DSSSB LDC (Jr. Assistant/Steno/LDC): (11 Oct 2025) Memory-Based Paper (Previous Year Paper)

The correct answer is ₹5 lakh per year.

In News

• The Ayushman Bharat Vay Vandana Scheme was launched in Puducherry to provide health benefits for senior citizens.
• Puducherry Lieutenant Governor K. Kailashnathan and Chief Minister N. Rangasamy inaugurated the scheme.
• The scheme provides free health insurance coverage of up to ₹5 lakh per year for senior citizens aged 70 and above.
• Eligible senior citizens were issued insurance scheme cards during the launch event.

Key Points

• The scheme aims to offer financial protection for medical expenses of senior citizens.
• It is a centrally sponsored scheme under the Ayushman Bharat initiative.
• Senior citizens aged 70 and above are eligible for the scheme.
• Healthcare workers have been urged to increase awareness so that more people can benefit.

Additional Information

• Ayushman Bharat Yojana
• Also known as Pradhan Mantri Jan Arogya Yojana (PM-JAY).
• Provides ₹5 lakh per family per year for secondary and tertiary healthcare.
• Targets economically weaker sections (EWS) and vulnerable groups.
• Ayushman Bharat Vay Vandana Scheme
• Specifically designed for senior citizens aged 70 and above.
• Offers free healthcare coverage up to ₹5 lakh per year.
• Implemented under public-private partnerships with hospitals.
• Puducherry's Role in Health Initiatives
• First Union Territory to implement Ayushman Bharat Vay Vandana Scheme.
• Has been proactive in launching senior citizen-friendly healthcare programs.
• Government officials encourage widespread awareness and enrollment.
• Health Insurance Benefits for Senior Citizens
• Coverage includes hospitalization, medical treatments, and critical illnesses.
• Designed to reduce out-of-pocket expenses for the elderly.
• Aims to ensure better healthcare access and financial security.

The correct answer is Article 243A

Key Points

• The Article of the Indian Constitution related to the Gram Sabha is Article 243A.
• This article defines the composition and powers of the Gram Sabha, which is the assembly of the villagers in a Panchayati Raj system at the village level.
• It empowers the Gram Sabha to approve plans for economic development and social justice, and it has the authority to make recommendations to the Panchayat regarding the implementation of these plans.

Additional Information

• Article 244A:
• It provides for the establishment of Autonomous District Councils in certain areas of Assam and Manipur, allowing these councils to have legislative, administrative, and financial powers to address the unique needs of the local populace.
• Article 245B:
• It grants the Parliament the power to make laws for the Union Territories and empowers the Legislative Assembly of a Union Territory to make laws for the areas under its jurisdiction, provided such laws do not conflict with the existing central laws.
• Article 242B:
• It is not a valid article in the Indian Constitution; however, Article 242 pertains to the establishment of Panchayats in Scheduled Areas and outlines the applicability of provisions of Part IX of the Constitution to these areas.

The correct answer is Radon.

1. Radioactivity is a nuclear phenomenon in which an unstable nucleus undergoes decay and is referred to as radioactive decay.
2. Three types of radioactive decay occur in nature : (i) α-decay (ii) β-decay (iii) γ-decay
3. Noble Gases
4. There are six elements in Group 18 of the Periodic Table - Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr) , Xenon (Xe) and Radon (Rn) which were earlier termed as inert gases or rare gases.
5. Both of these terms are now no longer used as they are not so rare and not completely inactive. They do show some chemical reactivity in the form of some xenon and krypton compounds and hence are termed as noble gases.
6. Occurrence
7. All the noble gases except Radon occur in the atmosphere. Xenon and radon are the rarest elements of the group.
8. Radon is a radioactive element. Radon (²²²Rn) is a decay product of Radium (²²⁶Ra) and is obtained by pumping off the gas from radium chloride solutions.
9. They are the minor constituent of the air, the atmospheric abundance being ~ 1% by volume of which argon is the major constituent. Ne, Ar, Xe and Kr are obtained by fractional distillation of liquid air.
10. Helium and sometimes neon is found in minerals of radioactive origin e.g., pitchblende, monazite, cleveite. The main commercial source of helium is natural gas to an extent of 2-7%.
11. They have closed valence shell electronic configuration due to which they have the least tendency to react.
12. The best-characterised compounds are those of xenon with fluorine and oxygen only under certain conditions and only with highly electronegative fluorine and oxygen.
13. Uses: These gases have several uses. Argon is used to provide an inert atmosphere, helium is used in filling balloons for meteorological observations, neon is used in discharge tubes and fluorescent bulbs.

The correct answer is 'Aurangzeb'.

Key PointsMoti Masjid

• The Moti Masjid is a white marble mosque inside the Red Fort complex in Delhi, India.
• It is located to the west of the Hammam and close to the Diwan-i-Khas.
• It was built by the Mughal emperor Aurangzeb from 1659 to 1660.
• He built it for his 2nd wife Nawab Bai.

Thus, the correct answer is Aurangzeb.

Important PointsLet's have a look at other options:

The correct answer is Consumer price index.

Key Points

• Many developing countries use changes in the consumer price index (CPI) as their central measure of inflation.
• In India, CPI (combined) is declared as the new standard for measuring inflation (April 2014).
• CPI numbers are typically measured monthly, and with a significant lag, making them unsuitable for policy use.
• Inflation is the measured surge in the average prices of goods and services over a longer period in the economy.
• It is a macro term in which the impact of inflation on a large basket of goods is seen.
• As the value of money is decreased, the cumulative impact of inflation is reported as the buying power of money is reduced.

Important Points

• A wholesale price index (WPI) is an index that measures and monitors changes in the price of goods at stages prior to the retail level. This applies to goods sold in bulk and exchanged between companies or companies (instead of between consumers).
• The Consumer Price Index (CPI) is a metric examining the weighted average of consumer goods and services basket prices such as transport, food and medical care.

The correct answer is Western Ghats.

• India receives rainfall from two monsoons:
• South-West Monsoon
• North-East Monsoon

Key Points

• South West Monsoon is a major one that occurs from July -September.
• The majority of Indian states receive the rainfall from this Monsoon.
• Rain hits first the state of Kerala and along with the coastal areas of Karnataka/Maharastra ( Konken coastal area).
• After it gains momentum it crosses the Western ghats and causes downpours in all other states of India.
• North-East Monsoon mostly starts at end of September.
• This monsoon wind gets obstructed by Eastern ghats and downpours at the eastern coastal area (Coramendal Cost) along with Andra Pradesh and Tamil Nadu.
• The coastal area of Andra Pradesh and the majority of Tamil Nadu receives most of the rainfall from this Monsoon.

Additional Information

• In- between the area of Western and Eastern ghats called Deccan Plateau (dry area) receives very little rainfall from both Monsoons.

The correct answer is 2001

Key Points

• Lata Mangeshkar was awarded the Bharat Ratna in 2001.
• The Bharat Ratna is India's highest civilian honour.
• Lata Mangeshkar was an Indian playback singer and songwriter who recorded songs in over 36 Indian languages and a few foreign languages.
• She was known as the "Queen of Melody," "Nightingale of India," and "Voice of the Millennium".
• She received many other awards and honours, including: 
• Padma Bhushan: 1969
• Dadasaheb Phalke Award: 1989
• Padma Vibhushan: 1999
• One Time Award for Lifetime Achievement: 2008
• Officer of the National Order of the Legion of Honour: 2007
• Lata Mangeshkar was born on September 28, 1929 in Indore, India and died on February 6, 2022.
• She was the second female singer to receive the Bharat Ratna, after M. S. Subbulakshmi.

The correct answer is "14 years".

Key Points

• No kid under the age of fourteen may be employed to work in a factory, mine, or in any other hazardous occupation, according to Article 24.
• Children under the age of 14 are never allowed to work in any dangerous jobs, factories, or mines, per this article.
• Children may, however, be employed in non-hazardous jobs.

Additional Information

• Article 23(1): Traffic in human beings and the beggar and other similar forms of forced labour are prohibited and any contravention of this provision shall be an offence punishable in accordance with the law.
• Article 23(2): Nothing in this article shall prevent the State from imposing compulsory service for public purposes, and in imposing such service the State shall not make any discrimination on grounds only of religion, race, caste or class or any of them.

The correct answer is Option 3.

Key Points

• The oldest stock exchange in India is the Bombay Stock Exchange (BSE), also known as the Stock Exchange, Mumbai.
• It was established in 1875 and is the oldest stock exchange in Asia.
• The BSE is located in Mumbai, Maharashtra, and has played a significant role in the development and growth of the Indian capital market.

Additional Information

• The Multi-Commodity Exchange of India Ltd. (MCX) is not the oldest stock exchange in India.
• It is actually a commodity derivatives exchange rather than a stock exchange.
• MCX was established in 2003 and is headquartered in Mumbai, India.
• It primarily facilitates trading in commodity futures contracts, including gold, silver, crude oil, natural gas, agricultural commodities, and more.
• MCX provides a platform for market participants to trade and hedge their price risks in various commodities.
• The National Commodity and Derivatives Exchange (NCDEX) is not the oldest stock exchange in India either.
• It is another commodity derivatives exchange operating in India.
• NCDEX was established in 2003 and is headquartered in Mumbai, India.
• It focuses on facilitating trading in agricultural commodities, such as wheat, rice, maize, soybean, cotton, etc.
• NCDEX provides a platform for market participants, including farmers, traders, and processors, to trade and hedge their price risks in agricultural commodities.
• The National Stock Exchange (NSE) is not the oldest stock exchange in India, but it is one of the major stock exchanges in the country.
• The NSE was established in 1992 and is headquartered in Mumbai, Maharashtra.
• It is a leading stock exchange in India and provides a platform for trading various financial instruments, including equities, derivatives, and exchange-traded funds (ETFs).
• The NSE has played a crucial role in the modernization and development of the Indian capital market and is known for its advanced trading technology and extensive market reach.

• Green and yellow vegetables in our diet mostly provide us Potassium as food.
• Symptoms of Potassium deficiency include weakness and fatigue, muscle cramps, muscle aches and stiffness, tingles and numbness, heart palpitations, breathing difficulties, digestive symptoms, and mood changes.
• Potassium element is rich in foods such as beet greens, yams, white beans, clams, white potatoes, sweet potatoes, avocado, pinto beans, and bananas.

The correct answer is Bahai.

Key PointsLotus Temple

• The Lotus Temple is located in Delhi, India.
• It is a Bahai House of Worship.
• It was dedicated in December 1986.
• Notable for its flowerlike shape, it has become a prominent attraction in the city.
• The building is composed of 27 free-standing marble-clad "petals" arranged in clusters of three to form nine sides with nine doors opening onto a central hall with a height of slightly over 34 meters.
• It has a capacity of 1,300 people.
• The Lotus Temple has won numerous architectural awards.

Additional Information

The correct answer is SEBI.

Key Points

• The Securities and Exchange Board of India (SEBI) was given statutory powers on 30 January 1992 through the SEBI Act, 1992.
• SEBI was initially established as a non-statutory body in 1988 and later got statutory powers to regulate the securities market in India.
• The primary objective of SEBI is to protect the interests of investors in securities and to promote and regulate the securities market.
• SEBI's functions include regulating stock exchanges and other securities markets, registering and regulating the working of intermediaries, and prohibiting fraudulent and unfair trade practices.
• SEBI has the authority to conduct inspections, audits, and investigations to ensure compliance with regulations.

Additional Information

• Role of SEBI:
• Regulating the business in stock exchanges and other securities markets.
• Registering and regulating the working of various intermediaries like brokers, merchant bankers, and portfolio managers.
• Prohibiting insider trading and regulating substantial acquisition of shares and takeovers of companies.
• Promoting and regulating self-regulatory organizations.
• Objectives of SEBI:
• To protect the interests of investors in securities.
• To promote the development of and to regulate the securities market.
• To ensure fair practices in the securities market and protect investors from fraudulent activities.
• Key Functions of SEBI:
• Regulatory functions such as imposing penalties and taking actions against market violations.
• Developmental functions aimed at promoting and improving the securities market.
• Investor protection functions including educating and informing investors about their rights and market conditions.
• SEBI's Structure:
• SEBI consists of a Chairman appointed by the Government of India, two members from the Ministry of Finance, one member from the Reserve Bank of India, and five other members out of which at least three shall be whole-time members.
• SEBI's headquarters is located in Mumbai, and it has regional offices in New Delhi, Kolkata, Chennai, and Ahmedabad.

The correct answer is Anusandhan National Research Foundation (ANRF)

In News

• J. C. Bose Grant (JBG): A research funding initiative by Anusandhan National Research Foundation (ANRF) aimed at supporting senior Indian scientists and engineers in advancing research.

Key Points

• Launched by: ANRF, the apex body guiding scientific research and innovation in India.
• Purpose: To foster high-quality research and technological innovations across multiple domains, offering extramural funding.
• Eligibility: Senior Indian scientists holding Professor-level positions (or equivalent) at recognized institutions with demonstrated research excellence (publications, patents, awards).
• Grant Details:
• Funding: ₹25 lakh per year for 5 years for research.
• Institutional Support: ₹1 lakh/year to the institution hosting the researcher.
• Multi-Disciplinary Scope: Supports research in science, technology, agriculture, medicine, humanities, and social sciences at the S&T interfaces.
• Superannuation Clause: Grant continues if the Principal Investigator (PI) retires, and the institution retains them.
• Goal: To enhance India’s R&D ecosystem, strengthening research infrastructure and promoting innovation in science and technology.

The correct answer is PM-AASHA

In News

• The Government of India has approved the continuation of the Pradhan Mantri Annadata Aay Sanrakshan Abhiyan (PM-AASHA) Scheme during the 15th Finance Commission Cycle until 2025-26.

Key Points

• The PM-AASHA Scheme aims to provide remunerative prices to farmers and control price volatility of essential commodities to ensure affordable prices for consumers.
• Under the Price Support Scheme (PSS) of PM-AASHA, pulses, oilseeds, and copra are procured by Central Nodal Agencies (CNAs) from pre-registered farmers through state agencies, conforming to Fair Average Quality (FAQ) standards.
• The Government will procure 100% of the Tur, Urad, and Masur production from states for the 2024-25 procurement year.
• Procurement of Tur, Urad, and Masur will continue for the next four years, aiming for self-sufficiency in pulses.
• Union Minister Shri Shivraj Singh Chouhan approved the procurement of Tur (Arhar) under PSS for the Kharif 2024-25 season in 9 states: Andhra Pradesh, Chhattisgarh, Gujarat, Haryana, Karnataka, Madhya Pradesh, Maharashtra, Telangana, and Uttar Pradesh.
• A total of 13.22 LMT of Tur (Arhar) will be procured, benefiting farmers in these states.
• Procurement has already started in Andhra Pradesh, Karnataka, Maharashtra, and Telangana, with 0.15 LMT of Tur procured till 15.02.2025, benefiting 12,006 farmers.
• The central nodal agencies (NAFED and NCCF) are committed to purchasing 100% of Tur produced

The correct answer is Rayon

• Rayon is obtained from the wood pulp.
• Rayon is a regenerated cellulose fiber.
• It is made from natural sources such as wood and agricultural products.
• There are two types of man-made fibers.
• Synthetic fibers: Synthetic fibers are made only from polymers found in natural gas and the by-products of petroleum. Examples: Nylon, Acrylics, Polyurethane, and Polypropylene
• Regenerated fibers: Regenerated fibers are made from cellulose polymers that occur naturally in plants such as cotton, wool, hemp, and flax.  Examples: Rayon and Acetate.

The correct answer is Narsimha Rao.

Key Points

• PV Narsimha Rao was the 9th Prime Minister of India (1991-1996).
• He is also referred to as “Chanakya of Modern India” for his ability to get legislation passed even while heading a minority government.
• The duo of PV Narsimha Rao and Manmohan Singh led the Economic reforms of 1991 and saved India from an Economic crisis.
• Under his leadership, India adopted LPG reforms (Liberalisation, Privatisation, and Globalisation).
• For his economic reforms, he is also called the “Father of Indian Economic Reforms”.

​​

Additional Information

• Economic liberalization simply refers to the elimination of any restraints or restrictions in the economy to ensure economic growth and development.
• Dr. Manmohan Singh is called the pioneer of the liberalization of the Indian Economy.
• He was the Finance Minister of India in 1991.
• The Government announced the new Industrial Policy whereby it:
• Delicensed most industries
• Reduced import tariffs
• Opened doors for foreign direct investment and
• Introduced a market-determined exchange rate system.

The Correct answer is Highest run scorer in the league.

Key Points

• The Orange Cap is awarded to the highest run scorer in a single season of the Indian Premier League (IPL).
• Introduced in the inaugural season of IPL in 2008, the Orange Cap symbolizes the batting excellence of a player throughout the league.
• The player who has scored the most runs wears the Orange Cap on the field during matches, and the final holder of the cap is announced at the end of the season.
• If two or more players score the same number of runs, the award is given to the player with the higher strike rate.
• Some notable players who have won the Orange Cap include Chris Gayle, David Warner, Virat Kohli, and KL Rahul.
• The Orange Cap is an incentive for players to perform consistently and contribute significantly to their team’s performance.
• This recognition enhances the profile of the winning player and demonstrates their role as a key contributor to the league.

Additional Information

• Youngest player of the league
• While the IPL does not have a specific award for the youngest player, it often highlights young talent through its Emerging Player Award.
• The youngest players in IPL history, such as Prayas Ray Barman and Noor Ahmad, have gained significant attention for their skills and potential.
• Emerging player of the league
• This award is given to a young player who has shown exceptional talent and promise during the tournament.
• Criteria for this award include being under the age of 25, having played fewer than five Test matches, and not having been part of more than two IPL seasons.
• Highest wicket taker in the league
• The highest wicket taker in the IPL is awarded the Purple Cap, which is equivalent to the Orange Cap for bowlers.
• Players like Lasith Malinga, Dwayne Bravo, and Bhuvneshwar Kumar have held the Purple Cap in previous seasons.

Correct Answer: Padma Vibhushan Shri Atal Bihari Vajpayee

Rationale:

• The book "Shakti se Shanti" was authored by Shri Atal Bihari Vajpayee, one of India's most iconic political leaders, statesmen, and poets. Known for his eloquence and literary prowess, Vajpayee has contributed significantly to Indian literature, particularly through his poetic works.
• "Shakti se Shanti" reflects his deep philosophical insights and his thoughts on achieving peace through strength. The book encapsulates his vision of India's role in promoting peace while maintaining a robust defense mechanism.
• Atal Bihari Vajpayee's literary contributions often blend his political ideology with poetic expressions, making his works both intellectually enriching and emotionally impactful.
• He received several honors during his lifetime, including the Padma Vibhushan, India's second-highest civilian award, for his unparalleled contributions to the nation in politics, governance, and literature.

Explanation of Other Options:

Shri Narendra Damodardas Modi

• Rationale: Narendra Modi, the current Prime Minister of India, is known for his governance and leadership but has not authored the book "Shakti se Shanti." While he has written other works such as "Exam Warriors," which provides motivational advice to students, "Shakti se Shanti" is not among his literary contributions.

Shri Chetan Bhagat

• Rationale: Chetan Bhagat is a popular contemporary Indian author known for his novels that appeal to the youth, such as "Five Point Someone" and "2 States." His writing primarily focuses on themes like relationships, aspirations, and societal issues. However, "Shakti se Shanti" does not belong to his literary repertoire.

Shri Vikram Seth

• Rationale: Vikram Seth is an acclaimed Indian author and poet, best known for his novel "A Suitable Boy" and his poetic works. While his writings are widely celebrated for their literary excellence, he is not the author of "Shakti se Shanti."

Conclusion:

• Among the given options, Padma Vibhushan Shri Atal Bihari Vajpayee is the correct answer. His book "Shakti se Shanti" exemplifies his poetic brilliance and philosophical depth, showcasing his thoughts on achieving peace through strength. Vajpayee's literary and political legacy continues to inspire generations.

The correct answer is Rajaditya Chola

In News

• The CISF Recruits Training Centre in Arakkonam has been renamed to honor Rajaditya Cholan, effective February 24, 2025.

Key Points

• Rajaditya Cholan, son of Parantaka I, was a notable warrior of the Chola dynasty.
• He was given the title ‘Yanaimel Thunjiya Devar’, meaning ‘The king who died on the back of an elephant’.
• He died in 949 CE during the Battle of Thakkolam while leading Chola forces against the Rashtrakutas.
• The battle was a significant moment in the Chola-Rashtrakuta conflict, demonstrating Rajaditya’s bravery and commitment.
• He was fatally wounded by an arrow from Butuga, an ally of the Rashtrakutas.
• Beyond warfare, Rajaditya was an effective administrator, overseeing the northern boundary of the Chola kingdom.
• He contributed to temple construction, agricultural development, and economic growth, improving local livelihoods.
• His death in battle solidified his status as a hero in Tamil culture, inspiring later Chola rulers.
• The Chola dynasty continued to thrive for 250 years, expanding its power despite setbacks.
• Rajaditya’s story is referenced in Tamil literature, including Kalki Krishnamurthy’s novel “Ponniyin Selvan”.
• His life and sacrifices are immortalized in Tamil inscriptions and historical texts, preserving his legacy for future generations.

The correct answer is Protection of refugees.

Key Points

• People who are compelled to flee their nation because of war, persecution, or a natural disaster are known as refugees. There is a need for international community engagement because the plight of the refugees transcends national bounds.
• The Cartagena Declaration, 1984
• Ten Latin American nations, including Colombia, Nicaragua, Panama, Venezuela, Mexico, Honduras, Guatemala, El Dorado, Costa Rica, and Belize, ratified this proclamation in 1984.
• Its non-binding character means that the countries are not obligated to abide by its stipulations.
• Compared to the 1951 Convention and the 1967 Protocol, the Cartagena Declaration permits a wider category of people who need international protection to be considered as refugees.

Additional Information

• The Nansen International Office for Refugees, a branch of the League of Nations High Commissioner for Refugees, was established in 1930 to offer material assistance and political support to people fleeing conflict zones between 1930 and 1939.
• Stateless people were given Nansen Passports, which made cross-border migration easy.
• The Conventions of 1933, which dealt with the international acknowledgement of refugees, served as the foundation for early legal attempts.
• 1951 Convention on Refugees
• A multilateral United Nations agreement known as the Convention Relating to the Status of Refugees establishes the characteristics of a refugee, the rights of those who are granted asylum, and the obligations of the countries that do so.
• Protocol pertaining to Refugee Status, 1967
• The 1967 Protocol eliminated both the temporal and geographic limitations of the 1951 United Nations Convention Relating to the Status of Refugees, which had limited refugee status to those whose circumstances had arisen "as a result of events occurring before 1st January 1951," with States Parties to the Convention having the option of interpreting this as "events occurring in Europe."
• This was required given the historical background of decolonization-related refugee migrations.

The correct answer is Article 134.

• Article 134 provides the appellate jurisdiction of the Supreme court in criminal cases.
• The Supreme court of India is the highest appellate court in India.
• The appellate jurisdiction of the Supreme Court can be invoked by a certificate granted by the High Court concerned under Article 132(1), 133(1), or 134 of the Constitution.
• In constitutional matters, an appeal lies to the supreme court if the High Court certifies that the case involves a substantial question of law as to the interpretation of the constitution.
• The Supreme court of India is also known as the court of record.
• Jurisdiction of the Supreme court are:
• Original jurisdiction.
• Writ jurisdiction.
• Appellate jurisdiction.
• Advisory jurisdiction.
• Revisory jurisdiction.

The correct answer is Tarapur (Maharashtra).

Key Points

Tarapur Atomic Power station (TAPS):

• The Tarapur Atomic Power Station (TAPS) is located near Boiser in the Thane District of Maharashtra.
• Begun as India's first atomic power project, the Indian Government decided to utilize Boiling Water Reactors (BWRs) for the plant.
• On 8 May 1964, a contract between the governments of India and the United States was signed for the construction of TAPS.
• Although the United States agreed to supply enriched uranium to TAPS for 30 years, this supply was cut off after the peaceful nuclear explosion at Pokhran in 1974.
• Since this time France, China, and Russia have all supplied uranium fuel to TAPS.
• Tarapur Atomic Power Station Units (TAPS 1 &2), connected to the grid in April and May 1969, have completed 50 years of safe operation.
• TAPS- 1&2 is currently the oldest operating power reactor in the world, producing reliable power at about two rupees per unit.
• The first of these reactors for Tarapur was acquired by Homi Bhabha, considered the father of India’s nuclear programme.
• Tarapur reactor is the second most powerful in India after the Kudankulam Nuclear Power Plant in Tamil Nadu.

Important Points

The correct answer is Comptroller and Auditor General of India.

Key Points

• According to Article 148 of the Indian Constitution, the Comptroller and Auditor General of India is the country's top auditing body.
• They have the authority to examine every rupee that the Indian government and the state governments receive and spend.
• The CAG is also the statutory auditor of Government-owned corporations.
• It performs extra audits of government-owned businesses or the subsidiaries of existing government-owned businesses in which the government owns at least a 51 per cent equity stake.
• In terms of precedent, the CAG is placed ninth and has the same authority as a sitting Supreme Court of India judge.
• The current CAG of India is G. C. Murmu (as of February 2023), a former lieutenant governor of the UT of Jammu and Kashmir.​

Additional Information

• Attorney General of India
• The Att orney General (AG) of India is a part of the Union Executive.
• He is the highest law officer in the country who can be part of any court in the Indian Territory.
• He got the right to speak and to take part in the proceedings of both the Houses of Parliament or their joint sitting and any committee of the Parliament of which he may be named a member.
• He has no right to vote when he participates in the proceedings of the Indian Parliament.
• Similar to a Member of Parliament, he also enjoys all powers related to immunities and privileges.
• He is not considered a government servant.
• He can practice privately too as he is not debarred from private legal practice.

Thus, the Pr esident of India appoints a person who is qualified for the post of Attorney General on the advice of the government.

• Advocate General of the India
• The Advocate General is a constitutional post in India, created by the Constitution of India under Article 165.
• The Advocate General is appointed by the Governor of the State and holds office during the pleasure of the Governor.
• The Advocate General is the highest law officer in the state and is responsible for providing legal advice to the government of the state.
• The Advocate General can appear in any court of law within the state and can also participate in the proceedings of the state legislature.
• Finance Commission of India
• The Finance Commission in India is constituted by the President under article 280 of the Constitution.
• The first finance commission was constituted in 1951.
• Finance Commission is a constitutional body for the purpose of allocation of certain revenue resources between the Union and the State Governments.
• The finance commission is appointed every five years.
• The President lays the reports of the Finance commission before both the Houses of the Parliament.
• The finance commission recommends to the President relating to the distribution of the net taxes to be shared between the centre and the states.
• The finance commission consists of a Chairman and four members.

The correct answer is Manipur.

In News

• President’s Rule was imposed in Manipur following the resignation of Chief Minister N Biren Singh.
• The Ministry of Home Affairs issued an official notification, citing Article 356 of the Indian Constitution.
• The Governor's report to President Droupadi Murmu led to the decision.
• The Manipur Legislative Assembly has been put under suspended animation.

Key Points

• President’s Rule refers to the imposition of direct central government control over a state due to governance failure.
• It is enforced under Article 356 of the Indian Constitution.
• During this period, the Governor acts as the constitutional head on behalf of the President.
• The state's legislative assembly may be dissolved or placed under suspended animation.

Additional Information

• Article 356 of the Indian Constitution
• Allows the President to take over a state’s administration if it fails to function constitutionally.
• Can be imposed for an initial period of six months, extendable up to three years with parliamentary approval.
• Manipur
• Capital: Imphal
• Governor: Ajay Kumar Bhalla
• Former CM: N Biren Singh (Resigned)
• Past Instances of President’s Rule in India
• Jammu & Kashmir (2018-2019)
• Maharashtra (2019, for 13 days)
• Uttarakhand (2016, later revoked by SC)

The correct answer is '(11320/382)'.

Key Points

• Population density is the measure of the number of people per unit area.
• In 2011, the population density for the NCT of Delhi was 11,320 people per square kilometre.
• The population density of NCT of Delhi increased from 1,793 people per square kilometre in 1961 to 11,320 people per square kilometre in 2011 growing at an average annual rate of 37.60%.
• The population density of India in 2011 was 382 per sq km.

Thus, as per Census 2011, the ratio of the density of population density for 'Delhi to India' is (11320/382).

Additional InformationCensus in India:

• It was done for the first time in 1872 under the British Viceroy Lord Mayo.
• After that, it is conducted at intervals every 10 years.
• However, the first complete census of India was conducted in 1881.
• Since 1949, it is conducted by the Registrar General and Census Commissioner of India under the Ministry of Home Affairs, Government of India.
• All censuses after 1951 were conducted under the 1948 Census Act.
• As of 2011, the Census of India has been conducted 15 times.

The correct answer is Article 75 (3).

Key Points

• The Constitution's original text included 395 articles divided into 22 divisions and 8 schedules.
• Article 75 in the constitution states that The Council of Ministers shall be collectively responsible to the House of the People.
• Article 75(3) of the Indian Constitution, which covers the unique requirements of this principle, contains the concept of collective responsibility.
• According to Article 75(3), the council of ministers must be assembled and answerable to the Lok Sabha.
• According to the principle of collective responsibility, the Lok Sabha is accountable to the council of ministers for the general management of the government's operations.
• All decisions made by the cabinet are a collective effort of the council of ministers, which functions as a team.

​

Additional Information

• Article 75 (2):
• ​The Minister will be in office as long as the President so directs.
• Article 80 (4):
• According to Article 80(4), the elected members of the State Legislative Assembly will elect each State's delegates to the Council of States.
• This is in keeping with the proportional representation system that uses a single transferable vote.
• Article 75 (1):
• A Council of Ministers led by the Prime Minister will assist and advise the President, who will follow their recommendations when performing his duties.
• The president may request that the council of ministers reevaluate this advise, and the president must then act in accordance with the revised advice.

The correct answer is SWAYATT.

In News

• SWAYATT initiative of Government e-Marketplace (GeM) marked its six-year milestone on 19th February 2025.

Key Points

• SWAYATT (Startups, Women & Youth Advantage Through e-Transactions) was launched on 19th February 2019.
• The initiative focuses on integrating startups, women entrepreneurs, and youth into public procurement.
• As of 2025, 8% of the total sellers on GeM are women entrepreneurs.
• The platform has onboarded 1,77,786 Udyam-verified women micro and small enterprises (MSEs), fulfilling orders worth ₹46,615 Crore.

Additional Information

• Government e Marketplace (GeM)
• Launched: 2016
• Managed by: Ministry of Commerce & Industry
• Purpose: Facilitating public procurement by government bodies.
• SWAYATT Initiative
• Objective: To promote startups, women entrepreneurs, and youth in public procurement.
• Components: Includes "Startup Runway" and "Womaniya" storefronts for dedicated visibility.
• Target: Onboarding 1 lakh DPIIT-registered startups onto the GeM portal.
• FICCI-FLO
• Full Form: Federation of Indian Chambers of Commerce & Industry - Ladies Organisation
• Represents: Over 9,500 women entrepreneurs across India.
• Collaboration: Signed an MoU with GeM to provide direct access for women entrepreneurs to government buyers.

The correct answer is  Maharashtra.

Key Points

• Warli painting  is a tribal art form primarily created by the Warli tribe from the North Sahyadri Range in the state of Maharashtra, India
• The Warli tribe, one of the largest in India, resides outside Mumbai and has a rich cultural heritage associated with their art.
• In modern-day, the Warli tribals live in the Thane district of Maharashtra.
• ​Warli paintings employ a set of basic geometric shapes: circle, triangle, and square.
• These shapes symbolize different elements of nature.
• The circle represents the sun and the moon.
• The triangle depicts mountains and conical trees.
• The square signifies a sacred enclosure or a piece of land.
• The central motif in each ritual painting is the square, known as the “chauk” or “chaukat”.
• The Warli tribals have their own animistic beliefs, life, customs, and traditions.
• The Warli speak the Varli language, classified as Konkani, with some degree of influence from Marathi.

Additional Information

• Other Famous Paintings
• Pattachitra
• A traditional art form from Odisha, Pattachitra is known for its intricate designs and mythological narratives.
• These paintings are based on Hindu mythology and are often inspired by Jagannath and the Vaishnava sect.
• Pithora
• A traditional art form from Gujarat, Pithora paintings are typically done on the walls of homes and temples.
• These paintings reflect the relationship between the Rathwa, Bhil, and Bhilala tribes of Gujarat and nature and spirituality.
• Marwar
• A traditional form of Indian painting that originated in the city of Jodhpur in Rajasthan.
• Pichwai
• A traditional form of painting from Rajasthan, Pichwai paintings are often found on the walls of temples or behind the deity.
• These paintings are still done with natural colors, although the natural paintbrushes have been replaced with cheaper and artificial ones.
• Tanjore
• A tribal art from the town of Thanjavur in Tamil Nadu, Tanjore painting celebrates the region's rich artistic tradition.

The correct answer is 

Key Points

• The International North-South Transport Corridor (INSTC) is a project to connect many modes of transportation, including road, rail, and ship, to facilitate the movement of goods between India, Russia, Iran, Europe, and Central Asia.
• INSTC would improve access to the landlocked countries of central Asia.
• 
• It is not a brand-new idea.
• European, Indian, and several other foreign traders exploited this historic route to access the marketplaces of Central Asia.
• There were reportedly 10,000 Indian traders operating throughout the Safavid dynasty's vast empire.
• In September 2000 in St. Petersburg, Russia, India, and Iran launched the present INSTC project.
• A multimodal transportation route connecting the Indian Ocean and the Persian Gulf to the Caspian Sea via Iran and then on to northern Europe via St. Petersburg in Russia is known as the INSTC in modern times.
• The route largely entails transporting cargo via sea, train, and road from India, Iran, Azerbaijan, and Russia.
• The corridor's goal is to improve the flow of commerce between important cities like Mumbai, Moscow, Tehran, Baku, Bandar Abbas, Astrakhan, Bandar Anzali, and others.
• The southernmost hub of the route is Mumbai.
• The route continues by sea to Bandar Abbas in Iran. On the narrow Strait of Hormuz, it holds a critical position.
• On the Iranian mainland, a route connects Bandar Abbas to Bandar-e Anzali. Another Iranian port, Bandar-e-Anzali, is situated on the Caspian Sea side. The Caspian Sea is traversed by a ship from Bandar-e-Anzali to Astrakhan.
• A Caspian port located in the Russian Federation is Astrakhan.
• The city is situated on the Volga River's two banks. Russian Railways connects Astrakhan to other parts of the Russian Federation and farther into Europe.

The correct answer is NSSO household consumption expenditure survey.

Key Points

• National Sample Survey Office (NSSO) carried out poverty estimates based on a large sample survey of household consumption expenditure of Indian families at an interval of approximately five years.
• National Sample Survey Office under the Ministry of Statistics and Programme Implementation (MOSPI) is the unit of NITI Aayog for the Poverty estimation in India.

Additional Information

• Poverty line estimation in India is based on the consumption expenditure.
• Alagh Committee(1979), Lakdawala Committee(1993), Tendulkar Committee(2009), Rangarajan committee(2012) are related to the poverty estimation and elimination.
• Causes of Poverty in India are Population explosion, Unemployment, Low agricultural productivity, Low rate of economic development, etc.

The correct answer is Sabarmati​.

Key Points

Sabarmati River:

• The Sabarmati basin extends over the states of Rajasthan and Gujarat having an area of 21,674 Sq.km with a maximum length and width of 300 km and 150 km.
• It lies between 70°58’ to 73°51’ east longitudes and 22°15’ to 24°47’ north latitudes.
• Sabarmati river originates from the Aravalli hills in Kotdi tehsil of Udaipur district of Rajasthan.
• The basin is bounded by Aravalli hills on the north and north-east, by Rann of Kutch on the west, and by the Gulf of Khambhat on the south.
• The basin is roughly triangular in shape with the Sabarmati River as the base and the source of the Vatrak River as the apex point.
• Sabarmati originates from Aravalli hills at an elevation of 762 m near village Tepur, in the Udaipur district of Rajasthan.
• Right Bank Tributaries: Sei, Siri and Dhamni
• Left Bank Tributaries: Wakal, Harnav, Hathmati, Khari, Watrak.

Confusion Points

• The Vindhya Range, at an elevation from 1,500 to 3,500 feet (450 to 1,100 metres), gives rise to the main southern tributaries of the Ganges-Yamuna system, including the Chambal, Betwa, Ken, and Tons rivers.

The correct answer is Forest Research Institute (FRI)

In News

• Supreme Court of India has appointed the Forest Research Institute (FRI), Dehradun, to create an action plan to enhance Delhi's green cover.

Key Points

• The court has given FRI a one-month deadline to submit an affidavit, which will outline the timeline, requirements, and funding needed for the project.
• The plan will focus on a massive afforestation drive to increase the tree cover in Delhi's jurisdiction (GNCTD), addressing concerns about the city's depleting green cover.
• Earlier directions from the Court had instructed the Delhi Government and civic agencies to convene meetings for a comprehensive strategy to tackle the issue and prevent illegal tree felling.
• The forest department, Tree Authority, and MCD have been tasked with ensuring illegal tree damage is monitored and minimized.

The correct answer is 2016.

Key Points

• The National Ganga Council was formed in 2016.
• It is chaired by the Prime Minister of India.
• It is an important body, which is responsible for various government schemes regarding the cleaning up of the River Ganga.
• In this article, you can read all about the National Ganga Council, its formation, mandate, composition, and functions for the IAS exam.
• The first meeting of the National Ganga Council was held on 14th December 2019.

Additional Information Namami Gange Programme

• ‘Namami Gange Program is an Integrated Conservation Mission, approved as a ‘Flagship Programme’ by the Union Government in June 2014 with a budget outlay of Rs.20,000 Crore to accomplish the twin objectives of effective abatement of pollution, conservation, and rejuvenation of the National River Ganga.

 Ganga action plan

• The Ganga action plan was started in 1986 with the objective of pollution abatement from the river Ganga.
• GAP – Ganga Action Plan is a 100% centrally sponsored scheme.
• Under this plan, the National River Ganga basin authority was established and declared Ganga as a national river of India.

Key Points

• In animal cells, Cuboidal epithelium forms the inner lining of the kidney to provide mechanical support.
• Cuboidal epithelium is a single layer thick and made of cube-shaped cells. This tissue is found lining parts of the body such as the kidney tubules and walls of the respiratory bronchioles.
• Glandular epithelium-It is a type of epithelial tissue that covers the exocrine and endocrine glands.
• Columnar epithelium- These tissues are made of a single layer of long epithelial cells in regions where absorption and secretion are important. They also form the lining of the stomach and intestines.
• Squamous epithelium- It is a single layer of flat cells. These are in contact with the basal lamina of the epithelium. The tissues are permeable and occur where small molecules need to pass through membranes via diffusion.

The correct answer is Natya Shastra.

 Key Points

• Bharatanatyam is a classical dance form that originated in South India and is known for its intricate footwork, expressive gestures, and graceful movements.
• The theoretical foundations of Bharatanatyam can be traced back to the Natya Shastra, an ancient Indian treatise on the performing arts written by the sage Bharata.
• The Natya Shastra covers a wide range of topics related to dance, music, and theater, including the classification of dance forms, the elements of performance, and the roles of the performer and the audience.

Additional Information

• Arth Shastra is a treatise on economics and political science.
• It was written by Kautilya.
• Vaimanika Shastra is a text on aeronautics.
• It is attributed to the ancient Indian sage Maharishi Bharadwaja.
• Dharma Shastra is a collection of religious and ethical guidelines for Hindus.
• These texts are based on Puranas.

The positional values of alphabet is:

The logic followed here is:

"LU" is written as "VN"

And,

"KI" is written as "LK"

Similarly,

“LUY” be written as

So "LUY" will be written as "ZWO".

Hence the correct answer is "ZWO".

The least possible Venn diagram for the given statements is as follows,

Conclusions:

I. Some plane is not train - True (Plane which is plot is not train)

II. All loco being train is a possibility. - True (As possibility is true)

Hence, Both conclusion I and conclusion II follows

Now draw a family tree using the following notations:

Family tree by Gunjan’s statement:

Family tree by Anjali’s statement:

By combining, we get,

So, Daksh is grandfather of Anjali.

Hence, ‘Grandfather’ is the correct answer.

The table shows the place value of the alphabet from A to Z.

The logic followed here is:

Sum of the place value + Total number of consonants = coded number

'RAIN' is coded as '44'

Total number of consonants = 2 (R, N)

RAIN → R(18) + A(1) + I(9) + N(14)

= 18 + 1 + 9 + 14 → 42 + 2 → 44

And,

'CLOUD' is coded as '58'

Total number of consonants = 3 (C, L, D)

CLOUD → C(3) + L(12) + O(15) + U(21) + D(4) 

= 3 + 12 + 15 + 21 + 4 → 55 + 3 → 58

Similarly,

UMBRELLA coded as

Total number of consonants = 5 (M, B, R, L, L)

UMBRELLA → U(21) + M(13) + B(2) + R(18) + E(5) + L(12) + L(12) + A (1)

= 21 + 13 + 2 +18 + 5 + 12 + 12 +1 → 84 + 5 → 89

Therefore, UMBRELLA is coded as '89'.

Hence,  "Option (2)" is the correct answer.

The positional values of the alphabets are:

The logic followed here is as follows:

"FIGURE" is written as "BORDFC"

And,

"TABLE" is written as "BIYXQ"

Similarly,

CHART will be written as follows:

So CHART will be coded as "QOXEZ".

Hence, the correct answer is "QOXEZ".

Logic:

and,

Similarly,

Hence, SRQP is the correct answer.

The pattern followed here is,

• From box 1 to box 2, All the symbols move one position in a clockwise direction.

• From box 2 to box 3,  the middle symbol along the sides interchange their position with the symbol in front of them, and symbols along the corners interchange their position diagonally.

• Again From box 3 to box 4, All the symbols move one position in a clockwise direction.

• So In the next step,  the middle symbol along the sides interchange their position with the symbol in front of them, and symbols along the corners interchange their position diagonally.

From box 4 to box 5, we get 

The figure which will come next is,

Hence, the figure in option 1 is the correct answer.

According to the question,

As, 'Team' is a group of players forming one side in a competitive game or sport. Similarly, Bouquet is an arranged bunch of flowers.

Hence, the correct answer is Flowers: Bouquet.

The logic followed here is:

Hence, the correct answer is "185".

The logic followed here is:

Hence, the correct answer is "185".

On arranging given word as per dictionary order,

1. Karyologic

2. Karyolymph

3. Karyosomes

4. Karyotypic

5. Kazillions

Hence, Kazillions comes at the end.

The pattern followed here is:

Option 1 → 10, 1010 → 10, 10³ + 10

Option 2 → 8, 520 → 8, 83 + 8

Option 3 → 5, 130 → 5, 53 + 5

Option 4 → 6, 210 → 6, 63 - 6

All follow the same pattern except "6, 210".

Hence, "6, 210" is the odd pair.

The positional values of the alphabets are:

The logic followed here is as follows:

• Vowels are coded as next vowels as they appear in the series.

A → E → I → O → U

• Consonants are coded as previous consonants as they appear in the series.

Given:

​"CLOCK" is written as "BKUBJ"

And

"WATCH" is written as "VESBG"

Similarly,

"TIME" be written as

Hence, the correct answer is "SOLI"

Angle: There are two types of angles that are made by the hands of a clock.

1) Internal Angle:- Angle between two needles (Hour and Minute hands of a clock) is less than 180º

2) External Angle:- Angle between two needles (Hour and Minute hands of a clock) is more than 180º

To find the angle between the hands of the clock,

Angle =  | Hour × 30 - 11 ÷ 2 × Minute |

Given,

Hour = 11

Minute = 16

Substitute the value of Hour and minute in the above formula.

Angle = | 11 × 30 - 11 ÷ 2 × 16 |

Angle = | 330 - 11 × 8 |

Angle = | 330 - 88 |

Angle = | 242 |

Angle =  242º             (More than 180º) 

Hence, 242º is the correct answer.

Given expression: 1390 M 1267 K 705 J 3 L 5

Expression after applying given replacements:

= 1390 - 1267 + 705 ÷ 3 × 5

= 1390 - 1267 + 235 × 5

= 1390 - 1267 + 1175

= 2565 - 1267

= 1298

Hence, '1298' is the correct answer.

When we will fold a given sheet of paper, (S, D), (2, 6) and (4, 7) are the pairs of opposite faces. In the figures 3, 2 and 4, these faces are lying adjacent to each other.

So, these three figures can’t be made from the given sheet of paper.

Only figure 1 is possible.

Hence, the figure in option 1 is the correct answer.

The pattern followed here is:

1) Punnet faces toward the north and sits third to the left of the person who is in front of Shashi.

2. Sinu is facing north and is seated to the immediate left of Naveen and Golu does not face the Punnet.

3) Naveen is not sitting at the end of any row.

(It means Naveen is not sit at the end of the row and faces toward north)

4) Golu and Mohit are immediate neighbors of Sonu. 

5) Golu does not face the Punnet.

6) Ajay is to the immediate right of the person who is sitting in front of Golu.

Clearly, Sonu sits second to the right of Shashi.

Hence, the correct answer is "Option 4".

In 2013, Deepesh's age was three times the age of Abhishek

Deepesh's age = 3 Abhishek's age

Let Deepesh = 3x years

then Abhishek = x years

In 2017

Deepesh's age = 3x + 4

Abhishek's age= x + 4

According to given question in 2017, Deepesh's age was two times the age of Abhishek,

Deepesh's age = 2 Abhishek's age

3x + 4 = 2 (x + 4)

3x + 4 = 2x + 8

3x - 2x = 8 - 4

x = 4

In 2013 Age of Deepesh = 3x = 3 × 4 = 12 years

Year of birth of Deepesh = 2013 - 12

Year of birth of Deepesh = 2001

Hence, 2001 is the correct answer.

The pattern followed here is;

Hence, "407" is the correct answer.

Alternate MethodThe pattern followed here is;

25² + 2 = 627

24² + 3 = 579

23² + 4 = 533

22² + 5 = 489

21² + 6 = 447

20² + 7 = 407

Hence, "407" is the correct answer.

The logic followed here is,

Logic: 2, 3 and 5 has been added in the first, second and third letter's positional value to get the coded letters.

First Number = (Number)², Second Number = (Number)³

Let's check as per the logic,

RUN 36: TXS 216 ⇒

Here, 36 = (6)² ⇒ (6)³ = 216

SRK 16: UUP 64 ⇒

Here, 16 = (4)² ⇒ (4)³ = 64

Similarly,

HUT 9: ? ⇒

Here, 9 = (3)² ⇒ (3)³ = 27

Hence, the correct answer is "JXY 27".

The path of Tanvi canbe traced as below:

Since at the end, she is facing East, her shadow must be fallen towards West at the starting.

Then the sun will be in the East and the time should be morning.

Hence Morning is the answer.

The pattern followed here is,

Similarly,

Hence, “RFKFNO” is the correct answer.

The logic is;

6 AM to 4 PM, 10 hours

watch gains 6 minutes in one hour,

In 10 hours it gains 10 × 6 = 60 minutes

Hence, at 4 PM, it shows 4 PM + 60 mins = 5 PM

The pattern is as follows;

It follows (+3/+5, +4/+6, +5/+7, +6/+8……) pattern.

Hence, S/30 is the correct answer.

Given:

1. Women 1 is 20th from the right end. 2. Women 2 is 11^th form the left end.

3. If they interchanged their position, Women 2 becomes fifteenth from the left end.

Therefore, total number of women is = (Women 1 position before interchanging + Women 2 position after interchanging - 1)

⇒ 20 + 15 - 1 = 34

Hence, the correct answer is "34".

From the above diagram, we can write

No. of children who like tiger = 85

No. of children who like leopard = 120

No. of children who like lion = 110

No. of children who like both tiger and leopard = 35

No. of children who like both leopard and lion = 90

No. of children who like both lion and tiger = 40

Difference between children who like leopard to those who like tiger = 120 - 85 = 35

The pattern follows here is:

Hence, the correct answer is "UDZ".

The logic is;

Hence, ‘ZUPK’ is the odd one.

Given statements: F > N > W < Y < R

Conclusions:

I. F > W → True (F > N > W → F > W)

II. R > N → False (N > W < Y < R → thus clear relation between N and R cannot be determined)

III. N > R → False (N > W < R → thus clear relation between N and R cannot be determined)

IV. R > W → True (W < Y < R → R > W)

 Thus, only conclusion I and IV are true.

Given series: 58Z31, 52Y29, 46X26, ?

The logic followed here is:

Hence, the next term will be 40W22.

There is a total of four numbers which are immediately preceded by a letter and immediately followed by a symbol

M B 6 & N C ! V 2 $ T 8 % 5 # 9 R S 4 @ 7 P

Hence, option 4 is correct.

Eight friends, Rewa, Nadiya, Inas, Bhim, Shreshti, Qarin, Lihan and Ednit, are sitting around a circular table, with their backs towards the centre.

1) Rewa is sitting second to right of Nadiya.

2) Bhim back faces to the person who is immediate left of Rewa.

3) Bhim sit in between Inas and Qarin and Qarin is third to right of Lihan.

Case(i) :

Case(ii) :

4) Ednit is second to left of Shreshti.

Case(ii) is doesn't satisfy the conditon.

∴ Here, 'Shreshti' sits second to the left of 'Lihan'.

Hence, the correct answer is "Shreshti".

The logic followed here is:

All options except "Velocity" are scalar quantities, while velocity is a vector quantity.

Hence, "Velocity" is the odd one.

Additional Information

A physical quantity is a scalar quantity that has only magnitude while a vector quantity is a physical quantity that has both magnitudes as well as direction. 

A scalar quantity is defined as the physical quantity that has only magnitude. 

For example: mass and electric charge.

On the other hand, a vector quantity is defined as the physical quantity that has both magnitude as well as direction.

For example: force and weight.

Solution:

The positional values of the alphabet are:

The logic followed here is:

Logic: (Sum of positional values of opposite letters) × 3 = Given Number

Similarly,

Hence, the correct answer is "165".

The least possible Venn diagram for the given statements is as follows,

Conclusions:

I. Some sent is not divert. - True (Part of sent which is arc is not divert)

II. All cover is divert. - False (This is possible but not definite) 

Hence, Only conclusion I follows

Hence, answer is option 4.

Given:

A, B, and C entered into a partnership with Rs. 5200, Rs. 6000 and Rs. 6800 respectively.

Total profit is Rs. 15600.

Concept Used:

(A’s share) : (B’s share) : (C’s share) = (A’s investment × time) : (B’s investment × time) : (C’s investment × time)

Calculation:

Let us assume, A, B, and C entered into a partnership with Rs. 5200, 6000, and 6800 respectively for 5x, 3x, and 5x month.

(A’s share) : (B’s share) : (C’s share) = (5200 × 5x) : (6000 × 3x) : (6800 × 5x)

⇒ 13 : 9 : 17

The total profit is Rs. 15600.

Share of A will be 15600 × 13/39

⇒ 5200

∴, the share of A will be rupees 5200.

Given:

Total matches = 225

Target win % = 80

Success rate out of 120 matches = 70%

Calculation:

Total match to win = 80/100 × 225 = 180

Matches won out of 120 = 120 × 70/100 = 84

Matches remaining = 225 - 120 = 105

Required win remaining = 180 - 84 = 96 

∴ Team needs to win 96 matches out of 105

Required success rate = 96/105 × 100

⇒ 640/7 = 91(\frac{3}{7})%

∴ The required success rate is 91(\frac{3}{7})%.

Given : 

Book was sold for Rs.704 at profit of 10%.

Calculation :

Profit = 10%

By applying ratio method,

CP = 10, SP = 11

SP = 11 = 704

⇒ 1 = 64

CP = 64 × 10 = 640

New SP = 664

Profit = 24/640 × 100 

⇒ 3.75% 

∴ The correct answer is 3.75%.

Shortcut Trick

Applying the continuous percentage growth method:

Final Value = Initial Value × (100 + r₁)% × (100 + r₂)% × (100 + r₃)%

⇒ Present Population = 2,50,000 × (103/100) × (104/100) × (106/100)

⇒ Present Population = (2,50,000 ÷ 10,00,000) × (103 × 104 × 106)

⇒ Present Population = (1/4) × 11,35,472 = 2,83,868

∴ The correct answer is 2,83,868.

Alternate Method

Given:

Initial population (P) 3 years ago = 2,50,000

Successive growth rates for the last 3 years: R₁ = 3%, R₂ = 4% and R₃ = 6%

Formula Used:

Present Population = P × (1 + R₁/100) × (1 + R₂/100) × (1 + R₃/100)

Calculations:

⇒ Present Population = 250000 × (1 + 3/100) × (1 + 4/100) × (1 + 6/100)

⇒ Present Population = 250000 × (103/100) × (104/100) × (106/100)

⇒ Present Population = (250000 ÷ 1000000) × (103 × 104 × 106)

⇒ Present Population = (1/4) × (10712 × 106)

⇒ Present Population = (1/4) × 1135472

⇒ Present Population = 283868

∴ The correct answer is 2,83,868.

Additional Information

Successive Percentage Change

If a value changes by x% and then y%, the net percentage change is given by (x + y + xy/100)%. For three years, this formula can be applied consecutively to find the effective compound rate.

Population Depreciation

If the population of a town decreases by R% annually, the population after n years is given by the formula: A = P × (1 − R/100)ⁿ.

Population 'n' Years Ago

If the present population is P and it has been growing at R% annually, the population 'n' years ago can be calculated as: P ÷ (1 + R/100)ⁿ.

Given:

Marked Price of the article = Rs.2560

Successive Discounts rates = 20% and x%

Selling Price of the article = Rs.1679.36 

Formula used:

Selling Price = Marked Price × (100 - Discount)%

Calculation:

Rs.1679.36 = Rs.2560 × (100 - 20)% × (100 - x)% 

⇒ 1679.36 = 2560 × 80/100 × (100 - x)/100 

⇒ 167936/100 × 100/80 × 100/2560 = (100 - x)

⇒ 20992/256 = 100 - x

⇒ 82 = 100 - x 

∴ x = 18

Shortcut Trick

Winner's share = Total Voters × Valid % × Winning %

Winner's share = 3,20,000 × 95% × 56%

Winner's share = 3,20,000 × (95 / 100) × (56 / 100)

Winner's share = 32 × 95 × 56 = 1,70,240

∴ The correct answer is 1,70,240.

Alternate Method

Given:

⇒ Total Voters = 3,20,000

⇒ Invalid Votes = 5% of Total

⇒ Winner's Share = 56% of Valid Votes

Calculations:

⇒ Total number of votes = 3,20,000

⇒ Number of valid votes = 95% of 3,20,000

⇒ Valid votes = (95 / 100) × 3,20,000 = 3,04,000

⇒ Winning candidate's votes = 56% of Valid votes

⇒ Winner's votes = (56 / 100) × 3,04,000

⇒ Winner's votes = 56 × 3,040 = 1,70,240

∴ The correct answer is 1,70,240.

Additional Information

Valid and Invalid Votes

Valid votes are those used to determine the winner and loser. Total Votes = Valid Votes + Invalid Votes.

Victory Margin

The margin of victory is the difference between the votes of the winner and the runner-up. Margin = (Winner's % − Loser's %) × Valid Votes.

Successive Percentages

When multiple percentage conditions apply (like invalid then winning share), the final value is found by multiplying successive factors: Final = Initial × (1 − r₁/100) × (r₂/100).

Shortcut Trick

Initial total ratio units = 17 + 25 = 42 units.

The total sum of money remains constant as the money is only transferred between A and B.

Initial ratio: 17 : 25 (Total = 42) | New ratio: 3 : 4 (Total = 7).

Equate totals: New ratio becomes (3 : 4) × 6 = 18 : 24 (Total = 42).

Change in A's share: 18 − 17 = 1 unit. Given 1 unit = ₹5.

Total sum = 42 units = 42 × 5 = ₹210.

∴ The correct answer is ₹210.

Alternate Method

Given: Initial ratio A : B = 17 : 25. New ratio after transfer of ₹5 = 3 : 4.

⇒ Let the initial amounts be 17x and 25x.

⇒ According to the question: (17x + 5) / (25x − 5) = 3 / 4

⇒ 4 × (17x + 5) = 3 × (25x − 5)

⇒ 68x + 20 = 75x − 15

⇒ 75x − 68x = 20 + 15

⇒ 7x = 35

⇒ x = 5

⇒ Total sum = 17x + 25x = 42x

⇒ Total sum = 42 × 5 = 210

∴ The correct answer is ₹210.

Additional Information

Concept of Constant Total

When a value is transferred from one entity to another within a system, the total sum remains unchanged. This property is used to equate ratios by making their sum equal.

Ratio Scaling

To compare two ratios with a common base, multiply each term of the ratio by a factor such that the sum or the common element aligns across both sets.

Cross Multiplication Method

Used for ratio change problems: (Initial Ratio 1 × Final Ratio 2) − (Initial Ratio 2 × Final Ratio 1) corresponds to the value change effect.

Given:

On selling a book at 5/12 of the marked price, there is a loss of 50 percent.

Concept:

Loss percentage is calculated using the formula:

Loss % = (Loss / Cost Price) × 100

Where Loss = Cost Price - Selling Price

Calculation:

Let the Marked Price (MP) be Rs. 12x.

Selling Price (SP) = (5/12) × MP

⇒ SP = (5/12) × 12x = 5x

Given, there is a loss of 50%, so:

Loss % = 50%

⇒ 50 = [(CP - SP) / CP] × 100

⇒ 50 = [(CP - 5x) / CP] × 100

⇒ 50 = [CP - 5x] / CP × 100

⇒ 50 = [1 - (5x / CP)] × 100

⇒ 50 = 100 - 500x / CP

⇒ 50CP = 100CP - 500x

⇒ 50CP = 500x

⇒ CP = 10x

Now, we need the ratio of Marked Price (MP) to Cost Price (CP):

MP : CP = 12x : 10x

⇒ MP : CP = 6 : 5

∴ The ratio of Marked Price to Cost Price is 6 : 5.

Given:

Average weight of 3 people = 50 kg

Weight of auto rickshaw and 3 people = 400 kg

Formula used:

Average = Sum of all observations/Number of observations

Calculation:

Sum of the weight of 3 people = 3 × 50 = 150 kg

Sum of the weight of 3 people and auto rickshaw = 400 kg

∴ Weight of auto rickshaw = 400 – 150 = 250 kg

Shortcut Trick

Time = 2 years 9 months = 2 + 9/12 = 11/4 years.

Net Rate of Interest = 8% × 11/4 = 22%.

Amount (in %) = 100% + 22% = 122%.

Given 122% = Rs. 915 ⇒ 1% = 915 ÷ 122 = 7.5.

Principal (100%) = 7.5 × 100 = Rs. 750.

∴ The correct answer is Rs. 750.

Alternate Method

Given:

Amount (A) = Rs. 915

Rate (R) = 8% per annum

Time (T) = 2 years 9 months = 2 + 9/12 = 2.75 years

Formula Used:

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

Amount (A) = P + SI = P × [1 + (R × T) ÷ 100]

Calculations:

⇒ 915 = P × [1 + (8 × 2.75) ÷ 100]

⇒ 915 = P × [1 + 22 ÷ 100]

⇒ 915 = P × [1 + 0.22]

⇒ 915 = P × 1.22

⇒ P = 915 ÷ 1.22

⇒ P = 750

∴ The correct answer is Rs. 750.

Additional Information

Simple Interest Definition

Simple interest is calculated only on the initial principal amount throughout the period: SI = (P × R × T) / 100.

Time Conversion

Always convert time into years if the rate is given per annum. Months ÷ 12 = years | Days ÷ 365 = years.

Amount Property

The amount is the sum of the principal and the interest earned: A = P + SI.

Shortcut Trick

Difference in Rates = (Difference in SI × 100) ÷ (Principal × Time)

⇒ ΔR = (13.50 × 100) ÷ (1500 × 3)

⇒ ΔR = 1350 ÷ 4500

⇒ ΔR = 0.3%

∴ The correct answer is 0.3%.

Alternate Method

Given:

Principal (P) = Rs. 1500

Time (T) = 3 years

Difference in Simple Interest (SI₁ − SI₂) = Rs. 13.50

Formula Used:

SI = (P × R × T) ÷ 100

Difference in SI = [ (P × R₁ × T) ÷ 100 ] − [ (P × R₂ × T) ÷ 100 ]

Calculations:

⇒ SI₁ − SI₂ = (P × T ÷ 100) × (R₁ − R₂)

⇒ 13.50 = (1500 × 3 ÷ 100) × (R₁ − R₂)

⇒ 13.50 = 45 × (R₁ − R₂)

⇒ R₁ − R₂ = 13.50 ÷ 45

⇒ R₁ − R₂ = 135 ÷ 450

⇒ R₁ − R₂ = 3 ÷ 10 = 0.3%

∴ The correct answer is 0.3%.

Additional Information

Simple Interest Rule

Simple Interest remains constant for every year if the principal and rate remain the same. Total SI is directly proportional to the Time and Rate.

Difference in Interest

When time and principal are constant, the difference in simple interest from two sources is directly proportional to the difference in their rates: ΔSI = P × T × ΔR ÷ 100.

Rule of 72

To estimate the number of years required to double the invested money at a given annual fixed compound interest rate, divide 72 by the annual rate of interest.

Given:

Average of 29 consecutive even no = 446

Calculation:

Since there is a gap of 2 in every even or odd no

N = 29, gap 29 - 1 = 28

So Difference between first and last no = 28 × 2 = 56

∴ Required answer is 56.

Shortcut Trick

For three equal distances covered at speeds x, y, and z, the average speed is the Harmonic Mean of the speeds.

Let the assumed distance for each segment be the LCM of (200, 300, 600) = 600 km.

Time taken for each segment = 600/200 = 3 h, 600/300 = 2 h, 600/600 = 1 h.

Total time = 3 + 2 + 1 = 6 hours | Total distance = 3 × 600 = 1800 km.

Average speed = 1800 ÷ 6 = 300 km/h.

∴ The correct answer is 300 km/h.

Alternate Method

Given: Three equal distances d = 100 km each; Speeds v₁ = 200 km/h, v₂ = 300 km/h, v₃ = 600 km/h.

Formula Used: Average Speed = (Total Distance) ÷ (Total Time)

⇒ Total Distance = 100 + 100 + 100 = 300 km

⇒ Time for 1^st part (t₁) = 100 ÷ 200 = 1/2 hour

⇒ Time for 2^nd part (t₂) = 100 ÷ 300 = 1/3 hour

⇒ Time for 3^rd part (t₃) = 100 ÷ 600 = 1/6 hour

⇒ Total Time = (1/2 + 1/3 + 1/6) = (3 + 2 + 1) ÷ 6 = 6/6 = 1 hour

⇒ Average Speed = 300 ÷ 1 = 300 km/h

∴ The correct answer is 300 km/h.

Additional Information

Average Speed for Equal Distance Segments

If a distance is divided into n equal parts with speeds v₁, v₂, ..., v_n, the average speed is n ÷ (1/v₁ + 1/v₂ + ... + 1/v_n).

Two Equal Distances Case

For two equal distances covered at speeds x and y, the Average Speed is (2 × x × y) ÷ (x + y).

Unit Conversion

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

Shortcut Trick

Total Time = Distance ÷ (Speed of Boat + Speed of Stream) + Distance ÷ (Speed of Boat − Speed of Stream)

Total Time = 105 ÷ (18 + 3) + 105 ÷ (18 − 3)

Total Time = 105 ÷ 21 + 105 ÷ 15

Total Time = 5 + 7 = 12 hours.

∴ The correct answer is 12 hours.

Alternate Method

Given:

Speed of boat in still water (u) = 18 km/h

Speed of stream (v) = 3 km/h

Distance covered each way (D) = 105 km

Formula Used:

Downstream Speed (D_s) = u + v

Upstream Speed (U_s) = u − v

Time = Distance ÷ Speed

Calculations:

⇒ Downstream Speed (D_s) = 18 + 3 = 21 km/h

⇒ Upstream Speed (U_s) = 18 − 3 = 15 km/h

⇒ Time taken downstream = 105 ÷ 21 = 5 hours

⇒ Time taken upstream = 105 ÷ 15 = 7 hours

⇒ Total Time = 5 + 7 = 12 hours

∴ The correct answer is 12 hours.

Additional Information

Speed of Boat and Stream from Downstream / Upstream

If downstream speed is D_s and upstream speed is U_s, then Speed of Boat = (D_s + U_s) ÷ 2, and Speed of Stream = (D_s − U_s) ÷ 2.

Average Speed for a Round Trip

For a journey traveling the same distance downstream and upstream, Average Speed = (D_s × U_s) ÷ Speed of Boat in still water.

Total Time Formula

If total time for a round trip is T, then Total Distance = (T × (u² − v²)) ÷ (2 × u), where u is boat speed and v is stream speed.

Shortcut Trick

Remaining days of work for the initial 12 men = 9 − 6 = 3 days.

Remaining work in terms of man-days = 12 men × 3 days = 36 man-days.

New number of men working = 12 + 6 = 18 men.

Days required to complete the remaining work = 36 ÷ 18 = 2 days.

∴ The correct answer is 2 days.

Alternate Method

Given:

Initial number of men = 12

Total days required = 9

Days they worked before others joined = 6

New men joined = 6

Formula Used:

Total Work = Number of Men × Days

Calculations:

⇒ Let the efficiency of 1 man be 1 unit/day.

⇒ Total work to be done = 108 units

⇒ Work completed by 12 men in 6 days = 12 × 6 = 72 units

⇒ Remaining work = 108 − 72 = 36 units

⇒ Total men present after 6 days = 12 + 6 = 18 men

⇒ Combined efficiency of 18 men = 18 units/day

⇒ Time taken to complete the remaining work = Remaining Work ÷ Combined Efficiency

⇒ Time taken = 36 ÷ 18 = 2 days

∴ The correct answer is 2 days.

Additional Information

MDH Rule (Chain Rule)

If M₁ men can do W₁ work in D₁ days working H₁ hours/day, and M₂ men can do W₂ work in D₂ days working H₂ hours/day, then the relation is given by: (M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂.

Work and Men Proportionality

The number of men required is inversely proportional to the number of days needed to complete the same amount of work. More men take fewer days, and fewer men take more days to complete identical work.

Work & Wages

Wages are always distributed in the ratio of the total work done by each person. If all individuals work for the same number of days, their wages are distributed directly in the ratio of their daily efficiencies.

Given:

(\left[ {\left{ {2\frac{1}{3} - \left( {5 + \left( {2 - 3} \right)} \right)} \right} + 3\frac{1}{2}} \right] = ?)

Concept used:

Calculation:

Using BODMAS rule:

⇒ 7/3 - 4 + 7/2

⇒ 35/6 - 4 = 11/6

∴ The value of '?' is 11/6.

Given 

Aman can do work = 30 days 

Formula Used 

Work = time × efficiency 

Calculation

Let the efficiency of Aman, Parul and Charu be A, P and C respectively 

⇒ A : P = 2 : 1 

⇒ P : C = 3 : 1 

⇒ A : P : C = 6 : 3 : 1 

⇒ So, total work = 6x × 30 = 180x 

⇒ Now, calculate number of days to complete the work when they work all together 

⇒ Total efficiency = 10x 

⇒ No. of days = total work/ total efficiency 

⇒ 180x/10x = 18 days 

∴ 18 days is required to complete the work when they work all together.

Given:

A can type 10 pages in 5 minutes.

B can type 5 pages in 10 minutes.

Concept used:

Work = Efficiency × Time

Calculation:

Pages type by A in 5 mins = 10

Pages type by A in 1 min = ((\frac{10}{{5}})) = 2 

Again, Pages type by B in 10 mins = 5

Pages type by B in 1 min = ((\frac{5}{{10}})) = (\frac{1}{{2}})

Now, Both A and B type pages in 1 min = (2 + (\frac{1}{{2}})) = (\frac{5}{{2}})

So, the number of pages typed in 30 mins = (30 × (\frac{5}{{2}})) = 75

∴ The require pages is 75.

Given:

95 ÷ 15 - 34 ÷ {18 - 4 ÷ (3 × 12) × 9} × 2

Concept used:

Calculation:

95 ÷ 15 - 34 ÷ {18 - 4 ÷ (3 × 12) × 9} × 2

⇒ 95 ÷ 15 - 34 ÷ {18 - 4 ÷ 36 × 9} × 2

⇒ 95 ÷ 15 - 34 ÷ {18 - 1/9 × 9} × 2

⇒ 95 ÷ 15 - 34 ÷ {18 - 1} × 2

⇒ 95 ÷ 15 - 34 ÷ 17 × 2

⇒ 19/3 - 2 × 2

⇒ 19/3 - 4

⇒ (19 - 12)/3

⇒ 7/3 = (2 \frac{{1}}{{3}})

∴ Required answer is (2 \frac{{1}}{{3}})

Given: 

A cistern regularly fills in 8 hours, but a leak in the bottom of it causes the process to take an additional 2 hours.

Calculation:

The filling time was 8 hours.

10 hours were needed to fill with leaks.

The full tank will be empty in x hours if the leak is left alone.

Assume there are 40 units of work overall (i.e., LCM of 8 and 10)

No-leak tank filling capacity (A) = 40/8 = 5 units per hour

Leakage tank filling capacity (A + x) = 40/10 = 4 units/hr

Hence, x = -1 unit.

The leakage is indicated by the Minus symbol.

∴ It will take 40 hours to completely leak out a full tank (40 units).

Calculation:

The total expenditure of the company in the year = (15 + 17.5 + 10 + 5 + 20 + 25 + 7.5)

⇒ 100

The expenditure on Research = 20

Required expenditure = 100/20

⇒ 5

∴ Required expenditure is 5

Given:

A rectangular playground of length 125 m and width 75 m

Walking strip of width 5 m is in the middle of the ground, parallel to shorter side

Formula Used:

Area of a rectangle = length × breadth

Calculation:

As per the given data

Area of the ground without the walking strip

= (125 × 75) - (5 × 75) = 9000 sq.m

Calculation:

Total number of students is 1200.

⇒ 100% = 1200

⇒ 1% = 12

The ratio between the number of students studying in BCA and B.sc,

⇒ BCA : B.sc = 12% : 18%

⇒ BCA : B.sc = 12 : 18 = 2 : 3

∴ The required ratio is 2 : 3

Shortcut Trick

Direct formula for Curved Surface Area (CSA) using Diameter (d): π × d × h = 1408

(22/7) × d × 56 = 1408

22 × d × 8 = 1408

176 × d = 1408

d = 1408 ÷ 176 = 8 cm = 0.08 m

∴ The correct answer is 0.08 m.

Alternate Method

Given:

Height (h) of the cylinder = 56 cm

Curved Surface Area (CSA) = 1408 cm²

Formula Used:

Curved Surface Area of a right circular cylinder = 2 × π × r × h

Where r is the radius and h is the height.

Calculations:

⇒ 2 × (22/7) × r × 56 = 1408

⇒ 44 × r × (56 ÷ 7) = 1408

⇒ 44 × r × 8 = 1408

⇒ 352 × r = 1408

⇒ r = 1408 ÷ 352

⇒ r = 4 cm

⇒ Diameter (d) = 2 × r = 2 × 4 = 8 cm

⇒ In meters: d = 8 ÷ 100 m = 0.08 m

∴ The correct answer is 0.08 m.

Additional Information

Total Surface Area (TSA) of Cylinder

The total surface area includes the curved surface and the areas of the two circular bases: TSA = 2 × π × r × (h + r).

Volume of Cylinder

The space occupied by the cylinder is given by the formula: Volume = π × r² × h.

Metric Conversion

To convert centimeters to meters, divide the value by 100 (1 m = 100 cm).

Shortcut Trick

Area of the floor = 9100 ÷ 65 = 140 m².

Ratio of Length : Breadth = 7 : 5 → Product of parts = 7 × 5 = 35 units².

35 units² = 140 ⇒ 1 unit² = 4 ⇒ 1 unit = 2 m.

Perimeter = 2 × (7 + 5) = 24 units.

Perimeter = 24 × 2 = 48 m.

∴ The correct answer is 48 m.

Alternate Method

Given:

Total cost of tiling = ₹9100

Rate of tiling = ₹65 per m²

Ratio of Length (L) and Breadth (B) = 7 : 5

Formula Used:

Area of rectangle = Length × Breadth

Perimeter of rectangle = 2 × (Length + Breadth)

Calculations:

⇒ Area of the floor = Total cost ÷ Rate

⇒ Area = 9100 ÷ 65 = 140 m²

⇒ Let Length = 7x and Breadth = 5x

⇒ 7x × 5x = 140

⇒ 35x² = 140

⇒ x² = 140 ÷ 35 = 4

⇒ x = √4 = 2

⇒ Length = 7 × 2 = 14 m

⇒ Breadth = 5 × 2 = 10 m

⇒ Perimeter = 2 × (Length + Breadth)

⇒ Perimeter = 2 × (14 + 10) = 2 × 24 = 48 m

∴ The correct answer is 48 m.

Additional Information

Area and Perimeter relationship

For a given area, a square has the minimum perimeter among all rectangles. Area = a² and Perimeter = 4a.

Cost of Fencing

The cost of fencing a rectangular field is calculated based on its perimeter. Cost = Perimeter × Rate per meter.

Diagonal of Rectangle

The diagonal (d) of a rectangular room is given by d = √(Length² + Breadth²).

Given:

Radius of big ladoo, R = 810 cm

Radius of small ladoo, r = 90 cm

Formula used:

The volume of a sphere = (4/3)πR³

The surface area of a sphere =  4πR²

Calculation:

Volume of big ladoo = Volume of all small ladoos together

⇒ (4/3)πR³ = n × (4/3)πr³

⇒ n = (R/r)³ (Where n is the number of small ladoos)

Total surface area of all small ladoos = n × 4πr² = (R/r)³ × 4πr²

The ratio of total surface area of all small ladoos to the surface area of big ladoo 

[(R/r)³ × 4πr²] : 4πR² = R/r = 810 : 90 = 9 : 1 

∴ The correct answer is 9 : 1

Calculation:

Total production of type A car in 5 years = 160 + 210 + 130 + 190 + 260

⇒ 950 (in thousands)

Product of type A can in 1995 = 190 (in thousands)

So, required % = (190/950) × 100

⇒ 20

∴ Required answer is 20%.

Given:

CP of an article = ₹2,100

Discount, D = 20% on MP

Profit = 90%

Concept used:

SP = (100 + Profit%) of CP

SP = (100 - D%) of MP

Calculation:

SP = 190% × 2100 = ₹3990

According to the question,

80/100 × MP = 3990

⇒ MP = 3990 × 100/80 = ₹4987.5

∴ The marked price is ₹4987.5.

Given:

The nine-digit number = 2x64y

Divisible by = 88

Concept used:

Divisibility rule of 8 - The last three digits of a number are divisible of 8

Divisibility rule of 11 - If the difference between the sum of the digits at odd places and even places equals 0 or divisible by 11 

Calculation:

We know that the last three digits of a number are divisible of 8

⇒ The number made from the last three digits without altering their position will be divisible by 8

⇒ Possible values of y = 8

Now, check the divisibility rule of 11

⇒ (2 + 6 + 8) - (x + 4) = 0 or 11

⇒ 12 - x =  0 or 11

Then, x = (12 – 11) = 1

Now,

⇒ (6x - 5y)

⇒ (6 × 1) - (5 × 8)

⇒ 6 - 40

⇒ - 34

∴ The required value is -34

Given:

Expenditure of A in 2018 = 60 lakhs

Concept Used:

Gain% = [(Revenue - Expenditure) / Expenditure] × 100

Calculation:

Expenditure of A in 2018 = 60 lakhs

So,

Gain% = [(R - 60) / 60] × 100

⇒ 65 = (R - 60) × 5/3

⇒ 195 = (R - 60) × 5

⇒ 195 = 5R - 300

⇒ 5R = 195 + 300 

⇒ 5R = 495

⇒ R = 495/5 = 99

Hence, revenue of A in 2018 was 99 lakhs.

∴ The correct answer is option (4).

Shortcut Trick

Let the Rate of Interest be R. Then Time T = 4R.

Using the direct relation: R² = (SI × 100) ÷ (P × 4)

R² = (11664 × 100) ÷ (32400 × 4) = 11664 ÷ 1296 = 9

R = √9 = 3%

∴ The correct answer is 3%.

Alternate Method

Given:

Principal (P) = ₹32,400

Simple Interest (SI) = ₹11,664

Rate (R) = T ÷ 4 ⇒ Time (T) = 4R years

Calculations:

⇒ SI = (P × R × T) ÷ 100

⇒ 11,664 = (32,400 × R × 4R) ÷ 100

⇒ 11,664 = 324 × 4R²

⇒ 11,664 = 1,296R²

⇒ R² = 11,664 ÷ 1,296

⇒ R² = 9

⇒ R = √9 = 3

∴ The correct answer is 3%.

Given:

 value of different computer companies

Solution:

The value of dell companies in this year = 28%

And the value of Apple company in this year = 14%

Total value of dell and Apple in this year =  (28 + 14) %

⇒ 42%

Value of all other companies = 100% - 42% 

⇒ 58%

The ration together Dell and Apple and All other companies = 42% : 58%

⇒ 21 : 29

The ration together Dell and Apple and All other companies = 21 : 29

Factorising 675 we get,

675 = 3 × 3 × 3 × 5 × 5 = 3³ × 5²

So we need one more 5 to make it 5³ 

3 × 3 × 3 × 5 × 5 × 5 = 33 × 5³ = 3375 whose cube root is 15

∴ By multiplying 5 with 675, a perfect cube number is obtained.

Alternate Method

We know that the prime factors of 675 are 3, 3, 3, 5 & 5

Since 3 is repeating for 3 times and 5 for only 2 times thus multiplying 675 with 5 the resultant number will be a perfect cube.

Hence, the required least number is 5.

Given:

The numerator is increased by 150%

The denominator is increased by 200%

Final fraction = 10/19

Concept used:

Percentage increase of a quantity = Initial quantity × (1 + percentage change)

Calculation:

Let the fraction be x/y

⇒ [(x) × (250/100)] / [(y) × (300/100)] = 10/19

⇒ (250x)/(300y) = 10/19

⇒ (5x)/(6y) = 10/19

⇒ x/y = (10/19) × (6/5)

⇒ x/y = 12/19

∴ The fraction is 12/19.

Shortcut Trick

Interest for 1st year = ₹200

Interest for 2nd year = ₹240

Interest earned on 1st year interest = 240 − 200 = ₹40

Rate of Interest = (Interest difference ÷ 1st year interest) × 100

Rate = (40 ÷ 200) × 100 = 20%

∴ The correct answer is 20%.

Alternate Method

Given:

Compound Interest for 1st year (CI₁) = ₹200

Compound Interest for 2nd year (CI₂) = ₹240

Formula Used:

Rate of Interest (R) = [(CI₂ − CI₁) ÷ CI₁] × 100

Calculations:

⇒ Let the Principal be P.

⇒ For the 1st year, CI = SI = ₹200.

⇒ For the 2nd year, interest is calculated on both the Principal and the interest of the 1st year.

⇒ Extra interest in 2nd year = 240 − 200 = ₹40.

⇒ This ₹40 is the interest earned on the 1st year interest (₹200) for one year.

⇒ R = (40 ÷ 200) × 100

⇒ R = (1 ÷ 5) × 100

⇒ R = 20%

∴ The correct answer is 20%.

Additional Information

SI and CI Relationship

For the first year, Simple Interest (SI) and Compound Interest (CI) are always equal, provided the interest is compounded annually.

Difference for 2 Years

The difference between CI and SI for 2 years is given by the formula: Difference = P(R ÷ 100)².

Successive Interest Calculation

If interest for two consecutive years (n and n+1) are given as I_n and I_n+1, then Rate R = [(I_n+1 − I_n) ÷ I_n] × 100.

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• जब से रमेश को चोरी में पकड़ा गया है, वह अपनों से आँख चुराता फिरता है।

Key Points

• मुहावरा - ऐसे वाक्यांश, जो सामान्य अर्थ का बोध न कराकर किसी विलक्षण अर्थ को प्रकट करते है, उसे मुहावरा कहते है।
• जैसे : ​​​खेत रहना का अर्थ- शहीद होना। वाक्य प्रयोग - पाकिस्तान से मुठभेड़ में कई भारतीय सैनिक "खेत रह गए"।

Additional Information

'जो रास्ता दिखाता है' वाक्य या वाक्यांश के लिए उपयुक्त शब्द होगा - मार्गदर्शक

Key Points  

• 'जो रास्ता दिखाता है' वाक्यांश के लिए उपयुक्त शब्द - मार्गदर्शक
• वाक्यांश के लिए उपयुक्त शब्द - अनेक शब्दों के लिए एक शब्द को प्रयुक्त करना ही वाक्यांश के लिए एक शब्द कहलाता है।

अन्य विकल्प -

Additional Information  कुछ महत्वपूर्ण वाक्यांश के लिए एक शब्द -

'जो संविधान के अनुकूल हो' वाक्यांश के लिए उपयुक्त शब्द - संवैधानिक

Key Points

• 'जो संविधान के अनुकूल हो' वाक्यांश के लिए उपयुक्त शब्द - संवैधानिक
• वाक्यांश के लिए उपयुक्त शब्द - अनेक शब्दों के लिए एक शब्द को प्रयुक्त करना ही वाक्यांश के लिए एक शब्द कहलाता है।

अन्य विकल्प -

Additional Information कुछ महत्वपूर्ण वाक्यांश के लिए एक शब्द -

'आँख' का पर्यायवाची शब्द है- नेत्र

Key Points

• 'आँख' का पर्यायवाची शब्द - 'नेत्र' होगा।
• 'आँख' के अन्य पर्यायवाची शब्द - नयन, चक्षु, दृष्टि, विलोचन, लोचन, अक्षि, अंबक, दृग आदि।
• पर्यायवाची - ऐसे शब्द जिनके अर्थ समान हों, पर्यायवाची शब्द कहलाते हैं।

अन्य विकल्प-

Additional Information कुछ महत्वपूर्ण पर्यायवाची शब्द -

सही उत्तर है - ज्येष्ठ

Key Points

• 'आयु में बड़ी व्यक्ति' वाक्यांश के लिए एक शब्द होगा - ज्येष्ठ
• वाक्यांश के लिए उपयुक्त शब्द - अनेक शब्दों के लिए एक शब्द को प्रयुक्त करना ही वाक्यांश के लिए एक शब्द कहलाता है।

अन्य विकल्प -

Additional Information कुछ महत्वपूर्ण वाक्यांश के लिए एक शब्द -

'हाथ का मैल होना' मुहावरे का सही अर्थ इनमें से होगा- अत्यंत तुच्छ होना

Key Points

• 'हाथ का मैल होना' का अर्थ - अत्यंत तुच्छ होना,
• वाक्य प्रयोग - अंबानी और अडानी के लिए तो पैसा "हाथ का मैल है", जो वस्तु चाहे खरीद ले।
• मुहावरा - ऐसे वाक्यांश, जो सामान्य अर्थ का बोध न कराकर किसी विलक्षण अर्थ को प्रकट करते है, उसे मुहावरा कहते है।
• उदाहरण के लिए - काठ का उल्लू - महामूर्ख व्यक्ति, वाक्य प्रयोग - रामू तो "काठ का उल्लू हैं"। उसकी समझ में कुछ नहीं आता।

अन्य विकल्प-

Additional Information 

'सर्प' शब्द के लिए पर्यायवाची अर्थ उपयुक्त रहेगा- व्याल

Key Points

• 'सर्प' का सही पर्यायवाची शब्द 'व्याल' होगा।
• 'सर्प' के अन्य पर्यायवाची शब्द है-​ नाग, विषधर, साँप, भुजंग, उरग, अहि पन्नग।।
• पर्यायवाची - जो शब्द समान अर्थ के कारण किसी दूसरे शब्द की जगह ले लेते हैं, उन्हें पर्यायवाची शब्द कहते हैं।

अन्य विकल्प-

Additional Information  कुछ अन्य महत्वपूर्ण पर्यायवाची शब्द:-

खंड, अवयव इन पर्यायवाची शब्दों का अर्थ है - भाग

Key Points

• 'भाग' का पर्यायवाची शब्द 'खंड, अवयव' है।
• 'भाग' के अन्य पर्यायवाची शब्द - अंश, टुकड़ा, हिस्सा, विभाजन।
• पर्यायवाची - ऐसे शब्द जिनके अर्थ समान हों, पर्यायवाची शब्द कहलाते हैं।

अन्य विकल्प-

Additional Information कुछ महत्वपूर्ण पर्यायवाची शब्द -

रिक्‍त स्‍थान की पूर्ति के लिए सर्वाध‍िक उपयुक्‍त शब्‍द "न‍िन्‍दा" है। अन्‍य व‍िकल्‍प असंगत हैं। 

Key Points

• वाक्‍य- जो लोग समय का ख्याल नहीं रखते, उनकी न‍िन्‍दा की जाती है।
• अत: र‍िक्‍त स्‍थान की पूर्ति के ल‍िए न‍िन्‍दा शब्‍द का प्रयोग होगा।
• न‍िन्‍दा का अर्थ- बुराई करना
• अन्‍य व‍िकल्‍प का प्रयोग करने से वाक्‍य का सार्थक अर्थ नहीं न‍िकलता है।

Additional Information

• दिनभर की दौड़ भाग वाली दिनचर्या और कठोर परिश्रम करने के बाद जब मनुष्य थक जाता है।
• जनता के पास लोकतंत्र में चुनाव ही वह अस्त हुआ करता है जिसके द्वारा वह शासक दल और विरोधी-दल दोनों पर अंकुश और नियंत्रण लगाए रख सकती है।
• भारत में बेल वृक्ष जंगली अवस्था में हिमालय के शुष्क पर्वतीय भागों में 1350 मीटर तक की ऊंचाई वाले भागों में देखने को मिल जाता है।

'किसी कार्य में निपुण' वाक्यांश के लिए एक शब्द होगा - पारंगत

Key Points

• 'किसी कार्य में निपुण' वाक्यांश के लिए एक शब्द होगा - पारंगत
• वाक्यांश के लिए उपयुक्त शब्द - अनेक शब्दों के लिए एक शब्द को प्रयुक्त करना ही वाक्यांश के लिए एक शब्द कहलाता है।

अन्य विकल्प -

Additional Information कुछ महत्वपूर्ण वाक्यांश के लिए एक शब्द -

सही उत्तर है - प्रलय

Key Points

• 'सृष्टि' शब्द का विलोम शब्द 'प्रलय' होगा।
• 'सृष्टि' शब्द का अर्थ है - निर्माण, रचना।
• 'प्रलय' शब्द का अर्थ - नाश, विलीनता लय।
• विलोम - जो शब्द किसी एक शब्द के विपरीत अर्थ को व्यक्त करते हैं, वे विलोम शब्द कहलाते हैं।

अन्य विकल्प-

Additional Information कुछ अन्‍य व‍िलोम शब्‍द- 

'मैदान मारना' मुहावरे का अर्थ है- युद्ध में विजय प्राप्त करना