DSSSB LDC (Jr. Assistant/Steno/LDC): (9 Oct 2025) Memory-Based Paper (Previous Year Paper)

The correct answer is Article 13.

Key Points

• Article 13 of the Indian Constitution declares that all laws inconsistent with or in derogation of Fundamental Rights shall be void.
• It ensures the supremacy of Fundamental Rights by invalidating laws that contradict or encroach upon them.
• Under Article 13(1), pre-constitutional laws inconsistent with Fundamental Rights shall be void to the extent of such inconsistency.
• Article 13(2) prohibits the State from making any law that takes away or abridges the Fundamental Rights, and such laws shall be void if enacted.
• This article is a key part of judicial review, empowering courts to strike down unconstitutional laws.

Additional Information

• Judicial Review: A process under which the judiciary reviews the constitutionality of legislative acts and executive decisions. It derives its authority from Articles 13, 32, and 226 of the Indian Constitution.
• Fundamental Rights: Enshrined in Part III of the Indian Constitution, these rights guarantee civil liberties, ensuring individuals can live with dignity and equality.
• Doctrine of Severability: If a part of a law is inconsistent with Fundamental Rights, only the offending part is declared void, not the entire law.
• Doctrine of Eclipse: Pre-constitutional laws inconsistent with Fundamental Rights are not void ab initio; they are eclipsed and become unenforceable until the inconsistency is removed.
• Article 32: Known as the "Right to Constitutional Remedies," it provides individuals the right to approach the Supreme Court for enforcement of Fundamental Rights.

The Correct answer is March 7th.

In News

• Jan Aushadhi Diwas 2025: Affordable Quality Medicines For A Healthier Future.

Key Points

• Jan Aushadhi Diwas is celebrated annually on March 7th to promote the use of generic medicines and raise awareness about the Pradhan Mantri Bhartiya Janaushadhi Pariyojana (PMBJP).
• The celebration is part of a week-long event from March 1st to 7th.
• The PMBJP was launched in November 2008 by the Department of Pharmaceuticals, Ministry of Chemicals & Fertilizers.
• PMBJP aims to provide quality medicines at affordable prices through Pradhan Mantri Bhartiya Janaushadhi Kendras (PMBJK).
• A significant initiative under PMBJP is the launch of Jan Aushadhi Suvidha Sanitary Napkins, priced at Rs. 1 per pad.
• The Jan Aushadhi SUGAM mobile app, launched in August 2019, helps locate PMBJKs and compare the prices of generic vs branded medicines.
• Jan Aushadhi medicines are 50%-80% cheaper than branded medicines available in the open market.
• Medicines under the scheme are sourced from WHO-GMP certified manufacturers and undergo testing in NABL-accredited laboratories.
• PMBJP offers incentives, including up to Rs. 20,000 per month for Kendras based on monthly purchases and a one-time incentive of Rs. 2 lakh for Kendras in specific areas, such as Northeastern States, Himalayan regions, and backward districts.

The correct answer is Lodi Dynasty.

Key Points

• Double Dome:-
• The double dome consists of two domes, one inner and one outer, with a space between them.
• The inner dome is smaller and supports the weight of the outer dome. This design allows for taller and more slender domes, and it also creates a dramatic visual effect.
• The Lodi dynasty introduced the "double dome" feature of Indo-Islamic architecture.
• The first example of a double dome in Indo-Islamic architecture is the tomb of Sikandar Lodi (1517/18) in Delhi. Other notable examples include the tomb of Humayun (1572) in Delhi, the Taj Mahal (1648) in Agra, and the Jama Masjid (1656) in Delhi.
• Lodi dynasty:-
• It was the last dynasty of the Delhi Sultanate, ruling from 1451 to 1526.
• During their reign, they made significant contributions to Indo-Islamic architecture, including the introduction of the double dome.
• The Lodi style of architecture is characterized by its simplicity, elegance, and use of high-quality materials.

Additional Information

• Slave Dynasty:-
• It was the first dynasty of the Delhi Sultanate, which ruled over northern India from 1206 to 1290.
• The dynasty was founded by Qutb-ud-din Aibak, who was a former slave of the Ghurid Sultan Muhammad of Ghor.
• Khilji Dynasty:-
• It was the second dynasty of the Delhi Sultanate, ruling over northern India from 1290 to 1320.
• The dynasty was founded by Jalal-ud-din Firoz Khilji, who was a former slave of the Mamluk dynasty.
• Jalal-ud-din was a skilled and ambitious general, and he quickly rose through the ranks of the Mamluk military.
• In 1290, he assassinated the last Mamluk sultan and seized control of Delhi for himself.
• Tughlaq Dynasty:-
• It was the third dynasty of the Delhi Sultanate, ruling over northern India from 1320 to 1413.
• The dynasty was founded by Ghazi Malik, who ascended the throne under the title of Ghiyath al-Din Tughluq.
• The Tughlaq Dynasty was a period of great expansion and consolidation for the Delhi Sultanate.

The Correct answer is Lord Canning.

Key Points

• Lord Canning was the last Governor-General and the first Viceroy of India.
• The Doctrine of Lapse, introduced by Lord Dalhousie, allowed the British to annex states where the rulers died without a male heir.
• It was widely criticized for being unjust and causing resentment among Indian princes and rulers.
• After the Revolt of 1857, Lord Canning sought to adopt a conciliatory approach and abolished the Doctrine of Lapse to ensure loyalty among Indian rulers.
• This abolition marked a shift in British policy, focusing on maintaining the support of princely states.
• Lord Canning introduced the Indian Councils Act of 1861, which aimed to increase Indian participation in governance.
• He also established the University of Calcutta, Bombay, and Madras, promoting education and modernization.

Additional Information

• Lord William Bentinck
• Lord William Bentinck served as Governor-General of India from 1828 to 1835.
• He is known for his social reforms, including the abolition of Sati in 1829.
• Bentinck introduced policies to improve education and administration, such as the promotion of English education.
• He is often regarded as the first reformist Governor-General of India.
• Lord Hardinge
• Lord Hardinge served as Governor-General of India from 1844 to 1848.
• He played a significant role in the First Anglo-Sikh War, resulting in the annexation of Punjab.
• Lord Hardinge emphasized military reforms and improved infrastructure in India during his tenure.
• Lord Ellenborough
• Lord Ellenborough served as Governor-General of India from 1842 to 1844.
• He is remembered for his role in the Afghan wars and the retrieval of the gates of Somnath temple.
• His administration faced criticism for its lack of stability and abrupt policy changes.

The correct answer is Fraternity.

Key Points

• The term Fraternity in the Preamble of the Indian Constitution signifies a sense of brotherhood among all citizens of India.
• It aims to promote the dignity of the individual and the unity and integrity of the nation.
• Fraternity ensures the feeling of mutual respect and compassion, transcending barriers of caste, religion, language, and region.
• The concept of fraternity aligns with the fundamental duty of every citizen to promote harmony and brotherhood under Article 51A(e) of the Indian Constitution.
• The framers of the Constitution were inspired by the ideals of the French Revolution, which emphasized Liberty, Equality, and Fraternity.

Additional Information

• Preamble of the Indian Constitution:
• The Preamble declares India to be a Sovereign, Socialist, Secular, Democratic, and Republic nation.
• It guarantees Justice (social, economic, and political), Liberty (of thought, expression, belief, faith, and worship), Equality (of status and opportunity), and Fraternity.
• Fraternity and National Integration:
• Fraternity helps in fostering national integration by eliminating prejudices and promoting inclusiveness.
• It emphasizes the concept of "Unity in Diversity," which is a cornerstone of Indian culture and society.
• French Revolution Influence:
• The ideals of Liberty, Equality, and Fraternity originated during the French Revolution (1789-1799).
• These principles have significantly influenced modern democratic constitutions, including India’s.
• Article 51A of the Constitution:
• It lays down Fundamental Duties for Indian citizens, including the duty to promote harmony and the spirit of common brotherhood.
• This article complements the spirit of fraternity mentioned in the Preamble.

The Correct answer is The Constitution (Forty-Fourth Amendment) Act, 1978.

Key Points

• The Right to Property was originally enshrined as a Fundamental Right under Article 31 of the Indian Constitution.
• However, the Constitution (Forty-Fourth Amendment) Act, 1978 repealed the Right to Property from the list of Fundamental Rights and reclassified it as a legal right under Article 300A in Part XII of the Constitution.
• This amendment was introduced during the tenure of the Janata Party government, headed by Prime Minister Morarji Desai.
• The primary reason for this change was to prevent the judiciary from interfering with the government's land reform policies, especially regarding the abolition of zamindari and redistribution of land to the landless.
• This amendment protects the citizens from being deprived of their property except by the authority of law, but it no longer enjoys the status of a Fundamental Right.
• The reclassification of the Right to Property ensured that the government could implement socialist land reforms without facing constitutional challenges.
• This change marked a significant shift in India's constitutional and political landscape, reflecting its commitment to socio-economic justice.

 Additional Information

• The Constitution (Forty-Second Amendment) Act, 1976
• Known as the Mini Constitution, this amendment made significant changes to the Indian Constitution.
• It added the words "Socialist," "Secular," and "Integrity" to the Preamble.
• It also strengthened the position of the Directive Principles of State Policy over Fundamental Rights.
• This amendment was enacted during the Emergency period (1975-1977) under the leadership of Indira Gandhi.
• The Constitution (First Amendment) Act, 1951
• This amendment introduced changes to restrict the misuse of Fundamental Rights, especially the Right to Freedom of Speech and Expression (Article 19).
• It also added Articles 31A and 31B to safeguard agrarian reforms and protect laws included in the Ninth Schedule from judicial review.
• This amendment was enacted to address judicial challenges to land reform legislation.
• The Constitution (Twenty-Fifth Amendment) Act, 1972
• This amendment was passed to ensure that the Directive Principles of State Policy could not be challenged on the grounds of inconsistency with Fundamental Rights.
• It also amended Article 31 to enable the government to acquire property for public purposes without full compensation.
• This was primarily aimed at facilitating land acquisition for developmental projects.

Alauddin Khalji  was the ruler of the Delhi Sultanate when it faced the Mongol onslaught.

Key Points

• Alauddin Khalji was the ruler of the Delhi Sultanate from 1296 to 1316.
• During his reign, he faced the Mongol onslaught, which was a series of invasions by the Mongols into the Indian subcontinent.
• The Mongols were a powerful nomadic group from Central Asia who had conquered much of Asia in the 13th century.
• They were feared for their military prowess and their ruthlessness.
• Alauddin Khalji was a brilliant military strategist and a ruthless ruler.
• He took a number of measures to defend the Delhi Sultanate from the Mongols, including:
• ​Building a new capital city, Siri, which was heavily fortified.
• Raising a large standing army.
• Imposing strict economic controls to ensure that the state had the resources to fight the Mongols.
• Using spies and informants to gather intelligence on the Mongols.
• As a result of these measures, Alauddin Khalji was able to defeat the Mongols in a series of battles.
• He also forced the Mongols to pay tribute to the Delhi Sultanate.
• This effectively prevented the Mongols from conquering India.
• Alauddin Khalji's victory over the Mongols was a major achievement.
• It helped to ensure the survival of the Delhi Sultanate and it protected India from Mongol rule.

​Therefore the correct answer is Alauddin Khalji.

The correct answer is Sansad Bhashini.

In News

• The Lok Sabha Secretariat and the Ministry of Electronics and Information Technology (MeitY) signed an MoU to develop the Sansad Bhashini initiative.

Key Points

• Sansad Bhashini aims to integrate AI-driven translation and speech-to-text conversion for parliamentary content.
• The initiative supports real-time translation of debates, committee meetings, and agenda files into multiple languages.
• An AI-powered chatbot will assist MPs and officials in retrieving parliamentary rules and procedural documents.
• The project includes automatic summarization of lengthy debates for improved decision-making and record-keeping.

Additional Information

• The initiative leverages Bhashini, a MeitY initiative, for advanced AI-based translation capabilities.
• Sansad Bhashini will improve linguistic accessibility for MPs, researchers, and the general public.
• It integrates noise reduction and customizable vocabulary for enhanced speech-to-text accuracy.
• The initiative aligns with India’s push for technology-driven governance and inclusive policymaking.

The correct answer is Mark Carney.

In News

• Mark Carney was sworn in as the 24th Prime Minister of Canada, succeeding Justin Trudeau.
• He emphasized a willingness to work with U.S. President Donald Trump despite past tensions.

Key Points

• Mark Carney is a former Governor of the Bank of Canada (2008-2013) and Governor of the Bank of England (2013-2020).
• He won the leadership of the ruling Liberal Party, replacing Trudeau after nine years in office.
• Carney reshaped his cabinet, reducing ministerial positions and appointing Francois-Philippe Champagne as Finance Minister.
• He signed an order eliminating the carbon tax in his first cabinet meeting.

Additional Information

• Canada's Political Landscape:
• Justin Trudeau led Canada for over nine years before stepping down.
• Carney’s appointment comes amid uncertainty over Canada-U.S. relations and economic concerns.
• The opposition Conservative Party remains a strong contender in upcoming elections.
• Mark Carney’s Economic Expertise:
• He managed economic crises during his tenure as a central banker in Canada and the UK.
• His policies as Prime Minister focus on economic stabilization and diplomatic cooperation.

The correct answer is Part VI.

Key Points

• The provisions related to the "Subordinate Courts" in the States are mentioned in Part VI of the Indian Constitution.
• It falls under Chapter VI (Articles 233 to 237), which deals with the structure, appointment, and jurisdiction of Subordinate Courts.
• The Subordinate Courts include District and Sessions Courts, along with other lower courts such as Magistrate and Civil Judge Courts.
• The High Court has supervisory authority over Subordinate Courts under its jurisdiction, ensuring proper administration of justice.
• The provisions ensure the independence of the judiciary by laying down guidelines for the recruitment and conditions of service of judicial officers.

Additional Information

• Subordinate Courts:
• Subordinate Courts function under the supervision of the respective High Courts in their states.
• They are primarily responsible for handling cases related to civil, criminal, and revenue matters at the district level and below.
• The District Judge is the highest judicial authority in a district.
• Articles 233 to 237:
• Article 233: Deals with the appointment of District Judges.
• Article 234: Relates to the recruitment of persons other than District Judges to the judicial service.
• Article 235: Grants control over Subordinate Courts to the High Court.
• Article 236: Defines the term "District Judge" and "Judicial Service".
• Article 237: Provides for the application of these provisions to certain classes of Magistrates.
• Independence of Judiciary:
• The Constitution ensures the independence of Subordinate Courts by entrusting control over the judiciary to the High Courts.
• Appointments, promotions, and disciplinary actions are supervised by the High Court to maintain impartiality and efficiency.
• Hierarchy of Courts:
• The Subordinate Courts are part of a judicial hierarchy, with the Supreme Court at the top, followed by High Courts, and then Subordinate Courts.
• This hierarchy ensures the streamlined delivery of justice.

The correct answer is number of shells increases.

Key Points:

• Atomic sizes drop as a period moves from left to right.
• The same shell receives progressively more electrons.
• As the atomic number rises, so does the nucleus's attraction to the valence b.
• The atomic size grows as one descends the group, top to bottom.
• This is so that more electron shells can be added when the atomic number rises.

Additional Information:

• The chemical elements are arranged in rows and columns on what is known as the periodic table, or periodic table of the (chemical) elements.
• It is frequently used in physics, chemistry, and other sciences and is frequently regarded as a symbol of chemistry.
• It is a visual representation of the periodic law, which claims that the atomic numbers of chemical elements have a roughly periodic relationship with their attributes.
• The table is divided into four blocks that are about rectangular in shape.
• The table's columns are referred to as groups and its rows are known as periods.
• The periodic table's elements in the same group have comparable chemical properties.

The correct answer is calcium and phosphorus.

Key Points:

• The structure that holds the body up is made of bone.
• Additionally, it supports the body's major organs and anchors the muscles.
• It is a solid, unyielding tissue.
• A dense matrix made of calcium and phosphate molecules contains the bone cells.
• A different kind of connective tissue called a ligament can join two bones together.
• This tissue is extremely flexible.
• Another form of connective tissue is the tendon, which links bones and muscles.

Additional Information:

• Tendons are fibrous tissues with little flexibility and tremendous strength.
• The cells of cartilage are widely spaced.
• Sugars and proteins make up the solid matrix.
• In addition to the nose, ear, trachea, and larynx, cartilage smoothes the surfaces of bones at joints.
• Areolar connective tissue can be found in the bone marrow, around blood vessels and nerves, and between the skin and muscles.
• It supports internal organs, fills empty space inside the organs, and aids in tissue restoration.

The correct answer is Narmada.

Key Points

• River Narmada emerges from Amarkantak Hill of Maikal Range, Madhya Pradesh.
• The mouth of this river is the Gulf of Khambhat (Arabian Sea), Gujarat.
• The mighty Narmada River as well the Son, the Mahanadi, and Arnadoh which is a major tributary of the Godavari all arise in the Amarkantak plateau.
• Major dams on the Narmada river are Sardar Sarovar Dam, Indira Sagar Dam, Omkareshwar Dam, Bargi Dam, etc.

Important Points

The correct answer is Plant and Animal fossils.

Important Points

• Paleontology is the study of past life forms using fossils.
• An example of paleontology is the branch of geology that studies dinosaurs.
• The study of the forms of life existing in prehistoric or geologic times, as represented by the fossils of plants, animals, and other organisms.

​

Additional Information

• Volcanology, also spelled vulcanology, the discipline of the geologic sciences that is concerned with all aspects of volcanic phenomena.
• Volcanology, A geologist uses a rock hammer to sample active pahoehoe lava for geochemical analysis on the Kilauea volcano, Hawaii.
• Meteorology is the study of the atmosphere, atmospheric phenomena, and atmospheric effects on our weather.
• The atmosphere is the gaseous layer of the physical environment that surrounds a planet. ... Meteorology is a subdiscipline of the atmospheric sciences, a term that covers all studies of the atmosphere.
• ​Petrology is the study of rocks - igneous, metamorphic, and sedimentary - and the processes that form and transform them.
• Mineralogy is the study of the chemistry, crystal structure, and physical properties of the mineral constituents of rocks.

The correct answer is a - 4, b - 2, c - 1, d - 3.

Important Points

Some Indian States and their dances:

The correct answer is Coach.

Key Points

• Dronacharya award is given by the Ministry of Youth Affairs and Sports, Government of India, for excellence in sports coaching.
• The award is known as after Drona, often referred to as "Dronacharya" or "Guru Drona", a personality from the Sanskrit epic Mahabharata of ancient India.
• The  Dronacharya award contains a medallion, a certificate, and a money prize of Rs 15 lakh(lifetime) and 10 Lakh (regular).

Additional Information

• Major Dhyan Chand Khel Ratna Award:
• It is that the highest sporting award given by the Ministry of Youth Affairs and Sports for the spectacular and top performance within the field of sports by a sportsperson.
• This, award contains a medallion, a certificate, and a money prize of Rs 25 lakh.
• Arjuna Awards:
• This award is given by the Ministry of Youth Affairs and Sports, Government of India to acknowledge outstanding action in National sports.
• Instituted in 1961, the award carries a money prize of Rs 15 Lakh, a bronze sculpture of Arjuna, and a scroll.

The correct answer is Amartya Sen.

Key Points

• Amartya Sen was born into a Brahman family in Santiniketan, Bengal, in India.
• In 1998, was awarded the Nobel Prize in Economics for his work in welfare economics.
• Book by Amartya Sen is Development as Freedom, The Idea of Justice, The Argumentative Indian, Garibi Aur Akaal, Identity & Violence, Inequality Reexamined, The Country of First Boys: And Other Essays, etc.

Important Points

The correct answer is Direct and Progressive. 

Important Points

• Income tax is a Direct tax.
• Direct taxes are progressive, because it is possible to help more people who do not earn as much, and at the same time, mobilize resources from those who earn well. This is what makes them progressive.
• This is the tax that is levied on the annual income or the profits which are directly paid to the government.
• Everyone who earns any kind of income is liable to pay income tax.
• A progressive tax imposes a higher rate on the rich than on the poor. It's based on the taxpayer's income or wealth. It's done to help lower-income families pay for basics like shelter, food, and transportation.
• A progressive tax allows them to spend a larger share of their incomes on the cost of living expenses.
• Examples of progressive tax include investment income taxes, tax on interest earned, rental earnings, estate tax, and tax credits.

The correct answer is Dadabhai Naoroji.

• Dadabhai Naoroji was the first to determine national income.
• He is also known as the grand old man of India.

Key Points

• He was also an unofficial ambassador of India.
• In the UK, he was a member of the house of Commons in 1892.
• He was the first Indian to become a member of the British parliament.
• He was born in Bombay.
• He was the co-founder of the Indian National Congress.
• He was an academician, politician, and trader.
• He propounded the theory of wealth drain from India.
• He was born in a Parsi family.
• Maharaja of Baroda, Sayajirao Gayakwad patronised him.
• The London society in 1865 was launched by him.

The correct answer is Hospitals.

Key Points

• Social infrastructure refers to facilities and services that improve the quality of life and promote social well-being, such as healthcare, education, and housing.
• Hospitals are a prime example of social infrastructure as they provide essential healthcare services to the population.
• Social infrastructure ensures access to basic health services, contributing to the overall development and productivity of a nation.
• Hospitals play a critical role in reducing mortality rates, managing diseases, and improving public health outcomes.
• Other examples of social infrastructure include schools, libraries, community centers, and sanitation facilities.

Additional Information

• Social Infrastructure vs. Physical Infrastructure:
• Social infrastructure focuses on services and institutions that enhance human capital (e.g., hospitals, schools).
• Physical infrastructure pertains to tangible assets like roads, railways, airports, and bridges.
• Healthcare Infrastructure:
• Healthcare facilities such as hospitals, clinics, and laboratories are vital components of social infrastructure.
• Public healthcare systems aim to provide affordable and accessible medical services to all citizens.
• Education Infrastructure:
• Schools, colleges, and universities are examples of social infrastructure that foster education and skill development.
• They contribute to economic growth by enhancing the knowledge base of a society.
• Government Initiatives:
• Programs like Ayushman Bharat aim to strengthen healthcare infrastructure in India.
• Investments in social infrastructure are critical for achieving sustainable development goals (SDGs).

The correct answer is National Innovation Challenge for Drone Application and Research.

In News

• The Ministry of Electronics and Information Technology (MeitY), in collaboration with Drone Federation India (DFI), has launched the National Innovation Challenge for Drone Application and Research (NIDAR) under the ‘SwaYaan’ initiative.

Key Points

• NIDAR focuses on advancing drone technology for applications in agriculture, disaster management, logistics, and healthcare.
• The challenge was inaugurated by S. Krishnan, Secretary of MeitY, at Electronics Niketan, MeitY.
• It offers a prize pool of INR 40 Lakhs, incubation opportunities, cloud credits, and internships with leading drone companies.
• The Drone Federation India (DFI), which represents over 550 drone companies and 5,500 certified drone pilots, will mentor participants.

Additional Information

• The SwaYaan initiative aims to build human resource capacity in Unmanned Aircraft Systems (UAS).
• The challenge is expected to attract over 100 student teams from institutions across India.
• It encourages the development of autonomous drones for applications like precision agriculture and disaster response.
• The initiative aligns with India’s vision of becoming a global drone hub by 2030.

The correct answer is Article 213.

Key Points

• Article 213 of the Indian Constitution empowers the Governor to promulgate ordinances when the state legislature is not in session.
• The Governor can issue ordinances under Article 213 only when he/she is satisfied that circumstances require immediate action.
• Ordinances issued under Article 213 have the same force and effect as laws enacted by the state legislature.
• These ordinances must be approved by the state legislature within six weeks of its reassembly; otherwise, they cease to operate.
• The provision ensures the Governor can address urgent matters when the legislature is not available, maintaining governance continuity.

Additional Information

• Ordinance: It is a temporary law enacted by the executive authority (Governor or President) when the legislature is not in session.
• Article 123: Similar to Article 213, it empowers the President to promulgate ordinances when Parliament is not in session.
• Limitations: The ordinance-making power cannot be used to bypass the legislature or amend the Constitution.
• Judicial Review: Ordinances are subject to judicial review to ensure compliance with constitutional provisions.
• Historical Context: The ordinance-making power was introduced in India as part of the Government of India Act, 1935, and later incorporated into the Constitution of India.

The correct answer is - Raja Man Singh I

Key Points

• Raja Man Singh I
• Raja Man Singh I was one of the Navratnas (nine gems) in the court of the Mughal Emperor Akbar.
• He was a trusted general and a close associate of Akbar.
• He played a significant role in military campaigns and administration during Akbar's reign.
• His loyalty and service earned him a prominent position among Akbar’s top advisors.

Additional Information

• Navratnas
• The Navratnas were a group of nine extraordinary men in the court of Emperor Akbar who were renowned for their talents and contributions in various fields.
• They included notable figures like Birbal (known for his wisdom and wit) and Tansen (a legendary musician).
• Raja Man Singh I
• He was the Kachwaha Rajput ruler of Amber (modern-day Jaipur).
• His contributions to the Mughal Empire included leading successful campaigns in regions like Bengal, Afghanistan, and Deccan.
• He also played a pivotal role in securing alliances for Akbar through marital diplomacy, including his own marriage into the Mughal family.
• Akbar’s Administration
• Akbar's administration was noted for its inclusivity and merit-based appointments, which included talents from various regions and communities.
• His policy of religious tolerance and strong administrative framework laid the foundations for a unified and prosperous empire.

The correct answer is Chlorine.

Key Points

• Bleaching powder is used as an oxidising agent in many chemical industries, for disinfecting drinking water.
• It is called Calcium Hypochlorite and is represented as CaOCl_2.
• Bleaching powder is produced by the action of Chlorine on dry slaked lime (Ca(OH)₂) and is soluble in water.
• When bleaching powder reacts with water, it hydrolysis to hypochlorous acid (HCIO), which hydrolysis further into Hydrochloric acid (HCl), releasing a strong smell due to Chlorine (Cl).
• In this reaction, we get the following chemical equation.
• Ca(OCl)₂+H₂O→Ca(OH)₂+Cl_{2 (gas).}
• So, when Bleaching powder reacts with water, Chlorine gas is released. Hence option 2 is correct.
• Chlorine gas is used in the manufacturing of bleaching powder.
• Bleaching powder is used for bleaching cotton and linen in the textile industry, and for bleaching wood pulp in paper factories.
• Hypochlorous acid is a weak acid that forms when Chlorine dissolves in water.
• The atomic number (Z) of Chlorine is 17 and it is a p-block element.

Additional Information

• Hydrogen (the atomic number is 1), in elemental form, exists as a diatomic molecule (H₂) and is called Dihydrogen.
• There are three isotopes of Hydrogen: Protium, Deuterium and Tritium.
• Carbon Monoxide (CO) is a colourless and odourless poisonous gas produced as a result of the incomplete combustion of carbon.
• Carbon monoxide binds to haemoglobin and forms carboxyhaemoglobin which is about 300 times more stable than the oxygen-haemoglobin complex.
• When this reaches about 3-4%, the oxygen-carrying capacity of blood is reduced.
• Carbon dioxide (CO₂) is a colourless and non-flammable gas at normal temperature and pressure.
• It is released into the atmosphere by respiration, the burning of fossil fuels and by decomposition of limestone.

The Correct Answer is ₹3,000.

In News

• Pradhan Mantri Shram Yogi Maandhan (PM-SYM), is a voluntary and contributory pension scheme launched by the Government of India to provide social security to unorganised workers.

Key Points

• Pradhan Mantri Shram Yogi Maandhan (PM-SYM) is a voluntary and contributory pension scheme launched by the Government of India for unorganised workers.
• The scheme guarantees a minimum monthly pension of ₹3,000 after the age of 60 for workers earning up to ₹15,000 per month.
• PM-SYM was introduced in the Interim Budget 2019.
• It is administered by the Ministry of Labour and Employment, in collaboration with Life Insurance Corporation of India (LIC) and Common Service Centres (CSCs).
• LIC is responsible for pension pay-outs and acts as the Pension Fund Manager.
• Enrolment in the scheme is facilitated through Common Service Centres (CSCs) across India.
• Exit and Withdrawal Provisions:
• Exit Before 10 Years: Refund of the contributed amount with savings bank interest rate.
• Exit After 10 Years but Before 60 Years: Return of contributions with accumulated interest (either actual or savings bank interest rate, whichever is higher).
• Death Before 60 Years: The spouse can either continue the scheme or withdraw the contributed amount with interest.
• Death After 60 Years: The spouse receives 50% of the pension as a family pension.
• After the death of both the subscriber and spouse, the entire corpus is credited back to the fund.
• In case of default (non-payment of contributions): The subscriber can regularize their contribution by paying the outstanding dues and penalty charges, if any.

The correct answer is Womesh Chandra Bonnerjee.

Key Points

• Womesh Chandra Bonnerjee was the first President of the Indian National Congress (INC), presiding over its inaugural session in 1885.
• The first session of the INC was held in Bombay (now Mumbai) from 28–31 December 1885.
• This historic session was attended by 72 delegates, marking the beginning of the Indian National Congress as a political platform.
• Womesh Chandra Bonnerjee was a prominent lawyer and statesman, deeply involved in the Indian freedom struggle.
• The INC was founded by A.O. Hume, a retired British civil servant, with the aim of providing a platform for civil and political dialogue among Indians.

Additional Information

• Indian National Congress (INC):
• Founded on 28 December 1885, the INC was one of the most significant political organizations in India's struggle for independence.
• The founders included A.O. Hume, Dadabhai Naoroji, and Dinshaw Wacha.
• The INC initially aimed at creating a dialogue with the British government for reforms but later evolved into a mass movement for complete independence.
• Womesh Chandra Bonnerjee:
• He was the first Indian to act as an Advocate-General of Bengal and the first Indian to contest elections for the British Parliament.
• Bonnerjee played a pivotal role in the early years of the INC, helping shape its policies and direction.
• Key Goals of Early INC:
• The early INC worked towards greater representation of Indians in administrative roles, reduction of military expenditure, and promotion of Indian industries.
• It sought constitutional reforms and civil rights for Indians under British rule.
• Legacy of INC:
• The INC played a central role in India's independence movement, with leaders like Mahatma Gandhi, Jawaharlal Nehru, and Sardar Patel emerging from its ranks.
• It continues to be a major political party in India post-independence.

The Correct Answer is ​Port Louis.

In News

• Prime Minister Narendra Modi to attend Mauritius National Day as chief guest on March 12.

Key Points

• Prime Minister Narendra Modi was on a two-day state visit to Mauritius starting March 11, 2025.
• He was invited as the Chief Guest for the National Day celebrations of Mauritius, which are held every year on March 12.
• The National Day of Mauritius commemorates the country's independence from British rule on March 12, 1968.
• Prime Minister Modi attended Mauritius' National Day celebrations as Chief Guest for the second time since 2015.
• The visit saw participation from various Indian Defence Forces, including a contingent of Indian Defence Forces, an Indian Navy ship, and the Indian Air Force Akash Ganga sky diving contingent.
• Mauritius is an island nation in the Indian Ocean, located about 2,000 kilometers off the southeastern coast of Africa. Its capital is Port Louis.

The correct answer is 42nd Amendment.

Key Points

• The 42nd Amendment Act of 1976 is popularly referred to as the "Mini Constitution" due to its vast and comprehensive changes to the Constitution of India.
• It was enacted during the Emergency period under the leadership of Prime Minister Indira Gandhi.
• This amendment brought significant changes to the Preamble, Fundamental Rights, Fundamental Duties, and Directive Principles of State Policy (DPSP).
• The words "Socialist," "Secular," and "Integrity" were added to the Preamble, redefining India's identity as a nation.
• It also curtailed the powers of the judiciary, giving more authority to the Parliament.

Additional Information

• Preamble Amendments: The terms "Socialist," "Secular," and "Integrity" were introduced to strengthen India's commitment to democracy and pluralism.
• Fundamental Duties: The amendment introduced ten Fundamental Duties under Article 51A, emphasizing the moral obligations of citizens.
• Judiciary vs. Legislature: It attempted to reduce the independence of the judiciary by limiting its power to review constitutional amendments.
• Directive Principles: The amendment gave precedence to the Directive Principles of State Policy over Fundamental Rights, emphasizing socioeconomic justice.
• Emergency Powers: It extended the duration of the Lok Sabha and State Assemblies during a National Emergency from five to six years.

The correct answer is Article 155.

Key Points

• Article 155 of the Constitution of India provides for the appointment of Governors in Indian states.
• The Governor of a state is appointed by the President of India by warrant under his hand and seal.
• The appointment process ensures that the Governor serves as the representative of the Union Government in the state.
• The term of office for a Governor is normally 5 years, but they serve at the pleasure of the President.
• The Governor's role is primarily ceremonial, but they hold powers as per the provisions of the Constitution, including executive, legislative, and discretionary powers.

Additional Information

• Article 154: It vests the executive power of the state in the Governor, to be exercised directly or through officers subordinate to them.
• Article 156: It specifies the conditions of service and tenure of the Governor, stating they hold office at the pleasure of the President.
• Federal Structure: The appointment of Governors reflects India’s quasi-federal structure, where the Union Government has oversight over states through the Governor.
• Role of the Governor: The Governor acts as a constitutional head, ensuring the state government operates within the framework of the Constitution.
• Discretionary Powers: In certain situations, such as the dissolution of the state assembly or during a constitutional crisis, the Governor can act independently of the Council of Ministers.

The correct answer is To build a more accountable, compassionate, and citizen-centric workforce.

In News

• Ministry of Ayush launches the Rashtriya Karmayogi Jan Seva Programme to build a citizen-centric workforce.

Key Points

• The Rashtriya Karmayogi Jan Seva Programme aims to build a more accountable, compassionate, and citizen-centric workforce in the Ministry of Ayush.
• The program emphasizes the spirit of “Seva Bhav” (service) and encourages public servants to use their roles to bring positive change to people's lives.
• It focuses on both service and self-improvement, aiming to upskill employees and broaden their perspectives on their responsibilities.
• Training involves hands-on activities like structured discussions, teamwork exercises, and problem-solving to engage employees and foster meaningful public service contributions.

Additional Information

• Seva Bhav
• “Seva Bhav” translates to the spirit of service and emphasizes the importance of public servants adopting a mindset of service to others.
• Capacity Building Commission
• The Capacity Building Commission is responsible for enhancing the skill sets of public servants and transforming the culture of public service in India.
• Self-Improvement in Public Service
• The program encourages personal growth and self-reflection, motivating employees to improve both in their professional and personal lives to better serve the public.

The Correct answer is Gram Sabha.

Key Points

• Article 243A of the Indian Constitution specifically deals with the Gram Sabha.
• The Gram Sabha consists of persons registered in the electoral rolls relating to a village within the area of a Panchayat at the village level.
• It is considered the foundation of the Panchayati Raj system and functions as a direct democracy at the grassroots level.
• The Gram Sabha enables the participation of people in decision-making, ensuring accountability and transparency in local governance.
• It has the authority to discuss and decide on matters related to the developmental activities and welfare schemes in its jurisdiction.
• Key roles include approving the village budget, auditing accounts, and monitoring the functioning of the Panchayats.
• The Gram Sabha promotes social inclusion, allowing marginalized communities to express their concerns.

 Additional Information

• Composition of Panchayats
• The composition of Panchayats refers to the structure and members of the Panchayat institutions at different levels—village, intermediate, and district.
• The members are elected by the people through direct elections, ensuring representation of every section of society.
• Constitution of Panchayats
• The constitution of Panchayats under Article 243B ensures the establishment of Panchayats at the village, intermediate, and district levels across India.
• This provision aims to strengthen local governance and decentralize power.
• Elections to Panchayats
• Article 243K mandates the State Election Commission to oversee the conduct of elections for Panchayats.
• Regular elections ensure the democratic functioning of Panchayats and uphold the principles of representation and accountability.

The correct answer is unsaturated compounds.

Key Points

• Unsaturated compounds
• ​Organic compounds known as unsaturated hydrocarbons are characterized by the presence of a double or triple bond between two carbon atoms that are adjacent to one another and are entirely composed of hydrogen and carbon.
• The position of the double or triple bond is either described by a number written before the compound's name in the IUPAC nomenclature of unsaturated hydrocarbons (as in 2,4 pentadiene) or by a number written before the suffix, such as "-ene" or "-yne," (as in pent-2-ene).
• Alkenes and olefins are hydrocarbons that have at least one double bond between two adjacent carbon atoms.
• Alkynes are hydrocarbons that have at least one triple bond between two carbon atoms that are right next to each other.

Additional Information

• Saturated compounds
• ​A saturated hydrocarbon is one in which every single carbon-carbon bond is present.
• Carbon and hydrogen are the only components of an organic compound known as a hydrocarbon.
• Saturated hydrocarbons, as the name suggests, are hydrocarbons in which all of the carbon atoms are bonded to four other atoms and are "saturated," indicating that these organic compounds lack multiple carbon-carbon bonds.
• The carbon chains of alkanes can be either straight or branched.
• These saturated hydrocarbons have sp3 hybridization on every carbon atom.
• Cycloalkanes have sp3 hybridized carbon atoms arranged in a ring. Saturated hydrocarbons, on the other hand, have a ring that can form side chains.

The correct answer is 7516.6 Kms.

Important Points

• India is one of the oldest civilizations in the world with a kaleidoscopic variety and rich cultural heritage.
• As the 7th largest country in the world, India stands apart from the rest of Asia, marked off as it is by mountains and the sea, which give the country a distinct geographical entity.
• Bounded by the Great Himalayas in the north, it stretches southwards and at the Tropic of Cancer, tapers off into the Indian Ocean between the Bay of Bengal on the east and the Arabian Sea on the west.
• Lying entirely in the northern hemisphere, the mainland extends between latitudes 8° 4' and 37° 6' north, longitudes 68° 7' and 97° 25' east and measures about 3,214 km from north to south between the extreme latitudes and about 2,933 km from east to west between the extreme longitudes.
• It has a land frontier of about 15,200 km.
• The total length of the coastline of the mainland, Lakshadweep Islands, and Andaman & Nicobar Islands are 7,516.6 km.

The correct answer is Regur Soil.

Key Points

• Black Soils are commonly referred to as regur but are widely known as “black cotton soils,” as cotton has been the most common conventional crop in areas where they are found.
• This type of soil is typical found in the Deccan Trap (Basalt) region which spreads over northwest Deccan plateau and is made from lava flows.
• The Black soil or Regur is found on the plateaus of Maharashtra, Saurashtra, Malwa, Madhya Pradesh, Chhattisgarh and stretch in the Southeast direction along the Godavari and the Krishna Valleys.
• The properties of such soils include the following: high compressibility, low bearing capacity, and low shearing strength.
• The Black soils are made up of clayey materials and are widely known for their capacity to hold moisture.
• The Black soils are highly prosperous in calcium carbonate, magnesium, potash, and lime.

The correct answer is Service Sector.

Important Points

• The service sector, also known as the tertiary sector, is the third tier in the three-sector economy.
• Instead of product production, this sector produces services maintenance and repairs, training, or consulting.
• Examples of service sector jobs include housekeeping, tours, nursing, and teaching.
• The services sector is the largest sector in India.
• The services sector accounts for 53.66% of the total India's GVA of Rs. 137.51 lakh crore.
• The industrial sector is at the second spot and contributing around 31% of the Indian GDP.
• The service sector makes an important contribution to GDP in most countries, providing jobs, inputs, and public services for the economy.
• Trade-in services can improve economic performance and provide a range of traditional and new export opportunities.
• The MSME sector is and regarded as the backbone of the Indian economy.
• It churns out over 6000 products that are highly sought after across the global marketplaces.
• It employs 40% of the country's workforce, next only to the agricultural sector.

​

Additional Information

• The Agriculture sectors comprise establishments primarily engaged in growing crops, raising animals, and harvesting fish and other animals from a farm, ranch, or their natural habitats.
• Agriculture is the most important sector of the Indian Economy.18 percent of India's gross domestic product (GDP) and provides employment to 50% of the countries workforce. India is the world's largest producer of pulses, rice, wheat, spices, and spice products.
• The Manufacturing sector comprises establishments engaged in the mechanical, physical, or chemical transformation of materials, substances, or components into new products.

Rooks are the members of the Crow's Family.

Similarly, Lemurs are the members of the Monkey's Family.

Hence, Option (4) is correct.

The pattern followed is:

Similarly,

Hence, “BPJPJ” is the correct answer.

Least possible venn diagram is:

Conclusions

I. All erasers can be bats → True

There is no direct relation between erasers and bats and also, there is no restriction on their relationship so, all erasers being bats is a possibility.

II. Some bats are not erasers → True

The bats which are balls can never be erasers.

Hence, both the conclusions follow.

Additional Information

The logic followed here is 

In each word, 3 is added to each consonant and 9 is added to each vowel.

The code for GARAGE is as follows:

The code for GARAGE is 101021101014.

Similarly,

The code for MEDIA is as follows:

The code for MEDIA is 1614071810.

Similarly, the code for DIAGRAM is as follows:

Hence, 'DIAGRAM' is coded as '07181010211016'.

According to given conditions,

1) B and H are the only siblings.

2. H is the only son of P.

As H is the only son of P, therefore B is the daughter and sister of P and H respectively.

3) D is the sister-in-law of B.

4) N is the paternal grandmother of G who is the daughter of D.

5) R is the son-in-law of N.

Thus, according to the final family tree R is the uncle of G.

Hence, "Uncle" is the correct answer.

The logic follows here is :-

According to the Alphabetic order the series follows here is :

Thus, the correct answer is 'NLR'.

The logic follows here is:-

Note:- Multiple of 400 years i.e. 800, 1200, 1600, 2000 have 0 odd days.

Calculating leap year: For Finding the number of leap year (1 - 99) years, divide the number of years by 4 and the quotient will be the number of leap years.

Code of weekdays:

Total odd days = 0 + 1 + 1 + 2 = 4 odd day.

4 is the code for Thursday

Thus, the correct answer is "Thursday".

The logic follows here:

(First Number × 4) + 1 = Second Number

(First Number × 2) + 1 = Third Number

1) (22, 89, 45) →

(22 × 4) + 1 = 89

(22 × 2) + 1 = 45

2) (15, 61, 31) →

(15 × 4) + 1 = 61

(15 × 2) + 1 = 31

3) (12, 49, 25) →

(12 × 4) + 1 = 49

(12 × 2) + 1 = 25

4) (13, 52, 27) →

(13 × 4) + 1 = 53 ≠ 52

(13 × 2) + 1 = 27

Hence, "(13, 52, 27)" is the correct answer.

Alternate Method

The logic follows here:

(First Number × 2) + Third Number = Second Number

1) (22, 89, 45) →

(22 × 2) + 45 

= 44 + 45

= 89

2) (15, 61, 31) →

(15 × 2) + 31

= 30 + 31

= 61

3) (12, 49, 25) →

(12 × 2) + 25

= 24 + 25

= 49

4) (13, 52, 27) →

(13 ×2) + 27

= 26 + 27

= 53 ≠ 52

Hence, "(13, 52, 27)" is the correct answer.

When we fold a given figure then we get,

By solving the options:

a)

 → It can be formed because there is no opposite phase adjacent to each other.

b)

 → It cannot be formed because opposite phase are adjacent to each other.

c)

 → It cannot be formed because opposite phase are adjacent to each other.

d)

 → It can be formed because there is no opposite phase adjacent to each other.

Hence, (a) and (d) is the correct answer.

Word is - S I G N A T U R E

Arranged according to English alphabetical order - A E G I N R S T U

Hence, only one letter i.e. G, will remain unchanged after rearrangement.

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

Conclusions: 

1. Some train are stones → False (As there is no direct relation between stones and train given, it is possible but not definite). 2. Some cars are stones → True (As all the stones are rivers and all the rivers are cars thus we can say some cars will also be stones is a definite conclusion). 3. Some trains are rivers → False (As there is no direct relation between trains and river given, it is possible but not definite).

Hence, the correct answer is "Only conclusion II follows".

Additional Information

The word ‘Sugar’ cannot be formed using the letters of the word ‘DEPASTURES’ because the letter ‘g’ is not present in ‘DEPASTURES’.

From the given information:

Total clockwise rotation = 90° + 135° =225°

Total anti-clockwise rotation = 120°

Therefore, resultant rotation = 225° - 120° = 105° (clockwise)

Thus, Vimal was initially facing west and then he takes a 105° turn in a clockwise direction as shown in the diagram below:

Hence, Vimal is facing the northeast direction now.

1. K sits fifth to the left of M.

2. O sits second to the left of M.

3. L is an immediate neighbour of M and sits fourth to the left of P.

4. J is not an immediate neighbour of K.

K and M are immediate neighbours of N.

Hence, option 3 is the correct answer.

Joystick, Microphone and trackball is the input device and Projector is the output device.

Hence, Projector is the correct answer.

Given Series: K15Z, N24T, Q35N, T48H, ?

The logic followed for the first letter:

First letters are: K, N, Q, T,

The logic followed for the digit:

Digits are: 15, 24, 35, 48,

4 × 4 – 1 = 15

5 × 5 – 1 = 24

6 × 6 – 1 = 35

7 × 7 – 1 = 48

8 × 8 – 1 = 63

The logic followed for the second letter:

Second letters are: Z, T, N, H,

Hence, the next term will be W63B.

From the first figure to the second figure, the circle goes inside the triangle and the triangle, in turn, goes inside the square, which turns on to its base. And, from figure third to fourth, the square goes inside the diamond and the diamond, in turn, goes inside the Pentagon, which turns onto its base.

Hence, Figure (a) is the correct answer.

The positions of the letters according to the English alphabet series:

The pattern for this code is as follows;

Number of letters × (Number of letters - 1)

In BRAVE →

In BRAVE there are 5 letters.

BRAVE = 5 × (5 - 1)

= 5 × 4 = 20

In COMMON →

In COMMON there are 6 letters.

COMMON = 6 × (6 - 1)

= 6 × 5 = 30

Similarly;

In KISHORE →

In KISHORE there are 7 letters.

KISHORE = 7 × (7 - 1)

= 7 × 6 = 42

Hence, "42" is the correct answer.

Five students: Zoya, Yash, Xenifer, William, and Vihan

1) Xenifer scored more than William but not as much as Vihan

Vihan > Xenifer > William

2) Vihan scored more than Zoya, who scored less than Yash

Vihan > Zoya

Yash > Zoya

There is no direct relationship given between Vihan and Yash.

Hence, Either Vihan or Yash scored the second-highest marks.

Eight points P, Q, R, S, T, U, V, and W.

1) Point P is 4 m north of point R.

2) Point R is the middle of the point of Q and point W.

3. Point Q is 6 m to the west of W.

4) Point U is 10 m east of point V, which is 5 m south of point W.

5)  Point Q is north of point S, which is west of point T.

Hence, point V is in North East of point S.

The positions of the letters according to the English alphabet series:

The pattern for this code is as follows;

And;

Similarly;

Hence, "5-31-19-25" is the correct answer.

Given statements: X = F < R > H > K

Conclusions:

I. K < R → True (R > H > K → R > K)

II. R > X → True (X = F < R → R > X)

III. H < X → False (X = F < R > H → clear relation between H and X cannot be determined)

IV. X < K → False (X = F < R > H > K → thus clear relation between X and K cannot be determined)

Only I and II are true.

According to the question:

MALE → 2375

⇒ M → 2; A → 3, L → 7; E → 5

CIRCULAR →  98496734

⇒ C → 9; I → 8; R → 4; U → 6; L → 7; A → 3; R → 4

Using the codes above, we can form the code for the word CLAIM i.e. 97382.

Hence, the code for the CLAIM is 97382.

According to the English Alphabet series with positional value;

The pattern followed here is:

Hence, RRST will complete the series.

If a mirror is placed along the AB line, then only the left and right sides of a given image will be interchanged in the mirror image while everything else will remain the same. Thus, we will get the following mirror image:

Hence, Option 3 is the correct answer.

The logic follows here is :-

Given, EIP : 223044

Similarly,

Thus, the correct answer is "JRV : 324856".

The pattern followed here is:

Therefore, “RSUY” is odd among them.

Hence, “RSUY” is the correct answer.

The positions of the letters according to the English alphabet series:

The pattern for this code is as follows;

Similarly;

Hence, "UAPDGER" is the correct answer.

The Formula used here is:

Angle = |(11/2) M - 30 H|

Where, M = minutes and H = hours

Here, M = 35 and H = 9

Therefore, we get the angle = |(11/2) M - 30 H|

Angle = |(11/2) × 35 - 30 × 9|

Angle = |192.5 - 270| = |-77.5|

Hence, the correct answer is "77.5⁰".

The pattern followed here is,

After replacing the symbol with their meaning, we get,

Option 1:

10 × 36 ÷ 18 - 7 + 6

= 10 × 2 - 7 + 6

= 20 - 7 + 6

= 26 - 7

= 19

Option 2:

15 ÷ 3 + 7 × 4 - 9

= 5 + 7 × 4 - 9

= 5 + 28 - 9

= 33 - 9

= 24

Option 3:

8 + 9 × 7 - 52 ÷ 13

= 8 + 9 × 7 - 4

= 8 + 63 - 4

= 71 - 4

= 67

Option 4:

56 - 9 + 8 × 39 ÷ 13

= 56 - 9 + 8 × 3

= 56 - 9 + 24

= 80 - 9

= 71

Hence, ‘8 ÷ 9 – 7 + 52 × 13 = 67’ is the correct answer.

Correct option - 1

1. Two persons were seated between the one who likes Black colour and the one who likes Pink colour and neither of them was seated at the end. The one who likes Black colour was seated second to the left of the one who likes Red colour.

2. The one who likes Green colour was seated at the right end. The one who likes Yellow colour was seated to the left of the one who likes Blue colour. 

The one who likes Yellow colour was seated second to the left of the one who likes Blue colour

Hence, option 1 is the correct answer

The pattern followed is,

In each step, elements shift from left to right column-wise. For example, all the elements of column 1 shift to column 2, those of column 2 shift to column 3.

Then, the symbols in the first column rotate in a cyclic manner from top to bottom.

The figure which will come next is,

Hence, option 4 is the correct answer.

Given Series: 32H5, 16K10, 8O20, 4T40, ?

The logic followed for first number is:

32 ÷ 2 = 16

16 ÷ 2 =   8

8 ÷ 2 =   4

4 ÷ 2 =   2

So, First digit will be 2.

The logic followed for the letters is:

Letters are: H, K, O, T

So, letter will be Z.

The logic followed for the number is:

Second numbers: 5, 10, 20, 40

5 × 2 = 10

10 × 2 = 20

20 × 2 = 40

40 × 2 = 80

Hence, the next term is 2Z80.

The series is:

11

11 × 2 - 2 = 20

20 × 3 - 3 = 57

57 × 4 - 4 = 224

224 × 5 - 5 = 1115

Hence, wrong term is 226, Option (3) is correct.

Given series: 30, 38, 52, ?, 98, 130

The logic is:

Hence, 72 is the correct answer.

Given: 

Mark up% = 60%

Discount = 10%

Concept used:

Marked price = C.P. + Markup % of C.P.

Selling Price = Marked price - Discount

Profit % = ({S.P. - C.P. \over C.P.}) ×  100%

Calculations:

Marked price = C.P. + Markup % of C.P.

Selling Price = Marked price - Discount

Profit % = ({S.P. - C.P. \over C.P.}) × 100%

Let the C.P. of the article = 100x

Marked price = 100x + 60% of 100x = 160x

Selling price = 160x - 10% of 160x = 144x

Profit % = ({144x - 100x\over 100x}) × 100 % = 44%

Let the C.P. of the article = 100x

Marked price = 100x + 60% of 100x 

 ⇒ Marked price = 160x

Selling price = 160x - 10% of 160x

 ⇒ Selling price = 160x - 16x

 ⇒ Selling price = 144x

Profit = ({144x - 100x\over 100x}) × 100 %

 ⇒ Profit = 44%

Hence option D is the correct answer.

Shortcut Trick⇒ M.P. = 160% of C.P

⇒ S.P. = 90% of M.P

⇒ (S.P.)/(C.P.) = (160/100) × (90/100) = 144/100

if, C.P. = 100, then S.P. = 144.

∴ Profit of Rs. 44 and P% of 44%, as we're calculating everything on 100.

GIVEN:

Money invested by P is Rs. 28000 per month and he has invested for 8 months.

Money invested by Q is Rs. 42000 per month and he has invested for 12 months.

CONCEPT:

In this type of questions, the profit ratio among the persons is the same as that of the ratio of their capital investment. So we will find the ratio of capital investment, which will be the same as the profit ratio and since we know the total profit and profit ratio, we can find the individual profit.

FORMULA USED:

Profit made by A = (Amount of money invested by A × Total profit) / Total money invested by A and B together)

CALCULATION:

Total money invested by A = 28000 × 8 = 224000

Total money invested by A and B together = 28000 × 8 + 42000 × 12 = 728000

Profit made by A = (224000 × 21125) / 728000 = 6500

∴ The profit made by A is Rs. 6500.

Given:

Sunil purchased a fan at a 10% discount on the labeled price.

If he had purchased it at a 15% discount, he would have saved ₹400.

Concept used:

Cost price = Labelled price × (100 - discount)%

Calculation:

Let the labeled price of the fan be Rs. 100x

Now,

After the actual discount cost price of the fan for Sunil was = 100x × 90%

⇒ 90x

Now,

If he gets a 15% discount then,

Cost price = 100x × 85%

⇒ 85x

According to the question,

90x - 85x = 400

⇒ 5x = 400

⇒ x = 80

So, 100x = 8000

∴ The labeled price of the fan is ₹8,000.

Shortcut Trick

​A difference of 5% discount saved Rs.400

Then 100% → 400/5 × 100 = 8000 (Marked Price)

Shortcut Trick

LCM of the denominators 6, 8, and 9 is 72. Multiplying fractions by 72 gives integer ratio.

A : B : C = (1/6 × 72) : (1/8 × 72) : (1/9 × 72) = 12 : 9 : 8

Total units = 12 + 9 + 8 = 29 units → ₹3,596

1 unit = ₹3,596 ÷ 29 = ₹124

Difference between A and C = 12 − 8 = 4 units → 4 × 124 = 496

∴ The correct answer is ₹496.

Alternate Method

Given:

Total amount to be divided = ₹3,596

Initial ratio of shares of A, B, and C = 1/6 : 1/8 : 1/9

Calculations:

⇒ LCM of the denominators 6, 8, and 9 is 72.

⇒ Multiplying each fraction by 72 to get simple integer ratios:

⇒ Share of A = 1/6 × 72 = 12 units

⇒ Share of B = 1/8 × 72 = 9 units

⇒ Share of C = 1/9 × 72 = 8 units

⇒ Simplified ratio of shares A : B : C = 12 : 9 : 8

⇒ Total sum of ratio units = 12 + 9 + 8 = 29 units

⇒ We know, 29 units = ₹3,596

⇒ 1 unit = 3596 ÷ 29 = 124

⇒ Difference in ratio between A and C = 12 units − 8 units = 4 units

⇒ Total difference in amount = 4 × 124 = 496

∴ The correct answer is ₹496.

Additional Information

Ratio Simplification

To convert fractional ratios into simplest integer ratios, multiply each fraction by the Least Common Multiple (LCM) of all the denominators.

Proportion

When two ratios are equal, they are said to be in proportion (a/b = c/d). The core rule of proportion is that the product of the extremes equals the product of the means (a × d = b × c).

Distribution of Amount

If a total quantity T is to be divided among participants in the ratio a : b : c, the individual share can be calculated as Share = (Individual Ratio Unit ÷ Total Ratio Units) × T.

Total no. of students = 56

Boy-girl ratio = 4 ∶ 3

⇒ Total no. of girls = 3/7 × 56 = 24

Ratio of girls scoring above 60% and below 60% = 5 ∶ 3

∴ No of girls scoring below 60% = 3/8 × 24 = 9

Given data:

Principal (P) = ₹500

Time (T) = 2 years

Difference between compound interest and simple interest (CI - SI) = ₹1.25

Concept Used:

The difference between compound interest and simple interest for two years is

given by the formula CI - SI = P × (r/100)²,

where r is the rate of interest.

Calculation:

⇒ Rate of interest (r) = √((CI - SI) × 100² / P)

⇒ Rate of interest (r) = √((1.25 × 100²)/500) = 5%

Hence, the rate of interest per annum is 5%.

Given:

S.I. for 5 years = 20% of Principal

Formula used:

S.I. = (P × R × T)/100

where P → Principal

R → Rate of interest

T → Time period

Calculation:

Let the principle be Rs. P

According to the question,

⇒ (P × 5 × rate)/100 = 20% of P

⇒ rate = 4%

Now, let in t years the simple interest will be equal to the principal

⇒ Simple interest = (P × 4 × t)/100

⇒ P = (P × t)/25

∴ t = 25 years

Shortcut TrickRatio of Principal to S.I. in 5 years = 100 : 20

Let the Principal be 100, so we are required to make S.I. = 100

⇒ S.I. of 20 = 5  years

⇒ S.I. of 100 = 5/20 × 100 = 25 years

Shortcut Trick

Total Cost = Length × Width × Rate per m²

Cost = 5.5 × 3.75 × 800

Multiply 3.75 by 800 first: 3.75 × 800 = 3000

Cost = 5.5 × 3000 = 16500

∴ The correct answer is Rs. 16500.

Alternate Method

Given:

Length of the room (L) = 5.5 m

Width of the room (W) = 3.75 m

Rate of paving = Rs. 800 per m²

Formula Used:

Area of a rectangle = Length × Width

Total Cost = Area × Rate per unit area

Calculations:

⇒ Area of the floor = 5.5 m × 3.75 m

⇒ Area = 20.625 m²

⇒ Total Cost = 20.625 × 800

⇒ Total Cost = 16500

∴ The correct answer is Rs. 16500.

Additional Information

Area of Rectangle

The total space enclosed within the boundaries of a rectangle. Formula: Area = Length × Breadth.

Perimeter of Rectangle

The total length of the boundary of a rectangle. Formula: Perimeter = 2 × (Length + Breadth). This is used for finding the cost of fencing or placing borders.

Area of Square

A square is a special type of rectangle where all four sides are equal. Formula: Area = Side².

Given :

Principal(P) = Rs.1250

Amount after two yrs.(A) = Rs.1800

Time = 2 yrs.

Formula used :

(A = P\bigg(1+\dfrac{R}{100}\bigg)^2)

Calculation :

Let the rate of interest be R % .

(1800 = 1250\bigg(1+\dfrac{R}{100}\bigg)^2) , (\dfrac{1800}{1250} = \bigg(1+\dfrac{R}{100} \bigg)^2) or (\dfrac{6}{5} = \bigg(1+\dfrac{R}{100}\bigg)) 

So, R = 20%

∴ The answer is 20 % .

Shortcut Trick ⇒ Ratio of Principle and Amount = 1250/1800 = 25/36

⇒ In 2 yrs Principle has changed from, 25x to 36x

To find Rate of change per year we've to take square root on both the sides as it has change in 2 yrs.

⇒ Principle → Amount

⇒ √{25} → √{36} 

⇒ 5 → 6

∴ % Rate of change per year = {(6 - 5)/5} × 100 = 20%

Shortcut Trick

If the area of a new circle is equal to the sum of the areas of two circles with radii r₁ and r₂, the radius R of the new circle is simply given by the Pythagorean relation: R = √(r₁² + r₂²).

Given, r₁ = 15 cm and r₂ = 8 cm.

R = √(15² + 8²)

R = √(225 + 64) = √289

R = 17 cm.

∴ The correct answer is 17 cm.

Alternate Method

Given:

Radius of the first circle (r₁) = 15 cm

Radius of the second circle (r₂) = 8 cm

Formula Used:

Area of a circle = πr²

Calculations:

Let the radius of the larger circle be R.

⇒ Area of new circle = Area of first circle + Area of second circle

⇒ πR² = π(r₁)² + π(r₂)²

⇒ πR² = π × (15² + 8²)

⇒ R² = 225 + 64

⇒ R² = 289

⇒ R = √289

⇒ R = 17 cm

∴ The correct answer is 17 cm.

Additional Information

Pythagorean Triplets

Three positive integers a, b, and c that satisfy a² + b² = c² form a Pythagorean triplet. Common examples are (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25). Spotting these saves calculation time.

Circumference Sum Relation

If the circumference of a circle equals the sum of the circumferences of two circles with radii r₁ and r₂, then the radius R of the new circle follows a direct linear addition: R = r₁ + r₂.

Area of Semicircle and Quadrant

Area of a Semicircle = ½ πr² and its Perimeter = πr + 2r. Area of a Quadrant = ¼ πr² and its Perimeter = πr/2 + 2r.

Shortcut Trick

Ratio of Volume (V) to Curved Surface Area (CSA) = r / 2

r / 2 = 1336.5 / 594 = 2.25

⇒ Radius (r) = 4.5 cm

Height (h) = CSA ÷ (2 × π × r)

h = 594 ÷ (2 × 22/7 × 4.5) = 21 cm

∴ The correct answer is 21 cm.

Alternate Method

Given: Curved Surface Area (CSA) = 594 cm², Volume (V) = 1336.5 cm³

Formula Used: CSA = 2πrh; Volume = πr²h

r

h CSA = 2πrh = 594 Vol = πr²h = 1336.5

⇒ Volume / CSA = (πr²h) / (2πrh) = 1336.5 / 594

⇒ r / 2 = 2.25

⇒ r = 4.5 cm

⇒ 2 × (22 / 7) × 4.5 × h = 594

⇒ (198 / 7) × h = 594

⇒ h = (594 × 7) / 198

⇒ h = 3 × 7 = 21 cm

∴ The correct answer is 21 cm.

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 = 2πrh + 2πr² = 2πr(h + r).

Volume of a Hollow Cylinder

If R is the outer radius and r is the inner radius, the volume is V = πh(R² − r²).

Diagonal of a Cylinder

The longest segment within a cylinder connects opposite points on the top and bottom circles, calculated as d = √(h² + (2r)²).

Let the radius, height and slant height of cone be ‘r’, ‘h’ and ‘l’ units respectively

Given, curved surface area = 90% of Total surface area of cone

⇒ πrl = (9/10) × πr(l + r)

⇒ 10l = 9l + 9r

⇒ l = 9r

Also, l² = h² + r²

⇒ 81r² = h² + r²

⇒ h² = 80r²

⇒ r² = h²/80

Now,

Volume of cone = (1/3)πr²h

⇒ Volume of cone = π/3 × h²/80 × h

⇒ Volume of cone = (π/240) × h³

∴ The volume of cone is (π/240) times the cube of the height of the cone

Given 

Area of square = 72 cm²

Formula Used 

Area of square = side²

Area of circle = πR²

Calculation 

Area of square = side²

⇒ side = √72 = 6√2 cm 

Diagonal of square = side√2

⇒ 6√2 × √2 = 12 cm 

Radius of circle = diagonal/2

⇒ 12/2 = 6 cm 

Area of circle = π(6)² 

⇒ 36π cm²

∴ The area of circle is 36π cm²

Short Trick:

U = upstream and D = downstream

3.6(U) + 5.4(D) = 54 and 5.4(U) + 3.6(D) = 58.5

Divide by 18

2U + 3D = 30 and 3U + 2D = 32.5

Now, Multiply by 3 in (1) and by 2 in (2), and then subtract (2) from (1), then

5D = 25 min

∴10D = 50 min

Detailed Method:

Let the speed of boat be x km/hr and speed of current be y km/hr

Upstream speed = (x – y) km/hr

Downstream speed = (x + y) km/hr

According to the question

3.6/(x – y) + 5.4/(x + y) = 54/60

5.4/(x – y) + 3.6/(x + y) = 58.5/60

Let 1/(x – y) = a and 1/(x + y) = b, then

3.6a + 5.4b = 54/60   ---(1)

5.4a + 3.6b = 58.5/60   ---(2)

Add equation (1) and equation (2)

9 (a + b) = 112.5/60

⇒a + b = 12.5/60

⇒a + b = 5/24   ---(3)

Subtract equation (2) from equation (1)

1.8 (b – a) = -4.5/60

⇒b – a = -2.5/60

⇒b – a = -1/24   ---(4)

Add equation (3) and equation (4)

2b = 4/24

⇒b = 1/12

⇒(x + y) = 12 km/hr

Downstream speed = 12 km/hr

∴Time taken to cover 10 km distance with downstream = 10/12 hr or (10/12) × 60 = 50 min

Shortcut Trick

Using the M₁D₁/W₁ = M₂D₂/W₂ chain rule.

Total work (W₁) = 1 unit.

Work part (W₂) = (M₂ × D₂) ÷ (M₁ × D₁)

W₂ = (207 × 20) ÷ (138 × 50) = 4140 ÷ 6900 = 3/5

∴ The correct answer is 3/5.

Alternate Method

Given:

Initial Men (M₁) = 138, Days (D₁) = 50, Work (W₁) = 1

Final Men (M₂) = 207, Days (D₂) = 20, Work (W₂) = ?

Formula Used:

M₁ × D₁ × W₂ = M₂ × D₂ × W₁

Calculations:

⇒ 138 × 50 × W₂ = 207 × 20 × 1

⇒ 6900 × W₂ = 4140

⇒ W₂ = 4140 ÷ 6900

⇒ W₂ = 414 ÷ 690

⇒ W₂ = (69 × 6) ÷ (69 × 10)

⇒ W₂ = 6 ÷ 10 = 3/5

∴ The correct answer is 3/5.

Additional Information

The MDH Formula

Total work is proportional to Men × Days × Hours. The general formula is (M₁D₁H₁)/W₁ = (M₂D₂H₂)/W₂.

Efficiency and Work

If efficiencies (E) are different, the formula becomes M₁D₁E₁/W₁ = M₂D₂E₂/W₂.

Unitary Method

1 man 1 day work = 1 / (M₁ × D₁). Therefore, work by M₂ in D₂ = (M₂ × D₂) / (M₁ × D₁).

Given 

Pipe A usually fills a tank = 2 hours.

Due to leakage tank fill in = 2.5 hours

Formula used 

Work = Time × Efficiency 

Calculation 

LCM of (2, 2.5) = 10 

Let the total work be 10 

A's efficiency = 10/2 = 5/hrs

(A + leakage)'s efficiency = 10/2.5 = 4/hrs

Leakage's efficiency = 1/hrs 

Leakage empty the tank in = 10/1 = 10 hours 

∴ The required answer is 10 hours

Shortcut Trick

Abhinav time = 4 hours | Praveen time = 3.5 hours (7/2 hours).

Assume Distance = LCM(4, 7) = 28 units.

Abhinav speed = 28 ÷ 4 = 7 units/hr | Praveen speed = 28 ÷ (7/2) = 8 units/hr.

At 8 am, Abhinav has covered 7 × 2 = 14 units. Remaining distance = 14 units.

Meeting time after 8 am = Remaining Distance ÷ Relative Speed = 14 ÷ (7 + 8) = 14/15 hours.

14/15 hours = 14/15 × 60 = 56 minutes. Time = 8 : 56 am.

∴ The correct answer is 8 : 56 am.

Alternate Method

Given:

Time taken by Abhinav (T_A) = 10 am − 6 am = 4 hours.

Time taken by Praveen (T_P) = 11 : 30 am − 8 am = 3.5 hours = 7/2 hours.

Let the distance between Mumbai and Bangalore be D.

⇒ Speed of Abhinav (S_A) = D/4

⇒ Speed of Praveen (S_P) = D/(7/2) = 2D/7

⇒ Distance covered by Abhinav by 8 am (2 hours) = (D/4) × 2 = D/2

⇒ Remaining distance at 8 am = D − D/2 = D/2

⇒ Relative speed = S_A + S_P = D/4 + 2D/7 = (7D + 8D)/28 = 15D/28

⇒ Time to meet after 8 am = (D/2) ÷ (15D/28) = (D/2) × (28/15D) = 14/15 hours

⇒ 14/15 hours = (14/15) × 60 minutes = 56 minutes

⇒ Meeting time = 8 : 00 am + 56 minutes = 8 : 56 am

∴ The correct answer is 8 : 56 am.

Additional Information

Relative Speed

When two objects move in opposite directions, their relative speed is the sum of their individual speeds (S₁ + S₂).

Meeting Time Formula

Meeting Time = (Initial Distance between them at the same start time) ÷ (Relative Speed).

Time-Speed Relationship

For a constant distance, speed is inversely proportional to time (S ∝ 1/T).

Shortcut Trick

Total work = LCM(20, 60) = 60 units.

Efficiency: A = 60 ÷ 20 = 3 units/day, B = 60 ÷ 60 = 1 unit/day.

Work done by B alone in the last 12 days = 12 × 1 = 12 units.

Remaining work done by A and B together from the beginning = 60 − 12 = 48 units.

Days A and B worked together = 48 ÷ (3 + 1) = 12 days.

∴ The correct answer is 12 days.

Alternate Method

Given:

Time taken by A alone to complete the work = 20 days

Time taken by B alone to complete the work = 60 days

Time taken by B to complete the remaining work = 12 days

Formula Used:

Total Work = Efficiency × Time Taken

Calculations:

⇒ Work completed by B alone in the last 12 days = Efficiency of B × Days = 1 × 12 = 12 units

⇒ Remaining work to be completed by A and B together = Total Work − Work done by B

⇒ Remaining work = 60 − 12 = 48 units

⇒ Combined efficiency of A and B = 3 + 1 = 4 units/day

⇒ Number of days A and B worked together initially = Remaining work ÷ Combined efficiency

⇒ Days A and B worked together = 48 ÷ 4 = 12 days

This means A worked for 12 days from the beginning before leaving the work.

∴ The correct answer is 12 days.

Additional Information

Total Work & Efficiency Trick

Total work is universally taken as the Lowest Common Multiple (LCM) of individual completion times. Efficiency is inversely proportional to the time taken.

Alternate Days Working

When individuals work on alternate days, calculate the work done in a complete cycle (e.g., 2 days for 2 persons) and scale it up to reach the closest multiple near the total work.

Work & Wages Distribution

Wages are always distributed in proportion to the total units of work completed by each individual. If they work for the same duration, wages are directly distributed based on their efficiencies.

Shortcut Trick

When a value is first increased by x% and then decreased by x%, there is always a net decrease.

Net Decrease % = (x² ÷ 100)%

Given x = 13%, Net Decrease % = (13 × 13) ÷ 100 = 169 ÷ 100 = 1.69%

∴ The correct answer is Decrease of 1.69%.

Alternate Method

Given:

Increase in salary = 13%

Decrease in salary = 13%

Calculations:

⇒ Let the initial salary of Neeta be 100 units.

⇒ Salary after 13% increase = 100 + (13% of 100) = 113 units.

⇒ Salary after subsequent 13% decrease = 113 − (13% of 113)

⇒ Decrease amount = (13 ÷ 100) × 113 = 14.69 units.

⇒ Final salary = 113 − 14.69 = 98.31 units.

⇒ Net change = Final salary − Initial salary = 98.31 − 100 = −1.69 units.

⇒ Net percentage change = (−1.69 ÷ 100) × 100% = −1.69%

⇒ The negative sign indicates a decrease in the final value.

∴ The correct answer is Decrease of 1.69%.

Additional Information

Successive Percentage Change

When a value is subjected to two successive percentage changes of a% and b%, the effective net percentage change is given by: a + b + (a × b) ÷ 100. Use a negative sign for any decrease.

Equal Increase and Decrease

If a number is first increased by x% and then decreased by the same x%, the net change is always a decrease, calculated as: Net Loss % = (x² ÷ 100)%.

Base Dependency

A fixed percentage increase followed by the same percentage decrease does not return the value to the original amount because the base for the decrease is larger than the original base.

Shortcut Trick

The LCM of 16, 21, 24, and 28 is 336.

Largest 4-digit number 9999 ÷ 336 leaves a remainder of 255.

Largest 4-digit multiple (x) = 9999 − 255 = 9744.

Sum of digits of 9744 = 9 + 7 + 4 + 4 = 24.

∴ The correct answer is 24.

Alternate Method

Given: Divisors are 16, 21, 24, and 28.

Formula Used: x = Largest 4-digit number − (Largest 4-digit number mod LCM of divisors).

⇒ Prime factorization of 16 = 2⁴

⇒ Prime factorization of 21 = 3 × 7

⇒ Prime factorization of 24 = 2³ × 3

⇒ Prime factorization of 28 = 2² × 7

⇒ LCM = 2⁴ × 3 × 7 = 16 × 21 = 336

⇒ Largest 4-digit number = 9999

⇒ 9999 ÷ 336 ⇒ Quotient = 29, Remainder = 255

⇒ Required number x = 9999 − 255 = 9744

⇒ Sum of digits = 9 + 7 + 4 + 4 = 24

∴ The correct answer is 24.

Additional Information

Least Common Multiple (LCM)

The LCM is the smallest positive integer that is exactly divisible by each of the given numbers. It is calculated by taking the highest power of each prime factor involved.

Divisibility Rule of 3

A number is divisible by 3 if the sum of its digits is a multiple of 3. Since 9744 is a multiple of 21 and 24, it must be divisible by 3.

Division Algorithm

For any dividend and divisor: Dividend = (Divisor × Quotient) + Remainder. To find the largest multiple below a limit, subtract the remainder from that limit.

Shortcut Trick

Difference in profit percentage = 20% − 16% = 4%

This 4% increase in profit corresponds to the increase in selling price of ₹ 100.

4% of CP = ₹ 100

1% of CP = 100 ÷ 4 = ₹ 25

100% of CP = 25 × 100 = ₹ 2500

∴ The correct answer is ₹ 2500.

Alternate Method

Given:

Initial Profit = 16%

Increased Selling Price = ₹ 100

New Profit = 20%

Formula Used:

Selling Price (SP) = CP × (100 + Profit%) ÷ 100

Calculations:

Let the cost price (CP) of the almirah be ₹ x.

⇒ Initial Selling Price (SP₁) = 116% of x = 1.16x

⇒ New Selling Price (SP₂) = 120% of x = 1.20x

⇒ SP₂ − SP₁ = 100

⇒ 1.20x − 1.16x = 100

⇒ 0.04x = 100

⇒ x = 100 ÷ 0.04

⇒ x = 10000 ÷ 4

⇒ x = 2500

∴ The correct answer is ₹ 2500.

Additional Information

Profit and Loss Basics

Profit occurs when SP > CP, and Profit = SP − CP. Profit percentage is always calculated on the Cost Price unless stated otherwise.

Successive Percentage Method

When two profits/losses are compared for the same base (CP), the difference in their percentages is directly proportional to the difference in their absolute values.

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP × (100 − Discount%) ÷ 100.

Shortcut Trick

Convert all bases to 3 and compare the powers directly.

LHS: (√3)⁵ × 9² = 3^2.5 × 3⁴ = 3^6.5

RHS: 3^x × 3√3 = 3^x × 3^1.5

Equate the powers: 6.5 = x + 1.5 ⇒ x = 5

∴ The correct answer is 5.

Alternate Method

Given:

(√3)⁵ × 9² = 3^x × 3√3

Formula Used:

Law of Exponents: a^m × aⁿ = a^m+n and (a^m)ⁿ = a^m×n

Calculation:

Convert all terms to the common base of 3:

⇒ (√3)⁵ = (3^1/2)⁵ = 3^5/2

⇒ 9² = (3²)² = 3⁴

⇒ 3√3 = 3¹ × 3^1/2 = 3^3/2

Now substitute these values back into the equation:

⇒ 3^5/2 × 3⁴ = 3^x × 3^3/2

Apply the multiplication rule of exponents on both sides:

⇒ 3^{(5/2 + 4)} = 3^{(x + 3/2)}

⇒ 3^13/2 = 3^{(x + 3/2)}

Since the bases are the same, equate the exponents:

⇒ 13/2 = x + 3/2

⇒ x = 13/2 − 3/2

⇒ x = 10/2

⇒ x = 5

∴ The correct answer is 5.

Additional Information

Product Rule of Exponents

When multiplying terms with the same base, add their exponents: a^m × aⁿ = a^m+n.

Power of a Power Rule

When raising a power to another power, multiply the exponents: (a^m)ⁿ = a^m×n.

Fractional Exponents

Roots can be written as fractional powers: √a = a^1/2 and ⁿ√a = a^1/n.

Equality of Exponents

If two exponential expressions with the same base are equal, their exponents must be equal. If a^x = a^y, then x = y (provided a ≠ 0, 1, or −1).

Shortcut Trick

Total Interest for 3 years at 20% = 20% × 3 = 60%

Amount % = Principal % + Interest % = 100% + 60% = 160%

Given: 160% of Sum = ₹3120

Interest for 1 year = 20% of Sum

Required value = (3120 ÷ 160) × 20 = 3120 ÷ 8 = 390

∴ The correct answer is ₹390.

Alternate Method

Given:

Amount (A) = ₹3120, Rate (R) = 20%, Time (T) = 3 years

Formula used:

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

Amount (A) = P + SI = P × (1 + RT/100)

Year 0 (P) Year 1 Year 2 Year 3 (A=3120)

+20% SI

+20% SI

+20% SI Total Amount = 160% of P

Calculations:

⇒ 3120 = P × (1 + (20 × 3) / 100)

⇒ 3120 = P × (1 + 60/100)

⇒ 3120 = P × (160/100)

⇒ P = (3120 × 100) / 160

⇒ P = 3120 ÷ 1.6 = 1950

⇒ Simple Interest for 1 year = (1950 × 20 × 1) / 100

⇒ Simple Interest for 1 year = 1950 × 0.2 = 390

∴ The correct answer is ₹390.

Additional Information

Simple Interest Nature

Simple Interest remains constant for every year because it is always calculated on the original Principal amount.

Amount vs Interest

Total Amount = Principal + (Principal × Rate × Time) / 100. If R=20% and T=1, then SI = 0.2P.

Rate Calculation

The annual rate of interest can be found using R = (SI × 100) / (P × T).

Given:

(\rm \left(3\frac{2}{3}\ of\ \frac{3}{4}-\frac{1}{4}\ of\ \frac{4}{3}\right)\div\left(\frac{1}{4}\div\frac{3}{2}\right)+1\frac{1}{2})

Concept used:

Calculation:

(\rm \left(3\frac{2}{3}\ of\ \frac{3}{4}-\frac{1}{4}\ of\ \frac{4}{3}\right)\div\left(\frac{1}{4}\div\frac{3}{2}\right)+1\frac{1}{2})

⇒ (\rm \left(\frac{11}{3}\ \times\ \frac{3}{4}-\frac{1}{4}\ \times\ \frac{4}{3}\right)\div\left(\frac{1}{4}\div\frac{3}{2}\right)+1\frac{1}{2})

⇒ (\rm \left(\frac{11}{4}\ -\frac{1}{3}\right)\div\left(\frac{1}{4}\div\frac{3}{2}\right)+1\frac{1}{2})

⇒ (\rm \left(\frac{33; -;4}{12}\right)\div\left(\frac{1}{4}\times\frac{2}{3}\right)+\frac{3}{2})

⇒ (\rm \left(\frac{29}{12}\right)\div\left(\frac{1}{6}\right)+\frac{3}{2})

⇒ (\rm \frac{29}{12}\times6+\frac{3}{2})

⇒ 29/2 + 3/2

⇒ 32/2

⇒ 16

∴ Required answer is 16

Given:

Cost price of articles = Rs.490

Loss % = 20%

Profit % = 16%

Formula:

Loss % = (CP - SP)/CP × 100

Profit % = (SP - CP)/CP × 100

Calculation:

Let cost price of one article be Rs.a and cost price of two article be Rs.(490 - a).

Selling price of one article = a × 80/100 = Rs.4a/5

Selling price of other article = (490 - a) × 116/100 = Rs.(568.4 - 29a/25)

Then,

⇒ 4a/5 = 568.4 - 29a/25

⇒ 49a/25 = 568.4

⇒ a = 290

∴ Cost price of article which sold at loss of 20% is Rs.290.

Debt of country F = $250 million

Percentage interest = 3%

∴ Interest paid per year = 3% of 250 = 3/100 × 250 = $7.5 million =$7500000

Debt of country A = $600 million

Debt of country F = $250 million

∴ Required ratio = 600 : 250 = 12 : 5

Debt of country A = $600 million

Debt of country B = $800 million

⇒ Difference in debt = 800 - 600 = 200

∴ Debt of country A is lesser than that of country B by = 200/800 × 100 = 25%

The company F has the lowest debt of $250 million, while the second lowest is company D of$500 million

∴ Company D has the second lowest debt

Given:

Simplify: (\frac{3}{2} \times \frac{11}{5} \div \left(\frac{25}{44} \times \frac{11}{5}\right) \div \frac{33}{15})

Calculation:

Step 1: Simplify the expression inside the parentheses:

(\frac{25}{44} \times \frac{11}{5} = \frac{25 \times 11}{44 \times 5} = \frac{275}{220} = \frac{5}{4})

Step 2: The expression now becomes:

(\frac{3}{2} \times \frac{11}{5} \div \frac{5}{4} \div \frac{33}{15})

Step 3: Simplify the division operations:

(\frac{11}{5} \div \frac{5}{4} = \frac{11}{5} \times \frac{4}{5} = \frac{44}{25})

Step 4: The expression now becomes:

(\frac{3}{2} \times \frac{44}{25} \div \frac{33}{15})

Step 5: Simplify the next division:

(\frac{44}{25} \div \frac{33}{15} = \frac{44}{25} \times \frac{15}{33} = \frac{44 \times 15}{25 \times 33} = \frac{660}{825} = \frac{4}{5})

Step 6: Final multiplication:

(\frac{3}{2} \times \frac{4}{5} = \frac{12}{10} = \frac{6}{5})

∴ The simplified value is (\frac{6}{5}).

Given:

Area of the square that is bent to form a circle = 169 cm2 

Formulas used:

The perimeter of the square with side a = 4a

Area of the square with side a = a²

The perimeter of the circle with radius r = 2πr

The area of the circle with radius r = πr²

Calculation:

Area of the square =  a2 

⇒  a2 = 169 

⇒ a = ± 13 

Side of the square = 13 cm 

When a wire is bent to form a square and then a circle, the perimeter of both the figures will be equal. 

4a = 2πr 

⇒ 4 × 13 = 2 × 22/7 × r 

⇒ r = (13 × 7)/ 11 

Area of the circle = πr2 

⇒ 22/7 × (13 × 7)/ 11 × (13 × 7)/ 11 

⇒ 2366/11 

⇒ 215.09 cm²

∴ Area of the circle = 215 cm² (nearest to a whole number)

Shortcut Trick

To find the LCM of fractions, calculate the LCM of the numerators divided by the HCF of the denominators.

Numerators: 2, 3, 4 → LCM = 12

Denominators: 5, 10, 15 → HCF = 5

Required LCM = 12/5

∴ The correct answer is 12/5.

Alternate Method

Given: Fractions are 2/5, 3/10, and 4/15.

Formula Used: LCM of (a/b, c/d, e/f) = LCM(a, c, e) ÷ HCF(b, d, f)

Step-by-step Calculation:

⇒ Numerators of the given fractions are 2, 3, and 4.

⇒ Find the Lowest Common Multiple (LCM) of 2, 3, and 4:

⇒ Multiples of 2: 2, 4, 6, 8, 10, 12, ...

⇒ Multiples of 3: 3, 6, 9, 12, ...

⇒ Multiples of 4: 4, 8, 12, ...

⇒ LCM(2, 3, 4) = 12

⇒ Denominators of the given fractions are 5, 10, and 15.

⇒ Find the Highest Common Factor (HCF) of 5, 10, and 15:

⇒ Factors of 5: 1, 5

⇒ Factors of 10: 1, 2, 5, 10

⇒ Factors of 15: 1, 3, 5, 15

⇒ HCF(5, 10, 15) = 5

⇒ Therefore, LCM of fractions = 12/5

∴ The correct answer is 12/5.

Additional Information

HCF of Fractions

To find the HCF of fractions, use the formula: HCF of Numerators / LCM of Denominators.

Relation between Two Numbers

For any two positive integers a and b, the product of the numbers is equal to the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b).

Co-prime Numbers

If two numbers are co-prime (their HCF is 1), then their LCM is simply the product of the two numbers.

Shortcut Trick

Convert the given fractional relation directly to a ratio: (3 × 5) : (4 × 8) = 15 : 32.

Total ratio parts = 15 + 32 = 47.

47 parts → 94 ⇒ 1 part → 2.

First part = 15 parts × 2 = 30.

∴ The correct answer is 30.

Alternate Method

Given:

Total value to be divided = 94.

Let the two parts be A and B.

Logic / Formula Used:

If a number N is divided in the ratio m : n, then First Part = N × [m ÷ (m + n)].

Calculations:

⇒ According to the question, (A ÷ 5) ÷ (B ÷ 8) = 3 ÷ 4

⇒ (A ÷ 5) × (8 ÷ B) = 3 ÷ 4

⇒ 8A ÷ 5B = 3 ÷ 4

⇒ A ÷ B = (3 × 5) ÷ (4 × 8)

⇒ A ÷ B = 15 ÷ 32

⇒ Ratio of A : B = 15 : 32

⇒ Sum of ratio terms = 15 + 32 = 47

⇒ First part A = 94 × (15 ÷ 47)

⇒ First part A = 2 × 15 = 30

∴ The correct answer is 30.

Additional Information

Dividing a Quantity in a Given Ratio

To divide a quantity N in the ratio a : b, the first part is calculated as (a ÷ (a + b)) × N and the second part as (b ÷ (a + b)) × N.

Compound Ratio

The compound ratio of two ratios a : b and c : d is given by (a × c) : (b × d). It involves multiplying the antecedent and consequent terms respectively to form a single combined ratio.

Proportion

If four numbers a, b, c, and d are in proportion (a : b = c : d), then the product of extremes equals the product of means (a × d = b × c).

Shortcut Trick

Required smallest number = LCM of divisors + Remainder

LCM(15, 20, 35) = 420

Required smallest number = 420 + 8 = 428

∴ The correct answer is 428.

Alternate Method

Given:

Divisors = 15, 20, and 35

Remainder in each case = 8

Formula Used:

Smallest Number = LCM(a, b, c) + R

Calculation:

⇒ Prime factorization of 15 = 3 × 5

⇒ Prime factorization of 20 = 2² × 5

⇒ Prime factorization of 35 = 5 × 7

⇒ LCM(15, 20, 35) = 2² × 3 × 5 × 7 = 420

⇒ Smallest number = 420 + 8 = 428

∴ The correct answer is 428.

Additional Information

LCM with Different Remainders

If a number when divided by a, b, c leaves remainders p, q, r respectively and (a − p) = (b − q) = (c − r) = k, the smallest such number is LCM(a, b, c) − k.

Relation between HCF and LCM

For any two numbers, Product of numbers = HCF × LCM.

Co-prime Numbers

Two numbers are co-prime if their HCF is 1. The LCM of two co-prime numbers is their product.

Given:

The curved surface area of a cylindrical object is 990 m2 and its volume is 4455 m3.

Formula used:

The curved surface area of the cylindrical = 2πrh

The volume of the cylindrical = πr²h 

Calculation:

The curved surface area of the cylindrical = 2πrh

⇒ 2πrh = 990

⇒ πrh = 495 →(1)

The volume of the cylindrical = πr2h 

⇒ r(πrh) = 4455

⇒ r = (\dfrac{4455}{495}) = 9 m 

From Eqn (1), We have

⇒ π× 9 × h = 495 

⇒ h = (\dfrac{495 \times7}{22 \times 9}) = 17.5 m

According to the question,

The ratio of the height and diameter = h : 2r

⇒ 17.5 : 18

⇒ 35 : 36

∴ The ratio of the height and diameter of this object is 35 : 36.

इसका सही उत्तर बात बनाना है। 

• बहाना करना उसकी आदत है। वाक्य के रेखांकित अंश को प्रतिस्थापित करने के लिए सही मुहावरा हैः बात बनाना उसकी आदत है। ।

Key Points

• बात बनाना का अर्थ है, किसी झूठे बहाने से किसी स्थिति को संभालना या छुपाना।
• मुहावरे - मुहावरा का शाब्दिक अर्थ ‘अभ्यास’ है। मुहावरा शब्द अरबी भाषा का शब्द है।
• हिन्दी में ऐसे वाक्यांशों को मुहावरा कहा जाता है, जो अपने साधारण अर्थ को छोड़कर विशेष अर्थ को व्यक्त करते हैं।
• उदाहरण - 1. अंडे सेना- घर में बेकार बैठना। वाक्य प्रयोग - इतनी उम्र होने पर भी आप अंडे सेना बने बैठे हो।
• अन्य विकल्प-

Additional Informationमुहावरों के अन्य उदाहरण -

‘पुरातन' का विलोम शब्द है- नवीन 

Key Points

• ‘पुरातन' शब्द का विलोम शब्द 'नवीन' होगा।
• ‘पुरातन' शब्द का अर्थ है - पुराना, प्राचीन।
• 'नवीन' शब्द का अर्थ - नया, नूतन।
• 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- 

पुल्लिंग ​शब्द है- व्यय

Key Points

• पुल्लिंग ​शब्द है- 'व्यय' जैसे - हमें अपनी आवश्यकताओं के अनुसार ही व्यय करना चाहिए।
• पुल्लिंग - शब्द के जिस रूप से पुरुष जाति का बोध होता है, उसे पुल्लिंग कहते हैं।
• जैसे- बकरा, घोड़ा, लड़का, आदमी, शेर, बन्दर, बालक, शिशु, राजा, राजकुमार आदि।
• स्त्रीलिंग - शब्द के जिस रूप से व्यक्ति या वस्तु की स्त्री जाति का बोध होता है, उसे स्त्रीलिंग कहते हैं।
• जैसे - माता, लड़की, भेड़, गाय, बंदरिया, शेरनी, नारी, रानी, राजकुमारी, बहन आदि।

अन्य विकल्प -

• स्त्रीलिंग शब्द - 'लहर, आय, नहर'​
• जैसे - उसके दिमाग में नए विचारों की लहरें उठ रही थीं।
• जैसे - कंपनी ने इस तिमाही में अच्छी आय दर्ज की है।
• जैसे - नहरों की जगह सड़कें बना दी गई हैं।

Important Points 

Additional Information 

  लिंग दो प्रकार के होते हैं-

1. पुल्लिंग
2. स्त्रीलिंग

"खूँटी" का सही बहुवचन खूँटियॉं है। अन्‍य व‍िकल्‍प असंगत हैं। 

Key Points

• ‘खूँटी’ का अर्थ है ‘कपड़े आदि टांगने की दीवार में लगी हुक'।
• इसका बहुवचन रूप ‘खूँटियाँ’ होगा।

Additional Information

इसका सही उत्तर 'ज़बान पर चढ़ना' है।

Key Points

• 'याद आना' का अर्थ है - ज़बान पर चढ़ना।
• वाक्य प्रयोग :- यह गाना सुनते ही मुझे अपने बचपन की सारी बातें ज़बान पर चढ़ गईं।

Additional Information

• ज़बान काट कर देना -स्वीकार करना, वादा करना, प्रतिज्ञा करना
• वाक्य प्रयोग :- मीरा ने अपनी दोस्त से ज़बान काट कर दी कि वह उसके साथ हर मुश्किल में खड़ी रहेगी।
  
• ​गाँठ में बाँधना - किसी बात या अनुभव को हमेशा याद रखना।
• वाक्य प्रयोग :- तुम मेरी ये महत्वपूर्ण बातें गाँठ में बांध लो।

Important Points

• मुहावरे की परिभाषा :-
• किसी भाषा की अभिव्यंजना के विशिष्ट रूप को ‘मुहावरा’ कहते हैं। विशिष्ट शब्दों, विचित्र प्रयोगों एवं प्रयोग-सिद्ध विशिष्ट वाक्यांशों को ‘मुहावरा’ कहते हैं।

इनमें स्त्रीलिंग शब्द है- रचना 

Key Points

• स्त्रीलिंग शब्द है - 'रचना' जैसे - कवि ने अपनी नई रचना मंच पर सुनाई।
• पुल्लिंग - शब्द के जिस रूप से पुरुष जाति का बोध होता है, उसे पुल्लिंग कहते हैं।
• जैसे- छात्र, चाचा, बूढ़ा, नौकर, शेर, बंदर आदि।
• स्त्रीलिंग - शब्द के जिस रूप से व्यक्ति या वस्तु की स्त्री जाति का बोध होता है, उसे स्त्रीलिंग कहते हैं।
• जैसे - छात्रा, चाची, बुढ़िया, नौकरानी, घास आदि।

अन्य विकल्प-

Additional Information लिंग दो प्रकार के होते हैं-

1. पुल्लिंग
2. स्त्रीलिंग

तद्भव शब्द है - जीभ

Key Points

• 'जीभ' एक तद्भव शब्द है, जबकि इसका तत्सम 'जिह्वा' शब्द होगा।
• तत्सम - जिन शब्दों को संस्कृत से बिना किसी परिवर्तन के ले लिया जाता है, उन्हें तत्सम शब्द कहते हैं। 
• जैसे- मार्ग, अक्षि, काक आदि।
• तद्भव - जिन शब्दों में समय और परिस्थितियों के कारण कुछ परिवर्तन होने से जो शब्द बने हैं, उन्हें तद्भव कहते हैं। 
• जैसे- पग, आँख, कौआ आदि।​

अन्य विकल्प-

Additional Information कुछ महत्वपूर्ण ​तत्सम और तद्भव शब्द -

'सोहन ने घर का सारा काम किया है।' वाक्य की पूर्ति उचित कर्ताकारक चिह्न है। अन्य विकल्प असंगत है। 

Key Points

• वाक्य- सोहन ने घर का सारा काम किया है।

Important Points