The correct answer is Only (b).

Key Points

• Gross Enrolment Ratio (GER) is a statistical measure used in the education sector to determine the number of students enrolled in a specific level of education, regardless of age, expressed as a percentage of the official school-age population for that level.
• According to the Economic Survey of India 2022-23, the GER in schools has shown varied trends across different levels of education when comparing 2021-22 to 2013-14.
• Primary level: The GER at the primary level did not witness a decline in 2021-22 compared to 2013-14. Instead, it remained stable or improved. Hence, statement (a) is incorrect.
• Upper primary level: The GER at the upper primary level saw a decline in 2021-22 compared to 2013-14, as highlighted in the survey. This indicates challenges in retaining students beyond the primary level of education. Hence, statement (b) is correct.
• Secondary level: The GER at the secondary level has generally improved over the years due to increased focus on secondary education policies, infrastructure development, and incentives for retention. Hence, statement (c) is incorrect.

Additional Information

• Gross Enrolment Ratio (GER):
• GER is calculated as the total enrolment of students at a particular level of education divided by the population of the age group that officially corresponds to that level. It is expressed as a percentage.
• A GER above 100% indicates that there are students outside the official age group enrolled in education, which is a positive indicator of inclusivity.
• Trends in GER in India:
• The primary level has seen consistent enrolment rates due to government initiatives like the Mid-Day Meal Scheme and the Right to Education Act, 2009, which focus on universal access to primary education.
• The upper primary level has witnessed a decline in GER, indicating challenges such as dropout rates due to socio-economic factors or lack of access to higher grades in rural areas.
• The secondary level has shown improvement, with the GER increasing significantly due to programs like Rashtriya Madhyamik Shiksha Abhiyan (RMSA) and scholarships for students from marginalized communities.
• Challenges in GER:
• Dropout rates at the upper primary level are influenced by factors such as poverty, lack of awareness, and gender-based disparities.
• Geographical and infrastructural barriers in rural and remote areas contribute to lower GER at higher education levels.

Important Points

• Government Initiatives to Improve GER:
• Samagra Shiksha Abhiyan: An integrated scheme for school education that aims to improve enrolment, retention, and quality of education at all levels.
• Mid-Day Meal Scheme: Provides free meals to children in schools to enhance enrolment and retention, especially at the primary level.
• Kasturba Gandhi Balika Vidyalaya: Focuses on improving GER for girls at the upper primary level in rural areas.
• Digital Education Initiatives: Programs like DIKSHA and e-learning platforms aim to increase accessibility to education resources and reduce dropout rates.

The correct answer is India.

Key Points

• Torneo del Centenario 2023: The Torneo del Centenario is an international hockey tournament organized to celebrate the centenary of the sport. It attracts top teams from across the globe to compete for the title.
• India's Victory: The Indian women's hockey team clinched the Torneo del Centenario 2023 title, showcasing their exceptional skills and teamwork throughout the tournament. This win highlights the growing prowess of Indian women in international hockey.
• Performance Highlights: India displayed a series of stellar performances against teams like Spain, England, and others. Their strategic gameplay, focused defense, and attacking prowess played a vital role in securing the championship.
• Historical Achievement: Winning the Torneo del Centenario 2023 is a significant achievement for Indian women's hockey, further strengthening their position in the global rankings and boosting morale for future tournaments.
• This victory is a testament to the hard work and dedication of the players, coaching staff, and support systems. It reflects the efforts to promote women's hockey in India.

Additional Information

• Indian Women's Hockey Team:
• Formation: The Indian women's hockey team has a rich history and has emerged as a strong contender in international tournaments over the years.
• Achievements: The team has consistently delivered exceptional performances, including qualifying for the Tokyo Olympics and finishing fourth, marking one of their best performances on a global stage.
• Role of Government and Federations:
• The Sports Authority of India (SAI) and Hockey India have been instrumental in providing infrastructure, training, and resources to improve the team's competitiveness.
• Under various schemes like Khelo India, players are nurtured from grassroots levels, ensuring a steady pipeline of talent for national teams.
• Global Competitors:
• Spain: Known for their aggressive playing style, Spain has been a strong contender in international hockey.
• England: England's women's hockey team has traditionally been a dominant force, often competing at the top levels in tournaments like the Olympics and World Cup.
• China: China's women’s hockey team is also regarded as a competitive team on the global stage, focusing heavily on strategic gameplay.

Important Points

• Significance of the Victory:
• This victory is a morale booster for Indian women's hockey, inspiring young players and promoting the sport in the country.
• It highlights the importance of teamwork, strategy, and resilience, serving as an example for upcoming athletes.
• Future Prospects:
• India's win at the Torneo del Centenario 2023 lays the foundation for better performances in tournaments like the Asian Games and World Cup.
• With continued support and investment in women's hockey, India aims to achieve greater success on international platforms.

The correct answer is Aurangzeb.

Key Points

• Alamgir Nama is a historical chronicle that provides a detailed account of the reign of the Mughal Emperor Aurangzeb, who ruled India from 1658 to 1707.
• The book was written by Mirza Muhammad Kazim, a court historian during Aurangzeb’s reign. It documents the events, policies, and achievements of the emperor.
• Aurangzeb was also known as Alamgir, which means "Conqueror of the World," and the chronicle is named after this title.
• The Alamgir Nama is considered an important historical source for understanding the political and administrative systems during Aurangzeb's rule.
• It covers key aspects of Aurangzeb’s reign, including his military campaigns, religious policies, and governance style.
• The chronicle ends in the 10th year of Aurangzeb's reign, as the author passed away before completing the full account of his rule.

Additional Information

• Aurangzeb’s Reign:
• Aurangzeb was the sixth Mughal Emperor, who ascended the throne in 1658 after defeating his brothers in a bitter succession war.
• He is known for his strict adherence to Islamic principles and his efforts to enforce Sharia law across his empire.
• Aurangzeb expanded the Mughal Empire to its greatest territorial extent, covering almost the entire Indian subcontinent.
• He implemented policies that were often criticized for being intolerant towards non-Muslims, such as the reimposition of the Jizya tax on non-Muslims.
• Other Mughal Chronicles:
• The Mughal dynasty is known for its rich historical chronicles, such as the Baburnama (memoirs of Babur), Akbarnama (chronicle of Akbar), and Shah Jahan Nama (chronicle of Shah Jahan).
• These works provide valuable insights into the reigns of different emperors, including their administrative systems, military campaigns, cultural achievements, and personal lives.
• Mirza Muhammad Kazim:
• Mirza Muhammad Kazim, the author of Alamgir Nama, was a prominent historian and writer of the Mughal court.
• His work is regarded as an authoritative account of the early years of Aurangzeb’s rule, offering detailed insights into the emperor’s policies and governance.

Important Points

• Key Features of Alamgir Nama:
• The chronicle provides detailed descriptions of Aurangzeb’s military campaigns, particularly in the Deccan region, against rulers like the Marathas and the Bijapur Sultanate.
• It documents the administrative reforms introduced by Aurangzeb, including his efforts to curb corruption and enforce Islamic law.
• The book also sheds light on Aurangzeb’s personal character, portraying him as a devout and disciplined ruler.
• Significance in Indian History:
• The Alamgir Nama serves as a vital source for historians studying the Mughal Empire, especially the transitional period leading to its decline.
• It highlights the challenges faced by Aurangzeb, such as internal dissent and external threats, which eventually contributed to the weakening of the Mughal dynasty.

The correct answer is A Civil Servant.

Key Points

• A permanent executive refers to individuals who are part of the administrative machinery of the government and serve irrespective of changes in political leadership.
• Civil servants are the backbone of the permanent executive. They are career bureaucrats who work in various government departments and are responsible for implementing policies, programs, and laws enacted by the legislature.
• Unlike the political executive (e.g., Prime Minister, Governor, and Cabinet Ministers), civil servants continue to serve across different governments and are not affected by elections or changes in ruling parties.
• Civil servants are selected through competitive exams like the Union Public Service Commission (UPSC) and state-level public service commissions. They are appointed based on merit and serve for a fixed tenure until retirement or resignation.
• The political executives, such as the Prime Minister, Governors, and Cabinet Ministers, are temporary executives because they hold office only as long as they retain political power or until their term ends. Hence, the correct answer is A Civil Servant.

Additional Information

• Permanent Executive:
• The permanent executive is responsible for the day-to-day administration of the country. They ensure the smooth functioning of government machinery by implementing laws, policies, and programs efficiently.
• Civil servants remain impartial and apolitical. Their role is to serve the government of the day without being influenced by political ideologies or biases.
• Selection and Functions of Civil Servants:
• Civil servants are selected through competitive exams like the UPSC Civil Services Examination, which recruits candidates for prestigious posts such as IAS, IPS, and IFS.
• Their functions include policy formulation, implementation, managing public resources, and advising political executives on administrative matters.
• Political Executives:
• The Prime Minister, Cabinet Ministers, and Governors are part of the political executive. They are temporary executives who hold office as long as they have political power or until the tenure of the government ends.
• Their role is to make decisions, set policies, and guide the administration. However, they rely on the permanent executive for effective implementation of these decisions.
• Examples of Permanent Executive:
• The Indian Administrative Service (IAS) and Indian Police Service (IPS) are prime examples of civil servants who are part of the permanent executive.
• Other examples include officers working in state-level administrative services, revenue departments, and other government agencies.

Important Points

• Difference Between Permanent and Temporary Executives:
• Permanent executives (civil servants) are selected based on merit and serve irrespective of changes in government, while temporary executives (political leaders) are elected for a fixed term and depend on electoral outcomes.
• Permanent executives focus on implementation and administration, while temporary executives focus on decision-making and policy formulation.
• Significance of Civil Servants:
• Civil servants ensure continuity and stability in governance, especially during political transitions.
• They act as a link between the government and the citizens, ensuring that public resources are managed efficiently.

The correct answer is Tanzania.

Key Points

• Indian Institute of Technology (IIT) is an internationally recognized institution established to promote technical education and innovation in India.
• In 2023, India announced plans to set up the first-ever IIT campus outside the country in Tanzania. This marks a significant step in extending Indian higher education globally.
• The campus will be established in Zanzibar, Tanzania, as part of the India-Tanzania bilateral agreement. This decision reflects India's commitment to fostering international academic cooperation. Hence, statement is correct.
• This initiative aligns with India's New Education Policy (NEP) 2020, which emphasizes internationalization of Indian education.
• The establishment aims to provide quality technical education to students in Africa and build stronger ties between India and Tanzania. Hence, statement is correct.
• The IIT Zanzibar campus will offer a variety of programs including undergraduate, postgraduate, and doctoral studies in engineering, technology, science, and mathematics.
• This campus is expected to foster research collaborations in emerging fields like Artificial Intelligence, Data Science, and Renewable Energy. Hence, statement is correct.
• The decision reflects India's growing emphasis on soft diplomacy through educational and cultural exchanges, strengthening its image as a global leader in education. Hence, statement is correct.
• Hence, the correct answer is Tanzania.

Additional Information

• Indian Institute of Technology (IIT):
• IITs are globally renowned for their quality education, research, and innovation. They are ranked among the top engineering institutions worldwide.
• Currently, India has 23 IITs, which specialize in diverse fields such as engineering, technology, science, and management.
• The establishment of an IIT campus in Tanzania will mark the first-ever expansion of IITs outside India.
• Why Tanzania?
• Tanzania is strategically located in East Africa, making it an accessible education hub for African nations.
• Zanzibar is known for its cultural and economic significance, attracting investment and partnerships in education, trade, and tourism.
• By setting up the IIT campus in Zanzibar, India aims to provide affordable and quality education to African students.
• India-Tanzania Relations:
• India and Tanzania share long-standing diplomatic, economic, and cultural ties.
• India has been actively involved in promoting developmental cooperation in Africa through projects in education, healthcare, and infrastructure.
• The IIT campus is part of a broader effort to enhance bilateral relations and contribute to the African continent's development.

Important Points

• Key Features of IIT Zanzibar Campus:
• The campus will offer programs in engineering, technology, and science to students from Africa and other regions.
• It aims to establish research facilities in emerging technologies and promote collaborative projects.
• The campus is designed to foster cultural exchange and strengthen India's image as a global leader in education.
• Significance of IIT Expansion:
• The move aligns with India's New Education Policy (NEP) 2020, which emphasizes internationalization.
• It contributes to global access to quality education and promotes India's diplomatic outreach through education.

The correct answer is Formic acid.

Key Points

• When an ant bites a human, it injects formic acid into the skin through its sting.
• Formic acid, also known as methanoic acid, is a chemical compound that causes a stinging or burning sensation upon injection. This is why ant bites often result in pain, redness, and swelling around the affected area.
• The acidic nature of formic acid irritates the skin, leading to inflammation and discomfort. Hence, the correct answer is Formic acid.
• In some cases, individuals may experience allergic reactions to formic acid, causing more severe symptoms such as excessive swelling, itching, or even anaphylaxis (in rare cases).
• Formic acid is not harmful in small quantities but can be neutralized by applying a basic substance, such as sodium bicarbonate, to the affected area to reduce irritation. This helps alleviate the pain and redness caused by the ant bite.
• The primary function of formic acid in ants is as a defense mechanism to protect themselves and their colonies from predators or threats.

Additional Information

• Formic Acid:
• Formic acid is a naturally occurring compound found in ants and some other insects. It is one of the simplest carboxylic acids, with the chemical formula HCOOH.
• It is used by ants as a defense mechanism and as a way to subdue prey. This acid is secreted through the ant's sting or bite, causing pain to the victim.
• Other Substances Mentioned in the Question:
• Calamine solution: This is a soothing lotion containing zinc oxide and ferric oxide, typically used to relieve itching and discomfort caused by insect bites or skin irritations. It is not injected by ants.
• Sodium hydrogencarbonate (baking soda): This is a basic compound that can neutralize acids, such as formic acid, to reduce irritation. It is used as a remedy, not injected by ants.
• Zinc carbonate: This is an inorganic compound used in industrial applications and as a treatment for skin conditions. It is unrelated to ant bites.
• Reactions to Ant Bites:
• The irritation and pain caused by an ant bite are due to the acidic nature of formic acid. This can be alleviated by applying a cold compress or a basic substance.
• Individuals allergic to ant bites may require medical attention if symptoms persist or worsen.

Important Points

• Neutralizing Formic Acid:
• Applying sodium bicarbonate (baking soda) to the site of the bite can neutralize the acidic effect of formic acid and reduce irritation.
• Over-the-counter antihistamines or hydrocortisone creams may also help alleviate symptoms.
• Role of Formic Acid in Ants:
• Apart from being a defense mechanism, formic acid helps ants in hunting or subduing prey. Some ant species also use it to mark territories or communicate with fellow ants.

The correct answer is No child is denied admission in a school according to this Act, for the lack of age proof..

Key Points

• Statement 1: The Right of Children to Free and Compulsory Education Act (RTE), 2009, mandates that no child shall be denied admission to a school for the lack of age proof. Schools are required to ensure that every child has access to education without imposing unnecessary restrictions. This statement is correct.
• Statement 2: The Act applies to the whole of India except the state of Jammu and Kashmir. However, after the abrogation of Article 370 in August 2019, the Act became applicable to Jammu and Kashmir as well. This statement is incorrect.
• Statement 3: Elementary education, as defined under the Act, refers to education from Class 1 to 8, not Class 1 to 6. This statement is incorrect.
• Statement 4: The Act provides for free education to all children aged 6 to 14 years, not up to the age of 16. This provision is in alignment with Article 21A of the Constitution of India. This statement is incorrect.
• Hence, the correct answer is "No child is denied admission in a school according to this Act, for the lack of age proof.".

Additional Information

• Right of Children to Free and Compulsory Education Act, 2009:
• The Act was enacted to provide free and compulsory education to children aged between 6 to 14 years as a fundamental right under Article 21A of the Constitution.
• It ensures that every child has access to education without discrimination based on gender, caste, religion, or socio-economic background.
• Schools are required to reserve 25% of seats for children from economically weaker sections (EWS) and disadvantaged groups.
• Key Features of the Act:
• The Act prohibits schools from charging any form of fees, ensuring that education is truly free for eligible children.
• It mandates the establishment of a neighborhood school within a certain distance to ensure accessibility.
• The Act prescribes norms for infrastructure, teacher qualifications, and pupil-teacher ratios to maintain quality education.
• Age and Coverage:
• The Act covers children aged 6 to 14 years, focusing on elementary education (Class 1 to 8).
• It applies to all government schools and aided schools, while unaided private schools are required to reserve seats for children from EWS and disadvantaged groups.

Important Points

• Prohibition of Discrimination:
• Schools are prohibited from denying admission based on age, gender, caste, or economic background.
• They cannot subject children to screening procedures or entrance tests for admission.
• Role of Local Authorities:
• Local authorities are responsible for identifying children who are out of school and ensuring their enrollment.
• They must ensure the availability of adequate infrastructure and trained teachers.
• Impact of the Act:
• The Act has significantly improved enrollment rates and reduced dropout rates among children in the target age group.
• It has empowered economically weaker sections and disadvantaged groups by ensuring access to quality education.

The correct answer is Duns.

Key Points

• Duns are elongated valleys located between the Lesser Himalayas (Middle Himalayas) and the Shivalik Hills.
• These valleys are formed due to the folding and faulting of the Earth’s crust during the process of Himalayan orogeny.
• Dehradun, Kotli Dun, and Patli Dun are prominent examples of duns in India. They serve as significant geographical and ecological features.
• The duns are characterized by their rich soil, making them suitable for agriculture. They are largely fertile plains surrounded by hills.
• These valleys are also important for human settlements due to their favorable climatic conditions and natural resources. Hence, the term "Duns" correctly refers to the longitudinal valleys lying between the Lesser Himalayas and Shivaliks.

Additional Information

• Formation of Duns:
• Duns are formed as a result of tectonic activity, specifically the collision between the Indian Plate and the Eurasian Plate.
• The folding and faulting during this collision created depressions or valleys between the mountain ranges.
• Characteristics of Duns:
• Duns are typically narrow and elongated, with fertile soil suitable for crops like rice, wheat, and sugarcane.
• They are surrounded by rugged terrain, making them distinct geographical features.
• The valleys have rich biodiversity, serving as habitats for various flora and fauna.
• Other Options Explained:
• Kullus: Refers to the Kullu Valley, located in Himachal Pradesh, and is not associated with the longitudinal valleys between the Lesser Himalayas and Shivaliks.
• Pir Panjal Range: A mountain range in the Himalayas, located in Jammu and Kashmir, and not a valley.
• Purvanchals: Refers to the hills located in northeastern India, which are not related to the Shivalik Hills or Lesser Himalayas.

Important Points

• Dehradun: The most famous dun valley in India, known for its scenic beauty, educational institutions, and tourist attractions.
• Human Settlements: Duns are preferred for settlements due to their fertile lands, availability of water, and pleasant climate.
• Geographical Importance: These valleys act as a transition zone between the mountainous regions and plains, influencing both climate and ecology.

The correct answer is Rivonia - South Africa.

Key Points

• Nuremberg - France: This statement is incorrect. Nuremberg is a city located in Germany, not France. It is historically significant due to the Nuremberg Trials, conducted after World War II to prosecute prominent leaders of Nazi Germany for war crimes.
• Rivonia - South Africa: This statement is correct. Rivonia is a suburb in South Africa. It is historically significant as the location where key leaders of the African National Congress (ANC), including Nelson Mandela, were arrested in 1963 during apartheid. The Rivonia Trial that followed led to Mandela's imprisonment for 27 years.
• Versailles - Germany: This statement is incorrect. Versailles is located in France, not Germany. It is historically significant for the Treaty of Versailles signed in 1919, which ended World War I and imposed harsh conditions on Germany.
• St. Petersburg - England: This statement is incorrect. St. Petersburg is located in Russia, not England. It is historically significant as a cultural hub, the former capital of Imperial Russia, and the site of significant events during the Russian Revolution.
• Hence, the correct answer is Rivonia - South Africa.

Additional Information

• Rivonia Trial:
• Year: Conducted in 1963-1964.
• Purpose: The trial targeted leaders of the ANC who were accused of sabotage against the apartheid government.
• Outcome: Key figures like Nelson Mandela, Walter Sisulu, and Govan Mbeki were convicted and sentenced to life imprisonment.
• Impact: The trial highlighted global opposition to apartheid and made Mandela a symbol of the anti-apartheid struggle.
• Nuremberg Trials:
• Location: Conducted in Nuremberg, Germany.
• Year: Held between 1945-1946.
• Purpose: To prosecute Nazi leaders for war crimes, crimes against humanity, and crimes of aggression during World War II.
• Significance: Established principles of international law and accountability for leaders committing atrocities.
• Versailles Treaty:
• Location: Signed at the Palace of Versailles, France.
• Year: 1919.
• Purpose: To formally end World War I and impose reparations and territorial losses on Germany.
• Impact: The treaty is considered one of the causes of World War II due to its harsh terms on Germany.
• St. Petersburg:
• Location: A city in Russia.
• Historical Significance: Served as the capital of Imperial Russia until 1918.
• Events: Key events include the October Revolution of 1917 and the siege during World War II.
• Current Status: Renamed from Leningrad to St. Petersburg in 1991 and remains a cultural and historical center in Russia.

Important Points

• Significance of Rivonia:
• The Rivonia Trial was pivotal in raising awareness about the oppression under apartheid in South Africa.
• It led to international condemnation of apartheid policies and increased support for the ANC.
• Nelson Mandela’s statement from the dock during the trial became a defining moment in the struggle for freedom.
• Other Historical Places:
• Nuremberg: Symbolizes justice and accountability in international law.
• Versailles: Represents the consequences of war and the challenges of international diplomacy.
• St. Petersburg: Reflects Russia's cultural and political history through centuries.

The correct answer is Kumar Mangalam Birla.

Key Points

• Kumar Mangalam Birla is a renowned Indian industrialist and the chairman of the Aditya Birla Group, one of India's largest multinational conglomerates.
• He was awarded the prestigious Padma Bhushan in 2023 for his exceptional contribution to the field of Trade and Industry.
• The Padma Bhushan is India's third-highest civilian award, conferred for distinguished service of high order in various fields including art, public affairs, science, and trade and industry. Hence, Kumar Mangalam Birla's recognition is highly significant.
• Kumar Mangalam Birla has been instrumental in transforming the Aditya Birla Group into a global entity, driving innovation and growth across diverse sectors such as metals, cement, textiles, financial services, and telecom.
• The group operates in over 100 countries with more than 140,000 employees, showcasing Kumar Mangalam Birla's visionary leadership. Hence, his award is a recognition of his immense contributions.

Additional Information

• About Kumar Mangalam Birla:
• Kumar Mangalam Birla was born on June 14, 1967, in Mumbai, Maharashtra, India.
• He succeeded his father, Aditya Vikram Birla, as chairman of the Aditya Birla Group at the young age of 28, following his father's untimely demise.
• Under his leadership, the group expanded globally, entering sectors like telecom, financial services, and retail.
• He is also known for his philanthropic contributions, particularly in education and healthcare, through initiatives like the Aditya Birla Centre for Community Initiatives and Rural Development.
• About the Padma Bhushan Award:
• The Padma Bhushan was established in 1954 and is awarded by the Government of India on Republic Day.
• It recognizes individuals for their distinguished contributions in various fields, including trade and industry, sports, arts, and science.
• Recipients are selected based on their achievements, irrespective of nationality, reflecting the award's global recognition.
• Other Notable Industrialists Considered:
• Adar Poonawalla: CEO of the Serum Institute of India, known for its contributions to vaccine manufacturing, especially during the COVID-19 pandemic.
• Gautam Adani: Chairman of the Adani Group, a leading infrastructure conglomerate in India.
• Mukesh Ambani: Chairman of Reliance Industries, one of India's largest corporations with a significant presence in energy, retail, and telecom.

Important Points

• Achievements of Kumar Mangalam Birla:
• Under his leadership, the Aditya Birla Group became one of India's first multinational corporations, with operations across Asia, Europe, America, and Africa.
• He pioneered expansions into high-growth sectors such as telecom, financial services, and luxury retail.
• He has been recognized with numerous awards, including the International Advertising Association’s CEO of the Year and the Ernst & Young Entrepreneur of the Year Award.
• Significance of the Padma Bhushan:
• The award highlights outstanding contributions to India’s growth and development, celebrating achievements that inspire the nation.
• It underscores the importance of leadership, vision, and innovation in driving progress across industries.

Given: Total number of students in the class is 80.

(I) 45 students of class 11th have got more than 80% marks in Physics in annual e×amination.

Here, the number of students who got e×actly 80% marks in Physics in annual e×amination cannot be determined.

(II) 30 students of class 11th have got less than 80% marks in Physics in annual e×amination.

Here, the number of students who got more than 80% marks in Physics in annual e×amination cannot be determined.

Combining (I) and (II): 45 students of class 11th have got more than 80% marks in Physics in annual e×amination. 30 students of class 11th have got less than 80% marks in Physics in annual e×amination.

Number of students who got e×actly 80% marks in Physics in annual e×amination = Total students - Students of class 11th have got more than 80% marks in Physics in annual e×amination - Students of class 11th have got less than 80% marks in Physics in annual e×amination 

→ 80 - 45 - 30 = 5

Here, the number of students who got e×actly than 80% marks in Physics in annual e×amination can be determined.

Thus, Both statements (I) and (II) together are necessary to answer the question.

Hence, "Option 2" is the correct answer.

Given statement: 

P < T

Y > W

P ≥ Y

Combining the statements: T > P ≥ Y > W

Conclusions:

I. W ≤ P → False (As T > P ≥ Y > W. So, we get P > W but not P = W, therefore is false.)

II. T > Y → True (As T > P ≥ Y > W. So, we get T > Y, therefore is true.)

Thus, Only conclusion (II) is true.

Hence, the correct answer is "Option 4".

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

Conclusions:

(I) Some frocks are caps. → Does not follow (As all caps are socks, all frocks are masks and all masks are socks. So it is possible but not definite.)

(II) Some masks are caps. → Does not follow (As all caps are socks and all masks are socks. So it is possible but not definite.)

∴ Here, Neither conclusion (I) nor (II) follows.​

Hence, the correct answer is "Option 2".

According to the given Venn diagram:

The shaded area represents the number of persons who buy both Champak and Nandan but not Sarita → 3

Hence, the correct answer is "Option 3".

Given Expression: S - G ÷ T - M × P + R

S - G → S is the mother of G

G ÷ T → G is the brother of T

T - M → T is the mother of M.

M × P → M is the sister of P

P + R → P is the father of R.

Thus, S is P's mother's mother.

Hence, "Option 4" is the correct answer.

Given: Eight girls G, K, P, A, D, Q, S and M are sitting around a square table but not necessarily in the same order. Four of them sit at four corners of the table while four sit in the middle of each of four sides. The one who sits at the four corners face outside the center while those who sit in the middle of the sides face inside.

1) 'Q' is sitting at one of the corners and she is third to the right of 'K'.

2. 'P' is sitting second to the left of 'K' and immediately right of 'S'.

3) 'K' and 'D' are facing each other. 

4. 'A' is not sitting at any of the corners.

After positioning D and A only two positions are left which will be occupied by the only two people left i.e. G and M.

Thus, D is sitting immediately left of 'Q'.

The correct answer is "Option 3".

According to the question:

Assertion (A): Government of India has banned more than 10 years old Diesel Vehicles on the roads of Delhi. → True

Reason (R): Diesel prices have increased in the past few years. → True

The government of India has banned diesel vehicles older than 10 years in Delhi to reduce air pollution and control harmful emissions, not because diesel prices have increased. while the assertion is true, the stated reason about fuel prices is unrelated.

Both (A) and (R) are true but (R) is not correct explanation of (A)

Hence, "Option 4" is the correct answer.

Given: Tanya wears T-shirts of seven different colours Red, Green, Yellow, Blue, Purple, Orange and Magenta on seven different days of the week starting from Monday.

1) She wears green T-shirt on Thursday.

2) She does not wear yellow or purple colour T-shirts on Friday.

3) She wears red colour T-shirt after the green colour T-shirt.

4) She wears only purple colour T-shirt on the day between the days on which she wears Blue and Magenta colour T-shirts.

5. She wears orange colour T-shirt after yellow colour T-shirt.

Thus, Tanya wears orange colour T-shirt on Sunday.

The correct answer is "Option 4".

Given:

Bhairav started from his home and travelled 50 meters towards East

then turned to his right and travelled 150 meters

from there he turned to his left and travelled 100 meters to reach a temple.

From the temple he moved 250 meters towards North and

then turned left and travelled 100 meters.

Finally, he turned to his left and moved 100 meters to reach a point 'P.

Thus, the shortest distance of Bhairav's home from the point 'P' is 50 m in the west direction.

Hence, "Option 2" is the correct answer.

Given series: L, X, J, K, L, 1, U, A, 5, 9, H, 2, T, %, 9, @, 1, #

According to the question, the first half is made the second half.

New Sequence: 9, H, 2, T, %, 9, @, 1, #, L, X, J, K, L, 1, U, A, 5

Thus, the letter/number/ symbol that will come at seventh place towards the left of the fifth place from the right end → 9, H, 2, T, %, 9, @, 1, #, L, X, J, K, L, 1, U, A, 5 → @

The correct answer is "Option 4".

Alternate MethodNew Sequence: 9, H, 2, T, %, 9, @, 1, #, L, X, J, K, L, 1, U, A, 5

Fifth place from the right end : This is the 5th element from the end, which is L (at position 14).

Seventh place towards the left of L: Moving left means moving towards the beginning (subtracting positions).

Target Position = 14 - 7 = 7th position.

Find the element at the 7th position in the New Sequence:

9, H, 2, T, %, 9, @, 1, #, L, X, J, K, L, 1, U, A, 5.

The 7th element is @

The correct answer is Microsoft PowerPoint.

Key Points

• Microsoft PowerPoint is a software application that is specifically designed for creating and presenting multimedia presentations.
• It allows users to include text, images, videos, animations, and other multimedia elements to enhance the presentation.
• PowerPoint offers features such as slide transitions, audio integration, and visual effects to make presentations engaging and interactive.
• For a topic like Cyber Security, PowerPoint can help create structured slides with diagrams, visuals, and key points to effectively convey information.

Additional Information

• Microsoft Word: This software is primarily used for word processing and creating text-based documents. It is not ideal for multimedia presentations.
• Microsoft Edge: A web browser used for accessing the internet, not suitable for creating presentations.
• Microsoft Excel: A spreadsheet software designed for data analysis, calculations, and charts, not for multimedia presentations.

The correct answer is Networking device.

Key Points

• A switch is a networking device used to connect multiple devices on a local area network (LAN).
• It operates at the Data Link Layer (Layer 2) of the OSI model and sometimes at the Network Layer (Layer 3).
• Switches use MAC addresses to forward data to the correct device within the network, ensuring efficient communication.
• They are essential in modern networks for managing traffic, reducing collisions, and improving overall network performance.

Additional Information

• Output device: An output device is hardware that conveys information from a computer to the user, such as a monitor, printer, or speaker.
• Input device: An input device is hardware used to provide data to a computer, such as a keyboard, mouse, or scanner.
• Storage device: A storage device is hardware used to store digital data, such as a hard drive, SSD, or USB drive.
• Switches: Unlike input, output, or storage devices, switches are specifically designed to connect devices within a network, enabling efficient data transfer.

The correct answer is Online Printer.

Key Points

• Online printers are generally less likely to be sources of virus infections compared to other options like downloaded free software, email attachments, or portable storage devices.
• This is because online printers typically do not execute files or programs that could carry malicious code.
• However, it’s important to ensure the printer firmware is updated and secured to avoid vulnerabilities.
• Other methods, like downloaded software or email attachments, are more prone to carrying viruses as they may contain executable files or malicious code.

Additional Information

• Downloaded Free Software: Free software from unreliable sources can often contain hidden malware or viruses that infect your system when installed.
• Downloaded Email Attachments: Email attachments are a common method for spreading viruses. Malicious actors often disguise malware as legitimate attachments.
• Portable Storage Devices: USB drives and external hard drives can carry viruses that automatically execute once connected to a computer.
• Online Printer: While less likely to be a direct threat, printers connected to the internet can still be exploited if not properly secured, but this risk is minimal compared to other options.

The correct answer is Option 3

Key Points

• Input devices are hardware components that allow users to send data or instructions to a computer system.
• Examples of input devices include the keyboard, mouse, scanner, microphone, and webcam.
• Option 3 contains only input devices:
• Keyboard: Used for typing and providing textual input to the computer.
• Mouse: Used for pointing, clicking, and interacting with graphical user interfaces.
• Scanner: Used for digitizing physical documents and images into electronic format.
• Other options include output devices like printers, speakers, and monitors, which are not input devices.

Additional Information

• Output Devices: These devices are used to display, project, or print information from the computer. Examples include printers, monitors, and speakers.
• Hybrid Devices: Some devices, like touchscreens, can function as both input and output devices.
• Understanding Input vs. Output: Input devices take user data and send it to the computer, while output devices take processed data from the computer and present it to the user.

The correct answer is Ctrl+'V'

Key Points

• Ctrl+'V' is the universal shortcut key used for pasting content in most MS Office applications, including Word, Excel, and PowerPoint.
• It is part of the standard keyboard shortcuts designed for copy-paste operations, where Ctrl+'C' is used for copying and Ctrl+'X' is used for cutting.
• Using Ctrl+'V' allows users to quickly paste copied or cut text, images, or other content into the desired location.
• This shortcut is widely recognized and utilized across various platforms and software applications.

Additional Information

• Ctrl+'X': This shortcut key is used to cut selected content, removing it from its original location and copying it to the clipboard.
• Ctrl+'Z': This shortcut key is used to undo the last action performed in most MS Office applications.
• Ctrl+'P': This shortcut key is used to open the print dialog box in MS Office applications, allowing users to print the current document.

The correct answer is LAN (Local Area Network).

Key Points

• LAN (Local Area Network): A LAN is generally used to connect computers and devices within a small geographical area, such as a school computer lab, office, or home.
• It provides high-speed connectivity using wired or wireless methods, enabling efficient data sharing and communication among connected devices.
• Networking devices: Devices such as switches, routers, and hubs are commonly used for establishing a LAN.
• LANs are cost-effective and provide secure communication within the network.

Additional Information

• MAN (Metropolitan Area Network): MAN covers a larger area than LAN, typically a city or campus, and is often used for interconnecting LANs within the same region.
• WAN (Wide Area Network): WAN spans large geographical areas, such as countries or continents, connecting multiple LANs and MANs. The internet is an example of a WAN.
• PAN (Personal Area Network): PAN is a small network used for connecting personal devices, such as smartphones, tablets, and laptops, typically within a few meters range.

The correct answer is Hyper Text Transfer Protocol Secure.

Key Points

• HTTPS stands for Hyper Text Transfer Protocol Secure.
• It is an extension of HTTP and uses a secure protocol to encrypt data transferred over the internet.
• HTTPS ensures data security by using SSL (Secure Sockets Layer) or TLS (Transport Layer Security).
• It protects users' sensitive information like passwords, credit card numbers, and other personal data from being intercepted by unauthorized parties.
• Websites with HTTPS can be identified by the padlock icon in the browser's address bar and the "https://" prefix in the URL.

Additional Information

• HTTP vs HTTPS: HTTP (Hyper Text Transfer Protocol) does not encrypt the communication between the client and server, making it less secure. HTTPS, on the other hand, provides encryption and ensures secure communication.
• SSL/TLS: Secure Sockets Layer (SSL) and Transport Layer Security (TLS) are cryptographic protocols used to provide secure communications over computer networks.
• Importance of HTTPS: It is essential for websites that handle sensitive user data, such as online shopping websites, banking portals, and other secure services.
• SEO Benefits: Search engines like Google prioritize HTTPS-enabled websites in their rankings, as they provide a secure browsing experience to users.

The correct answer is Android.

Key Points

• Web browsers are software applications used to access and view websites on the internet.
• Examples of popular web browsers include Edge, Firefox, and Opera, which are specifically designed for this purpose.
• Android, however, is an operating system designed for mobile devices, not a web browser.
• While Android devices can run web browsers, Android itself is not a browser.

Additional Information

• Edge: A web browser developed by Microsoft, known for its integration with Windows operating systems.
• Firefox: A free and open-source web browser developed by the Mozilla Foundation.
• Opera: A web browser known for its built-in features like ad-blocking and VPN services.
• Android: An operating system for mobile devices, developed by Google, which provides a platform for running applications, including web browsers.

The correct answer is Option 4

Key Points

• Memory units are hierarchical in terms of their storage capacity.
• Ascending order implies arranging memory units from smallest to largest capacity.
• The correct order is: Kilo Byte < Mega Byte < Giga Byte < Tera Byte.
• Explanation:
• Kilo Byte (KB): The smallest unit among the options, equivalent to 1,024 bytes.
• Mega Byte (MB): Larger than KB, equivalent to 1,024 KB.
• Giga Byte (GB): Larger than MB, equivalent to 1,024 MB.
• Tera Byte (TB): The largest among the options, equivalent to 1,024 GB.

Additional Information

• Memory Hierarchy: Memory hierarchy includes various storage units like bit, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte, and beyond. It is structured to optimize speed and capacity for different use cases.
• Binary System: Memory units follow the binary system, where each level is 1,024 times larger than the previous unit (e.g., 1 KB = 1,024 Bytes).
• Understanding memory hierarchy is important for computer storage, data processing, and optimizing system performance.

The correct answer is pdf.

Key Points

• Popular audio file extensions include: wav, flac, and mp3.
• pdf is not an audio file extension. It stands for Portable Document Format and is used for documents, not audio files.
• wav: A popular uncompressed audio file format often used for high-quality sound recordings.
• flac: A lossless audio compression format that provides high-quality sound while reducing file size.
• mp3: A common audio file format that compresses sound while maintaining acceptable quality.

Additional Information

• pdf files are primarily used to share documents that preserve their formatting across different devices.
• Audio files are typically used for music, podcasts, sound effects, and other sound-based media, while pdf files are used for textual and graphical document sharing.

Learning is a continuous process influenced by several internal and external factors such as motivation, interest, maturation, environment, and readiness. These factors determine how effectively an individual can acquire, retain, and apply knowledge or skills.

Key Points

• Co-curricular activities are organized beyond classroom learning to promote holistic development, social interaction, and practical exposure.
• Although they contribute to personality growth and life skills, they do not directly determine the process or pace of learning academic content.
• Learning is primarily affected by internal psychological and biological factors, while co-curricular activities serve as supportive, not decisive, elements.
• They enhance learning indirectly by fostering interest and motivation but are not fundamental determinants of learning outcomes. Hence, they are least likely to be considered a core factor affecting learning.

Hint

• Readiness is a crucial factor because learning occurs best when the learner is mentally, physically, and emotionally prepared to acquire new knowledge.
• Imitation strongly influences learning, especially in children, as they model behaviors and skills by observing others.
• Maturation plays a vital role as certain levels of physical and mental growth are necessary before specific learning tasks can be mastered effectively.

Hence, the correct answer is co-curricular activities.

Information and Communication Technology (ICT) tools play a vital role in modern education by supporting different teaching-learning approaches. In a learner-centered approach, ICT is used to promote active participation, collaboration, exploration, and self-directed learning.

Key Points

• Informative ICT tools mainly provide information in a one-way manner such as through digital textbooks, videos, or presentations.
• They do not promote interaction, exploration, or problem-solving. In a learner-centered approach, students are expected to engage, discuss, and construct understanding rather than just receive facts.
• Hence, informative tools are more teacher-directed and less participatory, making them less useful in learner-centered learning environments.

Hint

• Constructive tools such as concept mapping or simulation software allow learners to build their own understanding and apply knowledge creatively.
• Communicative tools like emails, discussion forums, or chats promote collaboration and sharing of ideas among learners and teachers.
• Situating tools, such as virtual reality or interactive environments, place learners in realistic contexts to explore and apply knowledge meaningfully.

Hence**, the correct answer is informative.**

Assessment items in education are designed in different formats such as objective, subjective, and essay-type to measure various learning outcomes. Objective tests like multiple-choice or matching type are used to assess recall and understanding, while essay or extended response items evaluate higher-order skills like analysis and creativity.

Key Points

• Objective type questions generally assess factual knowledge, comprehension, and application in a structured form with fixed answers.
• Creativity, however, requires open-ended expression, originality, and elaboration, which cannot be effectively measured through fixed-response formats.
• To evaluate creativity, essay-type or project-based assessments are more suitable. Hence, objective tests are not preferable for measuring students' creative ability.

Hint

• Matching type items indeed belong to the category of multiple-choice items since they involve selecting correct responses from given options.
• Supply type items, where learners generate answers, can often be converted into selection type by providing choices, although not always perfectly.
• Extended response items allow students to write detailed answers and express ideas freely, making them a form of essay-type assessment.

Hence, the correct answer is objective type of items are more preferable in measuring creative ability of the students.

A unit test is a teacher-made assessment tool designed to evaluate learners’ understanding of a specific unit or topic taught in class. It helps teachers identify students’ strengths and weaknesses, provide feedback, and plan remedial teaching accordingly.

Key Points

• Standardized achievement tests are developed by experts at a broader level to compare students’ performance across schools or regions.
• These tests are not specific to a single unit and are not prepared or controlled by individual teachers.
• Unit tests, on the other hand, are teacher-made, flexible, and focus on limited competencies within a unit. Therefore, the use of standardized achievement tests is not associated with unit testing, as their purpose and nature are entirely different.

Hint

• Results of unit tests are usually shared with parents to keep them informed about their child’s progress.
• Unit tests are confined to a limited number of competencies as they cover only a specific portion of the syllabus.
• They are completely controlled by the teacher in terms of preparation, administration, and evaluation.

Thus, the correct answer is use of standardised achievement tests.

Creativity refers to the ability to generate new, original, and valuable ideas or solutions. In education, creative students are those who go beyond rote memorization and demonstrate imagination, flexibility, and innovation in thinking.

Key Points

• A creative learner shows originality in thought, meaning they can come up with ideas that are new or different from the usual.
• Flexibility allows them to view a situation from multiple perspectives and adapt their thinking to find various possible solutions.
• Such students often express imagination and innovation in their work, demonstrating divergent rather than convergent thinking. Hence, creativity is best reflected through originality and flexibility of ideas rather than mere intelligence or memorization.

Hint

• Memorization ability involves recalling facts, which reflects rote learning, not creativity.
• Ability to solve problems is related to intelligence or reasoning but may not necessarily involve innovative or original approaches.
• Above-average IQ supports learning efficiency but does not ensure creativity, as creative thinking requires imagination and risk-taking beyond logical reasoning.

Hence, the correct answer is originality and flexibility of ideas.

The Play Way Method, developed by H. Caldwell Cook, emphasizes learning through play, activity, and joyful experiences rather than rote memorization. It is based on principles that promote natural development, freedom of expression, creativity, and self-learning.

Key Points

• When learners are given freedom in play-based activities, they also learn to take responsibility for their actions and decisions.
• This sense of responsibility gradually develops self-discipline, as children learn to follow rules, cooperate with peers, and manage their own behavior.
• Through responsible participation, they understand the balance between freedom and discipline, which is essential for social and emotional growth.
• Thus, the principle of responsibility helps cultivate self-discipline naturally through guided independence.

Hint

• Principle of creativity focuses on developing imagination and innovation rather than discipline.
• Principle of complete freedom may lead to lack of control if not guided properly, and does not necessarily build self-discipline.
• Principle of activity emphasizes learning by doing but does not directly aim at fostering responsibility or discipline.

Hence, the correct answer is principle of responsibility.

Teaching and learning are two interdependent processes. The effectiveness of teaching is judged not by what the teacher delivers but by what the learner understands, internalizes, and applies. Hence, the learning outcome is the true measure of successful teaching.

Key Points

• If students have not learned anything, it means the teaching process has failed to achieve its purpose.
• Teaching is meaningful only when it results in learning, comprehension, or change in behavior.
• Therefore, if no learning takes place, it cannot be considered that real teaching has occurred.
• This idea emphasizes that teaching is not about transmission of information but about facilitating understanding and growth.

Hint

• Examined refers to assessment or evaluation, which comes after learning, not during the teaching process.
• Observed relates to watching or noticing, which is not directly connected with the success of teaching.
• Studied refers to the learner’s effort but does not ensure that effective teaching has taken place.

Hence, the correct answer is taught.

Integrated textbooks combine content from various subjects or themes into a single book to promote holistic learning. They are designed according to child-centered and activity-based approaches, making learning more meaningful and interconnected.

Key Points

• Integrated textbooks follow a common structure designed for all learners, which may not align with every student’s preferred way of learning.
• Some students may require more subject-specific depth or different learning approaches that integrated materials do not always address.
• Hence, while they promote connected learning, they might not cater equally to individual learning differences, making this statement not an advantage of integrated textbooks.

 Hint

• They provide support to inexperienced teachers by offering structured lesson plans and integrated activities for effective classroom delivery.
• They can serve as a syllabus since they cover multiple subjects and align with curriculum objectives.
• They offer readymade materials like activities, worksheets, and stories that simplify lesson planning for teachers.

Hence, the correct answer is these may not suit student's individual learning styles.

In teaching, different approaches are used to help students understand concepts. The deductive approach begins with a general rule, principle, or theory and then illustrates it with specific examples. In contrast, the inductive approach starts with observations or examples and leads learners to infer the general principle.

Key Points

• When a teacher first presents a rule or principle and then provides examples to explain it, the method follows a deductive approach.
• This approach helps learners understand the general concept first and then see how it applies in specific situations. It is particularly effective when students need clear guidance or when the rule is complex and requires structured explanation.
• By showing examples after the principle, learners can easily relate abstract concepts to practical applications.

Hint

• Investigatory approach involves learners actively exploring, experimenting, and discovering concepts themselves rather than being told the rule.
• Inductive approach works from specific examples or observations to derive a general principle, opposite to the deductive method.
• Explanatory can be seen as a general description but specifically matches the deductive method of teaching rather than exploration or induction.

Hence**, the correct answer is deductive.**

Assessment for Learning (AfL) is a formative approach aimed at improving learning rather than merely judging it. It focuses on providing continuous feedback, guiding students to identify their strengths and weaknesses, and enabling them to take corrective actions.

Key Points

• Assessment for Learning is not primarily judgmental.
• Its goal is to support learning by giving constructive feedback and helping students improve.
• Being judgmental or evaluative focuses on ranking or grading, which aligns more with Assessment of Learning.
• AfL seeks to create a supportive environment where mistakes are opportunities for growth rather than reasons for judgment, fostering self-reflection and active learning.

Hint

• Providing continuous feedback helps learners understand what they have mastered and where they need improvement.
• Identifying strengths and weaknesses allows teachers to tailor instruction according to individual learner needs.
• Allowing students to reflect on their work encourages self-regulation and the development of strategies to improve performance.

Hence**, the correct answer is it is judgmental and hence evaluative.**

The National Education Policy (NEP) 2020 was formulated to overhaul and modernize India’s education system. A high-level committee was set up to draft the policy, bringing together experts from diverse fields of education, research, and administration to provide a comprehensive framework for school and higher education reforms.

Key Points

• Dr. K. Kasturirangan, a renowned space scientist and former chairman of ISRO, was appointed as the chairman of the committee for drafting NEP 2020.
• Under his leadership, the committee consulted experts, conducted public discussions, and reviewed global best practices to design a policy that emphasizes holistic, flexible, and inclusive education.
• His guidance was instrumental in integrating scientific, technological, and educational perspectives into the policy framework.

Hint

• Prof. Manjul Bhargava – A mathematician, not associated with chairing the NEP 2020 committee.
• Prof. M.K. Sridhar – Served as a member of the drafting committee, not as chairman.
• Prof. Vasudha Kamat – Was part of educational discussions but did not chair the NEP 2020 committee.

Hence, the correct answer is Dr. K. Kasturirangan.

The National Education Policy (NEP) 2020 restructured school education into the 5 + 3 + 3 + 4 system, aligning teaching with the cognitive and developmental stages of children. The Foundational Stage is the first stage, focusing on early childhood care and education (ECCE) and the initial years of formal schooling, emphasizing play-based and activity-oriented learning.

Key Points

• The Foundational Stage spans 5 years, which includes 3 years of pre-primary education (ages 3–6) and 2 years of Grades 1–2 (ages 6–8).
• This stage prioritizes developing literacy, numeracy, motor, socio-emotional, and language skills through interactive and experiential learning.
• Extending this stage ensures children build a strong base before moving to the Preparatory Stage, promoting holistic growth and readiness for formal academics.

Hint

• 3 years – Covers only pre-primary education and excludes Grades 1–2.
• 4 years – Shorter than the recommended 5 years for foundational development.
• 2 years – Insufficient to cover early childhood care and initial primary education adequately.

Hence, the correct answer is 5 years.

The National Education Policy (NEP) 2020 restructured school education into the 5 + 3 + 3 + 4 system: Foundational (5 years), Preparatory (3 years), Middle (3 years), and Secondary (4 years). The Secondary Stage aims to prepare students for higher education, vocational training, and life skills, focusing on multidisciplinary learning, critical thinking, and flexible subject choices.

Key Points

• The Secondary Stage in NEP 2020 spans grades 9 to 12. This 4-year stage builds on foundational and preparatory learning and provides opportunities for specialization in subjects of interest.
• Students are encouraged to pursue multidisciplinary curricula, including academic, vocational, and skill-based learning, preparing them for higher education or employment.
• The policy emphasizes experiential learning, critical thinking, and holistic development during these grades.

Hence, the correct answer is grades 9th, 10th, 11th and 12th.

Under the National Education Policy (NEP) 2020, school education has been restructured into the 5 + 3 + 3 + 4 system. The Middle Stage, also called Upper Primary, follows the Foundational and Preparatory Stages and is designed to build on foundational skills while introducing more formal learning and higher-order thinking skills.

Key Points

• The Middle or Upper Primary Stage spans 3 years, typically covering grades 6 to 8 (ages 11–14). This stage focuses on experiential learning, conceptual understanding, and critical thinking, preparing students for secondary education.
• Students are encouraged to engage in interactive, activity-based, and multidisciplinary learning, which bridges the gap between foundational/preparatory knowledge and secondary school rigor.

Hint

• 4 years – Longer than the NEP-recommended middle stage duration.
• 5 years – Refers to the Foundational Stage, not middle school.
• 2 years – Too short to cover grades 6–8 and the developmental needs of early adolescents.

Hence, the correct answer is 3 years.

The National Education Policy (NEP) 2020 restructured school education into a 5 + 3 + 3 + 4 system, with the Foundational Stage as the first stage. This stage focuses on early childhood care and education (ECCE) and the first years of formal schooling, emphasizing play-based, activity-oriented learning to develop literacy, numeracy, socio-emotional, and cognitive skills.

Key Points

• The Foundational Stage covers children aged 3 to 8 years, including 3 years of pre-primary education (ages 3–6) and Grades 1–2 (ages 6–8).
• This age range ensures that children acquire basic skills, socialization, and readiness for formal education.
• Play-based and experiential learning during this stage provides a strong foundation for future academic success and holistic development.

Hint

• 4 to 9 years – Slightly older age range; does not align with the NEP 3–8 years recommendation.
• 5 to 10 years – Excludes early childhood years critical for foundational learning.
• 2 to 7 years – Starts too early and ends before completing Grades 1–2, missing part of early formal education.

Hence, the correct answer is 3 to 8 years.

Calculation:

Given data:

Total distance covered, $d = x \text{ km}$

Total fare, $y = \text{Rs.}$

Fare for first $2 \text{ km}$ = $\text{Rs. } 25$

Rate for subsequent distance = $\text{Rs. } 8/\text{km}$

Subsequent distance $= x - 2$

Total Fare $y$ is calculated for $x \ge 2$:

$y = (\text{Fixed Fare}) + (\text{Rate} \times \text{Subsequent Distance})$

$\Rightarrow y = 25 + 8(x - 2)$

Simplifying the linear equation:

$\Rightarrow y = 25 + 8x - 16$

$\Rightarrow y = 8x + 9$

∴ The linear equation for the information is 8x - y + 9 = 0

Calculation:

Given data:

Total Fare paid, $y = \text{Rs. } 169$

Total distance covered, $x = \text{?}$

The total fare equation is:

$y = 25 + 8(x - 2)$

Substitute the value of $y$:

$169 = 25 + 8(x - 2)$

Subtract 25 from both sides:

$\Rightarrow 169 - 25 = 8(x - 2)$

$\Rightarrow 144 = 8(x - 2)$

Divide by 8:

$\Rightarrow \frac{144}{8} = x - 2$

$\Rightarrow 18 = x - 2$

Solve for $x$:

$\Rightarrow x = 18 + 2$

$\Rightarrow x = 20$

∴ The distance covered by him is 20 km.

Calculation:

1. Money Collected by School A $(M_A)$ (Quantities: 40, 50, 20):

$M_A = (40 \times 25) + (50 \times 100) + (20 \times 50)$

$\Rightarrow M_A = 1000 + 5000 + 1000$

$\Rightarrow M_A = \text{Rs. } 7,000$

2. Money Collected by School B $(M_B)$ (Quantities: 25, 40, 30):

$M_B = (25 \times 25) + (40 \times 100) + (30 \times 50)$

$\Rightarrow M_B = 625 + 4000 + 1500$

$\Rightarrow M_B = \text{Rs. } 6,125$

3. Money Collected by School C $(M_C)$ (Quantities: 35, 50, 40):

$M_C = (35 \times 25) + (50 \times 100) + (40 \times 50)$

$\Rightarrow M_C = 875 + 5000 + 2000$

$\Rightarrow M_C = \text{Rs. } 7,875$

4. Total Money Collected by All Schools $(M_T)$:

$M_T = M_A + M_B + M_C$

$\Rightarrow M_T = 7,000 + 6,125 + 7,875$

$\Rightarrow M_T = 7,000 + 14,000$

$\Rightarrow M_T = \text{Rs. } 21,000$

∴ The total amount of money collected by all three schools A, B and C is Rs. 21,000.

Calculation:

Given data for School A:

Handmade fans sold = 40

Mats sold = 50

Plates sold = 20

The total money collected by School A $(M_A)$ is:

$M_A = (\text{Fans} \times 25) + (\text{Mats} \times 100) + (\text{Plates} \times 50)$

$\Rightarrow M_A = (40 \times 25) + (50 \times 100) + (20 \times 50)$

$\Rightarrow M_A = 1000 + 5000 + 1000$

$\Rightarrow M_A = \text{Rs. } 7,000$

∴ The total money collected by School A is Rs. 7,000.

Calculation:

1. New Money Collected by School A $(M_A)$: (New Fans=20, Mats=50, New Plates=40)

$M_A = (20 \times 25) + (50 \times 100) + (40 \times 50)$

$\Rightarrow M_A = 500 + 5000 + 2000$

$\Rightarrow M_A = \text{Rs. } 7,500$

2. New Money Collected by School B $(M_B)$: (New Fans=30, Mats=40, New Plates=25)

$M_B = (30 \times 25) + (40 \times 100) + (25 \times 50)$

$\Rightarrow M_B = 750 + 4000 + 1250$

$\Rightarrow M_B = \text{Rs. } 6,000$

3. New Money Collected by School C $(M_C)$: (New Fans=40, Mats=50, New Plates=35)

$M_C = (40 \times 25) + (50 \times 100) + (35 \times 50)$

$\Rightarrow M_C = 1000 + 5000 + 1750$

$\Rightarrow M_C = \text{Rs. } 7,750$

4. Total Money Collected by All Schools $(M_T)$:

$M_T = M_A + M_B + M_C$

$\Rightarrow M_T = 7,500 + 6,000 + 7,750$

$\Rightarrow M_T = \text{Rs. } 21,250$

∴ The total money collected by these schools after the interchange is Rs. 21,250.

Calculation:

1. Money Collected by School B $(M_B)$:

$M_B = (\text{Fans} \times 25) + (\text{Mats} \times 100) + (\text{Plates} \times 50)$

$M_B = (25 \times 25) + (40 \times 100) + (30 \times 50)$

$\Rightarrow M_B = 625 + 4000 + 1500$

$\Rightarrow M_B = \text{Rs. } 6,125$

2. Money Collected by School C $(M_C)$:

$M_C = (\text{Fans} \times 25) + (\text{Mats} \times 100) + (\text{Plates} \times 50)$

$M_C = (35 \times 25) + (50 \times 100) + (40 \times 50)$

$\Rightarrow M_C = 875 + 5000 + 2000$

$\Rightarrow M_C = \text{Rs. } 7,875$

3. Total Money Collected by School B and School C $(M_T)$:

$M_T = M_B + M_C$

$\Rightarrow M_T = 6,125 + 7,875$

$\Rightarrow M_T = \text{Rs. } 14,000$

∴ The total money collected by school B and school C is Rs. 14,000.

Calculation:

Given data for the Old godown:

Base side, $x_o = x$

Height, $h_o = y$

Volume of the old godown, $V_o$:

$V_o = x_o^2 \times h_o$

$\Rightarrow V_o = x^2y$

Given conditions for the New Godown:

New base side, $x_n = 2x_o = 2x$

New height, $h_n = 3h_o = 3y$

Volume of the new godown, $V_n$:

$V_n = x_n^2 \times h_n$

$\Rightarrow V_n = (2x)^2 \times (3y)$

$\Rightarrow V_n = 4x^2 \times 3y$

$\Rightarrow V_n = 12x^2y$

Ratio of volume of new and old godown $\left(\frac{V_n}{V_o}\right)$:

$\frac{V_n}{V_o} = \frac{12x^2y}{x^2y}$

$\Rightarrow \frac{V_n}{V_o} = \frac{12}{1}$

∴ The ratio of volume of new and old godown is 12 : 1.

Calculation:

Given data for the godown with square base side $x$ and height $y$:

Area of walls, $A_w = 4xy$

Area of roof, $A_r = x^2$

Cost incurred for walls per square meter, $C_w = \text{Rs. } 5$

Cost incurred for roof per square meter, $C_r$, is 3 times the cost of the walls:

$C_r = 3 \times C_w$

$\Rightarrow C_r = 3 \times \text{Rs. } 5 = \text{Rs. } 15$

The total cost of constructing the godown, $C$, is:

$C = (\text{Cost for Walls}) + (\text{Cost for Roof})$

$\Rightarrow C = (A_w \times C_w) + (A_r \times C_r)$

$\Rightarrow C = (4xy \times 5) + (x^2 \times 15)$

$\Rightarrow C = 20xy + 15x^2$

Factoring out the common term 5:

$\Rightarrow C = 5(4xy + 3x^2)$

$\Rightarrow C = \text{Rs. } 5(3x^2 + 4xy)$

∴ The cost of constructing the godown is Rs. 5(3x² + 4xy).

Concept:

Volume of a Cuboid:

• The volume $(V)$ of a three-dimensional object is the space it occupies. The SI unit of volume is the cubic meter $(m^3)$.
• A cuboid is a solid figure with length $l$, width $w$, and height $h$.
• The formula for the Volume of a cuboid is: $V = l \times w \times h$.
• For a cuboid with a square base of side $x$, the length $l$ is $x$ and the width $w$ is $x$.
• The Volume formula specific to this godown is $V = x \times x \times h$.

 

Calculation:

Given dimensions for the cuboidal godown:

Length of base, $l = x$

Width of base, $w = x$

Height of godown, $h = y$

The Volume $V$ of the godown is:

$V = l \times w \times h$

$\Rightarrow V = x \times x \times y$

$\Rightarrow V = x^2y$

∴ The correct relation between $V$, $x$ and $y$ is V = x2y.

Calculation:

The expression for the cost $C$ is:

$C = \text{Rs. } 5(3x^2 + 4xy)$

The relation between Volume $V$, base side $x$, and height $y$ is:

$V = x^2y$

Expressing $y$ in terms of $V$ and $x$:

$\Rightarrow y = \frac{V}{x^2}$

Substitute $y$ into the cost equation:

$C = \text{Rs. } 5 \left[3x^2 + 4x \left(\frac{V}{x^2}\right)\right]$

Simplify the second term $4x \left(\frac{V}{x^2}\right)$:

$\Rightarrow C = \text{Rs. } 5 \left[3x^2 + \frac{4xV}{x^2}\right]$

$\Rightarrow C = \text{Rs. } 5 \left[3x^2 + \frac{4V}{x}\right]$

Calculation:

Let the radius of the circle be R

The diameter of the circle is $D = 2R$.

1. Circumscribed Square ($A_c$):

The circle is tangent to all four sides of the circumscribed square.

The side length of the circumscribed square, $s_c$, is equal to the diameter D of the circle.

$s_c = D = 2R$

The area of the circumscribed square, $A_c$, is:

$A_c = s_c^2 = (2R)^2 = 4R^2$

2. Inscribed Square ($A_i$):

The vertices of the inscribed square lie on the circle.

The diagonal of the inscribed square, $d_i$, is equal to the diameter D of the circle.

$d_i = D = 2R$

The area of the inscribed square, $A_i$, in terms of its diagonal is:

$A_i = \frac{d_i^2}{2}$

$\Rightarrow A_i = \frac{(2R)^2}{2} = \frac{4R^2}{2} = 2R^2$

The ratio of the areas of the circumscribed and the inscribed squares is $\frac{A_c}{A_i}$.

$\frac{A_c}{A_i} = \frac{4R^2}{2R^2}$

$\Rightarrow \frac{A_c}{A_i} = \frac{4}{2} = \frac{2}{1}$

$\Rightarrow A_c : A_i = 2 : 1$

∴ The ratio of the areas of the circumscribed and the inscribed squares is 2 : 1.

Calculation:

Given,

Length of the ladder (Hypotenuse) = 14m

Angle the ladder makes with the wall, θ = 60° 

Let the height of the wall Adjacent side be H

Using the cosine ratio:

$cosθ = \frac{Base}{ Hypotenuse} = \frac{B}{H}$

$\Rightarrow \text{cos}(60^{\circ}) = \frac{B}{14}$

$\Rightarrow \frac{1}{2} = \frac{B}{14}$

$\Rightarrow B = \frac{14}{2}$

$\Rightarrow Base= 7m$

 ∴The height of the wall  is 7m

∴ The Correct Answer is 7m

Concept:

Cross-section of a Right Circular Cone:

• A right circular cone is a three-dimensional figure with a circular base and an apex directly above the center of the base.
• A cross-section is the two-dimensional shape formed when a plane slices through a solid.
• When a plane intersects a right circular cone and is parallel to the base, the resulting cross-section is a shape that retains the circular symmetry of the base.
• The shape formed by this specific cut is a circle. This circle is smaller than the base circle, with its radius decreasing as the plane moves closer to the apex.
• The frustum of a cone is the 3D portion of the cone that remains after a smaller cone is cut off by a plane parallel to the base; it is not the 2D cross-section itself.

 

Calculation:

The question asks for the shape of the cross-section.

Given the cutting plane is parallel to the base of a right circular cone.

When a plane cuts a right circular cone parallel to its base, the intersection surface is a circle.

The resultant two-dimensional shape is a circle.

∴ The cross-section made by a plane parallel to the base is a circle.

Calculation:

Given,

Radius of the circle, r = 16cm

Arc length, l = 18.5cm

The area of the sector A is given by the formula:

$A = \frac{1}{2} \times r \times l$

$\Rightarrow \text{Area} = \frac{1}{2} \times 16\text{ cm} \times 18.5\text{ cm}$

$\Rightarrow \text{Area} = 8\text{ cm} \times 18.5\text{ cm}$

$\Rightarrow \text{Area} = 148\text{ cm}^2$

The area of a sector of a circle of radius 16 cm is 148 cm2

Given:

sinθ + cosθ = √2

Formula used:

(sinθ + cosθ)² = sin²θ + cos²θ + 2sinθcosθ

sin²θ + cos²θ = 1

tanθ + cotθ =

Calculation:

sinθ + cosθ = √2

⇒ (sinθ + cosθ)² = 2

⇒ sin²θ + cos²θ + 2sinθcosθ = 2

⇒ 1 + 2sinθcosθ = 2

⇒ 2sinθcosθ = 1

⇒ sinθcosθ = 1/2

⇒ tanθ + cotθ =

⇒tanθ + cotθ = 1 ÷ (1/2)

⇒ tanθ + cotθ = 2

∴ The correct answer is option (1).

Calculation:

Given data:

ABCD is acyclic quadrilateral

AB is a diameter

$\mathbf{\angle ADC = 140^{\circ}}$.

$\mathbf{\angle ABC + \angle ADC = 180^{\circ}}$

$\Rightarrow \mathbf{\angle ABC + 140^{\circ} = 180^{\circ}}$

$\Rightarrow \mathbf{\angle ABC = 180^{\circ} - 140^{\circ} = 40^{\circ}}$

Since AB is the diameter, the angle subtended by the diameter at any point on the circumference is $\mathbf{90^{\circ}}$.

$\Rightarrow \mathbf{\angle ACB = 90^{\circ}}$

$\mathbf{\angle BAC + \angle ACB + \angle ABC = 180^{\circ}}$

$\Rightarrow \mathbf{\angle BAC + 90^{\circ} + 40^{\circ} = 180^{\circ}}$

$\Rightarrow \mathbf{\angle BAC + 130^{\circ} = 180^{\circ}}$

$\Rightarrow \mathbf{\angle BAC = 180^{\circ} - 130^{\circ}}$

$\Rightarrow \mathbf{\angle BAC = 50^{\circ}}$

$\therefore$ The measure of ∠BAC is equal to 50°

Calculation:

Given points:

$\mathbf{A(x_1, y_1) = (5, -2)}$

$\mathbf{B(x_2, y_2) = (0, 7)}$

Dividing point: $\mathbf{P(x, y) = (\frac{5}{3}, 4)}$

Assume the point P divides the line segment AB in the ratio $\mathbf{k : 1}$.

Using the x-coordinate section formula:

$\mathbf{x = \frac{k x_2 + x_1}{k + 1}}$

$\mathbf{\frac{5}{3} = \frac{k(0) + 5}{k + 1}}$

$\Rightarrow \mathbf{\frac{5}{3} = \frac{5}{k + 1}}$

$\Rightarrow \mathbf{5(k + 1) = 3(5)}$

$\Rightarrow \mathbf{5k + 5 = 15}$

$\Rightarrow \mathbf{5k = 15 - 5}$

$\Rightarrow \mathbf{5k = 10}$

$\Rightarrow \mathbf{k = \frac{10}{5} = 2}$

Using the y-coordinate section formula (to verify):

$\mathbf{y = \frac{k y_2 + y_1}{k + 1}}$

$\mathbf{4 = \frac{k(7) + (-2)}{k + 1}}$

$\Rightarrow \mathbf{4(k + 1) = 7k - 2}$

$\Rightarrow \mathbf{4k + 4 = 7k - 2}$

$\Rightarrow \mathbf{4 + 2 = 7k - 4k}$

$\Rightarrow \mathbf{6 = 3k}$

$\Rightarrow \mathbf{k = \frac{6}{3} = 2}$

Since $\mathbf{k = 2}$, the ratio $\mathbf{k : 1}$ is $\mathbf{2 : 1}$.

$\therefore$ The ratio in which the line segment is divided is $\mathbf{2 : 1}$.

Calculation:

Given conditions:

$\mathbf{p > 0}$

$\mathbf{q < 0}$

Multiply both sides by $\mathbf{-1}$ and reverse the inequality sign:

 

$\Rightarrow \mathbf{-q > 0}$

This shows that the term $\mathbf{-q}$ is a positive value.

Add $\mathbf{p}$ to both sides of the inequality $\mathbf{-q > 0}$:

$\Rightarrow \mathbf{p - q > p + 0}$

$\Rightarrow \mathbf{p - q > p}$

Calculation:

Given: In $\mathbf{\triangle DEF}$ and $\mathbf{\triangle PQR}$,

$\mathbf{\angle D = \angle Q}$

$\mathbf{\angle E = \angle R}$

By AAA similarity criterion, the triangles are similar, and the correspondence of vertices is $\mathbf{D \leftrightarrow Q}$, $\mathbf{E \leftrightarrow R}$, $\mathbf{F \leftrightarrow P}$.

The ratio of corresponding sides is:

$\mathbf{\frac{\text{Side opposite to F}}{\text{Side opposite to P}} = \frac{\text{Side opposite to D}}{\text{Side opposite to Q}} = \frac{\text{Side opposite to E}}{\text{Side opposite to R}}}$

$\mathbf{\frac{DE}{QR} = \frac{EF}{RP} = \frac{DF}{QP}}$

 

$\therefore$ The statement which is not true is $\mathbf{\frac{DE}{PQ} = \frac{EF}{RP}}$.