The logic followed here is:

Hence, "Option 3" is the correct answer.

Shortcut Trick Let the smaller number be x and the greater be x + 2880. Using Division Algorithm: Greater = 6 × Smaller + 120 x + 2880 = 6x + 120 ⇒ 5x = 2760 ⇒ x = 552. Greater number = 552 + 2880 = 3432. HCF(3432, 3916): 3916 − 3432 = 484. Factors of 484 are 44 × 11. Checking 44: 3432 ÷ 44 = 78, 3916 ÷ 44 = 89. ∴ The correct answer is 44. Alternate Method

Given: Difference = 2880, Quotient = 6, Remainder = 120. Let the smaller number be S and the greater number be G. ⇒ G − S = 2880 --- (i) ⇒ G = 6S + 120 --- (ii) Substitute (ii) in (i): ⇒ (6S + 120) − S = 2880 ⇒ 5S + 120 = 2880 ⇒ 5S = 2760 ⇒ S = 552 Calculating the Greater Number (G): ⇒ G = 552 + 2880 = 3432 Finding HCF(3432, 3916) using long division or factor method: ⇒ 3916 = 3432 × 1 + 484 ⇒ 3432 = 484 × 7 + 44 ⇒ 484 = 44 × 11 + 0 ∴ The correct answer is 44. Additional Information Division Algorithm For any two integers, Dividend = (Divisor × Quotient) + Remainder, where 0 ≤ Remainder < Divisor. Euclidean Algorithm for HCF HCF of two numbers a and b is the same as the HCF of b and the remainder of a/b. This continues until the remainder is zero. HCF and Difference Rule The HCF of two numbers must also be a factor of their difference. This often helps in narrowing down options quickly.

Shortcut Trick

Arrange the data in ascending order: 13, 25, 27, 28, 43, 57, 73, 77, 81, 87, 89.

Count the total number of terms (n) = 11 (which is an odd number).

The median is the middle-most term, which is the ((11 + 1) ÷ 2) = 6^th term.

The 6^th term in the sorted sequence is 57.

∴ The correct answer is 57.

Alternate Method

Given: Data set = {13, 43, 81, 27, 25, 28, 87, 57, 77, 89, 73}

Formula Used: Median = ((n + 1) ÷ 2)^th term, where n is the number of observations (when n is odd).

⇒ Arrange the observations in ascending order: 13, 25, 27, 28, 43, 57, 73, 77, 81, 87, 89

⇒ Total number of observations (n) = 11

⇒ Median = ((11 + 1) ÷ 2)^th observation

⇒ Median = 6^th observation

⇒ Median = 57

∴ The correct answer is 57.

Additional Information

Median for Even Number of Terms

If the number of observations (n) is even, the median is the average of the (n ÷ 2)^th and ((n ÷ 2) + 1)^th terms.

Arithmetic Mean

The mean is the sum of all observations divided by the total number of observations (Sum ÷ n).

Mode

The mode is the value that occurs most frequently in a data set. A data set can be unimodal, bimodal, or multimodal.

Shortcut Trick

Given: CSA = 5904π, Radius (r) = 36 cm.

Using CSA = πrl ⇒ 5904π = π × 36 × l

l = 5904 ÷ 36 = 164 cm.

Height h = √(l² − r²) = √(164² − 36²) = √((164 − 36)(164 + 36)) = √(128 × 200) = √25600 = 160 cm.

∴ The correct answer is 160 cm.

Alternate Method

Given:

Curved Surface Area (CSA) = 5904π cm²

Diameter (d) = 72 cm ⇒ Radius (r) = 72 ÷ 2 = 36 cm

Formula Used:

1. Curved Surface Area (CSA) of cone = πrl
2. Slant height (l) = √(h² + r²) ⇒ h = √(l² − r²)

Calculations:

⇒ π × 36 × l = 5904π

⇒ 36 × l = 5904

⇒ l = 5904 ÷ 36

⇒ l = 164 cm

⇒ h² = l² − r²

⇒ h² = 164² − 36²

⇒ h² = (164 − 36)(164 + 36)

⇒ h² = 128 × 200

⇒ h² = 25600

⇒ h = √25600 = 160 cm

∴ The correct answer is 160 cm.

Additional Information

Total Surface Area of Cone

The total surface area includes the curved surface area and the base area: TSA = πr(l + r).

Volume of Cone

The volume of a right circular cone is exactly one-third of the volume of a cylinder with the same radius and height: V = (1/3)πr²h.

Pythagorean Relation

In a right circular cone, the height (h), radius (r), and slant height (l) always form a right-angled triangle: l² = h² + r².

The correct answer is Satpura Range.

Key Points

• The Tapti River originates from Multai, located in the Satpura Range of Madhya Pradesh, India.
• The Tapti River flows westward, one of the few rivers in peninsular India to do so, and drains into the Arabian Sea.
• It is approximately 724 km long, making it one of the major rivers of central India.
• The Tapti River passes through three states: Madhya Pradesh, Maharashtra, and Gujarat.
• The river is known for supporting agricultural activities in its basin, which covers a total area of around 65,145 square kilometers.

Additional Information

• Satpura Range:
• The Satpura Range is a hill range in central India, stretching across Madhya Pradesh and Maharashtra.
• The range is a part of the Deccan Plateau and is known for its rich biodiversity and dense forests.
• Prominent peaks in the Satpura Range include Dhupgarh (the highest point in Madhya Pradesh) and Pachmarhi.
• It is an important source of rivers such as the Tapti, Narmada, and Godavari.
• Westward Flowing Rivers in India:
• Most rivers in India flow eastward towards the Bay of Bengal; however, a few like the Tapti, Narmada, and Mahi flow westward.
• These rivers drain into the Arabian Sea, contributing significantly to the western coastal ecosystem.
• Arabian Sea Drainage System:
• The Tapti River forms part of the Arabian Sea drainage system along with other westward flowing rivers.
• These rivers often carve narrow valleys and are important for irrigation and hydroelectric projects.
• Multai:
• Multai is a town in Madhya Pradesh known as the origin point of the Tapti River.
• The name "Tapti" is derived from the goddess Tapti, worshipped in Hindu mythology.

The correct answer is To search for specific text and replace it with other text.

Key Points

• The Find and Replace feature in MS Word 2019 is used to locate specific text or phrases within a document and replace them with alternative text if required.
• It is accessed using the keyboard shortcut Ctrl + H or through the "Home" tab in the "Editing" group.
• This feature enables users to make bulk changes in a document efficiently, saving time and effort for repetitive edits.
• Advanced options in "Find and Replace" allow users to search for text with specific formatting, such as bold, italic, or specific fonts, and replace it with similar or modified formatting.
• It helps in maintaining consistency across large documents by ensuring uniform corrections or modifications.

Additional Information

• Search Options in Find and Replace:
• Users can perform case-sensitive searches by enabling the "Match Case" option.
• The "Find Whole Words Only" option ensures only complete words matching the search term are located.
• Wildcard characters can be used to perform advanced and flexible searches.
• Go To Feature:
• The "Go To" tab within the Find and Replace dialog box allows users to navigate to specific pages, sections, or line numbers in a document.
• Formatting Search:
• Users can search for text with specific formatting attributes, such as font size, color, or paragraph settings, using the "Format" option in the dialog box.
• Limitations:
• The feature does not support searching for non-text elements such as images or tables directly.
• Complex edits may require manual intervention despite using the Replace function.
• Applications:
• Ideal for editing large documents, such as legal contracts, research papers, or reports, where repetitive terms or formatting need adjustment.

Shortcut Trick

Put the direct values of a = 5 and b = 3 into the expression.

Expression = (3 × 5 − 2 × 3) : (6 × 5 + 2 × 3)

Expression = (15 − 6) : (30 + 6) = 9 : 36

Simplified Ratio = 1 : 4

∴ The correct answer is 1 : 4.

Alternate Method

Given: Ratio a : b = 5 : 3

Formula Used: Ratio substitution method where a = 5k and b = 3k.

⇒ Let a = 5k and b = 3k

⇒ Required Ratio = (3a − 2b) / (6a + 2b)

⇒ Required Ratio = [3(5k) − 2(3k)] / [6(5k) + 2(3k)]

⇒ Required Ratio = (15k − 6k) / (30k + 6k)

⇒ Required Ratio = 9k / 36k

⇒ Required Ratio = 1 / 4

∴ The correct answer is 1 : 4.

Additional Information

Componento and Dividendo

If a/b = c/d, then (a+b)/(a−b) = (c+d)/(c−d), used to simplify complex fractional ratios.

Duplicate and Sub-duplicate Ratio

Duplicate ratio of a:b is a²:b² and sub-duplicate ratio is √a:√b.

Inverse Ratio

The inverse ratio of a : b is 1/a : 1/b, which simplifies to b : a.

The correct answer is English.

Key Points

• Bal Gangadhar Tilak, a key leader of the Indian independence movement, was a staunch nationalist and one of the pioneers of the extremist faction.
• Tilak edited two newspapers: 'Kesari', published in Marathi, and 'Mahratta', published in English.
• The newspaper 'Mahratta' was founded to promote nationalism and disseminate Tilak's political ideologies among educated Indians.
• Through his writings in 'Mahratta', Tilak criticized British policies and advocated for Swaraj (self-rule).
• The English-language newspaper was instrumental in reaching a wider audience, including educated Indians and intellectuals across the country.

Additional Information

• Bal Gangadhar Tilak:
• He was popularly known as 'Lokmanya Tilak', meaning 'accepted by the people as their leader.'
• He is regarded as the 'Father of Indian Unrest' due to his strong opposition to British rule.
• Tilak was one of the first leaders to demand complete independence (Purna Swaraj) for India.
• His famous slogan was "Swaraj is my birthright, and I shall have it."
• 'Kesari' and 'Mahratta' Newspapers:
• 'Kesari' (Marathi) and 'Mahratta' (English) were used as platforms to spread anti-colonial sentiments.
• 'Kesari' was especially influential among the Marathi-speaking population.
• Both newspapers played a crucial role in inspiring Indians to fight for independence.
• Concept of Swaraj:
• Swaraj, meaning self-rule, was a central theme of Tilak's political philosophy.
• Tilak believed in empowering Indians politically, culturally, and economically to achieve independence.
• His ideas laid the foundation for future leaders like Mahatma Gandhi in the struggle for freedom.
• Legacy:
• Bal Gangadhar Tilak remains one of the most respected and influential leaders of India’s freedom struggle.
• His contributions continue to be studied and celebrated in Indian political and historical discourse.

The logic followed here is:

NJ-QM-TV

And,

JF-MI-PR

So, checking each option one by one:

Option 1) GB-IE-LM

Option 2) GB-ID-LM

Option 3) FB-IE-LM

Option 4) FB-IE-LN

​

Thus, out of all the options, 'FB-IE-LN' follows the same logic as given.

Hence, "Option 4" is the correct answer.

The logic followed here is:

Hence, "Option 1" is the correct answer.

The correct answer is Seven.

Key Points

• India Infoline Finance Limited (IIFL Finance) is one of India’s leading non-banking financial companies (NBFCs) offering diversified financial services.
• On the occasion of Women’s Day (8 March 2025), IIFL Finance rebranded seven of its existing branches as all-women staffed ‘Shakti’ branches.
• The ‘Shakti’ branches aim to promote women empowerment by creating an inclusive workplace environment and serving as centers for women-led financial services.
• These branches are staffed entirely by women and are designed to provide financial products and services tailored to women entrepreneurs and customers.
• The initiative emphasizes IIFL Finance’s commitment to gender diversity and the empowerment of women in the financial sector.

Additional Information

• Non-Banking Financial Companies (NBFCs):
• NBFCs are financial institutions that provide banking services without meeting the legal definition of a bank.
• They offer products such as loans, asset financing, and investment products but cannot accept demand deposits like savings accounts.
• NBFCs play a critical role in financial inclusion, especially in rural and underserved areas.
• Women Empowerment in Finance:
• Empowering women in the financial sector includes promoting gender diversity, leadership roles, and equal opportunities.
• Initiatives like all-women branches encourage women’s participation in economic decision-making.
• Importance of Women’s Day:
• International Women’s Day, celebrated annually on March 8, highlights the social, economic, cultural, and political achievements of women.
• The day is also a call to action for accelerating gender parity and women’s rights worldwide.
• Financial Products for Women:
• Several financial institutions offer customized products for women, including lower interest rates on loans and exclusive savings accounts.
• These products aim to encourage women’s entrepreneurship and financial independence.

Shortcut Trick

Net efficiency = 4 (fill) − 3 (empty) = 1 unit/hour.

Total Capacity (LCM of 18, 24) = 72 units.

One-fourth of the tank = 72 ÷ 4 = 18 units.

Time taken = 18 units ÷ 1 unit/hour = 18 hours.

∴ The correct answer is 18 hours.

Alternate Method

Given: Filling Tap (A) time = 18 hours, Emptying Tap (B) time = 24 hours.

Formula Used: Efficiency = Total Work ÷ Time; Required Time = Required Work ÷ Net Efficiency.

⇒ Net efficiency when both open = 4 + (−3) = 1 unit/hour.

⇒ Work to be done = 1/4 × Total Capacity = 1/4 × 72 = 18 units.

⇒ Time required = 18 ÷ 1 = 18 hours.

∴ The correct answer is 18 hours.

Additional Information

Net Work Done

When one pipe fills and another empties, net work per hour = (1/x − 1/y), where x is filling time and y is emptying time.

LCM Method

Always assume total capacity as the LCM of individual times to avoid working with complex fractions.

Inlet and Outlet Pipes

Inlet pipes have positive efficiency (+), whereas outlet/leakage pipes have negative efficiency (−).

Given: P, Q, R, S, T, U and V have an exam on different days of the week, starting on Monday and ending on Sunday. 

1) S has an exam on Tuesday.

2) Exactly 3 people have an exam between S and V.

3) T has an exam immediately before P and U has an exam immediately after P.

4) Only 1 person has an exam between T and R.

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

Thus, R has an exam on Monday.

Hence, "Option 2" is the correct answer.

The logic followed here is:

Given: # : MLI :: LKH : %

Option 1) # = POL, % = IHE → POL : MLI :: LKH : IHE

Option 2) # = FRL, % = QHE → FRL : MLI :: LKH : QHE

Option 3) # = UIL, % = IXC → UIL : MLI :: LKH : IXC

Option 4) # = FRL, % = QHF → FRL : MLI :: LKH : QHF

​

Hence, "Option 1" is the correct answer.

The correct answer is Nagar Panchayats.

Key Points

• es Nagar Panchayats are urban local bodiestablished under the provisions of the 74^th Constitutional Amendment Act, 1992.
• They are constituted for areas transitioning from rural to urban due to population growth or other factors of urbanization.
• The primary purpose of Nagar Panchayats is to manage urban governance in these transitional areas while ensuring smooth administrative operations.
• As per the Constitution, Nagar Panchayats are recognized as one of the three types of municipal entities: Municipal Corporations, Municipal Councils, and Nagar Panchayats.
• Nagar Panchayats consist of elected representatives and function under the control of the state government, addressing urban planning, development, and basic infrastructure needs.

Additional Information

• 74^th Constitutional Amendment Act, 1992
• This amendment introduced the concept of urban local bodies, including Municipal Corporations, Municipal Councils, and Nagar Panchayats.
• It provided constitutional recognition to local governance and decentralized decision-making in urban areas.
• The act aimed at empowering urban local bodies to function as institutions of self-government under Article 243Q.
• Urbanization in India
• India's urban population is steadily growing due to migration, industrialization, and expansion of economic opportunities.
• Transitional areas often require structured urban governance to address challenges like housing, sanitation, and infrastructure.
• Difference Between Nagar Panchayats and Rural Bodies
• While rural bodies like Gram Panchayats cater to villages, Nagar Panchayats focus on urban governance in transitioning areas.
• Nagar Panchayats deal with urban challenges such as traffic management, waste disposal, and urban planning.
• Role of State Governments
• State governments play a crucial role in defining the criteria for establishing Nagar Panchayats.
• They provide funds, guidance, and administrative support to enable effective urban governance.

Given: 

Radhe starts from Point A and drives 8 km towards North.

He then takes a left turn, drives 9 km, turns left and drives 12 km.

He then takes a left turn and drives 11 km.

He takes a final left turn, drives 4 km and stops at Point P. 

Thus, Radhe should drive 2 km (11 km - 9 km) in the west direction in order to reach Point A again.

Hence, "Option 4" is the correct answer.

The correct answer is 2.8%.

Key Points

• As per the IMF's April 2025 Global Financial Stability Report, the revised global growth forecast for 2025 is 2.8%.
• The IMF slightly adjusted its global economic outlook due to persistent inflationary pressures and geopolitical uncertainties.
• Developing economies are expected to contribute significantly to global growth, with a stronger rebound in sectors like manufacturing and services.
• Advanced economies are predicted to experience slower growth due to tightening monetary policies and sluggish consumer demand.
• The revised forecast reflects a cautious optimism, with the IMF emphasizing the need for structural reforms to sustain long-term economic resilience.

Additional Information

• International Monetary Fund (IMF):
• Established in 1944, the IMF aims to foster global monetary cooperation, secure financial stability, and promote sustainable economic growth.
• It publishes the Global Financial Stability Report biannually to analyze the stability of global financial markets and emerging risks.
• Global Growth Trends:
• Global growth rates fluctuate based on factors like inflation, trade policies, geopolitical conflicts, and technological advancements.
• Growth projections are essential for policymakers to plan fiscal and monetary interventions.
• Inflationary Pressures:
• Inflation impacts consumer purchasing power and overall economic activity, influencing growth forecasts.
• Central banks often adjust interest rates to manage inflation and stabilize economies.
• Structural Reforms:
• Reforms like enhancing labor market flexibility, improving infrastructure, and reducing trade barriers can boost long-term growth potential.
• Such measures are pivotal for emerging markets aiming for sustainable economic development.

The correct answer is Constitutional outline for governance.

Key Points

• The 74^th Amendment Act, 1992, provided a constitutional status to Urban Local Bodies (ULBs), ensuring their governance framework under the Indian Constitution.
• The amendment added Part IX-A (The Municipalities) to the Constitution, detailing the structure, composition, and functions of ULBs.
• It mandated the creation of three types of municipalities: Nagar Panchayats, Municipal Councils, and Municipal Corporations, based on population size.
• It introduced the concept of decentralized governance, empowering ULBs to plan and implement development programs and manage local resources effectively.
• The act also provided for the establishment of a State Finance Commission (SFC) to allocate financial resources to these bodies, ensuring fiscal autonomy.

Additional Information

• Part IX-A of the Constitution:
• Introduced by the 74^th Amendment, it provides a constitutional framework for urban governance.
• It includes Articles 243P to 243ZG, outlining the composition, powers, and responsibilities of municipalities.
• State Finance Commission (SFC):
• Established under Article 243-I, it ensures equitable distribution of financial resources between the state government and ULBs.
• The SFC reviews financial positions of ULBs and recommends measures for their fiscal sustainability.
• District Planning Committees (DPCs):
• Mandated under Article 243ZD, DPCs integrate plans prepared by Panchayats and Municipalities into a cohesive district development plan.
• Empowered Municipalities:
• The 12^th Schedule of the Constitution lists 18 functional areas for ULBs, including urban planning, water supply, sanitation, and public health.
• This ensures enhanced autonomy and accountability in addressing local governance issues.

The logic followed here is:

Option 1) TX – ZV

Option 2) CG – ID

Option 3) MQ – SN

Option 4) HL – NI

​

Thus, out of all 'TX – ZV' is the odd one out.

Hence, "Option 1" is the correct answer.

The correct answer is The State Governor.

Key Points

• Under Article 217 of the Indian Constitution, the President is required to consult the Chief Justice of India, the Chief Justice of the respective High Court, and the Governor of the concerned State before appointing judges to the High Courts.
• The role of the State Governor in this process is advisory, and the final decision is made by the President.
• The consultation process ensures the appointment of qualified and unbiased individuals to the judiciary, maintaining the integrity of the judicial system.
• The Chief Justice of India plays a critical role in providing recommendations to the President based on merit and judicial expertise.
• This constitutional provision is designed to promote a collaborative process involving key stakeholders in the judiciary and executive.

Additional Information

• Article 217 of the Constitution of India:
• It deals with the appointment and conditions of service of High Court judges.
• The President appoints judges after consultation with the Chief Justice of India, the Governor of the concerned state, and sometimes other judges as deemed necessary.
• Role of the Chief Justice of India:
• The Chief Justice of India provides recommendations to the President, ensuring judicial appointments are based on merit and integrity.
• This role is crucial for maintaining the independence of the judiciary.
• High Court Judges:
• They are responsible for adjudicating cases and upholding the Constitution within their respective jurisdictions.
• High Court judges hold office until the age of 62.
• Governor's Advisory Role:
• The Governor of the state provides input during the consultation process, representing the state’s interests.
• While the Governor’s role is advisory, the President has the final say in judicial appointments.

The correct answer is Sayyid Dynasty.

Key Points

• The Sayyid Dynasty ruled Delhi Sultanate from 1414 to 1451 CE after the fall of the Tughlaq Dynasty.
• The founder of the dynasty, Khizr Khan, claimed to be a descendant of the Prophet Muhammad through his lineage.
• Yahya bin Ahmad Sirhindi, a chronicler of the era, documented the claim of Khizr Khan's prophetic descent in his historical works.
• The Sayyids were known for their relatively weak control over the Delhi Sultanate and faced constant challenges from regional rulers.
• The dynasty ended when Bahlul Lodi established the Lodi Dynasty in 1451 CE, marking the end of the Sayyid rule.

Additional Information

• Delhi Sultanate:
• The Delhi Sultanate was a series of Islamic dynasties that ruled over India from 1206 to 1526 CE.
• It consisted of five dynasties: Slave Dynasty, Khilji Dynasty, Tughlaq Dynasty, Sayyid Dynasty, and Lodi Dynasty.
• The Sultanate played a significant role in the cultural and architectural development of India, introducing Persian art and Islamic architecture.
• Khizr Khan:
• Khizr Khan was the founder of the Sayyid Dynasty and ruled from 1414 to 1421 CE.
• He was appointed as the governor of Multan by Timur before ascending to power in Delhi.
• Khizr Khan did not assume the title of Sultan but ruled as a vassal of the Timurid Empire.
• Yahya bin Ahmad Sirhindi:
• He was a historian during the Sayyid period and authored the Tarikh-i-Mubarak Shahi, which chronicles the history of the Delhi Sultanate.
• His works provide valuable insights into the political, social, and cultural aspects of the era.
• Timur’s Invasion of Delhi:
• Timur invaded Delhi in 1398 CE, leading to massive destruction and weakening the Tughlaq Dynasty.
• This invasion set the stage for the rise of the Sayyid Dynasty, which emerged as Timur’s vassal rulers in Delhi.

The correct answer is Jayashree Vencatesan.

Key Points

• Jayashree Vencatesan was awarded the Ramsar Award for "Wetland Wise Use" in March 2025 for her significant contributions to wetland conservation and sustainable management.
• The Ramsar Award recognizes individuals, organizations, and governments for exceptional efforts in the conservation and wise use of wetlands.
• Jayashree Vencatesan is a renowned environmentalist and the managing trustee of Care Earth Trust, an organization working on biodiversity conservation.
• Her work includes promoting community-based wetland management and advocating for policies that ensure the ecological and socio-economic sustainability of wetlands.
• The Ramsar Award is one of the most prestigious global recognitions in the field of wetland conservation, presented by the Ramsar Convention on Wetlands.

Additional Information

• Ramsar Convention:
• It is an international treaty adopted in 1971 in Ramsar, Iran, aimed at conserving wetlands and promoting their sustainable use.
• The convention designates specific wetlands as "Ramsar Sites" for their ecological significance.
• Wetlands play a crucial role in biodiversity conservation, water purification, flood control, and climate regulation.
• Wetland Wise Use:
• Wise use refers to the sustainable utilization of wetlands to maintain their ecological character.
• It ensures that wetland resources are used in a way that benefits both biodiversity and local communities.
• India and Ramsar Sites:
• India is home to over 75 Ramsar Sites, making it one of the countries with the highest number of wetlands designated under the Ramsar Convention.
• These sites include Sundarbans, Chilika Lake, and Keoladeo National Park, among others.
• Care Earth Trust:
• Care Earth Trust is a Chennai-based NGO focused on biodiversity conservation and ecosystem management.
• It works extensively on wetland restoration, urban biodiversity, and climate change mitigation strategies.

The correct answer is Dual citizenship.

Key Points

• The Citizenship Act, 1955 governs the acquisition, determination, and termination of Indian citizenship.
• India does not allow dual citizenship. A citizen of India cannot hold citizenship of another country simultaneously.
• The Act provides for citizenship through five modes: birth, descent, registration, naturalization, and incorporation of territory.
• Dual citizenship is not permitted because India follows a policy of single citizenship, ensuring uniform national identity and allegiance.
• Indian citizens acquiring foreign citizenship must renounce their Indian citizenship as per the provisions of the Act.

Additional Information

• Naturalization:
• Naturalization is a mode of acquiring citizenship for foreign nationals who fulfill eligibility criteria like residence in India for a specified period and good character.
• Applicants must renounce their citizenship of another country to become Indian citizens.
• Descent-based Citizenship:
• A person born outside India is considered an Indian citizen by descent if either of their parents is an Indian citizen.
• Specific conditions apply based on the date of birth and registration requirements under the Citizenship Act, 1955.
• Registration:
• Citizenship through registration is available for individuals like persons of Indian origin or spouses of Indian citizens who meet prescribed conditions.
• They must reside in India for a specific period before applying for registration.
• Overseas Citizenship of India (OCI):
• Though dual citizenship is not allowed, the government offers the OCI scheme for people of Indian origin who are citizens of other countries.
• OCI status provides several rights but does not equate to full citizenship, such as voting rights or eligibility for government jobs.
• Renunciation and Termination of Citizenship:
• Citizenship can be renounced voluntarily by individuals or terminated by the government in case of fraud or disloyalty.
• The Act specifies detailed procedures for renunciation and termination to ensure compliance with legal frameworks.

The correct answer is Kazan.

Key Points

• The 2024 BRICS Summit was hosted in Kazan, Russia, from October 22-24, 2024.
• Kazan is the capital city of the Republic of Tatarstan, Russia, and is known for its rich cultural heritage and history.
• The summit focused on key issues like economic cooperation, global governance reform, sustainable development, and technological collaboration among BRICS nations.
• BRICS comprises five major economies: Brazil, Russia, India, China, and South Africa, collectively representing approximately 42% of the world’s population and 27% of global GDP.
• This summit marked the continuation of discussions on expanding the BRICS group and enhancing intra-member trade in local currencies.

Additional Information

• BRICS Overview:
• BRICS was established in 2009 as a platform for economic and political cooperation among emerging economies.
• Its members aim to reform global financial institutions like the IMF and World Bank to better reflect the interests of developing nations.
• Kazan’s Significance:
• Kazan is a prominent city in Russia, known for its unique blend of Eastern and Western cultures.
• It is a UNESCO-recognized city for its historical landmarks, including the Kazan Kremlin, a World Heritage site.
• Key Outcomes of the 2024 BRICS Summit:
• Discussions on the establishment of a new development bank to enhance financial collaboration among BRICS nations.
• Agreements to promote the use of national currencies for trade within BRICS countries, reducing reliance on the US dollar.
• Commitments toward advancing green energy projects and combating climate change.
• Future of BRICS:
• Continued efforts to include more member countries, enhancing the group’s global influence.
• Focus on achieving equitable growth and sustainable development across member nations.

The correct answer is the power of the judiciary to pronounce upon the constitutionality of laws and executive orders.

Key Points

• Judicial review in India is a power granted to the judiciary to examine the constitutionality of legislative acts and executive orders.
• This principle ensures that laws and executive actions do not violate the provisions of the Constitution of India.
• The concept is derived from Article 13, which states that any law inconsistent with the Constitution shall be void.
• Judicial review in India encompasses reviewing administrative decisions, legislative enactments, and constitutional amendments.
• It acts as a crucial mechanism for maintaining the supremacy of the Constitution and protecting fundamental rights.

Additional Information

• Judicial Review
• Judicial review originated in the United States through the landmark case of Marbury v. Madison (1803).
• It ensures checks and balances among the three organs of the government: executive, legislature, and judiciary.
• In India, judicial review is limited compared to the United States but is pivotal in safeguarding constitutional democracy.
• Articles Related to Judicial Review in India
• Article 13: Declares that laws inconsistent with or in derogation of fundamental rights are void.
• Article 32: Provides the right to constitutional remedies, allowing citizens to approach the Supreme Court for enforcement of rights.
• Article 226: Empowers High Courts to issue orders or writs for enforcement of fundamental rights and other purposes.
• Types of Judicial Review
• Review of Legislative Actions: Ensures that laws passed by the legislature adhere to constitutional provisions.
• Review of Executive Actions: Examines the validity of decisions made by the executive branch.
• Review of Constitutional Amendments: Determines whether amendments violate the basic structure of the Constitution.
• Basic Structure Doctrine
• This doctrine was established in the landmark Keshavananda Bharati Case (1973).
• The judiciary can strike down constitutional amendments if they violate the essential features of the Constitution.
• Examples of basic structure elements include the supremacy of the Constitution, secularism, and judicial independence.

According to the given information,

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

Hence, "Option 2" is the correct answer.

Given:

$\frac{\sqrt{0.028224}}{\sqrt{0.000784}}$

Calculation:

$\frac{\sqrt{0.028224}}{\sqrt{0.000784}}$

⇒ $\frac{\sqrt{0.028224 \times 10^6}}{\sqrt{0.000784 \times 10^6}}$

⇒ $\frac{\sqrt{28224}}{\sqrt{784}}$

⇒ $\frac{\sqrt{28224}}{\sqrt{784}}$

⇒ $\sqrt{36}$

⇒ 6

∴ The simplified value of the expression is 6.

The correct answer is Cumene process, cumene hydroperoxide.

Key Points

• The Cumene process, also known as the Hock process, is the most widely used industrial method for producing phenol globally.
• The process involves the oxidation of cumene (isopropylbenzene) to form cumene hydroperoxide as an intermediate.
• Cumene hydroperoxide is then cleaved to produce phenol and acetone as major products.
• This method is preferred due to its economic efficiency and the simultaneous production of acetone, which is a valuable byproduct.
• The process is primarily conducted in large-scale petrochemical plants and is used extensively in the production of plastics, resins, and other industrial materials.

Additional Information

• Cumene (Isopropylbenzene):
• Cumene is an organic compound derived from benzene and propylene.
• It serves as the precursor for the production of phenol and acetone via the Cumene process.
• Its synthesis involves Friedel-Crafts alkylation of benzene with propylene.
• Phenol:
• Phenol is an aromatic organic compound with the molecular formula C₆H₅OH.
• It is widely used in the production of plastics, resins, and other industrial chemicals such as bisphenol A.
• Phenol is also utilized in pharmaceuticals, dyes, and antiseptics.
• Acetone:
• Acetone (CH₃COCH₃) is a colorless, volatile solvent and a major byproduct of the Cumene process.
• It is commonly used in the production of acrylic plastics and as a solvent in various industries.
• Acetone is also used in household applications like nail polish removers.
• Industrial Importance of the Cumene Process:
• The Cumene process accounts for the majority of phenol production globally due to its cost-effectiveness.
• The co-production of acetone enhances the economic feasibility of the process.
• Advancements in catalyst technology have improved the efficiency and environmental sustainability of the process.

The correct answer is Trushula Gumpha.

Key Points

• Trushula Gumpha at Khandagiri in Odisha is renowned for its intricate carvings of twenty-four Jain Teerthankars.
• The carvings depict the Jain Teerthankars in meditative poses, showcasing a deep connection to Jain spirituality and philosophy.
• Khandagiri and Udayagiri caves are significant archaeological sites that date back to the reign of King Kharavela of the Mahameghavahana dynasty.
• Trushula Gumpha stands out for its artistic and religious importance, reflecting the influence of Jainism in ancient Odisha.
• The caves are located near Bhubaneswar and are visited for their historical, architectural, and religious significance.

Additional Information

• Jain Teerthankars:
• The Teerthankars are revered spiritual teachers in Jainism who have attained liberation and enlightenment.
• There are twenty-four Jain Teerthankars, with Lord Mahavira being the last and most significant.
• Khandagiri and Udayagiri Caves:
• These caves are part of a historical site that represents Jain rock-cut architecture.
• They were carved during the reign of King Kharavela in the 1^st century BCE.
• The site consists of numerous caves with inscriptions and carvings depicting Jain teachings and practices.
• King Kharavela:
• He was a ruler of the Mahameghavahana dynasty in ancient Odisha.
• Kharavela is known for his patronage of Jainism and contributions to art and architecture.
• The famous Hathi Gumpha inscription provides insights into his reign and achievements.
• Jain Rock-Cut Architecture:
• It involves carving sanctuaries, temples, and monasteries into natural rock formations.
• The architecture is marked by simplicity, reflecting Jain principles of non-attachment and minimalism.

Given number: 3154872

According to the question, 

So, the difference between the digits which are second from the left and second from the right in the new number thus formed → 8 - 2 = 6

Hence, "Option 4" is the correct answer.

The logic followed here is:

IJF is related to PQM

And,

RSO is related to YZV

Similarly,

EFB is related to

Hence, "Option 3" is the correct answer.

Shortcut Trick

Volume of 1 cube = 3.6³ = 46.656 cm³

Volume of machine part = (1/3) × 3.14 × 5.4² × (49 + 35) = 2563.9104 cm³

Number of cubes used = 2563.9104 ÷ 46.656 = 55

Surplus cubes = 731 − 55 = 676

∴ The correct answer is 676 cubes.

Alternate Method

Given: Total cubes = 731, Side (a) = 3.6 cm, Radius (r) = 5.4 cm, Heights (h₁, h₂) = 49 cm, 35 cm, π = 3.14

Formula Used: Volume of cube = a³; Volume of cone = (1/3)πr²h

⇒ Volume of 1 cube = 3.6 × 3.6 × 3.6 = 46.656 cm³

⇒ Total volume of machine part = (1/3) × π × r² × h₁ + (1/3) × π × r² × h₂

⇒ Volume = (1/3) × 3.14 × (5.4)² × (49 + 35)

⇒ Volume = (1/3) × 3.14 × 29.16 × 84

⇒ Volume = 3.14 × 29.16 × 28 = 2563.9104 cm³

⇒ Number of cubes used (n) = Total Volume ÷ Volume of 1 cube

⇒ n = 2563.9104 ÷ 46.656 = 55

⇒ Surplus cubes = Total cubes − Cubes used = 731 − 55 = 676

∴ The correct answer is 676 cubes.

Additional Information

Volume of Solid Figures

For a cone, Volume = (1/3)πr²h. For a cube, Volume = a³. When melting and recasting, the total volume remains constant.

Surplus Calculation

Surplus = Total Available Units − Units Utilized. Utilized units must be an integer if discrete items (like cubes) are used.

The correct answer is Bindusara.

Key Points

• Bindusara, the son of Chandragupta Maurya, मौर्य साम्राज्य के शासक के रूप में उनका स्थान लिया।
• He ruled between 297 BCE and 273 BCE, expanding and consolidating the vast empire established by his father.
• Historical texts refer to him as "Amitraghata," which translates to "Slayer of Enemies." This title reflects his military and administrative prowess.
• Bindusara maintained diplomatic relations with Hellenistic rulers, such as Antiochus I of the Seleucid Empire, ensuring stability in the western frontiers of his empire.
• He was succeeded by his son, Ashoka, who became one of the most famous rulers in Indian history due to his promotion of Buddhism and the spread of the Mauryan Empire's influence.

Additional Information

• The Maurya Empire:
• The Maurya Empire (321–185 BCE) was the first large-scale empire in India, founded by Chandragupta Maurya with guidance from his advisor Chanakya.
• It was known for its centralized administration, advanced infrastructure, and efficient governance.
• Bindusara's Reign:
• Bindusara inherited a vast empire and worked towards its further consolidation.
• His reign is considered a period of political stability and economic prosperity.
• Relations with Foreign Powers:
• Bindusara maintained diplomatic ties with Greek rulers, including Seleucus I Nicator and his successor Antiochus I.
• These relations helped secure the northwestern borders of the Maurya Empire.
• Succession:
• After Bindusara's death, his son Ashoka ascended the throne and became a prominent ruler, known for his role in spreading Buddhism.
• Ashoka's reign marked the zenith of the Maurya Empire in terms of territorial expansion and cultural influence.

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

1) Only two people sit between H and B when counted from the right of H. 

2) B sits to the immediate right of C. 

3) Only three people sit between A and C when counted from the right of C. 

4) G sits to the immediate right of I.

After positioning G and I only one position is left which will be occupied by the only person left i.e. D.

Thus, G sits fourth to the right of D.

Hence, "Option 4" is the correct answer.

The correct answer is International Darts Open.

Key Points

• The International Darts Open is a professional darts tournament part of the PDC (Professional Darts Corporation) European Tour.
• In 2025, the tournament took place at the SACHSENarena in Riesa, Germany, from 4 to 6 April.
• The event is renowned for attracting top darts players from across the globe and is a critical stop in the PDC calendar.
• It is one of several tournaments that form the European Tour, offering players ranking points and prize money.
• The International Darts Open provides an opportunity for players to qualify for other major PDC events, such as the European Championship.

Additional Information

• Professional Darts Corporation (PDC)
• The PDC is one of the leading organizations in the sport of darts, established in 1992.
• It hosts numerous prestigious tournaments, including the World Darts Championship and Premier League Darts.
• PDC events often feature the world's best players, ensuring high competition levels.
• SACHSENarena
• Located in Riesa, Germany, the SACHSENarena is a prominent venue for sporting and cultural events.
• It is known for hosting darts tournaments, concerts, and exhibitions.
• The venue offers modern facilities to accommodate large audiences and international events.
• European Tour
• The European Tour is a series of darts tournaments organized by the PDC.
• These events take place in various European cities, promoting darts across the continent.
• They are instrumental in providing opportunities for emerging players to compete on an international stage.
• Darts Ranking Points System
• PDC tournaments, including the European Tour, award ranking points to players based on their performance.
• These points contribute to players' standings on the PDC Order of Merit, determining qualification for major events.
• Higher rankings offer players greater career opportunities and sponsorship deals.

The correct answer is V Ramasubramanian.

Key Points

• Shri Justice V Ramasubramanian, former Judge of the Supreme Court of India, assumed the charge of the Chairperson of the National Human Rights Commission.
• The NHRC is tasked with protecting and promoting human rights in India, including rights related to life, liberty, equality, and dignity.
• Justice V Ramasubramanian succeeded Justice Arun Mishra, who previously held the position of NHRC Chairperson.
• Justice Arun Mishra is known for delivering several landmark judgments during his tenure at the Supreme Court of India.
• The appointment of the NHRC Chairperson is made by the President of India based on recommendations from a committee comprising the Prime Minister, Speaker of the Lok Sabha, Deputy Chairman of the Rajya Sabha, Leaders of Opposition in both Houses, and the Union Home Minister.

Additional Information

• National Human Rights Commission (NHRC)
• Established on October 12, 1993, under the Protection of Human Rights Act, 1993.
• It is a statutory body tasked with investigating complaints of human rights violations and ensuring their protection.
• The NHRC can recommend corrective measures and compensation for human rights violations but does not have judicial powers.
• It has powers of a civil court for summoning, examining witnesses, and requisitioning public records during inquiries.
• Composition of NHRC
• NHRC consists of a Chairperson, four full-time members, and seven ex-officio members.
• The Chairperson must be a retired Chief Justice or Judge of the Supreme Court of India.
• Other members include experts in law, human rights, and public administration.
• Judicial Contributions of Justice Arun Mishra
• Known for interpreting laws related to land acquisition, environment, and constitutional provisions.
• Played a key role in delivering judgments impacting corporate governance and public interest.
• Protection of Human Rights Act, 1993
• This Act provides for the establishment of NHRC and State Human Rights Commissions.
• Defines "human rights" as rights related to life, liberty, equality, and dignity guaranteed by the Constitution or international covenants.

Shortcut Trick

When Percentage Profit at SP₁ equals Percentage Loss at SP₂, the Cost Price (CP) is the average of the two selling prices.

CP = (SP₁ + SP₂) ÷ 2 = (3,471 + 2,577) ÷ 2 = 6,048 ÷ 2 = 3,024.

To make 25% profit, required SP = CP × 1.25 (or CP × 5/4).

Required SP = 3,024 × (125 ÷ 100) = 3,024 × 1.25 = 3,780.

∴ The correct answer is ₹3,780.

Alternate Method

Given → SP₁ = ₹3,471, SP₂ = ₹2,577, Profit% = Loss%, Target Profit = 25%. Formulas: Profit% = ((SP − CP) ÷ CP) × 100 | Loss% = ((CP − SP) ÷ CP) × 100 | New SP = CP × (100 + P%) ÷ 100.

⇒ Let CP be x. According to question: (3,471 − x)/x × 100 = (x − 2,577)/x × 100. ⇒ 3,471 − x = x − 2,577 ⇒ 2x = 3,471 + 2,577 = 6,048. ⇒ x = 3,024. ⇒ New SP = 3,024 × (100 + 25) ÷ 100 = 3,024 × 1.25. ⇒ New SP = 3,780.

∴ The correct answer is ₹3,780.

Additional Information

Equating Profit and Loss

If numerical profit equals numerical loss, CP is the midpoint. If Profit% = Loss%, it also results in CP being the midpoint because the denominator (CP) is the same for both calculations.

Fractional Conversion

25% profit is equivalent to a multiplier of 5/4. To find the new price, simply multiply the CP by 1.25.

Given: Seven boxes, A, B, C, D, E, F and G, are kept one over the other.

1) Only A is kept above C. 

2) Only B is kept below G.

3) Only F is kept between C and E. 

After positioning F and E only one position is left which will be occupied by the only box left i.e. D.

Thus, three boxes are kept above E.

Hence, "Option 3" is the correct answer.

The correct answer is Deregulation of interest rates.

Key Points

• Deregulation of interest rates was a key reform introduced in the Indian banking sector as part of the post-1991 economic reforms.
• Prior to this, the Reserve Bank of India (RBI) tightly regulated interest rates, but deregulation allowed banks to determine interest rates based on market conditions.
• This reform enhanced competition among banks, resulting in better services and improved financial efficiency.
• LiberalCreation approved financials to meet diverse customer demands to compete on deposits and loans
• It aimed to develop a more flexible and market-driven banking system, which was crucial for India's transition to a more liberalized economy.

Additional Information

• Statutory Liquidity Ratio (SLR):
• SLR is the percentage of a bank's net demand and time liabilities (NDTL) that must be maintained in liquid assets like cash, gold, or government-approved securities before providing credit to customers.
• It is used by the RBI to control inflation and regulate the credit flow in the economy.
• Repo Rate and Reverse Repo Rate:
• The repo rate is the rate at which the RBI lends money to commercial banks, while the reverse repo rate is the rate at which RBI borrows money from banks.
• These tools are used to control liquidity and inflation in the economy.
• Banking Sector Liberalization:
• Reforms after 1991 allowed the entry of private and foreign banks into India, leading to growth and innovation in services.
• This also led to significant investments in technology, improving efficiency and customer experience.
• Non-Performing Assets (NPAs):
• NPAs are loans or advances where the borrower has stopped making interest or principal repayments for a specified period.
• The banking reforms also aimed to address the issue of rising NPAs through better credit risk management and recovery mechanisms.

The correct answer is Performing last rites for unclaimed bodies.

Key Points

• Pooja Sharma was included in BBC's 100 Most Inspiring Women in December 2024 for her exceptional contributions to society.
• She is widely recognized for her work in performing last rites for unclaimed bodies, ensuring dignity in death for the neglected and abandoned.
• Her initiatives involve identifying unclaimed bodies, completing legal formalities, and conducting respectful cremation or burial rites.
• Pooja collaborates with local authorities, hospitals, and NGOs to carry out this humanitarian work effectively and ethically.
• Her efforts aim to bring attention to the plight of unclaimed bodies and encourage societal responsibility towards the deceased.

Additional Information

• Unclaimed Bodies:
• Unclaimed bodies are those found without any identifiable relatives or guardians to claim them.
• They are often the result of homelessness, estrangement, or unidentified accidents.
• Legal procedures are typically followed to determine the next steps, including post-mortem examinations and public notices.
• Importance of Last Rites:
• Last rites are rituals performed to honor the deceased and provide closure to their souls, as per various religious or cultural traditions.
• In many societies, performing last rites is considered essential for ensuring peace in the afterlife.
• For unclaimed bodies, these rites restore their dignity and humanity, regardless of their social status.
• Humanitarian Efforts:
• Individuals like Pooja Sharma play a critical role in addressing societal neglect and abandonment.
• Such efforts highlight the importance of compassion and inclusivity in society.
• Organizations and volunteers often work in collaboration to support these initiatives.
• BBC 100 Women:
• The BBC's 100 Women list celebrates influential and inspiring women globally.
• It highlights the contributions of women in various fields, including social work, science, arts, and activism.
• The initiative aims to recognize and amplify the voices of women making a difference.

The correct answer is Brahmaputra.

Key Points

• Majuli Island is located in the state of Assam, India, and is formed by the Brahmaputra River.
• The Brahmaputra River flows through Tibet (China), India, and Bangladesh, making it one of the major rivers in South Asia.
• Majuli became the world's largest river island and is renowned for its vibrant culture, particularly the neo-Vaishnavite monasteries called "Satras."
• The island is surrounded by the Brahmaputra River on the south and the Kherkutia Xuti and Subansiri River on the north.
• Majuli Island covers an area of approximately 352 square kilometers and is prone to erosion due to the dynamic nature of the Brahmaputra River.

Additional Information

• Brahmaputra River
• The Brahmaputra originates from the Angsi Glacier in Tibet, where it is known as the Yarlung Tsangpo.
• It is one of the few rivers in the world that is considered a male river due to its strong currents and dynamic nature.
• The Brahmaputra is known for its high sediment load, which contributes to the formation and erosion of islands like Majuli.
• It is vital for agriculture, transportation, and water resources in northeastern India.
• River Islands and Erosion
• River islands are formed due to sediment deposition caused by the dynamic flow of rivers.
• Majuli faces severe erosion, losing significant land area over time due to changes in the Brahmaputra's course.
• Efforts are underway to combat erosion and preserve the cultural heritage of Majuli.
• Cultural Significance of Majuli
• Majuli is a center for the neo-Vaishnavite tradition initiated by Srimanta Sankardeva in Assam.
• It hosts numerous "Satras," which are monasteries that serve as hubs for religious and cultural activities.
• The island is also known for its traditional art forms, pottery, and festivals.

The correct answer is Maharashtra.

Key Points

• In March 2025, Maharashtra witnessed violent clashes over demands to remove the tomb of Mughal emperor Aurangzeb.
• The clashes occurred in the town of Khuldabad, Aurangabad district, where the tomb is located.
• Protesters demanded the removal of the tomb, claiming that it symbolizes a controversial legacy of Aurangzeb's rule.
• The incident led to multiple injuries and heightened communal tensions, prompting the deployment of additional police forces to maintain order.
• The Maharashtra government called for restraint and emphasized the need for peaceful resolution of the issue.

Additional Information

• Aurangzeb's Tomb:
• Located in Khuldabad, Maharashtra, this modest tomb reflects Aurangzeb's wish for simplicity in death.
• Aurangzeb, the sixth Mughal emperor, ruled from 1658 to 1707 and is a polarizing historical figure.
• Khuldabad:
• A town in Aurangabad district, it is known as the "Valley of Saints" due to the presence of numerous Sufi shrines.
• It holds historical significance as a spiritual and cultural center during the Mughal era.
• Communal Tensions in India:
• India has a history of communal tensions rooted in its diverse religious and cultural fabric.
• Such incidents often require careful handling to prevent escalation and ensure harmony among communities.
• Government Response to Clashes:
• Authorities typically impose curfews and deploy additional security forces to maintain peace.
• Efforts are made to mediate between conflicting parties to prevent further violence.

Shortcut Trick

Salary is always 100%.

Savings = 17%

Expenditure = 100% − 17% = 83%

Expenditure = 4900 × 0.83 = 4067

∴ The correct answer is ₹4,067.

Alternate Method

Given:

Monthly Salary = ₹4,900

Savings Percentage = 17%

Calculations:

⇒ Monthly Savings = 17% of ₹4,900

⇒ Monthly Savings = (17 ÷ 100) × 4900 = 17 × 49 = ₹833

⇒ Monthly Expenditure = Total Salary − Monthly Savings

⇒ Monthly Expenditure = 4900 − 833

⇒ Monthly Expenditure = ₹4,067

∴ The correct answer is ₹4,067.

Additional Information

Income, Expenditure and Savings Relationship

The fundamental relation is Income = Expenditure + Savings. Any change in one component affects the others accordingly.

Percentage Change

If Income increases by x% and Expenditure increases by y%, the new values can be calculated using Base × (100 + Change)/100.

Effective Savings Ratio

Savings Ratio = (Savings ÷ Income) × 100. It represents the portion of total earning kept aside for future use.

Shortcut Trick

Total interest percentage = (Simple Interest ÷ Principal) × 100

Total interest % = (3500 ÷ 14000) × 100 = 25%

Annual Rate of Interest (x) = Total interest % ÷ Time

x = 25% ÷ 4 = 6.25

∴ The correct answer is 6.25.

Alternate Method

Given:

Principal (P) = ₹14,000

Time (T) = 4 years

Simple Interest (SI) = ₹3,500

Formula Used:

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

Calculations:

⇒ 3500 = (14000 × x × 4) / 100

⇒ 3500 = 140 × 4 × x

⇒ 3500 = 560 × x

⇒ x = 3500 ÷ 560

⇒ x = 350 ÷ 56

⇒ x = 25 ÷ 4

⇒ x = 6.25

∴ The correct answer is 6.25.

Additional Information

Simple Interest Components

The Principal is the initial sum, Rate is the annual percentage, and Time must be in years for the SI formula.

Total Amount Formula

The Total Amount (A) paid back is the sum of Principal and Interest: A = P + SI = P(1 + RT/100).

Rate and Time Relationship

If the Rate or Time doubles, the Simple Interest also doubles, provided the other variables remain constant.

The correct answer is 96^th.

Key Points

• India ranked 96^th in Transparency International's Corruption Perceptions Index (CPI) for the year 2024.
• The CPI measures perceived corruption in the public sector across 180 countries and territories using expert assessments and opinion surveys.
• Countries are scored on a scale of 0 (highly corrupt) to 100 (very clean); India's score has been improving gradually over the years.
• India’s ranking reflects its ongoing efforts to combat corruption and improve transparency in governance.
• Denmark, Finland, and New Zealand typically top the CPI rankings as the least corrupt countries globally.

Additional Information

• Transparency International:
• An independent, non-governmental organization focused on combating global corruption.
• Founded in 1993, headquartered in Berlin, Germany.
• Publishes the annual Corruption Perceptions Index (CPI) to highlight corruption trends globally.
• Corruption Perceptions Index (CPI):
• Ranks countries based on perceived levels of public sector corruption as scored by experts and businesspeople.
• Uses data sources from organizations like the World Bank, World Economic Forum, and others.
• Higher scores indicate lower levels of corruption; lower scores indicate higher corruption levels.
• India's anti-corruption initiatives:
• Implementation of laws like the Prevention of Corruption Act and the Lokpal Act.
• Promotion of digital governance to reduce bureaucratic corruption.
• Efforts to increase transparency in public procurement and financial transactions.
• Global perspective:
• Countries like Somalia and Syria often rank at the bottom of the CPI due to weak governance and systemic corruption.
• Strong institutions, freedom of press, and public access to information are key factors for higher CPI rankings.

Given series: (Left) 2 8 6 $ 4 * € 1 9 5 # 2 % 4 % © # 5 * 7 % * (Right)

According to the question,

Required condition: Number - Number - Number

(Left) 2 8 6 $ 4 * € 1 9 5 # 2 % 4 % © # 5 * 7 % * (Right)

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

Hence, "Option 4" is the correct answer.

The logic followed here is:

Hence, "Option 3" is the correct answer.

Shortcut Trick

Height of building (H) = 60 m.

Ratio of heights H : (H − h) = tan 60° : tan 30° = √3 : (1/√3) = 3 : 1.

Total height 3 units → 60 m, so 1 unit → 20 m.

Lamp post height (h) = 3 units − 1 unit = 2 units → 2 × 20 = 40 m.

∴ The correct answer is 40 m.

Alternate Method

Given: Height of building AB = 60 m. Let height of lamp post CD = h. Distance BD = x.

Formula Used: tan θ = Perpendicular / Base

⇒ In ΔABD: tan 60° = AB / BD

⇒ √3 = 60 / x

⇒ x = 60 / √3 = 20√3 m

⇒ In small triangle at top (height 60 − h): tan 30° = (60 − h) / x

⇒ 1 / √3 = (60 − h) / (20√3)

⇒ 20√3 / √3 = 60 − h

⇒ 20 = 60 − h

⇒ h = 60 − 20 = 40 m

∴ The correct answer is 40 m.

Additional Information

Angle of Depression

The angle formed between the horizontal line and the line of sight when looking downwards at an object.

Standard Ratios for 30-60-90 Triangles

In a right triangle with angles 30° and 60°, the sides opposite to them are in the ratio 1 : √3 : 2 respectively.

Relationship between two heights

When the distance is same, h = H × (1 − tan θ₁ / tan θ₂) where θ₁ is the top angle and θ₂ is the bottom angle.

Shortcut Trick Ratio of Selling Price (SP) to Cost Price (CP) can be derived from the given condition. 24 × SP = 30 × CP ⇒ SP ÷ CP = 30 ÷ 24 = 5 ÷ 4. Here, CP = 4 units and SP = 5 units. Since SP > CP, it is a gain. Gain = 5 − 4 = 1 unit. Gain% = (Gain ÷ CP) × 100 = (1 ÷ 4) × 100 = 25%. ∴ The correct answer is 25% gain.

Alternate Method Given → SP of 24 books = CP of 30 books. Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100.

⇒ Let the Cost Price of one book be Re. 1. ⇒ Cost Price (CP) of 30 books = Rs. 30. ⇒ Selling Price (SP) of 24 books = CP of 30 books = Rs. 30. ⇒ CP of 24 books = Rs. 24. ⇒ Profit = SP − CP = 30 − 24 = Rs. 6. ⇒ Profit% = (6 ÷ 24) × 100 = 1/4 × 100 = 25%. ∴ The correct answer is 25% gain.

Additional Information Profit and Loss on Article Quantity When the CP of 'x' articles equals the SP of 'y' articles, the Profit or Loss percentage is given by [(x − y) ÷ y] × 100. A positive result indicates profit, and a negative result indicates loss. Cost Price vs Selling Price If SP > CP, it is a Gain. If CP > SP, it is a Loss. Percentages are always calculated on the Cost Price unless stated otherwise.

The correct answer is Euglena.

Key Points

• Euglena is a unique single-celled organism that exhibits both autotrophic and heterotrophic modes of nutrition.
• In the presence of sunlight, Euglena performs photosynthesis using chlorophyll, making it autotrophic.
• In the absence of sunlight, Euglena can obtain nutrition heterotrophically by absorbing organic matter from its environment.
• Euglena belongs to the kingdom Protista and is often studied as an example of a mixotrophic organism.
• This dual nutritional capability enables Euglena to survive in a variety of habitats, making it highly adaptable.

Additional Information

• Autotrophic Nutrition:
• It refers to the mode of nutrition where organisms synthesize their own food using simple inorganic substances like carbon dioxide and water.
• Photosynthesis, using sunlight, is the most common method of autotrophic nutrition.
• Examples include plants, algae, and some bacteria.
• Heterotrophic Nutrition:
• In this mode, organisms depend on other organisms for food.
• Heterotrophs are unable to synthesize their own food and rely on consuming organic matter.
• Examples include animals, fungi, and certain protists like Amoeba.
• Mixotrophic Nutrition:
• Organisms like Euglena that can switch between autotrophic and heterotrophic modes of nutrition exhibit mixotrophic nutrition.
• This ability provides flexibility and survival advantages in fluctuating environmental conditions.
• Kingdom Protista:
• It includes a diverse group of eukaryotic organisms that are primarily unicellular.
• Protists can be autotrophic, heterotrophic, or mixotrophic.
• Examples include Euglena, Amoeba, and Paramecium.

Given: (Left) 194 932 446 225 493 (Right)

According to the question:

First digit of the highest number → 932 → 9

Second digit of the lowest number → 194 → 9

Thus, the resultant if the first digit of the highest number is added to the second digit of the lowest number is → 9 + 9 → 18

Hence, "Option 2" is the correct answer.

Shortcut Trick

For a continued proportion a : b :: b : x, the third proportional is x = b² ÷ a.

x = (40.6 × 40.6) ÷ 2.5

x = 1648.36 ÷ 2.5 = 659.344

∴ The correct answer is 659.344.

Alternate Method

Given:

Ratio 1 = 2.5 : 40.6

Ratio 2 = 40.6 : x

Formula Used:

If a : b :: c : d, then a × d = b × c

Calculations:

⇒ 2.5 ÷ 40.6 = 40.6 ÷ x

⇒ 2.5 × x = 40.6 × 40.6

⇒ 2.5x = 1648.36

⇒ x = 1648.36 ÷ 2.5

⇒ x = 659.344

∴ The correct answer is 659.344.

Additional Information

Fourth Proportional

If four quantities a, b, c, d are in proportion, then d is the fourth proportional where d = (b × c) ÷ a.

Mean Proportional

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

Third Proportional

In a continued proportion a : b :: b : c, c is called the third proportional and c = b² ÷ a.

The correct answer is stress on the environment.

Key Points

• Higher population density in cities increases resource consumption, leading to a strain on natural resources such as water, air, and land.
• Urban areas like Delhi experience elevated levels of air pollution due to increased vehicular emissions and industrial activities.
• Overcrowding and rapid urbanization cause improper waste management and disposal, contributing to environmental degradation.
• High population density results in deforestation and encroachment on green spaces to accommodate housing and infrastructure needs.
• Excessive human activity in densely populated cities disrupts ecological balance, impacting biodiversity and ecosystem services.

Additional Information

• Population Density:
• It refers to the number of people living per unit area, typically measured in persons per square kilometer.
• High population density can lead to increased demand for housing, transportation, and public services.
• Environmental Stress:
• This term denotes the pressure exerted on environmental systems due to human activities.
• Examples include pollution, resource depletion, and habitat destruction.
• Urbanization:
• It is the process by which rural areas transform into urban areas due to migration and infrastructure development.
• Unplanned urbanization often leads to environmental challenges like water scarcity and air pollution.
• Pollution Types:
• Air pollution: Caused by vehicle emissions and industrial activities.
• Water pollution: Results from untreated sewage and industrial discharge.
• Land pollution: Caused by improper waste disposal and deforestation.
• Sustainable Urban Development:
• Focuses on creating eco-friendly cities with efficient waste management, green spaces, and renewable energy usage.
• Encourages practices like rainwater harvesting and reducing carbon footprints.

Shortcut Trick

Let Urvashi's age be U. Ayushi = 2U − 6.

Mohan = 4U and Sanju = Ayushi + 8 = (2U − 6) + 8 = 2U + 2.

Sum of Mohan and Sanju: 4U + 2U + 2 = 50 ⇒ 6U = 48.

U = 48 ÷ 6 = 8 years.

∴ The correct answer is 8 years.

Alternate Method

Given:

2 × Urvashi = Ayushi + 6 ⇒ Ayushi = 2U − 6

Mohan = 4 × Urvashi = 4U

Sanju = Ayushi + 8 = (2U − 6) + 8 = 2U + 2

Calculations:

⇒ Mohan + Sanju = 50

⇒ 4U + (2U + 2) = 50

⇒ 6U + 2 = 50

⇒ 6U = 48

⇒ U = 8

∴ The correct answer is 8 years.

Additional Information

Age Relation Modeling

Express all individuals' ages in terms of a single variable (usually the youngest or the one mentioned most) to reduce the number of equations.

Sum and Difference Properties

The difference between the ages of two people remains constant regardless of the number of years passed or preceding.

Ratio of Ages

If the ratio of ages is given as a:b, their ages can be assumed as ax and bx for calculation purposes.

Given:

Simplify:

Calculation:

$\frac{96}{39}$​(91 + 26) - 103 = $\frac{96}{39}$(117) - 103

⇒ 96 × 3 - 103

⇒ 288 - 103

⇒ 185

∴ The correct answer is option (4).

$\frac{96}{39}$(91 + 26) - 103 = $\frac{96}{39}$(117) - 103

The correct answer is To promote communal harmony after religious violence.

Key Points

• Mahatma Gandhi traveled to Noakhali in 1946 to address the widespread communal violence that erupted between Hindus and Muslims in the region.
• He undertook a "peace mission" to restore harmony and rebuild trust between the communities affected by the riots.
• Gandhi adopted the strategy of walking through the villages of Noakhali, preaching non-violence and communal unity to the people.
• He stayed in the region for several months, undertaking constructive work such as promoting mutual understanding, resolving disputes, and advocating for peaceful coexistence.
• Noakhali became a symbol of Gandhi's commitment to non-violence and communal reconciliation, even in the face of intense societal strife.

Additional Information

• Background of Noakhali Riots:
• The Noakhali riots occurred in October 1946 in Bengal, marked by communal violence primarily targeted at the Hindu community in Muslim-majority areas.
• These riots were part of the larger communal unrest during the pre-Partition period in India, fueled by political and religious tensions.
• Gandhi's Non-Violent Approach:
• Gandhi emphasized the principles of ahimsa (non-violence) and satyagraha (truth force) to resolve conflicts.
• He believed in addressing the root causes of hatred and mistrust through dialogue and personal interaction.
• Key Activities in Noakhali:
• Gandhi conducted prayer meetings, encouraged interfaith dialogue, and engaged in relief efforts for victims of the violence.
• He advocated for women’s safety and empowerment, as many women were victims of violence during the riots.
• Significance of Noakhali Mission:
• Gandhi’s efforts in Noakhali are remembered as a testament to his unwavering commitment to peace and communal harmony.
• It highlighted the importance of grassroots-level engagement in addressing societal conflicts.

The correct answer is Utilising a predefined watermark template from the 'Watermark' gallery.

Key Points

• Predefined watermark templates in MS Word are designed for quick application but offer limited customization options for placement and size.
• These templates allow users to add watermarks like "Confidential," "Draft," or other predefined text, but the precise positioning and scaling are controlled automatically by MS Word.
• Unlike custom image or text watermarks, predefined templates restrict users from making fine-tuned adjustments to placement on the page.
• While predefined templates are convenient for general use, they lack the flexibility required to meet specific formatting or design requirements.
• Using other methods such as custom text, image watermarks, or graphic headers/footers provides greater control over design elements.

Additional Information

• Watermarking in MS Word
• A watermark is a text or image that appears behind the main document content.
• Commonly used for branding, document security, or indicating document status (e.g., "Draft").
• MS Word allows users to apply predefined or custom watermarks through the "Design" tab.
• Custom Picture Watermark
• Allows users to insert images as watermarks.
• Settings like "Scale" and "Washout" can be adjusted for better visual integration with the document.
• Provides flexibility in resizing and positioning the image.
• Custom Text Watermark
• Enables users to input specific text as the watermark.
• Offers options to adjust font, size, color, orientation, and placement.
• Highly customizable compared to predefined templates.
• Using Graphics in Headers/Footers
• Inserting graphics into headers or footers allows users to create custom watermarks.
• Provides full control over image placement, layering, and size.
• Graphics can be positioned behind text for a subtle watermark effect.

Shortcut Trick For a quadratic equation of the form x2 + bx + c = 0 to have equal real roots, the constant term must be the square of half the coefficient of x. Value of k = (Coefficient of x ÷ 2)2 k = (−6 ÷ 2)2 k = (−3)2 = 9 ∴ The correct answer is 9.

Alternate Method Given: Quadratic equation: x2 − 6x + k = 0 Comparing with the standard form ax2 + bx + c = 0: ⇒ a = 1, b = −6, c = k Formula Used: For a quadratic equation to have equal real roots, the discriminant (D) must be equal to zero. ⇒ D = b2 − 4ac = 0 Calculations: ⇒ (−6)2 − 4 × 1 × k = 0 ⇒ 36 − 4k = 0 ⇒ 4k = 36 ⇒ k = 36 ÷ 4 ⇒ k = 9 ∴ The correct answer is 9.

Additional Information Nature of Roots The nature of roots is determined by the Discriminant (D). If D > 0, roots are real and distinct; if D < 0, roots are imaginary; and if D = 0, roots are real and equal. Sum and Product of Roots For a quadratic equation ax2 + bx + c = 0, the Sum of roots is −b/a and the Product of roots is c/a. Quadratic Formula The roots of a quadratic equation can be found using x = [−b ± √(b2 − 4ac)] ÷ 2a.

The logic followed here is:

KG-NJ-PR

And,

MI-PL-RT

So, checking each option one by one:

Option 1) OK-RN-TU

Option 2) PK-RN-TU

Option 3) PK-RM-TU

Option 4) OK-RN-TV

Thus, out of all the options, 'OK-RN-TV' follows the same logic as given.

Hence, "Option 4" is the correct answer.

Given: (Left) 236 758 230 563 263 (Right)

According to the question:

First digit of the lowest number → 236 → 2

First digit of the highest number → 758 → 7

Thus, the resultant if the first digit of the lowest number is subtracted from the first digit of the highest number is → 7 - 2 → 5

Hence, "Option 1" is the correct answer.

The correct answer is Critical advancements in spacecraft and launch vehicle thermal management.

Key Points

• The S. Ramakrishnan Centre of Excellence focuses on cutting-edge research in fluid and thermal sciences, aimed specifically at improving spacecraft and launch vehicle thermal management systems.
• It plays a pivotal role in enhancing the thermal control mechanisms required for space exploration and satellite technology.
• Thermal management in spacecraft is critical to ensure operational efficiency, preventing overheating or freezing in extreme space environments.
• The research conducted at the center supports the development of advanced cooling systems, heat shields, and thermal protection materials for launch vehicles.
• The center collaborates with leading scientists, engineers, and institutions to foster innovation in the field of aerospace thermal management.

Additional Information

• Thermal Management in Spacecraft:
• Spacecraft face extreme temperatures ranging from freezing cold to intense heat, making thermal management systems vital for survival and functionality.
• Techniques include active cooling systems, radiators, heat pipes, and thermal insulation materials.
• Thermal shields prevent damage during re-entry into Earth's atmosphere.
• Fluid and Thermal Science:
• This field focuses on the behavior of fluids and heat transfer mechanisms in various systems, including aerospace applications.
• Research in fluid dynamics helps optimize fuel usage and propulsion systems for launch vehicles.
• Launch Vehicle Technologies:
• Launch vehicles require robust thermal systems to protect sensitive equipment during liftoff and operation.
• Advancements in thermal science improve launch vehicle efficiency, payload capacity, and reliability.
• Applications in Space Exploration:
• Thermal management research benefits satellite technology, interplanetary missions, and human space exploration.
• Improved systems ensure the safety of astronauts and scientific instruments in harsh space conditions.

Shortcut Trick

Sum of first three numbers = (2 × 77) + 128 = 154 + 128 = 282.

Sum of last two numbers = Total Sum − Sum of first three = 655 − 282 = 373.

Average of remaining two = 373 ÷ 2 = 186.5.

∴ The correct answer is 186.5.

Alternate Method

Given:

Total sum of 5 numbers = 655

Average of the first two numbers = 77

Third number = 128

Formula Used:

Sum = Average × Number of observations

Calculations:

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

⇒ Sum of the first three numbers = 154 + 128 = 282

⇒ Sum of the remaining two numbers = Total Sum − Sum of first three numbers

⇒ Sum of the remaining two numbers = 655 − 282 = 373

⇒ Average of the remaining two numbers = 373 ÷ 2

⇒ Average = 186.5

∴ The correct answer is 186.5.

Additional Information

Definition of Average

The arithmetic mean or average is the ratio of the Sum of all observations to the Total number of observations.

Combined Average Formula

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

Sum from Average

To find the total value when the average is known, use the relation: Sum = Average × Count.

The logic followed here is:

​

Hence, "Option 1" is the correct answer.

According to the given information,

Thus, 'O' is coded as '2'.

Hence, "Option 2" is the correct answer.

Shortcut Trick

Stoppage time per hour = (Difference in speed ÷ Faster speed)

Stoppage time per hour = (88 − 24) ÷ 88 = 64 ÷ 88 = 8/11 hours

Total travel time (with stoppages) = Distance ÷ Speed with stoppages = 528 ÷ 24 = 22 hours

Total stoppage time = 22 × (8/11) = 2 × 8 = 16 hours

∴ The correct answer is 16 hours.

Alternate Method

Given:

Average speed without stoppages = 88 km/hr

Average speed with stoppages = 24 km/hr

Total distance = 528 km

Calculations:

⇒ Time taken without stoppages = Distance ÷ Speed = 528 ÷ 88

⇒ Time taken without stoppages = 6 hours

⇒ Time taken with stoppages = Distance ÷ Speed = 528 ÷ 24

⇒ Time taken with stoppages = 22 hours

⇒ Total stoppage time = Time (with stops) − Time (without stops)

⇒ Total stoppage time = 22 − 6 = 16 hours

∴ The correct answer is 16 hours.

Additional Information

Stoppage Time Calculation

The formula for stoppage time per hour is: (S_fast − S_slow) ÷ S_fast. Multiply this by total travel time to get absolute stoppage time.

Average Speed

Average Speed = Total Distance ÷ Total Time. Stoppages reduce the average speed because they increase the total time taken for the same distance.

Relative Speed

When two objects move in the same direction, relative speed is S₁ − S₂. In opposite directions, it is S₁ + S₂.

Decoding signs:

Required resultant: 38

So, checking each option one by one:

Option 1) 32 S 8 R 30 Q 16 P 4 ⇒ 32 - 8 + 30 × 16 ÷ 4

⇒ 32 - 8 + 30 × 16 ÷ 4

⇒ 32 - 8 + 30 × 4

⇒ 32 + 120 - 8

⇒ 152 - 8

⇒ 148

Option 2) 32 R 8 S 30 Q 16 P 4 ⇒ 32 + 8 - 30 × 16 ÷ 4

⇒ 32 + 8 - 30 × 16 ÷ 4

⇒ 32 + 8 - 30 × 4

⇒ 32 + 8 - 120

⇒ 40 - 120

⇒ -80

Option 3) 32 Q 8 R 30 S 16 P 4 ⇒ 32 × 8 + 30 - 16 ÷ 4

⇒ 32 × 8 + 30 - 16 ÷ 4

⇒ 32 × 8 + 30 - 4

⇒ 256 + 30 - 4

⇒ 286 - 4

⇒ 282

Option 4) 32 P 8 S 30 R 16 Q 4 ⇒ 32 ÷ 8 - 30 + 16 × 4

⇒ 32 ÷ 8 - 30 + 16 × 4

⇒ 4 - 30 + 16 × 4

⇒ 4 + 64 - 30

⇒ 68 - 30

⇒ 38

Hence, "Option 4" is the correct answer.

Shortcut Trick

Remaining 25% of salary covers conveyance, grocery, and savings.

25% of Salary = ₹653 + ₹6,229 + ₹446 = ₹7,328

Total Salary (100%) = 4 × ₹7,328 = ₹29,312

∴ The correct answer is ₹29,312.

Alternate Method

Given House Rent = 75% of Salary

Given Conveyance = ₹653, Grocery = ₹6,229, Savings = ₹446

⇒ Let total monthly salary be S.

⇒ Total spending other than rent + Savings = 100% − 75% = 25% of S

⇒ 25% of S = 653 + 6229 + 446

⇒ (25/100) × S = 7328

⇒ S/4 = 7328

⇒ S = 7328 × 4

⇒ S = 29312

∴ The correct answer is ₹29,312.

Additional Information

Percentage Expenditure

Total Salary is always considered 100%. If X% is spent, then (100 − X)% is the remaining amount which equals the sum of all other expenses and savings.

Successive Percentage

If the question mentions 'spending X% of the remaining amount', apply the formula: Remaining = Total × (100 − r₁)/100 × (100 − r₂)/100.

Basic Salary Formula

Income = Total Expenditure + Savings. All individual expense components must be summed to find total expenditure.

The correct answer is Deleting a row or column that contains cells referenced by a formula in another worksheet.

Key Points

• The '#REF!' error in Excel occurs when a formula attempts to reference a cell that is no longer valid, often due to deletion of rows or columns.
• Deleting rows, columns, or worksheets containing referenced cells in formulas can break the link and result in a '#REF!' error.
• This error indicates the formula is unable to locate the cell or range it was previously referencing.
• To avoid this error, ensure that any referenced cells or ranges are not deleted or moved while formulas depend on them.
• Users can troubleshoot the error by reviewing the formula and updating the references to valid cells or ranges.

Additional Information

• '#REF!' Error:
• It is one of the most common error messages in Excel, signaling invalid cell references.
• Occurs when referenced cells or ranges in a formula are deleted or removed.
• Can also occur when trying to use a formula referencing another workbook that has been closed or moved.
• Other Common Excel Errors:
• #DIV/0!: Appears when attempting to divide by zero or an empty cell.
• #VALUE!: Indicates incorrect data types used in a formula.
• #NAME?: Occurs when Excel cannot recognize a text string as a valid name or function.
• #NUM!: Signals invalid numeric inputs or computations that exceed Excel's capabilities.
• Preventing Errors:
• Always verify cell references in formulas before deleting rows, columns, or worksheets.
• Use named ranges or structured references to minimize issues caused by cell movements.
• Regularly audit formulas when performing data modifications to avoid breaking dependencies.
• Excel Formula Limits:
• Excel formulas can have up to 8,192 characters, but exceeding this limit does not result in a '#REF!' error.
• Excel supports up to 255 arguments in a single formula.

The correct answer is Government of India Act, 1858.

Key Points

• The Government of India Act, 1858 marked the end of the East India Company’s rule and transferred the administration of India directly to the British Crown.
• The act established the position of a Secretary of State for India, who was responsible for overseeing Indian affairs in Britain.
• It introduced the Council of India to assist the Secretary of State, comprising 15 members, mainly former directors of the East India Company.
• This act formally ended the dual governance system and centralized power under the British government, following the failure of the East India Company during the 1857 Revolt.
• The Governor-General of India was renamed as Viceroy of India, representing the Crown directly in India.

Additional Information

• Charter Act, 1833
• This act centralized legislative powers in India by establishing a single legislative council for all British territories in India.
• It marked the end of the East India Company's trading rights and made it an administrative body.
• It introduced the idea of an open competition for civil services, but the provision was not implemented until later.
• Regulating Act, 1773
• This was the first attempt by the British government to regulate the affairs of the East India Company in India.
• It established a Governor-General in Bengal and created a Supreme Court at Fort William, Kolkata.
• The act aimed to curb corruption and mismanagement but had limited success.
• Pitt's India Act, 1784
• This act introduced the concept of dual control between the British government and the East India Company.
• It created a Board of Control to supervise civil, military, and revenue administration in India.
• The act aimed to address issues of governance after the shortcomings of the Regulating Act.
• Indian Rebellion of 1857
• The widespread uprising against British rule revealed the flaws in the East India Company's administrative structure.
• It directly led to the implementation of the Government of India Act, 1858, which centralized power under the Crown.
• The rebellion is considered one of the most significant events in Indian history, leading to the dissolution of the East India Company.

Shortcut Trick

Sum of two supplementary angles = 180°

Difference between the angles = 62°

Smaller angle = (Sum − Difference) ÷ 2

Smaller angle = (180° − 62°) ÷ 2 = 118° ÷ 2 = 59°

∴ The correct answer is 59°.

Alternate Method

Given:

Larger angle = Smaller angle + 62°

Sum of supplementary angles = 180°

Formula Used:

If two angles are supplementary, their sum is 180°.

Calculations:

⇒ Let the smaller angle be x.

⇒ Then the larger angle = x + 62°.

⇒ Since they are supplementary, x + (x + 62°) = 180°

⇒ 2x + 62° = 180°

⇒ 2x = 180° − 62°

⇒ 2x = 118°

⇒ x = 59°

∴ The correct answer is 59°.

Additional Information

The correct answer is S-shaped wave.

Key Points

• A sinusoidal wave signal completes one cycle in a characteristic smooth, oscillatory motion resembling an S-shaped curve.
• Sinusoidal waves are represented mathematically as y = A sin(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase.
• The wave transitions smoothly between its maximum and minimum values, creating a symmetrical S-shape over one complete cycle.
• Sinusoidal waves are fundamental in physics, engineering, and mathematics due to their periodic and harmonic nature.
• Such waves are commonly used in AC electrical signals, sound waves, and other oscillatory systems.

Additional Information

• Amplitude:
• The maximum displacement of the wave from its mean position.
• Represents the strength or intensity of the wave.
• Frequency:
• The number of cycles completed per second, measured in Hertz (Hz).
• Higher frequency corresponds to faster oscillations.
• Phase:
• Defines the offset of the wave relative to a reference point.
• Critical for understanding wave interference and synchronization.
• Applications of Sinusoidal Waves:
• Used in alternating current (AC) electricity supply systems.
• Fundamental to sound wave analysis and signal processing.
• Critical in studying harmonic motion in physics and engineering.
• Wave Equation:
• A sinusoidal wave can be expressed as y = A sin(2πft + φ).
• This equation helps model real-world oscillatory phenomena.

Shortcut Trick

When two parallel lines are intersected by a transversal, the corresponding angles are always equal.

Given: One corresponding angle = 75°

∴ The other corresponding angle = 75°.

∴ The correct answer is 75°.

Alternate Method

Given:

Lines L₁ ∥ L₂

Transversal line T cuts L₁ and L₂.

Measure of one corresponding angle = 75°

Formula Used:

For parallel lines, the Corresponding Angles Postulate states that corresponding angles are congruent (equal).

Calculations:

Let the two corresponding angles be ∠1 and ∠2.

⇒ ∠1 = 75°

⇒ Since L₁ ∥ L₂, ∠1 = ∠2 (Corresponding angles property)

⇒ ∠2 = 75°

∴ The correct answer is 75°.

Additional Information

Alternate Interior Angles

Angles on opposite sides of the transversal and between the parallel lines are always equal.

Given: 

Mukesh starts from point A and drives 9 km towards the north.

He then takes a right turn, drives 7 km, turns right and drives 10 km.

He then takes a right turn and drives 8 km.

He takes a final right turn, drives 1 km and stops at point P.

Thus, Mukesh should drive 1 km (8 km - 7 km) in the east direction in order to reach Point A again.

Hence, "Option 3" is the correct answer.

Shortcut Trick

Assume an average of 35 (approximate middle value).

Calculate deviations: (14−35), (16−35), (27−35), (31−35), (39−35), (44−35), (51−35), (58−35)

Deviations: −21, −19, −8, −4, +4, +9, +16, +23

Sum of deviations = −52 + 52 = 0

Since the net deviation is 0, the assumed average is the correct average.

∴ The correct answer is 35.

Alternate Method

Given: Numbers = 14, 16, 27, 31, 39, 44, 51, 58

Formula Used: Average = Sum of all observations ÷ Total number of observations

Calculations:

⇒ Sum = 14 + 16 + 27 + 31 + 39 + 44 + 51 + 58

⇒ Sum = 30 + 58 + 83 + 109 = 280

⇒ Total number of observations (n) = 8

⇒ Average = 280 ÷ 8

⇒ Average = 35

∴ The correct answer is 35.

Additional Information

Arithmetic Mean

The arithmetic mean of a set of data is the sum of all values divided by the total count of values.

Deviation Method for Average

Average = Assumed Mean + (Sum of Deviations ÷ Total Count). This is useful for large numbers.

Weighted Average

When different values have different importance (weights), use Average = (w₁x₁ + w₂x₂ + ...) ÷ (w₁ + w₂ + ...).

Average of Consecutive Numbers

For numbers in Arithmetic Progression (AP), Average = (First Term + Last Term) ÷ 2.

The correct answer is 72.

Key Points

• In Carnatic music, there are 72 Melakarta ragas, which are also called parent or fundamental ragas.
• The Melakarta system is a comprehensive framework for classifying all possible ragas based on specific scales.
• Each Melakarta raga consists of seven swaras (notes): Sa, Ri, Ga, Ma, Pa, Da, Ni, in ascending (Arohana) and descending (Avarohana) order.
• The 72 Melakarta ragas are divided into 12 chakras (groups), each containing six ragas.
• These Melakarta ragas serve as a foundation for deriving Janya ragas, which are more specific and commonly used in compositions.

Additional Information

• Melakarta Ragas:
• Each Melakarta raga must have all seven swaras (notes) in both ascending (Arohana) and descending (Avarohana) scales.
• They strictly follow the rules of Carnatic music theory, such as having a fixed set of intervals between notes.
• Chakras in Melakarta System:
• The 72 Melakarta ragas are grouped into 12 chakras (sets), each named after a specific concept (e.g., Indu, Netra, Agni).
• Each chakra contains six Melakarta ragas, differentiated by variations in the Ri, Ga, Da, and Ni swaras.
• Janya Ragas:
• Janya ragas are derived from Melakarta ragas and may include fewer than seven swaras or employ irregular note patterns.
• They are more commonly used in Carnatic compositions and improvisations.
• Swaras in Carnatic Music:
• The seven basic swaras are: Shadja (Sa), Rishabha (Ri), Gandhara (Ga), Madhyama (Ma), Panchama (Pa), Dhaivata (Da), and Nishada (Ni).
• Each swara has variants (e.g., Shuddha, Chatushruti, Antara) that define the raga's scale.

Given: Seven boxes, D, E, F, G, S, T and U, are kept one over the other but not necessarily in the same order. 

1) Only three boxes are kept below D.

2) Only G is kept above T.

3) Only two boxes are kept between D and U.

4) E is kept at some place below F and at some place above S. 

Thus, S box is kept at second position from the bottom.

Hence, "Option 2" is the correct answer.

Shortcut Trick

Use the ratio relationship between Cost Price (CP) and Marked Price (MP).

Formula: CP ÷ MP = (100 − D%) ÷ (100 + P%)

Let CP be 100. Then MP = 100 + 34 = 134.

100 ÷ 134 = (100 − D) ÷ (100 + 10)

100 ÷ 134 = (100 − D) ÷ 110 ⇒ 11000 = 13400 − 134D

134D = 2400 ⇒ D = 2400 ÷ 134 ≈ 17.91%

∴ The correct answer is 17.91%.

Alternate Method

Given → Marked Price (MP) = ₹578, Markup% = 34%, Profit% = 10%.

Formulas: CP = MP ÷ (1 + Markup%) | SP = CP × (1 + Profit%) | Discount% = (MP − SP) ÷ MP × 100

⇒ Step 1: Find CP. MP = 134% of CP ⇒ 578 = 1.34 × CP ⇒ CP = 578 ÷ 1.34 ≈ ₹431.34

⇒ Step 2: Find Selling Price (SP) for 10% profit. SP = 431.34 × 1.10 ≈ ₹474.47

⇒ Step 3: Calculate Discount. Discount = MP − SP = 578 − 474.47 = ₹103.53

⇒ Step 4: Discount Percentage = (103.53 ÷ 578) × 100 ≈ 17.9117%

∴ The correct answer is 17.91%.

Additional Information

Marked Price and Discount

Marked Price (MP) is the price printed on an item. Discount is always calculated on the MP to arrive at the Selling Price (SP). Formula: SP = MP × (100 − D%) ÷ 100.

CP-MP Relationship

The direct link between Cost Price and Marked Price bypassing SP calculation is given by: MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

Given series: 4917523

According to the question, arranged in ascending order from left to right:

4917523 → 1234579

Digits that will be third from the left end in the new number thus formed is → 1234579 → 3

Hence, "Option 1" is the correct answer.

According to the given information,

Thus, 'F' is coded as '1'.

Hence, "Option 1" is the correct answer.

Shortcut Trick

Let the assumed mean (A) be 22.

Calculate deviations (d_i = x_i − 22):

∑f_id_i = 98×(−10) + 74×0 + 17×36 + 28×57 + 44×67 = −980 + 0 + 612 + 1596 + 2948 = 4176

Total frequency (N) = 98 + 74 + 17 + 28 + 44 = 261

Actual Mean = A + (∑f_id_i ÷ N) = 22 + (4176 ÷ 261) = 22 + 16 = 38

∴ The correct answer is 38.

Alternate Method

Given:

Marks (x_i) and Number of Students (f_i).

Formula Used:

Mean = ∑(f_i × x_i) ÷ ∑f_i

Let us calculate the sum of the products of marks and number of students (∑f_ix_i):

⇒ 12 × 98 = 1176

⇒ 22 × 74 = 1628

⇒ 58 × 17 = 986

⇒ 79 × 28 = 2212

⇒ 89 × 44 = 3916

⇒ Total sum (∑f_ix_i) = 1176 + 1628 + 986 + 2212 + 3916 = 9918

⇒ Total number of students (∑f_i) = 98 + 74 + 17 + 28 + 44 = 261

⇒ Mean = ∑f_ix_i ÷ ∑f_i

⇒ Mean = 9918 ÷ 261 = 38

Why other options are incorrect:

⇒ Option (1) 53: This value is much higher than the actual weighted average because the majority of students (172 out of 261) scored lower marks (12 and 22).

⇒ Option (2) 22: This is one of the individual marks, not the overall mean of the entire distribution.

⇒ Option (4) 60: This value is incorrect as it does not represent the correct ratio of total marks to total students.

∴ The correct answer is 38.

Additional Information

Arithmetic Mean for Grouped Data

The mean of a grouped frequency distribution can be calculated using the direct method: Mean = ∑f_ix_i ÷ ∑f_i, where x_i is the class mark or individual value and f_i is the frequency.

Assumed Mean Method

This method simplifies calculations by choosing an arbitrary value 'A' as the assumed mean. The formula is Mean = A + ∑f_id_i ÷ ∑f_i, where d_i = x_i − A.

Step-Deviation Method

When class intervals are of equal width 'h', calculations can be further simplified using u_i = (x_i − A) ÷ h. The formula is Mean = A + h × (∑f_iu_i ÷ ∑f_i).

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

Conclusions:

(I) Some keys are doors → Does not follow (As all keys are doors. As whole keys comes in doors, therefore it is true.)

(II) All doors are cupboards → Follow (As all keys are doors and some doors are cupboards. So it is possible but not definite.)

∴ Here, Only conclusion (I) follows.​

Hence, the correct answer is "Option 4".

The logic followed here:

6 is related to 42 → 6 × 7 = 42

And,

4 is related to 28 → 4 × 7 = 28

Similarly,

7 is related to→ 7 × 7 = 49

Hence, "Option 2" is the correct answer.

The correct answer is First-Come, First-Served (FCFS).

Key Points

• FCFS is a non-preemptive scheduling algorithm where processes are executed in the order they arrive in the ready queue.
• This algorithm suffers from the convoy effect, where longer processes delay the execution of shorter ones, leading to inefficiency.
• Convoy effect occurs because FCFS does not consider the burst time of processes, causing an imbalance in CPU utilization.
• It is simple to implement but performs poorly in environments with a mix of long and short processes.
• In scenarios where a long process occupies the CPU, other processes must wait, leading to higher average waiting time and reduced throughput.

Additional Information

• Convoy Effect
• It is a situation in CPU scheduling where short processes get delayed due to a longer process occupying the CPU.
• It leads to increased waiting time, reduced throughput, and inefficient CPU utilization.
• Other Scheduling Algorithms
• Priority Scheduling (non-preemptive): Prioritizes processes based on a given priority, which can prevent convoy effect but may lead to starvation of lower-priority processes.
• Shortest Job First (SJF): Executes processes with the shortest burst time first, minimizing average waiting time and avoiding convoy effect in most cases.
• Round Robin: Uses a time quantum to ensure fair CPU allocation, effectively reducing the chances of convoy effect.
• Preemptive vs Non-Preemptive Scheduling
• Preemptive Scheduling: Allows the CPU to be taken away from a running process to execute a higher-priority or shorter process.
• Non-Preemptive Scheduling: Once a process starts execution, it runs to completion without interruption.
• Metrics for Evaluating Scheduling Algorithms
• Turnaround Time: Total time taken from process submission to completion.
• Waiting Time: Total time a process spends in the ready queue.
• Throughput: Number of processes completed per unit of time.
• CPU Utilization: Percentage of time the CPU remains active.