RRB NTPC Graduate Level CBT-II Official Paper (Held On: 13 Oct, 2025 Shift 1) (Previous Year Paper)

The logic followed here is:

WASH - HSWA - WSAH

And,

NEST - TSNE - NSET 

Similarly,

OILS - SLOI - OLIS

Hence, the correct answer is "Option 4"

Here, we use the BODMAS table given below:

Given Equation: 32 − 15 ÷ 5 + 10 × 2 = ?

If ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged.

New Equation: 32 + 15 ×  5 − 10 ÷ 2 = ?

32 + 15 ×  5 − 10 ÷ 2 = ?

32 + 15 ×  5 − 5 = ?

32 + 75 − 5  = ?

Hence, the correct answer is "Option 4"

Shortcut Trick

Rate of depreciation = 10% = 1/10.

Multiplying factor for each year = 1 − 1/10 = 9/10.

Value after 2 years = 1,00,000 × (9/10) × (9/10)

⇒ Value = 1,00,000 × 81/100 = 81,000

∴ The correct answer is ₹81,000.

Alternate Method

Given:

Initial Value (P) = ₹1,00,000

Rate of depreciation (R) = 10% per annum

Time (n) = 2 years

Formula Used:

A = P(1 − R/100)ⁿ

Current ₹1,00,000

−10%

1 Year ₹90,000

−10%

2 Years ₹81,000

Successive Depreciation Method

Calculations:

⇒ A = 1,00,000 × (1 − 10/100)²

⇒ A = 1,00,000 × (90/100)²

⇒ A = 1,00,000 × (9/10) × (9/10)

⇒ A = 1,00,000 × 81/100

⇒ A = 1000 × 81 = 81,000

∴ The correct answer is ₹81,000.

Additional Information

Appreciation Formula

If an item appreciates in value at R% per annum, the value after n years is given by A = P(1 + R/100)ⁿ.

Successive Percentage Change

For two consecutive percentage changes x% and y%, the net percentage change is given by (x + y + xy/100)%. For 10% depreciation twice, it is (−10 − 10 + 100/100)% = −19%. Value becomes 100% − 19% = 81% of the original.

Value n Years Ago

If the current value is P and it has been depreciating at R% per annum, its value n years ago was P ÷ (1 − R/100)ⁿ.

The correct answer is International Institute of Administrative Sciences (IIAS).

Key Points

• On 3 June 2025, India secured the presidency of the International Institute of Administrative Sciences (IIAS) by defeating Austria with 87 out of 141 votes.
• IIAS is a global organization dedicated to advancing administrative sciences and public governance worldwide.
• India’s presidency marks a significant achievement in strengthening its role in the field of governance and administrative reforms on an international scale.
• IIAS provides a platform for countries to exchange knowledge, best practices, and research related to public administration and governance.
• This achievement highlights India’s growing influence in shaping global discussions around administrative innovations and public sector efficiency.

Additional Information

• International Institute of Administrative Sciences (IIAS)
• Founded in 1930, IIAS is headquartered in Brussels, Belgium.
• It aims to promote understanding and innovation in administrative sciences and public governance globally.
• The institute organizes conferences, seminars, and publishes research to address administrative challenges and solutions.
• IIAS has members from over 100 countries, fostering international collaboration in public administration.
• India's Role in Global Governance
• India has been actively participating in global governance forums and organizations to contribute to policy-making and administrative reforms.
• Its presidency in IIAS enhances its reputation as a leader in promoting effective governance and public administration practices.
• India’s initiatives like Digital India and e-Governance have been recognized globally as innovative governance strategies.
• India’s leadership role in IIAS can facilitate sharing of indigenous knowledge systems and best practices with other nations.
• Impact of IIAS Presidency
• India’s presidency will enable it to host key events, seminars, and workshops to discuss global administrative challenges.
• It offers India an opportunity to influence international policies and standards in public administration.
• Strengthens India’s diplomatic relationships with member states through collaboration in governance initiatives.
• Provides a platform for Indian administrative professionals to share their expertise and learn from global counterparts.
• Global Trends in Public Administration
• Increased adoption of technology to enhance government efficiency and transparency.
• Focus on participatory governance, involving citizens in decision-making processes.
• Sustainability and green governance are becoming central themes in administrative reforms globally.
• Emphasis on capacity building and training programs for public officials to address emerging challenges.

The correct answer is Prayagraj.

Key Points

• The headquarters of the North Central Railway Zone is located in Prayagraj, Uttar Pradesh.
• It is one of the 18 railway zones in India, established on 1st April 2003.
• The North Central Railway Zone covers major states including Uttar Pradesh, Madhya Pradesh, Rajasthan, and Haryana.
• This zone is known as the "Workhorse of Indian Railways" due to its significant role in freight and passenger movement.
• The zone operates through three divisions: Prayagraj, Jhansi, and Agra.

Additional Information

• Railway Zones in India
• Indian Railways is divided into 18 zones, each headed by a General Manager.
• The zones are further subdivided into divisions, each managed by Divisional Railway Managers.
• Zones are categorized based on geographical coverage and operational efficiency.
• Importance of Prayagraj
• Prayagraj, formerly known as Allahabad, is historically and culturally significant in India.
• It is a major hub for railways, with important routes connecting northern and central India.
• The city hosts the Kumbh Mela, one of the largest religious gatherings in the world.
• North Central Railway Zone Infrastructure
• The zone is critical for freight operations, especially coal transportation from Madhya Pradesh.
• It handles key passenger routes, including Delhi-Mumbai and Delhi-Howrah corridors.
• It is equipped with modern infrastructure like automatic signaling systems.
• Other Railway Zones
• Some other major railway zones include Northern Railway Zone (New Delhi), Western Railway Zone (Mumbai), and Southern Railway Zone (Chennai).
• Each zone plays a unique role in ensuring connectivity and efficient transportation across India.

The correct answer is Ctrl + Backspace.

Key Points

• The Ctrl + Backspace shortcut in MS Word allows users to delete the entire word to the left of the cursor quickly.
• This shortcut is highly efficient for editing large documents as it saves time compared to manually deleting characters.
• It works irrespective of whether the word is selected or not, making it versatile for text editing.
• It is available across multiple versions of MS Word, including MS Word 2019.
• Keyboard shortcuts like Ctrl + Backspace improve productivity by minimizing the use of a mouse during text editing.

Additional Information

• Keyboard Shortcuts in MS Word:
• Ctrl + Delete: Deletes the word to the right of the cursor.
• Ctrl + Z: Undoes the last action performed.
• Ctrl + X: Cuts the selected text or object.
• Ctrl + C: Copies the selected text or object.
• Ctrl + V: Pastes the copied or cut text or object.
• Text Navigation Shortcuts:
• Ctrl + Left Arrow: Moves the cursor one word to the left.
• Ctrl + Right Arrow: Moves the cursor one word to the right.
• Home: Moves the cursor to the beginning of the line.
• End: Moves the cursor to the end of the line.
• Importance of Keyboard Shortcuts:
• Keyboard shortcuts boost productivity by speeding up repetitive tasks.
• They help reduce strain on the hands by minimizing mouse usage.
• They can be customized in MS Word to suit user preferences.
• MS Word 2019 Features:
• Improved collaboration tools for team editing in real-time.
• Advanced formatting options for better document layout.
• Integration with cloud services like OneDrive for seamless access.
• Enhanced accessibility features for individuals with disabilities.

Shortcut Trick

The sum of all interior angles of a quadrilateral is always 360°.

Total parts in the ratio = 2 + 3 + 3 + 4 = 12 parts.

12 parts = 360° ⇒ 1 part = 30°.

Value of ∠x = 3 parts = 3 × 30° = 90°.

∴ The correct answer is 90°.

Alternate Method

Given:

Ratio of angles ∠w : ∠x : ∠y : ∠z = 2 : 3 : 3 : 4

Formula Used:

Sum of interior angles of a quadrilateral = 360°

w (2k) x (3k) y (3k) z (4k)

Sum of interior angles = 360°

Calculations:

⇒ Let the four angles be 2k, 3k, 3k, and 4k respectively.

⇒ ∠w + ∠x + ∠y + ∠z = 360°

⇒ 2k + 3k + 3k + 4k = 360°

⇒ 12k = 360°

⇒ k = 360° ÷ 12

⇒ k = 30°

⇒ The value of ∠x = 3k

⇒ ∠x = 3 × 30° = 90°

∴ The correct answer is 90°.

Additional Information

Sum of Interior Angles

For any polygon with n sides, the sum of interior angles is calculated as (n − 2) × 180°. For a quadrilateral, it is (4 − 2) × 180° = 360°.

Sum of Exterior Angles

The sum of the exterior angles of any convex polygon, including a quadrilateral, is always 360° regardless of the number of sides.

Types of Quadrilaterals

If consecutive adjacent angles in a quadrilateral sum to 180°, the opposite sides are parallel. In this problem, ∠x + ∠y = 90° + 90° = 180°, meaning it forms a right-angled trapezium.

The logic follows here,

 Meal is coded as dv.

Hence, the correct answer is "Option 4"

The correct answer is Ananda Mohan Bose, Sib Chandra Deb and Umesh Chandra Dutta.

Key Points

• The Sadharan Brahmo Samaj was established in 1878 by dissatisfied followers of Keshab Chandra Sen who opposed his autocratic leadership and deviation from Brahmo principles.
• Its primary founders were Ananda Mohan Bose, Sib Chandra Deb, and Umesh Chandra Dutta, who sought to uphold the democratic and liberal ideals of Brahmoism.
• The organization emphasized equality, rationalism, and monotheism, which were core tenets of the Brahmo faith.
• The Sadharan Brahmo Samaj also advocated for social reform, including the abolition of caste discrimination, child marriage, and promotion of women's education.
• This division marked a pivotal moment in the history of the Brahmo movement, leading to a more progressive and inclusive approach within the Samaj.

Additional Information

• Brahmo Samaj:
• Founded by Raja Ram Mohan Roy in 1828, Brahmo Samaj was a socio-religious reform movement in India advocating monotheism and rejecting idol worship.
• It sought to promote rational thinking, social justice, and equality among all individuals.
• Keshab Chandra Sen:
• A prominent Brahmo leader, Keshab Chandra Sen emphasized the need for spiritual and social reform.
• His leadership style and theological deviations led to the split within the Brahmo Samaj in 1878.
• Ananda Mohan Bose:
• Ananda Mohan Bose was an educator, politician, and one of the prominent leaders of the Sadharan Brahmo Samaj.
• He played a significant role in promoting education and social reform in India.
• Social Impact:
• The Brahmo Samaj contributed significantly to India's socio-religious reform movements during British rule.
• It influenced other reform movements such as the Arya Samaj and helped shape modern Indian society.

The correct answer is Evergreen broad-leaf trees, such as oaks and chestnuts predominate here..

Key Points

• Montane forests are characterized by the presence of evergreen broad-leaf trees such as oaks, chestnuts, and other species adapted to cool and moist conditions.
• These forests are typically found in hilly and mountainous regions, especially at elevations ranging from 1000 to 3000 meters.
• They are known for their dense canopy cover, which supports a rich biodiversity including unique flora and fauna.
• Montane forests often experience cooler temperatures and higher rainfall, making them distinct from tropical forests.
• The vegetation in montane forests changes with altitude, ranging from evergreen forests at lower elevations to coniferous forests at higher altitudes.

Additional Information

• Montane Ecosystem:
• This ecosystem is associated with mountainous regions and is highly influenced by altitude, climate, and soil types.
• It supports a variety of flora and fauna, including species that are endemic to these regions.
• Altitudinal Zonation:
• The vegetation in montane forests varies by altitude, transitioning from tropical forests at lower elevations to alpine vegetation at higher altitudes.
• Common zones include tropical montane forests, temperate montane forests, and alpine meadows.
• Climatic Influence:
• Montane forests are typically found in areas with cool and moist climates.
• They play a crucial role in regulating water cycles and preventing soil erosion in mountainous regions.
• Biodiversity:
• Montane forests are home to a wide variety of plants and animals, including many rare and endangered species.
• The unique climate and elevation make these forests a biodiversity hotspot.

The correct answer is Article 243C.

Key Points

• Article 243C deals with the composition of Panchayats in India as per the 73rd Constitutional Amendment Act, 1992.
• The composition of Panchayats includes directly elected members at the village, intermediate, and district levels.
• It mandates that the Chairperson of a Panchayat at the village level is elected as per the procedure established by state legislation.
• It provides flexibility to states to determine the representation of members, reservation for Scheduled Castes (SCs), Scheduled Tribes (STs), and women, and other relevant details.
• Reservation of seats in every Panchayat is done according to Articles 243D and 243T, ensuring inclusivity.

Additional Information

• 73rd Constitutional Amendment Act, 1992:
• Introduced Panchayati Raj institutions (PRIs) in India to promote decentralized governance.
• Added Part IX to the Constitution and Articles 243 to 243O.
• Mandates a three-tier system: Village, Intermediate, and District levels.
• Article 243A:
• Empowers Gram Sabha as the foundation of the Panchayati Raj system.
• The Gram Sabha comprises all registered voters within a village Panchayat's jurisdiction.
• Article 243B:
• Provides for the establishment of Panchayats at various levels in every state.
• States have the discretion to decide whether to establish Panchayats at the intermediate level based on population.
• Article 243D:
• Mandates reservation of seats for Scheduled Castes (SCs), Scheduled Tribes (STs), and women in Panchayats.
• Reservation for women is not less than one-third of the total seats.
• Panchayati Raj:
• It is a system of governance at the rural level to ensure grassroots democracy.
• First introduced in Nagaur, Rajasthan, on 2nd October 1959.

The correct answer is Sustainable Development.

Key Points

• The concept of Sustainable Development was formally introduced in the Brundtland Report, titled Our Common Future, published in 1987 by the United Nations World Commission on Environment and Development (WCED).
• Sustainable development is defined as "development that meets the needs of the present without compromising the ability of future generations to meet their own needs."
• The Brundtland Report highlighted the interconnectedness of economic, social, and environmental dimensions, emphasizing the need for a balance between these factors to ensure long-term global sustainability.
• It paved the way for major international agreements and frameworks, such as the United Nations Sustainable Development Goals (SDGs), which were adopted in 2015.
• The report brought global attention to critical issues like environmental degradation, social inequality, and the need for sustainable resource management.

Additional Information

• Brundtland Commission:
• Also known as the World Commission on Environment and Development (WCED), it was established by the United Nations in 1983.
• The commission was chaired by Gro Harlem Brundtland, the former Prime Minister of Norway, hence the name.
• Its objective was to address the growing concern about environmental degradation and its impact on economic and social development.
• Sustainable Development Goals (SDGs):
• The SDGs are a set of 17 interconnected global goals adopted by the UN in 2015 as part of the 2030 Agenda for Sustainable Development.
• They aim to eradicate poverty, combat climate change, and promote economic growth, social inclusion, and environmental sustainability.
• Examples of SDGs include Goal 13 (Climate Action), Goal 1 (No Poverty), and Goal 7 (Affordable and Clean Energy).
• Key Principles of Sustainable Development:
• Intergenerational Equity: Ensuring that resources are available for future generations.
• Integration: Balancing environmental, social, and economic factors in decision-making.
• Precautionary Principle: Taking preventive action to protect the environment, even in the absence of full scientific certainty.
• Global Impact:
• The Brundtland Report inspired the 1992 Earth Summit in Rio de Janeiro, where nations adopted the Agenda 21, a comprehensive plan for sustainable development.
• It also influenced the creation of the Paris Agreement in 2015, aimed at combating climate change and limiting global temperature rise.

Shortcut Trick

Let pen price = P, notebook price = N. Initial: 4P + 5N = 130

New price equation: 2 × (1.25P) + 4 × (0.8N) = 82 ⇒ 2.5P + 3.2N = 82

Multiply new equation by 1.6 to equate P: 4P + 5.12N = 131.2

Subtracting initial from new: 0.12N = 1.2 ⇒ N = 10

Substitute N = 10: 4P + 50 = 130 ⇒ 4P = 80 ⇒ P = 20

∴ The correct answer is Rs. 40.

Alternate Method

Given:

Cost of 4 pens and 5 notebooks = Rs. 130

Increase in pen's price = 25%

Decrease in notebook's price = 20%

New cost of 2 pens and 4 notebooks = Rs. 82

Calculations:

⇒ Let the original price of 1 pen be P and 1 notebook be N.

⇒ 4P + 5N = 130   --- (Equation 1)

⇒ New price of 1 pen = P × (100 + 25) ÷ 100 = 1.25P

⇒ New price of 1 notebook = N × (100 − 20) ÷ 100 = 0.8N

⇒ According to the second condition:

⇒ 2 × (1.25P) + 4 × (0.8N) = 82

⇒ 2.5P + 3.2N = 82

⇒ Multiplying the entire equation by 10 to remove decimals:

⇒ 25P + 32N = 820   --- (Equation 2)

⇒ Multiplying Equation 1 by 25 and Equation 2 by 4:

⇒ 100P + 125N = 3250

⇒ 100P + 128N = 3280

⇒ Subtracting the two equations:

⇒ 3N = 30 ⇒ N = 10

⇒ Substitute N = 10 into Equation 1:

⇒ 4P + 5(10) = 130

⇒ 4P + 50 = 130

⇒ 4P = 80 ⇒ P = 20

⇒ Required price = 1 Pen + 2 Notebooks

⇒ Price = 20 + 2 × 10 = 20 + 20 = 40

∴ The correct answer is Rs. 40.

Additional Information

Simultaneous Linear Equations

When solving a system of two linear equations with two variables, methods such as substitution or elimination are used. Equating the coefficients by multiplying the equations with suitable constants is often the fastest approach to eliminate one variable.

Percentage Change

When a base value is increased by x%, the new value becomes Base × (100 + x) ÷ 100. Similarly, a decrease of y% results in Base × (100 − y) ÷ 100.

Given: Among 5 students, F, A, K, E and D each having a different height

Statements:

After combining both statements or using alone statement I or II, it is not possible to find which student is the shortest.

Data in statements I and II together are NOT sufficient to answer the question.

Hence, the correct answer is "Option 1"

The logic followed here is:

Similarly,

Hence, the correct answer is "Option 2"

The correct answer is Indigo farmers in Bihar.

Key Points

• The Champaran Satyagraha of 1917 marked Mahatma Gandhi’s first major involvement in India’s freedom struggle.
• It was launched in support of Indigo farmers in Bihar, who were oppressed under the exploitative tinkathia system.
• The farmers were forced to grow indigo on a portion of their land and sell it at fixed prices, leading to severe financial hardship.
• Mahatma Gandhi’s intervention in Champaran was aimed at addressing the farmers' grievances and demonstrating the power of nonviolent resistance.
• The success of the Champaran movement brought attention to the plight of farmers and strengthened Gandhi’s leadership in the national movement.

Additional Information

• Tinkathia System:
• Under this system, farmers were forced to cultivate indigo on 3/20th of their land, regardless of their own preferences.
• The system was exploitative and caused significant economic distress for the farmers.
• Role of Gandhi:
• Mahatma Gandhi visited Champaran in 1917 after being requested by local leaders like Raj Kumar Shukla.
• He adopted the method of Satyagraha (nonviolent resistance) to address the injustice faced by farmers.
• Impact of Champaran Movement:
• The movement led to the abolition of the tinkathia system and improved the condition of farmers in the region.
• It demonstrated the effectiveness of nonviolent resistance and became a precursor to future freedom struggles under Gandhi’s leadership.
• Indigo Cultivation:
• Indigo was a dye plant that was in high demand in Europe during colonial times.
• The forced cultivation of indigo caused soil depletion, which further impacted farmers’ livelihoods.

Shortcut Trick

The amount by which the Selling Price is less than the Marked Price is simply the Total Discount.

Effective percentage of two successive discounts (5% and 15%) = 5 + 15 − (5 × 15) ÷ 100

⇒ Effective discount = 20 − 0.75 = 19.25%

Total Discount Amount = 19.25% of ₹1200

⇒ Total Discount = (19.25 ÷ 100) × 1200 = ₹231

∴ The correct answer is ₹231.

Alternate Method

Given:

Marked Price (MP) = ₹1200

First successive discount (D₁) = 5%

Second successive discount (D₂) = 15%

Formula Used:

Selling Price (SP) = MP × (100 − D₁)÷100 × (100 − D₂)÷100

Difference = MP − SP

MP ₹1200

−5%

₹1140

−15%

SP ₹969

Total Discount = ₹231

Calculations:

⇒ Price after first discount = 1200 × (100 − 5) ÷ 100

⇒ Price after first discount = 1200 × 95 ÷ 100 = ₹1140

⇒ Final Selling Price (SP) = 1140 × (100 − 15) ÷ 100

⇒ Final Selling Price (SP) = 1140 × 85 ÷ 100 = ₹969

⇒ Amount by which SP is less than MP = MP − SP

⇒ Amount = 1200 − 969 = ₹231

∴ The correct answer is ₹231.

Additional Information

Successive Discount Formula

When two successive discounts d₁% and d₂% are given, the equivalent single discount is given by: D = d₁ + d₂ − (d₁ × d₂) ÷ 100.

Marked Price & Selling Price Relationship

Discount is always calculated on the Marked Price (MP). The Selling Price (SP) is strictly defined as MP minus the total Discount.

Three Successive Discounts

For three successive discounts, first calculate the effective discount of the first two. Then apply the same formula using that result and the third discount to find the final effective equivalent percentage.

The correct answer is 99.

Key Points

• India's ranking in the Sustainable Development Goals (SDG) Index for the year 2025 was 99, as per the Sustainable Development Report released in June 2025.
• The Sustainable Development Goals Index measures the progress of countries in achieving the 17 SDGs adopted by the United Nations in 2015.
• India showed improvement in areas such as renewable energy adoption, sanitation coverage, and access to basic services.
• Challenges remain in areas like climate action, gender equality, and quality education, which impacted India's overall ranking.
• The report is published annually by the Sustainable Development Solutions Network (SDSN) and tracks global progress toward achieving the SDGs.

Additional Information

• Sustainable Development Goals (SDGs)
• The SDGs are a set of 17 global goals aimed at addressing social, economic, and environmental challenges by 2030.
• They include goals such as no poverty, zero hunger, quality education, and climate action.
• Adopted by all United Nations member states in 2015, they provide a framework for sustainable global development.
• Sustainable Development Report
• The report is an annual publication that evaluates countries based on their progress toward achieving the SDGs.
• It includes the SDG Index, which ranks countries based on their performance across the 17 goals.
• Prepared by the Sustainable Development Solutions Network (SDSN) and experts from academia and research institutions.
• India’s Initiatives for SDGs
• Programs like Swachh Bharat Abhiyan, Ayushman Bharat, and National Solar Mission contribute to achieving SDGs in health, sanitation, and clean energy.
• India has been actively working on sustainable development through its National Action Plan on Climate Change (NAPCC).
• Challenges remain in areas like reducing greenhouse gas emissions and improving gender equality.
• Global Ranking Trends
• Nordic countries like Finland, Sweden, and Denmark often top the SDG Index due to their advanced social policies and environmental sustainability.
• Developing countries face challenges in achieving SDGs due to resource constraints and socio-economic disparities.

The correct answer is Value Added Tax (VAT).

Key Points

• Value Added Tax (VAT) is an indirect tax levied on goods and services at each stage of production or distribution, based on the value added at that stage.
• It is collected by businesses on behalf of the government and is included in the price paid by consumers, making it an indirect tax.
• Unlike direct taxes such as income tax or corporate tax, VAT is not paid directly by individuals but is included in the price of goods and services.
• Direct taxes, such as income tax, corporate tax, and tax on capital gains, are paid directly by individuals or entities to the government based on their income or earnings.
• The primary difference lies in the point of incidence: direct taxes are levied on income/profits, while indirect taxes like VAT are levied on consumption.

Additional Information

• Direct Taxes:
• Direct taxes are levied directly on the income or wealth of individuals, companies, or other entities.
• Examples include income tax, corporate tax, and capital gains tax.
• These taxes are progressive, meaning higher income earners pay a larger proportion.
• Indirect Taxes:
• Indirect taxes are levied on goods and services, and the burden is passed on to the final consumer.
• Examples include VAT, Goods and Services Tax (GST), excise duty, and customs duty.
• These taxes are regressive, as all consumers, regardless of their income level, pay the same rate.
• Value Added Tax (VAT):
• VAT is a consumption tax placed on a product whenever value is added at any stage of the supply chain.
• It is implemented in most countries, but India now uses Goods and Services Tax (GST), which subsumes VAT.
• VAT ensures tax collection at multiple points in the production and distribution process.
• Goods and Services Tax (GST):
• GST replaced VAT and other indirect taxes in India in July 2017.
• It is a unified tax system that simplifies indirect taxation by combining multiple taxes into one.
• GST is categorized into CGST, SGST, and IGST, based on intrastate and interstate transactions.

Shortcut Trick

By applying the successive percentage formula: Net % change = a + b + (a × b) ÷ 100

Here, a = +15 (price increase) and b = −8 (discount).

⇒ Net change = 15 − 8 − (15 × 8) ÷ 100

⇒ Net change = 7 − 1.2 = 5.8%

∴ The correct answer is 5.8%.

Alternate Method

Given:

Initial price increase = 15%

Discount applied afterwards = 8%

Method Used:

Let the initial price of the product be 100 units. We apply the changes sequentially.

         100 Initial  115 Increased  105.8 Final  +15%  −8%   Net: +5.8%

Calculation:

⇒ Price after 15% increase = 100 + (15% of 100)

⇒ Increased price = 100 + 15 = 115

⇒ Price after 8% discount = 115 − (8% of 115)

⇒ Discount amount = (8 ÷ 100) × 115 = 9.2

⇒ Final price = 115 − 9.2 = 105.8

⇒ Net increase = Final price − Initial price

⇒ Net increase = 105.8 − 100 = 5.8

⇒ Net percentage increase = (5.8 ÷ 100) × 100 = 5.8%

∴ The correct answer is 5.8%.

Additional Information

Successive Percentage Change

When a value is sequentially changed by a% and b%, the overall effect is given directly by: Net Change = (a + b + a × b ÷ 100)%. Use positive signs for percentage increases and negative signs for decreases (or discounts).

Multiplying Factor Method

For multiple successive percentage changes, you can simply convert each percentage to a decimal factor: Final Value = Initial Value × (1 ± a/100) × (1 ± b/100).

Equivalent Single Discount

If a shopkeeper offers two successive discounts of x% and y%, the single effective discount is calculated as: Equivalent Discount = (x + y − x × y ÷ 100)%.

Shortcut Trick

Apply the BODMAS rule directly to the expression to solve division first, then multiplication, then addition.

Part 1: 0.848 ÷ 0.8 × 1/2 = 1.06 × 0.5 = 0.53

Part 2: 0.125 ÷ 5/2 × 0.4 = 0.125 × 2/5 × 0.4 = 0.05 × 0.4 = 0.02

Total = 0.53 + 0.02 = 0.55

∴ The correct answer is 0.55.

Alternate Method

Given:

Expression: 0.848 ÷ 0.8 × 1/2 + 0.125 ÷ 5/2 × 0.4

Method Used:

BODMAS Rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction)

Calculations:

⇒ 0.848 ÷ 0.8 × 1/2 + 0.125 ÷ 5/2 × 0.4

⇒ (0.848 ÷ 0.8) × 1/2 + (0.125 ÷ 2.5) × 0.4

⇒ 1.06 × 0.5 + 0.05 × 0.4

⇒ 0.53 + 0.02

⇒ 0.55

∴ The correct answer is 0.55.

Additional Information

BODMAS Rule

The rule dictates the order of operations: Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

Dividing by Fractions

To divide by a fraction, multiply by its reciprocal. Example: A ÷ (B/C) = A × (C/B).

Decimal Multiplication

Multiply as whole numbers, then position the decimal point so the total decimal places match the sum of decimal places in the multiplied numbers.

Shortcut Trick

Multiply the ratio parts directly by their new percentage equivalents.

First employee's new salary equivalent = 3 × 110% = 330%

Second employee's new salary equivalent = 4 × 120% = 480%

New Ratio = 330% : 480% = 33 : 48 = 11 : 16

∴ The correct answer is 11 : 16.

Alternate Method

Given:

⇒ Initial ratio of salaries = 3 : 4

⇒ Increase in first employee's salary = 10%

⇒ Increase in second employee's salary = 20%

Employee 1 (10% Increase)

Old = 300x

New = 330x

Employee 2 (20% Increase)

Old = 400x

New = 480x

New Ratio = 330x : 480x = 11 : 16

Calculations:

⇒ To simplify percentage calculations, let the initial salaries of the first and second employees be 300x and 400x respectively.

⇒ New salary of the first employee = 300x + (10% of 300x)

⇒ New salary of the first employee = 300x + 30x = 330x

⇒ New salary of the second employee = 400x + (20% of 400x)

⇒ New salary of the second employee = 400x + 80x = 480x

⇒ New ratio of their salaries = 330x : 480x

⇒ Simplifying the ratio by dividing both sides by 30x:

⇒ New ratio = 11 : 16

∴ The correct answer is 11 : 16.

Additional Information

Ratio Simplification

A ratio remains unchanged if both of its terms are multiplied or divided by the same non-zero number. For instance, a : b = (a × k) : (b × k).

Percentage Increase

When a value is increased by R%, the new value becomes (100 + R)% of the original value. Final Value = Initial Value × (100 + R) ÷ 100.

Compound Ratio

If two ratios are a : b and c : d, then their compound ratio is formed by multiplying the antecedents and consequents respectively, resulting in (a × c) : (b × d).

The correct answer is All 1, 2, 3 and 4.

Key Points

• The legislative relations between the Centre and States in India are governed by Part XI of the Constitution, specifically Articles 245 to 255.
• Territorial extent of legislation: Article 245 specifies the extent of laws made by the Parliament and the State Legislatures within their respective territories.
• Distribution of legislative subjects: The Constitution lists subjects under the Union List, State List, and Concurrent List (Schedule VII), assigning legislative powers accordingly.
• Parliamentary legislation in state matters: Articles 249, 250, and 252 allow Parliament to legislate on matters in the State List under special circumstances like national interest or state consent.
• Centre's control over state legislation: Article 254 ensures that in case of conflict between a state law and central law on a Concurrent List subject, the central law prevails.

Additional Information

• Union List: Contains subjects on which only the Parliament can legislate, including defense, foreign affairs, atomic energy, etc.
• State List: Contains subjects on which State Legislatures have exclusive power to legislate, such as police, public health, agriculture, etc.
• Concurrent List: Includes subjects like education, marriage, trade unions, etc., where both the Centre and States can make laws. However, central law prevails in case of conflict.
• Residuary Powers: Matters not enumerated in any of the lists fall under the purview of the Parliament as per Article 248.
• President's role: State legislation on certain matters may require the President’s assent, especially if it affects the Centre-State legislative framework.

The correct answer is Wildlife Conservation Finance: Investing in People and Planet.

Key Points

• World Wildlife Day 2025 was observed with the theme Wildlife Conservation Finance: Investing in People and Planet, emphasizing the importance of financial investments in conserving wildlife and supporting human livelihoods.
• This theme highlights the role of sustainable financing mechanisms to address biodiversity loss and ecosystem degradation.
• The event aims to foster global collaboration to ensure the protection of wildlife species and habitats through innovative funding solutions.
• World Wildlife Day is an annual event proclaimed by the United Nations General Assembly (UNGA) in 2013 to celebrate and raise awareness of the world's wild fauna and flora.
• The theme aligns with the UN's Sustainable Development Goals (SDGs), particularly Goal 15: Life on Land, which focuses on protecting, restoring, and promoting sustainable use of terrestrial ecosystems.

Additional Information

• Wildlife Conservation Finance
• It refers to financial strategies, investments, and mechanisms aimed at conserving biodiversity and wildlife habitats.
• Examples include carbon credits, biodiversity offsets, environmental impact bonds, and private-sector financing.
• Innovative approaches such as nature-based solutions help integrate conservation efforts with sustainable economic growth.
• Importance of Biodiversity
• Biodiversity ensures ecosystem resilience, providing essential services such as pollination, water purification, and climate regulation.
• It underpins food security, health, and livelihoods for billions of people globally.
• Protecting biodiversity is critical to combating climate change and achieving sustainable development goals.
• Sustainable Development Goals (SDGs)
• The SDGs are a set of 17 global goals adopted by the UN in 2015 to address challenges such as poverty, inequality, and climate change.
• Goal 15 focuses on "Life on Land" to protect, restore, and promote sustainable use of terrestrial ecosystems.
• SDGs provide a framework for governments, businesses, and communities to work towards a sustainable future.
• United Nations General Assembly Resolution 68/205
• This resolution declared March 3 as World Wildlife Day to celebrate and raise awareness of wildlife globally.
• March 3 commemorates the signing of the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES) in 1973.
• CITES is an international agreement aimed at ensuring that the trade of wild animals and plants does not threaten their survival.

The correct answer is Agnishodh, the Indian Army Research Cell (IARC).

Key Points

• The Indian Army inaugurated Agnishodh, the Indian Army Research Cell (IARC), at IIT Madras in August 2025.
• The facility aims to bridge military requirements with advanced academic research to develop cutting-edge solutions.
• The Research Cell is a collaborative effort between the Indian Army and IIT Madras under the Defence Research and Development Organisation (DRDO).
• Its focus areas include Artificial Intelligence, Quantum Computing, Autonomous Systems, and Modern Military Technologies.
• General Upendra Dwivedi, the Chief of the Army Staff (COAS), inaugurated the facility, marking a significant step towards military-academic partnership.

Additional Information

• Indian Army Research Cell (IARC):
• A specialized research hub aimed at leveraging academic expertise for military advancements.
• It focuses on innovations in areas such as cybersecurity, unmanned aerial systems, and defense technologies.
• Promotes collaboration between scientists, academicians, and military experts.
• Role of IIT Madras in Defense Research:
• Renowned for its contributions in technology and engineering research, including defense applications.
• Collaborates with DRDO and other defense agencies on advanced projects.
• IIT Madras hosts several defense-focused labs, including those for AI and autonomous systems.
• Quantum Computing and Military Applications:
• Quantum computing has the potential to revolutionize encryption, secure communication, and data analysis.
• It enhances decision-making capabilities in complex battlefield scenarios.
• India is investing heavily in quantum research under national initiatives like the Quantum Mission.
• Artificial Intelligence in Defense:
• AI-based systems are being developed for autonomous drones, surveillance, and threat detection.
• AI enables real-time battlefield analysis for better operational strategies.
• India’s defense sector is increasingly adopting AI technologies for modern warfare.

Shortcut Trick

Ratio of number of students = 30 : 20 = 3 : 2.

Let the base average be 70; deviation of the second group = 80 − 70 = +10.

Average increase = (Deviation × Parts) ÷ Total parts = (10 × 2) ÷ (3 + 2) = +4.

Combined average = 70 + 4 = 74.

∴ The correct answer is 74 marks.

Alternate Method

Given:

Number of students in group 1 (n₁) = 30

Average marks of group 1 (A₁) = 70

Number of students in group 2 (n₂) = 20

Average marks of group 2 (A₂) = 80

Formula Used:

Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂)

Group 1: 30 Students Avg Marks = 70

Group 2: 20 Students Avg Marks = 80

Combined Average = 74

Calculations:

⇒ Total marks of group 1 = 30 × 70 = 2100

⇒ Total marks of group 2 = 20 × 80 = 1600

⇒ Total marks of both groups = 2100 + 1600 = 3700

⇒ Total number of students = 30 + 20 = 50

⇒ Combined Average = 3700 ÷ 50

⇒ Combined Average = 74

∴ The correct answer is 74 marks.

Additional Information

Weighted Average

When combining multiple groups, the overall average is computed as A_w = (w₁x₁ + w₂x₂) ÷ (w₁ + w₂), where w corresponds to the weight or sample size of each component.

Deviation Method

Calculations can be simplified by assuming an arbitrary base average, determining the net sum of positive and negative deviations from it, and distributing this net deviation equally across all elements.

Alligation Approach

The rule of alligation can also be utilized to discover the ratio in which two groups must be combined. It works on the principle that Ratio = (A₂ − A_c) : (A_c − A₁).

The correct answer is Bhutan.

Key Points

• Bhutan is unique for being a constitutional monarchy with a king referred to as the 'Dragon King' or Druk Gyalpo in Dzongkha, the official language of Bhutan.
• The monarchy was established in Bhutan in 1907, with Ugyen Wangchuck being the first king.
• The current king, Jigme Khesar Namgyel Wangchuck, ascended the throne in 2006 and is known for his progressive policies and focus on Gross National Happiness (GNH).
• The concept of Gross National Happiness was introduced as a guiding philosophy by Bhutan's monarchy to prioritize well-being over economic growth.
• Bhutan's monarchy is deeply respected and plays a significant role in the country's political and cultural identity.

Additional Information

• Constitutional Monarchy:
• A form of monarchy where the monarch's powers are limited by a constitution, ensuring democratic governance alongside the royal institution.
• Bhutan transitioned to a constitutional monarchy in 2008, with the adoption of its first constitution.
• Gross National Happiness (GNH):
• A development philosophy introduced by Bhutan that prioritizes collective happiness and well-being over material wealth.
• GNH focuses on sustainable development, environmental conservation, cultural preservation, and good governance.
• Druk Gyalpo:
• The title 'Druk Gyalpo' translates to 'Dragon King' and symbolizes Bhutan's identity as the 'Land of the Thunder Dragon.'
• The term 'Druk' refers to the mythical thunder dragon, an important symbol in Bhutanese culture.
• Bhutan's Political System:
• Bhutan has a two-tier parliamentary system, consisting of the National Council and the National Assembly.
• The king's role is primarily ceremonial, with executive powers vested in elected representatives.

The correct answer is It increases.

Key Points

• The speed of sound in a medium increases with the rise in temperature because the molecules of the medium move faster, enhancing the transmission of sound waves.
• In gases, the speed of sound is directly proportional to the square root of the absolute temperature (v ∝ √T), as per the formula v = √(γRT/M), where T is the temperature in Kelvin.
• An increase in temperature reduces the density of the medium, which also contributes to the increased speed of sound.
• For every 1°C rise in temperature, the speed of sound in air increases by approximately 0.6 m/s.
• The relationship between speed of sound and temperature is particularly significant in gases but less pronounced in liquids and solids.

Additional Information

• Speed of Sound:
• The speed of sound depends on the medium through which it travels: it is fastest in solids, slower in liquids, and slowest in gases.
• For example, in air at 20°C, the speed of sound is approximately 343 m/s, while in water, it is around 1,480 m/s, and in steel, it is about 5,960 m/s.
• Factors Affecting Speed of Sound:
• Temperature: Higher temperatures lead to a higher speed of sound due to increased molecular activity.
• Density: Lower density usually results in higher speeds in gases, while in solids and liquids, the relationship is more complex.
• Elasticity: A medium with higher elasticity transmits sound faster.
• Formula for Speed of Sound in Gases:
• The formula is v = √(γRT/M), where:
• γ: Adiabatic index (ratio of specific heats).
• R: Universal gas constant.
• T: Absolute temperature in Kelvin.
• M: Molar mass of the gas.
• Practical Applications:
• Understanding the speed of sound is crucial in fields like meteorology, aviation, and acoustics.
• The temperature dependence of sound speed is used in weather forecasting and studying atmospheric layers.

The correct answer is Because particles absorb latent heat from the surroundings during evaporation.

Key Points

• Evaporation is a surface phenomenon where particles at the surface of a liquid absorb energy and change into the gaseous state.
• During evaporation, particles absorb latent heat from their surroundings, which lowers the temperature of the surroundings and causes cooling.
• Latent heat is the energy required for a substance to change its state without a change in its temperature.
• Evaporation occurs faster in conditions such as higher temperature, increased surface area, lower humidity, and faster wind speed.
• This cooling effect is commonly observed in daily life, such as sweating, where evaporation helps regulate body temperature.

Additional Information

• Latent Heat:
• It is the heat energy absorbed or released during a phase change without altering the temperature.
• Types include latent heat of fusion (solid to liquid) and latent heat of vaporization (liquid to gas).
• Factors Affecting Evaporation:
• Temperature: Higher temperatures increase the rate of evaporation.
• Surface Area: Larger surface areas allow more particles to evaporate simultaneously.
• Humidity: Lower humidity increases evaporation as the air can hold more water vapor.
• Wind Speed: Faster winds remove water vapor from the surface, enhancing evaporation.
• Applications of Evaporation:
• Evaporation is used in cooling systems like air coolers and refrigerators.
• It plays a key role in the water cycle, contributing to cloud formation and precipitation.
• Industrial processes such as salt extraction rely on evaporation.
• Evaporation vs Boiling:
• Evaporation occurs at any temperature and only at the surface of the liquid.
• Boiling occurs at a specific temperature (boiling point) and throughout the liquid.

The correct answer is Panthalassa.

Key Points

• Panthalassa was the vast, global ocean that surrounded the supercontinent Pangaea during the late Paleozoic and early Mesozoic eras.
• The name Panthalassa is derived from Greek, meaning "all sea" (pan = all, thalassa = sea).
• It played a crucial role in shaping Earth's climate and ocean currents during the time of Pangaea’s existence, approximately 335 to 175 million years ago.
• As Pangaea began to break apart, Panthalassa gradually transformed into the Pacific Ocean, the largest ocean on Earth today.
• Panthalassa's size and characteristics significantly influenced the formation of new continents and the evolution of marine species.

Additional Information

• Pangaea
• Pangaea was a supercontinent that existed during the late Paleozoic and early Mesozoic eras.
• It began forming around 335 million years ago and started breaking apart about 175 million years ago.
• The breakup of Pangaea led to the formation of the current continents and oceans.
• Tethys Ocean
• The Tethys Ocean was a smaller body of water that existed on the eastern side of Pangaea.
• It eventually gave rise to the present-day Mediterranean, Black, and Caspian Seas.
• Laurasia and Gondwana
• Pangaea split into two major landmasses: Laurasia in the northern hemisphere and Gondwana in the southern hemisphere.
• Laurasia included the present-day continents of North America, Europe, and Asia, while Gondwana consisted of South America, Africa, Antarctica, Australia, and India.
• Plate Tectonics
• The breakup of Pangaea was driven by the movement of Earth's tectonic plates.
• Continental drift, caused by convection currents in the Earth's mantle, led to the gradual separation and current positions of continents.

The correct answer is 255 – Represents the number of characters in the default font that fit in a cell.

Key Points

• The maximum column width in MS Excel 2019 is 255, which defines the number of characters of the default font that can fit in a single cell.
• This width is measured in terms of the number of digits of the default font that can be displayed in a cell when zoomed to 100%.
• A column width of 1 equals the width of one digit of the default font size, typically Arial 10-point.
• Although the column width is limited to 255, the cell content can still store up to 32,767 characters, but not all will be visible without adjusting column width or using text wrapping.
• Setting an optimal column width ensures better visibility and readability of data in Excel worksheets.

Additional Information

• Row Height in Excel:
• The maximum row height in MS Excel is 409 points.
• This measurement is based on the height of characters in the default font size.
• Cell Character Limit:
• Each cell in MS Excel can store a maximum of 32,767 characters.
• However, only 1,024 characters are visible in a cell unless text wrapping or merging is applied.
• Pixel and Point Relationship:
• A point is a unit of measurement equivalent to 1/72 of an inch.
• Pixels represent the resolution of a display, and their size varies depending on the monitor's DPI (dots per inch).
• Adjusting Column Width:
• Column width can be adjusted manually by dragging the column boundary or automatically using the "AutoFit Column Width" feature.
• AutoFit adjusts the column width to fit the longest entry in the column.
• Excel Default Settings:
• The default column width in Excel is 8.43, which equals the width of 8 characters in the default font.
• The default row height is 15 points, sufficient to display a single line of text in the default font size.

Shortcut Trick

Total effective interest rate for 2 years = Rate × Time = 5% × 2 = 10%

Simple Interest = 10% of Principal

SI = (10 ÷ 100) × 5000 = 500

∴ The correct answer is ₹500.

Alternate Method

Given:

Principal (P) = ₹5,000

Rate (R) = 5% per annum

Time (T) = 2 years

Formula Used:

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

₹5000 Principal

5% p.a. for 2 years Total Interest = 10%

₹500 Simple Interest

Calculation:

⇒ SI = (5000 × 5 × 2) ÷ 100

⇒ SI = (5000 × 10) ÷ 100

⇒ SI = 50000 ÷ 100

⇒ SI = 500

∴ The correct answer is ₹500.

Additional Information

Compound Interest (CI)

When interest is compounded annually, Amount (A) = P × (1 + R÷100)^T and CI = A − P.

Difference between CI and SI

For 2 years, the difference between CI and SI on a certain principal P at a rate of R% is given by the formula: Difference = P × (R÷100)².

Amount in Simple Interest

The total amount at the end of the period is the sum of principal and interest: A = P + SI = P × [1 + (R × T)÷100].

The logic follows here,

Similarly,

Hence, the correct answer is "Option 1"

The correct answer is transpiration.

Key Points

• Transpiration is the process by which water evaporates from the aerial parts of plants, primarily through the stomata present in leaves.
• The evaporation of water creates a negative pressure or suction force, known as the transpiration pull, which helps to draw water upward through the xylem vessels.
• Transpiration plays a crucial role in maintaining the flow of water and nutrients from the roots to the leaves and other parts of the plant.
• This process is most significant in tall plants, where the force generated by transpiration pull is essential to overcome gravity and transport water to the top.
• Environmental factors such as temperature, humidity, wind, and light intensity influence the rate of transpiration.

Additional Information

• Xylem
• Xylem is the vascular tissue responsible for transporting water and dissolved minerals from the roots to the rest of the plant.
• It consists of specialized cells such as tracheids and vessel elements that facilitate the movement of water.
• The cohesion and adhesion properties of water molecules play a key role in maintaining the continuous water column in xylem vessels.
• Root Pressure
• Root pressure is a positive pressure generated by the active absorption of nutrients and water by root cells.
• Although root pressure contributes to water movement, it is insufficient for tall plants and is only effective in smaller plants.
• Guttation
• Guttation is the exudation of water droplets from the edges of leaves, typically occurring at night or under conditions of high soil moisture and low transpiration.
• It should not be confused with transpiration, which is the evaporation of water vapor from plant surfaces.
• Osmosis
• Osmosis is the passive movement of water molecules across a semi-permeable membrane from a region of low solute concentration to a region of high solute concentration.
• While osmosis is critical for water absorption by root cells, it does not contribute to the upward movement of water in tall plants.

Given: Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week.

• Q has an exam on Thursday.

• Exactly four people have their exam between U and P, neither of whom has an exam on Sunday.

• R has an exam immediately before S.

• V does not have an exam on Friday.

• U does not have an exam after S

• The Final Arrangement is

• | Monday | U | | --- | --- | | Tuesday | R | | Wednesday | S | | Thursday | Q | | Friday | T | | Saturday | P | | Sunday | V |

• Only one person have exams after P is V.

Hence, the correct answer is "Option 2"

The logic here is ,

Hence, the correct answer is "Option 3"

Shortcut Trick

Use the direct ratio formula combining discount, profit and free articles:

CP / MP = [(100 − D%) / (100 + P%)] × [Paid Quantity / Total Quantity]

CP / MP = [(100 − 10) / (100 + 35)] × [15 / (15 + 4)]

CP / MP = (90 / 135) × (15 / 19) = (2 / 3) × (15 / 19) = 10 / 19

Markup % = [(19 − 10) / 10] × 100 = 90%

∴ The correct answer is 90%.

Alternate Method

Given:

Discount given by trader = 10%

Free articles = 4 for every 15 bought

Paid articles by customer = 15

Overall transaction profit = 35%

Formula Used:

Total Selling Price (SP) = Total Cost Price (CP) × (100 + Profit)% / 100

Total SP = Paid articles × MP × (100 − Discount)% / 100

Total CP 19 × CP

+35% Profit

Total SP 19 × 1.35 CP

Total SP 15 × 0.9 MP

Equate

15 Paid + 4 Free Total = 19 Articles

13.5 MP = 25.65 CP ⇒ MP = 1.9 CP

Calculation:

⇒ Let the Cost Price of 1 article be CP and Marked Price be MP.

⇒ Total articles given to the customer = 15 (paid) + 4 (free) = 19 articles.

⇒ Total Cost Price for the trader = 19 × CP

⇒ Since discount is 10%, Selling Price of 1 article = 90% of MP = 0.9 MP.

⇒ Total Selling Price obtained by the trader = 15 × 0.9 MP = 13.5 MP

⇒ Given that overall profit is 35%:

⇒ Total SP = Total CP × 135%

⇒ 13.5 MP = 19 CP × 1.35

⇒ 13.5 MP = 25.65 CP

⇒ MP / CP = 25.65 / 13.5 = 1.9

⇒ This means MP is 190% of CP, which is 90% more than CP.

∴ The correct answer is 90%.

Additional Information

Marked Price and Discount

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

Buy X Get Y Free

The equivalent discount percentage when a trader gives Y items free on buying X items is given by [Y ÷ (X + Y)] × 100.

Direct Relationship between CP and MP

When no free items are given, the direct ratio between CP and MP is: CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%).

A, B, C, D, X and Y each scored different marks. Only two people have scored more than A. 

Only B has scored less than D. X has scored more than Y but less than C. 

Only one people have scored more than X is C

Hence, the correct answer is "Option 1"

Mistake Points 

When it is stated that 'Only B has scored less than D', it mathematically means every other person (A, C, X, Y) must have scored more than D. This places B at the 6th position and D at the 5th.

Combining this with other clues,

Thus, the order is C > X > A > Y > D > B.

Shortcut Trick

Solve directly by expanding powers and roots using BODMAS:

⇒ 6² + √(2²) − 5√25 − 11

⇒ 36 + 2 − 5 × 5 − 11

⇒ 38 − 25 − 11

⇒ 38 − 36 = 2

∴ The correct answer is 2.

Alternate Method

Given:

Expression: 6² + √(2²) − 5√25 − 11

Concept Used:

BODMAS Rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction)

Calculations:

⇒ Evaluate the powers and roots first (Orders):

⇒ 6² = 36

⇒ √(2²) = √4 = 2

⇒ √25 = 5

⇒ Substitute these evaluated terms back into the main expression:

⇒ 36 + 2 − 5 × 5 − 11

⇒ Perform multiplication:

⇒ 36 + 2 − 25 − 11

⇒ Perform addition and subtraction from left to right:

⇒ 38 − 25 − 11

⇒ 38 − 36

⇒ 2

∴ The correct answer is 2.

Additional Information

BODMAS Rule

The fundamental order of mathematical operations is Brackets, Orders (powers and roots), Division, Multiplication, Addition, and Subtraction.

Perfect Squares and Roots

Memorizing basic squares up to 30 significantly helps speed up simplification calculations. For instance, the principal square root of x² is x for any positive number.

Simplifying Multiple Subtractions

When an expression contains multiple numbers to be subtracted consecutively, you can add all the negative terms first and then subtract the sum. For example, −25 − 11 = −(25 + 11) = −36.

The correct answer is 73rd Amendment.

Key Points

• The 73rd Constitutional Amendment Act, passed in 1992, introduced provisions for the establishment of Panchayati Raj institutions in India.
• It mandated the reservation of one-third of seats for women, including the position of chairpersons, in Panchayati Raj institutions.
• This amendment added Part IX to the Constitution, titled "The Panchayats," and a new Schedule, Schedule XI, enumerating 29 subjects under the Panchayati Raj's jurisdiction.
• The amendment aimed at empowering women and ensuring their active participation in local self-governance.
• The reservation for women was designed to enhance political representation and decision-making capabilities for women in rural governance.

Additional Information

• Part IX of the Constitution:
• Part IX was introduced through the 73rd Amendment, focusing on rural self-governance through Panchayati Raj institutions.
• The Gram Sabha serves as the foundation of the Panchayati Raj system.
• It stipulates a three-tier structure: Gram Panchayat at the village level, Panchayat Samiti at the block level, and Zila Parishad at the district level.
• Reservation for Women in Local Governance:
• The provision for reservation of seats for women in Panchayati Raj institutions aims to enhance women's representation in politics.
• One-third of the total seats, including the positions of chairpersons, are reserved for women across all levels.
• This reservation is applicable to Scheduled Castes and Scheduled Tribes as well.
• Schedule XI:
• It lists 29 functional items that Panchayati Raj institutions are responsible for, such as agriculture, education, health, sanitation, and rural development.
• These subjects enable decentralized governance and decision-making at the local level.
• Impact of the 73rd Amendment:
• It strengthened grassroots democracy and decentralized governance.
• The amendment empowered marginalized groups, including women, Scheduled Castes, and Scheduled Tribes, to participate in governance.
• This institutionalized local self-government, making it a constitutional mandate.

The correct answer is National Cooperative Consumers' Federation of India.

Key Points

• The National Cooperative Consumers' Federation of India (NCCF) is an apex organization of consumer cooperatives in the country.
• It was established in 1965 under the Multi-State Cooperative Societies Act.
• NCCF is primarily responsible for promoting the distribution of essential commodities, including food items, to consumers at reasonable prices.
• The organization works to stabilize market prices and ensure the availability of goods, especially during times of crisis or shortage.
• NCCF supports initiatives like mobile van distribution of essential goods, as seen in Mumbai during September 2025, to make items like onions accessible at subsidized rates.

Additional Information

• Consumer Cooperatives in India:
• Consumer cooperatives are set up to ensure the supply of essential items at reasonable prices to the public.
• They operate through a network of retail outlets, wholesale centers, and mobile distribution systems.
• Multi-State Cooperative Societies Act:
• This Act governs the functioning of multi-state cooperatives like NCCF.
• It provides a legal framework for cooperatives operating in more than one state in India.
• Role of NCCF in Crisis Management:
• NCCF plays a critical role in stabilizing prices of essential commodities during times of inflation or shortage.
• It procures items directly from producers and ensures efficient distribution to consumers.
• Subsidized Food Programs:
• Subsidized food distribution programs are aimed at providing food items at affordable prices to the economically weaker sections of society.
• These programs help mitigate the impact of price hikes on essential commodities.

The correct answer is Ctrl + O.

Key Points

• The Ctrl + O shortcut is commonly used in Microsoft Office applications, including MS PowerPoint 2019, to open the "Open" dialog box for selecting files.
• Using Ctrl + O directly navigates users to the file selection interface without accessing menus manually.
• This shortcut enhances productivity by reducing the need for mouse clicks and allows quick access to previously saved files.
• It is a universally recognized shortcut in most Microsoft Office products, including Word, Excel, and PowerPoint.
• Ctrl + O is part of the essential keyboard shortcuts recommended for efficient software navigation in Microsoft Office tools.

Additional Information

• Keyboard Shortcuts in MS PowerPoint:
• Ctrl + S: Saves the current presentation.
• Ctrl + N: Creates a new presentation.
• Ctrl + P: Opens the print dialog box.
• Ctrl + M: Adds a new slide to the presentation.
• These shortcuts are designed to improve efficiency and ease of use for users.
• Importance of Shortcuts:
• Shortcuts help reduce reliance on manual menu navigation and allow faster software operation.
• They are especially useful for professionals who handle large-scale presentations regularly.
• Learning key shortcuts ensures better time management and productivity.
• Accessibility Features in MS PowerPoint:
• Microsoft PowerPoint includes accessibility options to support users with disabilities.
• Features include screen reader compatibility, keyboard navigation, and high contrast mode.
• These ensure that PowerPoint remains inclusive and usable for a wide range of users.
• Microsoft Office 2019 Enhancements:
• Improved collaboration features for real-time editing.
• Enhanced tools for data visualization and slide design.
• Integration with cloud services for easier file sharing and storage.

The correct answer is Article 358.

Key Points

• Article 358 of the Indian Constitution provides for the automatic suspension of Fundamental Rights under Article 19 during a National Emergency.
• It applies only when the emergency is proclaimed due to war or external aggression (not in cases of internal disturbance).
• During such emergencies, legislative and executive actions violating Article 19 cannot be challenged in a court of law.
• Article 358 ceases to operate once the Emergency ends, and Article 19 is automatically restored.
• Only rights under Article 19 are affected; other Fundamental Rights remain enforceable unless specifically suspended under Article 359.

Additional Information

• Article 359:
• Allows the President to suspend the right to move courts for enforcement of Fundamental Rights (except Articles 20 and 21) during a National Emergency.
• Unlike Article 358, Article 359 requires a specific presidential order for suspension.
• Article 352:
• Deals with the proclamation of National Emergency in case of war, external aggression, or armed rebellion.
• It forms the constitutional basis for invoking Articles 358 and 359 during emergencies.
• Fundamental Rights:
• These are enshrined in Part III of the Constitution, guaranteeing essential rights to Indian citizens.
• Key rights include the Right to Equality, Right to Freedom, Right to Constitutional Remedies, etc.
• Historical Context:
• The suspension of Fundamental Rights under Articles 358 and 359 was notably applied during the Emergency of 1975-77.
• The Emergency was declared under Article 352 due to "internal disturbance," later amended to "armed rebellion" by the 44th Constitutional Amendment Act, 1978.

Shortcut Trick

The bells will ring together again after the LCM of their individual intervals.

LCM of 12, 15, and 18 = 180 minutes.

180 minutes = 180 ÷ 60 = 3 hours.

Next ringing time = 10:00 a.m. + 3 hours = 1:00 p.m.

∴ The correct answer is 1:00 p.m.

Alternate Method

Given:

Intervals of the three bells = 12, 15, and 18 minutes.

Initial simultaneous ringing time = 10:00 a.m.

Concept Used:

The time after which all bells will ring together again is the Least Common Multiple (LCM) of their individual time intervals.

Calculations:

⇒ Prime factorization of 12 = 2² × 3

⇒ Prime factorization of 15 = 3 × 5

⇒ Prime factorization of 18 = 2 × 3²

⇒ LCM(12, 15, 18) = Highest power of all prime factors = 2² × 3² × 5

⇒ LCM = 4 × 9 × 5 = 180

⇒ Thus, the bells will ring together after 180 minutes.

⇒ Converting minutes into hours: 180 minutes = 180 ÷ 60 = 3 hours

⇒ Next time they ring together = 10:00 a.m. + 3 hours = 1:00 p.m.

∴ The correct answer is 1:00 p.m.

Additional Information

LCM in Real-Life Scenarios

LCM is used to find when different events running at different regular intervals will coincide again, such as bells ringing, traffic lights changing, or runners meeting on a circular track.

HCF vs LCM

HCF (Highest Common Factor) is used to split items into smaller equal sections or to distribute things equally, whereas LCM (Least Common Multiple) is used to find a common future event.

Relation between HCF and LCM

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

Shortcut Trick

Total distance travelled = Average speed × Total time

Average speed for a round trip = (2 × S_d × S_u) ÷ (S_d + S_u)

Average speed = (2 × 125 × 25) ÷ (125 + 25) = 6250 ÷ 150 = 125/3 km/hr

Total distance = (125/3) × 25 = 3125/3 km = 1041²/₃ km.

∴ The correct answer is 1041²/₃ km.

Alternate Method

Given:

Downstream speed (S_d) = 125 km/hr

Upstream speed (S_u) = 25 km/hr

Total time taken (T) = 25 hours

Downstream: 125 km/hr   Upstream: 25 km/hr Distance D Total Time = 25 hrs

Formula Used:

Time = Distance ÷ Speed

Total Time = (Distance ÷ S_d) + (Distance ÷ S_u)

Calculation:

⇒ Let the one-way distance be D km.

⇒ Total time = (D ÷ 125) + (D ÷ 25)

⇒ 25 = (D + 5D) ÷ 125

⇒ 25 = 6D ÷ 125

⇒ 6D = 25 × 125

⇒ 6D = 3125

⇒ D = 3125 ÷ 6 km

⇒ Total distance travelled by boat = 2D

⇒ Total distance = 2 × (3125 ÷ 6) = 3125 ÷ 3 km

⇒ Total distance = 1041²/₃ km.

∴ The correct answer is 1041²/₃ km.

Additional Information

Speed of Boat in Still Water

Speed of boat (u) = (Downstream Speed + Upstream Speed) ÷ 2

Speed of Stream

Speed of stream (v) = (Downstream Speed − Upstream Speed) ÷ 2

Average Speed

When equal distances are covered at speeds x and y, the Average Speed = (2 × x × y) ÷ (x + y)

The correct answer is Process Control Block.

Key Points

• A Process Control Block (PCB) is a data structure in the operating system that stores information about a process.
• PCB contains important details such as the process ID, process state, program counter, CPU registers, memory management information, and I/O status.
• It is used by the operating system to track and manage processes during execution.
• Whenever a context switch occurs, the PCB ensures that the state of the process is saved and restored correctly.
• The operating system maintains a PCB for each process to efficiently manage multitasking and resource allocation.

Additional Information

• Process States:
• Processes in an operating system can exist in various states such as New, Ready, Running, Waiting, and Terminated.
• The PCB keeps track of the current state of the process.
• Context Switching:
• Context switching refers to the process of storing the state of one process and loading the state of another process.
• The PCB plays a vital role in saving and restoring process information during context switches.
• Memory Management Information:
• The PCB contains details about the memory allocated to a process, such as page tables or segment tables.
• This information ensures efficient memory usage and prevents conflicts between processes.
• Process Scheduling:
• The operating system uses PCB to determine the priority and scheduling of processes.
• Scheduling decisions are based on information stored in the PCB, such as priority level and execution time.
• Interprocess Communication (IPC):
• PCBs also store information necessary for communication between processes, such as shared memory or message queues.
• Efficient IPC mechanisms are vital for the coordination of processes in a multitasking environment.

Shortcut Trick

If the ratio of two numbers is a : b (where a and b are co-prime) and their HCF is H, then:

LCM = H × a × b

Here, a = 5, b = 4, and H = 5.

LCM = 5 × 5 × 4 = 100

∴ The correct answer is 100.

Alternate Method

Given:

Ratio of two numbers = 5 : 4

HCF of the numbers = 5

HCF = 5

Ratio Part = 5

Ratio Part = 4

LCM = 5 × 5 × 4 = 100

Formula Used:

Number = HCF × Ratio part

LCM = Product of highest powers of all prime factors involved

Calculations:

⇒ Let the two numbers be 5x and 4x, where x is the common factor.

⇒ Since x represents the highest common factor, x = 5.

⇒ First number = 5 × 5 = 25

⇒ Second number = 4 × 5 = 20

⇒ Now, finding the LCM of 25 and 20 using prime factorization:

⇒ 25 = 5²

⇒ 20 = 2² × 5

⇒ LCM = 2² × 5²

⇒ LCM = 4 × 25 = 100

∴ The correct answer is 100.

Additional Information

Product Rule of HCF and LCM

The product of two numbers is always equal to the product of their HCF and LCM. Formula: N₁ × N₂ = HCF × LCM.

Relation between HCF and LCM

The HCF of two or more numbers is always a direct factor of their LCM. Thus, the LCM is always completely divisible by the HCF.

Co-prime Ratio Rule

When the ratio of two numbers is a : b (where a and b are co-prime), the numbers are H×a and H×b, and their LCM is derived directly as H×a×b.

Statements:

(I) Rahul was born when his father was 33 years old.

This only gives a relationship between Rahul’s age and his father’s age, not their actual ages.

So alone, it is not sufficient.

(II) Rahul is 29 years younger than his mother.

This gives a difference between Rahul’s age and his mother’s age, but not the actual ages.

So alone, it is not sufficient.

Combining (I) and (II):

From I: Father’s age = Rahul’s age + 33

From II: Mother’s age = Rahul’s age + 29

But still, we don’t know either parent’s current age — no absolute value is provided.

So, even together, the data are not sufficient to find Rahul’s age.

Hence, the correct answer is "Option 1"

The number of ministerswho are Managers but NOT Engineers is shaded in given below figure:

Hence, the correct answer is "Option 3"

The logic follows here,

All follow the same logic except RSW.

Hence, the correct answer is "Option 1"

Shortcut Trick

Effective CI rate for 2 years = X + Y + (X × Y)÷100 %

Effective rate for Scheme 1 (8%) = 8 + 8 + (8 × 8)÷100 = 16.64%

Effective rate for Scheme 2 (6%) = 6 + 6 + (6 × 6)÷100 = 12.36%

Difference in effective rate = 16.64% − 12.36% = 4.28%

Difference in Compound Interest = 4.28% of 25000 = 0.0428 × 25000 = ₹1070

∴ The correct answer is ₹1070.

Alternate Method

Given:

Principal (P) = ₹25,000

Time (T) = 2 years

Rate for Scheme 1 (R₁) = 8% per annum

Rate for Scheme 2 (R₂) = 6% per annum

Formula Used:

Compound Interest (CI) = P × [(1 + R÷100)^T − 1]

P = ₹25,000

8% CI 6% CI

Scheme 1 (8%) Yr 1 Int: 2000 Yr 2 Int: 2160 Total: ₹4160

Scheme 2 (6%) Yr 1 Int: 1500 Yr 2 Int: 1590 Total: ₹3090

Diff = ₹1070

Calculations:

⇒ CI for Scheme 1 = 25000 × [(1 + 8÷100)² − 1]

⇒ CI₁ = 25000 × [1.08² − 1]

⇒ CI₁ = 25000 × [1.1664 − 1] = 25000 × 0.1664

⇒ CI₁ = ₹4160

⇒ CI for Scheme 2 = 25000 × [(1 + 6÷100)² − 1]

⇒ CI₂ = 25000 × [1.06² − 1]

⇒ CI₂ = 25000 × [1.1236 − 1] = 25000 × 0.1236

⇒ CI₂ = ₹3090

⇒ Difference in CI = CI₁ − CI₂

⇒ Difference = 4160 − 3090 = ₹1070

∴ The correct answer is ₹1070.

Additional Information

Effective Rate of CI for 2 Years

For a rate of R% compounded annually, the effective compound interest rate for 2 years is calculated directly as R + R + (R²÷100)%.

Difference Between CI and SI for 2 Years

The difference between Compound Interest and Simple Interest for 2 years on a principal P at rate R% is given by the direct formula Diff = P × (R÷100)².

Difference Between CI and SI for 3 Years

The difference for 3 years is determined by the formula Diff = P × (R÷100)² × (3 + R÷100).

The logic follows here, 

All follow the same logic except NR-GL.

Hence, the correct answer is "Option 3."

Shortcut Trick

When multiplying expressions with the same exponent, directly multiply their bases.

⇒ 7⁻⁸ × 11⁻⁸ × 13⁻⁸ = (7 × 11 × 13)⁻⁸

⇒ (1001)⁻⁸ = 1 / 1001⁸

∴ The correct answer is 1 / 1001⁸.

Alternate Method

Given:

Expression: 7⁻⁸ × 11⁻⁸ × 13⁻⁸

Formula Used:

a^m × b^m × c^m = (a × b × c)^m

a^−m = 1 / a^m

Calculation:

⇒ 7⁻⁸ × 11⁻⁸ × 13⁻⁸

⇒ (7 × 11 × 13)⁻⁸

⇒ (77 × 13)⁻⁸

⇒ 1001⁻⁸

⇒ 1 / 1001⁸

∴ The correct answer is 1 / 1001⁸.

Additional Information

Product of Powers Rule

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

Power of a Power Rule

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

Negative Exponent Rule

A negative exponent means taking the reciprocal of the base raised to a positive power: a^−m = 1 / a^m.

Shortcut Trick

Let the total quantity of goods be 100 units.

The divided parts are: 50 units (+45%), 15 units (+27%), and 35 units (−43%).

Net Profit % = [(50 × 45) + (15 × 27) + (35 × −43)] ÷ 100

Net Profit % = [2250 + 405 − 1505] ÷ 100 = 1150 ÷ 100 = 11.5%

∴ The correct answer is 11.5%.

Alternate Method

Given:

50% of goods sold at 45% profit.

30% of remaining goods sold at 27% profit.

Still remaining goods sold at 43% loss.

50 units +45%

15 units +27%

35 units -43%

Total Base = 100 units Overall Net Profit = 11.5%

Calculations:

⇒ Let the total number of goods be 100 units with each unit costing ₹1.

⇒ Goods in the 1st part = 50% of 100 = 50 units

⇒ Remaining goods = 100 − 50 = 50 units

⇒ Goods in the 2nd part = 30% of 50 = 15 units

⇒ Goods in the 3rd part = Total goods − (1st part + 2nd part) = 100 − (50 + 15) = 35 units

⇒ Overall net profit/loss = (Profit on 1st part) + (Profit on 2nd part) − (Loss on 3rd part)

⇒ Overall net profit/loss = (50 × 45%) + (15 × 27%) − (35 × 43%)

⇒ Overall net profit/loss = 22.5 + 4.05 − 15.05

⇒ Overall net profit/loss = 26.55 − 15.05 = 11.5 units

⇒ Since the total cost price is 100 units, the overall profit percentage is 11.5%.

⇒ Comparing this with x%, the value of x is 11.5.

∴ The correct answer is 11.5%.

Additional Information

Weighted Average Profit & Loss

When a quantity is divided into parts n₁, n₂, ..., n_k and sold at respective profit/loss percentages p₁, p₂, ..., p_k, the overall percentage change is given by the weighted sum: (n₁p₁ + n₂p₂ + ... + n_kp_k) ÷ (n₁ + n₂ + ... + n_k).

Loss Percentage Convention

In profit and loss mixture equations, always treat profit as a positive value (+) and loss as a negative value (−) to easily calculate the net aggregate effect.

Remaining Quantity Calculation

When calculating successive proportions (e.g., "x% of the remaining"), it is essential to subtract the already allocated quantity from the total before calculating the new specific fraction.

Given:

• Namesh starts from point A and drives 4 km towards west.
• He then takes a left turn and drives 5 km.
• He takes a final left turn and drives 6 km and stops at point B.
• Rimit starts from point P, which is 16 km east of Point A, and drives 3 km towards east.
• He then takes a right turn and drives 5 km.
• He takes a final left turn and drives 3 km and stops at Point Q.

The final Diagram,

Shortest distance between Point Q and Point B is 20 km.

Hence, the correct answer is "Option 2"

Shortcut Trick

The given sides of the triangle are 42 cm, 56 cm, and 70 cm.

Ratio of the sides = 42 : 56 : 70 = 3 : 4 : 5.

Since the ratio of the sides follows the Pythagorean triplet (3² + 4² = 5²), the given triangle is a right-angled triangle.

Area of a right-angled triangle = (1/2) × Base × Height.

Area = (1/2) × 42 × 56 = 1176 cm².

∴ The correct answer is 1176 cm².

Alternate Method

56 cm 42 cm 70 cm

Given:

Sides of the triangle, a = 70 cm, b = 56 cm, and c = 42 cm.

Formula Used:

Heron's Formula for Area of a Triangle = √[s(s − a)(s − b)(s − c)]

Where s = Semi-perimeter = (a + b + c) ÷ 2

Calculations:

⇒ s = (70 + 56 + 42) ÷ 2

⇒ s = 168 ÷ 2 = 84 cm

⇒ Area = √[84 × (84 − 70) × (84 − 56) × (84 − 42)]

⇒ Area = √[84 × 14 × 28 × 42]

⇒ Area = √[(42 × 2) × 14 × (14 × 2) × 42]

⇒ Area = √[42² × 14² × 2²]

⇒ Area = 42 × 14 × 2

⇒ Area = 1176 cm²

∴ The correct answer is 1176 cm².

Additional Information

Heron's Formula

Used to find the area of a scalene triangle when all three side lengths are known. This method does not require identifying whether the triangle is right-angled or not.

Pythagorean Triplets

A set of three positive integers (a, b, c) that perfectly satisfy the relation a² + b² = c². Common fundamental triplets include (3, 4, 5), (5, 12, 13), (7, 24, 25), and (8, 15, 17).

Equilateral Triangle Properties

For a triangle with all equal sides (a), the Area = (√3 ÷ 4) × a² and the Altitude/Height = (√3 ÷ 2) × a.

The logic follows here, 

All follow the same logic except G K - IP.

Hence, the correct answer is "Option 4"

Shortcut Trick

For a number to be divisible by 39, it must be divisible by its co-prime factors 3 and 13.

Check divisibility by 3: The sum of digits for 625092 is 6 + 2 + 5 + 0 + 9 + 2 = 24 (Divisible by 3).

Check divisibility by 13: The difference of alternating 3-digit blocks for 625092 is |625 − 092| = 533.

Since 533 ÷ 13 = 41, it is perfectly divisible by 13.

∴ The correct answer is 625092.

Alternate Method

Given:

Options provided: 625649, 622710, 625092, 622776

Formula Used:

Divisibility by 39 = Divisibility by both 3 and 13.

Calculations:

⇒ First, check divisibility by 3 (the sum of all digits must be a multiple of 3).

⇒ 625649: 6 + 2 + 5 + 6 + 4 + 9 = 32 (Not divisible by 3)

⇒ 622710: 6 + 2 + 2 + 7 + 1 + 0 = 18 (Divisible by 3)

⇒ 625092: 6 + 2 + 5 + 0 + 9 + 2 = 24 (Divisible by 3)

⇒ 622776: 6 + 2 + 2 + 7 + 7 + 6 = 30 (Divisible by 3)

⇒ Next, check divisibility by 13 for the remaining valid options (difference between alternating 3-digit blocks must be a multiple of 13).

⇒ 622710: |710 − 622| = 88 → 88 is not divisible by 13.

⇒ 625092: |092 − 625| = 533 → 533 ÷ 13 = 41 (Divisible by 13)

⇒ 622776: |776 − 622| = 154 → 154 is not divisible by 13.

⇒ Only 625092 fully satisfies both conditions.

∴ The correct answer is 625092.

Additional Information

Co-prime Factor Rule

If a given number is perfectly divisible by two co-prime numbers a and b, it is guaranteed to be divisible by their product (a × b).

Divisibility by 13

Group the digits in sets of three starting from right to left. If the absolute difference of the alternating sums of these groups is 0 or a multiple of 13, the complete number is divisible by 13.

Divisibility by 7, 11, and 13

The 3-digit block alternating difference method works identically for 7, 11, and 13 since their product is exactly 1001.

Shortcut Trick

Total sum = Average × 3 = 49 × 3 = 147.

Ratio of First : Second : Third = 4 : 2 : 1.

Total ratio parts = 4 + 2 + 1 = 7 parts.

7 parts = 147 ⇒ 1 part = 21.

Largest number (4 parts) = 4 × 21 = 84.

∴ The correct answer is 84.

Alternate Method

Given:

The average of three numbers is 49.

The first number is twice the second.

The second number is twice the third.

First Number (4x) Second (2x) Third (x) 84 42 21

Total Sum = 7x = 147 Average = 49 × 3 = 147

Formula Used:

Sum of observations = Average × Total number of observations

Calculation:

⇒ Let the third number be x.

⇒ Second number = 2x.

⇒ First number = 2 × 2x = 4x.

⇒ Sum of the three numbers = 49 × 3 = 147.

⇒ 4x + 2x + x = 147

⇒ 7x = 147

⇒ x = 147 ÷ 7

⇒ x = 21

⇒ The largest number is the first number, which is 4x.

⇒ Largest number = 4 × 21 = 84.

∴ The correct answer is 84.

Additional Information

Averages

The average (or arithmetic mean) of a set of numbers is the total sum divided by the number of elements. Thus, Total Sum = Average × Count.

Ratios in Averages

When numerical terms are given in a proportional ratio (such as 4x, 2x, 1x), you can compute their overall sum to determine the actual value of a single ratio part.

Compound Ratio

If A : B = m : n and B : C = p : q, the combined ratio A : B : C can be formed by making the common term B strictly proportional between the two sets.

Given:

Eight people are sitting in two parallel rows containing 4 people each in such a way that there is equal distance between adjacent persons.

• In row 1 – A, D, O and P are seated and all of them are facing south.
• In row 2 – U,W, Y and F are seated and all of them are facing north.
• Thus each person faces another person from the other row.
• U sits third to the left of Y.
• The one facing P is an immediate neighbour of Y.
• A sits at some place to the right of P and is not facing W.
• D sits third to the right of O

The final Arrangement is 

A is faces F.

Hence, the correct answer is "Option 2"

The correct answer is Hindustani Classical Music.

Key Points

• The term Gharana refers to a system of social organization linking musicians or dancers by lineage or apprenticeship.
• In Hindustani Classical Music, Gharanas represent schools or traditions of music, each with its distinct style and techniques.
• Some well-known Hindustani Gharanas include Gwalior, Agra, Jaipur-Atrauli, Patiala, and Kirana.
• The Gharana system became prominent during the Mughal period, where court musicians passed on their skills to disciples or family members.
• Each Gharana has unique characteristics in terms of raga rendition, ornamentation, and improvisation techniques, contributing to the diversity of Hindustani Classical Music.

Additional Information

• Hindustani Classical Music:
• It is one of the two main traditions of Indian classical music, the other being Carnatic music from South India.
• This tradition is characterized by a greater emphasis on improvisation and exploration of ragas.
• It primarily evolved in North India and has influences from Persian and Mughal music.
• Key Elements of Hindustani Classical Music:
• Raga: A melodic framework for improvisation and composition.
• Tala: A rhythmic cycle that forms the foundation of performance.
• Alap: A slow, unmetered introduction to a raga, showcasing its essence.
• Notable Musicians from Hindustani Classical Music:
• Ustad Bismillah Khan: Shehnai maestro and Bharat Ratna awardee.
• Pt. Ravi Shankar: Renowned sitar player and global ambassador of Indian classical music.
• Ustad Amir Khan: Founder of the Indore Gharana.
• Difference Between Hindustani and Carnatic Music:
• Hindustani: More focused on improvisation and has influences from Persian music.
• Carnatic: Structured compositions with emphasis on kritis (compositions) and devotional themes.

Given Equation : 25 C 3 B 12 D 4 A 10 = ?

If ‘A’ stands for ‘+’, ‘B’ stands for ‘−’, ‘C’ stands for ‘×’ and ‘D’ stands for ‘÷‘,

New Equation : 25 × 3 − 12 ÷ 4 + 10 = ?

25 × 3 − 12 ÷ 4 + 10 = ?

25 × 3 − 3 + 10 = ?

75 − 3 + 10 = ?

85 − 3 = ?

Hence, the correct answer is "Option 2"

Shortcut Trick Convert the given ratios into approximate percentages for a quick comparison: 20 : 38 ⇒ (20 ÷ 38) × 100 ≈ 52.6% 19 : 43 ⇒ (19 ÷ 43) × 100 ≈ 44.2% 23 : 45 ⇒ (23 ÷ 45) × 100 ≈ 51.1% 13 : 40 ⇒ (13 ÷ 40) × 100 = 32.5% Comparing the values, 52.6% is the largest percentage. ∴ The correct answer is 20 : 38.

Alternate Method Given: The ratios to compare are 20 : 38, 19 : 43, 23 : 45, and 13 : 40.

20 : 38

52.6%

19 : 43

44.2%

23 : 45

51.1%

13 : 40

32.5%

Calculations: ⇒ Let's write the given ratios as fractions: 20/38, 19/43, 23/45, and 13/40. ⇒ Simplify 20/38 to 10/19 for easier calculation. ⇒ We can use the cross-multiplication method to compare fractions pairwise. ⇒ Compare 10/19 and 23/45: ⇒ 10 × 45 = 450 and 19 × 23 = 437 ⇒ Since 450 > 437, 10/19 > 23/45. ⇒ Compare 10/19 and 19/43: ⇒ 10 × 43 = 430 and 19 × 19 = 361 ⇒ Since 430 > 361, 10/19 > 19/43. ⇒ Compare 10/19 and 13/40: ⇒ 10 × 40 = 400 and 19 × 13 = 247 ⇒ Since 400 > 247, 10/19 > 13/40. ⇒ In all comparisons, 10/19 (which is exactly 20/38) is the largest value. ∴ The correct answer is 20 : 38.

Additional Information Cross-Multiplication Method For comparing two fractions a/b and c/d, evaluate the products a × d and b × c. If a × d > b × c, then a/b > c/d. This is typically the fastest manual method without division. Percentage Conversion Converting fractions to percentages by multiplying the fraction by 100 provides a common 100-point scale that easily highlights the exact relative magnitude of values, especially when denominators vary widely. Difference Method If the numerical difference between the numerator and denominator in given proper fractions is perfectly identical across all fractions, the fraction with the largest numerator represents the greatest value.

The correct answer is sin i ÷ sin r = constant.

Key Points

• Snell's law states that the ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is constant for a given pair of media and is equal to the refractive index.
• The mathematical expression for Snell's law is sin i ÷ sin r = n, where n is the refractive index of the second medium with respect to the first.
• This law explains the bending of light when it passes from one medium to another with a different refractive index.
• Snell's law is crucial in understanding optical phenomena such as refraction and total internal reflection.
• The constant value (n) depends on the optical density of the two media involved in the transition of light.

Additional Information

• Refractive Index (n):
• The refractive index is a dimensionless quantity that describes how light propagates through a medium.
• It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium: n = c/v.
• Angle of Incidence (i):
• This is the angle between the incident ray and the normal (perpendicular) to the surface at the point of incidence.
• Angle of Refraction (r):
• This is the angle between the refracted ray and the normal to the surface at the point of refraction.
• Total Internal Reflection:
• This phenomenon occurs when the angle of incidence exceeds the critical angle, causing the light to reflect entirely within the denser medium.
• Applications of Snell's Law:
• Used in designing lenses, prisms, and optical instruments like microscopes and telescopes.
• Essential in fiber optic communication for guiding light signals through cables.

The correct answer is Lord Dalhousie.

Key Points

• Lord Dalhousie served as the Governor-General of India from 1848 to 1856.
• He is best known for implementing the Doctrine of Lapse, a policy used to annex Indian states that lacked a legitimate male heir.
• Under this doctrine, princely states like Satara (1848), Jhansi (1854), and Nagpur (1853) were annexed by the British Empire.
• The Doctrine of Lapse was a controversial policy as it disregarded the traditional right of rulers to adopt heirs, leading to widespread discontent among Indian rulers.
• Dalhousie's annexation policies played a significant role in increasing British control over India but also contributed to the resentment that led to the 1857 Revolt.

Additional Information

• Doctrine of Lapse:
• A policy formulated by Lord Dalhousie, stating that if a ruler of a princely state died without a direct male heir, his state would "lapse" to the British Empire.
• This doctrine overrode the traditional rights of rulers to adopt heirs and was viewed as a coercive measure to expand British territories.
• Impact of Dalhousie's Policies:
• Dalhousie's policies led to the expansion of British territory but also increased dissatisfaction among Indian rulers and subjects.
• The annexations under the Doctrine of Lapse were a significant factor contributing to the Indian Revolt of 1857.
• Other Contributions of Lord Dalhousie:
• Dalhousie introduced modern infrastructure like railways, telegraphs, and postal services in India.
• He established English-medium education institutions and laid the foundation for modernization in India.
• Indian Revolt of 1857:
• The widespread discontent caused by annexation policies, including the Doctrine of Lapse, was one of the primary reasons for the revolt.
• The revolt marked the beginning of the end of the East India Company's rule, leading to the establishment of direct British governance in India.

Preparing the family tree diagram by using the following symbols:

As per the given information:

P ÷ Q x R – S + T

R is brother of S and S is mother of T. 

Hence, the correct answer is "Option 2"

The correct answer is Rowlatt Act.

Key Points

• The Rowlatt Act, officially known as the Anarchical and Revolutionary Crimes Act of 1919, was passed by the British colonial government to suppress nationalist activities.
• Mahatma Gandhi labeled the Rowlatt Act as the 'Black Act' due to its oppressive nature and disregard for civil liberties.
• The act allowed the British government to arrest and detain individuals without trial and search premises without warrants, leading to widespread public outrage.
• In response to the Rowlatt Act, Gandhi organized the All-India Hartal on April 6, 1919, marking one of the first mass protests against British rule.
• The act was a major factor behind the Jallianwala Bagh massacre in Amritsar on April 13, 1919, where peaceful protestors were brutally killed, further intensifying the freedom movement.

Additional Information

• Vernacular Press Act:
• Enacted in 1878 by Lord Lytton to control the vernacular press and curb criticism of British policies.
• Allowed the colonial government to confiscate press materials that were deemed seditious.
• Faced widespread opposition and was later repealed in 1882 by Lord Ripon.
• Indian Councils Act:
• Passed in 1861, 1892, and 1909 to expand Indian participation in legislative councils.
• The 1909 Act, also known as the Morley-Minto reforms, introduced separate electorates for Muslims.
• These acts were significant milestones in the evolution of legislative governance in colonial India.

Shortcut Trick

Apply the BODMAS rule directly, solving the brackets from the innermost to the outermost.

Expression: 72 ÷ [2 × [12 − (10 − 7)]]

72 ÷ [2 × [12 − 3]]

72 ÷ [2 × 9] = 72 ÷ 18

∴ The correct answer is 4.

Alternate Method

Given:

72 ÷ [ (12/6) × [3 + 9 − (5 + 5 − (2 + 5))] ]

Concept Used:

BODMAS Rule: Brackets, Order, Division, Multiplication, Addition, and Subtraction.

Calculations:

⇒ 72 ÷ [ (12/6) × [3 + 9 − (5 + 5 − 7)] ]

⇒ 72 ÷ [ 2 × [12 − (10 − 7)] ]

⇒ 72 ÷ [ 2 × [12 − 3] ]

⇒ 72 ÷ [ 2 × 9 ]

⇒ 72 ÷ 18

⇒ 4

∴ The correct answer is 4.

Additional Information

BODMAS Rule

It dictates the order of operations in simplification: Brackets, Orders (powers/roots), Division and Multiplication (left to right), Addition and Subtraction (left to right).

Types of Brackets

Always resolve brackets in this sequential order: Vinculum (Bar), Round Brackets ( ), Curly Brackets { }, and finally Square Brackets [ ].

Fraction Simplification

When solving divisions inside brackets such as 12/6, compute them exactly as regular division before applying outer operations.

The correct answer is Bay of Bengal.

Key Points

• Chennai Port is situated along the eastern coastline of India and faces the Bay of Bengal.
• It is one of the oldest and largest ports in India, established in the year 1881.
• Chennai Port is primarily used for handling bulk cargo, containers, automobiles, and petroleum products.
• The port plays a crucial role in India's maritime trade, serving as a gateway for exports and imports in the southern region of the country.
• Its strategic location on the Bay of Bengal provides easy connectivity to Southeast Asia and the Far East.

Additional Information

• The Bay of Bengal is the northeastern part of the Indian Ocean, bounded by India and Sri Lanka to the west, Bangladesh to the north, and Myanmar and the Andaman and Nicobar Islands to the east.
• It is the largest bay in the world, covering an area of around 2.2 million square kilometers.
• The Bay of Bengal is known for its high biodiversity, including coral reefs, mangroves, and marine species like dolphins, turtles, and whales.
• Prominent rivers such as the Ganges, Brahmaputra, and Mahanadi drain into the Bay of Bengal, making it a hub for sediment deposition.
• The region is prone to cyclones due to its climatic conditions, with several major cyclones originating here annually.

The logic followed here is:

Similarly, 

Hence, the correct answer is "Option 2".

The correct answer is Option 2: Only II.

Key Points

• Citizenship in India is covered under Articles 5 to 11 of the Constitution of India and deals with the different categories of persons who are entitled to citizenship at the commencement of the Constitution.
• Citizenship is not listed in the State List; it is in the Union List under the Seventh Schedule, making it a subject under the exclusive jurisdiction of the central government.
• Indian citizenship can be acquired through five ways: birth, descent, registration, naturalization, and incorporation of territory, as per the Citizenship Act, 1955.
• The Constitution provided initial provisions for citizenship, and subsequent changes have been made through amendments to the Citizenship Act.
• Correct statement here is "Articles 5 to 11 deal with various categories of persons entitled to citizenship," which aligns with the provisions in the Constitution.

Additional Information

• Indian Citizenship Act, 1955
• This Act governs the acquisition and termination of Indian citizenship.
• It lays down five modes of acquiring citizenship: birth, descent, registration, naturalization, and incorporation of territory.
• It also provides provisions for the termination and renunciation of citizenship.
• Union List vs State List
• The Union List contains subjects of national importance on which only the central government can make laws, including citizenship, defense, foreign affairs, and atomic energy.
• State List contains matters on which state governments can legislate, such as police, public health, and agriculture.
• Dual Citizenship
• India does not allow dual citizenship. Indian citizens cannot hold citizenship of another country simultaneously.
• However, the Overseas Citizenship of India (OCI) status provides certain rights to foreign nationals of Indian origin.
• Amendments to Citizenship Act
• The Citizenship Act has been amended several times, including the Citizenship (Amendment) Act, 2019, which provides citizenship to persecuted minorities from Afghanistan, Pakistan, and Bangladesh.
• This amendment has sparked debates around secularism and equality in India.

Given Expression:  26 + 8 × 4 − 10 ÷ 5 = ?

+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged

New Expression:  26 − 8 ÷ 4 + 10 × 5 = ?

26 − 8 ÷ 4 + 10 × 5 = ?

26 − 2 + 10 × 5 = ?

26 − 2 + 50 = ?

76 - 2 =?

Hence, the correct answer is "Option 3"

Shortcut Trick

Total Wall Volume = 81 × 29 × 0.8 = 1879.2 m³

Volume of 1 brick = 0.72 × 0.50 × 0.25 = 0.09 m³

Effective volume for bricks (60%) = 0.60 × 1879.2 m³ = 1127.52 m³

Number of bricks = 1127.52 ÷ 0.09 = 12528

∴ The correct answer is 12528 bricks.

Alternate Method

Given:

Wall dimensions: Length (L) = 81 m, Height (H) = 29 m, Thickness (W) = 0.8 m

Brick dimensions: Length (l) = 72 cm = 0.72 m, Width (w) = 50 cm = 0.50 m, Height (h) = 25 cm = 0.25 m

Sand and cement mixture = 40% (So, bricks occupy 100% − 40% = 60% of the wall)

L = 81 m H = 29 m W = 0.8 m

72 cm 25 cm 50 cm Wall contains 60% Bricks and 40% Mixture

Formula Used:

Number of bricks = (Volume of wall × % volume occupied by bricks) ÷ (Volume of one brick)

Calculations:

⇒ Volume of the wall = 81 × 29 × 0.8 = 1879.2 m³

⇒ Volume occupied by bricks = 60% of 1879.2 m³ = 1127.52 m³

⇒ Volume of one brick = 0.72 × 0.50 × 0.25 = 0.09 m³

⇒ Number of bricks required = 1127.52 ÷ 0.09 = 12528

∴ The correct answer is 12528 bricks.

Additional Information

Volume of a Cuboid

The amount of 3D space enclosed by a rectangular cuboid is given by the product of its length, width, and height (V = L × B × H).

Unit Conversion

Always ensure all dimensions are in the exact same unit before calculating volumes. To convert from cm to meters, divide by 100.

Effective Volume Fraction

When a structure contains multiple materials (like bricks and cement), the required quantity of one material equals its percentage fraction multiplied by the total volume.

Shortcut Trick

Combine terms with the same denominator first: 5/2 − 3/2 = 2/2 = 1

Simplify the complex fraction: 1 / (1 + 5/7) = 1 / (12/7) = 7/12

Add the results together: 1 + 7/12 = 19/12

∴ The correct answer is 19/12.

Alternate Method

Given:

Expression: 5/2 + 1 / (1 + 5/7) − 3/2

Calculations:

⇒ 5/2 + 1 / ((7 + 5) / 7) − 3/2

⇒ 5/2 + 1 / (12/7) − 3/2

⇒ 5/2 + 7/12 − 3/2

⇒ (5/2 − 3/2) + 7/12

⇒ 2/2 + 7/12

⇒ 1 + 7/12

⇒ (12 + 7) / 12

⇒ 19/12

∴ The correct answer is 19/12.

Additional Information

BODMAS Rule

Always solve Brackets first, then Of, Division, Multiplication, Addition, and Subtraction. Nested fractions act as implicit brackets which must be simplified before division.

Fraction Division

When dividing by a fraction, multiply by its reciprocal. Example: 1 ÷ (a/b) = b/a.

Grouping Like Terms

In expressions with additions and subtractions, grouping fractions with the same denominator saves calculation time. Example: a/c − b/c = (a − b) / c.

A, B, C, D, E, F, G and H are sitting around a square table facing the centre of the table.

• Some of them are sitting at the corners while some are sitting at the exact centre of the sides.
• F sits second to the right of G.
• F sits at one of the corners.
• Only three people sit between G and E when counted from the left of G.
• H sits third to the left of E. Only three people sit between H and B when counted from the left of H.
• C sits second to the right of B.
• D is not an immediate neighbour of E

The final arrangement is:

 Only one person is sit between E and D, when counted from the left of D is B.

Hence, the correct answer is "Option 1"

• Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week.
• S has an exam on Tuesday. Exactly two people have an exam between S and P.
• T has an exam immediately before U, and R has an exam immediately after Q.
• Only 1 person has an exam between U and Q

The final arrangement is:

Hence, the correct answer is "Option 2"

The correct answer is Hala.

Key Points

• Hala, a Satavahana king, is credited with composing the 'Gatha Saptasati', also known as 'Saptasati'.
• The text is a collection of around 700 Prakrit verses, primarily focusing on themes of love and human emotions.
• The Gatha Saptasati is written in Maharashtri Prakrit, which was a prominent literary dialect during the Satavahana period.
• It serves as a significant source for understanding the cultural and social life during the Satavahana dynasty, particularly in the Deccan region.
• Hala's contribution to classical literature highlights the importance of vernacular languages in ancient Indian literary traditions.

Additional Information

• Satavahana Dynasty:
• The Satavahanas ruled the Deccan region of India after the decline of the Mauryan Empire.
• They are known for their contributions to art, architecture, and literature, including the promotion of Prakrit as a literary language.
• Prominent rulers include Gautamiputra Satakarni and Hala.
• Maharashtri Prakrit:
• Maharashtri Prakrit was one of the primary literary dialects in ancient India, often used in poetry and drama.
• The Gatha Saptasati is one of the most notable works written in this language.
• Thematic Focus of Gatha Saptasati:
• The verses primarily explore themes of love, longing, and emotional relationships, reflecting the society and culture of the time.
• It provides insight into rural and urban life in ancient India, especially in the Deccan region.
• Historical Significance:
• The Gatha Saptasati is one of the earliest examples of secular literature in India.
• Its focus on human emotions and everyday life marks a shift from predominantly religious texts to secular literary traditions.

The correct answer is text/plain; charset=UTF-8.

Key Points

• text/plain is the default MIME Content-Type for plain text email messages.
• The charset=UTF-8 specification ensures support for a wide range of characters, including international ones.
• MIME (Multipurpose Internet Mail Extensions) standards define how email content is formatted and transmitted.
• Plain text emails are simple and do not contain formatting, such as bold or italic text, images, or hyperlinks.
• Plain text is widely used for compatibility across email clients and platforms, ensuring readability.

Additional Information

• MIME Content-Type Terminology:
• text/plain: Specifies unformatted text content.
• text/html: Indicates HTML-formatted text, allowing rich formatting and multimedia elements.
• multipart/mixed: Used for emails containing multiple parts, such as text and attachments.
• application/octet-stream: Represents binary data, typically used for file attachments.
• Charset:
• Defines the character encoding used in the email.
• UTF-8 is the most widely used encoding, supporting virtually all characters across languages.
• Plain Text vs HTML Emails:
• Plain text emails are lightweight and universally compatible.
• HTML emails allow for visually appealing designs but may not render correctly in all email clients.
• Email Header:
• Contains metadata about the email, such as sender, recipient, and Content-Type.
• The Content-Type header specifies the format of the message body.

Given: (Left) $ T 1 & 9 Z 7 * A M S 1 * D % 7 * (Right) 

All the symbols are dropped from the series-  (Left) T 1 9 Z 7 A M S 1 D 7 (Right) 

Seventh from the right -   (Left) T 1 9 Z 7 A M S 1 D 7 (Right)

Hence, the correct answer is "Option 3"

The logic followed here is:

All follow the same logic except PLK.

Hence, the correct answer is "Option 4"

Shortcut Trick

For 3 equal distances covered at speeds x, y, and z, Average Speed = (3xyz) ÷ (xy + yz + zx).

Here, the given speeds are x = 19, y = 8, z = 5.

Average Speed = (3 × 19 × 8 × 5) ÷ (19×8 + 8×5 + 5×19)

Average Speed = 2280 ÷ (152 + 40 + 95) = 2280 ÷ 287

Average Speed = 7 ²⁷¹/₂₈₇ km/hr

∴ The correct answer is 7 ²⁷¹/₂₈₇ km/hr.

Alternate Method

Given:

⇒ Speeds for three equal distances: S₁ = 19 km/hr, S₂ = 8 km/hr, S₃ = 5 km/hr.

Formula Used:

⇒ Average Speed = Total Distance ÷ Total Time

Distance = d Distance = d Distance = d

Speed: 19 km/hr Speed: 8 km/hr Speed: 5 km/hr

Time = d/19 Time = d/8 Time = d/5

Total Distance = 3d Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Let the equal distance covered in each part be d km.

⇒ Total Distance = d + d + d = 3d km.

⇒ Total Time = (d/19) + (d/8) + (d/5)

⇒ Taking LCM of 19, 8, and 5 which gives 760.

⇒ Total Time = d × [(40 + 95 + 152) ÷ 760]

⇒ Total Time = d × (287 ÷ 760)

⇒ Average Speed = 3d ÷ [d × (287 ÷ 760)]

⇒ Average Speed = (3 × 760) ÷ 287

⇒ Average Speed = 2280 ÷ 287 = 7 ²⁷¹/₂₈₇ km/hr.

∴ The correct answer is 7 ²⁷¹/₂₈₇ km/hr.

Additional Information

Average Speed for Two Equal Distances

When a person covers two equal distances at speeds x and y, the average speed is directly given by (2xy) ÷ (x + y).

Average Speed for Unequal Distances

If distinct distances d₁, d₂, d₃... are covered at individual speeds s₁, s₂, s₃..., then Average Speed = (d₁ + d₂ + d₃...) ÷ (t₁ + t₂ + t₃...).

Relative Speed

When two bodies move in the exact same direction, relative speed = |s₁ − s₂|. When moving in opposite directions, relative speed = s₁ + s₂.

The correct answer is Intercalary.

Key Points

• Intercalary meristem is a type of meristematic tissue located at the nodes of plants.
• It is responsible for the regrowth of grasses and contributes to the elongation of internodes.
• Intercalary meristems allow rapid regeneration in grasses after grazing or mowing.
• This tissue is present in monocots, particularly in grasses, which aids their survival in environments with regular disturbances.
• Unlike apical meristem, which is found at the tips of roots and shoots, intercalary meristem is strategically located at the base of nodes and leaf blades.

Additional Information

• Meristematic Tissue:
• Meristematic tissues are responsible for the growth of plants and consist of actively dividing cells.
• These tissues are classified into apical, lateral, and intercalary based on their location.
• Apical meristem contributes to the primary growth at the tips of roots and shoots.
• Lateral meristem is involved in secondary growth, leading to an increase in the girth of the plant.
• Monocots vs. Dicots:
• Monocots, like grasses, have intercalary meristems that help them regrow quickly after damage.
• Dicots generally lack intercalary meristems and rely on apical and lateral meristems for growth.
• Node and Internode:
• Nodes are points on the stem where leaves or branches originate.
• Internodes are the regions between two nodes, which elongate due to intercalary meristem activity.
• Adaptation in Grasses:
• Grasses are adapted to survive grazing, fire, or mowing due to the presence of intercalary meristems.
• These tissues regenerate leaf blades and stems quickly, ensuring survival and growth.