DSSSB MTS: (27th July 2026) Memory-Based Paper (Previous Year Paper)

The correct answer is Freedom of religion.

Key Points

• Article 25 of the Indian Constitution guarantees the Freedom of Religion to all persons in India. It ensures the freedom of conscience and the right to freely profess, practice, and propagate religion. Statement 1 is correct.
• This right is available to both citizens and non-citizens (foreigners) residing in the country. It highlights the secular nature of the Indian State.
• The exercise of this right is not absolute and is subject to public order, morality, and health, as well as other provisions of Part III of the Constitution.
• Under Article 25, the State is permitted to regulate or restrict any economic, financial, political, or other secular activity which may be associated with religious practice.
• It also allows the Government to provide for social welfare and reform or the throwing open of Hindu religious institutions of a public character to all classes and sections of Hindus.

Additional Information

• Cultural and Educational Rights: These rights are enshrined in Articles 29 and 30 of the Constitution. They protect the interests of minorities (linguistic and religious) by allowing them to conserve their language, script, or culture and establish educational institutions of their choice. Statement 2 is incorrect.
• Right to Constitutional Remedies: Provided under Article 32, this allows citizens to move the Supreme Court for the enforcement of Fundamental Rights. Dr. B.R. Ambedkar called this article the "Heart and Soul of the Constitution." Statement 3 is incorrect.
• Right to Equality before Law: Guaranteed under Article 14, it states that the State shall not deny to any person equality before the law or the equal protection of the laws within the territory of India. Statement 4 is incorrect.
• Secularism in India: Unlike the Western concept of separation of church and state, Indian Secularism means that the State maintains an equal distance from all religions and supports them equally. The word "Secular" was specifically added to the Preamble by the 42nd Amendment Act, 1976.
• Articles 25 to 28: Together, these four articles constitute the Right to Freedom of Religion in the Indian Constitution, covering individual and collective religious freedoms.

Important Points

• Definition of Hindu: For the purposes of Article 25, the term "Hindu" is defined to include people professing the Sikh, Jain, or Buddhist religions. This ensures that public religious institutions of these communities are also inclusive.
• Sikhism and Kirpans: Explanation 1 of Article 25 specifically mentions that the wearing and carrying of kirpans shall be deemed to be included in the profession of the Sikh religion.
• Article 26: While Article 25 protects the rights of individuals, Article 26 protects the rights of religious denominations or sections thereof to manage their own religious affairs.
• Fundamental Rights: These rights are contained in Part III of the Constitution, which was adopted on 26 November 1949 and came into effect on 26 January 1950.

The correct answer is To provide education to children aged six to fourteen years.

Key Points

• The Constitution (Eighty-sixth Amendment) Act, 2002, inserted Article 21A into the Indian Constitution, making the right to education a fundamental right for children aged six to fourteen years.
• It also amended Article 45, which directs the state to provide early childhood care and education for children below six years.
• Clause (k) was added to Article 51A (Fundamental Duties), making it the duty of every parent or guardian to provide opportunities for education to their child or ward aged six to fourteen years.
• This amendment paved the way for the enactment of the Right of Children to Free and Compulsory Education Act, 2009, which operationalizes Article 21A.
• The amendment reflects India's commitment to achieving universal elementary education and reducing dropout rates among children.

Additional Information

• Fundamental Duties
• Fundamental Duties were added to the Indian Constitution by the 42nd Amendment Act, 1976, upon the recommendations of the Swaran Singh Committee.
• These duties are enshrined in Article 51A and aim to promote patriotism, discipline, and moral values among citizens.
• Currently, there are 11 Fundamental Duties listed in the Constitution.

The correct answer is Weddings and festivals.

Key Points

• Tippani dance is a prominent folk dance originating from the Saurashtra region of Gujarat, particularly associated with the coastal towns of Chorwad and Veraval.
• The dance is traditionally performed by the women of the Koli and Bhil communities, who originally developed these rhythmic movements while working as laborers to level the ground during the construction of houses and forts.
• While it has its roots in manual labor, the performance has evolved into a celebratory art form conducted during significant social and cultural events, such as weddings and major Hindu festivals like Holi and Diwali.
• The performance is characterized by the use of the Tippani stick, a long wooden pole roughly 175 cm in length with a heavy square wooden or iron block (called a Garbo) attached at the base to strike the floor.
• The dancers arrange themselves in two rows and strike the floor in a synchronized, rhythmic pattern, creating a unique sound that serves as both music and a display of physical coordination and endurance.

 Additional Information

• Instruments and Music:
• The rhythmic thumping of the Tippani is accompanied by folk instruments like the Zanz, Manjira (cymbals), Tabla, and Dhol (drum) to maintain a steady tempo.
• The Turi and Shehnai are also frequently used to provide melodic accompaniment to the percussive nature of the dance.
• Cultural Context:
• Unlike purely Religious rituals that are confined to temples, Tippani is a social dance that brings the community together in public squares or household courtyards.
• The costumes worn are traditional Gujarati attire, including the Ghagra-Choli for women, often embellished with mirrors and vibrant embroidery typical of the Saurashtra folk style.
• It is often compared to other work-related folk dances, but it stands out due to its high energy and the percussive floor-striking technique which is rare in other Indian folk traditions.

The correct answer is 52nd Amendment, 1985.

Key Points

• The 52nd Amendment Act of 1985 added the Tenth Schedule to the Indian Constitution, introducing the Anti-Defection Law.
• The law aims to curb political defections by disqualifying members of Parliament and State Legislatures who switch parties after being elected.
• The Anti-Defection Law applies to both individual members defecting and cases where a political party splits and merges with another.
• The presiding officer of the legislature (Speaker or Chairman) is empowered to make decisions regarding disqualification under the Anti-Defection Law.
• Members can be disqualified if they voluntarily give up membership of their party or vote/abstain from voting against party directions without prior permission.

Additional Information

• 44th Amendment, 1978
• This amendment was enacted to repeal many provisions of the 42nd Amendment, which was passed during the Emergency period (1975-77).
• It restored the power of judicial review to the Supreme Court and High Courts.
• The 44th Amendment also ensured that fundamental rights like the Right to Property were removed from Part III and made a legal right under Article 300A.
• It introduced safeguards against misuse of the emergency provisions of the Constitution.
• 61st Amendment, 1989
• This amendment lowered the voting age for elections to the Lok Sabha and State Legislative Assemblies from 21 years to 18 years.
• The aim was to increase political participation among the youth of India, who constitute a significant portion of the population.
• 73rd Amendment, 1992
• This amendment provided a constitutional status to Panchayati Raj Institutions (PRIs) in India.
• It introduced Part IX to the Constitution and the Eleventh Schedule, listing 29 functional items to be transferred to the Panchayats.
• The amendment mandated the establishment of Gram Sabhas and a three-tier system of Panchayati Raj for rural governance.
• It also provided for the reservation of seats for Scheduled Castes, Scheduled Tribes, and women in Panchayati Raj bodies.

The correct answer is Net National Product at factor cost.

Key Points

• National income is the total value of a country’s final output of all goods and services produced in a year.
• National income is also known as NNP at factor cost.
• It is sum total of incomes of residents of a country in a given period of time including capital consumption or depreciation.
• All payments that are made to factors of production like land, labour, capital and entrepreneurship are at the factor cost at which goods and services are produced.
• National income = NNP at factor cost

Additional Information

• GDP (Gross Domestic Product) is the total value of goods and services which are produced  only within the territory of a country. It does not include any depreciation of capital goods. It is calculated by Income method, product or value-added method and expenditure method. It is given as,
• GDP = C + I + G + X – M
• C = consumption expenditure
• I = investment expenditure
• G = government expenditure
• M = import expenditure
• X = income from export
• GNP = GDP + Net factor income from abroad
• NNP = GNP – Depreciation of capital goods

The correct answer is - Jawaharlal Nehru

Key Points

• Jawaharlal Nehru
• The 1929 session of the Indian National Congress was held in Lahore under the presidency of Jawaharlal Nehru.
• During this historic session, the Congress passed the landmark resolution of Purna Swaraj, which translates to "Complete Independence" from British rule.
• On the midnight of December 31, 1929, Jawaharlal Nehru unfurled the newly adopted Tricolour flag of India on the banks of the River Ravi.
• The Congress fixed January 26, 1930, as the first Independence Day, which was to be celebrated by people all over the country.
• This session also authorized the Working Committee to launch a programme of Civil Disobedience, including non-payment of taxes.

Additional Information

• Vallabhbhai Patel
• Sardar Vallabhbhai Patel presided over the Karachi Session of the Indian National Congress in 1931.
• This session is significant for adopting resolutions on Fundamental Rights and the National Economic Programme.
• Rajendra Prasad
• Dr. Rajendra Prasad presided over the Bombay Session of the Indian National Congress in 1934.
• He later served as the first President of Independent India.
• Mukhtar Ahmed Ansari
• Dr. M.A. Ansari presided over the Madras Session of the Indian National Congress in 1927.
• It was during this session that the Congress decided to boycott the Simon Commission and passed a resolution for "complete national independence" for the first time.

The correct answer is 7th Schedule.

Key Points

• The 7th Schedule of the Constitution of India provides the framework for the division of powers between the Union Government and the State Governments.
• It implements Article 246 of the Constitution, which deals with the legislative competence of the Parliament and the State Legislatures.
• The schedule is divided into three lists: List I (Union List), List II (State List), and List III (Concurrent List).
• The Union List currently contains 100 subjects (originally 97), including critical matters of national importance such as Defense, Foreign Affairs, Railways, and Currency.
• The State List comprises 61 subjects (originally 66) like Public Order, Police, Public Health, and Sanitation, over which states have exclusive jurisdiction.
• The Concurrent List has 52 subjects (originally 47) including Education, Forests, and Criminal Law, where both the Union and States can make laws, with the Union law prevailing in case of conflict.

 Additional Information

• 5th Schedule
• Contains provisions relating to the administration and control of Scheduled Areas and Scheduled Tribes in any state except the four North-Eastern states of Assam, Meghalaya, Tripura, and Mizoram.
• 9th Schedule
• Introduced by the 1st Constitutional Amendment Act, 1951, to protect land reform laws and other statutes from judicial review on the grounds of violation of fundamental rights.
• 10th Schedule
• Known as the Anti-Defection Law, it was added by the 52nd Amendment Act, 1985, specifying grounds for disqualification of members of legislative bodies due to defection.

The correct answer is Shatadru.

Key Points

• The river Sutlej is referred to as Shatadru in ancient Sanskrit texts.
• Sutlej is one of the major rivers of the Indus River system.
• It originates from the Rakas Lake near Mansarovar in Tibet, which is in close proximity to the source of the Indus River.
• This river flows through the regions of India and Pakistan before merging with the Indus River.
• In ancient history, the Sutlej River played a critical role in the development of the Indus Valley Civilization.
• The Sanskrit name Shatadru translates to "flowing in a hundred streams," indicating the river's dynamic nature.
• It is also significant for its contribution to agriculture in the Punjab region, forming the backbone of irrigation in the area.
• The Sutlej is harnessed for various projects such as the Bhakra Nangal Dam, which provides hydroelectricity and water for irrigation.

Additional Information

• Iravati
• Iravati is the ancient Sanskrit name for the Ravi River, another significant river of the Indus system.
• The Ravi River flows through Himachal Pradesh, Punjab (India), and Pakistan.
• It is also known for its role in the Partition of Punjab and the Indus Waters Treaty.
• Vipasa
• Vipasa is the Sanskrit name for the Beas River, another important river in northern India.
• The Beas River originates in the Himalayas near the Rohtang Pass in Himachal Pradesh.
• It is known for its contribution to the irrigation systems in Punjab and Himachal Pradesh.
• Parushni
• Parushni is the Sanskrit name for the Ravi River, which is also known as Iravati.
• The term "Parushni" is mentioned in ancient texts like the Rigveda.

The correct answer is Article 29 and 30.

Key Points

• Article 29: This article provides protection to the rights of minorities to preserve their distinct language, script, and culture. It ensures that citizens having a unique cultural identity are safeguarded under the Constitution of India.
• Article 30: It grants minorities the right to establish and administer educational institutions of their choice. This helps preserve their heritage and promote education in their communities.
• Both articles are aimed at ensuring cultural and educational rights for minorities, reflecting India’s commitment to diversity and inclusion.
• These provisions prevent discrimination against minorities on grounds of religion, language, or culture, thus fostering a sense of equality and protection under the law.
• These rights are fundamental and enforceable through the judiciary, ensuring minorities can approach courts for their protection if required.

Additional Information

• Article 17: It abolishes "untouchability" and forbids its practice in any form. While significant for social justice, it is not directly related to minority rights.
• Article 32: Known as the "heart and soul of the Constitution," it provides the right to constitutional remedies. It allows individuals to seek enforcement of their fundamental rights but does not specifically address minority protection.
• Article 31: Relates to the right to property, which was removed as a fundamental right by the 44th Amendment in 1978 and is now a legal right under Article 300A. It is unrelated to minority protection.
• Importance of Articles 29 and 30:
• They are crucial for maintaining India's pluralistic character and protecting its diverse communities.
• Educational institutions established by minorities under Article 30 often contribute to national development by providing quality education.
• These articles ensure the representation and empowerment of minorities in social, cultural, and educational spheres.

Important Points

• Article 29 (1): Protects the interests of any section of citizens who have a distinct language, script, or culture.
• Article 29 (2): Prohibits discrimination by the state in granting admission into educational institutions based on religion, race, caste, language, or any of them.
• Article 30 (1): Empowers minorities to establish and administer educational institutions of their choice.
• Article 30 (2): Ensures that the state shall not discriminate when granting aid to educational institutions run by minorities.

The correct answer is Mughal and Hindu.

Key Points

• Kathak is one of the eight primary classical dance forms of India, originating from the nomadic bards of Northern India known as Kathakars or storytellers.
• The Hindu tradition provided the foundational narrative of the dance, which was deeply rooted in the Bhakti Movement. It focused on the Vaishnavite cult, specifically portraying the legends of Lord Krishna and Radha through Gat Bhava.
• Under the patronage of Mughal Emperors and their courts, the dance moved from temples to a secular environment, acquiring a more sophisticated and formal structure.
• The Mughal influence introduced distinct elements such as intricate footwork (Tatkar), rapid pirouettes (Chakkars), and a shift in costume to the Angarkha and Anarkali styles.
• This synthesis created a unique blend where Hindu devotional themes were expressed through high-speed rhythmic patterns and technical virtuosity favored in Islamic courts.
• The evolution of different Gharanas like Lucknow, Jaipur, and Benares showcases the varying degrees of these two cultural impacts on the dance style.

 Additional Information

• Technical Components of Kathak:
• Nritta: This refers to the pure dance aspect involving Bols (rhythmic syllables), Tukras, and Parans executed with high precision.
• Abhinaya: The expressive part of the dance where facial expressions and hand gestures (Mudras) are used to convey Rasa (emotion).
• Tala: The rhythmic cycle, commonly Teental (16 beats), serves as the temporal framework for the performance.
• Prominent Figures and Instruments:
• The dance is traditionally accompanied by the Tabla, Pakhawaj, Sarangi, and Cymbals.
• Nawab Wajid Ali Shah of Awadh was a crucial patron who helped establish the Lucknow Gharana, emphasizing grace and poetic expression.
• Modern legends like Pandit Birju Maharaj have been instrumental in globalizing the art form.

The correct answer is Arunachal Pradesh.

Key Points

• According to the 2011 Census, Arunachal Pradesh recorded the lowest population density in India.
• The population density of Arunachal Pradesh is just 17 persons per square kilometer. This is due to its rugged mountainous terrain and vast forest cover.
• Population density is a measurement of population per unit area; for the Census, it is calculated as the number of persons per square kilometer.
• The total population of Arunachal Pradesh was approximately 13,83,727 as per the 2011 data, spread across a geographical area of 83,743 square kilometers.
• The low density in this Northeastern state is a result of geographical constraints, limited habitable land, and the presence of dense Himalayan forests. Hence, the statement regarding Arunachal Pradesh being the least densely populated is correct.

Additional Information

• Mizoram:
• It is the second least densely populated state in India.
• As per the 2011 Census, Mizoram has a population density of 52 persons per square kilometer.
• The state is known for its high literacy rate, which was recorded at 91.33% in 2011.
• Rajasthan:
• It is the largest state in India by area, covering about 10.4% of the country's total land.
• Despite its size, its population density is 200 persons per square kilometer, which is lower than the national average due to the Thar Desert.
• The total population of Rajasthan in 2011 was 6.85 crores.
• Assam:
• Located in the Northeast, it has a significantly higher population density compared to its neighbors.
• The density of Assam is 398 persons per square kilometer, exceeding the national average.
• It is a major producer of tea and petroleum in India.
• Sikkim:
• It is the third least densely populated state with 86 persons per square kilometer.
• It holds the record for being the least populous state in India with a total population of 6,10,577 in 2011.

Important Points

• National Density: The overall population density of India increased from 324 in 2001 to 382 persons per square kilometer in the 2011 Census.
• Most Densely Populated State: Bihar is the most densely populated state in India, with 1106 persons per square kilometer. It overtook West Bengal (1028) in the 2011 survey.
• Union Territories: Delhi has the highest population density among all states and Union Territories, with a staggering 11,320 persons per square kilometer.
• Andaman and Nicobar Islands: This UT has the lowest density among Union Territories, with only 46 persons per square kilometer.
• Historical Context: The Census of 2011 was the 15th census of India and the 7th since Independence. The slogan was "Our Census, Our Future."

The correct answer is The State Governor.

Key Points

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

Additional Information

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

The correct answer is Fifth Five Year Plan.

Key Points

• The Fifth Five Year Plan was launched for the period 1974 to 1978 (though originally intended until 1979). The main objective of this plan was the eradication of poverty (Garibi Hatao) and the attainment of self-reliance.
• The slogan "Garibi Hatao" was coined by Indira Gandhi during the 1971 election campaign and was subsequently integrated as the core goal of the Fifth Five Year Plan.
• The plan was drafted and launched by D.P. Dhar. It focused on increasing the employment level, reducing social inequality, and achieving economic stability by controlling inflation.
• This plan was terminated one year early, in 1978, by the newly elected Janata Party Government led by Morarji Desai. They replaced it with the Rolling Plan for the period 1978-1980.
• The target growth rate for this plan was 4.4%, while the actual growth rate achieved was 4.8%, making it a successful plan in terms of economic output despite political instability.

Additional Information

• Fourth Five Year Plan (1969–1974):
• This plan was based on the Gadgil Strategy. It aimed at growth with stability and the progressive achievement of self-reliance.
• Significant events during this period included the nationalization of 14 major Indian banks in 1969 and the Green Revolution which boosted agricultural production.
• The Indo-Pakistan War of 1971 and the subsequent Bangladesh Liberation War took place during this plan, putting a strain on financial resources.
• Sixth Five Year Plan (1980–1985):
• This plan marked the beginning of economic liberalization in the Indian economy. Its focus was on poverty alleviation and technological self-reliance.
• Programs like the Integrated Rural Development Programme (IRDP) were given massive importance to tackle rural poverty.
• The National Bank for Agriculture and Rural Development (NABARD) was established on July 12, 1982, upon the recommendation of the Sivaraman Committee.
• Seventh Five Year Plan (1985–1990):
• The plan was implemented under the leadership of Rajiv Gandhi. Its objective was to improve productivity and create employment opportunities.
• The slogan for this plan was "Food, Work, and Productivity". It emphasized the growth of food grain production and social justice.
• For the first time, the private sector was given priority over the public sector in terms of investment allocation.

Important Points

• The concept of Five Year Plans in India was borrowed from the USSR (Soviet Union). India's first Prime Minister, Jawaharlal Nehru, was highly influenced by the centralized planning model of Joseph Stalin.
• The Planning Commission was the non-constitutional body responsible for formulating these plans. It was established on March 15, 1950.
• In 2015, the Narendra Modi government replaced the Planning Commission with a new think-tank called NITI Aayog (National Institution for Transforming India).
• The National Development Council (NDC) was the final authority that approved the Five Year Plans before they were implemented. It was established on August 6, 1952.
• The Twenty Point Programme (TPP) was also launched during the Fifth Five Year Plan in 1975 with the objective of improving the quality of life of the poor and under-privileged.

The correct answer is Lothal.

Key Points

• Lothal, situated in the Bhal region of modern-day Gujarat, was a vital maritime hub of the Indus Valley Civilization (IVC).
• The site is world-renowned for its artificial dockyard, which is considered the earliest known dockyard in the world, dating back to roughly 2400 BCE.
• This dockyard was a trapezoidal structure built with kiln-burnt bricks and measured approximately 218 meters in length and 37 meters in width.
• It was connected to an ancient course of the Bhogava River, a tributary of the Sabarmati, which allowed ships to enter from the Gulf of Khambhat during high tides.
• The presence of this dockyard signifies that Lothal was a major center for maritime trade, facilitating the exchange of goods like beads, gems, and ivory with civilizations in Mesopotamia and Sumer.

 Additional Information

• Mohenjo-daro:
• Located in the Larkana district of Sindh (Pakistan) on the banks of the Indus River.
• It is famous for the Great Bath, the Great Granary, and the discovery of the Bronze Dancing Girl statue.
• Harappa:
• The first site of the civilization to be excavated in 1921 by Daya Ram Sahni, located near the Ravi River in Punjab (Pakistan).
• Key features include granaries located outside the citadel and stone symbols of Lingam and Yoni.
• Kalibangan:
• Situated in the Hanumangarh district of Rajasthan on the banks of the dried-up Ghaggar River.
• It is significant for the discovery of the world’s earliest ploughed field and several fire altars used for rituals.

The correct answer is option 1.

Key PointsBandipur Tiger Reserve:

• It was established in 1973 under Project Tiger.
• In 1985, by including adjacent areas from Venugopala Wildlife Park, it was enlarged and named Bandipur National Park.
• It is situated in the tri-junction area of the States of Karnataka, Tamil Nadu and Kerala.
• It forms a part of the Nilgiri Biosphere Reserve.
• The park is located between the Kabini river in the north and the Moyar river in the south.
• The Nugu river runs through the park. Hence, pair 1 is not correctly matched.
• The Kabini Reservoir separates the Bandipur and Nagarahole Tiger Reserves on the North-west.
• It is endowed with rich floral and faunal diversity and is recognized as one of the Mega Biodiversity Areas in the country.

Orang National Park:

• It is located on the north bank of the Brahmaputra River in the Darrang and Sonitpur districts of Assam, India. Hence, pair 2 is correctly matched.
• It was established as a sanctuary in 1985 and declared a National Park on 13 April 1999.
• It is also known as the mini Kaziranga National Park (IUCN site) since the two parks have a similar landscape made up of marshes, streams and grasslands and are inhabited by the Great Indian One-Horned Rhinoceros.
• Flora and fauna include great Indian rhinoceros, pygmy hog, Asian elephant, wild water buffalo and Bengal tiger.

Ranthambore Tiger Reserve:

• It lies in the eastern part of Rajasthan state in Karauli and Sawai Madhopur districts, at the junction of the Aravali and Vindhya hill ranges.
• It is located near the confluence of the Banas and Chambal rivers, but none of the rivers does not flow through the tiger reserve. Hence, pair 3 is not correctly matched.
• The vegetation includes grasslands on plateaus and dense forests along the seasonal streams.
• The forest type is mainly tropical dry deciduous with ‘dhak’ (Butea monsoperma), a tree capable of withstanding long periods of drought, being the commonest.
• This tree is also called as 'Flame of forest' and is one of the many flowering plants that add colour to the dry summers here.

Jaldapara National Park:

• It is located at the foothills of the Eastern Himalayas in the Alipurduar District of northern West Bengal and on the banks of the Torsa River. Hence, pair 4 is not correctly matched.
• It is home to the Indian leopard, Indian elephants, sambar, barking deer, spotted deer, hog deer, wild boars, gaur, etc.
• Jaldapara is a paradise for bird watchers.
• It is one of the very few places in India, where the Bengal florican is sighted.

The correct answer is Sama Veda.

Key Points

• Sama Veda is considered the origin of Indian music and is often referred to as the "Veda of melodies and chants."
• It primarily contains hymns and chants that are meant to be sung rather than recited, providing the foundation for musical scales and compositions in Indian classical music.
• The chants in Sama Veda were designed to invoke divine blessings and establish a spiritual connection, making it highly significant in religious rituals. Hence, the correct option is Sama Veda.
• The hymns in Sama Veda are derived from the Rig Veda, but they are set to specific melodies or tunes, which are believed to be the precursor to the musical traditions of India.
• Sama Veda is closely associated with Indian classical music, including the development of raga systems, which form the core of both Hindustani and Carnatic music traditions.

Additional Information

• Sama Veda:
• Sama Veda is one of the four Vedas and holds an integral place in the spiritual and musical traditions of ancient India.
• It consists of 1,875 verses, most of which are derived from the Rig Veda. These verses are set to music and are intended for liturgical purposes.
• Sama Veda lays the foundation for Indian musical traditions and emphasizes the importance of melodic chanting to enhance spiritual experience.
• Comparison of the Four Vedas:
• Rig Veda: Focuses on hymns and praises dedicated to the gods. It is the oldest and most foundational text in the Vedic literature.
• Sama Veda: Contains musical chants and melodies derived from the Rig Veda, forming the basis of Indian music.
• Yajur Veda: Deals with the rituals and ceremonies associated with sacrifices and practical aspects of religious worship.
• Atharva Veda: Focuses on practical knowledge, spells, charms, and everyday life aspects, including medicine and healing practices.
• Indian Music and Sama Veda:
• Indian classical music evolved from the melodic structures outlined in Sama Veda, particularly the raga system.
• Both Hindustani and Carnatic music traditions trace their roots to the Sama Veda, highlighting its significance in shaping the musical heritage of India.

Important Points

• Historical Significance:
• Sama Veda played a crucial role in the development of religious rituals and ceremonies in ancient India.
• The musical chants of Sama Veda were used in temple rituals and were believed to have divine powers to connect humans with the spiritual realm.
• Role in Music Evolution:
• Sama Veda is considered the earliest source of Indian classical music, influencing not only music but also dance and drama traditions.
• The raga system, which forms the backbone of Indian classical music, finds its origins in the melodic structures outlined in Sama Veda.

The correct answer is Qutb-ud-din Aibak.

Key Points

• Qutb-ud-din Aibak was the first ruler of the Slave Dynasty, also known as the Mamluk Dynasty, which ruled Delhi in the 13th century CE.
• He was a former slave of Mohammad Ghori and rose to prominence after Ghori's death in 1206 CE. Following Ghori's death, Qutb-ud-din declared himself the ruler of the territories in India.
• Qutb-ud-din Aibak established his capital at Lahore and laid the foundation of the Slave Dynasty, marking the beginning of the Delhi Sultanate.
• He is known for commissioning the construction of the Qutub Minar in Delhi, which was later completed by his successor, Iltutmish.
• He earned the title of Lakh Baksh (Giver of Lakhs) due to his generous nature and patronage of scholars and poets during his reign.
• Qutb-ud-din Aibak ruled until his death in 1210 CE, which occurred due to a fall from a horse while playing polo.

Additional Information

• Slave Dynasty (1206–1290 CE):
• The Slave Dynasty was the first of the five dynasties of the Delhi Sultanate. It was founded by Qutb-ud-din Aibak in 1206 CE.
• It was called the Slave Dynasty because its rulers were former slaves who had risen to power.
• The dynasty included notable rulers such as Qutb-ud-din Aibak, Iltutmish, and Balban.
• Contributions of Qutb-ud-din Aibak:
• He started the construction of the Qutub Minar to commemorate the victory of Mohammad Ghori over the Rajputs.
• He built the Quwwat-ul-Islam Mosque, the first mosque in Delhi, near the Qutub Minar.
• Iltutmish (1211–1236 CE):
• He was the successor of Qutb-ud-din Aibak and completed the construction of the Qutub Minar.
• Iltutmish introduced the Iqta system and consolidated the Delhi Sultanate's territories.
• Balban (1266–1287 CE):
• Balban is remembered for his strict administration and policy of blood and iron.
• He strengthened the central authority and suppressed rebellions during his reign.
• Razia Sultan (1236–1240 CE):
• She was the first and only female ruler of the Delhi Sultanate.
• Razia faced opposition from nobles and was eventually overthrown, highlighting the patriarchal nature of the era.

Important Points

• Qutub Minar:
• The Qutub Minar is a UNESCO World Heritage Site and a famous symbol of Indo-Islamic architecture.
• Its construction was started by Qutb-ud-din Aibak and completed by Iltutmish.
• Mohammad Ghori:
• Mohammad Ghori was a ruler of the Ghurid Empire and the mentor of Qutb-ud-din Aibak.
• His conquest of northern India laid the groundwork for the establishment of the Delhi Sultanate.

The correct answer is Zabti system.

Key Points

• The Zabti system, also known as the Dahshala system, was a land revenue administrative framework introduced by Raja Todar Mal, the finance minister (Mushrif-i-Diwan) of the Mughal Emperor Akbar, around 1580-1582.
• This system was based on a meticulous survey of crop yields, prices, and areas cultivated over a ten-year period (1570−1580) to establish a stable revenue demand.
• The state revenue demand was fixed at one-third of the average produce, and unlike earlier systems, the valuation was converted into cash based on local price schedules (Dasturs).
• For accurate land measurement, Akbar replaced the traditional hemp rope with the Jarib, which utilized bamboo sticks joined by iron rings to prevent fluctuations caused by moisture.
• The land was categorized into four types based on the continuity of cultivation: Polaj (cultivated annually), Parauti (left fallow for 1−2 years), Chachar (left fallow for 3−4 years), and Banjar (uncultivated for 5 years or more).

 Additional Information

• Mansabdari system:
• A unique administrative and military ranking system introduced by Akbar to organize the nobility.
• Ranks were divided into Zat (personal status and salary) and Sawar (number of cavalrymen the officer was required to maintain).
• Jagirdari system:
• A mechanism of resource allocation where Mansabdars were assigned Jagirs (land grants) instead of cash salaries.
• The Jagirdar had the right to collect revenue from the assigned territory to meet his official expenses.
• Ryotwari system:
• A land revenue system introduced much later by the British (specifically Thomas Munro and Alexander Read) in South India.
• It established a direct contract between the government and the Ryots (individual peasants) for tax payment.

The correct answer is Odisha.

Key Points

• The Paika Rebellion, also known as the Paika Bidroha, was a fierce armed uprising against the British East India Company that broke out in Odisha in 1817.
• The Paikas were the traditional landed militia of Odisha, who rendered military and policing services to the Gajapati rulers of Khurda in exchange for rent-free agricultural lands known as Nish-kar Jagirs.
• The rebellion was primarily triggered by the British conquest of Odisha in 1803, which led to the deposition of the Raja of Khurda and the subsequent resumption of the Paikas hereditary lands by the colonial administration.
• The movement was led by Bakshi Jagabandhu Bidyadhar, the former military commander of the Khurda forces, who galvanized the Paikas and the tribal Kandhas to revolt against the oppressive land revenue system.
• Economic grievances including the skyrocketing price of salt due to the British monopoly and the abolition of the traditional Cowrie currency system intensified the local resentment.
• The uprising spread across regions like Puri, Pipli, and Cuttack, and although the British officially suppressed it by 1818, guerrilla resistance continued until 1825.

 Additional Information

• Bengal:
• It was the central administrative hub of the British East India Company and witnessed the Sanyasi Rebellion (1763−1800) and the Chuar Uprising, but it was not the location of the Paika revolt.
• Maharashtra:
• This region saw significant anti-colonial resistance such as the Bhil Uprising (1818) and the Ramosi Rebellion (1822) led by Chittur Singh against the British revenue policies.
• Assam:
• Resistance in this region included the Ahom Revolt of 1828 led by Gomdhar Konwar and the Phulaguri Dhawa (1861), which was the first peasant uprising in Assam.

The correct answer is 'Participation of Indians in British Indian Government'

Key Points

• Gandhi-Irwin Pact, 1931:
• The Gandhi-Irwin Pact was a political agreement signed on March 5, 1931, between Mahatma Gandhi and the then Viceroy of India, Lord Irwin.
• It marked a significant step in the Indian freedom struggle, aiming to create a mutual understanding between the Indian National Congress and the British government.
• The pact led to the suspension of the Civil Disobedience Movement and facilitated the participation of the Congress in the Second Round Table Conference.
• Promises made in the Gandhi-Irwin Pact:
• Suspension of Civil Disobedience Movement: Gandhi agreed to suspend the ongoing Civil Disobedience Movement, which included acts such as the non-payment of taxes and the breaking of salt laws.
• Not to press for enquiry into police excesses: As a conciliatory gesture, Gandhi agreed not to insist on an inquiry into police actions and violence during the movement.
• Participation of Congress in the Round Table Conference: The Congress agreed to participate in the Second Round Table Conference to discuss constitutional reforms in India.
• Why 'Participation of Indians in British Indian Government' is incorrect:
• The Gandhi-Irwin Pact did not include any provision or promise about Indian participation in the British Indian Government.
• The pact primarily dealt with addressing civil disobedience issues and ensuring Congress’s participation in constitutional discussions, rather than political representation in governance.

Additional Information

• Other outcomes of the Gandhi-Irwin Pact:
• The pact ensured the release of political prisoners who were not charged with violence.
• Confiscated properties of satyagrahis (protesters) were to be returned, and fines that had not been collected were to be remitted.
• The right to make salt for personal use was granted to coastal villages, marking a partial concession on the salt tax issue.
• Significance of the pact:
• It demonstrated Gandhi’s willingness to negotiate and his pragmatic approach to achieving freedom within a constitutional framework.
• The agreement highlighted the influence of mass movements like the Civil Disobedience Movement in pressuring the colonial government.
• While the pact did not lead to immediate constitutional reforms, it paved the way for future negotiations and international recognition of India’s struggle for independence.

The correct answer is Assam.

Key Points

• The Ambubachi Mela is a prominent Hindu festival held annually at the Kamakhya Temple in Guwahati, Assam, and is considered the most important event of the temple's calendar.
• This festival is celebrated during the monsoon season, specifically in the middle of June, coinciding with the Assamese month of Ahaar.
• It celebrates the annual menstrual cycle of the goddess Kamakhya; during this three-day period, the temple remains closed to the public as it is believed the Mother Earth is undergoing menstruation.
• On the fourth day, the temple doors are opened with great fanfare, and devotees are allowed to enter to receive Prasad and seek blessings from the goddess.
• The festival is popularly known as the Mahakumbh of the East because it attracts millions of pilgrims, Sadhus, Tantriks, and Bauls from across India and neighboring countries.

 Additional Information

• Kamakhya Temple:
• Situated atop the Nilachal Hills, this temple is one of the 51 Shakti Peethas and represents the yoni (genitals) of Goddess Sati.
• The temple follows the Nilachal style of architecture, featuring a unique hemispherical dome resting on a cruciform base.
• It is a primary center for Tantric Shaktism, where the deity is worshipped in the form of a natural stone fissure kept moist by a natural spring.
• Cultural Significance:
• The Ambubachi Mela promotes the idea of fertility and challenges social taboos by openly celebrating the biological process of menstruation.
• The devotees are often given small pieces of red cloth called Angodak as Prasad, which is highly sought after for its spiritual significance.
• While Bihar, Jharkhand, and Chhattisgarh host significant regional festivals like Chhath Puja, Sarhul, and Bastar Dussehra respectively, they do not observe the Ambubachi Mela.

The correct answer is Water and Gender.

In News

• World Water Day is observed globally on 22 March every year, with the 2026 edition focusing on the intersection of water and gender roles.

Key Points

• 2026 Theme: This year’s theme, “Water and Gender”, highlights the specific challenges and roles women and men play in water management and sanitation.
• Global Coordination: The activities are coordinated by UN-Water, the United Nations' mechanism for water and sanitation issues.
• Sustainable Development: The day is a key tool for achieving SDG 6 (Clean Water and Sanitation for all by 2030).
• Critical Need: The observance aims to address the needs of the 2.1 billion people worldwide who currently lack access to safe drinking water.
• Origin: World Water Day was first proposed at the 1992 United Nations Conference on Environment and Development (UNCED) in Rio de Janeiro.

SDG 6

• United Nations Goal
• Sustainable Development Goal 6 aims to ensure availability and sustainable management of water and sanitation for all. It includes targets for drinking water, sanitation, hygiene, water quality, and transboundary cooperation.

The correct answer is Galacturonic acid.

Key Points

• Pectin is a complex carbohydrate that is found in the cell walls of plants and is responsible for the firmness and softness of fruits.
• The main acid unit that makes up pectin is galacturonic acid, which is a sugar acid that is derived from glucose.
• Pectin is made up of complex polysaccharides, which are widely distributed in the green parts of terrestrial plants and found in the primary cell walls of plants.
• The main element of the middle lamella, where pectin binds cells, is pectin.

Additional Information

• Aspartic acid is an amino acid that is not found in pectin**,** but is found in proteins.
• Lentils, soybeans, garbanzo beans, and other legumes are plant sources of aspartic acid.
• Lactic acid is a simple organic acid that is produced by bacteria during fermentation and is not found in pectin.
• Our body creates lactic acid when our cells digest carbohydrates for energy.
• Glutamic acid is an amino acid that is not found in pectin, but is found in proteins.
• It transforms into glutamate inside the body.
• This substance aids in the transmission and reception of information between **brain nerve cells.**​

When a chemical element is present in one or more forms in the same physical state then it is known as allotrope. Swedish scientist Jons Jakob Berzelium proposed the concept of allotropes in 1841.

Ozone (O₃) is an allotrope of oxygen. It is more soluble than oxygen in the water.

Ozone is used for air purification at the crowded places. It is also used in sterilizing drinking water as it oxidizes all germs and bacteria.

Albert Einstein proposed a quantum of light (the photon) which behaves like a particle. Einstein's other theories explained the equivalence of mass and energy, the particle-wave duality of photons, the equivalence principle, and special relativity.

The correct answer is As biomass.

Key Points

• Each trophic level has a certain mass of living material at a particular time called the standing crop, this standing crop is measured as the biomass of living organisms, as the number in a unit area.
• An ecological pyramid is a pictorial representation of the relationship between different organisms in an ecosystem.
• It is of three types: Pyramid of the number, Pyramid of biomass, and Pyramid of energy.

Additional Information

• The pyramid of energy represents the total amount of energy consumed by each trophic level in a given food chain.
• According to the 10% law of energy transfer, only 10% of the total energy is transferred from one trophic level to another.
• Therefore the total amount of energy available for utilization in the layers above is less than the energy available in the lower levels, so the pyramid is always upright.

The correct answer is Indian Football League.

In News

• The All India Football Federation (AIFF) has officially announced the rebranding of the I-League as the 'Indian Football League' starting from the 2026-27 season.

Key Points

• Objective: The rebranding is part of AIFF's 'Vision 2047' to professionalize Indian football and make the league more commercially viable and appealing to a global audience.
• Historical Context: The I-League was originally launched in 2007, replacing the National Football League (NFL).
• Promotion/Relegation: The league will continue to serve as the second tier in the Indian football pyramid, with the winners earning promotion to the Indian Super League (ISL).
• New Identity
• The rebranding includes a new logo and a standardized broadcasting format to align with international standards.
• It aims to strengthen the "Indian" identity of the domestic league structure.

Additional Information

• AIFF (All India Football Federation)
• The governing body for football in India, affiliated with FIFA and the Asian Football Confederation (AFC).
• Headquarters: Football House, New Delhi.
• Indian Football Pyramid
• Tier 1: Indian Super League (ISL)
• Tier 2: Indian Football League (formerly I-League)

The correct answer is (i) - (a), (ii) - (c), (iii) - (b), (iv) - (d).

Key Points

• Alkali metal:
• Group 1 elements in the periodic table, consist of lithium, sodium, potassium, rubidium, cesium, and francium.
• They are highly reactive, easily losing an electron to form a positive ion, and are stored under oil or inert gas to prevent reactions with air and moisture.
• Alkali metals have low densities, and low melting points, and are good conductors of heat and electricity.
• They have various uses, including in batteries, alloys, and as a coolant in nuclear reactors.
• Alkaline earth metal:
• Group 2 elements in the periodic table, including beryllium, magnesium, calcium, strontium, barium, and radium.
• They are also reactive and easily lose two electrons to form a positive ion but are less reactive than alkali metals.
• Alkaline earth metals have higher densities and melting points than alkali metals and are also good conductors of heat and electricity.
• They have many practical applications, such as in construction materials, alloys, and fireworks.
• Transition metal:
• Elements in the d-block of the periodic table, consisting of groups 3-12, including iron, copper, silver, and gold.
• They have multiple valence electrons and can form various oxidation states, giving them the ability to form complex compounds and exhibit colourful properties.
• Transition metals have high densities, and melting points, and are good conductors of heat and electricity.
• They have numerous applications in technology, such as in catalysts, electronic devices, and construction materials.
• • Group 18 elements in the periodic table, consisting of helium, neon, argon, krypton, xenon, and radon.
• They are characterized by their extremely low reactivity and are usually found as monatomic gases in the atmosphere.
• Noble gases have complete valence electron shells, making them chemically stable and unreactive with other elements.
• They have applications in lighting, cryogenics, and as a shielding gas in welding.

The correct answer is transfer of electrons between two reactants.

Key Points

Redox Reactions

• Redox reactions are chemical reactions in which the oxidation states of atoms are changed.
• These reactions involve the transfer of electrons from one substance to another.
• One substance is oxidized (losing electrons) and another is reduced (gaining electrons).

Explanation:-

1. Zn + CuSO4 → ZnSO4 + Cu

• Zn goes from 0 to +2 oxidation state (oxidation).
• Cu goes from +2 to 0 oxidation state (reduction).
• This is a redox reaction.

2. 2KClO3 + I2 → 2KIO3 + Cl2

• Cl in KClO3 goes from +5 to 0 oxidation state (reduction).
• I in I2 goes from 0 to +5 oxidation state in KIO3 (oxidation).
• This is a redox reaction.

3. H2 + Cl2 → 2HCl

• H goes from 0 to +1 oxidation state (oxidation).
• Cl goes from 0 to -1 oxidation state (reduction).
• This is a redox reaction.

The correct answer is Use of fabric filters to trap dust and fly ash.

Key Points

• Fabric filters, commonly referred to as baghouses, are specialized industrial air pollution control devices designed to remove particulate matter (PM) from flue gas or exhaust streams.
• They function by passing contaminated air through a series of long, cylindrical bags made of woven or felted fabric, which physically trap solid pollutants such as dust, soot, and fly ash.
• The filtration process involves several physical mechanisms including inertial impaction, interception, and diffusion; as the operation continues, a dust cake forms on the fabric, which significantly increases the removal efficiency of fine particulates.
• These systems are highly effective for particulate control, often achieving collection efficiencies of over 99 percent for particles as small as 0.5 to 1 micrometer in diameter.
• They are essential in high-pollution industries such as thermal power plants, cement factories, and metal smelting units to prevent the release of harmful fly ash into the atmosphere.

 Additional Information

• Absorption of gases (Liquid Scrubbers):
• This method primarily targets gaseous pollutants like Sulfur Dioxide (SO2) and Nitrogen Oxides (NOx) by dissolving them in a liquid solvent (often water or an alkaline solution).
• While wet scrubbers can capture some particulates, the specific process of absorption is a mass-transfer operation meant for chemical gas removal rather than solid particle filtration.
• Catalytic Combustion:
• This technique is used to treat Volatile Organic Compounds (VOCs) and Carbon Monoxide (CO) by oxidizing them at lower temperatures using a catalyst (such as Platinum or Palladium).
• It does not effectively remove non-combustible particulates like mineral dust or ash.
• Increasing Chimney Height:
• A dispersion strategy that utilizes stack height to release pollutants higher into the atmosphere, allowing for dilution by wind before they reach ground level.
• This is not a control method as it does not reduce the total mass of pollutants emitted into the environment.
• Electrostatic Precipitators (ESP):
• Another major device for particulate control that uses electric charges to collect particles on large collector plates, widely used for managing fine fly ash in coal-fired power stations.

The correct answer is Dubai CommerCity.

In News

• IIT Madras Global Research Foundation is set to establish its first Applied Artificial Intelligence Innovation Centre at Dubai CommerCity.
• The initiative aims to accelerate applied AI innovation and support technology-led economic growth.

Key Points

• The Centre will initially host six applied AI startups with a combined valuation of approximately US$118 million.
• Projected revenues of these startups are estimated at US$281 million over the next five years.
• The initiative is facilitated by MCA Gulf, a strategic partner of IITM Global in Dubai.
• The Centre aims to position Dubai as a regional and global launchpad for applied AI innovation.

Additional Information

• Dubai CommerCity: A leading free zone dedicated exclusively to digital commerce in the Middle East, Africa and South Asia (MEASA) region.
• IIT Madras Global Research Foundation: A strategic platform designed to take IIT Madras’s academic, research and innovation capabilities to the global stage.
• Applied Artificial Intelligence: Refers to the practical deployment of AI technologies to solve real-world business and societal challenges.
• MEASA Region: Stands for Middle East, Africa and South Asia, a rapidly growing market for digital and technology-driven enterprises.

The correct answer is Article 280.

Key Points

• Article 280 of the Indian Constitution provides for the establishment of the Finance Commission of India.
• The Finance Commission is constituted by the President of India every five years or earlier as deemed necessary.
• The primary role of the Finance Commission is to make recommendations on the distribution of net proceeds of taxes between the Union and the States, and the allocation among states themselves.
• The Finance Commission also advises on matters related to grants-in-aid to the states by the Union government from the Consolidated Fund of India.
• The first Finance Commission was established in 1951 under the chairmanship of K.C. Neogy.
• The recommendations of the Finance Commission are advisory in nature and are not binding on the government.

Additional Information

• Constitutional Provisions for Finance Commission:
• Article 280: This article mandates the President to set up the Finance Commission and outlines its functions and responsibilities.
• Article 275: Provides for grants-in-aid to needy states as determined by the Finance Commission.
• Article 282: Allows both the Union and State governments to make discretionary grants for public purposes.
• Key Functions of Finance Commission:
• Distribution of net tax proceeds between the Centre and the States.
• Determination of principles governing grants-in-aid to the states.
• Recommendations regarding measures to improve the financial position of states.
• Reviewing the fiscal policies of both the Union and the State governments to ensure financial stability.
• Significant Finance Commissions:
• First Finance Commission (1951): Chaired by K.C. Neogy, it laid the foundation for federal fiscal relations in India.
• 14th Finance Commission (2015-2020): Chaired by Dr. Y.V. Reddy, it recommended increasing the states' share of central taxes to 42%.
• 15th Finance Commission (2020-2025): Chaired by N.K. Singh, it addressed fiscal challenges posed by the COVID-19 pandemic.
• Key Characteristics of Finance Commission:
• It is a quasi-judicial body established under the Constitution of India.
• Its recommendations aim to ensure fiscal equity and financial stability in the country.
• The commission is typically composed of a chairperson and four other members, with qualifications specified by Parliament.

Important Points

• Comparison of Articles:
• Article 268: Deals with duties levied by the Union but collected and appropriated by the States.
• Article 246: Specifies the subject matter of laws made by Parliament and by the Legislatures of States.
• Article 365: Deals with the effect of failure to comply with, or to give effect to, directions given by the Union government.
• Evolution of Finance Commission:
• The Finance Commission has played a pivotal role in balancing the financial relations between the Centre and the States since India’s Independence.
• It ensures that states have adequate financial resources to carry out their responsibilities under the federal structure.
• Role in Governance: The recommendations of the Finance Commission significantly influence budgetary allocations and fiscal policies in India.

The correct answer is Mridangam – Hindustani classical.

Key Points

• Mridangam is primarily associated with Carnatic classical music, which is a major genre of South Indian classical music. Hence, the statement is incorrect.
• Ektara is a simple, single-stringed instrument widely used in Baul music, a traditional folk music genre from Bengal. Hence, the statement is correct.
• Tumbi is a high-pitched, single-string instrument associated with Punjabi folk music. It is often used in Bhangra performances. Hence, the statement is correct.
• Algoza is a double-flute instrument that is also closely tied to Punjabi folk music. It is commonly played during festive and celebratory events. Hence, the statement is correct.
• The incorrect pairing is Mridangam with Hindustani classical music, as it is traditionally used in Carnatic music rather than Hindustani music.

Additional Information

• Mridangam:
• Origin: The Mridangam is a percussion instrument originating from South India, where it plays a vital role in Carnatic music.
• Material: It is typically made from jackwood and features two drumheads that produce unique sounds.
• Usage: The Mridangam is considered the primary rhythm instrument in Carnatic classical music performances.
• Distinctive Feature: It produces complex rhythmic patterns and is often paired with other instruments like Veena and Flute.
• Ektara:
• Origin: This single-stringed instrument is most commonly associated with Baul singers of Bengal.
• Material: It is made using a wooden stem and a resonator, often crafted from dried gourds.
• Usage: The Ektara is used in folk music to convey spiritual and philosophical themes.
• Distinctive Feature: It is known for its simplicity and ability to produce soulful melodies.
• Tumbi:
• Origin: A traditional instrument from Punjab, it is commonly used in Punjabi folk music.
• Material: Made with a wooden stick and a resonator, often crafted from a hollowed-out pumpkin or gourd.
• Usage: It is prominently featured in upbeat Bhangra music performances.
• Distinctive Feature: Known for its sharp and rhythmic tone, it adds vibrancy to Punjabi music.
• Algoza:
• Origin: This double-flute instrument is traditionally played in Punjab.
• Material: Made from wood, with two flutes tied together to produce simultaneous melodies.
• Usage: Often used in folk songs and festive celebrations, it requires skillful breathing techniques.
• Distinctive Feature: Known for its melodious and intertwined dual tones.

Important Points

• Hindustani vs Carnatic Music:
• Hindustani classical music is predominantly practiced in North India and features instruments like Tabla, Sitar, and Harmonium.
• Carnatic classical music is primarily practiced in South India and includes instruments like Mridangam, Veena, and Violin.
• The Mridangam is exclusively used in Carnatic music, while Hindustani music often employs instruments like Tabla for rhythm.
• Baul Tradition:
• The Baul music tradition originates from Bengal and focuses on mysticism and spiritual themes.
• Bauls are wandering minstrels who use simple instruments like Ektara to convey their messages.
• Punjabi Folk Music:
• Instruments like Tumbi and Algoza are integral to Punjabi folk music.
• They are used in traditional songs, celebratory events, and Bhangra performances.

The correct answer is Vishnu Digambar Paluskar.

Key Points

• Vishnu Digambar Paluskar was a renowned Hindustani classical musician.
• He founded the Gandharva Mahavidyalaya in 1901, which was one of the first music schools in India.
• He is credited with popularizing Hindustani classical music and making it accessible to the common people.
• His book Sangeet Bal Prakash is an important contribution to the field of Indian classical music education.

Additional Information

• Hindustani Classical Music:
• Hindustani classical music is one of the two major traditions of Indian classical music, the other being Carnatic music.
• It originated in North India and has a rich history dating back thousands of years.
• It is characterized by its extensive use of improvisation and the raga system, which is a framework for composition and performance.
• Some of the well-known forms of Hindustani classical music include Dhrupad, Khayal, Thumri, and Tappa.
• Gandharva Mahavidyalaya:
• Founded by Vishnu Digambar Paluskar in 1901 in Lahore.
• It was one of the first institutions to offer formal training in Hindustani classical music.
• The institution played a pivotal role in popularizing classical music among the masses and providing a structured curriculum.
• The Gandharva Mahavidyalaya continues to be a prominent institution for music education in India.
• Contribution of Vishnu Digambar Paluskar:
• He is known for his efforts to revive and popularize Hindustani classical music in the early 20th century.
• He introduced the concept of public concerts, which helped in making classical music accessible to a wider audience.
• His efforts in music education laid the foundation for many future musicians and music educators in India.
• Paluskar's work and legacy continue to influence the field of Indian classical music today.

The correct answer is Odisha.

In News

• The President of India approved the prestigious 'Police Colour' award for the Odisha Police in April 2026.

Key Points

• The award coincides with Odisha’s 91st Foundation Day. Odisha was the first state in India to be formed on a linguistic basis on April 1, 1936.
• The 'Police Colour' is the highest national honor bestowed upon a police force for exceptional dedication and success in law and order.
• The recognition reinforces the Odisha Police motto: "Service and Security".
• Odisha Foundation Day (Utkala Dibasa)
• Date: April 1
• 91st Anniversary (2026): Celebrated with a 14-day "Odia Pakhya" (fortnight) from April 1 to April 14.

Additional Information

• Ministry of Home Affairs (MHA)
• The MHA conveys the Presidential approval for such honors to the State's Chief Secretary.
• Symbolism
• The force's flag will be formally adorned with an emblem of distinction during a ceremonial event.
• Linguistic Basis
• Odisha became a separate province in 1936, carved out of the Bihar and Orissa Province and the Madras Presidency.

Confusion Points

• Andhra Pradesh was the first state to be created on a linguistic basis after India's independence. But before our independence, Odisha was created on a linguistic basis.

The correct answer is When the government expenditure exceeds revenue.

Key Points

• A deficit budget occurs when the government's expenditure exceeds its revenue.
• This situation leads to the government borrowing money to cover the gap between expenditure and revenue.
• Deficit budgeting is often used by governments to stimulate economic growth, especially during periods of recession.
• It can also lead to an increase in public debt if the deficit is persistent over time.

Additional Information

• Government Revenue:
• It includes all the money received by the government from taxes, non-tax sources like fees, fines, grants, and investments.
• Tax revenue is the major source and includes income tax, corporate tax, sales tax, etc.
• Government Expenditure:
• It includes all the spending by the government on goods, services, and public projects.
• Major components include spending on defense, education, health, infrastructure, social security, and interest payments on debt.
• Budget Deficit:
• A budget deficit occurs when spending exceeds revenue and indicates the financial health of a government.
• It is a common economic phenomenon and is typically measured as a percentage of the Gross Domestic Product (GDP).
• Public Debt:
• It is the total amount of money that a government owes to external lenders and domestic creditors.
• It includes all the borrowings from domestic and international sources.

The correct answer is ₹3,000.

Key Points

• The Pradhan Mantri Kisan Maandhan Yojana (PM-KMY) is a government-backed pension scheme introduced to provide social security to small and marginal farmers in India.
• Under this scheme, eligible farmers receive a monthly pension of ₹3,000 after attaining the age of 60 years.
• The scheme primarily targets farmers who own cultivable land of up to 2 hectares and are aged between 18 and 40 years at the time of enrolment.
• Farmers are required to make a monthly contribution (ranging from ₹55 to ₹200 depending on their age) towards the pension fund, which is matched by an equivalent contribution from the Government of India.
• The scheme is voluntary and contributory, ensuring long-term financial security for farmers during their old age.

Additional Information

• Eligibility Criteria:
• The beneficiary must be a small or marginal farmer owning up to 2 hectares of cultivable land.
• The farmer should be aged between 18 to 40 years and not be a member of any other pension scheme like EPFO, ESIC, or NPS.
• The individual should not be an income taxpayer.
• Features of PM-KMY:
• After the age of 60, a beneficiary is entitled to receive a monthly pension of ₹3,000.
• In the event of the farmer's death, the spouse is eligible to receive 50% of the pension amount as a family pension.
• If the beneficiary opts out of the scheme before the age of 60, their contributions will be returned along with interest or the equivalent savings bank interest rate.
• Implementation:
• The scheme is administered by the Ministry of Agriculture and Farmers’ Welfare.
• The Life Insurance Corporation (LIC) of India functions as the pension fund manager for PM-KMY.
• Farmers can enroll in the scheme through Common Service Centres (CSCs) across the country.
• Importance:
• The scheme is designed to secure the livelihood of small and marginal farmers during their old age.
• It aims to reduce dependency on family members and provide financial independence to farmers.
• By ensuring a steady source of income, the scheme helps improve the overall quality of life for farmers in their later years.

Important Points

• The Pradhan Mantri Kisan Maandhan Yojana was launched on 12th September 2019 by Prime Minister Narendra Modi.
• Farmers can join the scheme by submitting their details like Aadhaar number, bank account details, and other relevant information at the nearest Common Service Centre (CSC).
• The contribution amount varies based on the age of the farmer at the time of joining. For example, an 18-year-old has to pay ₹55 per month, while a 40-year-old pays ₹200 per month.
• The government matches the farmer’s contribution, ensuring that the pension fund is sufficient to provide the promised payouts after retirement.
• The scheme is part of a larger effort by the Indian government to support the agricultural sector and enhance the economic well-being of farmers.

The correct answer is 7.

Key Points

• The Sun Temple at Konark, located in Odisha, India, is renowned for its unique architectural design resembling a giant chariot.
• The chariot has 24 wheels (12 pairs), symbolizing the 24 hours of a day or the 12 months of the year.
• It is pulled by 7 magnificently sculpted horses, representing the seven days of the week.
• The temple was built in the 13th century by King Narasimhadeva I of the Eastern Ganga dynasty and is dedicated to the Sun God (Surya).
• The 7 horses signify the strength and spiritual energy needed to traverse the cosmic journey of life. Hence, the correct answer is 7.

Additional Information

• History and Architecture of the Sun Temple:
• The Sun Temple at Konark was constructed in 1250 CE during the reign of King Narasimhadeva I.
• The temple is designed in the shape of a massive chariot with 24 wheels and 7 horses, symbolizing the Sun God’s chariot that traverses the heavens.
• The wheels act as sundials, showcasing ancient Indian expertise in astronomy and timekeeping.
• The temple follows the Kalinga architectural style, characterized by its towers and elaborate stone carvings.
• The temple was declared a UNESCO World Heritage Site in 1984.
• Significance of Horses in the Sun Temple:
• The 7 horses of the Sun Temple symbolize the seven days of the week or the seven colors of light (VIBGYOR).
• The horses are sculpted to convey a sense of motion, depicting the energy of the Sun as it moves across the sky.
• They also represent strength, speed, and vitality, qualities associated with the Sun.
• Tourism and Cultural Importance:
• It hosts the annual Konark Dance Festival, which celebrates classical Indian dance forms like Odissi.
• The temple is often referred to as the "Black Pagoda" due to its dark color and magnetic properties (historically).

Important Points

• Location: The Sun Temple is situated in Konark, Odisha, near the Bay of Bengal.
• Chariot Design: The temple represents a cosmic journey, pulled by 7 horses and supported by wheels that function as sundials.
• Symbolism: The temple reflects ancient Indian beliefs in the cycle of time and the Sun’s universal power.

The correct answer is Department of Drinking Water and Sanitation (DDWS).

In News

• The Department of Drinking Water and Sanitation (DDWS) conducted "Jal Mahotsav 2026" from March 8 (International Women’s Day) to March 22 (World Water Day).

Key Points

• The campaign aims to strengthen Jan Bhagidari (people's participation) in rural drinking water management under the Jal Jeevan Mission (JJM).
• It features a three-tier framework: Jal Mahotsav (National), Rajya Jal Utsav (State), and Lok Jal Utsav (Village/Panchayat).
• A National Mega Event was held on March 11, 2026, at Vigyan Bhawan, New Delhi, with the President of India as the Chief Guest.
• Key activities include "Jal Arpan"—the symbolic handing over of water supply schemes to Gram Panchayats and Village Water & Sanitation Committees (VWSCs).

Additional Information

• Jal Jeevan Mission (JJM)
• Launched in 2019, it envisions providing safe and adequate drinking water through individual household tap connections to all households in rural India.
• Sujal Gram
• Refers to water-secure villages that have sustainable drinking water governance and adequate water supply.
• Nal Jal Mitra Programme
• An initiative to provide multi-skilling training to village youth to help maintain water supply infrastructure at the local level.
• Vigyan Bhawan
• A premier convention centre of the Government of India in New Delhi, used for hosting national-level events and conferences.

The correct answer is Umri Village, Guna district, Madhya Pradesh

In News

• The Samriddh Gram: Integrated Phygital Service Delivery Model Enabled by BharatNet, an initiative of the Department of Telecommunications (DoT), has been nominated for the prestigious WSIS Prizes 2026.

Key Points

• Union Minister of Communications Shri Jyotiraditya M. Scindia inaugurated India’s First Samriddhi Kendra at Umri Village in Guna district of Madhya Pradesh.
• The Samriddh Gram initiative aims to establish Samriddhi Kendras as one-stop community hubs for integrated “phygital” services (physical + digital).
• These centers leverage the BharatNet backbone to provide rural citizens access to healthcare, education, agriculture, governance, financial inclusion, and e-commerce.
• The nomination for the WSIS (World Summit on the Information Society) Prizes 2026 is under the category Action Line AL C6: Enabling Environment.
• While other options mention districts in Madhya Pradesh, the first center was specifically established in Guna district at Umri Village.

Additional Information

• The WSIS Forum 2026 is scheduled to be held from 6–10 July 2026 in Geneva.
• The public voting phase for the WSIS Prizes is open until 03 May, 2026.
• Key technologies utilized in the model include High-speed broadband, FTTH connectivity, and public Wi-Fi.

Important Points

• The model is driven through a community-based entrepreneurial framework, making it scalable and replicable.
• Phygital services facilitate transformative use cases such as telemedicine, smart classrooms, and technology-enabled agriculture.

The logic followed here is:

Thus, code for 'snacks' is '6'.

Hence, the correct answer is "Option 1".

The Venn diagram that best represents the relationship between Infectious diseases, Deficiency diseases, Goitre, Rickets, Chickenpox is shown below:

Chicken Pox is an infectious disease.

Goitre and Rickets are Deficiency diseases.

Hence, 'option 1' is the correct answer.

According to the given information:

Aman starts from point A and walks 5 km towards north. He turns left and walks 10 km. He turns left and walks 15 km. He turns to the left and walks 5 km. Finally he turns left and walks 10 km.

Thus, Aman is now in 'West' direction from the starting point A

Hence, the correct answer is "West".

Solution :

The direction of Tanmay's journey is shown in the figure below.

We can clearly see in the above figure that Tanmay travelled in West direction in the beginning.

Hence the correct answer is "West".

Given:

'A $ B' means 'A is the father of B'.

'A # B' means 'B is the daughter of A'.

'A × B' means 'B is sister of A'.

'A @ B' means 'B is the husband of A'.

Let us first decode the given symbols and then draw a family tree

On checking: P @ Q $ R @ S # T

1) P@Q

Here, Q is the husband of P.

2. Q$R

Here, Q is the father of R.

3. R@S

Here, S is the husband of R.

4) S # T

Here, T is daughter of S.

• Thus, the following family tree can be drawn:

• Clearly P is 'Maternal Grandmother' of T.

Hence, the correct answer is "Maternal Grandmother".

The logical and meaningful order is:

The order is in accordance with size of the given options.

5- Asia : Continent 

3- South-East Asia : Part of continent 

2- India : Country 

4- Kerala : State 

1- Haripad : City 

 Hence the correct answer is option 3.

Given : 320, 328, 338, 350, 364, ?

The logic follows here is:

Hence, the correct answer is "380".

The arrangement as per the dictionary order is as follows :

4. Toothier
5. Total
6. Totem
7. Totted
8. Totter

Hence, the correct answer is 41352.

In all the options except 'option 1', letters are arranged in parallelly, while in 'option 1', letters are arranged perpendicularly.

​

Hence, 'option 1' is the odd one out.

The logic followed here is :- Alternately (1) is added to and subtracted from the position value according to the English alphabetic series.

​So,

• RAIN : SZJM

​

And,

• FALL : GZMK

​

Similarly,

• JUMP : ?

Hence, the correct answer is "KTNO".

According to the question:

1. The age of a father is twice the sum of the ages of his 3 children.

2) After 15 years, his age will be equal to the sum of the ages of his children.

Let the age of the father be = F

Let the age of the 3 children be = C1, C2 and C3

So, 

F = 2 (C1 + C2 + C3) --------- (1)

After 15 years,

F + 15 = (C1 + 15) + (C2 + 15) + (C3 + 15)

F + 15 = (C1 + C2 + C3) + 45

F = (C1 + C2 + C3) + 30 ------------- (2)

From (1) and (2), we get

F = (F ÷ 2) + 30

2F = F + 60

F = 60

Thus, father's ager after 15 will be:

F = 60 + 15 = 75 years

Hence, "Option 4" is the correct answer.

1. INDUCTIVELY → can be formed

2. JUVENILITY → can be formed

3. INDUCTED → cannot be formed as there is only single D in DISJUNCTIVELY.

4. DECLIVITY → can be formed

Hence, INDUCTED cannot be formed from the letters used in DISJUNCTIVELY.

All options except 'Jharkhand' are name of capital cities of different states in India, while 'Jharkhand' is the name of a state in India.

Hence, ‘Jharkhand’ is the odd one out.

This is an alternate number series .

It follows the following pattern :

Hence, the correct answer is 16 .

Statements:

No pen is a pencil.

All pencils are chalks.

The least possible diagram for the given statements is as follows

Conclusions:

I. No chalk is a pen → False (It is possible but not definite)

II. No pencil is a pen → True (because no pen is a pencil so definitely no pencil is a pen)

III. Some chalks are pencils → True (because all pencils are chalks so some chalks are definitely pencils)

Hence, “Only conclusions II and III follow” is the correct answer.

BODMAS Table: 

Given equation I. 7 - 5 + 1 × 3 ÷ 6 = 20

Now, if '1 and 6' are interchanged, then:

⇒ 7 - 5 + 6 × 3 ÷ 1 = 20

⇒ 7 - 5 + 6 × 3 = 20

⇒ 7 - 5 + 18 = 20

⇒ 25 - 5 = 20

⇒ 20 = 20

LHS = RHS.

Given equation II: 1 × 7 + 6 - 4 ÷ 2 = 40

Now, if '1 and 6' are interchanged, then:

⇒ 6 × 7 + 1 - 4 ÷ 2 = 40

⇒ 6 × 7 + 1 - 2 = 40

⇒ 42 + 1 - 2 = 40

⇒ 43 - 2 = 40

⇒ 41 ≠ 40

LHS ≠ RHS.

Here, Only Equation I are the correct after interchanging the given symbol.

Hence, the correct answer is "Option 1".

The logic followed here is:

Consonants coded as the next letter and vowels remain the same vowels.

Similarly,

Therefore,

Hence, the correct answer is "GIOHES".

The pattern followed here is:

Given: Seven people A, H, D, F, T, E, and G are sitting in a straight row, facing north.

1) Only three people sit to the left of E.

(It means E sits on the middle of the row)

2) A sits at the extreme right of the row.

3) F sits second to the left of E.

4) G and H are immediate neighbours of E.

(Position of G and H is not clear but they sit either side of E)

5)  D is the immediate neighbour of A.

6. So, T sits on the vacant place.

Clearly, T sits extreme left of the row.

Hence, the correct answer is "T".

The Venn diagram that best represents the relationship between Saturn, Planet, and Cadminum is shown below:

Saturn is a Planet and Cadmium is a chemical element.  

Hence, ‘option 1’ is the correct answer.

To form the code, the first letter is replaced by its predecessor, the second letter is replaced by its successor, the third letter is replaced by its second predecessor, the fourth letter is replaced by its second successor and so on as per the English alphabetical series.

Similarly,

Hence, MARKET will be coded LBPMBW.

The logic followed here is:

Logic: All the numbers are perfect cube.

Now,

For, (8, 27, 125)

⇒ 8 = Cube of 2.

⇒ 27 = Cube of 3.

⇒ 125 = Cube of 5.

For, (64, 1331, 1728)

⇒ 64 = Cube of 4.

⇒ 1331 = Cube of 11.

⇒ 1728 = Cube of 12.

Now checking the options,

Option 1) (289, 212, 196) 

⇒ 289 = Not a Cube number.

⇒ 212 = Not a Cube number.

⇒ 196 = Not a Cube number.

Option 2) (200, 215, 256) 

⇒ 200 = Not a Cube number.

⇒ 215 = Not a Cube number.

⇒ 256 = Not a Cube number.

Option 3) (125, 172, 144) 

⇒ 125 = Cube of 5.

⇒ 172 = Not a Cube number.

⇒ 144 = Not a Cube number.

Option 4) (216, 343, 512) 

⇒ 216 = Cube of 6.

⇒ 343 = Cube of 7.

⇒ 512 = Cube of 8.

Hence, the correct answer is "Option 4".

By using the symbols in the table given below, we can draw the following family tree:

Clearly, Kapil is the maternal uncle of Neha.

Hence, ‘Maternal uncle’ is the correct answer.

1. × and –

Given expression: 3 × 6 + 2 – 4 ÷ 8 = 13

After replacing the symbols, we get:

LHS =3 - 6 + 2 × 4 ÷ 8

= 3 – 6 + 1

= 4 – 6

= - 2 ≠RHS

2. • and ×

Given expression: 3 × 6 + 2 – 4 ÷ 8 = 13

After replacing the symbols, we get:

LHS = 3 + 6 × 2 – 4 ÷ 8

= 3 + 12 – 0.5

= 15 – 0.5

= 14.5 ≠ RHS

3. • and -

Given expression: 3 × 6 + 2 – 4 ÷ 8 = 13

After replacing the symbols, we get:

LHS = 3 × 6 - 2 + 4 ÷ 8

= 12 – 2 + 0.5

= 12.5 – 2

= 10.5 ≠ RHS

4. ÷ and +

Given expression: 3 × 6 + 2 – 4 ÷ 8 = 13

After replacing the symbols, we get:

LHS = 3 × 6 ÷ 2 – 4 + 8

= 9 – 4 + 8

= 17 – 4

= 13 = RHS

Hence, ‘÷ and +’ is the correct answer.

Given :

Explanation : If two dice have the same face value in the given image then their clockwise or anti clockwise rotation of the face are formed the opposite pair in dice.

while moving the clockwise direction :

From the both dices :

Now, E is opposite to D

Hence, E is the correct answer.

The logic followed here is :-

'BROWN' is written as 'ORBNW'.

Similarly,

'LUCKY' will be written as :

Hence, the correct answer is "CULYK".

By using the symbols in the table given below, we can draw the following family tree:

Clearly, the man is the nephew of the lady.

Hence, ‘Nephew’ is the correct answer.

The pattern followed here is:

Hence, the correct answer is "Option 4".

The pattern followed here is,

7 : 42 → 7 : [7 × (7 – 1)]

Similarly,

9 : ? → 9 : [9 × (9 – 1)]

Or, ? = 72

Hence, ‘72’ is the correct answer.

The logic followed here is:

So, 'TKWJ' will replace the question mark in the given series.

Hence, the correct answer is "TKWJ".

The image obtained when the paper is unfolded is,

Hence, option 1 is the correct answer.

Given,

5 + 6 - 2 × 8 ÷ 4 = 30

1. Interchange × and -

5 + 6 × 2 - 8 ÷ 4 = 30

5 + 6 × 2 - 2 = 30

5 + 12 - 2 = 30

17 - 2 = 30

15 ≠ 30

2. Interchange + and ÷

5 ÷ 6 - 2 × 8 + 4 = 30

0.833 - 2 × 8 + 4 = 30

0.833 - 16 + 4 = 30

4.833 - 16 = 30

11.167 ≠ 30

3. Interchange × and + 

5 × 6 - 2 + 8 ÷ 4 = 30

30 - 2 + 2 = 30

32 - 2 = 30

30 = 30

4. Interchanging ÷ and -

5 + 6 ÷ 2 × 8 - 4 = 30

5 + 3 × 8 - 4 = 30

5 + 24 - 4 = 30

29 - 4 = 30

25 ≠ 30

Hence, the correct answer is option 3.

We need to find the day on 10^th October 2027,

10.10.2027 = 2026 years + period from 1.1.2027 to 10.10.2027.

Counting number of odd days :

The number of odd days in 2000 years = 0. ( odd days is 0 for every 400 years)

Number of odd days in 26 years = 6 leap years + 20 Ordinary years = 6 × 2 + 20 × 1 = 32 days = 4 weeks + 4 days = 4 odd days.

Number of odd days from 1.1.2027 to 10.10.2027= 31(Jan) + 28(Feb) + 31(March) + 30(April) + 31(May) + 30(June) + 31(July) + 31(Aug) + 30(Sep) + 10(Oct) = 283 days = 40 weeks + 3 days = 3 odd days 

Total number of odd days till 10.10.2027 = 4+3 =7 = 0 odd days.

Therefore, the day on 10th October 2027 is Sunday.

Important Points Here we use odd days as Sunday = 0 , Monday = 1, Tuesday = 2, Wednesday = 3, Thrusday = 4, Friday = 5, and Saturday = 6.

The number of squares are  following figures is shown below:

Hence, '7' is the correct answer.

The logic followed here is:

BREATH is coded as HTAERB

Similarly,

BROKEN is coded as

Hence, the correct answer is "Option 2".

The logic followed here is:

Step I: 1 small straight line is added in each images.

Step II: 1 small straight line are removed from each images.

So, the complete series will be:

Hence, the correct answer is "Option 3".

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘SPJ’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Similarly,

Hence, ‘65’ is the correct answer.

The correct mirror image of the given figure is shown below:

Hence, the correct answer is " Option 4 ".

Given:

YUA, SOC, MIE, GEG, ?

Logic:

Here, 'AAI' is the correct answer as per logic.

Hence, the correct answer is "AAI".

Let us consider Khan's present age is - x years

After 15 years Khan's age will be - (x + 15)

Khan's present age to 5 years back age will be - (x - 5) years

From given data - 

x + 15 = 5 × ( x - 5)

x + 15 = 5x - 25

-4x = - 40

x = 10

Thus, Khan's present age is x = 10 years

Hence, '10 years' is the correct answer.

Shortcut Trick

When an equal distance is covered at two different speeds x and y, the average speed is given by the Harmonic Mean formula.

Average Speed = (2 × x × y) / (x + y)

Here, x = 5 km/h and y = 4 km/h.

Average Speed = (2 × 5 × 4) / (5 + 4) = 40 / 9 ≈ 4.44 km/h.

∴ The correct answer is 4.4 km/h.

Alternate Method

Given:

Speed from A to B (v₁) = 5 km/h

Speed from B to A (v₂) = 4 km/h

Formula Used:

Average Speed = Total Distance ÷ Total Time

⇒ Let the distance between A and B be 'd' km.

⇒ Time taken to go from A to B (t₁) = Distance ÷ Speed = d / 5 hours.

⇒ Time taken to return from B to A (t₂) = Distance ÷ Speed = d / 4 hours.

⇒ Total Distance for the whole journey = d + d = 2d km.

⇒ Total Time taken = t₁ + t₂ = d/5 + d/4 = (4d + 5d) / 20 = 9d / 20 hours.

⇒ Average Speed = Total Distance ÷ Total Time = 2d ÷ (9d/20)

⇒ Average Speed = (2d × 20) / 9d = 40 / 9 km/h

⇒ Average Speed ≈ 4.44 km/h

∴ The correct answer is 4.4 km/h.

Additional Information

Average Speed (Equal Time Intervals)

If a person travels at speed v₁ for time t and speed v₂ for the same time t, the average speed is the Arithmetic Mean: (v₁ + v₂) / 2.

General Average Speed Formula

For any journey with different distances d₁, d₂ and speeds v₁, v₂, Average Speed = (d₁ + d₂) / (d₁/v₁ + d₂/v₂).

Relative Speed

When two objects move in opposite directions, relative speed = v₁ + v₂. In the same direction, relative speed = |v₁ − v₂|.

Shortcut Trick

Winner = 82% of Valid votes → Loser = 18% of Valid votes.

Victory Margin = 82% − 18% = 64% of Valid votes.

64% = 80 → 1% = 1.25 → 100% (Valid) = 125 votes.

Total Votes = Valid + Invalid = 125 + 1780 = 1905 votes.

∴ The correct answer is 1905 votes.

Alternate Method

Given:

Invalid votes = 1,780

Winner's share = 82% of valid votes

Margin of victory = 80 votes

Calculations:

⇒ Let Total Valid Votes = V

⇒ Winner's Votes = 82% of V = 0.82V

⇒ Loser's Votes = (100 − 82)% of V = 18% of V = 0.18V

⇒ Margin = Winner's Votes − Loser's Votes

⇒ 80 = 0.82V − 0.18V

⇒ 80 = 0.64V

⇒ V = 80 ÷ 0.64 = 125

⇒ Total Votes Cast = Valid Votes + Invalid Votes

⇒ Total Votes Cast = 125 + 1780 = 1905

∴ The correct answer is 1905 votes.

Additional Information

Election Margin Calculation

In a two-candidate election, if the winner gets x% of votes, the margin is (x − (100 − x))% = (2x − 100)% of the total valid votes.

Valid vs Invalid Votes

Total votes cast = Valid votes + Invalid votes. Percentages are always calculated on the base of valid votes unless specified otherwise.

Percentage to Fraction Conversion

To simplify calculations, convert percentages to fractions: 64% = 64/100 = 16/25. Thus, (16/25) × Valid = 80 ⇒ Valid = 125.

The correct answer is 60 seconds

Shortcut Trick

Ratio of Distance (Pole : Platform) = 240 : (240 + 360) = 240 : 600 = 2 : 5.

Since Speed is constant, Time is directly proportional to Distance.

2 units of time = 24 seconds ⇒ 1 unit = 12 seconds.

5 units of time = 5 × 12 = 60 seconds.

∴ The correct answer is 60 seconds.

Alternate Method

Given: Length of train = 240 m, Time taken to pass a pole = 24 s, Length of platform = 360 m.

Formula: Speed = Distance ÷ Time; Total Distance = Train Length + Platform Length.

⇒ Speed of the train = Distance ÷ Time = 240 ÷ 24 = 10 m/s.

⇒ Total distance to pass the platform = Length of train + Length of platform.

⇒ Total distance = 240 + 360 = 600 m.

⇒ Time taken to pass the platform = Total distance ÷ Speed.

⇒ Time = 600 ÷ 10 = 60 seconds.

∴ The correct answer is 60 seconds.

Additional Information

Relative Speed

When two trains move in the same direction, relative speed = S₁ − S₂. In opposite directions, relative speed = S₁ + S₂.

Unit Conversion

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

Distance Rule

When a train crosses a stationary object with length (like a bridge or tunnel), the total distance covered is the sum of their lengths.

Shortcut Trick

Volume of cylinder = π × r² × h

Given: radius (r) = 5 cm, height (h) = 10 cm, π = 3.14

Volume = 3.14 × 5² × 10

Volume = 3.14 × 25 × 10 = 785 cm³

∴ The correct answer is 785 cm³.

Alternate Method

Given:

Radius (r) = 5 cm

Height (h) = 10 cm

π = 3.14

Formula Used:

Volume of Cylinder = πr²h

Calculations:

⇒ Volume = 3.14 × (5)² × 10

⇒ Volume = 3.14 × 25 × 10

⇒ Volume = 78.5 × 10

⇒ Volume = 785 cm³

∴ The correct answer is 785 cm³.

Additional Information

Curved Surface Area (CSA) of Cylinder

The area of the side surface of the cylinder is given by 2πrh.

Total Surface Area (TSA) of Cylinder

The sum of the CSA and the areas of the two circular bases: 2πr(h + r).

Volume of a Cone

A cone with the same radius and height as a cylinder has exactly one-third of its volume: (1/3)πr²h.

Shortcut Trick

For a solid hemisphere, equating Volume and Total Surface Area: (2/3) π r³ = 3 π r².

Simplifying the terms, we get r = 3 × (3/2) = 4.5 cm.

The Diameter is 2 × radius = 2 × 4.5 = 9 cm.

∴ The correct answer is 9 cm.

Alternate Method

Given:

The Volume of the solid hemisphere is numerically equal to its Surface Area.

Formula Used:

1. Volume of Hemisphere = (2/3) π r³
2. Total Surface Area of Solid Hemisphere = 3 π r²
3. Diameter (d) = 2 × Radius (r)

Calculations:

⇒ Volume = Surface Area

⇒ (2/3) π r³ = 3 π r²

⇒ (2/3) r = 3 (By dividing both sides by π r²)

⇒ r = 3 × 3 / 2

⇒ r = 9 / 2 = 4.5 cm

⇒ Diameter (d) = 2 × r

⇒ d = 2 × 4.5

⇒ d = 9 cm

∴ The correct answer is 9 cm.

Additional Information

Curved Surface Area (CSA) of Hemisphere

The area of the curved part only is 2 π r². For a hollow hemisphere, this is the only surface area.

Total Surface Area (TSA) of Solid Hemisphere

It includes the curved part plus the flat circular base: 2 π r² + π r² = 3 π r².

Properties of a Sphere

A full sphere has a Volume of (4/3) π r³ and a Surface Area of 4 π r².

Numerical Equality Concept

When values are numerically equal, we ignore the units (cm² vs cm³) and equate the magnitude.

Shortcut Trick

Average Selling Price (SP) = (80 × 10 + 20 × 6) / 100 = 9.2

Cost Price (CP) = 8

Profit % = [(9.2 − 8) / 8] × 100

Profit % = (1.2 / 8) × 100 = 15%

∴ The correct answer is 15% profit.

Alternate Method

Given:

Total oranges = 100

Cost Price (CP) per orange = ₹8

Selling Price (SP) of 80 oranges = ₹10 each

Selling Price (SP) of 20 oranges = ₹6 each

Formula Used:

Total CP = Total Quantity × CP per unit

Total SP = (Quantity₁ × SP₁) + (Quantity₂ × SP₂)

Profit % = [(Total SP − Total CP) / Total CP] × 100

⇒ Total CP = 100 × 8 = ₹800

⇒ SP of 80 oranges = 80 × 10 = ₹800

⇒ SP of 20 oranges = 20 × 6 = ₹120

⇒ Total SP = 800 + 120 = ₹920

⇒ Profit = Total SP − Total CP = 920 − 800 = ₹120

⇒ Profit % = (120 / 800) × 100

⇒ Profit % = 15%

∴ The correct answer is 15% profit.

Additional Information

Profit and Loss Basics

Profit occurs when SP > CP, and Loss occurs when CP > SP. Both percentages are always calculated on the CP.

Weighted Average in SP

When items are sold at different prices, the overall SP per unit is the weighted average: (n₁s₁ + n₂s₂) / (n₁ + n₂).

Marked Price and Discount

Selling Price = Marked Price − Discount. Discount percentage is always calculated on the Marked Price (MP).

Shortcut Trick

Direct relation: r² = (3 × Volume) / (π × h)

r² = (3 × 48π) / (10π) = 144 / 10 = 14.4

r = √14.4

Since 3.8² = 14.44, then r ≈ 3.8 cm.

∴ The correct answer is 3.8 cm.

Alternate Method

Given:

Volume of cone (V) = 48π cm³

Height of cone (h) = 10 cm

Formula Used:

Volume of a cone = (1/3) × π × r² × h

Calculations:

⇒ 48π = (1/3) × π × r² × 10

⇒ 48 = (10/3) × r²

⇒ r² = (48 × 3) / 10

⇒ r² = 144 / 10

⇒ r² = 14.4

⇒ r = √14.4

⇒ r ≈ 3.7947 cm

⇒ r ≈ 3.8 cm (rounding to nearest one decimal place)

∴ The correct answer is 3.8 cm.

Additional Information

Slant Height of a Cone

The slant height (l) is the distance from the apex to any point on the base circumference: l = √(r² + h²).

Surface Area of a Cone

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

Relationship with Cylinder

For the same radius and height, the volume of a cylinder is exactly three times the volume of a cone (V_cyl = πr²h).

Shortcut Trick

Total age of 5 members = 5 × 20 = 100 years

Total age of 6 members = 6 × 18 = 108 years

New member's age = 108 − 100

⇒ 8 years

∴ The correct answer is 8 years.

Alternate Method

Given:

Average age of 5 members = 20 years

Average age of 6 members = 18 years

Formula Used:

Total Age = Average × Number of Members

5 Members = 100 6 Members = 108 + New Member 108 − 100 = 8

Calculations:

⇒ Total age of 5 members = 5 × 20 = 100 years

⇒ Total age of 6 members = 6 × 18 = 108 years

⇒ Age of new member = 108 − 100

⇒ = 8 years

∴ The correct answer is 8 years.

Additional Information

Average Formula

Average = Total Sum ÷ Number of Observations.

Adding a New Member

New Value = New Total Sum − Old Total Sum.

Average Decrease Concept

If the average decreases after adding a member, the new member's value is below the original average.

Shortcut Trick

Using the Ratio Method:

P : Q = 120 : 100 = 6 : 5

R : Q = 80 : 100 = 4 : 5

Combining them, P : R = 6 : 4 = 3 : 2

P is more than R by (3 − 2) = 1 unit over base 2.

Required % = (1 / 2) × 100 = 50%.

∴ The correct answer is 50%.

Alternate Method

Given:

P = Q + 20% of Q

R = Q − 20% of Q

Formula Used:

Percentage More = [(Value₁ − Value₂) / Value₂] × 100

Calculations:

⇒ Let the value of Q be 100.

⇒ P = 100 + 20% of 100 = 100 + 20 = 120.

⇒ R = 100 − 20% of 100 = 100 − 20 = 80.

⇒ Difference between P and R = 120 − 80 = 40.

⇒ Required Percentage = (Difference / R) × 100

⇒ Required Percentage = (40 / 80) × 100

⇒ Required Percentage = 1/2 × 100 = 50%.

∴ The correct answer is 50%.

Additional Information

Percentage Change Formula

The percentage change is calculated as [(Final Value − Initial Value) / Initial Value] × 100. Always identify the correct base value (the value after 'than').

Base Comparison Rule

If A is x% more than B, then B is [x / (100 + x)] × 100% less than A. This is useful for quick inverse percentage calculations.

Fraction to Percentage Conversion

Common fractions help in speed: 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, and 1/8 = 12.5%.

Shortcut Trick

Discount of 20% means the Sale Price is 80% of the original price.

Sale Price = 80% of 400

Sale Price = 0.8 × 400

Sale Price = 320

∴ The correct answer is 320.

Alternate Method

Given:

Original Price (Marked Price) = 400

Discount Percentage = 20%

Formula Used:

Sale Price = Original Price − (Discount% × Original Price)

Calculations:

⇒ Discount Amount = 20% of 400

⇒ Discount Amount = (20/100) × 400 = 80

⇒ Sale Price = 400 − 80

⇒ Sale Price = 320

∴ The correct answer is 320.

Additional Information

Marked Price (MP)

The price at which an article is listed or printed on the label is called the Marked Price or List Price.

Discount Formula

Discount is always calculated on the Marked Price. Formula: Discount = MP − SP.

Successive Discounts

If two discounts a% and b% are given successively, the single equivalent discount is (a + b − ab/100)%.

Shortcut Trick

Identify operations using BODMAS: Bracket → Multiplication → Addition/Subtraction.

91 − 56 + 78 − (54) + 90

Combine positive terms: 91 + 78 + 90 = 259

Combine negative terms: 56 + 54 = 110

Net result: 259 − 110 = 149

∴ The correct answer is 149.

Alternate Method

Given expression: 91 − 56 + 78 − (31 + 23) + 45 × 2

Following the BODMAS order of operations:

⇒ 91 − 56 + 78 − 54 + 45 × 2 (Solved Bracket: 31 + 23 = 54)

⇒ 91 − 56 + 78 − 54 + 90 (Solved Multiplication: 45 × 2 = 90)

⇒ 35 + 78 − 54 + 90 (Subtraction: 91 − 56 = 35)

⇒ 113 − 54 + 90 (Addition: 35 + 78 = 113)

⇒ 59 + 90 (Subtraction: 113 − 54 = 59)

⇒ 149

∴ The correct answer is 149.

Additional Information

BODMAS Rule

It defines the sequence to solve mathematical expressions: Brackets (), Of (orders/powers), Division (÷), Multiplication (×), Addition (+), and Subtraction (−).

Handling Signs

While performing addition and subtraction, grouping like-signed numbers (all positives together and all negatives together) reduces the risk of calculation errors.

Unit Digit Check

In competitive exams, verify the unit digit: 1 − 6 + 8 − 4 + 0 = −1. Since the result is positive, 10 − 1 = 9. The answer must end in 9.

Shortcut Trick

Total interest to be earned = 16,800 − 12,000 = 4,800

Interest for 1 year = 8% of 12,000 = 960

Time required = Total Interest ÷ Yearly Interest

Time = 4,800 ÷ 960 = 5 years

∴ The correct answer is 5 years.

Alternate Method

Given:

Principal (P) = ₹12,000

Total Amount (A) = ₹16,800

Rate of Interest (R) = 8% per annum

Formula Used:

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

Amount (A) = Principal (P) + Simple Interest (SI)

⇒ SI = Amount − Principal

⇒ SI = 16,800 − 12,000 = 4,800

⇒ 4,800 = (12,000 × 8 × T) ÷ 100

⇒ 4,800 = 120 × 8 × T

⇒ 4,800 = 960 × T

⇒ T = 4,800 ÷ 960

⇒ T = 5 years

∴ The correct answer is 5 years.

Additional Information

Simple Interest Concept

Simple interest is calculated only on the initial principal amount throughout the entire period of the loan or investment.

Total Amount Formula

The total amount can be expressed as A = P(1 + RT/100), where R is the annual rate and T is the time in years.

Rate and Time Relation

For a fixed principal and interest, the rate of interest is inversely proportional to the time period (R ∝ 1/T).

Shortcut Trick

Total Surface Area (TSA) of hemisphere = 3πr² = 4158 m².

⇒ πr² = 4158 ÷ 3 = 1386 m².

New radius (R) = r/3. New Curved Surface Area (CSA) = 2πR².

⇒ New CSA = 2π(r/3)² = (2/9) × πr².

⇒ New CSA = (2/9) × 1386 = 2 × 154 = 308 m².

∴ The correct answer is 308 m².

Alternate Method

Given:

Total Surface Area (TSA) of hemisphere = 4158 m²

New radius (R) = Original radius (r) ÷ 3

Formula Used:

TSA of hemisphere = 3πr²

CSA of hemisphere = 2πr²

Calculations:

⇒ 3 × (22/7) × r² = 4158

⇒ (66/7) × r² = 4158

⇒ r² = (4158 × 7) ÷ 66

⇒ r² = 63 × 7 = 441

⇒ r = √441 = 21 m

Now, new radius R = 21 ÷ 3 = 7 m

⇒ New CSA = 2 × π × R²

⇒ New CSA = 2 × (22/7) × 7 × 7

⇒ New CSA = 2 × 22 × 7

⇒ New CSA = 44 × 7 = 308 m²

∴ The correct answer is 308 m².

Additional Information

Volume of a Hemisphere

The amount of space occupied by a hemisphere is given by the formula V = (2/3)πr³.

Surface Area of a Sphere

A sphere has only one surface area (TSA = CSA), which is calculated as 4πr².

Volume of a Sphere

The volume of a complete sphere is exactly double that of a hemisphere: V = (4/3)πr³.

Shortcut Trick

Given ratio: 42 : 5 = 7x : 10

Compare denominators: 10 is 5 × 2.

Therefore, compare numerators: 7x must be 42 × 2.

7x = 84 ⇒ x = 84 ÷ 7 = 12.

∴ The correct answer is 12.

Alternate Method

Given:

Ratio 1 = 42 : 5

Ratio 2 = 7x : 10

Ratios are equal: 42 : 5 = 7x : 10

Formula Used:

If a : b = c : d, then a/b = c/d

Product of extremes = Product of means (a × d = b × c)

Calculations:

⇒ 42 ÷ 5 = 7x ÷ 10

⇒ 42 × 10 = 5 × 7x

⇒ 420 = 35x

⇒ x = 420 ÷ 35

⇒ x = 12

∴ The correct answer is 12.

Additional Information

Proportion Rule

Four numbers a, b, c, d are in proportion if a : b = c : d, which implies a × d = b × c.

Fourth Proportional

If a : b = c : x, then x is the fourth proportional to a, b, and c, calculated as x = (b × c) ÷ a.

Simplifying Ratios

A ratio remains unchanged if both its terms are multiplied or divided by the same non-zero number.

Shortcut Trick

Perimeter of square = 12 × 4 = 48 m.

Rectangle perimeter ratio (L : W = 2 : 1) → 2 × (2 + 1) = 6 units.

6 units = 48 m → 1 unit = 8 m.

Dimensions of rectangle = 16 m and 8 m.

Difference in area = 12² − (16 × 8) = 144 − 128 = 16 m².

∴ The correct answer is 16 m².

Alternate Method

Given:

Side of square (s) = 12 m

Length of rectangle (L) = 2 × Width (W)

Perimeter of square = Perimeter of rectangle

Formula Used:

Perimeter of square = 4 × side

Perimeter of rectangle = 2 × (length + width)

Area of square = side²

Area of rectangle = length × width

⇒ Perimeter of square = 4 × 12 = 48 m

⇒ Perimeter of rectangle = 2(L + W) = 48 m

⇒ 2(2W + W) = 48

⇒ 6W = 48 → W = 8 m

⇒ L = 2 × 8 = 16 m

⇒ Area of square = 12² = 144 m²

⇒ Area of rectangle = 16 × 8 = 128 m²

⇒ Difference in area = 144 − 128 = 16 m²

∴ The correct answer is 16 m².

Additional Information

Maximum Area Property

For a fixed perimeter, a square always has a larger area than any other rectangle.

Perimeter and Side Relationship

If a square and rectangle have the same perimeter, the side of the square is the arithmetic mean of the rectangle dimensions: s = (L + W) ÷ 2.

Area Formulas

Area of Square = side² and Area of Rectangle = length × width. Units are always in square measure (m², cm², etc.).

Shortcut Trick

When two articles are sold at the same price, one at x% profit and the other at x% loss, there is always an overall loss.

Shortcut formula: Overall Loss % = (x / 10)²

Given: x = 10%

Overall Loss % = (10 / 10)² = 1² = 1%

∴ The correct answer is 1% loss.

Alternate Method

Given: SP₁ = SP₂, Profit % = 10%, Loss % = 10%

Formula: CP = SP × [100 / (100 ± Profit/Loss %)]

Let the Selling Price (SP) of each article be ₹99.

⇒ CP₁ = 99 × (100 / 110) = ₹90

⇒ CP₂ = 99 × (100 / 90) = ₹110

⇒ Total CP = 90 + 110 = ₹200

⇒ Total SP = 99 + 99 = ₹198

⇒ Overall Loss = 200 − 198 = ₹2

⇒ Overall Loss % = (2 / 200) × 100 = 1%

∴ The correct answer is 1% loss.

Additional Information

Equal Cost Price Case

If two articles are sold at the same Cost Price, one at x% profit and another at x% loss, the net result is always 0% (No Profit, No Loss).

Successive Percentage Formula

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

Same SP with Different %

If two items are sold at same SP with x% profit and y% loss, net % = [100(x−y) − 2xy] / [200+x−y].

Shortcut Trick

Profit Ratio M : N = (28 × 4 + 20 × 8) : (32 × 4 + 40 × 8)

⇒ 272 : 448 = 17 : 28

Total Ratio Parts = 17 + 28 = 45 units

45 units = ₹54,000 → 1 unit = ₹1,200

N's Share = 28 units × 1,200 = ₹33,600

∴ The correct answer is ₹33,600.

Alternate Method

Given:

Initial Capital: M = ₹28,000, N = ₹32,000

After 4 months: M's Capital = 28,000 − 8,000 = ₹20,000; N's Capital = 32,000 + 8,000 = ₹40,000

Total Profit = ₹54,000, Total Time = 12 months

Formula Used:

Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂)

Calculations:

⇒ Total Investment of M = (28,000 × 4) + (20,000 × 8)

⇒ M's Share = 1,12,000 + 1,60,000 = ₹2,72,000

⇒ Total Investment of N = (32,000 × 4) + (40,000 × 8)

⇒ N's Share = 1,28,000 + 3,20,000 = ₹4,48,000

⇒ Ratio of M's profit to N's profit = 2,72,000 : 4,48,000 = 17 : 28

⇒ N's share of profit = (28 ÷ (17 + 28)) × 54,000

⇒ N's share = (28 ÷ 45) × 54,000

⇒ N's share = 28 × 1,200 = ₹33,600

∴ The correct answer is ₹33,600.

Additional Information

Simple Partnership

When investments of all partners are for the same time, profit is distributed in the ratio of their capitals: P₁ : P₂ = C₁ : C₂.

Compound Partnership

When investments are for different time periods, profit ratio is the product of capital and time: P₁ : P₂ = (C₁ × T₁) : (C₂ × T₂).

Working vs. Sleeping Partner

A working partner manages the business and may receive a fixed salary or percentage of profit before the remaining profit is divided.

Shortcut Trick

Total work (LCM of 10 and 15) = 30 units.

Efficiency: A = 3, B = 2. Combined efficiency = 5 units/day.

Work done in 3 days = 5 × 3 = 15 units.

Remaining work = 30 − 15 = 15 units.

More days for B = 15 ÷ 2 = 7.5 days.

∴ The correct answer is 7.5 days.

Alternate Method

Given:

Time taken by A = 10 days

Time taken by B = 15 days

They work together for 3 days.

Calculations:

⇒ Efficiency of A = 30 ÷ 10 = 3 units/day

⇒ Efficiency of B = 30 ÷ 15 = 2 units/day

⇒ Total work done by A and B in 1 day = 3 + 2 = 5 units

⇒ Work done in 3 days = 5 × 3 = 15 units

⇒ Remaining work = Total work − Work done together

⇒ Remaining work = 30 − 15 = 15 units

⇒ Extra time taken by B = Remaining work ÷ B's efficiency

⇒ Time = 15 ÷ 2 = 7.5 days

∴ The correct answer is 7.5 days.

Additional Information

LCM Method for Time & Work

Total work is assumed as the LCM of individual days, making efficiency (Work ÷ Time) a simple integer for easier calculation.

Work and Wages

Wages are always distributed in the ratio of the actual work done by each person, or the ratio of their efficiencies if they work for the same duration.

Alternate Day Work

In alternate day problems, calculate the work done in one complete cycle (e.g., 2 days) and then find the total cycles needed to approach the total work.

Shortcut Trick

Net interest rate for 3 years = Rate × Time = 5% × 3 = 15%.

Given that 15% of the Principal is equivalent to ₹180.

Value of 1% = 180 ÷ 15 = 12.

Value of 100% (Principal) = 12 × 100 = ₹1200.

∴ The correct answer is ₹1200.

Alternate Method

Given:

Simple Interest (SI) = ₹180

Time (T) = 3 years

Rate of Interest (R) = 5% per annum

Formula Used:

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

Where P is the Principal.

Calculations:

⇒ 180 = (P × 5 × 3) ÷ 100

⇒ 180 = (P × 15) ÷ 100

⇒ P = (180 × 100) ÷ 15

⇒ P = 12 × 100

⇒ P = 1200

∴ The correct answer is ₹1200.

Additional Information

Simple Interest vs Compound Interest

In Simple Interest, the interest is calculated only on the initial principal. In Compound Interest, interest is calculated on the principal plus any accumulated interest from previous periods.

Total Amount Formula

Amount (A) = Principal (P) + Simple Interest (SI). It represents the total money returned to the depositor after the time period T.

Rate and Time Units

Ensure that the Rate (R) and Time (T) are in the same time units (usually annual). If time is given in months, divide by 12 to convert to years.

Shortcut Trick

Apply BODMAS: First solve the bracket (21 + 18) = 39.

Multiply the result by 2: 39 × 2 = 78.

Combine all terms: 77 − 41 + 34 + 78 − 55 = 189 − 96 = 93.

∴ The correct answer is 93.

Alternate Method

Given expression: 77 − 41 + 34 + (21 + 18) × 2 − 55

Method: BODMAS Rule

⇒ 77 − 41 + 34 + (39) × 2 − 55 ⇒ 77 − 41 + 34 + 78 − 55 ⇒ (77 + 34 + 78) − (41 + 55) ⇒ 189 − 96 ⇒ 93

∴ The correct answer is 93.

Additional Information

BODMAS Rule

It stands for Brackets, Of, Division, Multiplication, Addition, and Subtraction. It dictates the order of operations in any mathematical expression.

Bracket Types

Brackets should be solved in the order: small brackets (), then curly brackets {}, and finally big brackets [].

Addition and Subtraction Priority

Addition and Subtraction have the same priority level and can be performed from left to right or by grouping like-signed terms.

Given:

The percent of tigers in Z1 is 15%.

The percent of tigers in Z3 is 30%.

Calculation:

We know that,

100% ≡ 360º ( central angle of the pie chart is 360º)

Now, the central angle of the sectors for Z1 = 15% × 360º

The central angle of the sectors for Z3 = 30% × 360º

According to the question,

Z3 - Z1 =  360º × (30% -  15%)

⇒ 360º × (15/100) = 54º

∴ The difference in the central angle of the sectors for Z1 and Z3 is 54º.

Shortcut Trick

Initial average of 5 numbers = 38

New average of 4 numbers = 30 (Decrease of 8 per number)

Removed value = Old Average + (Change in Average × Number of remaining items)

Removed value = 38 + (8 × 4) = 38 + 32 = 70

∴ The correct answer is 70.

Alternate Method

Given:

Average of 5 numbers = 38

Average of 4 numbers = 30

Formula used:

Sum = Average × Number of observations

Calculations:

⇒ Sum of 5 numbers = 5 × 38 = 190

⇒ Sum of 4 numbers = 4 × 30 = 120

⇒ Removed number = Sum of 5 numbers − Sum of 4 numbers

⇒ Removed number = 190 − 120

⇒ Removed number = 70

∴ The correct answer is 70.

Additional Information

Average Concept

The average (arithmetic mean) is the sum of all values divided by the total number of values: Average = Total Sum ÷ Count.

Effect of removing a number

If the removed number is greater than the average, the new average will decrease. If the removed number is less than the average, the new average will increase.

Weighted Average

When combining two groups, the combined average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Given:

Radius of cylinder = R

Height of cylinder = 2R

Radius of hemisphere = R

Formula Used:

Volume of cylinder = π × radius² × height

Volume of hemisphere = (2/3) × π × radius³

Calculation:

⇒ Volume of cylinder = π × R² × 2R = 2πR³

⇒ Volume of hemisphere = (2/3) × π × R³ = (2πR³) ÷ 3

⇒ Ratio of volumes = Volume of cylinder ÷ Volume of hemisphere

⇒ Ratio = (2πR³) ÷ ((2πR³) ÷ 3)

⇒ Ratio = 3 : 1

∴ The correct answer is 3 ∶ 1.

Shortcut Trick

Total Area = Area of Rectangle + Area of 1 Full Circle (since 2 semicircles = 1 circle)

Area = (Length × Width) + πr²

Area = (14 × 7) + (3.14159 × 7²)

Area = 98 + 153.9379

Area ≈ 251.94 cm²

∴ The correct answer is 251.94 cm².

Alternate Method

Given:

Length of the rectangle (l) = 14 cm

Width of the rectangle (w) = 7 cm

Radius of each semicircle (r) = 7 cm

Formula Used:

Area of Rectangle = Length × Width

Area of Semicircle = (1/2) × πr²

⇒ Area of the rectangle = 14 × 7 = 98 cm²

⇒ Area of one semicircle = (1/2) × π × (7)²

⇒ Area of two semicircles = 2 × [(1/2) × π × 49]

⇒ Area of two semicircles = π × 49 ≈ 3.14159 × 49 ≈ 153.94 cm²

⇒ Total area of the figure = Area of rectangle + Area of two semicircles

⇒ Total Area = 98 + 153.94 = 251.94 cm²

∴ The correct answer is 251.94 cm².

Additional Information

Area of a Circle

The area of a full circle is calculated using the formula A = πr², where r is the radius.

Perimeter of the Combined Figure

The perimeter of this specific figure includes only the two widths of the rectangle and the two curved arcs: P = 2w + 2πr.

Properties of Semicircles

A semicircle is exactly half of a circle. Its area is (1/2)πr² and its arc length is πr.