It is a key demographic indicator used to assess population growth and replacement levels.
• The replacement level of fertility is generally considered to be 2.1 children per woman, which ensures stable population levels.
• National Family Health Survey (NFHS):
• NFHS is a nationwide survey conducted by the Ministry of Health and Family Welfare, Government of India, in collaboration with the International Institute for Population Sciences (IIPS).
• It provides essential data on health, nutrition, family planning, and demographic indicators.
• NFHS surveys play a crucial role in policy formulation and program implementation.
• Factors influencing TFR:
• Improved access to family planning methods and contraceptives.
• Better education levels, especially among women.
• Economic development and urbanization.
• Awareness campaigns and healthcare outreach programs.
• Implications of a declining TFR:
• A declining TFR can lead to an aging population, reducing the workforce over time.
• It emphasizes the need for sustainable population policies and economic adjustments.
• Balanced demographic shifts are essential for long-term socio-economic stability.

Given: (Left) 535 647 232 804 152 (Right)

According to the question:

Second digit of the highest number → 804 → 0

Third digit of the lowest number → 152 → 2

Thus, the resultant if second digit of the highest number is subtracted from the third digit of the lowest number will be → 0 + 2 = 2

Hence, "Option 1" is the correct answer.

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

Conclusions:

(I) No jam is a can → Follow (As all jams are bands, all bands are sacks and no sack is a can. As whole jams comes in bands which whole comes in snacks which cannot be can, therefore it is true.)

(II) Some sacks are jams → Follow (As most buildings are papers and all papers are frogs. As whole jams comes in bands which whole comes in snacks, therefore it is true.)

∴ Here, Both conclusions (I) and (II) follow.​

Hence, the correct answer is "Option 2".

The correct answer is To serve as the executive body of village self-government.

Key Points

• The Gram Panchayat is the basic unit of local self-governance in rural India under the Panchayati Raj system.
• It acts as the executive body responsible for implementing development programs and schemes for the welfare of the village.
• Key responsibilities include maintaining village infrastructure, sanitation, water supply, and public health.
• Gram Panchayats are headed by the elected representative known as the Sarpanch, assisted by other members.
• It also plays a role in ensuring community participation and governance at the grassroots level.

Additional Information

• Panchayati Raj System:
• It is a three-tier system of governance comprising Gram Panchayat (village level), Panchayat Samiti (block level), and Zila Parishad (district level).
• It was institutionalized through the 73^rd Constitutional Amendment Act of 1992.
• This system aims to decentralize governance and enhance democratic participation at the grassroots level.
• Funding of Gram Panchayats:
• Gram Panchayats receive funds through taxes, government grants, and contributions from villagers.
• Central and state governments provide financial assistance under schemes like Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA).
• Sarpanch:
• The Sarpanch is the elected head of the Gram Panchayat and acts as the primary decision-maker and representative.
• They are responsible for presiding over meetings and ensuring the execution of resolutions passed by the Panchayat.
• Gram Sabha:
• The Gram Sabha consists of all registered voters in the village and serves as the general assembly of the village.
• It plays a crucial role in decision-making and oversight of the Gram Panchayat's activities.

Shortcut Trick

To find the maximum volume of each identical container, calculate the HCF (Highest Common Factor) of the given quantities.

Quantity of Oil A = 168 litres

Quantity of Oil B = 234 litres

Difference = 234 − 168 = 66 litres

HCF must be a factor of 66. Factors are 1, 2, 3, 6, 11, 22, 33, 66. Checking 6: 168/6 = 28 and 234/6 = 39. Both are divisible.

∴ The correct answer is 6 litres.

Alternate Method

Given: Volume of Oil A = 168 litres; Volume of Oil B = 234 litres.

Formula: Maximum capacity of container = HCF of (Volume A, Volume B).

⇒ Prime factorization of 168 = 2³ × 3 × 7

⇒ Prime factorization of 234 = 2 × 3² × 13

⇒ HCF (168, 234) = 2¹ × 3¹

⇒ HCF = 2 × 3 = 6

∴ The correct answer is 6 litres.

Additional Information

Highest Common Factor (HCF)

The greatest number that divides two or more numbers without leaving a remainder. It is also known as GCD (Greatest Common Divisor).

Number of Containers

If the question asks for the minimum number of containers, divide the total volume by the HCF. Total containers = (168/6) + (234/6) = 28 + 39 = 67.

LCM vs HCF

Use HCF when dividing or partitioning into equal parts. Use LCM when finding a common multiple or meeting point in time/distance.

Shortcut Trick

If x − 1/x = k, then x² + 1/x² = k² + 2.

Given k = 3 ⇒ x² + 1/x² = 3² + 2 = 11.

For higher power, x⁴ + 1/x⁴ = (x² + 1/x²)² − 2.

∴ x⁴ + 1/x⁴ = 11² − 2 = 121 − 2 = 119.

∴ The correct answer is 119.

Alternate Method

Given: x − 1/x = 3

Formula Used: (a − b)² = a² + b² − 2ab and (a + b)² = a² + b² + 2ab

⇒ Squaring both sides of x − 1/x = 3:

⇒ (x − 1/x)² = 3²

⇒ x² + 1/x² − 2 × x × (1/x) = 9

⇒ x² + 1/x² − 2 = 9

⇒ x² + 1/x² = 11

⇒ Now, squaring both sides of x² + 1/x² = 11:

⇒ (x² + 1/x²)² = 11²

⇒ x⁴ + 1/x⁴ + 2 × x² × (1/x²) = 121

⇒ x⁴ + 1/x⁴ + 2 = 121

⇒ x⁴ + 1/x⁴ = 121 − 2 = 119

∴ The correct answer is 119.

Additional Information

Algebraic Reciprocal Identities

If x + 1/x = k, then x² + 1/x² = k² − 2. This is used when the starting sign is positive.

Power Relation

To find x⁴ + 1/x⁴, we always square the expression for x² + 1/x² and subtract 2, regardless of the original sign of (x ± 1/x).

General Form for xⁿ

The process of successive squaring allows finding values for x², x⁴, x⁸, and so on, by iterating the k² − 2 or k² + 2 logic.

The correct answer is Tamar Revolt.

Key Points

• Bholanath Singh was a key leader of the Tamar Revolt, which took place in the late 18^th century and early 19^th century.
• The Tamar Revolt was primarily led by the tribal communities in the Chotanagpur region, located in present-day Jharkhand.
• The revolt was triggered by the imposition of oppressive taxes and exploitation by the British East India Company and local landlords (zamindars).
• Bholanath Singh played an instrumental role in organizing the tribal resistance to safeguard their autonomy and traditional rights over their lands.
• The Tamar Revolt is considered one of the prominent tribal uprisings against colonial oppression in India.

Additional Information

• Tribal Uprisings in India:
• Tribal revolts like the Tamar Revolt were often fueled by the British policies of land revenue, deforestation, and interference in traditional tribal practices.
• Other notable tribal uprisings include the Santhal Revolt (1855-56), led by Sidhu and Kanhu, and the Munda Rebellion (1899-1900), led by Birsa Munda.
• Causes of Tribal Revolts:
• Imposition of land taxes and seizure of tribal lands by colonial authorities.
• Exploitation by zamindars, moneylenders, and traders in tribal regions.
• Suppression of tribal customs, religious practices, and community autonomy.
• British Revenue Policies:
• The Permanent Settlement system introduced by Lord Cornwallis in 1793 often favored landlords and left the tribal population vulnerable to exploitation.
• Shifting cultivation, a traditional practice of many tribal groups, was curtailed under British forest policies.
• Impact of Tribal Revolts:
• These uprisings highlighted the resistance of tribal communities to colonial exploitation and the need to address their grievances.
• Many tribal revolts were brutally suppressed, but they inspired later nationalist movements and reforms in tribal policies.

Shortcut Trick

Apply the Cross-Multiplication Method on Income, Expenditure, and Savings.

Income ratio (7 : 8) and Expenditure ratio (11 : 16) with Savings (15,000 : 9,000).

Cross product 1: (7 × 16) − (8 × 11) = 112 − 88 = 24 units.

Cross product 2: (11 × 9,000) − (16 × 15,000) = 99,000 − 240,000 = 141,000 (absolute value).

24 units = ₹141,000 ⇒ 1 unit = ₹5,875. Seema income = 7 × 5,875 = ₹41,125; Darshan income = 8 × 5,875 = ₹47,000.

Total Expenditure = (41,125 − 15,000) + (47,000 − 9,000) = 26,125 + 38,000 = ₹64,125.

∴ The correct answer is ₹64,125.

Alternate Method

Given: Ratio of Income = 7 : 8, Ratio of Expenditure = 11 : 16, Savings = ₹15,000 and ₹9,000.

Formula Used: Income − Savings = Expenditure

⇒ Let the Incomes of Seema and Darshan be 7x and 8x.

⇒ (7x − 15,000) ÷ (8x − 9,000) = 11 ÷ 16

⇒ 16 × (7x − 15,000) = 11 × (8x − 9,000)

⇒ 112x − 240,000 = 88x − 99,000

⇒ 24x = 141,000

⇒ x = 141,000 ÷ 24 = 5,875

⇒ Seema's Expenditure = 7(5,875) − 15,000 = 41,125 − 15,000 = ₹26,125

⇒ Darshan's Expenditure = 8(5,875) − 9,000 = 47,000 − 9,000 = ₹38,000

⇒ Total Expenditure = 26,125 + 38,000 = ₹64,125

∴ The correct answer is ₹64,125.

Additional Information

Income, Expenditure and Savings Relationship

The fundamental relation is Income = Expenditure + Savings. If any two components or their ratios are given, the third can be calculated using algebraic or cross-product methods.

Cross-Multiplication Method

This is used when an initial ratio changes to a new ratio after specific additions or subtractions. Difference in cross products of ratios = Difference in cross products of values.

Ratio and Proportion Basics

A ratio a : b implies that the quantities can be represented as ax and bx. Proportions allow comparing two ratios as a/b = c/d.

The correct answer is Absence of RBC rupture and reduced clinical symptoms.

Key Points

• Plasmodium falciparum typically matures into merozoites in the liver, which then invade red blood cells (RBCs), causing cyclic RBC rupture and fever episodes.
• The mutation described prevents the parasite from maturing into merozoites, halting its ability to infect RBCs and thereby reducing the hallmark symptoms of malaria, including fever and anemia.
• Without RBC invasion and rupture, the immune response to Plasmodium falciparum remains subdued, as the primary triggers of inflammation (hemozoin release and debris from lysed RBCs) are absent.
• This mutation would likely decrease the severity of clinical malaria, as the parasite would fail to propagate significantly within the host.
• The life cycle of Plasmodium falciparum is disrupted, limiting its ability to cause systemic disease and reducing overall parasitemia levels in the host.

Additional Information

• Plasmodium falciparum Life Cycle:
• Plasmodium falciparum is a protozoan parasite that causes malaria in humans.
• The life cycle involves two hosts: humans (intermediate host) and Anopheles mosquitoes (definitive host).
• In humans, sporozoites enter the liver, mature into merozoites, and then infect RBCs, leading to clinical symptoms.
• Red Blood Cell (RBC) Invasion:
• Merozoites infect RBCs, multiply asexually, and rupture them, releasing toxins such as hemozoin, which trigger fever and immune responses.
• This RBC destruction leads to anemia and other complications in malaria patients.
• Malarial Symptoms:
• Classic symptoms of malaria include fever, chills, sweats, headaches, and muscle pain, which are directly linked to RBC rupture.
• Severe cases can lead to cerebral malaria, organ failure, and death.
• Mutation Impact:
• The described mutation disrupts the parasite’s liver stage progression, preventing it from becoming infectious to RBCs.
• This reduces the parasite’s capacity to cause systemic disease and limits its ability to spread.
• Malaria Control Efforts:
• Global initiatives like insecticide-treated nets, antimalarial drugs, and vaccines (e.g., RTS,S/AS01) aim to reduce malaria incidence and mortality.
• Understanding genetic mutations in Plasmodium species can contribute to developing new therapeutic strategies.

The correct answer is Evaluating advancements and investments in quantum computing technologies.

Key Points

• The 'Future Front: Quarterly Frontier Tech Insights' report by NITI Aayog primarily focuses on advancements in quantum computing technologies.
• Quantum computing leverages principles of quantum mechanics to perform computations far beyond traditional computing capabilities.
• The report aims to evaluate investments, technological progress, and applications in quantum computing within India and globally.
• India has been actively working on quantum technologies through initiatives such as the National Quantum Mission, launched in 2023.
• Quantum computing is expected to revolutionize sectors such as cryptography, material science, artificial intelligence, and drug discovery.

Additional Information

• Quantum Computing:
• Quantum computing uses quantum bits (qubits) instead of classical bits for processing information.
• Qubits can exist in multiple states simultaneously due to the principle of superposition.
• Quantum entanglement enables qubits to be interconnected, allowing faster and more complex computations.
• National Quantum Mission:
• India launched the National Quantum Mission in 2023 to accelerate quantum research and development.
• The mission aims to develop 50-qubit quantum computers and advanced quantum communication systems by 2030.
• It also focuses on skill development and collaboration with global institutions.
• Applications of Quantum Computing:
• Quantum computing has potential applications in cryptography, enhancing data security.
• It aids in solving complex problems in fields like drug discovery and material science.
• It is also being explored for applications in machine learning and artificial intelligence.
• Global Efforts in Quantum Computing:
• Countries like the US, China, and the EU have invested heavily in quantum research.
• Leading companies like IBM, Google, and Microsoft are developing cutting-edge quantum computing systems.
• International collaboration is key to advancing quantum technologies globally.

The correct answer is Chhau.

Key Points

• Chhau is a traditional Indian dance form primarily performed in the states of Odisha, West Bengal, and Jharkhand.
• Unlike many other classical Indian dance forms, Chhau does not use vocal music during performances.
• The music accompanying Chhau performances is primarily instrumental and consists of traditional Indian instruments such as dhol, dhamsa, and shehnai.
• Chhau is characterized by its martial movements, masks (in certain variants), and themes often derived from Indian mythology.
• This dance form is known for its vigorous and dramatic movements, making it distinct from other Indian classical dances like Bharatanatyam, Kathak, and Odissi which incorporate vocal music.

Additional Information

• Bharatanatyam
• A classical dance form from Tamil Nadu, Bharatanatyam heavily incorporates vocal music alongside instrumental music.
• The themes often revolve around spiritual ideas, stories from Hindu mythology, and devotional content.
• It uses intricate hand gestures (mudras) and facial expressions to narrate stories.
• Odissi
• Originating from Odisha, Odissi is one of the oldest classical dance forms in India.
• It is performed to both vocal and instrumental music, often based on compositions of Jayadeva's "Gita Govinda."
• Odissi emphasizes fluid movements and tribhangi (three-bend posture).
• Kathak
• A classical dance form from northern India, Kathak incorporates vocal music and instrumental tabla and sitar performances.
• The dance form is characterized by intricate footwork and spins.
• Its themes often include storytelling from epics like the Mahabharata and Ramayana.
• Traditional Indian Instruments in Dance Forms
• Dhol: A percussion instrument used in Chhau performances.
• Shehnai: A wind instrument that provides melody in many Indian traditional performances.
• Tabla: A pair of drums often used in classical Indian music.

The correct answer is Designing Future Society for Our Lives.

Key Points

• The theme for Expo 2025 in Osaka, Japan, is "Designing Future Society for Our Lives", emphasizing innovative solutions for global challenges.
• Expo 2025 will aim to explore sustainable development goals (SDGs) and address pressing global issues such as health, environment, and technology.
• It will be held on Yumeshima Island, Osaka, from April 13 to October 13, 2025.
• The event is expected to attract over 28 million visitors from around the world, fostering cultural and technological exchange.
• The Expo is being organized by the Bureau International des Expositions (BIE), the intergovernmental organization responsible for overseeing world exhibitions.

Additional Information

• World Expos:
• World Expos, also known as World Fairs, are large international exhibitions showcasing achievements in science, technology, art, and culture.
• The first World Expo was held in London in 1851, called "The Great Exhibition."
• They are organized by the Bureau International des Expositions (BIE) and occur every five years.
• Osaka's Role in Expo History:
• Osaka previously hosted the Expo 1970, which was the first World Expo held in Japan.
• The theme of Expo 1970 was "Progress and Harmony for Mankind."
• It attracted 64 million visitors, making it one of the most successful Expos in history.
• Sustainable Development Goals (SDGs):
• Expo 2025 aligns with the United Nations' 17 Sustainable Development Goals, promoting global collaboration for a better future.
• Key focus areas include climate action, health and well-being, and technological advancements.
• Yumeshima Island:
• Yumeshima is a man-made island in Osaka Bay, chosen as the venue for Expo 2025.
• It is being developed as a hub for innovation, sustainability, and tourism.
• The island will also host integrated resort facilities, including casinos, after the Expo.

Shortcut Trick

Assumed Mean = 800

Net Deviation = 8×(550−800) + 10×(1000−800) + 12×(850−800)

Net Deviation = −2000 + 2000 + 600 = +600

Average Adjustment = 600 ÷ (8 + 10 + 12) = 600 ÷ 30 = +20

Actual Average = 800 + 20 = ₹820

∴ The correct answer is ₹820.

Alternate Method

Given: 8 shirts @ ₹550, 10 pants @ ₹1000, 12 shoes @ ₹850.

Formula: Average Expenditure = (Total Cost of all articles) ÷ (Total Number of articles)

₹550 8 Shirts

₹1000 10 Pants

₹850 12 Shoes

Avg: ₹820

⇒ Total Cost of Shirts = 8 × 550 = ₹4,400

⇒ Total Cost of Pants = 10 × 1,000 = ₹10,000

⇒ Total Cost of Shoes = 12 × 850 = ₹10,200

⇒ Total Expenditure = 4,400 + 10,000 + 10,200 = ₹24,600

⇒ Total Number of Articles = 8 + 10 + 12 = 30

⇒ Average Expenditure = 24,600 ÷ 30 = ₹820

∴ The correct answer is ₹820.

Additional Information

Weighted Average Formula

When items have different quantities, Average = (n₁x₁ + n₂x₂ + ... + n_kx_k) ÷ (n₁ + n₂ + ... + n_k).

Deviation Method

Calculated as: Assumed Average + (Sum of individual deviations from assumed average ÷ Total count).

Combined Average

If average of group A is x and group B is y, the combined average lies strictly between x and y.

Shortcut Trick

Let Mother = M and Daughter = D.

From 2^nd condition: M − 3D = 4 ⇒ M = 3D + 4.

Substitute in 1^st condition: 3(3D + 4) = 5D + 36 ⇒ 9D + 12 = 5D + 36.

4D = 24 ⇒ D = 6 years and M = 3(6) + 4 = 22 years.

Difference = 22 − 6 = 16 years.

∴ The correct answer is 16 years.

Alternate Method

Given:

Condition 1: 3 × Mother's age = 5 × Daughter's age + 36

Condition 2: 3 × Daughter's age = Mother's age − 4

⇒ 3M − 5D = 36 ... (i)

⇒ M − 3D = 4 ... (ii)

Multiply equation (ii) by 3:

⇒ 3M − 9D = 12 ... (iii)

Subtract (iii) from (i):

⇒ (3M − 5D) − (3M − 9D) = 36 − 12

⇒ 4D = 24

⇒ D = 6 years

Substitute D = 6 in (ii):

⇒ M − 3(6) = 4

⇒ M − 18 = 4

⇒ M = 22 years

Age Difference = M − D = 22 − 6 = 16 years.

∴ The correct answer is 16 years.

Additional Information

Linear Equations in Two Variables

Problems involving two people's ages often lead to a system of two equations that can be solved using substitution or elimination methods.

Constant Age Difference

The difference between the ages of two individuals remains constant regardless of how many years pass or go back in time.

Ratio of Ages

If the ratio of ages is given as a:b, we can assume the ages as ax and bx to simplify algebraic calculations.

Shortcut Trick

Ratio of length : width : height = 10 : 17 : 14

Let common factor be x. Then TSA = 2(10x×17x + 17x×14x + 14x×10x) = 1096

⇒ 2(170x² + 238x² + 140x²) = 1096 ⇒ 548x² = 548 ⇒ x = 1

Length = 10 × 1 = 10 cm

∴ The correct answer is 10 cm.

Alternate Method

Given: Ratio of dimensions = 10 : 17 : 14, Total Surface Area = 1096 cm²

Formula Used: Total Surface Area of Cuboid = 2(lb + bh + hl)

⇒ Let l = 10x, b = 17x, and h = 14x

⇒ 2[(10x × 17x) + (17x × 14x) + (14x × 10x)] = 1096

⇒ 2[170x² + 238x² + 140x²] = 1096

⇒ 2[548x²] = 1096

⇒ 1096x² = 1096

⇒ x² = 1 ⇒ x = 1

⇒ Length = 10 × 1 = 10 cm

∴ The correct answer is 10 cm.

Additional Information

Volume of Cuboid

The space occupied by a cuboid is calculated as Length × Width × Height (l × b × h).

Diagonal of a Cuboid

The longest rod that can be placed inside a cuboid is √(l² + b² + h²).

Lateral Surface Area (LSA)

The area of the four side walls is given by the formula 2h(l + b).

Shortcut Trick

Difference in Principal = ₹9,000 − ₹5,000 = ₹4,000

Interest difference for 3 years = ₹360

Interest difference for 1 year = 360 ÷ 3 = ₹120

Rate of Interest = (Interest difference for 1 year ÷ Principal difference) × 100

Rate % = (120 ÷ 4,000) × 100 = 3%

∴ The correct answer is 3%.

Alternate Method

Given:

Principal of Rakesh (P_R) = ₹5,000

Principal of Shivam (P_S) = ₹9,000

Time (T) = 3 years

Interest difference = ₹360

Formula Used:

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

Calculations:

⇒ Interest for Shivam − Interest for Rakesh = 360

⇒ [(9000 × R × 3) ÷ 100] − [(5000 × R × 3) ÷ 100] = 360

⇒ 270R − 150R = 360

⇒ 120R = 360

⇒ R = 360 ÷ 120

⇒ R = 3%

∴ The correct answer is 3%.

Additional Information

Simple Interest Relationship

When time and rate are constant, the difference in interest is directly proportional to the difference in principal: ΔSI = (ΔP × R × T) ÷ 100.

Effective Rate of Interest

The effective rate for a period is R × T. In this case, the total effective percentage difference is (3 × R)%, which applied to the principal difference gives the total interest difference.

Comparison of SI and CI

Simple Interest remains constant every year on the original principal, whereas Compound Interest is calculated on the accumulated amount (Principal + previous Interest).

Given:

1) F is the brother of G.

2. G is the husband of H.

3) H is the daughter of I.

4. I is the wife of J.

Thus, F is J's daughter's husband's brother.

Hence, the correct answer is "Option 1".

The correct answer is Chaddhas.

Key Points

• The Jarawa tribe inhabits parts of the Andaman Islands, primarily in the South and Middle Andaman region.
• They refer to their home or territory as "Chaddhas." This term is intrinsic to their language and cultural identity.
• The Jarawas are one of the indigenous groups in the Andaman Islands, known for their traditional hunter-gatherer lifestyle.
• Efforts to preserve the autonomy and culture of the Jarawa tribe have been made by restricting external interference in their designated areas.
• The tribe's language and customs are unique and are critical to their understanding of the world around them, including their connection to their land, "Chaddhas."

Additional Information

• Jarawa Tribe:
• The Jarawas are believed to have migrated to the Andaman Islands around 26,000 years ago.
• They are classified as a Particularly Vulnerable Tribal Group (PVTG) under Indian law.
• They primarily rely on hunting, fishing, and gathering for sustenance, staying largely isolated from modern civilization.
• Andaman Islands:
• The Andaman Islands are an archipelago in the Bay of Bengal, forming part of the Indian Union Territory of Andaman and Nicobar Islands.
• The islands are home to several indigenous tribes, including the Great Andamanese, Onge, and Sentinelese.
• Conservation Efforts:
• The Indian government has implemented policies to protect the Jarawas, including the establishment of the Jarawa Tribal Reserve.
• Tourism and other activities in their regions are heavily regulated to reduce external influence and exploitation.
• Languages of the Andaman Tribes:
• The languages spoken by the indigenous tribes, such as the Jarawas, are unique and are part of the Ongan language family.
• These languages are unwritten and transmitted orally, making cultural preservation crucial for their survival.

The logic followed here is:

Option 1) EH - BE

Option 2) GJ - DG

​

Option 3) RK - JH

Option 4) PS - MP

Thus, out of all 'RK - JH' is the odd one out.

Hence, "Option 3" is the correct answer.

The correct answer is 1798-99.

Key Points

• The Chuar Rebellion was a series of uprisings by the tribal communities, primarily the Chuar and Bhumij tribes, in Bengal and Bihar against British colonial rule.
• The rebellion occurred due to severe economic grievances, including the imposition of heavy land revenue and exploitation by British officials.
• The peak of the Chuar rebellion was witnessed during the years 1798-99, when widespread unrest impacted regions such as Midnapore and Jungle Mahal.
• British policies, such as the Permanent Settlement Act of 1793, further alienated the tribal population by depriving them of their traditional rights to land and forest resources.
• The rebellion was ultimately suppressed through military interventions and administrative measures by the British.

Additional Information

• Permanent Settlement Act (1793):
• Implemented by Lord Cornwallis, this act introduced the zamindari system of land revenue collection.
• It fixed the revenue payable by zamindars permanently, depriving the tribal communities of their customary land rights.
• Jungle Mahal:
• A region in Bengal that included parts of present-day West Bengal, Odisha, and Jharkhand.
• The area was historically inhabited by tribal communities such as the Bhumij and Chuar.
• Tribal Uprisings:
• In the 18^th and 19^th centuries, several tribal rebellions occurred due to British exploitation, including the Santhal Rebellion (1855-56) and the Kol Rebellion (1831-32).
• These uprisings highlighted the socio-economic struggles faced by tribal populations under colonial rule.
• Colonial Economic Policies:
• British colonial policies disrupted the traditional tribal economy, leading to widespread poverty and dispossession.
• Heavy land taxes and restrictions on forest use exacerbated the grievances of tribal communities.

Given:

The value of 17³ - 10² + ((26)/(13))² - 12 + 20 × 12 = ?

Formula used:

Follow the BODMAS rule (Bracket, Order, Division/Multiplication, Addition/Subtraction)

Calculation:

17³ = 4913

10² = 100

(26 ÷ 13)² = 2² = 4

20 × 12 = 240

⇒ 4913 - 100 + 4 - 12 + 240

⇒ 4913 - 100 - 8 + 240

⇒ 4913 + 132

⇒ 5045

∴ The correct answer is option (1).

The correct answer is To group related files together for better management.

Key Points

• Subfolders help in organizing files systematically, allowing users to group related files together for efficient management.
• They make it easier to locate and access files, especially when dealing with large volumes of data.
• Subfolders contribute to improved workflow by reducing clutter and ensuring proper categorization of files.
• They enable users to implement hierarchical structures, ensuring logical arrangements of data within directories.
• By grouping files in subfolders, users can also assign specific permissions or access control to protect sensitive information.

Additional Information

• File Organization
• File organization refers to the systematic arrangement of files and folders for easy access and management.
• Common methods include categorization by file type, date, project, or purpose.
• Proper organization reduces the risk of losing important files and enhances productivity.
• Directory Hierarchy
• A directory hierarchy is the structure of folders and subfolders within a computer's file system.
• It allows users to create a parent-child relationship among folders for better logical arrangements.
• This hierarchy is crucial for maintaining organization and accessing files efficiently.
• Access Control
• Access control refers to the ability to manage permissions for users to access specific files or folders.
• By using subfolders, administrators can restrict access to sensitive files.
• Common methods include password protection, encryption, or role-based permissions.
• File Management Tools
• Modern operating systems offer file management tools, such as Windows File Explorer and macOS Finder, for managing subfolders effectively.
• These tools allow users to search, rename, move, and organize files quickly.
• Third-party applications like Google Drive and Dropbox also provide advanced file organization options.

Given number: 8271634

According to the question, 

So, digits that appeared more than once in the new number thus formed → 2 and 4 = Two

Hence, "Option 3" is the correct answer.

Shortcut Trick

Successive percentage change method:

Final Price = Original Price × (100 − 12)/100 × (100 + 25)/100

Final Price = 8000 × 0.88 × 1.25

Final Price = 8000 × 1.1 = 8800

∴ The correct answer is ₹8,800.

Alternate Method

Given:

Original Price = ₹8,000

First change = 12% decrease

Second change = 25% increase

Calculations:

⇒ Price after 12% decrease = 8000 − (12/100 × 8000)

⇒ Price after 12% decrease = 8000 − 960 = ₹7,040

⇒ New price after 25% increase = 7040 + (25/100 × 7040)

⇒ New price after 25% increase = 7040 + 1760

⇒ New Price = ₹8,800

∴ The correct answer is ₹8,800.

Additional Information

Successive Percentage Formula

The effective percentage change for two successive changes of a% and b% is given by [a + b + (ab/100)]%.

Net Change Application

In this case: a = −12 and b = +25. Net % change = −12 + 25 + [(−12 × 25)/100] = 13 − 3 = 10% increase.

Base Value Rule

Always calculate the second percentage change on the updated value, not the original base value, unless specified.

Given: 

Prakesh starts from point A and drives 11 km towards the south.

He then takes a right turn, drives 7 km, turns right and drives 13 km.

He then takes a right turn and drives 9 km.

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

Thus, Prakesh should drive 2 km (9 km - 7 km) in the west direction in order to reach point A again.

Hence, "Option 3" is the correct answer.

Shortcut Trick

Weight of B = [2 × (Avg of A & B) + 2 × (Avg of B & C)] − [3 × (Avg of A, B & C)]

⇒ Weight of B = [2 × 40 + 2 × 42] − [3 × 45]

⇒ Weight of B = [80 + 84] − 135

⇒ Weight of B = 164 − 135 = 29 kg

∴ The correct answer is 29 kg.

Alternate Method

Given:

Average weight of A, B, and C = 45 kg

Average weight of A and B = 40 kg

Average weight of B and C = 42 kg

Formula Used:

Total Sum = Average × Number of items

Calculations:

⇒ Total Weight (A + B + C) = 45 × 3 = 135 kg --- (1)

⇒ Total Weight (A + B) = 40 × 2 = 80 kg --- (2)

⇒ Total Weight (B + C) = 42 × 2 = 84 kg --- (3)

⇒ Adding (2) and (3): (A + B) + (B + C) = 80 + 84

⇒ A + 2B + C = 164 kg --- (4)

⇒ Subtracting (1) from (4): (A + 2B + C) − (A + B + C) = 164 − 135

⇒ Weight of B = 29 kg

∴ The correct answer is 29 kg.

Additional Information

Average of Group

If the average of n items is x, then the Total Sum is n × x. If one item is shared between two overlapping subgroups, the value of that item equals the sum of the subgroups minus the total sum.

Net Deviation Method

The sum of deviations of all observations from the mean is always zero. This property is used to find missing values in a data set when the average is known.

Weighted Average

When combining two groups with averages A₁ and A₂ and sizes n₁ and n₂, the Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

The correct answer is Reserve Bank of India.

Key Points

• The Reserve Bank of India (RBI) was established on April 1, 1935, under the Reserve Bank of India Act, 1934.
• The RBI is India's central bank, responsible for regulating the country's monetary policy, currency issuance, and financial stability.
• It initially started its operations in Kolkata but was permanently shifted to Mumbai in 1937.
• The Reserve Bank of India will complete 90 years of establishment in 2025.
• The RBI's primary functions include controlling inflation, managing foreign exchange, and regulating banks and non-banking financial companies.

Additional Information

• History of RBI
• The RBI was conceptualized based on the recommendations of the Hilton Young Commission.
• It was initially established as a private entity but was nationalized in 1949.
• RBI's Governance Structure
• The RBI is governed by a central board of directors, which includes government-appointed officials and experts.
• The Governor of RBI serves as the chief executive officer and represents the bank.
• Key Functions of RBI
• Formulating and implementing monetary policy to maintain price stability and economic growth.
• Issuing and managing India's currency under the Currency and Coinage Act.
• Regulating and supervising banks and financial institutions to ensure financial stability.
• Maintaining foreign exchange reserves and managing exchange rates.
• Important Milestones
• The RBI played a critical role in the economic reforms of 1991 that liberalized India's economy.
• In recent years, it has introduced various digital initiatives like the Unified Payments Interface (UPI) for promoting financial inclusion.

The logic followed here is:

​​​

Hence, "Option 2" is the correct answer.

Given series: (Left) 4 6 & 8 $ 7 & 3 9 # % 4 6 @ £ 5 Ω 9 # 1 * 7 (Right)

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

Required condition: Symbol - Number - Another Number

(Left) 4 6 & 8 $ 7 & 3 9 # % 4 6 @ £ 5 Ω 9 # 1 * 7 (Right)

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

Hence, "Option 3" is the correct answer.

The correct answer is 608 days.

Key Points

• Sunita Williams, a NASA astronaut of Indian origin, has spent a cumulative 608 days in space over the course of her missions.
• She held the record for the most spaceflight time by a woman until it was surpassed by Peggy Whitson in 2017.
• Her most recent mission aboard a SpaceX capsule concluded in March 2025, marking her return to Earth.
• Sunita Williams has participated in two long-duration missions aboard the International Space Station (ISS), namely Expeditions 14/15 and 32/33.
• She is one of the most experienced astronauts in NASA's history and has conducted seven spacewalks totaling 50 hours and 40 minutes.

Additional Information

• SpaceX Crew Dragon:
• SpaceX's Crew Dragon is a spacecraft designed to transport astronauts to and from the ISS.
• It is part of NASA's Commercial Crew Program, which aims to enable private companies to provide human spaceflight services.
• Sunita Williams was part of one of the Crew Dragon missions, showcasing advancements in commercial spaceflight.
• International Space Station (ISS):
• The ISS is a modular space station in low Earth orbit, serving as a laboratory for scientific research and international collaboration.
• It has been continuously inhabited since November 2000, with astronauts from various countries contributing to its operations.
• Sunita Williams' missions aboard the ISS focused on scientific experiments, maintenance, and outreach activities.
• Spacewalks:
• A spacewalk, or Extravehicular Activity (EVA), is when an astronaut exits a spacecraft to work in space.
• Sunita Williams has performed seven spacewalks, placing her among the most experienced astronauts in this domain.
• Her spacewalks include tasks such as repairing equipment and installing components on the ISS.
• NASA's Human Spaceflight Program:
• NASA has been at the forefront of human space exploration since the Apollo program in the 1960s.
• Programs such as the Space Shuttle, ISS, and Artemis are key milestones in NASA's efforts to explore space.
• Sunita Williams' contributions to human spaceflight have been a significant part of NASA's achievements.